A111DS M7t,bfifi

NJST

PUBLICATIONS

NisrUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1500-2

Materials Reliability Series

NIST Technical Note 1500-2

Materials Reliability Series

Procedures for the Electron-Beam

Moire Technique

E.S. Drexler

Materials Reliability Division

Materials Science and Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

March 1998

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1500-2, 140 pages (March 1998)

CODEN:NTNOEF

2XIC

/Up'

.''~ SVCi:

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

- - ..-. • • -fVFor sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Contents

Foreword iv

Electron-Beam Moire 1

Specimen Preparation 6

Electron-Beam Lithography 7

Thermal Testing 9

Mechanical Testing 10

Analysis ofthe Moire Fields 11

References 13

Appendix A: Publications 15

Al Electron Beam Moire by Dally and Read (1993) 16

A2 Local Strain Measurement by Electron Beam Moire by Read and Dally ( 1 993) 25

A3 Electron Beam Moire Study ofFracture ofa Glass Fiber ReinforcedPlastic Composite

by Read and Dally (1994) 33

A4 Local Deformation ofPlated Through Holes under Thermomechanical Loading

by Read and Drexler( 1994) 42

A5 Thermomechanical Behavior of a High Density Polymer Overlay MCM Interconnect

Structure: Experiments andAnalysis by Read; et al. (1995) 53

A6 Theory ofElectron Beam Moire by Read and Dally (1996) 65

A7 Electron-Beam Moire Study ofLocal Deformation in Conductive Adhesives

byDrexlerandBerger(1996):...: t .....:... 81

A8 Mechanical Deformation in Conductive Adhesives as Measured with Electron-Beam

Moire by Drexler and Berger( 199?) 88

A9 Error Analysis and Thermal Expansion Measurement with Electron-Beam Moire

byBerger, etal. (199?) 110

Appendix B: Program Disk 134

iii
Foreword

The Materials Reliability Series ofNIST Technical Notes are reports covering significant research

accomplishments of the Materials Reliability Division. The Division develops measurement

technologies that enable the producers and users of materials to improve the quality and reliability

of their products. Measurement technologies are developed for process control to improve the

quality and consistency of materials, for nondestructive evaluation to assure quality of finished

materials and products, and for materials evaluation to assure reliable performance. Within these

broad areas of measurement technology, the Division has focused its resources on three research

themes:

• Intelligent Processing ofMaterials—To develop on-line sensors for measuring the materials'

characteristics and/or processing conditions needed for real-time process control.

•

•

Ultrasonic Characterization ofMaterials—To develop ultrasonic measurements for

characterizing internal geometries of materials, such as defects, microstructures, and lattice

distortions.

Micrometer-Scale Measurements for Materials Evaluation—To develop measurement

techniques for evaluating the mechanical, thermal, and magnetic behavior ofthin films and

coatings at the appropriate size scale.

This report is the second in the series. It covers research on electron-beam moire, one ofthe

projects in our research on Micrometer-Scale Measurements.

IV
PROCEDURES FOR THE ELECTRON-BEAM MOIRE TECHNIQUE

E. S. Drexler

National Institute of Standards and Technology

Boulder, Colorado 80303

The background, setup, and procedures for the electron-beam moire technique are described here. This document is intended to give the reader as many details as

possible about the technique, so that the reader will have the information required

to conduct e-beam moire experiments in his or her own laboratory. Essential

equipment include a scanning electron microscope (SEM), access to electron-beam

or another type of lithography process, and computers to run the lithography

process and to aid in reducing and analyzing the data.

Keywords: electron-beam lithography; electron-beam moire; experimental

mechanics; lithography; moire.

Electron-Beam Moire

Electron-beam (e-beam) moire is a recently developed technique first described by Robinson [1],

followed by Kishimoto et al. [2]. The technique has been refined and fostered at NIST by Dally

and Read [3], its theory described by Read and Dally [4], and its application reported in

Referecnes [5-9].

Utilizing many ofthe principles of video moire [10], e-beam moire displays better resolution, as it

is conducted in the scarming electron microscope (SEM). E-beam moire is based on the

fundamentals of optical moire while exploiting the spatial resolution ofthe SEM. Imaging with an

electron beam circumvents the limitations on resolution due to the wavelength of light. In

addition to the resolution capabilities ofthe technique, e-beam moire has the advantage of being

able to see the substrate through the moire fringe field, so that you can identify how the materials'

systems and their structures contribute to local deformations.

As with moire interferometry, e-beam moire does not require a separate, tangible reference

grating. The reference grating is an integral part of the SEM—the rastering ofthe electron

beam—and exists whenever the current in the filament is sufficient to produce an image. The

electron beam rasters across the field of view at regular intervals: 480 raster scans per image for a

typical imaging system. The pitch pr ofthe "reference grating" depends, therefore, on the

magnification and viewing area ofthe system; specifically, pr = S/MR, where S is the nominal

image size, Mis the magnification, and R is the number of raster scan lines. S and R are constants

that can be obtained from the service manual or the manufacturer of the SEM.
The specimen grating is a series of ridges and trenches generated by e-beam lithography. This

lithography takes place in the SEM with the aid of a computer program that controls the location

and dwell time ofthe electron beam. Figure 1 shows the procedure used to make the specimen

grating. The polished surface of the specimen is made conductive, then a thin coating of

radiation-sensitive resist is spun on, and the specimen is baked to drive off the volatiles from the

resist. The radiation-sensitive resist is then exposed to an electron beam in the desired pattern,

followed by development of the pattern using a solution of alcohol and solvent to dissolve the

exposed areas. Table 1 shows the various grating sizes, types, and pitches that have been

obtained with this lithography system.

The magnification is nominally the same for the lithography as it is for imaging. The number of

lines contained in the specimen grating is one or two times the number of rasters ofthe electron

beam so that the initial correlation is approximately one-to-one (or one-to-two). A null field, one

for which there is an exact one-to-one correlation exists between the specimen and reference

gratings, is very rare. Because the SEM is focused and tuned using electromagnetic lenses to

adjust for differences in focal distance, it is virtually impossible to replicate tuning conditions

between sessions on the SEM. An additional complication is that the SEM used at NIST is not

1. Polish

1 1

1

4. Expose

Au-Pd Rim \ fl

2. Coat fl

5. Develop

fl Au-Pd Film mm 3. Spin on resist 6. Coat

Figure 1

.

Schematic showing the processing steps in making the specimen grating for e- beam moire.
Table 1. Sizes and pitches of patterns produced.

PATTERN WIDTH, ^m LINE PITCH, nm MAGNIFICATION

1000 (L: S, X)* 900 lOOx

500 (L: S, X) 900 200x

(L: S, X) 450

200 (L: S, X) 350 500x

(L:S;D)** 175

100 (L: S; D) 175 lOOOx

50(D) 90 2000x

*L = lines, S = single orientation, X = crossed-line gratings ** D = antidots (holes in PMMA)

capable of continuous magnifications; that is, magnifications are available only in increments

preset by the manufacturer.

If the pitch of the specimen grating is slightly different than that ofthe reference grating, moire

fringes will be present for the initial condition. With e-beam moire, light and darkfringes are

not the result oflight passing through a grating, but rather the result ofthe electron beam

interacting with the topography ofthe specimen grating lines. The electron signal originating

from the corners ofthe ridges will produce light fringes, whereas the trenches absorb the

electrons, producing dark fringes.

A change in the moire fringe density is the result of the presence of physical deformation in the

region ofthe grating. Expansion in the specimen can produce either an increase or decrease

in the density offringes depending on the initial condition. If in the initial condition the pitch of

the specimen grating is larger than that ofthe reference grating, expansion will lead to more

fringes. If, however, the pitch of specimen grating is smaller than that of the reference grating,

expansion will move the pitch size closer to a one-to-one correspondence, and therefore fewer

fringes. Figure 2 demonstrates this concept. The origin of the x-axis is defined as the null

condition, fringes to the right of the origin are fringes of expansion, (+)N, and fringes to the left are fringes of contraction, (-)N. If our initial condition is to the left ofthe origin and the

specimen is expanded, the number offringes will decrease until the null condition is achieved,

after which the number of fringes will again increase. If, rather, the specimen is contracted, the

number of fringes of contraction will increase. The reverse is true if the initial condition is to the

right ofthe origin. Expansion will result in an increased number offringes of expansion, and

contraction will lead to fewer fringes until the null condition results, followed by an increasing

number of fringes of contraction.
LOAD

(TEMPERATURE)

TENSION

(T>T )

Initial field witn Pg <

Pref Null initial field with pfl = pref

Initial field Wit Pg> Pref

FRINGES/mm

COMPRESSION

(T >T)

Figure 2. Diagram showing the relationship between positive and negative fringes, and the

relative pitch of the specimen and reference gratings in the initial fringe field. In

this figure, (+)N are fringes of expansion and (-)N are fringes of contraction.

In the more familiar optical-moire system shown in Figure 3, for every line from the specimen

grating that moves out of the field of view, one moire fringe appears [11]. Knowing the pitch of

the "reference grating" and the initial fringe density allows the quantification of strain either across the entire grating or at a local feature.

The resolution ofthe technique ranges from 90 to 900 nm/fringe order. Determination ofvalues

for strain from the moire images depends on the pitch ofthe specimen grating and the ability to

perceive fractions of fringes. How well you can discern fractions offringes depends on the total

number of fringes in the field ofview and on the contrast. If only 4 fringes were present, it would

be easy to detect, say, 1/10 or even 1/20 of a fringe with good contrast. However, if 25 fringes

were in the field ofview, perhaps 1/4 of a fringe is the best that you could delineate. Therefore,

the resolution ofthe technique would fall in a band ranging from 225 nm to 9 nm.

The mathematical developments for determining engineering normal (e) and shear (y) strains

follow those for geometric moire. For small strains and small rotations

ex = duJdx, sy= duyldy,

and yxy = duJcty + duyldx,

(1)

(2)

where ux and % are the displacements measured from the and 90° images, respectively. In moire

(ux,Uy) = N(x,ypr, where Afcy) is the fringe order. (Throughout the remainder ofthis paper wx-field
Oil film separation

Incident

light I-

>•

re

re

0)

D

O2

o.

1 1 1 -»•

Transmitted light

(Actual) (Average)

- E >

•21 •

o) r —

"8

s

3

H

-T

-f

Dark band

Gray

area

Light

band

Gray

area

Dark band

Gray

area

Light

band

Gray

area

Dark

band

Light intensity

Figure 3. Schematic of an optical moire system showing the light transmission through a specimen and reference grating wherepT *ps . (From J.W. Dally and W.F. Riley,

Moire methods, Chapter 1 1 in Experimental Stress Analysis. New York:

McGraw-Hill; 1991 [1 1]. Used with permission of McGraw-Hill.)
and will refer to the observed images where the grating lines are perpendicular to the longest

dimension ofthe specimen, and uTfield and 90° to images having the grating lines parallel to the

longest dimension.)

Please see Dally and Riley [11] and Durelli and Parks [12] for a complete review of the

mathematical development characterizing geometric moire, and References [3 and 4] for the

theory behind e-beam moire. (Appendix A contains all published material from NIST researchers

on e-beam moire.)

There are limitations to this technique, as it is conducted at NIST. Displacements are available

only from the in-plane surface ofthe specimen. No attempt has been made to measure out-ofplane displacements. A single e-beam moire image cannot provide any quantitative information;

the technique relies on the changes observed in the fringe field from an initial condition. Another

disadvantage is the inability to assign a precise fringe order to the moire fringes observed.

Because the pattern covers a limited area and not a region extending to a free surface, fringe

orders must be assigned arbitrarily. The significance ofthis is that absolute displacements are not

usually quantifiable; strains, however, are.

Specimen Preparation

At the Materials Reliability Division ofNIST we have studied a number of electronic packaging

specimens with e-beam moire. These include plated through-hole, ball-grid array, isotropically

and anisotropically conductive adhesive, and high-density interconnect specimens. The e-beam

moire technique has been used to measure regions of high relative displacements among the

materials contained within the package.

A specimen is cross sectioned so that it is approximately 3mm to 4 mm thick. The sectioned

specimen is ground flat and parallel on both sides using SiC paper in several steps from 120 to

1200 grit if the materials have nearly the same hardness, and on diamond-imbedded film if there is a great disparity in hardnesses. Lapping/polishing fixtures are commercially available to aid in

making specimens that are flat with parallel faces. One side ofthe specimen is then polished with

6 jjm diamond spray on a napless synthetic silk polishing cloth. Following the polish the surface

is cleaned with methanol and cotton batting, and dried with clean, filtered (to 0. 1 um) compressed

air.

On the day that the gratings are to be written, each specimen receives a final polish with 1 um

diamond spray on synthetic silk polishing cloth. Once again the specimen is cleaned with

methanol and cotton batting, and the surface is dried with clean, filtered compressed air. The

specimen is placed in a methanol ultrasonic bath for 30 s, followed by surface cleaning with

acetone and cotton batting, and drying with compressed air.

AuPd is deposited using a sputter coater [13]. A sputter coater works by dislodging material

from a source with argon ions accelerated in an electric field and depositing the source atoms

onto the surface of the specimen. The specimen remains cool throughout the process.
To apply a thin, even coat of polymethyl methacrylate (PMMA), it is spun onto the surface of the

specimen. The PMMA is purchased in a chlorobenzene solution with 4 percent solids. For our

purposes this solution is cut in half by mixing a one-to-one solution ofthe purchased PMMA with

chlorobenzene to form a 2 percent solids solution ofPMMA. Held onto the surface of the spinner

by a vacuum, 3 to 5 drops of2 percent PMMA are placed on the surface of the specimen, then the

specimen is spun at 2250 rpm for 30 s. The specimen is then placed on an aluminum block on a

hot plate with the block preheated to 170 °C, and cured at this temperature for 1 h to drive off the

chlorobenzene. If 170 °C exceeds the temperature limit for the specimen, an alternative cure schedule of 100 °C for 2 h is acceptable. The specimen is now ready for lithography.

Electron-Beam Lithography

The lithography is performed in an SEM [14]. D.T. Read ofNIST wrote a BASIC program

(Appendix B) that controls the location and dwell time of the electron beam, generating regularlyspaced straight lines. Lines are actually a series of closely-spaced, overlapping spots. To obtain

crossed-line gratings the lines are written in one orientation first, then the specimen is "rotated"

90° and the lithography process is repeated. This "rotation" takes place electronically rather than

physically—the x output from the photomultiplier is sent to they input ofthe CRT, and vice

versa. The effect is the same as if the specimen were rotated clockwise -90°. (The rotation is accurate to ±1° and precise to ±20" .) The rotation unit [15] used performs the input/output

exchange with a flick of a switch.

Through an input file into the program, the operator specifies the size ofthe pattern in

magnification, the number of lines, the probe current, and the number of dwell stops on the scan

line. The PMMA is very sensitive to the electron beam, so at no time can one look at the surface

ofthe specimen under normal "illumination," but must locate where to place the pattern using a probe current of extremely low intensity (<0.2 pA).

The microscope is set to 20 kV of accelerating voltage to write the patterns. An aperture of 50

um is chosen to focus the beam as tightly as possible. The astigmatism, centering ofthe aperture,

working distance, and focus are also carefully adjusted and tuned in order to obtain as small a spot size as possible. A small spot size for the electron beam is necessary, particularly when we

attempt to obtain line pitches of 90 to 225 nm.

Writing the actual patterns is a matter of locating where you want to place the pattern, setting the

magnification to the desired viewing area, and adjusting the probe current with the fine and coarse

potentiometers on the SEM to that specified in the computer input file. A Faraday cup measures

the probe current and blocks the beam from reaching the surface of the specimen until the

computer takes control of the electron beam to begin writing the pattern.

When all the patterns on a given specimen are written, the specimen is removed from the SEM for

development. During exposure the electron beam breaks the polymer chains of the PMMA, but

development ofthe specimen is required to wash those broken polymer chains away. The

developer is a 3: 1 solution of isopropanol and methyl isobutyl ketone (MTBK). Gently the

specimen is agitated in the isopropanol/MTBK solution for 40 s, then rinsed in a stream of

isopropanol for 20 s, followed by a 30 s rinse in deionized water. Clean, filtered compressed air is
used to dry the specimen. At this point it is often possible to see diffraction of light on those

patterns with line pitches >350 nm. The lines are visible in the optical microscope for line pitches

ofthe same magnitude. But in order to see the quality of lines with finer pitches, it is necessary to

look at them in the SEM. Following development, however, the surface of the specimen is a nonconductive polymer. This surface will become electrically charged in the SEM so that it is impossible to view the patterns. Deposition of a thin (<10 nm) coating of AuPd is deposited over

the polymer provides a conductive surface.

Once the surface of the specimen is coated with AuPd, it can be returned to the SEM and the

quality ofthe patterns evaluated. There are three reasons a pattern can be rejected for use; it may

be overexposed, underexposed, or inconsistently exposed. Inconsistent exposure can arise when

the specimen is not perfectly flat in the area ofthe pattern—either the specimen as a whole is not

flat or the softer regions are gouged out. If the beam's focal point is above the surface of the

specimen, the pattern will be insufficiently exposed, resulting in lines with poor contrast or no

lines at all. If the beam's focal point is below the surface, the interaction area may be so large that

the overexposed lines touch each other, or all the PMMA is exposed and removed upon

development.

Another cause of inconsistent exposure is having a specimen containing components with vastly

differing molecular or atomic masses. As the primary electron beam enters a material, the

electrons interact with that material (Figure 4). The secondary electrons used to image the

Secondary election

Backscatter electron

Incident electrons

rAuger electron

Figure 4. Origin and depth of incident, secondary, backscattered, and Auger electrons. The

incident electrons affect the area ofthe dark bulb, the secondary electrons emit

from the near-surface, the backscatter and Auger electrons originate from the

intermediate area, and the lightest stippled area indicates the region from which the

electrons are unable to reach the surface.

8
surface scatter elastically from near the surface. Backscattered electrons are the result of inelastic

collisions. The heavier the material the more energy the backscattered electrons have. This

energy allows the backscattered electrons from a larger interaction area to reach the surface.

Herein lies the problem with electron-beam lithography across materials with disparate

backscattered-electron energies. The PMMA resist is sensitive to electrons—whether secondary

or backscattered. If, for example, an exposed region contains Si and Au, the Si has an atomic mass of ~28 g/mol and the Au 197 g/mol. The exposed Au will have a much larger interaction area than the Si, resulting in the Au being overexposed as compared with the Si.

Thermal Testing

The thermal load testing of a specimen is conducted in the SEM using a heating/cooling stage

[16] (Figure 5). The stage has a temperature range of-196 to 400 °C, but testing of electronic

packages is usually conducted in the nominal range of-50 to 150 °C. Cooling is provided by

liquid-nitrogen-cooled nitrogen gas that flows through tubing in the stage. A PID (proportional,

integral,_derivative) controller maintains the set temperature by balancing the heater output with

the chilled gas.

The patterns are usually observed under a low accelerating voltage (5 kV to 7 kV), a working

distance of 13 mm to 1 5 mm, and a probe current of 10 pA to 12 pA in order to optimize the

resolution without damaging the PMMA. Before any images are acquired, the stage is cycled

between C and 100 °C (or over an appropriate temperature range in the elastic-strain regime)

twice before returning to the ambient temperature noted when the filament was first saturated.

The objective is to ensure that any macroscopic adjustments occur before the start of image

i

"« " v

Figure 5. Photograph of the heating/cooling stage used at NIST.

9
acquisition. The one-hour period required to do this cycling also gives the electron beam time to

stabilize. The electron beam must be stable in order for the data to be reproducible [17]. Images

are then stored digitally from both orientations at ambient temperature. Typically 0° and 90°

images are collected at regular temperature intervals (usually 50 °C) until the maximum

temperature is attained. During thermal unloading, images are collected at an intermediate and at the minimum temperature.

Mechanical Testing

Mechanical tests are conducted in the SEM on a stage [18] with a motor-driven screw-type

actuator and a load capacity of -4450 N (Figure 6). With the present hardware it is capable of

only uniaxial compression and tension. A universal joint used to drive the stage, and the wires

that monitor the load and displacement, have access into the SEM chamber through a plate that

replaces the side port.

The gage length of the specimen is limited to -15 mm. It is loaded onto the stage with wedge

grips, and each end is tightened with two bolts. The motor speed is regulated with a pot-type

knob that sets the rate between and 100 percent of 330 rpm. Most of the loadings are conducted at -15 percent, taking <1 min to load 90 N. The load is read off a digital display on

the controller for the stage. Images from the 0° and 90° orientations are acquired at regular load

intervals, and a final image is collected at the end of the test at a load of N.

The conditions for observing the moire fringe fields are an accelerating voltage of 5 to 7 kV, a working distance of 16 to 18 mm, a probe current of 10 to 20 pA, and the appropriate

imf i 2

i 3s ! 4f l § 'b* ''T 'S 1

f 3

!

' !

! h V2 ! !!3 ' t& ' VS

Figure 6. Photograph of the mechanical stage used at NIST.

10
magnification. The filament should be saturated for a minimum of 60 min before the first images

are acquired.

Analysis of the Moire Fields

A fringe tracing program that was written by D.T. Read ofNIST-Boulder (Appendix B) allows

you to assign a locus of points that defines the center of the fringe. This fringe center is also a contour of equal displacement on the surface of the specimen. The effect of the crossed-line

grating is analogous to having a full-view 0-90° displacement gage with resolution on the

order oftens ofnanometers. Thus, strains calculated from data obtained with this technique are

fully quantitative.

Once the fringe centers have been identified, analysis may be completed in the manner described

by Reference [19] in the chapter on geometric moire. Figure 7 shows the general procedure

followed. The fringe centers are identified on the w-field and v-field images. Line profiles are chosen running perpendicular and parallel to the orientation ofthe lines ofreference grating on

each image.

Programs designed to reduce and analyze moire fringe fields are commercially available. This

author cautions the reader to verify that the analysis program works on e-beam moire images.

Because the substrate material is visible through the fringes, the fringe intensity, or gray-scale,

may be different on different adjacent materials.

A graph is made of the distance along the chosen trace versus the assigned fringe order. The

fringe order is then converted into length by multiplying by the pitch ofthe reference grating, pr. (Recall that each fringe is the result of a frequency mismatch between the specimen and the

reference gratings of one complete line.) The example shown in Figure 7 assumes that the initial fringe field is null. However, with e-beam moire the initial fringe field is rarely null, so every

subsequent image is analyzed by studying the difference between it and the initial condition image.

In the thermal tests an initial room-temperature image is collected, followed by images collected

at regular temperature intervals between -50° and 150 °C. Similarly, in the mechanical loading

tests an image is collected before applying a load, then subsequent images are collected at regular

load intervals. The slopes obtained from the line profiles from the initial images must be

subtracted from the slopes from the line profiles from subsequent images to see how each loading

step affected the fringe field. Strain data are calculable from these plots of relative displacement versus position along the trace. The slopes of the curves, duJdx and duyldy, from the line profiles

perpendicular to the orientation of the reference grating in the Wx-field and %-field images,

respectively, are the normal strains as given by eq (1). The shear strain is the sum of the slopes

from the curves obtained parallel to the orientation ofthe lines ofthe reference grating, duJdy +

duyldx, as given by eq (2). The strains are, therefore, fully quantifiable and locally significant.

11
Orientation of reference grating

V

D ^—=£—6 —

/ b

r" 4 Afel- .___ \B

/

C

" >* - x \ Orientation of

reference grating

+ -

I, 3N, AN„

Position along AB Position along AB

Position along CO

*-Y

Figure 7. Procedure used to analyze the moire fringe data (From V.J. Parks, Geometric

moire, in Handbook on Experimental Mechanics, edited by A.S. Kobayashi, first edition, published for the Society ofExperimental Mechanics, Inc. Englewood

Cliffs, NJ: Prentice-Hall; 1987 [19]. Used with permission ofPrentice-Hall.)

12
References

[I] Robinson, D.W. High resolution moire contouring by a hybrid technique combining light

and electron optics. Opt. Laser Techno!. 13: 145-149; 1981.

[2] Kishimoto, S.; Egashire, M.; Shina, N. Measurements of grain boundary sliding and

observations of microgrids for high temperature use. J. Soc. Mater. Sci. Jpn. 40: 637-

641; 1991.

[3] Dally, J. W.; Read, D.T. Electron-beam moire. Exp.Mech. 33: 270-277; 1993.

[4] Read, D.T.; Dally, J.W. Theory of electron-beam moire. J. Res. Natl. Inst. Stand

Technol. 101: 47-61; 1996.

[5] Read, D.T.; Dally, J.W. Local strain measurements by electron beam moire. P.A. Engel

and W.T. Chen, eds. Proc., ASME 199international electronics packaging conference,

Advances in electronic packaging, Vol. 1: Structural analysis materials andprocesses

design reliability, EEP-4-1; 1993 Sept. 29-Oct. 2, Binghamton. NY. New York:

ASME: 163-169; 1993.

[6] Read, D.T.; Dally, J.W. Electron-beam moire study of fracture of a glass fiber reinforced

plastic composite. Trans. Amer. Soc.Mech.Eng. 61: 402-409; 1994.

[7] Read, D.T.; Drexler, E.S. Local deformation of plated through holes under

thermomechanical loading. M.A. Schen, H. Abe, and E. Suhir, eds. Proc, ASME 1994

international mechanical engineering congress and exposition, Mechanics and materials

for electronic packaging, Vol. 2: Thermal and mechanical behavior and modeling.

AMD-187; 1994 Nov. 6-11, Chicago, JX. New York: ASME: 185-194; 1994.

[8] Drexler, E.S. Thermal and mechanical deformation ofconductive adhesives using

electron-beam moire. M. S. Thesis in Materials Science. Golden, CO: Colorado School

ofMines: 116 pp.; 1996.

[9] Drexler, E.S.; Berger, J.R Electron-beam moire study of local deformation in conductive

adhesives. S.K. Groothuis, P.S. Ho, K. Ishida, and T. Wu, eds. Materials Research

Society Symposium Proceeding 445: Electronic Packaging Materials Science LX.

Pittsburgh, PA: MRS: 75-80; 1997.

[10] Morimoto, Y.; Hayashi, T. Deformation measurement during powder compaction with a

scanning moire method. Exp. Mech. 24: 1 12-1 16; 1984.

[II] Dally, J.W.; Riley, W.F. Moire methods, Chapter 1 1 in Experimental stress analysis.

New York: McGraw-Hill: 389^23; 1991.

[12] Durelli, A.J.; Parks, V.J. Moire analysis ofstrain. Englewood Cliffs, New Jersey:

Prentice-Hall: 399 pp; 1970.

13
[13] Model 6.2 Hummer sputter coater, manufactured by Anatech Limited.

[ 1 4] Model 6 1 00 SEM, manufactured by JEOL. *

[15] Rotation unit, designed by Advanced Microscopy Technology. *

[16] Model CI 003 heating and cooling stage, manufactured by Oxford Instrumemts.*

[17] Berger, J.R.; Drexler, E.S. Error analysis and thermal expansion measurement with

electron-beam moire. Submitted to Exp. Mech.

[ 1 8] Mechanical stage, no. 1 82 1 1

, manufactured by Ernest Fullam, Inc. *

[19] Parks, V.J. Geometric moire in Handbook on experimental mechanics, A.S. Kobayashi,

ed. Englewood Cliffs, New Jersey: Prentice-Hall: 282-313; 1987.

* Trade names are furnished to provide the reader with exact details on the equipment used by NIST and to evince the commercial availability of the equipment discussed Such identification implies neither recommendation nor endorsement by NIST; other apparatus from other sources may be found that work as well.

14
Appendix A: Publications

15
Al

Electron Beam Moire

by Dally and Read (1993)

16
Electron Beam Moire

by J. W. Dally and D.T. Read

ABSTRACT—A method of writing very high frequency line and dot patterns, in excess of 10,000 lines/mm, is described. This method uses a very small diameter, 1 to 20

nm, beam of electrons to sensitize a 1 00-nm thick layer of electron resist. The line and dot patterns are produced by

etching the sensitized resist. Moire fringe patterns occur when the line arrays are observed in the scanning electron microscope. Moire fringes with excellent contrast have

been produced at magnifications as high as 1900x. This

capability permits e-beam moire to be employed in mi- cromechanics. Examples of line arrays, dot arrays and

moire fringe patterns on a brass disk and on a tensile specimen fabricated from glass-fiber-reinforced plastic are demonstrated to introduce the possibilities for mi- cromechanics applications.

Introduction

Since its introduction by Weller and Shepard1 in 1948,

the moire method of displacement and strain analysis has been improved by introducing new techniques and new

technologies. The development of geometric or mechanical moire methods, which occurred during the period from

1948 to 1970, has recently been reviewed by Parks

2 and

has been described in detail by Theocaris.

3 Since 1980, most of the development has involved moire inter- ferometry where diffraction gratings are produced by in- terference of two plane beams from a coherent light source.

4' 5 Moire interferometry represented a major ad- vance because the frequency of the specimen grating was

increased by a factor of about 50 to 4,000 €/mm. This

increase improved the sensitivity of the method and ex- tended the applicability of the moire method to a wider

range of problems.

6

Since further increases in the frequency of the specimen

gratings are limited by the wavelength of light, it is necessary to employ a nonoptical method to achieve line arrays with frequencies of 10,000 <7mm or higher. Our colJ.W. Dally (SEM Fellow) is Professor ofMechanical Engineering, University ofMaryland, College Park, MD20742. D.T. Read(SEM Member)

is Physicist, National Institute ofStandards and Technology, Materials

Reliability Division, Boulder, CO 80303.

Original manuscript submitted: June 10, 1992. Final manuscript re- ceived: April 14, 1993.

leagues

7 in high resolution lithography have already solved

this problem by writing very fine lines using an electron beam. Patton used lines written with an electron beam to study slip at grain boundaries. Kishimoto et al.

9' 10 were the

first to introduce e-beam moir£ and to demonstrate its application to study microdeformation. In these studies, relatively coarse gratings were produced with pitches be- tween 3.7 and 7.1 urn. The moire fringe patterns were produced by interfering the lines in the array with the scanning lines in a conventional scanning electron micro- scope (SEM). This method of moire fringe formation is similar to video-scanning moir£ introduced by Morimoto

era/." in 1984. This paper describes a study of e-beam writing methods

to produce very high-frequency line and dot gratings

(10,000 €/mm) which are suitable for moir6 applications.

Examples of line and dot gratings are presented to show

the quality of the arrays which can be produced with this method. The ability to write patterns on both homogenous

and heterogenous materials such as glass-fiber-reinforced

plastics is demonstrated. The application of e-beam moire

at high magnification (l,900x), which is required in mi- cromechanics, is emphasized. Finally, a moir6 pattern from a high frequency line array (10,000 €/mm), which

represents the displacement field at interfaces in a GFRP

specimen, is described.

e-Beam Generation and Control

Let us consider the column of a typical SEM shown in Fig. 1 to introduce the methods used to generate and

control an electron beam. The electrons are generated by

thermionic emission at a heated tungsten filament, which

has a V-shaped tip about 200 urn in diameter. The filament

is maintained at a high negative voltage during operation.

The electrons emitted are accelerated to the anode (ground) with acceleration voltages that are adjustable from about 1 to50kV.

A Wehnelt cylinder with a circular aperture centered on

the filament apex is biased negatively with respect to the cathode. The effect of the filament, Wehnelt cylinder, and anode is to produce a stream of electrons which converge

with a crossover diameter do and a divergence angle oto as

270 • December 1993

17
Specimen

Stage

Fig. 1 (a)—Schematic diagram of elements in the vacuum column of an SEM

Its magnetic field must not affect the collection of secon- dary electrons from the specimen. Also, the bore ofthe lens must accommodate scanning coils, stigmator, and beam

aperture. The objective lens is used to focus the electron beam at different specimen working distances, which usually range from about 10 to 40 mm. The spot size is minimized by reducing the working distance to improve

resolution of the SEM. However, the depth of field is increased by increasing the working distance, which pro- duces a smaller divergence angle a. The depth of field is also dependent on the beam limiting aperture as indicated

in Table 1

TABLE 1—TYPICAL DEPTH OF FIELD WITH A

WORKING DISTANCE OF 10 MM'2

Magnification Aperture Diameter (urn) 50 100 200 500

Depth of Field (urn) 8000 4000 2000 800

800 400 200 80

80 40 20 8

8 4 2 0.8

101

102

103

104

e-beam Characteristics

\

\

Filament — F 1

Wehnelt

Etoctrod*"-"

[ G

Electron 8«j Cronoiim wJf •* - de

The diameter of the e-beam is of critical importance in writing either line or dot patterns to produce a high resolution moir£ grating. The variables which affect the beam

diameter include the filament material, the accelerating

voltage, and the probe current. The probe current is the

electrical current transmitted as the electron beam from the filament to the specimen. Typical results

12 for the beam

diameter as a function of probe current are shown in Fig.

2. Since we seek to minimize beam diameter, low probe

currents (10 to 50 pA) are employed with higher accelerFig. 1 (b)—The gun used in forming the electron beam

illustrated in Fig. 1(b). A typical value of do is 25 um, and

a typical value of oto 3 mrad. Conventional electromagnetic

lenses are positioned in the SEM column to focus the

electron beam by the interaction of the electromagnetic

field of the lens on the moving electrons. The condenser and objective lens are used to reduce the beam diameter by

a factor of 1 ,000 or more, to the final spot diameter df of 5

to 20 run on the specimen.

The objective (or probe-forming) lens is different from

the axially symmetric condenser lenses. This lens must accommodate many detectors located near the specimen.

