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PUBLICATIONS

NIST SPECIAL PUBLICATION 400-100

U.S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

C

00

. 57

iZ 400-100

1 98

Semiconductor Measurement Technology:

Thin Film Reference Materials Development

Final Report for CRADA CN-1364
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Semiconductor Measurement Technology:

Thin Film Reference Materials Development

Final Report for CRADA CN-1364

Barbara J. Belzer, Keith Eberhardt,* Deane Chandler-Horowitz,

James R. Ehrstein, and Prabha Durgapalt

Semiconductor Electronics Division

Electronics and Electrical Engineering Laboratory

* Statistical Engineering Division

Information Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

tVLSI Standards, Inc. San Jose, CAN 95134

April 1998

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

TECHNOLOGY ADMINISTRATION, Gary Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Special Publication 400-100

Natl. Inst. Stand. Technol. Spec. Publ. 400-100, 42 pages (Apr. 1998)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
TABLE OF CONTENTS

Page

Abstract 1 Introduction 1 Overview of the CRADA Procedure 3

Experimental Design 4

Materials Preparation 4

Sample Uniformity 5

Sample Stability Baseline Determination 6

Comparison of Ellipsometric Techniques (CNE, RAE, PA-RAE) 7

CNE (Conventional Null Ellipsometry) 7

RAE (Rotating Analyzer Ellipsometry) 8

PA-RAE (Principal Angle Rotating Analyzer Ellipsometry) 9

Results and Discussion 10

Comparison of A and \J/ 10

A Values Measured by NIST and VLSI Standards at 70° Angle of Incidence 12

T Values Measured by NIST and VLSI Standards at 70° Angle of Incidence 13

Film Thickness and Modeling 14

One-Layer Model, 70° Angle of Incidence and Principal Angle of Incidence 14

Principal Angle Measurements 17

Comparison of CNE, RAE, and PA-RAE One-Layer Calculated Thickness 20

Two-Layer Model, 70° Angle of Incidence and Principal Angle of Incidence 21

Conclusions . 23

References 26

Appendix 1 Calculation of Expanded Uncertainties 28

Appendix 2 Between- and Within-Exchange Variation in Ellipsometry Measurements .... 29

Appendix 3 Thickness Values Using Regression Technique for Si02 Film on Silicon

Substrate 35

LIST OF FIGURES

1 Change in A and \Jj with a 0.05

0 change from 70° in the angle of incidence

for different Si02 film thicknesses 12

2 Change in A and \J/ with a 0. 1 nm change in the thickness of oxide film at 70°

angle of incidence for different film thicknesses 12

3 T values at 70° Angle of Incidence, First Thickness Cycle

A = 632.8, nf= 1.460 14

4 Comparison of calculated one-layer thickness values for three measurement

methods: VLSI Standards at 70° angle of incidence, NIST at 70° angle of

incidence, and NIST at the principal angle 16

iii
LIST OF FIGURES (Cont'd.) Page

5 Comparison of calculated one-layer thickness values, all calculated using the

MAIN1 algorithm 19

6 Comparison of two algorithms for calculating thicknesses, using the VLSI

Standards (A,i|/) data 20

7 Comparison of calculated two-layer thickness values for three measurement

methods: VLSI Standards at 70° angle of incidence, NIST at 70° angle of incidence

and NIST at the principal angle 22

A2.1 NIST 70° data. Plots of A versus a time index corresponding to the four

artifact exchanges in the interlaboratory comparison 31

A2.2 VLSI Standards data. Plots of A versus a time index corresponding to the four

artifact exchanges in the interlaboratory comparison 32

A2.3 NIST 70° data. Plots of i|/ versus a time index corresponding to the four

artifact exchanges in the interlaboratory comparison 33

A2.4 VLSI Standards data. Plots of i|j versus time index corresponding to the four

artifact exchanges in the interlaboratory comparison 34

LIST OF TABLES

1 Single-Wavelength Uniformity Measurements Performed by VLSI

Standards, Inc 6

2 Measured Values of A at AI = 70° 11

3 Measured Values of i|j at AI = 70° 11

4 Calculated Thickness (one-layer model, using own algorithms) 15

5 Calculated Thickness (one-layer model, both using MAIN1) 18

6 Calculated Thickness (two-layer model) 21

A2.1 NIST 70° Data 36

A2.2 VLSI Standards, Inc., 70° Data 37

A2.3 NIST Principal Angle Data 38

iv
Semiconductor Measurement Technology:

Thin Film Reference Materials Development:

Final Report for CRADA CN-1364

Barbara J. Belzer, Keith Eberhardt,

+ Deane Chandler-Horowitz, James R. Ehrstein,

Semiconductor Electronics Division

^Statistical Engineering Division

National Institute of Standards and Technology

Gaithersburg, MD 20899

Prabha Durgapal, VLSI Standards, Inc., San Jose, CA 95134

Abstract

Independent single-wavelength ellipsometric measurements of thermally grown silicon

dioxide thin films on silicon substrates and data analyses were compared between two

laboratories (National Institute of Standards and Technology and VLSI Standards,

Inc.) under a Cooperative Research and Development Agreement (CRADA). The

primary intent, based on a sequence of sample exchanges, was to establish a measurement baseline enabling the demonstration of traceability to NIST for several

silicon dioxide film thicknesses that are outside the range of Standard Reference

Materials® (SRMs) available from NIST. Thin films less than 10 nm thickness were

of particular interest. The results of the intercomparison show that there are small

systematic differences in the values of the ellipsometric parameters A and \|r between

the two laboratories along with occasional larger differences. Artificial differences in

the calculated film thicknesses exist because of the use of different algorithms for

computation. A single-layer model and a fixed value of the oxide index of refraction are assumed for the primary comparison in this collaboration; a two-layer model of

the oxide/interface/substrate system is also presented.

Key words: calibration; ellipsometry; metrology; reference material; silicon dioxide;

standards; thin films; traceability.

Introduction

The semiconductor industry makes much use of thin grown and deposited silicon dioxide films. There

is a need for traceable film thickness artifact standards for the calibration of a wide range of optical

instruments used for process development and monitoring of these films. In addition, there is a need

to develop general, simple procedures to calibrate these instruments. Shrinking geometries and

increasingly complex processes continue to place increasing demands on metrology equipment and

associated standards.

The 1994 National Technology Roadmap for Semiconductors (NTRS), in place when this

collaboration was initiated, envisioned the need for 4.5 nm gate oxides with a process tolerance of

1
±0.18 nm (3a) at the 0.18 urn technology node (200 1 ) [1]. The 1997 NTRS has moved this date up

by several years. The microelectronics industry has requested that a standard with a nominal value

of this order and an uncertainty lower than the process tolerance be developed to support the process

equipment and instrumentation. In addition, current industry-wide adherence to the practices set forth in ISO 9000 and the certification of laboratories and processes under the auspices of those

guidelines emphasize the need to have standards keep pace with the demands of the microelectronics

industry.

While the relative process tolerances appear constant, changing manufacturing practices and methods

continue to shrink the absolute value of the tolerances in the microelectronics industry at each

technology node. The costs associated with the fabrication equipment and the metrology equipment

which supports it are very high. It is an objective of NIST to provide standards and/or traceability at each of the processing nodes stated in the NTRS. The manner in which the NIST ellipsometrically

characterized thin-film standards, Standard Reference Material (SRM®) Series 2530, have customarily

been certified does not allow convenient recertification measurement on a single sample as is often

required for ISO registration. The research and development for new standards is a time-consuming

and costly process because it includes, aside from the metrology and data collection, characterization

of the instrumentation used, collaboration with NIST statisticians for a complete analysis of errors and uncertainties, and a stringent peer review process. Therefore, the CRADA reported on here had

a focus, as part of the collaboration, on the development of a more expedient approach to NIST

traceable standards.