1.0 10 PROBE CURRENT, pA

Fig. 2—Electron beam diameter as a function of probe current, filament material and accelerating

voltage

18
ating voltages (20-30 kV). The filament material used was

tungsten, although lanthanum hexaboride, LaB6 , produces

a tighter beam. Inspection of Fig. 2 shows that the beam

diameter ranges from about 10 to 20 nm as the probe

current increases from 10 to 50 pA with an accelerating

voltage of 30 kV. The beam diameter increases as the

accelerating voltage is decreased.

It is important to note the difference between the fila- ment current and the probe current. The filament current, about 200 to 240 u\A, heats the tungsten filament and

produces the electrons at the gun [see Fig. 1 (b)]. The probe

current is the incident current produced by the electron beam striking the specimen. The probe current is adjusted with the condenser lenses (for a given aperture). Increasing

the magnification of a condenser lens increases the diver- gence angle, and a larger portion of the electron beam is blocked by the beam-limiting aperture. This blockage re- duces the current in the beam. The probe current is measured with a Faraday cup, that

is inserted into the beam of electrons. Because the Faraday cup does not allow either backscattered or secondary elec- trons generated by the incident beam to escape, the current flowing from the cup to ground is due entirely to the

incident beam. The probe current is measured with a dc

picoammeter.

This description shows that a beam of electrons with a

diameter in the range of 10 to 20 nm can be produced in a

typical SEM. Moreover, by controlling the scanning coils, this beam can be directed over the surface of the specimen

to trace any specified pattern on the x-y plane. This beam

is employed to write high density line and dot gratings for application in micromechanics.

e-beam—PMMA Interactions

The interaction of the electron beam with solids has been

employed since 1968

7 to write intricate patterns required

to fabricate very dense microelectronic devices. Certain

plastics, such as polymethylmethacrylate (PMMA), un- dergo a chemical change during electron bombardment.

The electrons sensitize the exposed material to etching in a suitable solvent. The etching rate is controlled by the

electron dose, and etch boundaries are determined by

contours of electron energy deposition. The electrons in- volved in sensitizing the PMMA come from the incident

electron beam, the backscattered electrons, and the secon- dary electrons. The shape of the etch pit in monolithic PMMA resembles a pear because of inelastic and elastic scattering of the electrons. The depth and width of the pear-shaped cavity depends on the electron dose, number

of electrons per unit volume, and the developing time in the solvent. Writing in a thin uniform layer of PMMA on a substrate

is more difficult than writing in monolithic PMMA, be- cause backscattered electrons and secondary electrons from the substrate also contribute to the electron dose. One

attempts to write either line or dot patterns in e-beam moire' with exceedingly small pitch. The incident beam is the most important source of the electron dose. Indeed, if the incident beam were the only source of electrons, it would

be possible to write line and dot arrays with a pitch of 20

to 40 nm, since the incident beam diameters in the range of 10 to 20 nm can be achieved. The effect of elastic and

inelastic scattering of the electrons as the incident beam

enters the PMMA is to increase the diameter of the beam. However, this effect is minimized by reducing the thick- ness of the layer of PMMA to 100 nm.

Backscattered electrons from the substrate increase the diameter of the spot of PMMA being exposed. The number

of backscattered electrons, those that enter the substrate and reemerge in the PMMA layer, is relatively large (about 30 percent in copper

12

). Large numbers of backscattered

electrons are useful in scanning electron microscopy be- cause they provide a signal that is detected to define the surface features of a specimen. However, in e-beam writ- ing, the backscattered electrons are detrimental because

they increase the minimum feature size that can be sub- jected to a controlled dosage. The fraction of electrons

(relative to the incident beam) that is backscattered de- pends on the atomic number of the substrate with the backscatter coefficient increasing with atomic number.

Line and dot arrays with very small pitch can be achieved

in a very thin PMMA layer on substrate materials with low

atomic number.

e-beam Writing Experiments

A series ofexperiments were performed to determine the parameters to employ in writing line and dot arrays and the minimum pitch which could be achieved. Aluminum,

brass, and GFRP were used as the substrate materials. The

metallic substrates were disks 12.7 mm in diameter and 1 to 2 mm thick. The GFRP was a strip 6 x 32 mm by 2 mm

thick. The surfaces of the specimens were ground smooth

and flat using a series of water-lubricated abrasive-coated papers ending with 5-um grit. The final polish was

achieved by finishing with 3- and then 1-u.m diamond

particles. The substrates were cleaned in acetone subjected

to ultrasonic activation. The specimens were coated with PMMA within a few

hours of polishing. The PMMA resist used for coating is a two-percent solution of PMMA, 950,000 relative molecular weight, with chlorobenzene as the solvent. The PMMA

resist was spun on the specimens, at a speed of 3000 RPM

for 30 s. The specimens were then baked on a hot plate for 30 minutes at 160°C. This process produces a cured layer of PMMA resist that is approximately 100-nm thick. The

application is performed in a class- 100 clean room. The specimens were mounted on a specimen stage in a

digitally controlled SEM that was equipped with a Faraday cup and a beam blanker. The SEM was operated with an

accelerating voltage of 20 kV and a 50-ujii aperture. The

working distance was set at 25 mm and the specimen

surface was 23 mm from the objective lens. The Faraday cup was inserted into the electron beam, and the beam

current ib was adjusted to a specified value in the range from 10 to 40 pA.

The e-beam in the SEM is computer controlled, and

patterns are written in the PMMA resist in accordance with programmed instructions that involve three different soft- ware packages. The first is a CAD (computer-aided drafting) program where the length, pitch, and number of lines are

272 • December 1993 19
Fig. 3—Effect of electron exposure on width of trench and ridge (pitch 400 nm, substrate brass)

specified to define a line array. Similarly, for a dot array, the pitch in x and in y and the number of dots are specified.

The second program provides instructions to the SEM

for controlling the electron beam in writing the partem

specified in the CAD file. When a line is written, the electron beam is moved from point to point, and the line is produced by many closely spaced points. To write a line with a series of points, the center-to-center distance is about 1/4 the final line width. To properly expose the PMMA, we adjust the line dose and the area dose. The line dose Dl is DL = iBtJcc

and the area dose DA is

where

DA = (iBtc Y(cc) (p)

ia = beam current

t. = exposure time per point cc = center-to-center distance p = pitch of the line array.

(1)

(2)

The units commonly used for DL and DA are nC/cm and

u.C/cm2. We specify is, tr, and cc in this second program, and the pitch p in the CAD program to give the line and

area doses that are required for the most suitable exposure

of the PMMA resist. The final program executes the instructions provided in

the files of the two previous programs. This program

provides digital signals to the scanning coils and the beam

blanker to move the beam so as to generate the specified

line or dot array. After the patterns are written, the specimen is developed

in a solution consisting of three parts (by volume) of

isopropyl alcohol to one part of methyl isobutyl ketone for 40 s. The specimen is immediately rinsed in isopropyl

alcohol for 20 s followed by a second rinse in deionized water for 30 s. Next, the specimen is blown dry with a clean

gas. The development of the resist is an etching process, and precise control is critical. Finally, the specimen was coated with a very thin layer

( 1 to 20 nm) of a gold-palladium alloy by plasma sputtering. This metallic coating is necessary to provide a con- ductive surface that prevents a surface charge from

developing when viewing the specimen in the SEM.

20
Experiments were conducted to write lines and square

arrays of dots with pitches of 400, 200, 100, 75, and 50 nm.

Line and area dosage was varied for each pitch to establish writing parameters. Typical results are presented in Figs. 3 through 7.

Fig. 4—Demonstration of quality of a line array with a 200-nm pitch

The effect of exposure, measured in terms of line dosage

and area dosage, is shown in Figs. 3(a)-3(d) for a line array with a 400-nm pitch. These images were recorded on an SEM at a magnification of 50,000x. The scale bar repre- senting 100 nm is given. In the illustrations, the dark

regions represent trenches where the PMMA resist has been etched away, and the light areas show ridges where

the resist is intact. The thin dark lines that are inclined to the trenches and ridges are scratches left by polishing the

surface of the brass substrate. In Fig. 3(a), with the largest

line and area dosage, the trenches are about 225-nm wide, and the ridges are only 175-nm wide. The wandering of

the edges separating the trenches and the ridges is due to oscillations in the position of the incident electron beam

and the random nature of electron backscattering. As the exposure is decreased, while holding the developing (etching) time constant, the width of the trench decreases. In

Fig. 3(b), the trench and ridges are of equal width. In Fig.

3(c), the trench width is only 150 nm and the ridge width

is 250 nm. An example of underexposure, in Fig. 3(d), shows that the trenches are not well defined. The line array shown in Fig. 4, at a magnification of

100,000x, is at a pitch of 200 nm. In this experiment, the

line and area dosages were 1.25 nC/cm and 62.5 u,C/cm2. The trench width was about 85 nm and the ridge width was

1 15 nm. The waviness of the edges between the trenches and the ridges is more apparent because the reduced pitch

required higher magnification.

The line array shown in Figs. 5(a) and 5(b) is at a pitch of 100 nm. In Fig. 5(a), the lines and the trenches are nearly

the same in width. The waviness of the edges becomes more apparent with decreasing width. In Fig. 5(b), we

show the same pattern with an exposure near the lower

limit for this 100-nm pitch. In this experiment, the trenches

are only 25 nm wide. This result indicates the possibility of producing line arrays with frequencies of 20,000 €/mm.

The current limit on the pitch of the fine arrays that was

achieved in this series of experiments is 75 nm. An inspection of the SEM image recorded at 1 20,000x presented in Fig. 6 shows that the pitch varies from line to line ranging

M m m m m -* * * w

Fig. 5(a)—Lines on 100-nm centers shown at 100,000x

Fig. 5(b)—Lower exposure shows trenches 25-nm wide

Fig. 6—Line array with a pitch of 75 nm at a magnification of 1 20,000x

274 • December 1993 21
.i «•,» *4 — » • «&«»„.

Fig. 7—A dot pattern on 200-nm centers at 50,000x

ft. *•£

band is very wide, ranging from 2.5 to 4.0 nC/cm. Al- though the ratio of the trench-to-ridge width varies across

this band, the line arrays are suitable for moire applications. However, as the pitch decreases, the exposure band

decreases markedly. At pitches of 100 nm, the line dosage must be controlled within a band from 0.55 to 0.75 nC/cm.

It appears that a good first approximation for line dosage

as a function of pitch is

DL = 6.5 p

where DL is in nC/cm and p is in um.

Moire Fringe Formation

(3)

o

c

UJCOO

o

UJ

3 .

Brass, 40 s Development 2% pmma Resist 3000 RPM /A

A SuccaiHul O OwExpcwd D Undtr Exposad a

Ox OrarExpoaM S

S Expoaura ^>

Sand ^*^

Ao O/^^D Under ExpOMd

100 200 300 400 UNE PITCH, nm

Fig. 8—Line dosage as a function of line pitch

from 55 to 95 nm, although the average pitch over 10 lines

is 75 nm. The apparent pitch variation is local and is due

to the waviness of the trenches. The electron beam is oscillating with an amplitude of about 20 nm as it moves

along from point to point in writing a line. A dot pattern on 200-nm centers is presented in Fig. 7. The dots are somewhat elongated, with an aspect ratio of about 2 to 1 . We believe the elongation is'due to astigma- tism of the electron beam in this particular experiment, because we have produced much more nearly circular dots

in other experiments. Each dot is produced with an exposure time of 1,000 u\s and a probe current of 10 pA. The

dot patterns have the advantage that they can be produced

in much less time per unit area of pattern than the line arrays. Also, the resulting pattern serves as a cross grating

which is necessary in two-dimensional moire. From these experiments, we have deduced the electron beam line dosage required to write line arrays of various

pitches. Fig. 8. For line pitches of 400 nm, the exposure

The line or dot patterns can be interrogated either by line counting that involves a fast-Fourier transform (FFT) of a

digital image14 or by producing scanning moir£ fringes.

8" I0

In this paper, we illustrate typical moir6 fringe patterns that are produced by the scanning lines in a SEM. The scanning

lines in a SEM have a pitch p, that depends on the magnification and the scan rate selected for observation or photography. The pitch pr is given by

pr = s/(mM)

(4)

where

s = characteristic length (about 90 mm)

dependent on the SEM

m = number of scan lines in the image

M = magnification

The reference pitch can be varied by adjusting either m

or M; however, the variation is not continuous since the choices of m are very limited and the magnification is varied from 10 to 300,000x in discrete steps. Moire fringe patterns are observed when

/>, = p>f (l+a)

(5)

where

ps = pitch of the lines on the specimen P = Post's multiplication factor

15 a = mismatch factor ranging from to 0.

Examples of typical moire fringe patterns are shown in Fig. 10. The fringe pattern in Fig. 10(a) has formed over a 50 x 50 |im square patch of lines on 100-nm centers. The

irregularities in this pattern are due to surface imperfections that were frequently encountered on brass surfaces. These pits usually range in size from 1 to 5 u\m. The moire

pattern in Fig. 9(b) was formed over a 50-u.m square patch of dots arranged on 200-nm centers. The specimen in this case was GFRP, and the ends of the fibers can be seen in the background.

22
jggSSE^SPSp98?^5?!

P^^K^siii^ffiBS^^'J

s.eKU xi^eee 10M»

(b)

Fig. 9—Moire fringe formation in a SEM: (a) 100-nm

lines on brass, (b) 200-nm dot pattern on GFRP

Discussion and Conclusions

Electron beam moir6 avoids the limits imposed on optical methods of moire" by the wavelength of light. Both line and dot patterns can be written on metallic and composite

specimens with spatial frequencies as high as 13,300

€/mm. Moire fringe patterns can be formed using the scanning lines of an SEM as the reference gratings at magnifications as high as l,900x with 100-nm pitch line patterns. The potential applications of e-beam moire in mi- cromechanics are evident from the line frequencies which

can be achieved and the magnifications involved in forming the image of the moire fringes. To illustrate the mi- cromechanics potential of the method, a dot pattern, on 200-nm centers, is shown in Fig. 1 0. In Fig. 1 0(a) at 5500x,

the dot pattern covers one complete fiber end, parts of three

others, and part of a longitudinal fiber. About 40 rows of

dots are written over the end of a fiber 8 \xm in diameter. The triangular matrix region between three fibers is shown

(a)

#;*•»

mmm

mm:

(b)

Fig. 10—Dot patterns on 200-nm centers on a cross-ply

GFRP specimen with 8 um fibers at 5,500x and 20,000x

in Fig. 10(b) where the dot partem is represented at a

magnification of 20,000x.

A moire fringe partem obtained from a 1 00-nm pitch line array positioned at an interface between a longitudinal ply and a crossply is illustrated in Fig. 1 2. The specimen in this case was fabricated from a cross-ply glass-fiber-reinforced epoxy 2-mm thick 6-mm wide and 33-mm long. The

specimen was loaded in tension within the vacuum chamber of the SEM using a specially adapted tensile loading

system. The fringe pattern in Fig. 1 1(a) is with a small nominal

load and is due to mismatch. The fringe pattern in Fig.

11(b) is due to both mismatch and imposed strain. The

fringe distortion was not expected since mismatch fringes

are straight. The distortions are due to the small changes

in expansion of the glass and the epoxy that occurred between the time of the etching and the time of testing. These local deformations may be produced by either differential expansion of the epoxy due to diffusion or due to temperature. An inspection of the interface region between the longitudinal and the cross plies shows that the change in the

276 • December 1993 23
Fig. 1

1 —Moire fringe pattern at an interface between lon- gitudinal and cross plies (100-nm line grating): (a) zero

load pattern, (b) pattern at a nominal tensile stress of 146 MPa.

number of fringes over the characteristic dimensions of the

fiber diameter (8 Jim) is very small. This fact indicates that the localized strain concentrations at the interface are not

large. Subsequent experiments have shown that large in- terface shearing strains occur only after cross-ply cracking

develops at higher loads.

Acknowledgments

Thanks are due to R.E. Harris and J. Martinis for the use of the lithographic facility in the Electromagnetic Technol- ogy Division at NIST; and to Greg Zimmerli for introduc- ing us to electron beam lithography.

References

1. Welter, R. and Shepard, BM., "Displacement Measurement by Mechanical Interferometry, " Proc. Soc. for Exp. Stress Analysis. 6 (J), 35-38 (1948).

2. Parks, V.J., Geometric Moire, Handbook on ExperimemalMechanics, ed A.S. Kobayashi, Prentice-Hall, Englewood Cliffs, NJ. 282-313

(1987).

3. Theocaris, P.S., Moiri Fringes in Strain Analysis, Pergamon Press, Elmsford NY (1969).

4. Post, D., "Optical Interference for Deformation Measurements - Classical, Holographic and Moire Interferometry, " Mechanics of Nondestructive Testing, ed. W. W. Stinchcomb, Plenum Press, New York 1-53

(1980).

5. McDonach, A., McKelvie, J. and Walker, C-A.,

" Stress Analysis of

Fibrous Composites Using Moire Interferometry, " Opt. and Laser Eng.,

1, 85-105 (1980).

6. Post. D., "Moire Interferometry: Advances and Applications,

experimeotal mechanics. 31 (3), 276-280(1991).

7. Haller, I.. Hatzakis, M. and Srinivasan, R., "High Resolution

Positive Resistsfor Electron-beam Exposure, " IBM J. Res. andDev., 12, 251 (1968).

8. Patton, N.E. and Mahoney, M.W., "Creep of Titanium-Silicon

Alloys. " Met. Trans. A, 7A, 1685-1692 (1976).

9. Kishimoto, S., M. Egashira, Shinya, N. and Carolan, RA., "Local Micro-Deformation Analysis by Means ofMicrogrid and Electron Beam

Moire Fringe Method, " Proc. 6th Int. Conf. on Meek. Behavior of

Materials, ed. M. Jono and T. Inoue, 4, 661-666 (1991).

10. Kishimoto. S., Egashira, M. and Shinya. "Measurement of Grain Boundary Sliding and Observation ofMicrogridsfor High Temperature

Use, "J. Soc.for Mat. ScL Japan (in Japanese). 49(452), 637-641 (1991).

11. Morimolo, Y. and Hayashi, T.. "Deformation Measurement During Powder Compaction by a Scanning Moiri Method, " experimental

mechanics, 24, 112-116(1984).

12. Goldstein, J.I.. Newbury, D.E., Echlin, P., Joy, D.C, Fiori, C. and

Lifshin, E., Scanning Electron Microscopy and X-Ray Microanalysis, Plenum Press, New York, 19-203 (1981).

13. Everhart, T.E., Herzog, R.F., Chung, M.S. and Devore, WJ.,

"Electron Energy Dissipation Measurements in Solids, " 6th Int. Cong, on X-Ray Optics and Microanalysis, 81-86 (1971).

14. Santo. M., Dally, J.W. and Read D.T., "A Grid-Moire Hybrid Methodfor Measuring Strain and Displacement, " Optical Engineering,

in press.

15. Post, D., "Sharpening and Multiplication of Moiri Fringes,

" EXPERIMENTAL MECHANICS, 7 (4), 154-159 (1967).

24
A2

Local Strain Measurement by Electron Beam Moire

by Read and Dally (1993)

25
EEP-Vol. 4-1, Advances in Electronic Packaging

ASME 1993

LOCAL STRAIN MEASUREMENT BY ELECTRON BEAM MOIRE

David T. Read

Materials Reliability Division National Institute of Standards and Technology

Boulder, Colorado

James W. Dally

Department of Mechanical Engineering

University of Maryland

College Park, Maryland

ABSTRACT

Moire fringe patterns can occur when high-frequency

line arrays are observed in the scanning electron microscope. We have applied this phenomenon to local deformation measurement in a glass-fiber-reinforced

plastic and in a plated-through-hole. In the GFRP, local

strain measurements were made by interpreting the moire

fringe patterns over gage lengths from 10 to 30 urn at a 0-90 ply interface during tensile testing. Load shedding

by the transverse ply was evident from the fringe

patterns. On a cross section of a plated-through-hole,

inhomogenous strains were observed.

INTRODUCTION

Since its introduction by Weller and Shepard [1] in 1948, the moire method of displacement and strain analysis has been improved by introducing new

techniques and new technologies. The development of

geometric or mechanical moire methods, which occurred

during the period from 1948 to 1970, has recently been

reviewed by Parks [2] and has been described in detail by Theocaris [3]. Since 1980, most of the development

has involved moire interferometry where diffraction gratings are produced by interference of two plane beams

from a coherent light source [4,5]. Moire interferometry

represented a major advance because the frequency of the specimen grating was increased by a factor of about 50

to 4 000 lines/mm. This increase improved the

sensitivity of the method and extended the applicability of the moire method to a wider range of problems [6]. D. Post and colleagues presented moire interferometry

data showing the shear-strain differences among 0° plies,

90° plies, and resin-rich regions between plies [7]. They

have applied well-developed techniques to a series of issues

in the behavior of composite materials and interfaces [8-10].

In particular, the stiffness difference between fiber and matrix produced zig-zag fringes [8]. Since further increases in the frequency of the specimen

gratings are limited by the wavelength of light, it is necessary

to employ a different form of energy to achieve line arrays with frequencies of 10 000 lines/mm or higher. Our

colleagues in high resolution lithography have already solved

this problem by writing very fine lines using an electron beam [11]. Paton used lines written with an electron beam

to study slip at grain boundaries [12]. Kishimoto et al. [13,14] were the first to introduce e-beam moire and to demonstrate its application to study microdeformation. In

these studies, relatively coarse gratings, with pitches between

3.7 and 7.1 urn, were used. The moire fringe patterns were

produced by interfering the lines in the array with the scanning lines in a conventional scanning electron microscope

(SEM). This method of moire fringe formation is similar to the video scanning moire techniques introduced by Morimoto

et al. [15] in 1984.

In this paper we first demonstrate the use of electron beam

lithograhy to to produce very high frequency line and dot

gratings (10 000 lines/mm) which are suitable for moire

applications. The ability to write gratingss on both homogenous and heterogenous materials such as glass fiber- reinforced plastics is demonstrated. The application of e- beam moire at high magnification (1 900X), which is required in micromechanics, is emphasized

We then describe the use of electron-beam moirwe to study

displacements and strains in a tensile specimen fabricated from a [0^90], glass fiber reinforced epoxy, and discuss

163

26
II

I.Polish

4. Expose

fl J}

S. Develop

u

3. Spin on resist

Figure 1 . Electron-beam lithography steps to produce

line gratings for electron beam moire.

progress on applying this technique to the study of

thermomechanical displacements in the plated-throughhole.

GRATING PREPARATION

A series of experiments were performed to determine

the parameters to employ in writing line and dot arrays and the minimum pitch which could be achieved. Aluminum, brass, and GFRP were used as the substrate materials. The metallic substrates were disks 12.7 mm

in diameter and 1 to 2 mm thick. The GFRP was a strip 6 x 32 mm by 2 mm thick. Figure 1 summarizes the grating preparation.

The surfaces of the specimens were ground smooth and

flat using a series of water-lubricated abrasive-coated papers ending with 5 um grit. The" final polish was

achieved by finishing with 3 and then 1 pm diamond

particles. The substrates were cleaned in acetone

subjected to ultrasonic activation. Non-conductive

specimens were coated with a conductive layer. The specimens were coated with PMMA within a few

hours of polishing. The PMMA resist used for coating

is a 2% solution of PMMA, 950 000 relative molecular

weight, with chlorobenzene as ihe solvent. The PMMA

resist was spun on the specimens, at a speed of 3000

RPM for 30 s. The specimens were then baked on a hot

plate for 30 minutes at 160°C. This process produces a cured layer of PMMA resist that is approximately 100 nm thick. The application is performed in a class- 100

clean room. The specimens were mounted on a specimen stage with

a built-in glass-on-carbon resolution standard, in a

digitally controlled SEM that was equipped with a

Figure 2. An SEM microphotograph of a line grating

with a pitch of 10 000 lines/mm on GFRP.

Faraday cup and a beam blanker. The SEM was operated

with an accelerating voltage of 20 kV and a 50 pm aperture. The working distance was set at 25 mm and the specimen

surface was 23 mm from the objective lens. The Faraday cup was inserted into the electron beam, and the beam current was adjusted to a specified value in the range from 1 to 40 pA. The e-beam in the SEM is computer conrolled; gratings

are written in the PMMA resist point-by-point. To write a

line with a series of points, the center-to-center distance is about 1/4 the final line width. To properly expose the PMMA, we adjust the line dose and the area dose. The line dose is about 0.8 nC/cm for lines with a pitch of 100 nm, and

increases nearly linearly with the pitch. After the gratings are written, the specimen is developed in a solution consisting of three parts (by volume) of isopropyl alcohol to one part of methyl isobutyl ketone for 40 s. The

specimen is immediately rinsed in isopropyl alcohol for 20 s followed by a second rinse in deionized water for 30 s. Next,

the specimen is blown dry with a clean gas. The

development of the resist is an etching process; precise control is critical. Finally, the specimen is coatied with a very thin layer (10

to 20 nm) of a gold-palladium alloy by plasma sputtering.

This metallic coating is necessary to prevent surface charge

accumulation when viewing the specimen in the SEM.

Figure 2 shows a line grating from a GRFP specimen that

is discussed further below. This grating, shown at a magnification of 20 000X, has a pitch of 100 nm. The thin dark lines correspond to trenches in the PMMA resist formed

by etching the regions struck by the electron beam. The

wider light lines are ridges in the resist. The dark lines on a diagonal are due to a malfunction in the e-beam control during the exposure of the resist. Fortunately, the primary

lines, which are horizontal and on 100 nm centers, are

164

27
tMe&gglfe

Figure 3. An SEM microphotograph of a GFRP

specimen with a 200-nm-pitch dot grating,

shown at 50 000X.

iui]!i!i|iiiijmi|it!ijumii!niiiim

Figure 5a. Tensile specimen, after failure. The black drops are conductive paste, which

electrically grounds the specimen surface

to the grips.

• HV'^ c * - %

Btziz-A

:> ?Jl 4£

-Alt; :??>

:U "V 'V

rtI::' v ^:Vi:* I vj l > T-.

--'

<*^.c* i 1 V*' .

Figure 4. Line gratings on the tensile specimen. The

different shades indicate different line densities and exposures.

dominant since they cover about 85% of the area. Although the grating was flawed, it produced well- defined moire fringes with good contrast. Figure 3 shows a dot grating with a pitch of 200 nm.

=—|K««l!!llflllBI|llll|ll!ll!lll|ll|IU1H|!l)l|l!!||l1i!lll!l' , ""!;Hii!''':::. 1 "i.WJIIIllllliOIIIIWinPliiiiv

Figure 5b. Tensile testing stage for the scanning

electron microscope.

STRAIN FIELD DEVELOPMENT IN GFRP UNDER

TENSION

Specimen Preparation

The composite material investigated is a glass fiber reinforced epoxy known as 52/3501-6. The panels were laid up by hand and cured in an autoclave. The lay-up included 48 layers of prepreg oriented [O^O],. The lay-up was

symmetrical, with a surface to midplane sequence of

0/0/90/0/0/90/ ... 0/0/90|. This composite was

165

28
Figure 3. An SEM microphotograph of a GFRP

specimen with a 200-nm-pitch dot grating,

shown at 50 000X.

iHijim|!iii|iii!|i!iijmmiii|!ium

Figure 5a. Tensile specimen, after failure. The black drops are conductive paste, which

electrically grounds the specimen surface

to the grips.

arwiK^

^llt|nil|UII|i«ljlttl|llt[|llll)J|ll|U]ljrnij|!ll|>i:!jl|il!«l!'!|l!i»n!i:i'l: '"'•i'!iii!ii!l:i;:il,ii:''"i;'- .

Figure 4. Line gratings on the tensile specimen. The

different shades indicate different line densities and exposures.

dominant since they cover about 85% of the area. Although the grating was flawed, it produced welldefined moire fringes with good contrast. Figure 3 shows a dot grating with a pitch of 200 nm.

Figure 5b. Tensile testing stage for the scanning

electron microscope.

STRAIN FIELD DEVELOPMENT IN GFRP UNDER

TENSION

Specimen Preparation

The composite material investigated is a glass fiber reinforced epoxy known as 52/3501-6. The panels were laid up by hand and cured in an autoclave. The lay-up included 48 layers of prepreg oriented [Oj/90],. The lay-up was

symmetrical, with a surface to midplane sequence of

0/0/90/0/0/90/ ... 0/0/90J. This composite was

165

29
Figure 8. Cross-section of a plated-through-hole

showing gratings as square patterns.

that the strain in the 0° ply has increased, and significant

shearing strain has occurred over the resin-rich area at the interface. Failures in the 90° ply above and below

the grating area were visible in the SEM. This cross ply

cracking markedly degraded the contribution of the 90°

ply to the tensile stiffness of the composite.

Analysis of Fig. 7, obtained at an applied stress of 524 MPa, gives the following results. The strains in the 90°

ply are 0.9 x 10"3

, although the global strain on the specimen, as estimated from the global Young's modulus,

is 14 x 10"3. Clearly, the cross ply cracking has nearly eliminated the load-carrying capability of the 90° plies. The strain in the first fiber of the 0° ply varies over its length in the field of view. Over the bottom portion of

this fiber, the strain is 13.5 x 10"3

. Over the top portion of this fiber, the strain is only 8.65 x 10"3

. The average

strain over both the top and the bottom portions is 10.9 x 10'3

. The damage in the cross plies and other fractures must have affected the local region being analyzed.

The effect of damage is most evident at the interface, where moire fringes that are inclined 17° to the vertical indicate significant shear in the resin-rich region

between the 0° and 90° plies. Normal and shear strains were determined from observed displacement gradients, using analysis

procedures familiar from geometric optical moire. Shear

strains were approximated by assuming that the x- direction displacements were insignificant. We

Figure 9. Moire fringes on a plated-through-hole

cross section at the interface between

figerglass, copper, and solder. Note the bent fringes.

determined y^ by noting a shift of 5 fringe orders across the

interface as we move from the lower fiber end in the 90° ply

to the first longitudinal fiber in the 0° ply. The

thickness of the resin-rich area at the lower fiber is 5.29 urn. The resulting engineering shear strain y^ = 9.3%. This is a very large shearing strain that is supported by the matrix

material, preventing delamination. A final feature, evident in Fig. 7, is a crack in one of the longitudinal fibers. This fiber was not perfectly straight in the lay-up and in polishing we have formed a dagger-shaped

section. We observe a discontinuity of the moire fringe to the left of crack, indicating another localized shear strain. Measurements of Av and Ax indicate that y^ in the matrix

material just above and to the left of the crack was about 4.5%.

THERMOMECHANICAL STRAINS IN A PLATEDTHROUGH-HOLE

A plated-through hole in a printed wiring board is a composite structure that includes glass-fiber-reinforced

plastic, copper, and solder. The difference between the out-of- plane thermal expansion rate of the board and those of copper and solder is well known to be large, and consequently to be

the driving force in potential failure mechanisms which can be a problem if the manufacturing process is not carefully controlled. The plated-through-hole specimen was cut from a large

167

30
circuit board from a commercial electronic product. A

cross-section was potted in epoxy and ground and

polished to expose cross-sections ofplated-through-holes.

Gratings were applied by electron-beam lithography as described above. For examining thermally -induced

displacements, a commercially-supplied heating stage for the SEM was used. A thermocouple was placed on the top surface of the specimen.

Quantitative use of electron-beam moire in thermomechanical experiments is complicated by electric and magnetic deflection of the electron beam by the heater in the stage, and by small progressive

displacements of the specimen caused by thermal expansion of the stage. Figure 8 shows a cross section of a plated-through-hole in a printed wiring board with two internal copper layers in addition to the front and

back surface layers. The squares on this micrograph are

line gratings produced by electron beam lithography. A

variety of grating pitches wre used. The observations reported below come from a grating with a pitch of 1 urn. Figure 9 shows electron beam moire patterns on a plated-through-hole at 144° C. This image shows, left- to-right, fiberglass printed-circuit-board (PCB), copper, and solder. The large thermal expansion of the PCB

creates a shear deformation, indicated by the slanting

moire fringes. Note the concentrated deformation at the copper-solder interface. Engineering (angle) shear

strains of over 1 percent have been observed in the neighborhood of the copper-solder interface. Fringes at angles corresponding to even higher shear strains have

been seen, however the interpretation is difficult. The

fringe mismatches may be indicating local decohesion

between the solder and the copper. By contrast, the

fringes in the copper and the GFRP seem to be the same

after heating as before.

SUMMARY CONCLUSIONS

(1) Line gratings with a pitch of 100 nm can be

fabricated by electron beam lithography with sufficient contrast and efficiency to form electron beam moire

patterns at a magnification of 1900 X, where the raster scan of the scanning electron microscope provides a

virtual reference grating with a similar pitch with 500

lines across the field of view.

(2) These moire patterns can be formed on unstressed specimens and also on tensile specimens during testing,

and on specimens heated up to 150CC. Local strains over

fields tens of um can be evaluated with a strain resolution of a few parts in 10"4

. (3) During a tensile test of a glass-fiber-reinforced

plastic composite several interesting phenomena were

observed:

a) Before failure of the 90° ply, we measured a local modulus E, = 36 GPa over a gage length of about 25 um.

b) When the 90° ply failed by transverse cracking, its load- carrying capability effectively vanished. Failure of the 90°

ply produced shearing strains in the resin-rich area between

the 0° and 90° plies. c) After failure of the 90° ply, the strain increments at different locations were not proportional to the increments of

the average stress. The increasing numbers of cracks in the 90° plies and in the longitudinal fibers produced a new strain distribution.

(4) The electron beam moire technique can be applied to theromechanical stressing of plated-through-holes. It has

revealed high, irreversible shear strains in the solder near the copper plating.

ACKNOWLEDGMENTS

The preparation of plated-through-hole specimens by

Elizabeth Drexler is appreciated.

REFERENCES

1

.

Weller, R. and Shepard, B.M., "Dislacement Measurement

by Mechanical Interferometry," Proc. Society for Experimental Stress Analysis. Vol. 6. No. 1, pp. 35-38, 1948.

2. Parks, V.J., Geometric Moire, Handbook on Experimental

Mechanics. Ed. A.S. Kobayashi, Prentice-Hall, Englewood

Cliffs, N.J., pp. 282-313, 1987.

3. Theocaris, P.S., Moire Fringes in Strain Analysis. Pergamon Press, Elmsford, N.Y., 1969.

4. Post, D., "Optical Interference for Deformation Measurements -Classical, Holographic and Moire

Interferometry," Mechanics of Nondestructive Testing. Ed. W.W. Stinchcomb, Plenum Press, New York, pp. 1-53, 1980.

5. McDonach, A., McKelvie, J., and Walker, C.A., "Stress Analysis of Fibrous Composites Using Moire Interferometry,"

Optics and Laser Eng.. Vol. 1, pp. 85-105, 1980.

6. Post, D., "Moire Interferometry: Advances and

Applications," Experimental Mechanics. Vol. 31, No. 3, pp. 276-280, 1991.

7. Post, D., Dai, F. L., Guo, Y., and Ifju, P., "Interlaminar shear moduli of cross-ply laminates: An experimental

analysis," Journal of Composite Materials 23 (3), 1989, 264-

279.

168

31
8. Post, D., Czamek, R., Joh, D., Jo, J., and Guo, Y., "Experimental Study of Metal-Matrix Composite,"

Experimental Mechanics 27 (2), June, 1987, 190-194.

9. Post, D., Czamek, R., and Joh, D., "Shear Strains in a Graphite/PEEK Beam by Moire Interferometry,"

Experimental Mechanics 27 (3), September, 1987, 246-

249.

10. Post, D. and Wood, J. D., "Determination of

Thermal Strains by Moire Interferometry," Experimental

Mechanics 29 (3), September, 1989, 318-322.

11. Haller, I., Hatzakis, M. and Srinivasan, R., "High

Resolution Positive Resists for Electron-beam Exposure,"

IBM Journal Research and Development. Vol. 12. pp. 251, 1968.

12. Paton, N.E. and Mahoney, M.W., "Creep of

Titanium-Silicon Alloys," Metallurgical Transactions A.

Vol. 7A. pp. 1685-1692, 1976.

13. Kishimoto, S., M. Egashira, Shinya, N. and Carolan,

R.A., "Local Micro-Deformation Analysis by Means of

Microgrid and Electron Beam Moire Fringe Method,"

Proceedings of the Sixth International Conference on

Mechanical Behavior of Materials. M. Jono and T. Inoue,

eds., Kyoto, Japan, Vol. 4, pp. 661-666, 1991.

14. Kishimoto, S., Egashira, M. and Shinya, "Measurement of Grain Boundary Sliding and

Observation of Microgrids for High Temperature Use,"

Journal of the Society for Materials Science Japan. Vol.

40, No. 452, pp. 637-641, 1991 (in Japanese).

15. Morimoto, Y. and Hayashi, T., "Deformation Measurement During Powder Compaction by a Scanning

Moire Method," Experimental Mechanics. Vol. 24. pp. 112-116,1984.

169

32
A3

Electron Beam Moire Study ofFracture ofa Glass Fiber Reinforced Plastic

Composite

by Read and Dally (1994)

33
D. T. Read

Materials Reliability Division, National Institute of Standards and Technology,

Boulder, CO 80303

J. W. Dally

Mechanical Engineering Department,

University of Maryland,

College Park, MD 20742

Electron Beam Moire Study of

Fracture of a Glass Fiber

Reinforced Plastic Composite

Using the method of electron beam moire, a small region at an interface of a [Q/

90b glassfiber reinforcedplastic composite has been examined during tensile testing. The tensile test was conducted inside a scanning electron microscope, with a high

spatial frequency line grating (10,000 lines/mm) at the interface between a longi- tudinal ply and a transverse ply. During the test, this region was observed at a

magnification of 1900'x . Local strain measurements were made by interpreting the moirefringe patterns over gage lengths that variedfrom 10 to 30 pm. The magnitude

and distribution of the local strains depended on the damage that occurred with monotonically increasing load. Load shedding by the transverse ply was evident from the fringe patterns. Extremely high local strains were observed: longitudinal fiber strains up to threepercent, normal strains up to threepercent, andshear strains up to 40 percent in the epoxy matrix.

Introduction

Glass fiber reinforced plastic fabricated from several layers or plies is classified as a laminated composite. Although each

layer is orthotropic, and the layers may have different ori- entations, the laminate acts as a single body with a global

stiffness that is related to the stiffness and orientation of the

individual plies (Halpin, 1984). In a structural analysis of a

laminated composite, planes through a typical cross-section are assumed to remain plane after deformations due to tensile or bending loads (Tsai and Hahn, 1981, and Vinson and Sier- akowski, 1986). Stresses vary from ply to ply because of changing elastic constants, but the displacements are continuous

across the interfaces. Experiments with tension members,

beams, plates, and shells (Halpin, 1984) confirm that the results of analysis using laminate theory are not always adequate, and more involved micromechanics theories (Chamis, 1974) are

necessary to predict the loss of stiffness and strength. Here we

report experimental results showing some deviations from the plane sections remain plane assumption of the simple laminate

theory even prior to extensive ply damage. The need for mi- cromechanics theory when damage occurs is clearly established. Electron beam (e-beam) moire (Kishimoto et al., 1991 ; Dally

and Read, 1992) was used to study displacement and strains

in a tensile specimen fabricated from a [O2/90]s glass fiber

Contributed by the Applied Mechanics Division of The American Society

of Mechanical Engineers for publication in the ASME Journal of Applied Mechanics.

Discussion on this paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of

Houston, Houston. TX 77204-4792, and will be accepted until four months after

final publication of the paper itself in the ASME Journal of Applied Mechanics. Manuscript received by the ASME Applied Mechanics Division, Oct. 1 , 1992;

final revision, Feb. 23, 1993. Associate Technical Editor: W. N. Sharpe, Jr.

reinforced epoxy. Displacement and strain were measured on

a microscale during four phases of loading:

(1) prior to cross ply cracking,

(2) after cross pry cracking,

(3) after extensive damage, but before delamination, and

(4) after delamination, prior to rupture. The analysis was performed with a high-frequency line grat- ing (10,000 lines/mm) that was written with an e-beam over an area SO x 80 /tin . The patch of grating was positioned at an interface between a cross ply and a longitudinal ply. The

measurement field included three rows of fibers associated with

the cross ply, the resin-rich interface, and several fibers in the

longitudinal ply. Background. Some experimental studies of the deformation and failure of composite materials have utilized detailed observations of the behavior of specimens under load. To cite an outstanding example, D. Post and colleagues presented

moire interferometry data showing the shear strain differences among deg plies, 90 deg plies, and resin-rich regions between

plies (Post et al., 1989). They have applied well-developed

techniques to a series of issues in the behavior of composite

materials and interfaces (Post et al., 1987a, Post et al., 1987b, Post and Wood, 1989). In particular, the stiffness difference between fiber and matrix-produced zig-zag fringes (Post et al., 1987a). High-magnification observation of fracture surfaces was used by Bandyopadhyay et al. (1989) to support their explanation of the difference in fracture toughness between two types of

carbon fiber composites. The techniques of Raman spectros- copy (Galiotis et al., 1988) and of speckle interferometry (Anastasi et al., 1987) have also been used to map stresses and

deformations in composites at lower spatial resolution. Detailed theoretical models ofthe micromechanical behavior

34
fl

u

III 4. Elpo»

5. Develop

4 3. Spin on rem JUBBJE3LJ9

I l

Fig. 1 Electron-beam lithography procedure to produce line gratings

for electron beam moire on the GFRP tensile specimen

of composites have been formulated (Lee et al., 1989), but

their verification has relied on macroscopic observations. It is well recognized that demonstration of the macroscopic usefulness of such models does not constitute proof of their mi- cromechanical assumptions.

e-Beam Moire. e-Beam moire is similar to optical moire

except that an electron beam is used to produce the line gratings and a scanning electron beam is then employed to generate the moire fringe pattern. The technique for producing the line grating is shown in Fig. 1. We first prepared the surface of

the specimen by grinding it smooth and flat with a series of

water-lubricated abrasive papers ending with 5 /*m grit. The

final polish was achieved by finishing with 3 and then 1 pm

diamond particles. The second step was the application of a

very thin (10 to 20 nm) gold palladium coating by plasma

sputtering. This metallic coating is necessary to render the specimen surface conductive, to prevent a surface charge from

developing on the glass fiber reinforced plastic specimen under

the electron beam. The specimens were then coated with polymethylmethacrylate (PMMA) which serves as an electron beam resist. The

PMMA solution used for coating was two percent PMMA,

molecular weight of 950,000, with chlorobenzene as the sol- vent. The PMMA resist was spun on the specimens, at a speed

of 3000 RPM for 30 seconds. The specimens were then baked on a hot plate for 30 minutes at 160°C. This process produces

a cured layer of PMMA resist that is approximately 100 nm

thick. The specimen was mounted on a specimen stage in a digitally controlled scanning electron microscope equipped with a Far- aday cup and a beam blanker. The scanning electronic microscope was operated with an accelerating voltage of 20 kV and

a 50 ftm aperture. The probe current was adjusted to 10 pA,

which produces a focussed beam of electrons 10 to 15 .im in diameter. The e-beam in the scanning electronic microscope was computer controlled and patterns were written in the PMMA resist with programmed instructions. These instructions defined both the geometry of the pattern and the electron dosage. After the patterns were written, the specimen was developed

in a solution consisting of three parts (by volume) of isopropyl

alcohol to one part of methyl isobutyl ketone for 40 s. The

specimen was immediately rinsed in isopropyl alcohol for 20

s followed by a second rinse in deionized water for 30 s. The

development of the resist is an etching process; precise control of the development is critical. Finally, the specimen was coated

again with a very thin layer (10 to 20 nm) of a gold palladium

alloy to provide a conductive surface on top of the PMMA.

Fig. 2 Line and dot gratings on the tensile specimen

Fig. 3 An SEM micrograph oi the moire grating used in this study with

pitch p, = 100 nm

Twelve different patterns were written on the specimen as

illustrated in Fig. 2. The top three patterns, along row 1 , are

lines 250 itm. long on 200 nm centers. The next three patterns, along row 2, are dots placed in a rectangle 240 x 200 ^m in

size on 200 nm centers. The three patterns on row 3 are lines 80 ftm long on 100 nm centers; 500 lines are included in each

pattern. Two dot patterns placed in an 80 /tm square on 100 nm centers are shown along row 4. The third pattern located

at column 3 in row 4 was underexposed. The difference in the shading indicates different line densities and exposures of the

patterns. The pattern at site 9, the third pattern in the third row, was

selected for observation in the study. This pattern, having a

density of 10,000 lines/mm, was located at an interface between

a cross pry and a longitudinal ply. Also, the line array provided

80 or more lines across each of several glass fibers (8 to 10 ^m

in diameter) which was enough to investigate intraply and

intrafiber deformations. Finally, the quality of the line grating was sufficient to produce scanning moire fringes with good

contrast. A scanning electron microscope micrograph of the moire

grating at site 9 taken at 20,000 x , presented in Fig. 3, shows

the detail of the line array. The thin dark lines correspond to

Journal of Applied Mechanics

35

JUNE 1994, Vol. 61 / 403
i ooss rsscc

Rg. 4(a) Tensile specimen after failure. The black drops are conductive

paste, which electrically grounds the specimen surface to the grips.

Fig. 4(4) Tensile testing stage for the scanning electron microscope

trenches in the PMMA resist formed by etching the regions

exposed by the electron beam. The wider light lines are ridges

in the resist. The dark lines on a diagonal are due to a malfunction in the e-beam control during the exposure of the resist. Fortunately, the primary lines, which are horizontal and on

100 nm centers, are dominant since they cover about 85 percent of the area. Although the grating was flawed, it produced well- defined moire fringes with good contrast. Moire fringe patterns are formed by scanning the grating

lines with the electron beam in a scanning electron microscope.

The pitch p, of the raster scan in the SEM can be controlled by adjusting either the magnification M or the number of scan

lines used to form the image. In these experiments the number

of scan lines was held constant at 500 and the reference pitch

pr was adjusted with the magnifications setting. At a magnification of 1900 x,pr = 98 nm and is nearly equal to the pitch

ps of the specimen grating. The signal from the secondary

electrons which is sensed by a detector in the scanning electron microscope is strongly affected by the difference in frequencies,

fs - J, = \/ps - \/p, of the two line arrays. When this frequency difference is small, a pattern of light and dark bands

corresponding to moire fringes is formed. Since these fringes are formed by electrons, the method is not limited by the wavelength of light, and microscale measurements at high magnification are possible.

Specimen and Load Fixture The composite material investigated is a glass fiber rein- forced epoxy known as 52/3501-6. The panels were laid up by

hand and cured in an autoclave. The lay-up included 48 layers

,

of prepreg oriented [02/90]s

. The lay-up was symmetrical, with a surface to midplane sequence of 0/0/90/0/0/90 .... 0/0/

Fig. 5 Moire fringe pattern at an interface between a longitudinal ply and a cross ply, at initial load

901. The finished panels were 6.22 mm thick, with a void

content of less than one percent. A thin strip 2 mm thick and 33 mm long oriented in the

longitudinal 0-deg direction was cut from the composite panel

by using an abrasive cutoff wheel flooded with water. The

strip was turned on its side to show the cross-section of the laminate and adhesively bonded to a polishing block. The strip was reduced to a thickness of 0.406 mm by sanding and polishing with standard metallographic polishing equipment. The

high-density gratings were written on the specimen surface at the sites defined in Fig. 2. The ends of the specimen were reinforced by bonding alu- minum plates to both surfaces as shown in Fig. 4(a). The

specimen was placed in a small universal testing machine that was designed to fit into the vacuum chamber of a scanning

electron microscope. This testing machine, shown in Fig. 4(b), employs clamped wedge grips for specimen attachment. Both

spur and worm gears are used to turn a pair of lead screws

that drive both loading platens at equal speeds. The applied load and platen displacement were measured with a load cell and a LVDT, respectively.

Strain Field Development With Load

Before Cross Pry Cracking. The glass fiber reinforced plastic tensile specimen was mounted on a scanning electron microscope loading machine, and a small initial load of 75 N

was applied. The moire pattern at site 9 was brought into focus

at a magnification of 1900 x . At this magnification, the pitch of the specimen gratings.ps and the pitch of the scanning elec- tron beamp„ which serves as the reference grating, were nearly

equal. The electron beam raster lines and the specimen grating

lines were aligned. The small difference between pr and ps produced the mismatch fringes presented in Fig. 5. This figure shows the interface between a 90-deg or cross ply and a 0-deg

or longitudinal ply. The three columns of circles are fiber ends

in the 90-deg ply that range in diameter from 8 to 10 ;*m. The

resin-rich area at the interface varies in thickness from 3.5 to

5.3 nm. Portions of five different fibers and two resin regions from the 0-deg ply can be identified in Fig. 5. The next moire fringe pattern, presented in Fig. 6, corre- sponds to a nominal tensile stress of 347 MPa. The fringes are continuous across the interface, indicating that the deformations are continuous from the 90-deg to the 0-deg ply. The

continuity of the displacements across the interface is consistent

36
Fig. 6 Moire binge pattern prior to eross-ofy cracking, at a stress of 347 MPa

Table 1 Strain distribution across an interface in a O2/9O glass fiber reinforced plastic composite prior to 90-deg pry failure a = 347 MPa

Ply Strain t, 90deg

Interface Odeg

8.6x10"

9.5x10"

10.1x10"

with elementary laminate theory. However, the gradient dN/

dy of the fringe field differs among the 90-deg pry, the interface, and the 0-deg ply, indicating a strain gradient dty/dx across

this interface. This strain gradient is not consistent with the plane section assumption of elementary laminate theory.

The strain at any location in the field is given by

v ANpr

€y ~L~ L

(1)

where v is the displacement along the axis of the specimen and

normal to the grating lines, pr = 98.3 nm is the reference pitch

at 1900 x , and L is a gage length.

The fringe order difference AN is AN=N„-N (2) where N„ is the number of fringes at load P and N is the number of fringes at initial load. Combining Eqs. (2) and (3) gives

€y=(Np -N )Pr (3) where N'p and N are fringe gradients AN/Ay at load P and

the initial load. The fringe gradients N'p and No were determined over a gage

length Ay of 25 to 30 /xm along the lines 1, 2, and 3 defined

in Fig. 6. These lines refer to the first column of fibers in the 90-deg ply, the resin-rich interface, and the first longitudinal

fiber in the-deg ply. The results are given in Table 1

The distance between lines 1 and 3 was 12.9 /tin and the

strain difference across the interface was 1.5 x 10" 3

. Thus,

the strain gradient from fiber center line to fiber center line across the interface was dty/dx = 0.12 x 10" 3 dun)

-1

. Next, a local elastic modulus Et was determined from

Ei = a/eaye (4) where the applied tensile stress a = 347 MPa, and the average

strain is

«»« = (2*0 + e9o)/3 = 9.6 x 10" (5)

Fig. 7 MPaMoire fringe partem after cross-ply cracking, at a stress of S24

csoss PII CBtCX WDPflS SITS

The form of the numerator in Eq. (5) was employed because

Fig. 8 Cross-pry cracking near the grating and longitudinal fiber cracks

over the whole field, at a stress of 700 MPa

the laminate was fabricated with two 0-deg plies for every 90- deg ply. The value ofthe local modulus was 36. 1 GPa, which is within

five percent of the expected global modulus of 37.9 GPa.

After Cross-Ply Cracking. The moire fringe pattern pre- sented in Fig. 7 shows a dramatic change in the deformations

across the same interface. A cursory inspection of the fringe pattern shows that (a) the strain in the 90-deg ply has decreased,

(b) the strain in the 0-deg ply has increased, and (c) significant shearing strain has occurred over the resin-rich area at the

interface. Failures in the 90-deg ply above and below the grating area are shown in Fig. 8. This cross-ply cracking markedly

degraded the contribution of the 90-deg ply to the tensile stiff- ness of the composite.

Analysis of Fig. 7 gives the results presented in Table 2. The

strains in the 90-deg ply have decreased to about ten percent of their former value, although the global stress on the spec- imen increased from 347 to 524 MPa. Clearly, the cross-ply cracking has nearly eliminated the load-carrying capability of

Journal of Applied Mechanics

37

JUNE 1994, Vol. 61/405
Table 2 Strain distribution across an interface in a Oj/90 glass fiber reinforced plastic composite after 90-deg ply failure a = 524 MPa

Ply Strain, t, 90deg 8.9 x 10" 4 Odeg 10.9 xlO"3

Table 3 Strains at several locations near the interface

a = 700 MPa

Location Strain

7*5- Cross ply -3.9x10""

Interface 13.5 xlO" 3 First longitudinal fiber 13.5 x 10" 3 Second longitudinal fiber 16.7 x 10" 3 Resin between first and second fiber 17.6xl0" 3 Resin by crack in dagger fiber —

0.093

0.014

0.133

the 90-deg plies. The strain in the first fiber of the 0-deg ply

varies over its length in the field of view. Over the bottom

portion of this fiber, the strain is 13.5 x 10" 3

, but over the top portion of this fiber, the strain is only 8.7 x 10" 3

. The

average strain over both the top and the bottom portions is 10.9 x 10" 3

, which represents an increase of eight percent over strains due to the previous load. Because the globally

applied stress was increased by 51 percent, the damage in the

cross plies and other fractures of individual fibers has affected the strain distribution in the local region being analyzed.

The effect of damage is most evident at the interface, where

moire fringes that are inclined 17 deg to the vertical indicate

significant shear in the resin-rich region between the 0-deg and

90-deg plies. The engineering shear strain is defined as

1*> ~{dx+

dy)-

(6)

If we assume that du/dy is small enough relative to dv/dx to be neglected in the interface region, the engineering shear strain can be approximated as

(7)

The assumption that du/dy = is reasonable because the

longitudinal fibers adjacent to the interface are observed to remain straight under axial tensile stresses. Using Eq. (7), y^

is determined by noting a shift of five fringe orders across the

interface from point A to point B in Fig. 7. This shift due to shear gives Av = ANpr = 0.49 fim. The thickness of the resin- rich area at the lower fiber, corresponding to Ax in Eq. (7),

is 5.29 jim. The resulting engineering shear strain yv = 9.3

percent. Clearly, a very large shearing strain is supported by

the matrix material, preventing delamination. A final feature, evident in Fig. 7, is a crack in one of the

longitudinal fibers. This fiber was not perfectly planar in the lay-up and appears with a dagger shape after polishing. One

observes rotation of the moire fringes to the left of the crack,

indicating another localized shear strain. Measurements of Av

and Ax indicate that y^ in the matrix material just above and

to the left of the crack was about 4.5 percent. Extension of Shearing into the 0-deg Ply. Moire patterns

in Figs. 9(a), 9{b), and 9(c) show the effect of increasing the

tensile stress in the presence of 90-deg ply damage. A cursory

inspection of Fig. 9(d), which corresponds to a = 700 MPa,

shows the unloading of the 90-deg ply and the extension of

the shearing strains from the interface into the resin-rich areas of the 0-deg ply. Measurements were made of the normal

Fig. 9(a) Moire fringe pattern showing development of shea- at the

interface between the longitudinal pfy and the cross ply, at a stress of 700 MPa

Fig. 9(d) Moire fringe pattern showing exteixSng shear deformation

into the tongitucfinal ply, at a stress of 828 MPa

Fig. 9(c) Moire fringe pattern prior to delamination cracking at the

location marked, at a stress of 933 MPa

strains ey in the fibers and the shear strains yv in the regions of epoxy between the fibers. The results are presented in Table

3.

38
Table 4 Strains at several locations near the interface 828 MPa

Location Strain

txy Dross ply 9.8 xl(T4 .nterface 16.0xl0" 3 0.119

-irst longitudinal fiber 16-OxlO-3 —

second longitudinal fiber 22.8x10-' —

iesin between first and second fibers adjacent first fiber — 0.084

center of region 21.4X10 -3 0.055

adjacent second fiber —

iesin near crack in dagger- — 0.133

like fiber

Table 5 Strains at several locations near the interface a = 993 MPa

Location Strain

Dross ply

Interface

i^rst longitudinal fiber Second longitudinal fiber

ilesin between first and second fibers adjacent first fiber center of region

adjacent second fiber

3.93 xlO"4 12.4 xlO-3

12.4 xlO"3 25.4X10" 3

25.7x10"

7*>

0.072

0.167

The compressive strain indicated in the cross ply is not real. Phe magnitude of this strain, ty = 3.9 x 10 , shows the

esolution of the method. It is believed that the cross ply is otally unloaded at this load increment. The shear strain at the

nterface did not change as the applied tensile stress increased rom 524 to 700 MPa. The strain ey in the first longitudinal

iber has increased but not in proportion to the loading. The

trains in the second longitudinal fiber and the resin between

he first and second fibers are nearly the same, and both are

ligher than the strain in the first longitudinal fiber. Shearing strains of 1.36 percent were measured between the

irst two fibers in the resin region below the dagger-shaped

ongitudinal fiber. Shearing strains near the crack in the daggerihaped fiber were 13.3 percent on the left side and higher than

his value on the right side. The moire fringe pattern shown in Fig. 9(b) corresponds to

l tensile stress of 828 MPa. The normal and shear strains at

several locations are shown in Table 4. The strains in the longitudinal fibers and the shear strains

it the interface all increased on this increment of the load. However, the increases in strains were not all proportional to

:he increase in the load. The strain in the second longitudinal

fiber exceeds two percent and the strain in the first longitudinal

fiber is 1.6 percent. Another crack in a longitudinal fiber to

the far right in Fig. 9(b) is evident. The curvature of the fringes

in the resin region between the first and second fibers is due

to a decrease in the value of the shearing strain across the

region. The shearing strain is a maximum adjacent to the first fiber and is nearly zero adjacent to the second fiber. The final moire pattern in this series, Fig. 9(c), corresponds

to a tensile stress of 993 MPa, an increase of 20 percent from

828 MPa. The strains at several locations are shown in Table

5. While the applied stress increased 20 percent from Fig. 9(b)

to Fig. 9(c), the shearing strains at the interface and the normal

strains in the first longitudinal fiber decreased markedly, be- cause these regions were beginning to unload. The interface has shifted to the right side of the first longitudinal fiber. This

shift is apparent from the sharp increase in the shear strain

(to 16V7 percent) in the resin region adjacent to and to the right of the first fiber. The normal strain in the resin region and in the second longitudinal fiber has increased to 2.5 percent. The

Fig. 10(a) Fringe partem after 0-deg ply delamination cracking, at a

stress of 1075 MPa

&? ass.

IBS i

Fig. 10(b) Moire pattern to the right of the delamination crack, at a

stress of 1075 MPa

shifting of load from the first to the second fiber is due to extensions of the cross-ply cracks, above and below the moire

grating, that cut across the first longitudinal fiber (see Fig.

11).Finally, a pending delamination plane is marked in Fig. 9(c), just to the right of the second complete longitudinal fiber. At

this interface, continuous moire fringes are observed that in- dicate high normal strain (2.5 percent) but relatively small

shearing strains.

Longitudinal Ply Failure by Delamination. On the next load increment, to a = 1075 MPa, a delamination crack ap

peared in the moire grating as shown in Fig. 10(a). The de- lamination produced a step-like deformation of the top edge of the moire grating as illustrated in Fig. 10(b), although the specimen continued to support the applied load. An analysis of the regions to the left of the delamination crack gave the

strains presented in Table 6. The delamination did not markedly affect the trends under way at locations to the left of the longitudinal crack. The cross ply at the site is essentially free. The interface and the first longitudinal fiber continue to unload. The strains in the region between the first and second fibers and in the second fiber continue to increase, exceeding 3.2 percent. The shear strain adjacent to the first longitudinal fiber is so high that it was

Journal of Applied Mechanics

39

JUNE 1994, Vol. 61/407
Table 6 Strains at several locations after delamination

a = 1075 MPa

Strain Location h Ix, Cross ply 1.96X10 -4

Interface 7.66X10 -3 0.067

First longitudinal fiber 7.66xl0-3 —

Second longitudinal fiber 33.4 xlO-3 —

Resin between first and second fibers adjacent first fiber — -0.2*

center of region 32.3 xlO" 3 adjacent second fiber —

* too large to resolve small

not possible to resolve the fringes. It is believed that the shear

strain is in excess of 20 percent. The moire pattern to the right of the delamination crack is shown in Fig. 10(fc). The normal strains in the longitudinal

fibers are nearly zero. A very high shearing strain exists to the

right of the delamination crack. Measurements of the angle of top boundary of the grating across the 2.35 /im wide shear band adjacent to the delamination crack give a shear strain of

41.4 percent. A photograph at 160 x in Fig. 11 shows the different types of damage developed during the monotonic loading to a global

tensile stress of 1075 MPa. The cross-ply cracks near the meas- urement site and in an adjacent 90-deg ply are evident. Extension of the cross-ply cracks into the 0-deg ply and the failure of the first longitudinal fiber explains its unloading at the higher stress levels. Transverse cracks in the longitudinal fibers occur at many locations. These cracks in the longitudinal fibers are to be expected because local strains in the fibers of 3.3 percent give local uniaxial fiber stresses of about 2400 MPa.

Delamination cracks have formed between the 0-deg and 90- deg plies and at several locations in the 0-deg plies. These

delaminations produce step discontinuities as large as 7.5 /an

in the v displacement field. The distribution of strain ey across the measurement site is shown in Fig. 12. This graph shows that the strain in the second

fiber and the adjacent resin region increased monotonically

with the applied stress. Tensile strain in the transverse ply increased at first, then decreased because of cracking in that

ply. The resin between the longitudinal and transverse plies had a similar history. The shear strains measured locally in the epoxy resin were

very large. Before delamination, shear strains of 16.7 percent were measured. After delamination, the shear strains were 41 .4 percent in a shear band 2.35 /im wide adjacent to a longitudinal crack in the 0-deg ply. Neglecting biaxial effects, the normal

stresses in the epoxy in resin-rich areas between fibers are estimated to be at least 1100 MPa.

Following this delamination, the specimen was unloaded and

found to be intact. It was then reloaded until failure occurred

at a nominal tensile stress of a = 1220 MPa.

Discussion and Conclusions

The e-beam moire method with a high-frequency One grating (10,000 lines/mm) enabled an examination of a small region about 45 nm square at an interface of a [CV90]S glass fiber reinforced plastic. The examination, performed at 1900 x , per- mitted measurement of normal and shearing strains in the cross

ply, in the resin-rich region between plies, in the longitudinal

fibers, and in resin regions between these longitudinal fibers. The specimen was loaded in uniaxial tension until failure oc- curred at 1220 MPa. Local strain measurements were made

by interpreting the moire fringe patterns over gage lengths

ranging from 10 to 30 urn. The magnitude and the distribution of the strains depended

Fig. 1 1 Cross ply, longitudinal fiber, and longitudinal ply cracking. Also,

intrapty delamination.

30

s 1 <4

N

ai

& 347UP1 O 7XMPJ O 82SUP1 O 993UP» * 1075 MP!

=3? =Oc=

Pry Basin Row Resin Fiber LOCATION

Fig. 12 Strain distribution across the grating tor several different ap- plied stress levels

on the damage that occurred in the specimen as the load was

increased and on the location of the damage. From several

local strain measurements at a number of locations the fol- lowing conclusions have been drawn:

(1) Before the failure of the 90-deg ply, there was a dif- ference of 14 percent in ey across the interface between 0-deg

and 90-deg plies with the higher strains in the 0-deg ply. At a nominal stress of 347 MPa, the gradient de/dx = 1.2 x 10" 4 pin-1

. Higher strains in the 0-deg ply may indicate that very

isolated 90-deg cracking occurred at even lower global stress. (2) Before failure of the 90-deg ply, we measured a local modulus Ei = 36.1 GPa over a gage length of about 25 urn.

(3) When the 90-deg ply failed by transverse cracking, its load-carrying capability effectively vanished.

(4) Failure of the 90-deg ply produced shearing strains in the resin-rich area between the 0-deg and 90-deg plies. These

shearing strains were large and increased with load to 11.9 percent before they were relieved by fracture of adjacent fibers in the 0-deg ply.

(5) Isolated transverse cracks occurred in large numbers in longitudinal fibers at nominal stresses as low as 347 MPa.

These cracks produced shearing strains in the epoxy which

increased with load to about 13 percent.

(6) After failure of the 90-deg ply, the strain increments

at different locations were not proportional to the increments

40
of the applied (global) stress. The increasing numbers of cracks

in the 90-deg plies and in the longitudinal fibers produced a new local geometry at each load increment. This progressive

damage by cracking resulted in strain redistribution.

(7) Cross-ply cracks extended into the O-deg ply and ef- fectively shifted the interface between plies. This shift produced

shear strains as large as 16.7 percent in the matrix between

longitudinal fibers.

(8) Local delamination occurred due to cracking between

O-deg and 90-deg plies and cracking between longitudinal fibers in the O-deg ply. However, the specimen remained intact and

supported the applied load.

(9) After delamination in the O-deg ply at a = 1075 MPa,

fiber strains of 3.34 percent were measured. The corresponding

fiber stress, neglecting biaxial effects, was 2400 MPa, which was 2.23 percent larger than the global applied tensile stress. (10) A delamination crack passing through the moire grat- ing produced a step discontinuity of 7.5 displacement field. This slippage is consistent with crack-opening displacements

associated with transverse cracks in the adjacent 90-deg ply. (11) A localized shear band was evident in the epoxy matrix

material adjacent to the delamination crack. This band was

2.35 /im wide and was produced by an average shearing strain of 41.4 percent.

(12) The epoxy matrix between longitudinal fibers sup- ported normal strains as large as 3.23 percent, which corre- sponds to a local tensile strength in excess of 1100 MPa if biaxial effects are neglected.

(13) While these experimental results are typical, they are not unique. The strain distributions at each load are clearly dependent on the many different types of damage and the

location of each damage site relative to the measurement position. (14) It is always difficult to specify the accuracy of a meas- urement and this statement is particularly true when the ex- perimental method is as new as e-beam moire\ The results were

obtained from Eq. (3) and involved measuring fringe gradients.

It is estimated that the gradients could be determined to ± 4 (± 0.2 fringes in a count of five percent over a gage length of 20 to 30 jim). A second source of error is in the reference

pitch pr- The value of pr depends on the magnification which was fixed at 1 900 x to produce all of the moire fringe patterns. Variations in the magnification due to electronic instabilities in the scanning electron microscope are known to occur, but

they have not been studied to date.

(15) Measurements of the strain ey

in the cross ply at high

loads after the region was essentially stress-free indicate that the resolution of the measurements was about ± 1000 fie or ± 0.1 percent.

Acknowledgments

Thanks are due to R. E. Harris and J. Martinis for the use of the lithographic facility in the Electromagnetic Technology

Division at NIST, and to Greg Zimmerli for introducing us to

electron beam lithography.