In 1988, after several years of research and development, NIST issued SRM® 2530-01 (50 nm),

2530-02 (100 nm), and 2530-03 (200 nm) which were measured using single wavelength

ellipsometry. NIST has certified the ellipsometric parameters, values of the relative phase, A, and

amplitude, iJj, the principal angle of incidence where A = 90°, a derived film thickness based on a two-layer model of the dielectric film, and a calculated value for the refractive index of the silicon

dioxide film [2], The two-layer model includes a top layer of silicon dioxide and an interlayer, the

composition and nature of which continues to be a research effort. The measurements were made

using the ellipsometer specifically designed and built at NIST [3] with the intent to be able to obtain

the most accurate ellipsometric parameters possible. A modeling method was developed concurrently

to enable use of those data to determine the derived thickness and refractive index of the films

thought to be most representative of the "true" values. The values presently certified by NIST

obtained at the wavelength of 633 nm and the so-called principal angle of incidence, while believed

to be very accurate, cannot presently be simply transferred or used to calibrate other instruments.

These include spectroscopic and single-wavelength ellipsometers with the capability of either fixed or variable angle of incidence, reflectometers, and prism couplers.

Because ellipsometry does not directly measure a thickness, the problems associated with certification

should not be underestimated. Depending on the method of ellipsometry used to determine the

ellipsometric parameters, regardless of whether it is single-wavelength or spectroscopic, a variety of

algorithms can be employed to calculate the thickness and refractive index of the material. The

derived thicknesses and indices are highly dependent upon the layer structure assumptions and optical

indices in the model applied and the algorithm used to adjust the model parameters to fit the data for

the calculations [4,5].

2
Nominal thickness values for the current NIST certified standards include 10 nm, 14 nm, and 25 nm,

in addition to the original 50 nm, 100 nm, and 200 nm Si02 films which were thermally grown on

76 mm diameter silicon substrates. The certified values and the method by which certification was

achieved were developed at NIST [2]. Besides these certified values, supplemental, uncertified values

of the derived film thickness based on a one-layer model are given. Also given are uncertified derived

values of A and \Jj for integer values of the angle of incidence, including 70°, based on the two-layer

model and on the experimental A and \|r obtained at the principal angle. However, most instruments

used to monitor industrial semiconductor thin-film processes cannot use the certified values directly.

They rely on either the uncertified derived thickness based on the one-layer model or the uncertified

values for A and iJj expected at integer values of the angle of incidence.

VLSI Standards, Inc. has been offering NIST-traceable film thickness standards (FTS) on a variety

of substrate sizes for a number of years. They have also been providing a nontraceable reference

material for 7.5 nm thick Si02 and plan to provide a traceable standard in that and thinner dielectric

film regimes. Both NIST and VLSI Standards have recognized the need to provide state-of-the-art

standards for the microelectronics industry in a timely manner. It was the intent of the collaboration

in this Cooperative Research and Development Agreement (CRADA) between the Semiconductor

Electronics Division at NIST and VLSI Standards, Inc. to develop and test artifacts with Si02 film

thicknesses <10 nm and devise a method by which transferability and traceability could be more

quickly and directly established and maintained for single wavelength ellipsometry measurements.

Overview of the CRADA Procedure

VLSI Standards manufactured and provided the artifacts used in this study, two each of nominally

4.5 nm, 7.5 nm, 10 nm, 50 nm, 100 nm, and 1000 nm thick oxides. Following the manufacture of the

materials, VLSI Standards performed a number of measurements to ensure that the artifacts were of

equal or better quality than their FTS series material. The artifacts were then sent to NIST for an

initial round of measurements to gain familiarity with the artifacts, test and refine the NIST

measurement protocol that would be required, and to establish a baseline for monitoring their

stability. Upon completion of the initial round of NIST measurements and analysis, the staff from

VLSI Standards and NIST met to discuss and agree upon the procedure for collecting the data and

performing the analysis.