References

Anastasi, R. F., Serabian, S. M., Shuford, R. J., and Das-Gupta, D., 1987, "Nondestructive Detection of Simulated Delaminafions in Composite 1 aminatrs by Laser-Speckle Shearography," Experimental Techniques, Vol. 11, No. 6, June, pp. 28-31. Bandyopadhyay, S., Gellen, E. P., Silva, V. M., and Underwood, J. H.,

1989, "Microscopic Aspects of Failure and Fracture in Cross-Ply Fibre Reinforced Composite Laminates," Journal of Composite Materials, Vol. 23, Dec., pp. 1216-1231. Charms, C. C, 1974, "Micromechanics Strength Theories for Composite

Materials," Fracture and Fatigue, Vol. 5, L. J. Broutman, ed., Academic Press, New York, pp. 93-151.

Dally, J. W., and Read, D. T., 1993, "Electron Beam Moire," Experimental

Mechanics, Vol. 33, No. 4, Dec., pp. 270-277.

Galiotis, C, Melanitis, N., Batchelder, D. N., Robinson, I. M., and Peacock,

J. A., 1988, "Residual Strain Mapping in Carbon Fibre/PEEK Composites."

Composites, Vol. 19, No. 4, July, pp. 312-324.

Halpin, J. C, 1984, Primer on Composite Materials: Analysis, Technomic,

Lancaster, PA.

Kishimoto, S., Egashir, M., Shinya, N., and Carolan, R. A., "Local Micro- Deformation Analysis by Means of Microgrid and Electron Beam Moire Fringe Method," Proceedings of the Sixth International Conference on Mechanical

Behavior of Materials, M. Jono and T. Inoue, eds., Kyoto, Japan, Vol. 4, pp. 661-666, pp. 1991. Lee, J-W., Allen, D. H., and Harris. C. E., 1989, "Internal State Variable Approach for Predicting Stiffness Reductions in Fibrous Laminated Composites

with Matrix Cracks." Journal ofComposite Materials, Vol. 23, Dec., pp. 1273-

1291. Post, D., Czarnek, R., Joh, D., Jo, J., and Guo, Y., 1987a, "Experimental Study of Metal-Matrix Composite," Experimental Mechanics, Vol. 27, No. 2, June, pp. 190-194.

Post, D., Czarnek, R., and Joh, D., 1987b, "Shear Strains in a Graphite/ PEEK Beam by Moire Interferometry," Experimental Mechanics, Vol. 27, No.

3, Sept., pp. 246-249.

Post, D., and Wood, J. D., "Determination of Thermal Strains by Moire

Interferometry," Experimental Mechanics, Vol. 29, No. 3, Sept., pp. 318-322.

Post, D., Dai. F. L., Guo. Y., and Ifju, P., 1989, "Interlaminar Shear Moduli

of Cross-ply Laminates: An Experimental Analysis," Journal of Composite

Materials, Vol. 23, No. 3, pp. 264-279.

Tsai, S. W., and Harm, H. T., 1980, Introduction to Composite Materials, Technomic, Lancaster, PA, 1980. Vinson, J. R., and Sierakowski, R. L., 1986, The Behavior of Structures Composed of Composite Materials, Martinus Nijhoff, Boston, MA.

Journal of Applied Mechanics

41

JUNE 1994, Vol.61 /409
A4

Local Deformation ofPlated Through Holes under Thermomechanical Loading

by Read and Drexler (1994)

42
AMD-Vol. 187, Mechanics and Materials for Electronic Packaging:

Volume 2 - Thermal and Mechanical Behavior and Modeling

ASME 1994

LOCAL DEFORMATION OF PLATED THROUGH HOLES

UNDER THERMOMECHANICAL LOADING

David T. Read and Elizabeth S. Drexler

Materials Reliability Division

Boulder Laboratories

National Institute of Standards and Technology

Boulder, Colorado

ABSTRACT

We have studied the thermomechanical deformation of plated through holes in commercial-grade printed wiring board (PWB)

made from FR-4 resin reinforced with glass cloth. We used a novel experimental technique, electron-beam moire. On cross

sections through the PWB thickness, line gratings were observed

in the scanning electron microscope (SEM). Moire patterns could be observed when the spatial frequency of the scanning electron beam matched the spatial frequency of the line grating. These

patterns were analyzed to obtain local deformation and strain data. We gradually heated the specimens up to near the melting point of their Sn-Pb 63-37 solder and observed thermomechanical

deformations. Here we report observations made at SEM

magnifications of 1 10-550X.

INTRODUCTION

Motivation: Verification of finite element analysis of electronic packaging and interconnect structures

This study is motivated by the need to improve the understanding and predictability of the reliability of electronic packaging and interconnect structures. The mechanical

sophistication of these structures and their importance to the costs, manufacturability, and reliability of electronic devices have been

described by many authors. The treatment of manufacturability and reliability of packaging and interconnect structures (Guo, et

al., 1993, Choi, et al., 1993, Lau and Erasmus, 1993) is reaching

a high level of sophistication, utilizing finite element analysis. It

has been reported that savings in cost and time-to-market have

been achieved through the use of finite element analysis of mechanical behavior to streamline and focus procedures in design, inspection, and test (Corbin, 1993).

Finite element analyses are only valuable to the extent that they are known to be accurate. Usual issues affecting their accuracy are the assumed boundary conditions, the failure modes, and the appropriateness of the material behavior models and mesh

design for the problem at hand. The use of experimental mechanics to validate finite element analyses is common for analyses of macrostructures (McNeill el al., 1885). It is expected

that microscale experimental mechanics studies will contribute

significantly to the value of finite element analyses of electronic packaging and interconnect structures, by providing guidance

regarding the assumptions needed to begin such analyses, and by

adding to the credibility of the analyses by providing verification of some of the results.

Background: Electron Beam Moire

Electron-beam moire has much in common with geometric

optical moire. A review of this classic experimental mechanics

technique is beyond the scope of this paper, excellent references are Weller (1948), Parks (1987), and Theocaris (1969). Since 1980, most of the development has involved moire interferometry, where a virtual reference grating is produced by interference of two plane beams from a coherent light source. Examples include Post (1980), McDonach, et al. (1980), Post and Wood (1989), and

Post (1991). Moire interferometry represented a major advance because the density of the specimen grating was increased by a factor of about SO, to 4 000 lines/mm. This increase improved

the sensitivity of the method and extended the applicability of the moire method to a wider range of problems (Post, 1991, and Han,

el al., 1994).

185 43
TABLE 1. HANDBOOK THERMAL EXPANSION COEFFICIENTS FOR MATERIALS OF CONSTRUCTION OF PTH

SPECIMENS.

Material Coefficient of thermal expansion, ppm/°C

SnPb eutcctic solder1 23

Cu2 17

Glass-fiber-rein forced FR-4

x and y directions'

16

Glass-fiber-reinforced FR-4

z (out-of-plane) direction 1 80

1 Minges(1989)

2 Lide (1993)

Electron-beam moire takes advantage of the higher

magnification and depth-of-focus possible with scanning elecron microscopy as compared to optical microscopy. Electron-beam

moire offers two specific advantages relative to optical: finer grating pitch, and higher magnification that does not interfere with

the fringe formation process (Kishimoto el al., 1991a and b). The

disadvantages of this new technique include: the difficulty of

electron-beam lithography, which is needed to produce precise, high-density line gratings and crossed gratings; the lack of developed techniques to record displacements in both x and y

directions from the same field (although this seems possible); the need to place the specimen within the vacuum chamber of the SEM; and the general lack of stability of the formation of the SEM image compared to optical images, because the SEM

employs electronic components where the optical systems employ

lenses and mirrors. The recent development of electron-beam moire' with high

density gratings has been described in the literature. Kishimoto

et al. (1991a and b) were the first to introduce electron-beam moiri and to demonstrate its application to study mic rode formation. In these studies, relatively coarse gratings with

pitches between 3.7 and 7.1 urn were used. We have used line gratings with a pitch of 100 nm to demonstrate the ability to produce electron-beam moire (Dally and Read, 1993), and in a study of mechanical deformation of a composite (Read and Dally, 1993, and Read and Dally, 1994).

Background: Plated through holes (PTH)

The use of PTH as a support and interconnect system for electronic components predates the beginnings of semiconductor

electronics. These material systems are described in detail in Minges (1989), and Tummala and Rymaszewski (1989). Modem

PWBs may have 18 or more layers, and may have closed and

buried vias, as well as PTH. The most popular material for commercial-grade PWB is a resin type known as FR-4, which is reinforced with glass fibers. The most common reliability problem with PTH on GFRP

(glass-fiber-reinforced plastic) PWB arises from out-of-plane thermal expansion. The volume ratio of glass fibers to resin is

chosen so that the PWB as a whole has an in-plane coefficient of

thermal expansion of about 17 ppm/ °C, matching that of Cu. This choice minimizes the thermomechanical stresses on the Cu

interconnect traces. However, the resin and the glass interact to produce an out-of-plane thermal expansion coefficient much larger than the in-plane value. Values of thermal expansion coefficients from Minges (1989) and Lide (1993) are listed in Table 1. Furthermore, the thermal-expansion coefficient of these PWBs has been reported to increase dramatically at the glass transition temperature, around 125 °C (Guo et al., 1993). The expansion of

the GFRP PWB in the through-thickness or z-direction, applies

tensile strains to the Cu barrels of the PTH. This loading is a known threat to the manufacturability and reliability of glass- reinforced FR-4 PWB with PTH (Davidson, 1991). Tensile

strains along the Cu barrels of the PTH occur every time the PWB is heated. These strains are reversed when the PWB is cooled. This strain cycling can produce fatigue cracks in the Cu, which in turn can interrupt the electrical connection along the PTH, resulting in functional failure of the device. Careful quality control of the manufacturing operations involved in producing the PTH is necessary in order to avoid reliability problems.

EXPERIMENT

Technique

Preparation of line gratings on cross sections of PWB was

accomplished using electron-beam lithography. Because of the novelty of the technique, a brief summary is given. We used a

series of SiC-coated papers with grit sizes ranging from 260 to 5 um to grind the specimen to a thickness of 3 mm or less, to produce smooth a surface containing the mid-planes of several PTH. Final polish was obtained with 3 and 1 pm natural diamond

aerosol spray. The surface of the specimen was swabbed with methanol. The specimen was cleaned in a methanol ultrasonic bath for 30 s, and, finally, the surface was scrubbed with acetone on a soft polishing cloth. Within 2 h of the final polish and

cleaning, the specimen was sputter-coated with AuPd. Two percent polymethyl methacrylate (PMMA) in chlorobenzene solution was used as a positive electron-sensitive

resist (Haller, 1968). The specimens were spin-coated with

186

44
PMMA at rates of 2000 to 3000 rpm, and baked for 90 min at 170 °C to cure the PMMA. To prevent degradation of the resist, patterns were written on the specimens within a few hours of the curing of the PMMA.

The SEM has been used to write line gratings ranging in size from 60 to 1200 u.m. We started with gratings of 512 lines, and

progressed to 1024 lines. Three different sized gratings were used

in this study—1200, 600, and 240 u.m. The line pitches range from 200 to 1000 nm. For writing the line gratings, the SEM was

operated with an accelerating voltage of 20 kV and a working

distance of 13-14 mm. The lines were exposed with beam

currents between 50 and 750 pA. The time required to write each

grating varied from 4 to 22 min.

After exposure, the specimen was developed in a 3: 1 solution of isopropanol (IPA) and methyl isobutyl ketone (MIBK) for 40

s. This was followed by a 20 s rinse in IPA and a 30 s rinse in deionized water. Finally, the specimen was sputter-coated with AuPd, to provide a thin (5 nm) conductive layer. Figure 1 is a photomicrograph of the lines written on a sample of metal. These lines have a pitch of 160 nm. We always

wrote lines parallel to the PWB surface, to enable us to measure

the z-direction (out-of-plane) deformation. The dark stripes are trenches in the PMMA, produced where the electron-beam exposure causes unlinking of the PMMA molecules, so they arc

preferentially dissolved by the IPA:MIBK solution. The brighter regions adjacent to the dark trenches are ridges. Figure 1 shows

that the line profile as imaged by the SEM is not a simple square wave. The line corners show up more intensely than the line centers or the spaces. This complex profile reappears in the moire

fringes.

FIGURE 1. SEM MICROGRAPH OF A LINE GRATING WITH A PITCH OF 0.16 Mm,

ON METAL.

To observe thermally-induced displacements, we mounted the specimen on a heating stage within the SEM, as shown in figure

2. The stage is rated for temperatures up to 1000 °C, but we have

used it only up to 180 °C. One thermocouple was mounted on

the heater chip, and a second was attached between the specimen

clamp and the specimen. We focussed the microscope on the selected line grating, at a magnification that produced moire

fringes. Because the magnification of our microscope is adjustable only in discrete steps, we were unable to produce a null

field (an exact match between the line pitch and the pitch of the rastered electron beam). We started our experiments with 3 to 10

carrier fringes present. The step wise-adjustable magnification and

the possible initial rotation of the specimen can only produce

straight, regularly spaced fringes, which may be horizontal or may

be slanted if rotation is present Depending on whether the magnification was above or below the value that would produce

null field, the fringe density increased or decreased with

extensional strain. We took photographs of the SEM display, and we also recorded the images digitally. The computer sdores the images as 480 lines of 512 8-bit pixels. The electrical power to the heater is manually controlled. We

heated the specimen to temperature, waited for equilibrium, and

recorded the moire fringe pattern. The recording of an image

required about 30 s. Two problems were discovered with the heating stage. First, the heater produced an electric field, which

caused the images to be distorted. To avoid such problems, we

used a non-inductively wound ceramic heater chip, we placed

magnetic shielding between the heater and the specimen, and we

grounded the heater circuit to the microscope chamber. The

Spring wire,

FIGURE 2.

^Anchor to stage

Retainer (washer)

^r Specimen T/C

.^CXi plate

Mu-Metal shield

Heater T/C

SCHEMATIC DRAWING OF THE

HEATING STAGE USED WITH THE

SEM.

second problem was that as the stage and specimen heat, the specimen moved relative to the position of the electron beam.. Because the moire fringe spacing would be affected if the specimen were moving during the recording of the image, we

recorded images only after making sure that the motion had

stopped, by observing an individual line of the grating at high

magnification. Changing temperature sometimes required 30 min

or more. Data reduction was accomplished by manually tracing the

fringes, to produce a list of x,y pairs for each fringe. Subsequent

calculations of displacement and strain as functions of position were automated. Spline fitting was used to interpolate from the traced points to a regular grid, and to calculate strains from

displacements. We can obtain the y-direction displacement v as a function of x and y. From these data we can calculate e^ , the normal strain in the y direction, as E^ = dv/dy . This strain is available as a function of x and y. Because we were able to measure only v, the displacement in the y-direction, we were

187

45
TABLE 2. DIMENSIONS OF PTH USED IN THIS

STUDY.

PWB thickness 1.56 mm (1/16 in)

Hole spacing, center-to-center 2.54 mm (1/10 in)

Diameter, drilled hole in GFRP 1.11 mm (0.044 in)

Cu thickness, in PTH 45 fim (0.002 in)

FIGURE 3. SEM MICROGRAPH OF A CROSSSECTION PTH SPECIMEN.

Line grating

eei ZA

SnPb solder Plated Cu Fiberglass

FIGURE 4. SCHEMATIC DIAGRAM OF THE PTH

USED IN THIS STUDY.

unable to properly calculate shear strain, since the engineering

shear strain y^ is given as y = dv/dx + du/dy . Similarly, the

rotation u) is given by (0 = dv/dx - du/dy . However, these equations suggest a way to estimate the shear strain. If the —

direction displacement u is either constant or small, the shear

strain can be estimated as Y^ = dv/drt . On our moire fringe images, slanted fringes correspond to significant values of dv/dx. We try to avoid slanted fringes in our initial conditions. When

slanted fringes are present, we know that either shear strain or

rotation has occured. If we can eliminate the likelihood of

rotation, or show that u is small or constant, then we can estimate

the shear strain.

Plated-Through-Hole Specimens

We studied cross sections of PTH extracted from an FR-4

commercial grade PWB, that had been soldered with eutectic SnPb. Our PWB had 4 layers of copper conductors, one on each

surface and 2 within the PWB. Table 2 gives the dimensions of

the PWB and the PTH.

Figure 3 shows a photograph of a typical cross-section. The

printed circuit board with its reinforcing glass fibers is visible between the through holes. The narrow rim (-0.05 mm thick) at the edges of the through holes is the Cu plating. The lighter colored fill is the SnPb solder, and the darker oblongs within the PTH are Cu pins. The light squares are line gratings.

Figure 4 shows the PTH schematically. A line grating placed

at the comer of the PTH is indicated.

RESULTS AND DISCUSSION

This paper presents in detail the results of three experiments on three different specimens from the same PWB. Table 3 lists the basic conditions of these three experiments. In each of these

cases, we present moire fringe images and data from one grating. Additional gratings on these specimens and other specimens from

this PWB were also studied. Those additional results contributed

to our understanding and interpretation of the behavior of these PTH.

Extensive shear

In two experiments, we observed what appears to be extensive shear deformation allowing accommodation of the high oui-of- plane thermal expansion of the GFRP with the lower expansion of the PTH by extensive shear deformation. Both examples were

seen at PTH comers. The more striking example, from specimen

number 1 is shown in figures 5a-c. Figure 5a shows

schematically the location of the line grating. Figure 5b shows

the condition at 35 °C, before heating. Figure 5c shows the

condition after heating to 136 °C.

188

46
TABLE 3. LINE GRATINGS USED IN THIS STUDY.

Experi- ment

Purpose Location Magnification Field Width, um

Line Pitch, um

Number of

lines

PTH 1 Extensive shear comer 250 405 0.40 1023 PTH2 Extensive shear comer 220 455 0.45 1023 PTH 3 Local shear comer 550 180 0.35 511

Moire

Fringes

Crack

FIGURE 5. PTH 1, NEAR CORNER, SHOWING

ELECTRON-BEAM MOIRE FRINGE

PATTERNS. (A) SCHEMATIC.

(B) BEFORE HEATING . (C) AFTER

HEATING TO 136 °C.

In the SnPb and Cu, there are about 3 fringes in figure 5b, and about 5 in figure 5c. If we consider 20 x 10"* / °C as a rough average thermal-expansion coefficient in the Cu and Sn, we

calculate a thermal strain of about 2 * 10'\ Since this grating has 1023 lines, this strain should add 2 fringes, as observed in figure

5c. More detailed measurements of thermal strains, discussed below, will show that we can indeed measure thermal strains in SnPb and Cu using the electron-beam-moire technique, but that the agreement in this case between the observation and the

coefficient of free thermal expansion is only coincidental. The

18947
TABLE 4. LOCATIONS OVER WHICH THERMOMECHANICAL STRAINS WERE AVERAGED FOR FIGURE 6c.

Specimen Location Material Distance from: XI,

u.m

X2,

urn

Yl, Y2,

2 PWB

comer GFRP Cu 25 200 25 100

SnPb Cu 20 25 100

In figure 5c, note the many fringes at a steep angle to the horizontal. These tilted fringes are suggestive of shear strain. Because we have measured only the y-direction deformation in this experiment, we cannot distinguish, on the basis of the local fringe angles alone, between shear and rotation, as discussed above. But in these patterns the fringes bend sharply at the

interface between the Cu and the GFRP, so rigid body rotation can be excluded. The bent fringes indicate a shear or a rotation of the fiberglass relative to the metal parts of the PTH. We favor shear over rotation because an extensive region of rotation would

require impossibly large displacements within the body of the PWB. The fringes in the GFRP in figure 5c indicate mat, at this PTH, the out-of-plane displacement of the PWB surface increased

rapidly with distance from the PTH.

Based on the free thermal-expansion coefficients of GFRP

and of SnPb solder, we would expect a strain difference, from

solder to fiberglass, of 0.0058 between figure 5b and figure Sc, at 35 and 136 °C, respectively. Over the distance from the PWB

centerline to the surface, this would produce a displacement

difference of 4.6 \xm. Because the fringe pitch in this grating was

0.40 (am, such a displacement would produce a total climb of

1 1 1/2 fringes from SnPb to GFRP. The strain difference between SnPb and GFRP would also produce a difference in fringe density of 6 fringes over the frame height Figures 5b and 5c clearly show fringe climb of at least 6 fringes across the frame. This is consistent with expectation, because the remaining climb could occur outside the region shown in figure 5, further away from the PTH. At first glance the density difference appears large also, but

closer examination shows that the density in the vertical direction

is about 7 fringes per frame height in the center of the frame, compared to about 5 in the SnPb. This indicates that the GFRP

next to the PTH is not expanding freely, but is partially restrained by the PTH structure. The striking deformation portrayed in figures 5b and 5c is consistent with expected behavior for PTH. Figures 5a-c provide one unexpected finding, the highly localized strain in the GFRP,

at the regions where the fringes curve. These localized strains occurred in the resin-rich regions of the PWB. Although

generally similar deformation to that shown in figures 5a-c was

observed on other PTH, the deformation gradient near the PTH

was much less intense in other specimens. This is discussed

further below.

Figures 6a-e display the use of moire fringe data to obtain thermal strains. Figures 6 are from specimen 2 near the PTH

comer. Figure 6a indicates the locations of the PTH components

relative to the line grating. Figures 6b-6d show the moire fringe patterns at 22, 78, and 125 °C. The thermal strains are plotted against temperature in figure 6e. In figure 6e, we show handbook

values for thermal strain for GFRP calculated for free expansion. These "handbook" strains are not expected to actually predict the behavior of the PTH structure, but they provide a baseline for comparison. Table 4 gives the locations of the specific regions over which the strains were averaged.

The behavior at the PTH comer shown in figures 6 was also seen in other specimens. The data indicate a low rate of expansion near room temperature, followed by an increasing rate of expansion as the temperature rises above about 75 °C. The big

drop in the strain in the GFRP in figure 6 at -120 °C was

accompanied by a local failure of the GFRP, indicated by a complex fringe pattern. The thermal expansion continued after this disturbance. As the temperature was increased further, the expansion took on its expected positive value. The deviation of

these strains from handbook values are indicative of the thermomechanical interaction among the different materials in this composite structure. Precedent exists for the highly non-linear, and somewhat

counter-intuitive, behavior indicated by the present results. Hall (1984), in a well-known experiment on the thermomechanical

behavior of structures including solder and PWBs, reported nonlinear deformation with temperature, hysteresis, and, over a

small range, deformation of the opposite sign than predicted by a

linear bimaterial model. From the present results we would expect that much greater damage at the comers of PTH structures should occur when they are cycled to temperatures above 75 °C than when temperatures

are restricted to 75 °C or less. The one observation we have of

the behavior in the middle of the PWB indicates that at this location, thermal strains are high from the beginning.

Shear near the fiberglass-SnPb-Cu interface Specimen 3 provided moire images that displayed shear

strain near the fiberglass-SnPb-Cu interface, figures 7a-7c. Figure 7a is the schematic indicating the location relative to a PTH..

Figure 7b shows a typical fringe pattern taken near a PTH comer

cooled to 40 °C after the specimen had been heated to 143 °C. This image shows shear deformation in the SnPb of the PTH. As

noted above, shear strain can only be estimated from our moire

fringe images. In this image, local rotation can be ruled out, so

the slanted fringes are attributed to shear. Figure 7c shows the dependence of the shear deformation on distance into the SnPb

from the plated Cu. Some shear deformation was present near the

190 48
7—7

7—7—TT

Moire

Fringes

/ / / / / —£—t—./ / /

i Potting / / /—? 7—/ / ,-- .:tDtSMJLMT AU£ INTG WBBEU PHOT 1 i^-: '."- • ^H^S'WI ^s**s>s»-.-.» v.. ^^^^ii

!'*^°8HI

-iftj*--^., "1s»*!5'\i359B(

^ . -v;-*--:-.v ;

', .£- •-, **'^P(

-?^"JiA^.f_ ' "jwp'jmi'j"'

'

S|*?*- t^ssa**.,, . "^"IW||^^1 ^Ksi'•'v-,^*'"" ?** Jfcfc 'TTTtiBfrM^ 1 ^^^f^^fr^jjfljj^ iH ^te^^wWS&a^^^MIWHWtfc^.HWW> '

'

. . IjgS?**"**. :

'^t'.^Wfi^h """"" * •"'<!* BfciL

v -^* .._ _ ^^F^*wtiiiitir&,. F4 L01

» *tt»iS

^*jj§s®»- H8^^fe6-> t . """

z

<

cr

</> <

tr

0.005

0.004

0.003

0.002

0.001

0.000

-0.001

PTH Specimen No. 2, Comer Pattern

i i '—'). -- SnPb, measured

i i

-*- GFRP, measured /

GFRP, handbook/ / > i

t / / \ 4

. / J Mr .

1 1 1 i i 25 50 75 100 125 150 TEMPERATURE, 'C

FIGURE 6. PTH 2, NEAR CORNER, SHOWING

ELECTRON-BEAM MOIRE FRINGE

PATTERNS. (A) SCHEMATIC.

(B) BEFORE HEATING . (C) AFTER

HEATING TO 78°C. ( D) 125°C.

(E) THERMAL STRAINS, PLOTTED

AGAINST TEMPERATURE.

191

49
Molr6

Fringes

0.01

>

to

-0.01 -

-0.02 -

-0.03

1 n r— GFRP ; Cu

' 1

. SnPb

1 \ /

i

i

i

i

i " 25 *C, before heating * 40 *C, after heating

to 143 mc ;

i

1 I-! I

i

1

40 80 120 160 X POSITION, pm

200

a, MOJNtI«*fWE "Z*0K

ggSr-^^Jbii

TM

-M

- ''**"*: 5" ^^>j - © k u

"* - -<--.-»k

s

5-1 '£*£* r' *

J^m

- 1—->-_.. •_._ . m*met* *[JSSJJ'" ^J «uNi .*: »^jbp» <Mjpiii mSm-i£**

, 10 urn 1

FIGURE 7. ELECTRON-BEAM MOIRE FRINGE

PATTERN ON PTH 3, NEAR CORNER.

(A) SCHEMATIC. (B) AFTER HEATING

TO 143 °C, AND COOLING TO 40 °C. (C) APPROXIMATE SHEAR STRAIN

PLOTTED AGAINST POSITION.

PTH comer when the specimen was first observed before heating, as indicated in Figure 7c. We atttribute this deformation to the recovery of residual deformations introduced during the curing of

the PMMA coating on the specimen. We have observed other

instances of deformation present in PTH specimens upon initial examination. We interpret this deformation as follows. The

specimens are baked at 1 SO °C to harden the PMMA that is used

as the electron resist in writing the line gratings. This heating

introduces thermomechanical deformations, some portion ofwhich

remain as residual deformation after the specimen is cooled. This

residual deformation recovers gradually, over a period of days or

longer. Over the time between the writing of the grating and

initial observation, this recovery process progressed. The

deformation indicated by the initial fringes is part of this recovering residual deformation. This indicates that the PTH

structures are somewhat fragile as regards microdeformations. These initial shear deformations were not present in every

location imaged, but they were seen more than once. The present study is not intended to provide accurate statistics, but we have

probably looked at a total of 20 locations on 5 PTH specimens. Shears as shown in figures 7a-7c were seen 2 or 3 times. SUMMARY CONCLUSIONS

(1) Line gratings with pitches down to 160 nm can be

fabricated by electron-beam lithography on cross sections ofPTH,

and can be used to form electron-beam-moire patterns at magnifications of 1 10 to 5S0X. These patterns carry information about local deformations in the surface. (2) By heating such specimens in the SEM and recording the changing moire patterns, thermomechanical deformations can be

measured. Even though we could only record digitally scans of 500 lines, we obtained better results with 1023-line gratings than we did with SI 1-line gratings. The phenomenon of fringes of

division, which is related to fringe multiplication, allows us to

utilize the full grating density. These moire patterns were formed on unstressed specimens and on specimens heated up to ISO *C. (3) The moire fringe images obtained allowed us to make

separate measurements of local thermomechanical behaviors in the

192

50
three materials within our PTH specimens: the PWB, the Cu

plating, and the SnPb solder. We observed several thermomechanical deformation phenomena: shear that appeared

both before the specimen was heated and during heating;

differences between the strains in GFRP and nearby SnPb solder, with low deformation on initial heating followed by an increasing deformation rate with temperature above 75 "C at the PTH

comers; and extensive shear at the top of PTH to accommodate

the greater expansion of the GFRP.

(4) We observed considerable variability in the behaviors of our PTH specimens—variability from location to location on

individual specimens, and variability from specimen to specimen. Because the PTH specimens used here were commercial-grade

PWB made with SnPb eutectic solder and GFRP, the variability

is understandable. We had no way of testing our PTH to failure. However, some of these variable behaviors appeared to be

possible precursors to failure of the PTH. These include local shear and slip at SnPb-Cu interfaces, and extensive shear in the GFRP near PTH comers. We don't list fiberglass breakup as a

variable behavior because it seemed to occur in at least one

location in every test. The fact that slip and shear were variable behaviors indicates

the possibility that they can be avoided. The local shear and slip

at the Cu-SnPb interface seem related to the solderability of the

plating; this is a well-known issue in PTH reliability. The

extensive shear deformation of the GFRP near the PTH is related

to the documented difference in out-of-plane thermal expansion of

the GFRP relative to Cu and SnPb solder. The surprise was that

this deformation does not always manifest itself right up to the PTH barrel. Perhaps, through the use of thick solder fillets or

extra-well-rein forced GFRP, the PTH barrels can be protected from the through-thickness, thermally-induced strains. ACKNOWLEDGEMENTS

The assistance of J. W. Dally in revising this paper is appreciated.

REFERENCES

Choi, H.-C, Guo, Y, LaFontaine, W., and Lim, C.K., 1993,

"Solder Ball Connect (SBC) Assemblies under Thermal Loading:

II. Strain Analysis Via Image Processing, and Reliability Considerations," IBM Journal ofResearch andDevelopment, Vol.

37, pp. 649-659.

Corbin, J.S., 1993, "Finite Element Analysis for Solder Ball Connect (SBC) Structural Design Optimization," IBM Journal of

Research and Development, Vol. 37, pp. 585-596.

Dally, J.W., and Read, D.T., 1993, "Electron Beam Moire,"

Experimental Mechanics, Vol. 33, pp. 270-277.

Davidson, D.L., 1991, "Stereoimaging Determination of

Strains in Surface Mounted Components and Plated Through

Holes Resulting from Thermal Cycling," Materials Research

Society Symposium Proceedings, Vol. 226, Mechanical Behavior of Materials and Structures in Microelectronics, E. Suhir, R.C. Cammarata, D.D.L. Chung, and M. Jono, Eds, Materials Research

Society, Pittsburgh, pp. 357-361.

Guo, Y., Lim, C.K., Chen, W.T., and Woychik, C.G., 1993,

"Solder Ball Connect (SBC) Assemblies under Thermal Loading:

I. Deformation Measurement Via Moire Interferometry, and Its Interpretation," IBM Journal of Research and Development, Vol.

37, pp. 635-648.

Hall, P.M., 1984, "Forces, Moments, and Displacements

During Thermal Chamber Cycling of Leadless Ceramic Chip

Carriers Soldered to Printed Boards," IEEE Transactions on

Components, Hybrids, and Manufacturing Technology, Vol. CHMT-7, pp. 314-327.

Haller, I., Hatzakis, M. and Srinivasan, R., 1968, "High

Resolution Positive Resists for Electron-Beam Exposure," IBM

Journal Research and Development, Vol. 12, pp. 251-256.

Han, B., Guo, Y., and Lim, C.K., 1994, "Applications of Moire and Microscopic Moire Interferometry to Electronic Packaging Product Development," Conference Proceedings of the 4th Annual IEEE Dual-Use Technologies and Application Conference, Rome, NY (in press). Kfouri, A.P., Wong, H.D., and Miller, K.J., 1992, "ElasticPlastic Finite Element Analyses of Cracked Notches in Plates under Mixed-Mode Loading," Fatigue andFracture ofEngineering

Materials and Structures, Vol. 15, pp. 743-762.

Kishimoto, S., M. Egashira, Shinya, N. and Carolan, R.A., 1991, "Local Micro-Deformation Analysis by Means of Microgrid and Electron Beam Moir£ Fringe Method," Proceedings of the Sixth International Conference on Mechanical Behavior of

Materials, Vol. 4, M. Jono and T. Inoue, Eds., Kyoto, Japan, pp. 661-666.

Kishimoto, S., Egashira, M. and Shinya, 1991, "Measurement

of Grain Boundary Sliding and Observation of Microgrids for High Temperature Use," Journal of the Society for Materials Science Japan, Vol. 40, pp. 637-64 1 (in Japanese). Lau, J., and Erasmus, S., 1993, "Review of Packaging Methods to Complement IC Performance," Electronic Packaging and Production, Vol. 33, No. 6, pp. 50-56.

Lide, D.R., Ed., 1993, Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, pp. 12-134. McDonach, A., McKelvie, J., and Walker, CA., 1 980, "Stress Analysis of Fibrous Composites Using Moire Interferometry," Optics and Laser Engineering, Vol. 1, pp. 85-105.

McNeill, S. R. , Sutton, M. A., and Turner, J. L., 1985,

"Stress Analysis of a Reversed Dish Head of a Cylindrical Pressure Vessel, International Journal of Pressure Vessels and

Piping, Vol. 18, pp. 81-90. Minges, ML., Technical Chairman, 1989, Electronic Materials Handbook, Vol. 1: Packaging, ASM International, Materials Park, OH.

Parks, V.J., 1987, "Geometric Moire," Handbook on

Experimental Mechanics, A.S. Kobayashi, Ed., Prentice-Hall, Englcwood Cliffs, N.J., pp. 282-313.

Post, D., 1980, "Optical Interference for Deformation Measurements—Classical, Holographic and Moire Interferometry," Mechanics of Nondestructive Testing, W.W. Stinchcomb, Ed., Plenum Press, New York, pp. 1-53.

Post, D., 1991, "Moire Interferometry: Advances and

Applications," Experimental Mechanics, Vol. 31, pp. 276-280.

193

51
Post, D. and Wood, J. D., 1989, "Determination of Thermal

Strains by Moiri Interferometry," Experimental Mechanics, Vol.

29, pp. 318-322.

Read, D.T., and Dally, J.W., 1993, "Local Strain Measurement by Electron Beam Moire," in Advances in Electronic Packaging 1993, EEP-Vol. 4-1, Proceedings of the 1993 A SMEInternationalElectronics Packaging Conference, PA.

Engel and W.T. Chen, Eds., ASME, New York, pp. 163-169. Read, D.T., and Dally, J.W., 1994, "Electron-Beam Moire

Study of Deformation of a GFRP Composite," Journal of A pplied

Mechanics, Vol. 61, pp. 402-409..

Theocaris, P.S., 1969, Moiri Fringes in Strain Analysis,

Pergamon Press, Elmsford, N.Y. Tummala, R.R., and Rymaszewslci, E.J., Eds., 1989,

Microelectronics Packaging Handbook, Van Nostrand Reinhold,

New York, NY, 1194p.

Weller, R. and Shepard, B.M., 1948, "Displacement Measurement by Mechanical Interferometry," Proceedings of the Society for Experimental Stress Analysis, Vol. 6, pp. 35-38.

194

52
A5

Thermomechanical Behavior ofa High Density Polymer Overlay MCM

Interconnect Structure: Experiments andAnalysis

by Read, et al. (1995J

53
EEP-Vol. 11/MD-Vol. 64, Application of Fracture Mecha . m

Electronic Packaging and Materials

ASME 1995

THERMOMECHANICAL BEHAVIOR OF A HIGH DENSITY POLYMER OVERLAY

MCM INTERCONNECT STRUCTURE: EXPERIMENTS AND ANALYSIS1

D. Read and E. Drexler National Institute of Standards and Technology

U. S. Dept. of Commerce, Boulder Laboratories

Boulder, Colorado

E. Bernard

General Electric Corporate Research and

Development

Schenectady, New York

I. Grosse, J. Benoit, and J. DiTomasso

Department of Mechanical Engineering

University of Massachusetts

Amherst, Massachusetts

D. Holzhauer, P. Rocci, and M. Stoklosa

Rome Laboratories/ERDS

Griffis Air Force Base, New York

ABSTRACT

Thcrmomechanical strains in a high density polymer overlay

multichip module (MCM) interconnect structure have been studied experimentally with electron-beam moire and numerically using

finite element analysis (FEA). The interconnect structure includes micron-thickness copper traces and laminated dielectric layers with a thermoplastic adhesive to bond the first layer and a polyimide-epoxy blend for the other layers. Copper vias connect

the layers. On heating from ambient to ISO C, the experimentally measured out-of-plane strains inside the vias approached 1 percent, and the strain in the polyimide away from vias reached about 1.5 percent. A two-dimensional plane stress analysts was used for this comparison. The finite element model utilized predetermined

temperature-dependent material properties and nonlinear

elastoplastic material behavior. Comparison of the analysis and

the experiment was carried out using total out-of-plane strain, which includes both a free thermal expansion component and a

structural, or thcrmomechanical component Good quantitative agreement was found in some regions of the interconnect

structure, while in other regions the measured strain values were

a factor of two or higher than predicted by finite element analysis. Possible sources for the large differences are discussed.

INTRODUCTION

Motivation: Verification of finite element analysis of electronic packaging and interconnect structures This study is motivated by the need to improve the understanding and predictability of the reliability of electronic packaging and interconnect structures. The mechanical

'Contribution of the U.S. National Institute of Standards and

Technology, not subject to copyright in the U. S. A.

sophistication of these structures and their importance to the costs, manufacturability, and reliability of electronic devices have been

widely documented, e.g., in the National Technology Roadmap for Semiconductors ( 1994). The treatment of manufacturability and

reliability of packaging and interconnect structures (Guo el al., 1993, Choi, el al., 1993, Lau and Erasmus, 1993) is reaching a high level of sophistication, utilizing finite element analysis. It has been reported that savings in cost and time-to-market have

been achieved through the use of finite element analysis of

mechanical behavior to streamline and focus procedures in design,

inspection, and test (Corbin, 1993).

Finite element analyses are only valuable to the extent that they

are known to be accurate. Usual issues affecting their accuracy

are the assumed boundary conditions, the failure modes, and the appropriateness of the material behavior models and mesh design

for the problem at hand. The use of experimental mechanics to validate finite element analyses is common for analyses of

macrostructures (McNeill el al., 1985). It is expected that microscalc experimental mechanics studies will contribute

significantly to the value of finite element analyses of electronic packaging and interconnect structures. Such studies provide

guidance regarding the assumptions needed to begin such

analyses, and add to the credibility of the analyses by providing

verification of some of the results. An important difference between macroscale experimental mechanics studies and the present study is that in most macroscale

studies the applied stress has been produced by the application of

force or pressure. In electronic interconnect structures, the

significant stresses are thcrmomechanical. These stresses arise from the presence of materials with different thermal expansion

coefficients in structures that are subjected to temperature changes. The techniques used here have been specially adapted

to the observation of thermomechanical strains.

251

54
Background: Electron Beam Moire

Electron-beam moire has much in common with geometric

optical moire. A review of this classic experimental mechanics

technique is beyond the scope of this paper; excellent references

are Weller (1948). Parks (1987), and Theocaris (1969). Since

1 980, most of the development has involved moire interferometry, where a virtual reference grating is produced by interference of two plane beams from a coherent light source. Examples include

Post (1980), McDonach, et o/.(1980X Post and Wood (1989), and

Post (1991). Moire interferometry represented a major advance

because the density of the specimen grating was increased by a

factor of about SO, to 4 000 lines/mm. This increase improved

the sensitivity of the method and extended the applicability of the moire method to a wider range of problems (Post, 1991, and Han,

et al., 1994). Electron-beam moire takes advantage of the higher

magnification and depth-of-focus possible with scanning electron microscopy (SEM) as compared to optical microscopy. Electron- beam moire offers two specific advantages relative to optical: a wider range of grating pitch, and higher magnification that does

not interfere with the fringe formation process (Kishimoto et al., 1991a and b). The disadvantages of this new technique include:

the difficulty of electron-beam lithography, which is needed to produce precise, high-density line gratings and crossed gratings;

the lack of developed techniques to record displacements in both

x and y directions from the same field (although this seems

possible); the need to place the specimen within the vacuum

chamber of the SEM; and the general lower stability of the SEM

image as compared to optical images, because the SEM employs

electronic components where the optical systems employ lenses and mirrors. Kishimoto et al. (1991a and b) were the first to introduce electron-beam moire

1 and to demonstrate its application to study microdeformation. In these studies, relatively coarse gratings with

pitches between 3.7 and 7.1 |im were used. We have used line gratings with a pitch of 100 nm to demonstrate the ability to produce electron-beam moire (Dally and Read, 1993), and in a

study of mechanical deformation of a composite (Read and Dally,

1993, and Read and Dally, 1994).

SPECIMENS

The structure evaluated in this study was designed to be an economical, high-performance packaging and interconnect

structure for multichip modules. The structure is designated as high density interconnect (HDI), and it has several distinguishing

features (Fillion et al, 1994). A schematic diagram is shown in Figure 1. Pockets are milled in the alumina substrate to accommodate the chips. An initial sputtered TiAl metallization layer forms the substrate input-output connections. The first overlay layer is polyimide, bonded to the underlying metallization layer with a thermoplastic resin. After the formation of via holes

in the polyimide, a TiCuTi metallization layer is added. This tri- metal layer forms connections to the underlying metallization by

covering the via holes and is patterned to provide in-layer connections. Subsequent layers repeat this design. The subsequent

dielectric overlays are also polyimide, bonded to their undcrlaycrs

by a polyimide/epoxy thermoset adhesive. The subsequent metal

layers are TiCuTi. The nominal layer thicknesses are given in Table 1.

Polyimide

Passivation

Layer

Polyimide

Layers Metallization

- ir

\n^-Lrn/ -

1—"\r~\r

-u—\r

\m\ \V//////2b\\ mm mm

i

,

.

i T

Alumina

1 \ k

Substrate

Polyimide

Overlay

Ole

Pad

Mounted

Die

Specimen versus Device-in-Service Comparisons The purpose of this paper is to compare finite element analysis and high resolution experimental mechanics results for a specific case relevant to advanced electronic interconnect structures. Because the experimental mechanics technique requires access to a cross section, the behavior examined here is not identical to the behavior in a working device with its structure intact However,

both the analysis and the experiment can treat the cross-sectioned specimen. In this way the analysis can be verified or adjusted if need be. The analysis can then be recast to eliminate the crosssection surface and thus treat the actual structure as it exists in the

application. During the course of this study, certain observations were made which revealed additional issues regarding preparedspecimen versus intact-device comparisons. These observations and issues are discussed below.

FIGURE 1. HIGH DENSITY POLYMER OVERLAY

MULTICHIP MODULE INTERCONNECT STRUCTURE

STUDIED HERE

EXPERIMENT

Specimen preparation

The first step in the specimen preparation was to produce a very flat cross-section. It was anticipated from studies of other

similar structures that the highest deformations would be

perpendicular to the plane of lamination of the structure, that is, in the global z direction. Accordingly, the specimen device was

sectioned perpendicular to the substrate. The section was potted

in epoxy and prepared using metallographic-style procedures with extremely careful handling. At the end of the specimen

preparation procedure, the epoxy was removed from 1

252

55
TABLE 1. NOMINAL THICKNESSES OF THE

LAYERS IN THE HDI STRUCTURE TESTED

HERE.

Layer Thickness, um

Substrate

metallization (Al)

4

Interlayer adhesives 11

Polyimide 21

Upper-layer

metallization: TiCu

Ti

0.1 -0.15

4

0.1 -0.15

or more sides of the specimen, so that neither specimen was

completely encased in epoxy. We used a series of SiC-coated

papers with grit sizes ranging from 260 to 5 \im to grind the specimen to a thickness of 3 mm or less to produce a smooth

surface with vias visible. Final polish was obtained with 3- and

1 -\xm natural diamond aerosol spray. The surface of the specimen was swabbed with methanol. The specimen was cleaned in a

methanol ultrasonic bath for 30 s, and, finally, the surface was

scrubbed with acetone on soft sterile cotton. Within 2 h of the

final polish and cleaning, the specimen was sputter-coated with AuPd.

Preparation of line gratings on cross sections of HDI was

accomplished using electron-beam lithography. Because of the

novelty of the technique, a brief summary is given. Two percent

polymethyl mcthacrylate (PMMA) in chlorobenzene solution was

used as a positive electron-sensitive resist (Haller, 1968). The

specimens were spin-coated with PMMA at 2000 rpm and baked

for 60 min at 170 °C to cure the PMMA. The final thickness of

the PMMA was 150 nm or less. To prevent degradation of the

resist, line gratings were written on the specimens within a few

hours of the curing of the PMMA. After exposure the specimen was developed in a 3:1 solution of isopropanol (IPA) and methyl

isobutyl ketone (MIBK) for 40 s. This was followed by a 20 s

rinse in IPA and a 30 s rinse in deionized water. Finally, the specimen was sputter-coated with AuPd, to provide a thin (5 nm)

conductive layer. The SEM has been used to write line gratings ranging in size from 60 to 1200 (am. Figure 2 is a photomicrograph of lines

written on a sample of silicon. These lines have a pitch of 160

nm. The dark stripes are trenches in the PMMA, produced where

the electron-beam exposure causes unlinking of the PMMA

molecules, so they are preferentially dissolved by the developing

solution. The brighter regions adjacent to the dark trenches are

ridges. Figure 2 shows that the line profile as imaged by the SEM is not a simple square wave. The line comers show up

more intensely than the line centers or the spaces. This complex

profile reappears in the moire fringes.

FIGURE 2. SEM MICROGRAPH OF A LINE GRATING

WITH A PITCH OF 160 NM, ON SILICON.

In this study we used gratings of 512 lines with pitches of 175 and 350 nm. We always wrote lines parallel to the HDI surface

to enable us to measure the z-direction (out-of-plane) deformation. The two directions in the cross-section plane are x and z. The

time required to write each grating varied from 4 to 22 min. The

parameters for these line gratings are listed in Table 2. Specimen HDI 1 has one via starting on the substrate, and specimen HDI 2 has two vias on higher layers of the structure. Figures 3 and 4 show the configuration of the regions studied.

Recording of Moire Fringe Patterns To observe thermally-induced displacements, we mounted the specimen on a heating stage within the SEM, as shown in Figure

5. The stage is rated for temperatures up to 1000 "C, but we

have used it only up to 180 °C. The stage and heater were

carefully grounded to avoid distortion of the SEM image. One

thermocouple was mounted on the heater chip, and a second was

attached between the specimen clamp and the specimen. Wc

focussed the microscope on the selected line grating at a magnification that produced moire fringes. Because the magnification of our microscope is adjustable only in discrete

steps, we were unable to produce a null field (an exact match

between the line pitch and the pitch of the rastered electron beam). We started our experiments with about 3 carrier fringes present Figures 6 and 7 show the initial moire fringe patterns. For the specimens in this paper, thermal expansion corresponded

to increased fringe density. We took photographs of the SEM

display, and we also recorded the images digitally. The computer

stores the images as 480 lines of 512 8-bit pixels. The electrical power to the heater was manually controlled. We

heated the specimen to temperature, waited for equilibrium, and

recorded the moire fringe pattern. The recording of an image

required about 30 s. Because the moire fringe spacing would be

affected if the specimen were moving during the recording of the image, we recorded images only after making sure that the motion

had stopped by observing an individual line of the grating at high

magnification. Reaching equilibrium sometimes required 30

minutes or more.

253

56
BLE 2. EXPERIMENTAL CONDITIONS.

Specimen HDI 1 HDI 2

Magnification 1100 550

Grating lines in frame

4S0 480

Grating pitch, nm 175 350

Temperatures

studied, C

23.51,87,

122. 151 22.41, 70.98, 123, 144 Maximum

temperature change, C

128 122

Vias in frame 1 2

Structure continues

PotytnMe

PolylmkJe-epoxy Cu

Potylmlde

Thermoplastic resin AiSDcon

GURE 3. TRACING OF VIA ON SPECIMEN HDI 1 HOWING SIZE SCALE, STRUCTURAL FEATURES*

MD PATHS AND LOCATIONS FOR STRAIN RESULT

-OTS.

FIGURE 4. HIGH-CONTRAST RENDERING OF SEM

MICROGRAPH OF VIA ON SPECIMEN HDI 2. SHOWING

SIZE SCALE, STRUCTURAL FEATURES, AND PATHS

AND LOCATIONS FOR STRAIN RESULT PLOTS.

Spring wire, Anchor to stag©

Retainer (washer)

Specimen T/C

•I^Cu plate

Mu-Metal shield

_ Heater T/C

FIGURE 5. SCHEMATIC DRAWING OF THE HEATING

STAGE USED WITH THE SEM.

la Reduction

)ata reduction was begun by manually tracing the fringes to duce a list of (x, z) pairs giving the locus of each fringe. >sequent calculations of displacement and strain as functions of

ition were automated. Spline fitting was used to interpolate ge numbers from the traced points to a regular grid and to :ulate strains from displacements. At each temperature we

ained the z-direction displacement w as a function of x and z

hin the field of observation. From these data we calculated

the normal strain in the z direction, as e^ = dw/dz . This

.in is available as a function of x and z. Obtaining displacement information between moire fringes

uires either some way to measure partial fringes or

interpolation. Partial fringes could not be measured here, so

interpolation was used. Fractional fringe number was interpolated from about 10 actual fringes in the frame at the highest strains to a total of 25 positions. The strain was tabulated at the same number of positions in the X-direction. The results would not have changed significantly had a different level of detail been

chosen. Therefore, the experimental results consisted of a set of 625 total z-direction strain values at each temperature. The

starting temperature, 22 or 23 C, was considered to be a zerostrain temperature, so all strains reported here are the difference between the strain at temperature and the strain at room

temperature.

254

57
FIGURE 6. MOIRE FRINGE PATTERN OF VIA HDI 1. INITIAL CONDITION AT 24 *C, BEFORE HEATING. THE

VIA IS SHOWN RIGHT-SIDE-UP.

FIGURE 7. MOIRE FRINGE PATTERN OF VIA HDI 2. INITIAL CONDITION AT 22 °C. BEFORE HEATING.

MODELING

Two-dimensional Plane Stress Finite Element Model of HDI Via A two-dimensional plane stress Gnite element model of the

tested via structure was developed to compare with the axial strain results derived from the electron beam moire data. The sectioned or cut surface of the via structure on which in-plane displacements were measured is a free surface. Therefore near-plane-stress conditions exist on the cut surface. The finite element model geometry was constructed to match

as closely as possible to specimen HDI 1. Although the via in specimen HDI 1 appears slightly asymmetric about its center.

Constrained

InX-dlrectlon

Symmetry

boundary

condition

FIGURE 8. VIA AS MODELED BY FINITE ELEMENT

ANALYSIS, SHOWING PATHS FOR STRAIN RESULT

PLOTS.

symmetry was assumed through the application of symmetry

boundary conditions at the left side of the Gnite clement model of

the via as shown in Figure 8. The right side of the via was

constrained to have zero displacement in the x-direction. This boundary condition is consistent with the fact that the HDI layer

is in reality attached to a rigid ceramic substrate with a low

thermal expansion coefficient which constrains the motion of this surface. The mesh consisted of mainly eight-noded, quadratic

quadrilateral isoparametric elements with some transition six- noded quadratic triangular elements. The copper barrel (the nearvertical side wall of the via) where yielding was expected was

modeled by only undistorted eight-noded quadrilateral elements. The model consists of approximately 1000 elements and 6000

total degrees of freedom. A mesh convergence study indicated convergence in the total strain range in the copper barrel with this mesh which consists of four elements through the thickness of the copper barrel. Temperature-dependent, nonlinear elastoplastic material properties were employed for the copper and polymers. The same

set of property values documented by Prabhu et at. (199S) was

used here, except that the copper properties were provided

separately (Johnson, 1995). The titanium passivation layer in the

trilayer metallization was assumed not to affect the mechanical

properties. The basic properties used are listed in Table 3. Additional details were given by Prabhu et aL (199S).

Perfect adhesion was assumed at all material interfaces. Note

that orthotropic coefficient of thermal expansion (CTE) properties were used to model the polymer materials. However, since no

orthotropic material property data could be found for the various modulus of elasticity and Poisson's ratio for the copper and

polymers, isotropic conditions were assumed for these properties. However, the values used were "thin-film" in-plane values. This

leads to the possibility oferrors introduced due to incorrect values

for these properties in the out-of-plane direction.

255

58
TABLE 3. MATERIAL PROPERTIES USED IN ANALYSIS OF HDI STRUCTURE.

Material Young's

Modulus,

GPa

Coefficient of

thermal expansion,

10"* /C

In-plane Outof- plane

Alumina 275 7.0 7.0

Silicon 190 2.5 2.5

Copper 43 17.0 17.0

Thermoplastic

resin At23C

At 100 C

4.0

2.9

56.0 56.0

29.0

29.0

Polyimide At 23 C

At 100 C

5.0 4.0

20.0

20.0

112.0

112.0

Thermosct

adhesive

4.0 40.0 85.0

Loading consists of multiple uniform-temperature load steps beginning at 23 C and increasing to 122 C. The application of a uniform temperature at each load step implies that the transient

effects that produce temperature gradients in the via structure are

negligible. Previous work has shown this to be indeed true for the relatively slow thermal cycling loading conditions due to the

large surface/volume ratio for the HDI layer and MCMs in general (Prabhu et al.). The automatic load stepping algorithm

required nine load steps to reach 120°C beginning at 23°C and

using an initial load substep of 20 °C.

RESULTS and DISCUSSION

Moire fringe patterns taken at 150°C are shown in Figures 9 and 10. Comparison with the initial fringe patterns, shown

earlier, indicate that the fringe patterns have clearly changed. The

strains as measured by electron beam moire are displayed as contour plots in Figures 1 1 and 12.

atOM »HBJ

T0T £d

08 X 'IX nxez

FIGURE 9. MOIRE FRINGE PATTERN OF VIA HD1 1. AT 151 °C, THE HIGHEST TEMPERATURE REACHED

IN THIS EXPERIMENT.

FIGURE 10. MOIRE FRINGE PATTERN OF VIA HDI 2. AT 144 °C. THE HIGHEST TEMPERATURE REACHED

IN THIS EXPERIMENT.

The analysis focussed on the strains near 120°C, because this was the highest temperature where material property data for the polyimide-epoxy adhesive layer have been reported. A contour

plot showing the total out-of-plane strain as a function of position

is displayed in Figure 13. The experiment and analysis are compared in plots of strain versus position along selected paths, and in plots of strain versus temperature at selected locations. Figures 3, 4, and 8 show the paths and locations used. Plots of strain against position are shown in Figures 14-18; plots of strain against temperature, for the experiment only, are shown in Figures 19 and 20.

256

59
HDI 1 122 C

85.2 -r

I I I I " I I I I" 10 20 30 40 50 60 70 80 90 X-Position

FIGURE 11. CONTOUR PLOT OF MEASURED OUT-OFPLANE STRAINS AROUND VIA HDI 1 AT 122 °C. HDI 2 123 C

100 X-Position

FIGURE 12. CONTOUR PLOT OF MEASURED OUT-OFPLANE STRAINS AROUND VIAS IN SPECIMEN HDI 2

AT 123 °C.

-O.001J!

-0.00422

J

-0.004901 -0.00JS74 -0.012231

•O. 014*27

H>. 017(02

-4.020271 •0.022*33

FIGURE 13. CONTOUR PLOT OF OUT-OF-PLANE

STRAINS CALCULATED BY FINITE ELEMENT

ANALYSIS, CORRESPONDING TO 120 'C

0.025

-mEBM - (me U

-*- EBM -lineP

•m- EBM -line J

FEA- line U

FEA- lineP

FEA- line J

20 40 60 80 100

X-position, pm

RGURE 14. MEASURED AND PREDICTED OUT-OFPLANE STRAINS AROUND VIA HDI 1 PLOTTED ALONG

PATHS j. p. AND u AT 122 *C.

The general character of the total z-direction strain in this interconnect structure is that the strain within the vias and in the

via walls is lower than the strain in the polyimide away from the

vias. Both the experimental mechanics results and the analysts showed this general character. In the polyimide layers at 120°C,

away from the vias and away from delaminations discussed below, the total normal strain in the z-direction averaged about 12 percent in the experiment, while the analysis gave a value of

1.1 percent This experimental value can be seen in the plots of

Figure 14 (EBM-line j). Figure IS (all lines, at the highest z257

60
0.025

0.020 f

H 0.015

S 0.010 f

0.005

0.000

HDI 1. 122 C

LJi

*****

20 40 60 80 100

Z-position, pm

FIGURE 15. OUT-OF-PLANE STRAINS AROUND VIA

HDI 1 PLOTTED ALONG PATHS a, c, c\ h, AND h' AT

122 °C.

Line a

Linec

Line c"

Line h

Line h'

n 0.010

1 c

CO

l_ 55 0.005

0.000

0.020

0.015 "

\ ,- —»—

0.005

0.000

0.015 -

0.010

0.005

0.000

iHDI 2.123 C

_y w T

HDI 2. 123 C

-. ^ZF*^**

iT V

;j0

ill ig

J3_

IP]

U>2_

50 100 150

X-position, |jm

200

FIGURE 16. OUT-OF-PLANE STRAINS AROUND VIA

HDI 2 PLOTTED ALONG PATHS HORIZONTAL PATHS

p1 AND p2 AND JO. ]1. j2. AND j3 AT 123 °C.

values), Figure 16a (at the highest x-values), and Figure 18

(outside the vias). The model value can be seen in Figure 14 (FEA-u and j) and Figure 17 (highest z-values). This excellent agreement is taken as evidence for two points: first, that the

material properties used for the polyimide layers are correct; and

second, the strains were being measured correctly.

la

ic

Lh

20 40 60 80

Z-position, pm

FIGURE 17. OUT-OF-PLANE STRAIN PREDICTED BY

THE REFERENCE FINITE ELEMENT MODEL PLOTTED

ALONG PATHS a. c, AND h, FOR A TEMPERATURE OF

120 °C.

0.020

0.015 -

0.005 f

**- - **'

I 0.010

co

0.000

0.015 --

N is**-*^ N

| 0.010

co 0.005

0.000

HDI 2. 123 C

±m X**—*

HDI 2. 123 C

*** 5 .•_x

C1

c2

-ac3

-*- C4

a1

a2

50 100 150 200

Z-position, pm

FIGURE 18. EXPERIMENTALLY MEASURED OUT-OFPLANE STRAINS AROUND VIA HDI 2 PLOTTED ALONG

VERTICAL PATHS a1 AND a2 AND d, c2, c3, AND c4 AT 123 °C.

258

61
0.020

0.015

s 0010 '

ra 0.005 o

0.000

-0.005

HDI 1

Polyimide

-K- Inside via

Via wall

20 40 60 80 100 120 140 160

Temperature, C

0.020

0.015

0.000 -

-0.005

HDI 2

Polyimide

-X- inside via

Via wall

20 40 60 80 100 120 140 160

Temperature.C

FIGURE 19. OUT-OF-PLANE STRAIN PLOTTED

AGAINST TEMPERATURE AT THREE LOCATIONS FOR

SPECIMEN HDI 1.

FIGURE 20. OUT-OF-PLANE STRAIN PLOTTED

AGAINST TEMPERATURE AT THREE LOCATIONS FOR

SPECIMEN HDI 2.

It was initially suspected that the use of isotropic elastic

sti finesses for the thin polymer layers in this structure might

introduce incorrect values for these properties in the out-of-plane

direction. In particular, one would expect a significantly smaller modulus of elasticity in die out-of-plane direction for the polymers due to the alignment of the long molecules in the plane of the thin polymer layers. In essence, one would expect the alignment of long polymer molecules in the plane to produce the opposite effect in Young's modulus as in the coefficient of

thermal expansion: larger in-plane E, smaller out-of-plane E value. Thus, our finite element model based on in-plane E values would

have been elastically too stiff in the out-of-plane direction. Fairly good quantitative agreement between analysis and

experiment was found regarding the strain inside the vias. In Figure 14 in the center of the via (lines j) the strain was measured

at 0.6%, while the FEA model predicted the strain to be 0.5%. However, the analysis predicted a sharp dip in the strains across

the copper via wall thickness to a value of 03% at the wall. This was not observed in the experimental results. The predicted low

strain in the copper arose from the much higher stiffness and

lower thermal expansion coefficient of the copper compared to the surrounding polymers. The results from HDI 2, in figure 16, show the same results as HDI 1, that is, the predicted low strains

in the copper were not found. It is possible that the discrepancy

is due to the difficulty of detecting local regions of low strain with the electron beam moire technique. Additional experiments may clarify this point This is an important issue, because the

strain in the copper has a significant effect on the lifetime. Other

possible causes of this discrepancy include problems with the

material properties of the copper and three-dimensional effects on

the actual via structures not included in the two-dimensional

analysis considered here.

Laminations The experimental data showed some regions of high strains at the adhesive lamination between polyimide layers. The highest strains observed were 0.036 in HDI 1 at 151°C and 0.028 in HDI

2 at 144°C. These regions of high strain are also evident in the moire fringe patterns. Figures 1 1 and 12. However, the specimens were cross-sections. The cross-sectioning process could have damaged the interconnect structure, leading to the high observed

strains. High strains were not seen near vias which pass through the lamination region. The high strains show the capability of the technique to detect localized regions of high strain. The situation for localized regions of low strain is different. For the conditions of these experiments, regions of low strains are regions of low fringe density, which means that a region of low

strain that is localized in the z-direction, but lies along the x- dircction, may be difficult to detect This is believed to be the case with the Cu traces away from the vias. In Figure 17, line h shows a significant dip in die strain at the Cu trace. The

comparable experimental plots, such as figure 15, lines h and h'. do not show the dip. Here the conclusion is that the experiment was incapable of resolving the localized low strains in the Cu

layeT. There are two remaining significant discrepancies between the experiment and the analysis beyond the strains in the vias discussed above. First the analysis does not have regions of high

strains along the laminations; these were observed in both experiments. They are evident in all the traces in Figure IS, at around z = 60 \un. Second, the analysis has very local regions of high tensile strain, up to 0.023 at 120 °C. just above the via wall (Figure 14). Only very attenuated hints of these "strain spikes" could be found in the experimental data. This difference is interpreted as follows. The delamination strains are the result of some damage or imperfection in the structure; this damage was

259

62
not considered in the analysis. The possibility that this damage

was created during specimen preparation was noted above. It is believed that the "strain spikes" seen in the analysis are a correct

result for the configuration analyzed, but are not present in the experimental data because they have been relieved by the dclamination strains. The effect of this is that the highest strains seen in the experiment at 120 °C, which were 0.027 in HDI 1 and

0.019 in HDI 2, seem to bracket the highest strains in the

analysis, which were 0.023, from Figure 14, FEA-line p. However, in the analysis these strains occur in a very small area,

right above the via wall, whereas in the experiment the high

strains are spread along the lamination, and the highest

experimental values occur away from vias, rather than over the

via wall.

Is There a "Worst Case"? The highest strains observed in this experiment were 0.036 in HDI 1 at ISO °C and 0.028 in HDI 2 at 144 °C. These strains occurred locally along the poiyimide-epoxy bond between

polyimide layers, where no metallization was present Clearly, these high strains may have been the result of damage done to the

structure during specimen preparation. Much lower strains, around 0.006 experimentally and 0.003 analytically, were seen at the via walls, where the bond between the polyimide layers is reinforced by the copper via wall. Prabhu el aL derived "worst case" strains by postulating a

stress concentration of 3 in a plastic region and applying Neuber's

rule. Their "worst case" strains were about 0.01S for a

temperature change of 130aC. Using these strain levels, they derived a predicted fatigue life ranging from 1000 cycles during

severe temperature cycling to over 100,000 in typical application environments. The significance for complete devices of the highest strain values seen in the present experiment cannot be assessed based on

the experiments and analysis in this study, because the strains might have resulted from damage during specimen preparation and because near-planc-stress behavior is being observed on the

free surface, while the actual structure is subject to full three- dimensional stress fields. In a subsequent paper we will show

that both axisymmetric and three-dimensional finite element models predict a significant concentration of strain in the via

barrel for a via completely embedded in the surrounding structure. Therefore, "worst case" strains cannot be derived directly from

the present results. The present results do suggest that high

strains can occur at the laminations between polyimide layers. However, no information can be deduced concerning the mode or degree of damage which might occur in other types of tests, such

as thermal cycling of intact devices. The present results do

suggest that nondestructive examinations of the .bonding between

layers of the HDI structure at intervals during thermal cycling

tests may be useful in understanding the observed device

lifetimes.

Lessons Learned

Experimental analyses of advanced electronic interconnect

structures offers some opportunities and challenges not present in analogous experiments on macroscopic structures. Whole

advanced interconnect structures can be placed under an optical microscope, or within the chamber of a SEM. Loading can be done using a heating stage. The most obvious challenge is the need for strain observation

in very small regions. This challenge was met by the choice of

electron beam moire as the experimental technique. The

additional important challenge revealed by this study was the

difficulty of accounting for the effects of specimen preparation on

the measurement results. Ideally, finite element analysis can account for the direct geometrical effect ofcross-sectioning on the

stresses and strains. However, undetectable local damage may be produced during specimen preparation. The prepared cross- section may not behave exactly like the intact device. Additional examinations, beyond those customary in experimental mechanics

studies of macroscopic structures, may be needed in order to verify the condition of the specimen after cross-sectioning and

surface preparation. SUMMARY and CONCLUSIONS

There was sufficient agreement, both qualitative and

quantitative, between the experiments and the analyses done in this study to allow the conclusion that both the experimental

results and the analytical results are generally correct. That is, the analysis correctly simulates the model via, and the experiment

correctly describes the behavior of the specimens. A convincing

point of agreement was that the strain in the polyimide layers away from all other features was about 0.012 in the experiment and 0.011 in the analysis.

A qualitative discrepancy between experiment and analysis was

that, while both gave nearly the same maximum strain, this strain was found in different locations. In the experiment regions of

high strains extend along approximately one third of the total length oflamination between polyimide layers; in the analysis, the high strains are localized above the via walls. This discrepancy was attributed to damage or incipient delaminations in the specimen cross-sections, possibly but not necessarily produced

during specimen preparation.

Quantitative agreement was found regarding the strains inside the vias. In both the experiment and the analysis, the strains in the vias are half or less of the strains in the surrounding

polyimide. The values were 0.00S in the analysis and 0.006 in the experiment However, in the analysis the lowest strains are in the Cu via walls, at about 0.003. while in the experiment the

strains in the via walls, are about 0.006. The possibility that the experimental technique was inadequate to spatially resolve these

strains remains, along with two additional possibilities: problems

with the material property values used in the analysis, and three- dimensional effects not considered in the two-dimensional model

used here. Increasing the model value of out-of-plane stiffness of

the polymer layers would also reduce this discrepancy.