It was decided at that time (June 1996) to base the comparison on single-wavelength ellipsometry at 70° angle of incidence. The final report would include calculations based on a one-layer analysis of

the dielectric layer using a refractive index of the Si02 layer of 1.460, the value used by VLSI

Standards for their certification, and the silicon substrate optical constants, nsi = 3.875 -i0.0156 [6].

The participants would perform data analysis using their own algorithm. Included in the analysis

would be the film thicknesses of 7.5 nm, 10 nm, 50 nm, 100 nm, and 1000 nm. An analysis would

also be made of the data obtained for the 4.5 nm oxide films and a determination made for the need

to perform any additional data acquisition and analysis. Also, ancillary to this analysis, NIST would

calculate thicknesses from the data obtained at each laboratory, utilizing common algorithms based on the described one-layer model and two-layer model using its software, MATN1 [7]. A statistical analysis to evaluate the uncertainty of the observed differences between the two laboratories for the

set of film thicknesses would be included in the report. The calculated thickness values from data

3
obtained by NIST at the individually determined principal angle of incidence, which is the protocol

used in the certification of the NIST SRM 2530 series, were to be compared to the thicknesses

calculated from the data obtained at the angle of incidence of 70°. It was also agreed that a midexperiment statistical analysis would be performed to enable early detection of any problems with the

measurement systems or artifact stability, or any needed revisions to the experiment design.

Experimental Design

Based on NIST's experience with interlaboratory studies [8], it was expected that an experimental

design that incorporated several artifact exchanges, with relatively few measurements per exchange,

would be appropriate for this study. The following sequence of measurements was agreed upon:

• The artifacts would be exchanged four to six times for measurements at each facility with no

cleaning performed at either location other than using clean, dry, filtered nitrogen to remove

dust particles.

• The artifacts would be measured at the center of the wafer over a 2- to 3 -week period for

each exchange, providing three to five independent measurements (e.g., all wafers would be

independently mounted for each measurement) during that time.

• NIST would perform measurements at both the 70° angle of incidence, for use in direct

comparison to the values obtained by VLSI Standards, and at the individually determined

principal angle of incidence.

In fact, there were four exchanges of artifacts during the 6 months from June to December 1996,

during which time five independent measurements were made on each sample during a 2- to 3 -week

time period.

The collaboration between NIST and VLSI Standards, by virtue of existing instrumentation at each

laboratory, employed several ellipsometric methods: Conventional Null Ellipsometry (CNE) and

Spectroscopic Ellipsometry (SE) were used at VLSI Standards, and Rotating Analyzer Ellipsometry

(RAE) and Principal Angle-Rotating Analyzer Ellipsometry (PA-RAE) were used at NIST. The data were modeled to derive thicknesses and indices by several different methods as described above.

Materials Preparation

The silicon wafers that were used by VLSI Standards to manufacture the experimental artifacts met

the SEMI Standard Ml Specifications for Polished Monocrystalline Silicon Wafers. The silicon

material is 100 mm diameter, boron-doped, p-type <100> surface prime silicon. The resistivity range

is 14 Q»cm to 26 Q»cm. The wafers were polished on one side only.

Two each of silicon dioxide films with the nominal thicknesses of 4.5 nm, 7.5 nm, 10 nm, 50 nm,

100 nm, and 1000 nm were manufactured. The silicon dioxide was grown at a temperature of

1000 °C in a purely dry 100% oxygen atmosphere. The time of growth was adjusted to yield

different film thickness values. After oxidation, wafers with oxide thickness less than 10 nm were

4
annealed in nitrogen for 10 min and those with oxide thicknesses > 10 nm were annealed for 20 min.

Special care was taken to ensure consistent processing and film composition. The wafers carry an

identification number and are not patterned in any way. These thicknesses were selected because the

10 nm, 50 nm, and 100 nm are all representative of existing NIST SRMs and very commonly used

in the calibration of ellipsometers during installation and setup in a microelectronics fabrication or thin

dielectric film research environment; the 7.5 nm value is currently offered by VLSI Standards as a non-traceable reference artifact and was the principal thickness of interest for the duration of this

CRADA. The 4.5 nm thickness value was included as a research vehicle intended to begin evaluating

the possibility ofits certification and establishing its traceability to NIST in the very near future. The

1 000 nm value was included to provide a measurement base for those film thicknesses beyond the

first ellipsometric period (0 nm to -290 nm). VLSI Standards also offers film thickness standards

with nominal values of 285 nm, 400 nm, 675 nm, and 940 nm.