Two big problems with the experimental technique were related

to specimen preparation. One was the difficulty of producing

perfect line gratings, which is related to the difficulty of producing flat surfaces on this heterogenous HDI structure that includes both very hard ceramic and much softer polymers. The

other problem was the difficulty of avoiding damaging the

delicate interconnect structure, especially when it is laminated to

260

63
a hard alumina substrate. Additional non-destructive examination of structures of this sort during thermal cycling might be capable of resolving the issue of what degree of dclamination, if any, is found in the intact structures. Another problem with the experiment was found to be inability to detect small regions of low strains. Use of a higher density of initial fringes, as carrier fringes, might solve this problem, but might also make data reduction more difficult

REFERENCES

Choi, H.-C., Guo. Y., LaFontaine, W., and Lim, CJC, 1993, "Solder Ball Connect (SBC) Assemblies under Thermal Loading:

II. Strain Analysis Via Image Processing, and Reliability Considerations," IBMJournal ofResearch andDevelopment, Vol. 37, pp. 649-659.

Corbin, J.S., 1993, "Finite Element Analysis for Solder Ball Connect (SBC) Structural Design Optimization," IBM Journal of

Research and Development, Vol. 37, pp. 585-596.

Dally, J.W., and Read, D.T., 1993, "Electron Beam Moire," Experimental Mechanics, Vol. 33, pp. 270-277.

Fillion, Ray, Wqjnarowski, Robert, Gorcyzca, Tom, Wildi, Eric, and Cole, Herb, 1994, "Development of a Plastic Encapsulated

Multichip Technology for High volume. Low Cost Commercial

Electronics," 1994 Proceedings, 44th Electronic Components &

Technology Conference, edited by Iwona Turlik and Rao

Tummala, Institute of Electrical and Electronics Engineers, New

York, pp. 805-809. Guo, Y., Lim, C.K., Chen, W.T., and Woychik, C.G., 1993, "Solder Ball Connect (SBC) Assemblies under Thermal Loading:

I. Deformation Measurement Via Moire" Interferomctry, and Its Interpretation," IBM Journal ofResearch and Development, Vol.

37, pp. 635-648.

Haller, I., Hatzakis, M. and Srinivasan, R., 1968, "High

Resolution Positive Resists for Electron-Beam Exposure," IBM

Journal Research and Development, Vol. 12, pp. 251-256. Han, B., Guo, Y., and Lim, C.K., 1994, "Applications of Moire and Microscopic Moire Interferomctry to Electronic Packaging

Product Development," Conference Proceedings ofthe 4th A nnual IEEE Dual-Use Technologies andApplication Conference, Rome,

NY (in press). Johnson, Eric, 1994, private communication.

Kishimoto, S., M. Egashira, Shinya, N. and Carolan, RA.,

1991, "Local Micro-Deformation Analysis by Means of Microgrid and Electron Beam Moire Fringe Method," Proceedings of the Sixth International Conference on Mechanical Behavior of

Materials, Vol. 4, M. Jono and T. Inoue, Eds., Kyoto, Japan, pp. 661-666.

Kishimoto, S., Egashira, M. and Shinya, 1991, "Measurement

of Grain Boundary Sliding and Observation of Microgrids for High Temperature Use," Journal of the Society for Materials Science Japan, Vol. 40, pp. 637-641 (in Japanese). Lau, J., and Erasmus, S., 1993, "Review of Packaging Methods

to Complement IC Performance," Electronic Packaging and

Production, Vol. 33, No. 6, pp. 50-56. McDonach, A., McKelvie, J., and Walker, C.A., 1980, "Stress Analysis of Fibrous Composites Using Moire Interferometry," Optics and Laser Engineering, Vol. 1, pp. 85-105.

McNeill, S. R. , Sutton, M. A., and Turner, J. L., 1985, "Stress Analysis of a Reversed Dish Head of a Cylindrical Pressure Vessel, InternationalJournal ofPressure Vessels and Piping, Vol.

18, pp. 81-90. National Technology Roadmap for Semiconductors, Semiconductor Industry Association, 1994, pp. 20-21.

Parks, VJ., 1987, "Geometric Moire," Handbook on

Experimental Mechanics, A.S. Kobayashi, Ed., Prentice-Hall, Englewood Cliffs, N-L, pp. 282-313.

Post, D., 1980, "Optical Interference for Deformation Measurements—Classical, Holographic and Moire Interferometry," Mechanics of Nondestructive Testing, W.W. Stinchcomb, Ed., Plenum Press, New York, pp. 1-53.

Post, D., 1991, "Moire Interferometry: Advances and

Applications," Experimental Mechanics, Vol. 31, pp. 276-280.

Post, D. and Wood, J. D., 1989, "Determination of Thermal

Strains by Moire Interferometry," Experimental Mechanics, Vol. 29, pp. 318-322.

Prabhu, Ashok S., Barker, Donald B., Pecht, Michael G., Evans, John W„ Grieg, William, Bernard, Edward S., and Smith, Eric, 1995, "A Thermo-Mechanical Fatigue Analysis of High Density

Interconnect Vias," Advances in Electronic Packaging 1995, Vol.

1, American Society of Mechanical Engineering, New York. pp. 187-216. Read. D.T„ and Dally, J.W., 1993, "Local Strain Measurement by Electron Beam Moire," in A dvances in Electronic Packaging

1993, EEP-VoL 4-1, Proceedings ofthe 1993 ASME International Electronics Packaging Conference, PA. Engel and W.T. Chen,

Eds., ASME, New York, pp. 163-169. Read, D.T., and Dally, J.W., 1994, "Electron-Beam Moire

Study of Deformation of a GFRP Composite," Journal ofApplied

Mechanics, Vol. 61, pp. 402-409.. Theocaris, P.S., 1969, Moiri Fringes in Strain Analysis,

Pergamon Press, Elmsford, N.Y.

Weller, R. and Shepard, B.M., 1948, "Displacement Measurement by Mechanical Interferomctry," Proceedings of the Society for Experimental Stress Analysis, Vol. 6, pp. 35-38.

261

64
A6

Theory ofElectron Beam Moire

by Read and Dally (1996)

65
Volume 101. Number 1, January-February 1996 Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 101. 47 (1996)]

Theory of Electron Beam Moire

Volume 101 Number 1 January-February 1996

David T. Read

National Institute of Standards and

Technology,

Boulder, CO 80303

and

James W. Dally

Mechanical Engineering Department, University of Maryland,

College Park, MD 20742

When a specimen surface carrying a high- frequency line grating is examined under a scanning electron microscope (SEM),

moire fringes are observed at several differ- ent magnifications. The fringes are characterized by their spaual frequency, orientation, and contrast. These features of the moire pattern depend on the spatial fre- quency mismatch between the specimen

grating and the raster scan lines, the diameter of the electron beam, and the detailed topography of the lines on the specimen. A mathematical model of e-beam moire

is developed that expresses the spatial de- pendence of the SEM image brightness as a product of the local intensity of the scan- ning beam and the local scattering function from the specimen grating. Equations are

derived that give the spatial frequency of

the moire" fringes as functions of the microscope settings and the spatial frequency of

the specimen grating. The model also describes the contrast of several different types of moire fringes that are observed at different magnifications. We analyze the formation of these different fringe patterns, and divide them into different categories in- cluding natural fringes, fringes of multiplication, fringes of division, and fringes of

rotation.

Key words: contrast; division: experimental mechanics: fringe: multiplication; pitch;

rotation: spaual frequency; stress analysis.

Accepted: September 26, 1995

1. Introduction

When a specimen surface that carries a regular array of lines is examined under a scanning electron microscope (SEM), moire fringes can be observed at several

different magnifications. Some confusion can arise in the interpretation of the different fringe patterns, be- cause the spatial frequency of the moire fringes changes

with mismatch, rotation, a multiplication phenomena,

and a division phenomena. In this paper we first demonstrate these different fringe patterns, and then explain

their formation based on a Fourier series representation.

Optical moire fringes, either geometric or interfero- metric, are widely employed in experimental mechanics. The classical treatments of geometric moire by

Parks [1], Durelli and Parks [2], and Theocaris [3], and

the descriptions of interferometric moire by Post [4], Graham [5], and McKelvie [6] are most helpful in interpreting fringe pattern formation in e-beam moire.

However, certain features of the phenomenon of elec- tron beam moire' were not anticipated in these classic treatments of optical moire. These features result from

the fact that in electron beam moire, no actual reference

grating exists. Instead, the electron beam raster scan

replaces the reference grating.

The e-beam raster scan is similar in may respects to

the video raster scan employed by Morimoto [7] in forming moire fringes using low frequency specimen

gratings. Kishimoto [8] recognized the similarity be- tween the video and SEM raster scans and was the first $
Volume 101. Number 1. January-February 1996 Journal of Research of the National Institute of Standards and Technology

to report the use of e-beam moire fringes for experi- mental mechanics. However, neither Morimoto or Kishimoto discussed the many fringe patterns that may

be observed when scanning lines are employed as the reference grating. With the controls available on a typical SEM it is possible to vary the e-beam diameter, the pitch of the raster scan, and the angle between the scan

lines and the grating lines. All affect the fringe pattern. We develop a mathematical model of e-beam moire

fringe formation that allows us to reproduce and extend

certain results previously derived for optical moire. The

model is based on two postulates used in treatments of

optical moire [5]:

1

.

The spatial dependence of the pattern of the scan

lines, and the spatial dependence of specimen grating, can be described using Fourier series. 2. The SEM image can be represented numerically

as a set of intensity values given by the product of the scattering power of the specimen grating and the intensity of the scanning lines. Spatially extended interac- tion of the beam with the near-surface region of the specimen is incorporated as a contribution to the width of the scanning lines. Based on these postulates, a model is derived that concisely describes natural moire fringes, fringes of

multiplication, and fringes of division. Experimental

examples are demonstrated. The model is well-suited to determine the fringe contrast and the fringe shape as functions of the raster scan pitch, the scan line width,

and specimen grating parameters.

2. Observation of Specimen Gratings and

e-beam Moire Fringes

Several high-density gratings, with spatial frequencies^ of 2.5 u.m"' to 10 u.m"', were written on a brass specimen using the methods described in [9]. A macroscopic view of the small areas written with different frequencies and different e-beam exposures is presented

in Fig. 1 . Examination of a grating with f% = 5 u.m~' at high magnification, Fig. 2, shows the appearance of the grating lines on the specimen. Depending on the effec- tiveness of the process used to fabricate such lines, they

may appear in the SEM display as high-contrast stripes of black and white, as shown in Fig. 2, or as low contrast stripes represented by intensity modulations in a gray

field. Local imperfections in the specimen surface and

in the grating produce irregularities in the brightness of

the image. Additional imperfections are generated by

the imaging process, even though the SEM image is recorded at a slow scan rate.

Fig. 1. Several line gratings written with different frequencies and exposures, on a brass specimen.

48

67
Volume 101. Numher 1 . January-February 1996 Journal of Research of the National Institute of Standards and Technolosv

Fig. 2a. SE.M image of a line grating with pf - 220 nm. at a magnification of 55 000.

When a grating with f^ « 5 |im*' is observed, moire

fringes appear at several different magnifications over

the range 300 to 3000. Typical moire patterns are illus- trated in Figs. 3 to 5. We have divided these fringe

patterns into three categories, based on the relative sizes of fl. the spatial frequency of the specimen grating, and

/,, the spatial frequency of the raster scan. Moire fringes

oi division, where /g >/b. are presented in Figs. 3a and

3b. Natural moire fringes where fl and fb are nearly

equal axe shown in Figs. 4a to 4e. Most of these fringe

patterns represent a slight mismatch between the pitch of the raster scan and the pitch of the grating; however.

Fig. 4c represents nearly a perfect match. Moire I iges

of multiplication, first observed optically by Pos [8]. are also observed with c-beam moire when fb >J^.

Multiplication by two and three is illustrated in Figs. 5a

and 5b.

3. Theory of e-beam Moir£ Fringe Formation

We introduce a theory to describe the formation of

the several different types of moire fringes that are

observed in an SEM. The theory is similar to that intro- duced to describe the formation of fringes in optical

geometric moire. Fourier scries representations are used

to describe the SEM raster scan, the specimen line grating, and the moire fringes. The results are interpreted to explain the occurrence of fringes classified as natural, multiplied, and divided. The description of fringes of

rotation is adapted directly from optical moire.

3.1 The SEM Raster Scan System

The image observed in an SEM is produced by scanning the specimen grating with an e-beam raster scan. We locate a point in this image by its coordinates (jr. y ). The e-beam is scanned continuously across die imaged

field in the x direction. The e-beam scan lines are

equally spaced, with pitch pb in the y direction. The

magnified image, viewed on the CRT display, has a nominal size of 90 mm in the y direction. This dimension is related to a common photomicrograph size. The

design of the SEM is such that the raster pattern is always aligned with the viewing screen and the camera

frame, so in all the SEM images the x-axis is horizontal and the v-axis is vertical.

68
Volume 101. Number 1. January-February 19%

Journal of Research of the National Institute of Standards and Technology

Fig. 2b. As in Fig. 2a. except at a magnification of 15 000.

Fifi. 3a. Mure fringes of division on a 200 nrr. line gra:ing. .tt a rr.agr.ifiLration of

50

69
Volume 101. Number i. January-February 1996 journal of Research of the National Institute of Standards and Technology

Fig. 3b. As in Fig. 3a except at a magnification of 500.

Fi". 4a. Natural rr.v.re fringes with p, - 200 r.m. at a magnii'icaiion oi 9i0.

70
Volume I0J. Number 1. Janur-r.-Fehruarv i (W'i Journal of Research of the National Institute of Standards and Technology

Fig. 4b. As in Fig. 4a cxccpi 21 a masnificaiinn of 900.

Fig. 4c. As in Fig, 4a. exeepi ai a maanifteaiion of 950.

71
Journal of Research of The Nation

Volume 10 1. Number 1. January -February lWf> nal Institute of Standards and Technology

Fi°. 4d. As in Fie. da. c\ccp: at a magnification of :000.

Fis- -*e. As in F:?- *i- "ccp: a: a mi?r,::ica:;on of 1 iOO.

^3 72
Volume iOI. Number I . January-February 1996 Journal of Research of the National Institute of Standards and Technoloev

Fig. 5a. Moire fringes of multiplication with pc - 200 nm ai a magnification of 2000.

Kit;. 5b. As in Fig. 5a. except at a magnification of 5001

73
Volume 101. Number 1. January-Februar\ 1996 Journal of Research of the National Institute of Standards and Technology

The specimen carries a line grating that consists of an

array of lines extending in the r x' direction, spaced

equally with pitch pj in the y -direction. The reciprocal

of/?,! is/], the spatial frequency of the specimen gratrng. The beam and specimen coordinates may be rotated with respect to one another by a control on the SEM.

The angle between the .r and .v' axes is 8. The number of scan lines used to form the image can

be set at various values. Typical nominal settings are 500. 1000. or 2000 scans to produce an image. The

images in Figs. 3 to 5 were made with 500 lines. Possible magnification values range from 10 to 300 (XX). Because of the design of our microscope, only certain

discrete values of the magnification are available. As a consequence, it is very unusual for us to achieve a nullfield moire fringe pattern. The pitch of the electron beam raster scan lines, p- . depends on the magnification. M . the nominal image

size, 5 . and the number of raster scans used to make the imase. R . as

Pt-SiMR. (1)

For example, with 500 lines per image, a nominal

image height of 90 mm. and a magnification of 1900.

the scan pitch pt is 95 nm. The effective width of the electron beam scan lines depends on the actual e-beam diameter and the interaction of the beam with the specimen surface. Beam

diameters of 5 nm to 20 nm are reported in the literature and in the specifications for our SEM. Attainment of

very small beam diameters (10 nm) requires very low beam currents, a well-aligned microscope, a small aperture, and extremely sharp focussing. The interaction zone diameter depends on the specimen material and the electron beam energy (accelerating voltage). We believe

a value of 15 nm to 30 nm is typical for the effective width of the raster scan lines used in this study. The specimen gratings are formed by etching thin troughs in a polymeric film about 100 nm thick. The

frequencies obtained vary from 2.5 u.m~' to 10 u-m"

1 . The lines (troughs) appear as dark stripes in the image

and th ridges between the troughs appear as light stripes in our densest gratings, the width of the troughs and the ridges Is approximately equal. A y'-dircction

trace of the image intensity shows a profile with gradual, rather than abrupt, changes in the image intensity.

3.2 Fourier Representations of the Grating and

Scanning Lines

We follow the approach introduced by Sciamarella

[8] for optical moire; we assume that the local intensity

(brightness) of the image is proportional to the product

of the iocal scattering power of the specimen grating

and the local intensity of the e-beam scan line. Tne

scattering function G(v') for the specimen grating is represented by a Fourier series:

G (%') = ~-zf + jZ S* cos dzraly') (1)

where the ;'„ are Fourier coefficients and/; is the spatial frequency of the grating lines. After deformation, the specimen grating frequency f. can \ar> with position over the specimen. However, in this treatment we simplify the analysis by considering only deformation fields that produce constant strain over the local region of

interest. The frequency fc represents the current value at the time of image formation, which is usually different from the original value. The intensity of the e-beam scan lines B(y ) is also represented by a Fourier series:

B(y ) - — + 2^ bn cos (2-eth/sv ) (3)

where the bm are Fourier coefficients and/;, is the spatial frequency of the raster lines. In both Eqs. (2) and (3). the cosine representation is sufficiently general because somewhere in the image an origin can be found such

that the sine terms vanish.

In the simplest case, the y and y axes coincide. But

the raster scan lines can be rotated at an angle t> relative to the grating axes to produce anguiar misalignment.

When 6 — . we will transform G{y') into the coordi- nates of the raster scan and the image. Since G(y'> is a periodic function y' with no dependence on x'. the Fourier representation is valid in the transformed coordinates. However, for ~ the dependence of the grat- ing scattering function on .r' cannot be ignored, and we

will consider the specimen grating to be represented b\

G{x\ y'). It is convenient to measure the moire fringe

spatial frequency/ along the y -direction, which is verti- cal in the SEM images. The spatial frequency of the e-beam raster scan pattern is naturally measured along

the y-direction. It is convenient to have all spatial fre- quencies referred to the same axis, so for calculations we transform the value of the grating frequency into a new value. /s

, the effective grating frequency in the raster scan coordinate system. Wc take/. =_£ cosid) -

cos(9)/pg . where pi is the physical grating pitch, measured in the y' direction. In practice. 9 is usualK

adjusted to be when moire fringe patterns are being

recorded, so in such cases

/

E -fl = \lp'

g

. The moire pattern intensity fix. y) is represented as the product of the raster function and the grating function:

74
Volume 101, Number 1, January-February 1996 Journal of Research of the National Institute of Standards and Technology

I(y) = B(y) G(y). (4)

Substituting Eqs. (2) and (3) into Eq. (4) and arranging

the products of the cosine terms into sum and difference cosine functions gives a relation of the form

I(y) = C + F(y) + S(y) + D(y), (5)

where C = gobJA is a constant. The function

^Cy)=(^)i gn COS (2777!/^)

+ (^)JLbm cos{2irmfo)

exhibits a frequency that is too high to be observed. The sum function

S(y) = S 2 (^7=) cos 2TT{nfg + mfb)y

m-I n-l \ Z /

also exhibits a frequency that is too high to be observed. The difference function

D(y) = n (^t") cos 2TT(nfs -mfb)y

is the term in the double series expansion that produces

the image observed and identified as the moire fringe

pattern. We simplify Eq. (5) to give

I(y) = C, + 2 2 (^) cos 27r(/z/

g + m/b)y (6)

where C, = C + F(y) + S(y) is the intensity of the background.

The result is similar to that obtained in optical moire. When the magnification yields moire fringes, neither

the grating lines nor the scan lines can be clearly imaged.

The coefficients gn in the specimen grating function G (y ') fall off rapidly with n because of the topography

of the grating. The coefficients bm of the scanning beam

raster function B(v) do not decay as rapidly with in- creasing order m of the expansion. The reason for the persistence in bm is described later.

33 Natural Moire Fringes

The simplest condition for fringe formation in optical

moire is when/g is approximately equal to/b ; this is the near-match condition. Similarly in e-beam moire we

refer to fringes formed under this near-match condition

as natural fringes. Because only discrete values of magnification are available on our SEM, we have never been

able to achieve a perfect null field, where /g =/b and the

pitch of the moire fringes pm becomes infinite. Considering the first term in the sum in Eq. (6) (n - m = 1 ) for the near match condition where fb = fg gives the frequency f, of the moire fringe intensity function I(y):

/-/«-/b (7)

In Eq. (7), negative values of the moire fringe frequency

are allowed, because moire fringes are formed both for /g >/b and for/g </b. Because the cosine is a symmetric

function of its argument, it is impossible to determine

from Eq. (6) whether/b or/g is greater. This is important

in measurements, because it represents the difference between expansion and contraction of the specimen. In

practice this ambiguity is resolved by changing the magnification which in turn changes fb in a known sense. The result is a change in f, that can be observed and

interpreted to determine if/b is higher or lower than/g

. Consider small uniform longitudinal strains along the y direction, relative to the ideal null condition where

fe -fb and 0-0. Equation 7 implies that the tensile strain e is given by

e = - fi (/;+/)

(8)

The periodic form of Eqs. (2) to (6) makes it possible

to adopt a vast body of previous developments to inter- pret e-beam moire fringes. Some familiar wave phe- nomena have analogs in SEM images of line gratings. For example, it is clear from Eq. (7) that the moire

fringes are analogous to the beat frequency due to two

pure sound tones of slightly different frequencies.

Another example is the Doppler phenomena. We

observed a changing frequency of the moire fringe pat- tern when the specimen was moved under the scanning

electron beam.

The contrast of the natural moire fringes is deter- mined primarily by the amplitude term gib,/2 , although

higher order terms also affect the contrast. Higher order harmonics of the fringe frequency occur for m - n - 2, 3, . . . etc. These harmonics distort the pure sinusoid of

the fundamental. Other higher order terms that occur

56

75
Volume 101. Number 1 . January-February 1996 Journal of Research of the National Institute of Standards and Technology

when n + m produce signals with a very high frequency

that can be disregarded except for their detrimental

effect on contrast. Post [9] has used specially selected aspect ratios between bar and space widths in optical

moire to produce "fringe sharpening" effects. Equation

(6) shows that the effect of bar and space widths on

moire fringe shape can be calculated by Fourier series techniques. This phenomenon is qualitatively observable

in e-beam moire as a resemblance between the appear- ances of the grating lines at high magnification and the moire fringes at low magnification.

3.4 Fringes of Multiplication

Post [11] showed that fringe multiplication occurred

in optical moire when the spatial frequency of the refer- ence grating was a near multiple of the spatial frequency

of the specimen grating. The same fringe multiplication occurs in e-beam moire. We express the spatial fre- quency of the scan lines, following the notation intro- duced by Post [11] as:

/b -0(l + A)/g (9)

where /3 is a positive integer and A is a small fraction. Substituting Eq. (9) into Eq. (7) shows that the spatial frequency of the moir£ fringe pattern intensity is:

/ = [n - mjS(l + A)] /, = [(/i - fim ) - m\p\ft

.

(10)

Moire fringes may be observed when n-j3ra; then /

becomes

fi ~-m\fifl

. (11)

The amplitude of the moire fringe terms in Eq. (6) is given by g„bm ll. Since j3 is typically an integer from 2

to 5, n - fim is always greater than one, while maximum

contrast requires m be fixed at 1 . This fact means that fringes of multiplication occur when we match the fun- damental frequency of e-beam raster scan with the second, third, etc., harmonics of the grating function.

Difficulties in obtaining high contrast fringes of multiplication are due to the decreasing Fourier amplitudes of

higher harmonics of the grating function. To illustrate this important result, let /3 = 2 and consider a specimen

grating that is represented by a symmetric square wave

(an amplitude grating with bar width equal to space

width). Since g2 , the coefficient of the second harmonic

for a square wave, is 0, the contrast goes to zero and

these fringes of multiplication cannot be observed.

These results show the importance of the grating

scattering function for the contrast of fringes of multiplication. A grating with narrow lines and wide spaces

exhibits stronger even harmonics than a balanced grat- ing with equally wide lines and spaces. However, for all shapes, except the periodic delta function, the general

rule is that the coefficients g„ decrease rapidly with

increasing order of the harmonic. Unfortunately, we

have not been able to produce high-density specimen

lines that scatter like delta functions by e-beam lithography. Our highest-density gratings scatter much like sinusoids. Our experience with fringes of multiplication is that they are difficult if not impossible to observe, as is consistent with the preceding development. Examples of

fringe multiplication by two and three, Fig. 5, show

fringes with lower contrast than those in Figs. 3 and 4.

3.5 Fringes of Division

Moire fringes of division also occur, but in this case

the specimen grating frequency is a multiple of the scan

line frequency. Fringes of division are commonly observed at low magnification settings on the SEM, where

pb is larger than p%

. The formation of the fringes of

division and their contrast can be explained by using the Fourier representation. Consider an observation in the SEM with a frequency relation given by

ft = o(l + y)fb (12)

where a is an integer and y is a small fraction. The

frequency of the resulting moire fringe intensity is obtained from Eq. (7) as:

f, = [(an-m) + ayn)fb. (13)

The moire pattern can be observed when an = m and

Eq. (13) reduces to:

f\ - aynf* (14)

Since a is an integer typically from 2 to 5, m = an is always greater than one. This shows that moire fringes of division are formed by combining the fundamental

frequency component of the specimen grating with higher harmonics of the e-beam raster pattern. The e- beam scan lines that are produced at low magnification have relatively high coefficients b„ for n as large as 10. To show the strength of the higher order harmonics

associated with the e-beam scan lines, consider a magnification M = 500. With the number of raster lines R = 500, this setting on the SEM gives a pitch

57

76
Volume 101. Number 1. January-February 1996 Journal of Research of the National Institute of Standards and Technology

pb = 360 nm by Eq. (1). This value of pb is about 20

times larger than the effective width of the scan line ( 1

8

nm). Since the raster scan is only sampling about 5 % of

the specimen surface, it behaves like a periodic series of

delta functions in y . We show the relative magnitude of

the Fourier coefficients for a scan line width wb = 0.05 pb in Fig. 6. It is evident that the coefficients bm decrease

slowly with increasing m. For this reason fringes of

division may be observed at many low magnifications with excellent contrast as illustrated by Fig. 3. As the magnification is increased, pb decreases and

the portion of the field sampled by the scan lines in- creases. When the ratio wblpb increases, the coefficients of the higher harmonics of B(y) decrease more rapidly with order m. This phenomenon is illustrated in Fig. 6

where the coefficients are shown for M = 2500 and wb/pb = 0.25.

Electron beam intensity function

-0.2

Magnification

500

2500

4 5 6 7 Harmonic number10

Fig. 6. Estimated relative amplitudes of terms in the Fourier expansion of the electron beam raster scan function B {y ), for magnifications of 500 and 2500.

3.6 Fringes of Rotation

Fringes of rotation occur in optical moire when the pitch of the specimen and reference gratings are closely

matched and one grating is rotated relative to the other

[1]. Similar fringes of rotation also occur in e-beam

moire. We restate the relevant equation here because the phenomenon is quite commonly observed in e-beam

moire, and is useful. We consider the specimen grating

lines to be along the x' axis and the scan lines along

the x axis. The angle measured from the x axis to the x' axis is 6, which can be of either sign. When the rotation knob on the SEM is turned clockwise, the specimen's

image also appears to rotate clockwise. Of course, the specimen is not actually rotating. The raster scan lines are rotating in the opposite sense. From alignment at

= 0, counterclockwise rotation of the SEM rotation control produces a clockwise rotation of the raster scan

pattern, and thus a positive angle 6. We measure the fringe angle <}> from the x axis. The moire fringes of

rotation make an angle of <p with the x axis, as shown in Fig. 7.

tan$

sin0

COS0 - &

(15)

Pb

At match conditions where pt = pb , Eq. (15) reduces to:

(16)

. it 6 *=2 + 2-

Equation (16) indicates that at match for small 0, the moire fringes are nearly perpendicular to both the grating lines and the raster scan lines. For typical mis- match but small misalignment where sin Q- 0, Eq. (15) reduces to:

<£= (17)

Equation (17) shows that small misalignments produce

much larger fringe angles, because fg/f, is a large quan: tity whenever moire fringes are visible. In Eq. (17), <f>, 0, and f\ can be positive or negative, but /g

is always

positive. The value of can easily be adjusted in the SEM by a control which rotates the direction of the

raster scan pattern. This is helpful because Eq. (17) shows that the sense of the change of <^ with gives the sign offi.

Moire Fringes

Fig. 7. Definition of geometry and signs of angles when the speci- men grating and the electron beam raster scan are not aligned.

58 77
Volume 101. Number 1, January-February 1996 Journal of Research of the National Institute of Standards and Technology

4. Magnification, Field Size, and Mismatch

We showed in Eq. (1) that the magnification M and

the number R of lines in the SEM raster scan determine

the pitch pb of the scanning lines. As the settings on the SEM are changed, both the size of the field and the e-beam moire" fringe pattern change. A schematic illus- tration of the field size, the specimen grating, the scan

line raster, and the moire" fringe pattern is presented in Fig. 8.

R Scanning Lines k Grating Lines N Moire Fringes H=SIM Pg Fixed Pi = H/W=S IMN

p^^H/R^S /MR

Fig. 8. Illustrations of raster scan lines, grating lines and moire

fringes when the grating area exceeds the field of view.

The field size or observation height H is given by:

(18) *-h

The pitch of the specimen grating is fixed at ps for a

given experiment. Here we assume that the specimen

grating and the raster scan lines are perfecdy aligned, so we do not need to differentiate between primed and unprimed coordinates. As long as the height of the grating, h exceeds the field size H, he number of grating

lines in the field of observation, k, changes with M as:

definition, we admit both positive and negative fringe

orders. By combining these equations, we can show the

relation between the moire fringe frequency and the SEM settings (R and M) as

J'\ c

P< Pt J

(22)

Equation (22) derives from Eq. (7), which was/ =ft -/,. At

high magnifications, the spatial frequency of the elec- tron beam raster scan is higher than that of the specimen

grating, so the frequency of the moire fringe pattern f;

is negative. The conventional usage [2] is that/, p„ and N are all positive by definition. However, this choice

gives rise to the ± in many equations. To avoid this awkward notation, we allow /, p„ and N to be either positive or negative so that the relevant equations are single-valued.

The number of fringes N observed in the field of view

is: N = Hf, = H(ft -fb) - H(/g - ^r) (23)

when the grating height h > H, the field size. Otherwise

»-*(/,-f) (24,

when the grating height h < H.

The match condition, which gives the null field, / = 0, is the same in both cases:

SJ_ S

Rpg ~R- M-SzT-lifr (25)

k = Mpt (19)

The number N of moire fringes across the field of view

is:

; N = R-k

and the pitch of the moire fringes px is: H S

N~ MN

(20)

(21)

We have defined the fringe order N as positive when the number of specimen grating lines in the field of view

exceeds the number of scan lines [(Eq. 7)]. With this

For example, a specimen grating with /g -5 u.m"' observed in an SEM with S - 90 mm and R set at 500

will yield a null field associated with the natural match

condition when M - 900. Match conditions for fringes of division and multiplication will occur at magnifications of 900/ a -or at 900 /3 , for a and /? integers. An experiment was conducted using a specimen

grating with fe = 5 Lim"1 . The grating area was small

(h = 63 u.m) so that h < H for all choices of M used in the experiment. The SEM was operated with nominal

values of R - 500 and S - 90 mm. The magnification was changed so we observed mismatch conditions with

both positive and negative fringes. The results for N as a function of A/, presented in Fig. 9, show a linear

relation as expected from Eq. (24). The slope of the N

vs M relation is [from Eq. (24)]

59

78
Volume 101. Number 1. January-February 1996 Journal of Research of the National Institute of Standards and Technology

dW _-hR

AM~ S

(26) The actual magnifications given in Fig. 1 were employed in preparing the data presented in Fig. 9.

The slope was determined from the least squares fit of

the data as -0.325 . We also noted that the match condition occurred at M = 977. From the match condition we

could determine that S/R = 195.4 u,m. For S = 90 mm

we find that R = 478 lines. This result for R agrees with

the nominal value supplied by the manufacturer of the SEM.

40

24

? -8

S -24

-40

Slope of best-fit line corresponds to 478 scan lines in SEM raster pattern

850 900 950 1000

Actual magnification 1050 1100

Fig. 9. Fringe count N over specimen grating at different magnifications.

5. Magnification Calibration

The interpretation of moire fringe patterns depends on precise knowledge of the magnification at any setting

M employed to produce a pattern. To check the accuracy of the magnification of the SEM, we measured the

length of a distinctive feature on the surface of a speci- men at M = 1000 . We then measured the length of this same feature at other magnifications as indicated on the SEM character display. We found that the actual magnifications were different from the indicated magnifications, as shown in Fig. 10. In preparing Fig. 10 we

assumed that the microscope was absolutely correct at M - 1000. An improved calibration technique should employ a calibration standard so that the accuracy of all magnification settings could be established. Examination of Fig. 10 shows that the magnification

errors are less than 5 %. Nevertheless the errors are

significant in the present analysis as accurate magnification values must be employed in Eq. (23) to properly

characterize the scanning line function produced by the SEM. Similarly, the micrometer bar, which also appears

in the image display of many microscopes, must also be

accurately calibrated if it is to be useful in the quantitative interpretation of e-beam moire fringes.

1150

1100

I

1050

"5f 1000 a| 950

CD | 900

850

800

; Check of SEM magnification;

! data normalized at 1000

Measured ;

Indicated

800 850 900 950 1000 1050 1100 1150

Indicated magnification

Fig. 10. Actual versus indicated magnification showing relative errors in the SEM magnification calibration. Data normalized to a magnification of 1000.

6. Conclusions

The formation of e-beam moire fringes in a SEM can be described with a model based on a Fourier series representation of the specimen grating line function G(v') and the raster scan line function B(y). The moire

fringe intensity function /(y) is the product of these two

functions. The model describes the variation in the spatial frequency f, of the moire fringes with the magnification used in producing the image. It also provides a means for estimating the contrast of different moire

fringe patterns that are observed in the SEM. The spatial frequency/ of the moire fringes can be used to measure

the spatial frequency^ of the specimen grating to deter- mine local displacements and strains. The sensitivity and resolution of measurements made

with e-beam moire are limited by the frequency of the specimen grating. Fringes of multiplication offer en- hanced displacement sensitivity per fringe, but require

that the specimen grating be fabricated with a troughridge ratio that produces substantial higher order Fourier components. Fringes of division are observed as easily as natural moire fringes because the raster scan lines at low magnifications exhibit significant Fourier coeffi- cients for the higher order terms in the expansion.

Fringes of division are useful because they permit a

larger field of observation while maintaining the same

displacement sensitivity per fringe as is achieved with

the natural moire patterns. Fringes of rotation are easy to observe by operating

the SEM control for the e-beam scan line direction. This

control is useful for alignment and for establishing the sign of the moire fringe frequency /.

60

79
Volume 101. Number 1, January-February 1996 Journal of Research of the National Institute of Standards and Technology

A method was described for characterizing the SEM

based on determining mismatch fringes at different magnifications. The method is dependent on the use of

accurate magnification values. We found that calibration of the SEM at each discrete magnification setting was

essential.

7. Acknowledgments

J. W. Dally thanks the Office of Naval Research and

the National Science Foundation for support during this study.

8. References

[1] Vincent J. Parks, Geometric moirf, in Handbook on Experi- mental Mechanics. Albert S. Kobayashi. ed.. Prentice-Hall, Englewood Cliffs. New Jersey (1987) pp. 282-313.

[2] A. J. Durelli and V. J. Parks, MoinS Analysis of Strain, PrenticeHall, Englewood Cliffs. New Jersey (1970).

[3] P. S. Theocaris. Moir£ Fringes in Strain Analysis. Pergamon

Press. Elmsford, New York (1969).

(4) Daniel Post, Moire interferomeiry, in [1].

[5) S. M. Graham, Sensitivity and resolution limitations of various moire methods. Opt. Lasers Eng. 12, 1 19-133 (1990).

[6] J. McKelvie, On the limits to the information obtainable from

a moire fringe pattern, in Proceedings of the 1986 SEM Spring Conference on Experimental Mechanics, Society for Experi- mental Mechanics, Bethel, Connecticut (1986) pp. 971-980.

[7] Y. Morimoto T. and Hayashi, Deformation measurement muring powder compaction by a scanning moire method, Exper. Mech. 24, 112-116(1984).

[8] S. Kishimoto. M. Egashira, and N. Shina, Measurements of

grain boundary sliding and observation of microgrids for high temperature use. J. Soc. Mat. Sci. Japan. 40 (452), 637-641

(1991) (in Japanese).

[9] J. W. Dally and D. T. Read. Electron beam moire; Exper. Mech.

33. 270-277 (1993).

[10] C. A. Sciamaralla, Basic optical law in the interpretation of

moire patterns applied to the analysis of strains—part I. Exper. Mech. 5, 154-160(1965).

1 1

1 J D. Post, Sharpening and multiplication of moire fringes. Exper. Mech. 28 (4), 329-335 (1988).

About the authors: David T. Read is a physicist with

the Materials Reliability Division of the Materials

Science and Engineering Laboratory at NIST. James W. Dally is recently retired from the Mechanical Engineering Department at the University of Maryland. The

National Institute of Standards and Technology is an

agency of the Technology Administration, U.S. Depart- ment of Commerce.

61 80
A7

Electron-Beam Moire Study ofLocal Deformation in Conductive Adhesives

by Drexler and Berger (1996)

81
ELECTRON-BEAM MOIRE STUDY OF LOCAL DEFORMATION

IN CONDUCTIVE ADHESIVES

E. S. Drexler* and J. R. Berger"

"Materials Reliability Division, National Institute of Standards and Technology, Boulder,

Colorado 80303

"Division of Engineering, Colorado School of Mines, Golden, Colorado 80401

ABSTRACT

Electron-beam (e-beam) moire is a recently developed technique for micromechanics. It allows one to combine the resolution of the scanning electron microscope (SEM) with the strain measurement capabilities of moire. With e-beam moire

we are able to study locally the effect of temperatures ranging between -50 and 150

°C on conductive adhesives (CAs) and their interfaces. With this technique we

measured the local displacements due to the thermal expansion of the copper and the

CA. The modified lap-shear specimens were made of copper-to-copper attached with

CAs and cured according to the manufacturer's instructions. A cross section of each

material was polished and a moire grating was written on the surface using e-beam

lithography techniques. Digital images of the moire were collected from the SEM at regular temperature intervals. The images were compared and the displacements

measured. Local regions of large displacements were observed in the paste specimen. Permanent deformations in the film specimen resulted from exceeding the glass

transition temperature of the CA.

INTRODUCTION

E-beam moire is a recently developed technique first described in [2] and

advanced in [1, 3-5]. Utilizing many of the principles of video moire [6], e-beam

moire is an advancement in resolution, as it is conducted in the scanning electron

microscope (SEM). E-beam moire is based on the fundamentals of optical moire while

exploiting the spatial resolution of the SEM. The limitations of the relatively long wavelength of light are circumvented by imaging with an electron beam. As with moire

interferometry, e-beam moire does not require a separate, tangible reference grating.

The reference grating is an integral part of the SEM-the rastering of the electron

beam--and exists whenever the current in the filament is sufficient to produce an

image. The electron beam rasters across the field of view at regular intervals, 480

raster scans per image for a typical imaging system. The pitch of the "reference

grating" is, therefore, dependent on the magnification and the viewing area of the

system. The specimen grating is a series of ridges and trenches generated by e- beam lithography. This lithography takes place in the SEM with the aid of a computer

program that controls the location and dwell time of the electron beam.

The magnification for the lithography is nominally the same as for the imaging.

The number of lines written is 1 or 2 times the number of rasters of the electron beam

so that the initial correlation is approximately 1-to-1 (or 1-to-2). Because the SEM is focussed and tuned using electromagnetic lenses to adjust for differences in focal

distance, it is virtually impossible to replicate tuning conditions between sessions on

82
the SEM. A null field, one for which an exact 1-tc-1 correlation exists between the

specimen and reference gratings, is very rare; therefore, moire fringes will usually be

present for the initial condition.

The resolution of the technique ranges from 90 to 900 nm/fringe order.

Resolving values for strain using the technique depends on the" pitch of the specimen

grating and the ability to discern fractions of fringes. The ideal initial condition would

have a few high-contrast fringes, such that resolving to 1/10 of a fringe is possible.

The fringe center is a contour of equal displacement on the surface of the

specimen. The effect of the cross-line grating is analogous to having a full-view 0-90°

displacement gage with resolution on the order of tens of nanometers. Thus, strains

calculated from data obtained with this technique are fully quantitative.

Thermal loading tests were conducted on 2 specimens, a CA paste and a film,

in a temperature range from -50 to 150 °C. Moire images were acquired at each

temperature and compared with the image from the initial condition.

EXPERIMENT

Tests presented here were conducted on two different isotropic CAs (ICAs),

one in paste form and the other a film. The specimens are made up of OFHC copper

and CA, as shown in Figure 1. The film specimen was cured at 150 °C for 30 min

under continuous pressure, then allowed to cool to room temperature before the

pressure was relieved. The paste specimen was assembled and cured without

pressure in an oven set to 150 °C for 6 min. The specimen was then removed from

the oven and allowed to cool to room temperature.

Each specimen was nominally prepared according to the description given in

[5]. The only major deviation is that once the pattern was written a second pattern

was superimposed 90° to the first. This provided cross-line gratings needed for the

complete determination of in-plane displacements.

The thermal load testing of each CA material was conducted in the SEM using a combined heating and cooling stage over a nominal temperature range of -50 to

150 °C. Cooling was provided by liquid-nitrogen -cooled nitrogen gas flowing through

tubing in the stage. A controller maintained the set temperature by balancing the

heater output with the chilled air. Before any images of Pattern A in Figure 1 were acquired, the stage was cycled

between °C and 100 °C twice before returning to the ambient temperature noted

when the filament was first saturated. This was to ensure that any reseating of the

specimen due to heating and cooling of the stage occurred prior to the start of image

acquisition. The one-hour period required to do this cycling also gave the electron

beam time to stabilize. Images were then stored digitally from both 0° and 90°

orientations at ambient temperature. (Throughout the remainder of this paper u-field

and 0° will refer to the observed images where the grating lines were perpendicular to

the interface. V-field and 90° images have the grating lines parallel to the interface.)

Subsequent 0° and 90° images were acquired at temperature intervals of -50 °C.

In the film specimen (location B in Figure 1) images were collected from the

and 90° orientations one hour after saturating the filament, but before thermally cycling

the stage. The stage was then cycled between and 100 °C twice, as before. A

second pair of images was acquired at the noted ambient temperature after the

thermal cycling. These images were used as the initial condition for the test. Digital

83
images from the and 90° orientations were stored at temperature intervals of 50 <C.

The fringe centers from each image from both tests were traced.

The fringe centers were identified on the iy-field and v-field images. Line profiles

were chosen running perpendicular and parallel to the orientation of the reference

grating on each image. For the u-field images three line profiles were chosen such

that one was through the CA and the other two were approximately equidistant from

the CA, one in the 9.5 mm copper and the other in the 0.4 mm copper.

A graph was made of the distance along the chosen trace versus the assigned

fringe order. The fringe order was then converted into length by multiplying by the

pitch of the reference grating pr With e-beam moire, since the initial fringe field is rarely null, every subsequent image is analyzed by studying the difference between it and the initial condition image. The slopes obtained from the line profiles from the

initial images must be subtracted from the subsequent images to see how each

loading step affected the fringe field. Strain data were calculable from these plots of

relative displacement versus position along the trace. The slope Bu/dc and 8//cy of

the curves from the line profiles perpendicular to the orientation of the reference

grating in the u-field and v-field images, respectively, are the normal strains. The

shear strain is the sum 3u/dy + dv/3x of the slopes from the curves obtained parallel

to the orientation of the reference grating,

RESULTS

CA paste. As one looks at the images collected of the fringe field at each temperature, the amount of local deformation occurring in the CA at 150 °C was notable.

In Figure 2a of the u-field, the fringes curve through the CA paste and the fringe density was not regular. The corresponding v-field image (Figure 2b) shows the fringes

following a circuitous path through the CA. (The moire fringe field images displayed in this study were colorized by computer manipulation to aid in locating the fringe

centers. All micrographs acquired from an SEM image are originally black and white.)

The analysis of the series of the t/-field images showed that the behavior in the

thin copper, the CA, and the thick copper were all very similar. Below room temperature the curves exhibited a gradual negative slope, indicative of contraction. Above

room temperature there was little sign of expansion at 50 °C, especially in the thin

copper. By 100 °C the slope had steepened sharply at all three line traces, in a

positive sense, and it steepened still more by 150 °C. The magnitude of the value for

the slope when the temperature was increased by 100 °C was far greater than it was

when decreasing the temperature 100 °C. The glass transition temperature T

Q

of the

paste is 80 °C. When T

g was exceeded the coefficient of thermal expansion nearly

quadruples. The line profile from the CA is shown as an example in Figure 3. One other significant point to note is the behavior of the curve at the two

highest temperatures, particularly in the thin copper and in the CA. In both cases the

slope flattened out as it approached the top of the image. The pattern was located at the edge of the lap of the specimen. The flattening of the slope was the effect of the

free surface on the thin copper and the CA. That is, there are no normal or shear

stresses (or corresponding strains) at a free surface.

The displacement-versus-position curves for the v-field showed very unusual

behavior at the higher temperatures (see Figure 4 from the center of the pattern).

Through 50 °C the curves acted in a regular and supportable manner. As the

84
temperature was reduced the slope became increasingly more negative, with a

sharper drop occurring in the CA. As the temperature increased it looked as though

the material would behave in the reverse fashion at 50 °C; the curve demonstrated a

positive slope becoming more positive through the CA. However at 100 °C the slope

became slightly negative, and at 150 °C, significantly negative through the CA. It was

clear that locally, around the CA, between 50 and 100 °C the fringe field passed

through a null, and the fringe density started to increase in the region, giving the

appearance of being in a state of contraction, whereas the region was actually in a

condition of greater expansion.

CA film. The first image collected from the paste specimen in the 0° orientation

showed that the fringes were bending as they crossed the CA. Because the image

was acquired after the specimen and stage were cycled twice between and 100 °C,

it was unknown whether the shear deformation was the result of relaxation of residual

stresses before exposure to temperature extremes, or whether it was due to thermal

cycling. In this test on CA film, images were collected before and after thermally cycling the specimen and stage. Figure 5 shows the ambient temperature images from

the 0° orientation before and after cycling. The shear that developed in the CA was

the direct result of thermally cycling the specimen and stage between and 100 °C.

The post-cycling ambient-temperature images were used for the initial condition

when analyzing the data from this test. The u-field data exhibited the anticipated

behavior; the slopes become increasingly more negative as temperatures decrease,

and increasingly more positive as temperatures increase for all three line profiles (eg.

from the CA is shown in Figure 6).

Tracing the fringes from the v-field was very difficult, because the fringe center

in the CA was ambiguous. The data would appear to suggest that the CA remains

contracted regardless of whether the temperature was increasing or decreasing (see

the displacement versus position curves from the center of the specimen shown in

Figure 7). The fringe density in the local region of the CA gives some indication that

the pattern experienced a null between 0.4 and -9.9 °C. However, the data were not

clear enough to unequivocally support this. CONCLUSIONS

The experiments conducted on the two forms of ICAs yielded useful information

on the conduct of these materials under these testing conditions. Both the CAs

performed well under the imposed thermal loading conditions. Even though T

exceeded T and regions of great expansion resulted, the materials did not debond at the copper/CA interface, nor did the silver particles shift or rotate. The CAs kept

enough stiffness at the higher temperatures to function as they were designed to in this specimen.

If these materials are to replace solder in fine-pitch applications, it is of concern

that they retain the deformation induced at 100 °C. Figure 5 shows that the bending

of the fringes in the CA after thermal cycling has a magnitude of approximately half a

fringe or 225 nm, in the case of this pattern, which has a specimen pitch ps « 450 nm.

At the end of the thermal loading test an image was again acquired at approximately

room temperature. That image shows the shift through the CA was nearly a full fringe.

Indications are that the deformation does not continue to accumulate at the same rate

however, as the final image from a second thermal loading test on the same specimen

85
and pattern shows the fringe shift has the same magnitude at the^nd of the test as it had at the start. Deformations of this magnitude are probably insignificant for a wellplaced, properly aligned surface-mount device with a lead pitch of 300 //m. But if pitches continue to become smaller these deformations will eventually lead to failed

components.

REFERENCES

1. J. W. Dally and D. T. Read, Exp. Mech. 33, 270 (1993).

2. S. Wshimoto, M. Egashire, and N. Shina, J. Soc. Mat Sci. Jpn. 40, 637 (1991).

3. D. T. Read and J. W. Dally, ASME J. Appl. Mech. 61, 402 (1994).

4. D. T. Read and J. W. Dally, J. Res. Natl. Inst. Stand. Technol. 101, 47 (1996).

5. D. T. Read and E. S. Drexler, ASME Proc. Mech. Mat Electron. Pack. AMD-187 2,

185 (1994).

6. Y. Morimoto and T. Hayashi, Exp. Mech. 24, 112 (1984).

Copper

Conductive Adhesiv

9.5 mm

Figure 1 . Sketch of the specimen configuration used in the thermal loading tests. The

site of the observed pattern for the paste thermal test is A, the film thermal test is B.

Figure 2. Images at 220 x from the CA paste acquired at 150.2 °C of (a) the u-field

image, and (b) the v-field image

86
2.00

1.00

0.00

-1.00

1 1 • 7 - -4*J *C * T - B1J *C AT- -M *C T • 10CU *C T-M'C • T - 1SOJ *C

T - 2*J *C

« •—-

« i »

< I

100 200 300

POSITION, pm

400

Figure 3. Displacement versus position

plots of the t/-field data on the CA

paste.

2.00

1.00

0.00

1 1 r

• T • -*7J *C • T - *1.T *C AT- -&* *C • T - 100.3 *C T»t2*C • T 150.1 *C

. T - 28.0 *C

-1.00 -

-2.00 100 200 300 400

POSITION, fim

Figure 4. Displacement versus position

plots of the v-field data on the CA

paste.

Figure 5. £/-field images from the CA film acquired at -28 °C (a) before and (b) after

thermally cycling the specimen and stage twice between -50 °C and 150 °C.

E

a.

2.0

1.0

0.0

-1.0

i

1 r

• T - -50jO *C • T • 5Z0 *C A T • -M 'C • T - 100.5 'C • T - -0.4 *C 4 T • 150J "C

2.0

-2.0

1 1 1 r • T -50.0 *C T - 2«J *C • T " 100.5 *C *T- -SJ 'C * T - 5Z0 *C «!• 150J "C T -CA *C

100 200 300 400

POSITION, Mm

Figure 6. Displacement versus position

plots of the t/-field data on the CA film.

100 200 300 400

POSITION. Mm

Figure 7. Displacement versus position

plots of the v-field data on the CA film. 87
A8

Mechanical Deformation in Conductive Adhesives as Measured with ElectronBeam Moire

by Drexler and Berger (199?)

88
Mechanical Deformation in Conductive Adhesives as Measured with

Electron-Beam Moir£

E. S. Drexler J. R. Berger

Materials Reliability Division Division of Engineering

National Institute of Standards and Technology Colorado School of Mines

Boulder, CO 80303 Golden, CO 80401

Abstract

Two forms (paste and film) of isotropically conductive adhesives (CAs) were mechanically loaded in shear mode.

The specimens were instrumented with crossed-line gratings so that normal and shear displacements could be measured.

The CA paste specimen failed outside the observed region at a stress 28% below the manufacturer's predicted value. In

the observed region there were no normal strains, only shear strains restricted to the CA In the film specimen the

conducting particles began breaking away from the matrix epoxy at very low loads. However, the specimen continued

carrying the additional loading increments until the load was transferred to the adjacent material.

Introduction

The electronics packaging industry routinely uses conductive adhesives (CAs) for packaging applications, most

commonly for die attachment, and is considering its use for a number of other applications. When industry is evaluating

CAs for different applications, the tests they use typically involve assessment of the electrical properties under various

environmental conditions. In addition to measuring the contact resistance, some laboratories also measure certain

mechanical properties of the CA joint with respect to the temperature and/or temperature/humidity exposure. Most of

these laboratories assess the adhesion strength of an attached component through use of tests designed to provide a

comparative value for the shear strength (Gilleo, 1993; Hogerton, et al., 1990; Honored et al., 1992; Keusseyan and

Dilday, 1993; Kreutter, et al., 1992; Li and Morris, 1995; Liu and Rorgren, 1993; Liu, et al., 1995; Nguyen, et al., 1993;

Contribution of the U.S. National Institute of Standards and Technology, not subject to copyright in the U.S.A.

89
Rusanen and Lenkkeri, 1995; Stam, et al., 1995).

In this study the mechanical behavior of CAs will be characterized through the use of the electron-beam (e-beam)

moire technique (Dally and Read, 1993; Read and Dally, 1996). This technique is ideal for marry electronic packaging

situations where features are small and one is interested in knowing the influence of one material on the adjacent material.

E-beam moire is a fully quantifiable technique with which one can measure displacements on the order of tens of

nanometers. The visual nature of the technique not only allows one to measure the u-field and v-field displacements from

the area of interest, but upon loading the specimen one can also see developing regions of larger strains—potential failure

sites.

Materials Evaluated and Specimen Preparation

Tests presented here were conducted on two different materials (see Drexler, 1996 for details on the sample

preparation). Both materials were commercially available isotropicalfy conductive adhesives, one a paste and the other a

film. The CAs were stored in a standard freezer for three months, then moved to an ultra-low-temperature freezer set at

-^5°C.

The specimen geometry was a double-lap-shear specimen as shown in Fig. 1. The copper pieces were pickled in a

50/50 solution of nitric acid (70.6%) and deionized water to remove the oxide layer. The larger pieces sat in the acid

solution for 90 s, and the thinner pieces for 20 s. The pieces were rinsed in deionized water, put in a methanol ultrasonic

bath for 30 s, then assembled as shown in Fig. 1.

The film specimen was prepared first The film was first applied to both 12.7 x 12.7-mm pieces, preheated to 50 °C

on a hot plate, then attached to the 15.9 x 12.7-mm pieces. A 140-kPa strain-gage clamp applied pressure during cure.

The manufacturer recommends preheating the bonding surface to 45 °C and curing with continuous pressure of at least

35-70 kPa. The specimen was cured for 30 min, as specified by the manufacturer of the film, in a strain-gage oven with

the temperature set to 150 °C. At the end of this period the specimen was removed from the oven and allowed to cool to

room temperature before the clamp was removed.

90
A second specimen was fabricated with the paste CA The CA was stroked with a wooden stick on the surface to be

bonded. Teflon tape was wrapped around the 15.9 x 12.7-mm pieces to prevent a butt joint from forming. The specimen

was assembled and cured in the oven set to 150 °C. As specified by the manufacturer, no clamping pressure was used.

The specimen was allowed to cure for 6 min because after the 3 min recommended by the manufacturer it did not appear

completely set The specimen was then removed from the oven and allowed to cool to room temperature.

The day after both specimens were cured, each was cut into approximate thirds, so that each piece was 3-4-mm thick.

Each piece was ground flat on both sides using SiC paper in several steps from 120 to 1200 grit. One side of each

specimen was then polished with 6-um diamond spray on a napless synthetic silk polishing cloth. One of the three pieces

from each type of CA was used to evaluate the CAs thermally (Drexler and Berger, 1997), the second piece was used for

the mechanical deformation tests discussed here, and the third piece was held in reserve.

To provide adequate strength to the copper/CA specimens with respect to the anticipated shear strength of the CA,

small pieces (12.2 x 3 x 1 mm) of 316LN stainless steel were glued onto the copper sheet using a low-shrinkage epoxy

that cured at room temperature. During curing they were held together with binder clips, which exerted an indeterminate

pressure. The polishing process as described above was then repeated.

Cross-gratings were prepared on each of the specimens on a different day. Immediately before writing the gratings,

each specimen received a final polish with 1-fjm diamond spray on synthetic silk polishing cloth. A thin coat of 2% poly

methyl methacrylate (PMMA) was spun at 2250 rpm onto the surface of the specimen. The specimen was cured on a hot

plate fori h at 170 °C.

E-beam Lithography

The lithography was performed in a scanning electron microscope (SEM). A computer program controlled the

location and dwell time of the electron beam, generating regularly spaced lines. Lines are actually a series of closely

spaced, overlapping spots. To obtain cross-line gratings the lines are first written in one orientation, then the specimen is

rotated 90°, and the lithographic process is repeated. This rotation takes place electronically rather than physically, the xinput is sent to the .y-output, and vice versa, thereby changing the orientation of the beam. The effect is to rotate the

specimen clockwise 90°.

91
To write the patterns, the microscope was set to 20 kV of accelerating voltage. An aperture of 50 pm and a probe

current of SO pA were chosen to focus the beam as tightly as possible. The astigmatism, centering of the aperture,

working distance, and focus were also carefully adjusted and tuned in order to obtain as small a spot size as possible. A

small spot size for the electron beam is necessary to obtain line pitches of 90-225 run.

When all the patterns on a given specimen were completed, the specimen was removed from the SEM for

development During exposure the electron beam breaks up the polymer chains of the PMMA, but development of the

specimen is required to wash those broken polymer chains away. The developer used was a 3:1 solution of isopropanol

and methyl isobutyl ketone (MEBK). Following development, a thin (<10-nm) coating of gold-palladium (AuPd) was

deposited over the polymer using a sputter coater to provide a conductive surface. The specimen remains cool throughout

the sputtering process.

Mechanical Tests

The mechanical tests were conducted on a tension/compression stage situated within the vacuum chamber of the SEM The stage has a motor-driven screw-type actuator with a load capacity of 4450 N. It is capable of only uniaxial

compression and tension with the present hardware. A universal joint used to drive the stage, and the wires that monitor

the load and displacement have access into the SEM chamber through a plate that replaces the side port

The gage length of the specimen is limited to 15 mm. The specimen is installed on the stage with wedge grips, each

end of which is tightened with two bolts. The motor speed is regulated with a pot-type knob that sets the rate between

and 100% of 330 rpm. The stage showed no discernable movement below 10%, however. Most of the loadings were

conducted at 15%, taking less than 1 min to load 90 N. The load is indicated by a digital display on the controller for the

stage.

Both mechanical tests were performed on the same day. The patterns had crossed-line gratings with a pitch of 350

nm, so displacement data were available from both the and 90° orientations. The rotation of the scanning electron beam

to interrogate both directions of displacement was performed using a controller designed specifically for precise 90°

rotations. The gratings were located on the specimens near the inside free surface of the larger copper block. Their

92
locations in Fig. 1 are indicated by A for the paste specimen and B for the film specimen. The specimen was loaded in

tension with the loading axis parallel to the long dimension of the specimen.

The specimen containing the CA paste was tested first The moire* effect was observed at an accelerating voltage of 7

kV, a working distance of 18 mm, a probe current of 15 pA, and a magnification of 550x. The filament was saturated 130

min before the first images were acquired. Images from both orientations were accumulated at nominal loads of to 600

N in 80-N increments. At the end of each load increment, images were acquired after the SEM image had stabilized. A

final set of images was also acquired at N after the specimen was unloaded. The images were exported onto a computer

where the fringe centers were digitally traced for later analysis.

The specimen containing the CA film was tested second. The working distance for this test was 17 mm The

accelerating voltage was 7 kV, the magnification was 550x, and, at the start of the test, the probe current was IS pA. The

probe current was reset to 18 pA later in the test because fringe contrast was poor in the CA. Due to time constraints, the

filament was saturated for only 25 min before the first images were acquired. Images were accumulated from both

orientations at nominal loads of to 540 N in 80-N increments. The images were again exported to a computer where the

fringe centers from each image were digitally traced.

Analysis of the Moire Fields

The fringe-tracing program mentioned previously allows one to assign a locus of points that define the center of the

fringe. This fringe center is also a contour of constant displacement on the surface of the specimen. The effect of the

crossed-line grating is analogous to having a full-view and 90° displacement gage. For the tests described here, the

pitch of the specimen grating was 350 nm, resolvable to 1/10 of a fringe, translating to 35 nm of displacement Thus,

strains calculated from data obtained with this technique are fully quantitative.

Once the fringe centers were identified, analysis was completed in the manner described by Parks (1987). The fringe

centers were identified on the u-field (0°) and v-field (90°) images. Line profiles were chosen running perpendicular and

parallel to the orientation of the reference grating on each image. Three line profiles were chosen perpendicular to the

orientation of the reference grating in each of the u-field and v-field images, and one trace was chosen at the midpoint of

5

93
the images from the u-field and v-field images perpendicular to the orientation of the reference grating. For the w-field

images the three line profiles were chosen so that one was through the CA and the other two were approximately

equidistant from the CA, one in the 9.5-mm copper and the other in the 0.4-mm copper.

The distance along the chosen trace was graphed versus the measured fringe order. The fringe order was then

converted into displacement by multiplying by the pitch of the reference grating. Since with e-beam moire the initial

fringe field is rarely null, an image was collected before applying the first load increment The slopes obtained from the

line profiles of the initial images were then subtracted from the data obtained from subsequent images obtained under

load. Strain data were then calculated from these plots of relative displacement versus position along the trace. The

slopes of the curves, duldx and dv/dy, from the line profiles perpendicular to the orientation of the reference grating in the

u-field and v-field images, respectively, are the normal strains. The engineering shear strain, yv, is the sum of the slopes

from the curves obtained parallel to the orientation of the reference grating, duldy + dvldx.

Results: Conductive Adhesive Paste

The shear strength of the CA paste was evaluated using the modified lap-shear specimen shown in Fig. 1. The

specimen was loaded until catastrophic failure occurred. The failure took place outside the field of view of the pattern

studied. Failure was anticipated by rapid movement of the grating lines that were being observed, followed by the load

dropping to N. The fringe fields exhibited very little activity either locally or regionally while the loading was applied.

The fringe density did not change significantly, however, the tilt of the fringes through the CA did change as the test

progressed, indicating a change in the shear strain in the CA.

An error was made during testing when the microscope was refocused after the first loading was applied. Although

the fringe field did not appear significantly different, it became apparent during analysis that the images acquired at N

were not appropriate to use as the initial condition for the remaining test Berger, et al. (1997) found in previous studies

that the initial fringe field was dependent on all SEM-controlled parameters such as focus, working distance, and

accelerating voltage. Since it was not known whether plastic deformation occurred in the area of the pattern studied, the

6

94
final N image also could not be reliably used for the initial condition. We therefore used the images from the first load

increment (82 N) for the initial condition.

Fig. 2 shows the curves for displacement versus position for the line trace located in the CA in the w-field images.

These curves are representative of the curves obtained from each of the traces in the copper. All the curves remain

essentially horizontal, indicating that there was no normal strain, except for the curve acquired at 260 N. That curve

displays what seems to be significant compression for all three line profiles as the top of the pattern is neared. This

behavior must be considered anomalous for the following reasons. Firstly, because of the specimen geometry there is no

location where both the 9.5-mm copper and the 0.4-mm copper will simultaneously be in compression under tensile

loading given a line drawn perpendicular to the loading direction. Secondly, the pattern itself is located near the midpoint of the specimen. This is the region where the 0.4-mm copper is subject to the greatest amount of tension. Finally,

images acquired at loads above and below 260 N do not display similar behavior, and the loading was smooth and

continuous, showing no jumps or drops indicative of slip occurring outside the field of view. This anomalous behavior

was probably the result of the specimen or stage not being completely stabilized after the loading step was completed and

the image was collected.

Since the curves for the other load increments are horizontal, no normal strain is detectable for any load. It should be

noted that no normal strains were discernable in the region occupied by the grating including at the load increment prior

to catastrophic failure.

Fig. 3, showing the v-field, displacement-versus-position curves, displays similar habitude to that of the u-field

images. Again, the center line trace is representative of those obtained from the top and bottom of the pattern. All the

curves are essentially horizontal except for the post-failure 0-N curve. The implication of the horizontal curves is that the

material did not strain normally at any load increment all the way to nearly 600 N from its initial load of 82 N.

The post-failure 0-N curve exhibits a slightly negative slope. There are two possible sources for this: this slope

difference could be the difference one would have observed if an initial image with 0-N load had been used, or the failure

could have caused the specimen to move slightly out-of-plane, changing the focal plane from the surface of the specimen

causing the fringe field to alter.

The reason why no normal strains are observed in the u- and v-fields becomes evident when the u-field displacement

versus y position is studied. This information is displayed in Fig. 4. This figure shows that all the deformation was

7

95
carried in the CA—each additional loading increment results in the increased magnitude ofthe slope of the corresponding

curve. In this set of collected images dv/dx was insignificant, so yv = duldy. Fig. 5 shows the shear stress versus shear

strain for this data The elastic region is difficult to establish without a data point at N and with so few data points.

However, the general shape of the stress-strain curve is discernable.

Results: Conductive Adhesive Film

The mechanical loading of the film specimen showed many of the same effects as those observed in the paste

mechanical test; insignificant normal strains were observed in the a-field or v-field images. However very little load was

applied to the specimen (246 N) before the fringes were no longer traceable in the CA (Fig. 6a). Already at this load the

fringes in the 0.4-mm and the 9.5-mm copper were no longer parallel (see Fig. 6b). This indicates that significant

deformation has occurred in the CA The specimen continued to carry the load without catastrophic failure and the

images were collected in approximately 8S-N increments to nearly 600 N. At this point the specimen would no longer

carry the load, but was yielding in the 0.4-mm copper (see Fig. 7). Data were not available from within the CA from

loads of 246 N and greater, but the duldy data from the first three load increments (Fig. 8a) suggest that this component

the shear strain increased with each load increment The dv/dx data (Fig. 8b) from the 0.4-mm copper in comparison,

show that the shear strains are barely changing with each load increment until the S37-N load is achieved. The slope

increases dramatically at that load, with evidence pointing to greater shear strains as the center of the specimen is

approached.

Discussion and Conclusions

The experiments performed on the two forms of isotropicalfy conductive adhesives yielded useful information on the

conduct of these materials under these testing conditions. The mechanical tests revealed some fundamental behavioral

differences between the conductive adhesive paste and the film. The CA paste specimen carried the load to failure with

96
virtually no deformation to the copper and with measurable amounts of shear within the CA. Inspection of the CA in the

fractured region showed deformation within the silver particles, but good continuity at the epoxy/sirver interface. The

specimen failed at 8.4 (±0.1) MPa though the manufacturer predicted a failure shear stress of 11.7 MPa. The only

difference between the manufacturer's specification and the test described here was that the manufacturer's shear strength

was based on an aluminum-to-aluminum specimen.

A 28% drop in expected shear strength leaves one speculating on possible explanations. The materials were stored

for three months in a standard freezer before being transferred to an ultra-low-temperature freezer. The manufacturer

specifies a storage life of six months at 10 °C, and one year at -40 °C for the CA paste. The material should not have

degraded during the nine months that it was in storage. The mechanical paste specimen was prepared and instrumented

with gratings four times, essentially thermally cycling it four times before any testing was conducted. A thermal fatigue

test may indicate whether thermal cycling affects the shear strength to this degree.

The mechanical test on the film specimen showed evidence of failure at such low loads that one must wonder whether

the film degraded during storage. The manufacturer suggests storing the film at 5 °C with shelf life of six months. (The

manufacturer in 1995 updated the acceptable storage conditions to include one year at -40 °C. It is not clear if the

chemistry changed during that time.) As with the paste the fHm was stored for a total of nine months before the specimen

was made, three months in a standard freezer and an additional six months in an ultra-low—temperature freezer.

The film specimen showed curiously contrasting behavior during the test Although damage occurred in the CA at

low load levels, catastrophic failure of the CA never occurred in this test The CA continued yielding until the strain,

carried entirely by the CA, was sufficient to induce yielding in the copper, and once the copper started yielding and the CA no longer carried the load, the test was over. The manufacturer predicted a shear strength of 17.2 MPa for an

aluminum-to-aluminum specimen. And although loads never approached this level, the CA never in fact actually failed

mechanically.

Though the CA film never actually failed, damage had occurred. Evaluating the CA for use as a replacement for

solder requires not only that it have mechanical strength, but that it also maintains a conducting path during that loading

Although this specimen was not designed to evaluate both situations, Fig. 9 shows that the conducting path, at least

locally, has been compromised. The silver particle in the center of the image has broken away from the epoxy so that it is

9

97
now isolated from the copper. As a result, at this location, a conducting path no longer exists between the copper and the

conducting silver particles.

Acknowledgments

JRB acknowledges the support of the National Science Foundation and the National Institute of Standards and

Technology under the joint NSF-NIST program CMS-9522147.

References

Berger, J. R, Drexler, E. S., and Read, D. T., 1997, "Error Analysis and Thermal Expansion Measurement Using

Electron-Beam Moire\" submitted to Experimental Mechanics.

Dairy, J. W., and Read, D. T., 1993, "Electron-Beam Moire," Experimental Mechanics, Vol. 33, pp. 270-277.

Drexler, E. S., 1996, "Thermal and Mechanical Deformation Measurements of Conductive Adhesives Using

Electron-Beam Moire\" MS. Thesis, Department of Materials Science, Colorado School of Mines, CO, 116 p.

Drexler, E. S., and Berger, J. R, 1997, "Election-Beam Moire Study of Local Deformation in Conductive

Adhesives," Symposium Proceedings ofthe Fall 1996 Meeting ofthe Materials Research Society: Electronic Packaging

Materials Science IX, Vol. 445, S. K. Groothuis, P. S. Ho, K_ Ishida, and T. Wu, eds, Materials Research Society,

Pittsburgh, PA, pp. 75-80.

Gilleo, K., 1993, "Intrinsically clean polymer bonding: What are the trade-offs? " Proceedings ofthe Surface Mount

International Conference and Exposition, pp. 655-661.

Hogerton, P. B., Carlson, K. E., HalL J. B., Krause, L. J., and Tingerthal, J. M, 1990, "An evaluation of a heatbondable, anisotropicalfy-conductrve adhesive as an interconnection medium for flexible printed circuitry," Proceedings

of the IEPS Technical Conference, pp. 1026-1033, 1990.

Honored J. P., Rubin, H. D., and Zierold, M K., 1992, "Reliability testing of conductive adhesives," Proceedings of

the NEPCON West Technical Program, Vol. 3, pp. 1372-1380.

10

98
Keusseyan, R L., and Dilday, J. L., 1993, "Electric contact phenomena in conductive adhesive connections,"

Proceedings ofthe Surface Mount International Conference and Exposition, pp. 567-571.

Kreutter, N. P., Grove, B. K., Hogerton, P. B., and Jensen, C. R., 1992, "Effective polymer adhesives for

interconnect," Proceedings ofthe 7th Electronic Materials and Processing Congress, pp. 249-256.

Li, L., and Morris, J. E., 1995, "Structure and selection models for anisotropic conductive adhesive films," Journal of

Electronic Manufacturing, Vol. 5, pp. 9-17.

Liu, J., and Rorgren, R, 1993, "Joining of displays using thermosetting anisotropically conductive adhesives,"

Journal ofElectronics Manufacturing, Vol. 3, pp. 205-214.

Liu, J., Ljungkrona, L., and Lai, Z., 1995, "Development of conductive adhesive joining for surface-mount electronics

manufacturing," IEEE Transactions on Components, Packaging, and Manufacturing Technology—Part B, Vol. 18, pp.

313-319.

Nguyen, G. P., Williams, J. R, and Gibson, F. W., 1993, "Conductive adhesives," Circuits Assembly, Vol. 4, pp. 36-

38, and 41.

Parks, V J., 1987, "Geometric moire," in Handbook on Experimental Mechanics, A. S. Kobayashi, ed., Prentice HalL

Englewood Cliffs, NJ, pp. 282-3 13.

Read, D. T., and Dally, J. W., 1996, "Theory of electron-beam moire," Journal ofResearch ofthe National Institute

ofStandards and Technology, Vol. 101, pp. 47-61.

Rusanen, O., and Lenkkeri, J., 1995, "Reliability issues of replacing solder with conductive adhesives in power

modules," IEEE Transactions on Components, Packaging, andManufacturing Technology—Part B, Vol. 18, pp. 320-325.

Stam, F., O'Grady, P., and Barrett, J., 1995, "Characterisation and reliability study of anisotropic conductive

adhesives for fine pitch package assembly," Journal ofElectronics Manufacturing, VoL 5, pp. 1-8.

11

99
List of Figs.

Fig. 1. Specimen geometry for the specimens tested in this study. A indicates the pattern location for the paste test, and B

the location for the film test

Fig. 2. Normal displacement versus position (x) for the u-field taken from the center of the pattern (the CA) from the

specimen fabricated with the CA paste.

Fig. 3. Normal displacement versus position (y) for the v-field taken from the center of the partem from the specimen

fabricated with the CA paste.

Fig. 4. Shear displacement versus position du/dy for the specimen fabricated with the CA paste.

Fig. 5. Shear stress versus shear strain for the specimen fabricated with the CA paste.

Fig. 6. Images at SSOx of the (a) u-field and (b) v-field moire fringe fields at a load of 246 N on the specimen fabricated

with the CA film.

Fig. 7. F-field image at 550x of the moire fringe field at a load of 537 N on the specimen fabricated with the CA film

Fig. 8. Shear (a) du/dy data from the CA for the first three load increments, and (b) dvldx data from the 0.4-mm-thick

copper from the specimen fabricated with CA the film

Fig. 9. Image at 6500x of the CA film specimen at a load of 328 N. (The ubiquitous array of dots is the crossed-line

grating.)

12

100
U

MlH

><

101
CM

o> to *- z (VI r- O ^ Ifl <D O

II II II II Q_ Q_ Q_ Q_

+ A #

<*> 00 O "*

t- <D <D Tf

CO i— CM CO

II II II II Q. Q. CL Q. < • *

,1'

_L X

o s-l 3

10 £30 •H

o

o

o

CO

o

Q.

q

csi

o

o

o

T

q

c\i

l

uurf

f

n

102
CO

3

00

•H

fa

q

cvj

y +

+

•' «>

-I

-i

1

O

o

r*- "3- o> 2:

CsJ i- OJ ^ lO lO o

II II II II Q_ 0- Q_ Q.

+ T «

o

in

o

o

o

LO

C7)

o

a.

00 oo o> CO

t- <o m ^t

00 i- c\j CO

II II u II Q. Q_ Cl O.

< • •¥

I o

T

q

c\i

I

uirf 'a

103
u

•H

P4

00 00 O ^t (O »" 2 r- CO <D "^ i- O

CO i- CM co in <D O

II II II II II II II £L Q_ Q_ a, Q- Q_ CL < • + A •

o

o

CM

O

ID

OO

O

O

in

q

c\i

o

o

o

T

ujrf

f

n

104
u

En in

o

o

E

E

o

o

If)

o

o

o

<

CC

\-

tn

rr

<

LLI

c/>

o

o

in q in

(BdlN) x *SS3dlS UV3HS

105
- .-" -. * -• i ,;;> ."'..; " .'. '- ':•*.; :

: --.» **?-

i -.~N.-;- 1 <-' .^.,-iv. , j-ti( TM

. Nf. -' ' - - ,:?'-' ^ i"' V >- - '-rtji* -V ;

-'' -^" * -'\ .':, . *

,i

•-.Y?*:. ft «i*

J! ' "'' 1 i.i* " t - -' -—' -' ** •"«! •' - -. J ;r r/ -

- t >; - - - " .' -- * * J* -J ;•<'*. *: I--:* ' ''it T-*«

u n -.- ; • v- £»»JrK . :•* '- ' -*.. > .v *• if *;

; ; -<•-,<-* £ * 4, »'-:? • f*#w •-**

.^\ -7.=;- -.^ . » . ; .'-^" ' ""

'

' ~r- * ^ •*jNr

' 5 ** " ;^ >••> '*";;.£? &&\ 2 -

: X • . ^ ,•"- i^ ?'*"'-< ~-5-"'

- -. . -.-i L^ X.V '^ '.if'/-;-**!!

• •> .: # > -•*-*?•* * '' :

"•

-• - i tfe%i>.

. ». '-; •\ I --,-• - ri *&kri* <*

.,'' ^-< *-s--i-fjy f - r» - -_._ .

-.

• ,-'' - ?* ift; -: ?*'<-•- ei w *| =

r —* * r *** t : - t

' vr a -," i S" -

'» ff-5

~ -.'.' ~.*-""-i'^.~'*.; >-* v'i5 * • ..^< i-' ^ «

... '.*" »:':*; r " ^

" '-<'- W«^. -

J.,v*T--V>"***i.»., . ,

'.* _ "<: V ;r

': -..'/''''' '^^-•*^*'t *-";ii *^¥s*'».*

»i.».U*,j, ., ... ,. , . -,. - '-Si

- ?r' - ;->•" *-.-^-:-

;'-.-?- *•' -

""".' *- "> c- .

'."*"» ;' . ~— '- ,

~> T-'

i*'

v

,' TV^'J_*57

a^ ik&j ft&la fcftai^ VS* a***W s-S-s?^(^* AJjr^

Figure 6

106
Figure 7

107
1.5

1.0

0.5

0.0 -

-0.5

P - N

a P = 83.6 N • P = 163 N

50 75 100

Y POSITION jjm

1.0

0.0

-1.0

r 1 rTM

B

P = N

a P - 83.2 N • P - 163 N

P - 246 N

* P = 330 N + P - 419 N

4 P - 503 N

P = 537 N

• • 50 100 150 200

X POSITION, fim

Figure 8

108
* •/^ '^n^ 5 ..-% .*> *

*"• ':-. • * < a ^ t

*•- '> s- >-" ' * ;loi fflra

>.> 3 - J - itt *-0« -i. * 3 JOO«, 2 . - c .3

—.. . . > ^> > 9

'

•Aft- • '"5 ?-?<-» •»—?-»>

i|i >' . '-€:"

TM-i >_ •" -.->

;i v-'..._

Figure 9

109
A9

Error Analysis and Thermal Expansion Measurement with Electron-Beam Moire

byBerger, etal. (199?)

no
Error Analysis and Thermal Expansion Measurement with Electronbeam Moire*

J. R. Berger1 , E. S. Drexler2

, and D. T. Read2

'Division of Engineering

Colorado School of Mines

Golden, Colorado 80401

2 Materials Reliability Division

National Institute of Standards and Technology

Boulder, Colorado 80303

Abstract

We present a study of errors incurred when using the experimental technique of

electron-beam moire. We find that there are two sources of error: error manifested as an apparent magnification drift and error due to fringe tracing. The

error due to fringe tracing is nearly negligible in comparison to the error due to magnification drift. We demonstrate the usefulness of the error estimate by

investigating the thermal expansion of commercially pure copper. We find that our average result for the coefficient of thermal expansion is within 1.8% of

handbook values for this material with a possible error due to apparent

magnification drift of 9%.

Introduction

The experimental technique of electron-beam moire is a relatively new member to the family of moire

methods. Based on the initial work of Kishimoto, et al. [1], Dally and Read [2, 3] developed the

method to its present, mature state. The method relies extensively on the use of a scanning electron

microscope (SEM) for both production of the specimen gratings and formation of a reference grating.

Contribution of the National Institute of Standards and Technology, not subject to copyright

111
The specimen gratings are produced using electron-beam (e-beam) lithography. Details of producing

the specimen gratings are given in [2] where the importance of strict control over the process variables

is emphasized.

The reference grating for e-beam moire is produced by the raster scanning motion of the electron beam

in the vacuum chamber of the SEM. As such, it is necessary to perform all tests within the SEM. The

raster scanning of the electron beam is very similar to the scanning video moire technique developed

by Morimoto and Hayashi [4] for low-frequency specimen gratings. Unlike the traditional geometric

[5] or interferometric [6] moire methods, e-beam moire allows one to easily vary the effective pitch of

the reference grating by varying the beam controls on a typical SEM. Read and Dally [3] developed a

model to interpret fringe fields obtained as the electron-beam diameter, the pitch of the raster scan, and

the angle between the scan lines and grating lines were varied.

Our concern here is a determination of factors which may influence a measurement made with e-beam

moire at "fixed" settings on the SEM. This investigation was motivated by an attempt at

benchmarking the method through a determination of the coefficient of thermal expansion in a bulk

copper specimen. Initial measurements indicated that the fringe pattern appeared to change over time.

This led us to a parametric study of the influence of instrument drift resulting in an apparent change in

magnification and fringe tracing errors on the quantitative measurement of displacements.

112
Magnification Errors

Before studying possible error sources with e-beam moire, it is instructive to identify the key

parameters in formation of the reference grating. We are considering a scenario where the specimen

grating has been prepared and the specimen placed within the vacuum chamber of the SEM. We view

the moire fringe pattern with no thermal or mechanical load on the specimen. As noted in previous

studies [2, 3] it is usually not possible to obtain an ideal null field with e-beam moire since the

magnification is adjusted in discrete increments. Under these conditions, variations in the observed

fringe field must be due to variations in those parameters which contribute to the formation of the

reference grating. We first consider those factors which affect the pitch of the reference grating. As

described in [2, 3], the pitch of the reference grating for e-beam moire can be calculated as

S_

MR P*=-rz:> 0)

where S is the nominal image size, M is the magnification of the SEM, and R is the number of raster

scan lines. The nominal image size, S, and the number of raster scan lines, R, are fixed for a given

SEM during a given experiment. Therefore, according to eq (1), only a change in magnification over

time can contribute to an apparent change in the pitch of the reference grating. The apparent change in

magnification may be due to a number of instrument-related issues (accelerating voltage stability,

stability of the electronic magnification unit, etc.). For this paper, we will treat all of these sources as

an apparent change in magnification. Note that small changes in the magnification can contribute

strongly to the apparent pitch of the reference grating since they are inversely proportional to each

other. Read and Dally noted in [3] that the value of M must be precisely known for proper

113
interpretation of the moire fringe fields. They further noted that the apparent magnification from the

SEM character display differed from actual measured magnifications by approximately 5% for the

SEM used in their investigations. No time variation of Mwas considered by the authors.

If some variation occurs in the magnification of the SEM, we can write the pitch of the reference

grating as

S

Prr/ ~(M+AM)R ' (2)

where AM is the variation in the magnification. We consider the case of uniform axial strain on a

specimen and calculate the error in the strain measurement due to the magnification variation. Relative

to a null condition, Read and Dally [3] calculated the tensile strain in terms of reference and specimen

grating frequencies as

\U + f,)

Including a variation in magnification from eq (2) which effects both f, and fnf , eq (3) rewritten in

terms of grating pitches is

£ = PEMR_

i +

PI

RAM

S S

where the last term represents the error term. It is helpful to consider the total strain as an apparent

strain,

^ odd ~ E true

"*" S AM » \^>

114
where

e,n,e =^r-"I, (6)

pgRM

pvRAM

£ m=

s

• (7)

For purposes of this analysis, we can further simplify eq (7) by noting that, for small strains,

P* R 1 ££- ~ —• (8) S M W

Equation (7) can then be written as

£ - s

"F- (9)

For a specific example, consider a specimen grating with pg = 1 80 nm observed in the SEM at a

nominal magnification of 1100X. From eq (1) we obtain a nominal reference grating pitch ofpn/ =

170.5 nm for our SEM where S = 90 mm and R = 480 lines. Assume we subject the specimen to a

uniform strain of 1200 us. From eq (3), assuming no change in the magnification, our specimen

grating then has a pitch ofpg = 170.7 nm. At a value of AM= 0.20X (with a nominal magnification of

1100X) the additional strain obtained from eq (9) is 182 us. The error in the strain measurement

would then be 15%, a significant error. To maintain less than 5% error in the strain measurement

would require control on the magnification such that AM < 0.07X.

The above analysis highlights the necessity of strict control on magnification for quantitative

measurements with e-beam moire. As noted by Read and Dally [2], the nominal magnification must be

accurately known for proper interpretation of the moire field. It is now clear that not only must the

nominal magnification be well known but the control on factors influencing the magnification must be

115
exceptionally stable. We have treated all time-dependent errors as magnification errors for the reasons

outlined at the beginning of this section. It is important to note that this error is manifested as an

apparent drift in the magnification. Any drift in the instrument such as working distance, accelerating

voltage, electronic magnification control, or other instrument-related issues can produce an apparent

drift in the magnification. Our goal here is to study the influence of these apparent magnification drifts

and not to isolate the precise cause for a given test on our particular instrument.

Studies ofthe Temporal Variation ofthe Fringe Fields

A series of experiments were performed in order to identify and quantify factors which varied with

time in a typical e-beam moire experiment. For each of the experiments, a single homogeneous,

polycrystalline copper specimen (99.999% pure copper) was used. The specimen was disk-shaped

with a diameter of 5 mm and a thickness of 2 mm. The specimen was instrumented with a line grating

located near the center of the specimen with p = 1 80 nm. The specimen grating was etched into the

surface of the copper. The specimen was placed in the SEM and all tests were performed at a

magnification setting of 1 100X. This is the magnification setting associated with the near null-field for

the specimen grating frequency used in this experiment. The temperature of the testing stage was

monitored during the acquisition of images. The maximum temperature variation observed in all of

our tests was ± 0.6 °C.

116
For our initial test, moire fringe fields were obtained at fixed settings on the SEM over a period of 240

minutes at 30 minute intervals. For the particular test analyzed here we had an initial field of

approximately 4 fringes. We have also observed that the number of fringes in the initial field may vary

for a given specimen grating due to slight changes in either working distance or focus as the SEM is set

up for a particular experiment.

Each acquired image was analyzed to obtain the average number of moire fringes across the image.

The analysis was based on a fringe analysis program developed at NIST. The program requires the

user to specify points located along a fringe center. The software then performs a spline-fit to the data.

Obviously some statistical variation can occur due to errors in locating the fringe center or from the use

of different subsets of data from the same moire field. Similar errors were noted by Barker, et al. [8] in

analyzing moire data collected near crack tips. We address the variation in the average number of

fringes due to these errors below.

The average number of fringes across each acquired image as a function of time is shown in Fig. 1. A

clear variation in the average number of fringes occurs over time. Note that the first data point shows

the greatest variation from the mean value. This was typical of all the experiments we performed. For

the data shown in the figure, we obtain a mean value of 4.34 fringes with a standard deviation of 0.14

fringes. Our field of observation at 1 100X is 81.8 urn which yields a mean moire fringe frequency of

0.0530 fringes/urn with a standard deviation of 0.0017 fringes/urn. Assuming this variation in the

fringe field is strictly due to factors influencing the magnification of the SEM, we can calculate from

the apparent change in magnification required to produce one standard deviation. We first calculate

117
from eqs (1) and (2) the nominal magnification required to produce the observed moire field frequency.

We obtain a nominal magnification of M= 1056X. The magnification was set on the SEM at 1 100X,

our calculated value is within the usual 5% error allowed in the magnification calibration. To produce

one standard deviation in the fringe field we predict a value of AM = 0.32X for the data shown in Fig.

As noted above we usually observed the greatest variation in the fringe field with the first data point.

This suggests that the instrument has not yet stabilized and experiments should only be performed after

waiting a period of time. If we only consider the data points obtained after 30 minutes had elapsed we

obtain a mean value of 4.30 fringes with a standard deviation of 0.07. The mean value is comparable

to that obtained previously with all data points. Therefore, our nominal magnification is approximately

the same {M= 1056X). We note that the standard deviation has decreased from 0.14 to 0.07. We

obtain a value of AM= 0.16 required to produce one standard deviation in the fringe field. This is

perhaps a more realistic estimate for expected variations in the apparent magnification.

The probe current in the SEM was initially suspected of producing apparent variations in the fringe

field. This was based on recordings of probe current over time as each experiment was performed. To

investigate the likelihood of probe current causing variations in the fringe field we performed a series

of tests where the probe current was varied and images acquired. The average number of fringes

plotted as a function of probe current is shown in Fig. 2. For this particular data set, the mean number

of fringes is 4.95 with a standard deviation of 0.10. In comparison with Fig. 1 it is clear that the

variation we observed over time is approximately the same as the variation observed over the time we

118
varied the probe current. Note in Fig. 2 that the probe current was varied from approximately pA to

-100 pA. The observed variation in probe current during tests similar to that which provided the data

in Fig. 1 was only ±0.6 pA. We therefore concluded that the probe current was not responsible for

the observed temporal variation in the fringe field.

Finally, we considered the variation in the average number of fringes due to the fringe tracing

procedure. To investigate this we acquired an image and performed six independent tracings of the

fringe centers with the fringe analysis software used in our study. Of concern here was variation in the

location of the center of the fringes and the effect of the number of points along each fringe center in

the spline-fit to the data. The results are shown in Fig. 3 for the average number of fringes across the

entire image for each of our tracings. As shown in the figure, a variation of approximately ± 0.05

fringes occurs with a standard deviation of 0.02 fringes This is far below the observed variation over

time shown in Fig. 1 . We conclude that fringe tracing is not responsible for the observed variation in

the fringe field.

Coefficient of Thermal Expansionfor Copper

To provide a benchmark for the e-beam moire method in thermal stress studies we performed two

experiments to determine the coefficient of thermal expansion, a, of copper. The first experiment used

a copper specimen with a geometry identical to that of the specimen previously described but with a

119
line grating of pitch 900 nm. The second experiment was performed using the same specimen used for

the studies of the temporal variation of the fringe field. Both specimens had line gratings which were

etched into the surface of the specimen to avoid high temperature deterioration of the PMMA coating

normally used for producing gratings with e-beam lithography. Both specimens were tested on a

thermal stage in the SEM. The heating/cooling stage fits securely on the shuttle base within the SEM

chamber. The resistive heating unit has a temperature range to 400 °C. The stage is cooled by

circulating liquid nitrogen chilled nitrogen gas through the stage. The stage can be cooled down to -

185 °C. A platinum resistance thermocouple is located just below the specimen and the desired stage

temperature is achieved through balancing the heater output and the chilled gas. The entire stage is

electrically grounded and the 10"5 torr vacuum of the SEM chamber minimizes heat transfer.

The procedure for both experiments was the same. The specimen was placed in the vacuum chamber

of the SEM and thermally cycled twice between -50 °C and +150 °C. The temperature was then set at

the starting temperature for the test of -50 °C. Images of the moire field were acquired at intervals of

approximately 50 °C. After each increment in temperature the specimen was allowed to equilibrate

before acquisition of the moire field. For assessing equilibrium we waited until the fringe field

changed less than 0.25 fringes per minute across the field of view. This required waiting a maximum

of 30 minutes. Typical fringe fields are shown in Fig. 4 at temperatures of -49.6 °C and 150.6 °C.

The average number of fringes across the field as a function of temperature are plotted in Figs. 5a and

5b for the two tests we performed. The first test, shown in Fig. 5a, was conducted before we were

aware of possible errors due to temporal variations in the fringe field. Only three data points were

obtained in that test. After observing the temporal variations in the fringe fields detailed in the first

120
part ofthis paper we repeated the experiment but collected data during both heating and cooling of the

specimen. Shown in Fig. 5b are the mean values of the data at each temperature with bars indicating

the spread in the data.

We calculate the coefficient of thermal expansion from the fringe field following Bowles, et al. [9]. We are only interested in the change of fringe order with temperature over the uniform displacement

field so we calculate the slope of the average number of fringes with respect to temperature, sf The

coefficient of thermal expansion can then be directly calculated as

a =^- . (10)

From eq (10) we can estimate a by dividing the slope of a best-fit line through the data in Figs. 5a and

5b by R (recall that R - 480 for our SEM). Summarized in Table I are the results of this calculation.

121
Table I

Coefficient of Thermal Expansion from the E-beam Moire Data

Test SlQPMr Correlation Coefficient, r Pt (/°Q

1 (Fig. 9) 8.61 x lO 3 0.997 17.6x10*

2 (Fig. 10) 6.96x10° 0.966 14.8 x 10"6

Average <x= 16.2 xlO"1

The average coefficient of thermal expansion from the moire data can be compared to a handbook

value [10] of a = 16.5 x 10"6 /°C for pure copper. Our average result is apparently within 1.8% of the

handbook value. However, we must inspect our result in light of the parametric studies performed on

the apparent magnification drift.

Estimate ofthe Error

Based on the parametric studies detailed in the previous section we concluded that variation in the

apparent magnification in the SEM is the principal source of error. This variation is not due to probe

122
current- drift. Magnification drift in the SEM can occur through slight variations in the high

accelerating voltage, through drift of the magnification control unit, or other instrument-related factors.

Clearly we are expecting a level of performance and stability from the SEM which it was not intended

to meet The drift of ± 0.32X at 1 100X which produced one standard deviation in the fringe field for

the experiment of Fig. 1 represents a variation of only ± 0.03% in the magnification.

We now consider a variation in apparent magnification during a thermal expansion test. The apparent

coefficient of thermal expansion can be calculated from the apparent strains as

Ae

<*« =——(11)

provided the thermal strains are linear over the temperature increment AT. Writing the apparent strains

as shown in eq (5) we have

As Ae^,,

<*<**, =i±^. + —^L. m (12)

AT AT

We can put this equation in a more useful form as

*opt =<* lne AM \

-y (13)

alm MAT

123
where

««

»^J*-

(H)

Based on our investigations concerning the apparent variation in magnification, we are concerned with

apparent variations in magnification of approximately 0.32X at 1 100X. From eq (13) we obtain

-^- = 1.088.

We can therefore anticipate obtaining an estimate of the coefficient of thermal expansion to within

approximately 9%. If we consider the average value of the coefficient of thermal expansion given in

Table I and the values obtained from the individual experiments of Figs. 5a and 5b, we obtain a = 16.2

x 10"6 /°C ± 8.5%. This is consistent with the anticipated error in the measurement predicted from eq

(13).

Summary

We have presented a study concerning the magnitude of errors from a variety of sources when using ebeam moire. Based on parametric studies of the temporal variation of the fringe patterns we identified

the major source of error as being an apparent magnification drift It was demonstrated that the

magnification error causes a change in the frequency of the observed moire field. For the simple case

124
of uniform strain the error was non-negligible for typical values of magnification drift. This

demonstrates the need for strict monitoring and control of the magnification when performing

measurements with e-beam moire. Finally, we calculated the coefficient of thermal expansion for

copper in light of these potential errors. We obtained an average value for the coefficient of thermal

expansion within 1.8% of handbook values. This result was fortuitous as our expected error in the

measurement due to the apparent drift in magnification was approximately 9%. Future work will focus

on the issue of magnification control and stability in the SEM.

Acknowledgment

One of us (JRB) acknowledges the support of the National Science Foundation and the National

Institute of Standards and Technology under the joint NSF-NIST program CMS-9522147 and

additional support provided by the Materials Reliability Division ofNIST.

References

[1] Kishimoto, S., Egashira, M., and Shina, N., "Measurements of Grain Boundary Sliding and

Observations of Microgrids for High Temperature Use," Journal of the Society for Materials Science

Japan, Vol. 40, pp. 637-641 (1991).

[2] Dally, J. W. and Read, D. T., "Electron-beam Moire," Experimental Mechanics, Vol. 33, pp. 270-

277(1993).

125
[3] Read, D. T. and Dally, J. W., "Theory of Electron-beam Moire," Journal of Research of the

National Institute ofStandards and Technology, Vol. 101, pp. 47-61 (1996).

[4] Morimoto, Y. and Hayashi, T., "Deformation Measurement During Powder Compaction be a

Scanning Moire Method," Experimental Mechanics, Vol. 24, pp. 112-116 (1984).

[5] Durrelli, A. J. and Parks, V. J., Moire Analysis of Strain, Prentice-Hall, Englewood Cliffs, NJ,

1970.

[6] Post, D., Moire Interferometry, Handbook on Experimental Mechanics, Society for Experimental

Mechanics, Bethel, CT, 1989.

[7] Dally, J. W. and Riley, W. F., Experimental Stress Analysis,T)tiid. Edition, McGraw Hill (1992).

[8] Barker, D. B., Sanford, R. J., and Chona, R., Determining K and related stress-field parameters

from displacement fields, Experimental Mechanics, Vol. 25, 399-407 (1985).

[9] Bowles. D. E., Post, D., Herakovich, C. T., and Tenney, D. R., "Moire Interferometry for Thermal

Expansion of Composites," Experimental Mechanics, Vol. 21, pp. 441-447 (1981).

[10] Handbook of Chemistry and Physics, David R. Lide, Editor in Chief, 74th Edition, CRC Press,

Boca Raton, Florida (1993).

126
List of Figure?

Fig. 1 Average number of fringes for the copper specimen as a function of time.

Fig. 2 Average number of fringes as the probe current is varied.

Fig. 3 Average number of fringes from different tracings of the fringe pattern with the fringe pattern

analysis software used in this study.

Fig. 4 Typical e-beam moire fields acquired at temperatures of -49.6° C and 150.6° C

Fig. 5a First test for the average number of fringes as a function of temperature change for the copper

specimen.

Fig. 5b Second test for the average number of fringes as a function of temperature change for the

copper specimen. Shown are the mean values obtained at each temperature increment The error bars

indicate the variation in the experimental data.

127
"3-

CO

-3-

CM•

O

LO

CM

O

CM

O

LO

E

LU

o

o

o

LO

SBONIbld JO ON OAV

Berger, Drexler, and Read, Fig. 1

128
CM

in LO

o

in

CO

o

CM

I

o

I

o

CO

I

o

CO

I

o

o

T

<

Q.

LLI

CC

CC

O

LU

CD

O

CC

Q.

S30NIHd dO ON OAV

Berger, Drexler, and Read, Fig. 2

129
CO

m

- -*t

CO

o

o

<

h-

- CM

in ^* CO CVJ o

o> o> o> o> o> o>

S30Nmd dO ON DAV

Berger, Drexler, and Read, Fig. 3

130
-49.6 C 150.6 C

131
qcd

in o in

S3DNIdd JO ON OAV

O

o

CM

o

10

o

o

o

in

- o

q

o

in

I

O

LLI

<

Ql

UJ

Berger, Drexler, and Read, Fig. 5a

132
o

o

CM

O

in

o

o

o

o

ULI

DC

<

a:

LLJ

a.

LJJ

- o

o

o

in q in

co" q

CO

o

in

I

SBDNIUd dO ON OAV

Berger, Drexler, and Read, Fig. 5b

133
Appendix B: Program Disk

134
NISTTechnical Publications

Periodical

Journal of Research of the National Institute of Standards and Technology—Reports NIST research

and development in those disciplines of the physical and engineering sciences in which the Institute is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement methodology and the basic

technology underlying standardization. Also included from time to time are survey articles on topics

closely related to the Institute's technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—Major contributions to the technical literature on various subjects related to the Institute's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes)

developed in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NIST, NIST annual reports, and

other special publications appropriate to this grouping such as wall charts, pocket cards, and

bibliographies.

Applied Mathematics Series—Mathematical tables, manuals, and studies of special interest to physicists,

engineers, chemists, biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical

properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NIST under the authority of the National Standard Data Act (Public

Law 90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published bi- monthly for NIST by the American Chemical Society (ACS) and the American Institute of Physics (AIP).

Subscriptions, reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington,

DC 20056.

Building Science Series—Disseminates technical information developed at the Institute on building

materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental functions and the durability

and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of

the subject area. Often serve as a vehicle for final reports of work performed at NIST under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures published by the Department of Commerce

in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized

requirements for products, and provide all concerned interests with a basis for common understanding of

the characteristics of the products. NIST administers this program in support of the efforts of private- sector standardizing organizations.

Consumer Information Series—Practical information, based on NIST research and experience, covering

areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

Order the above NISTpublications from: Superintendent of Documents, Government Printing Office,

Washington, DC 20402.

Order the following NIST publications—FIPS and NISTIRs—from the National Technical Information

Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the

official source of information in the Federal Government regarding standards issued by NIST pursuant to the Federal Property and Administrative Services Act of 1949 as amended, Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of

Title 15 CFR (Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by

NIST for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield,

VA 22161, in paper copy or microfiche form.
U.S. Department of Commerce

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3337

Official Business

Penalty for Private Use, $300