Sample Uniformity

Prior to using the samples for this CRADA, it was necessary to see if the oxide grown for different

thickness values satisfied accepted typical industrial specifications. The samples selected were free

of any contamination, microscopic defects, and cosmetic flaws. Following the visual inspection, the

samples were inspected for flatness, uniformity, and manufacturing tolerances. In particular, the

"uniformity" ofthe film thickness in the measurement region needed to satisfy the following criteria: oxide films with nominal thickness below 12 nm should vary by less than 0.2 nm, films with thickness

50 nm should vary by less than 0.6 nm, films with thickness of 1000 nm should vary by less than

2.0 nm over the measurement region, an area of 5 mm diameter in the wafer center.

Initial measurements were made at VLSI Standards to determine the uniformity for film thickness in the measurement area of the artifact. Uniformity was determined by both single wavelength

ellipsometry utilizing the CNE method and SE.

Two sets of measurements were made on VLSI Standards' manual single-wavelength conventionalnull ellipsometer (Rudolph Research Model 436 with a HeNe laser source)1 immediately following

oxidation, to ensure that the VLSI Standards uniformity criteria were satisfied. Two sets of

measurements were also made on a commercial spectroscopic ellipsometer (SOPRA Model ES4G).

Each set consisted of five measurement locations, one at the center and four at off-center points. The

off-center points were located 2.5 mm from the center ofthe wafer. Table 1 shows measurement data

together with the calculated values of thickness for the two measurement cycles made prior to the

sample exchange. (The table in Appendix B lists the results of the spectroscopic measurements.) The

measurement locations are given with the wafer flat at the bottom. Thickness values were calculated

using a single-layer model. For the single-wavelength ellipsometer data analysis, the value of 1.460 was used for the refractive index of Si02 and the value of 3.875 -i0.0156 was used for the complex

refractive index of the silicon crystal substrate. The spectroscopic ellipsometer data analysis listed

1 Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

5
in Appendix B uses the spectra of refractive indices for both Si02 and silicon crystal substrate from

The Handbook of Optical Constants of Solids. ED. Palik [9,10].

In Table 1, the parameter "nonuniformity" is defined as the difference between the maximum and

minimum value ofthickness calculated for a sample. The uniformity in the measurement region was

determined to be in accordance with calibration requirements as employed by VLSI Standards, Inc.

Table 1 : Single-Wavelength Uniformity Measurements Performed By VLSI Standards, Inc. Run 1 Thickness in Nanometers for Fixed Index of Refraction, n =1.460

Wafer Serial Number

Center Top Bottom Left Right Average Nonuniformitv

Standard

Deviation

3723-001 4.89 4.90 4.89 4.89 4.92 4.90 0.03 0.01 3723-002 5.05 5.06 5.06 5.01 5.09 5.05 0.08 0.03 3722-001 7.55 7.54 7.55 7.56 7.53 7.55 0.03 0.01 3722-002 7.55 7.57 7.56 7.58 7.55 7.56 0.03 0.01 3721-001 10.47 10.47 10.48 10.47 10.53 10.48 0.06 0.03 3721-002 10.44 10.44 10.43 10.34 10.48 10.43 0.14 0.05

3365-003 49.67 49.66 49.7 49.7 49.68 49.68 0.04 0.02

3365-004 50.02 50.07 49.95 49.98 50.06 50.02 0.12 0.05

3718-001 99.09 98.99 99.2 98.95 99.24 99.09 0.29 0.13 3718-003 98.65 98.62 98.78 98.64 98.72 98.68 0.16 0.07

3562-005 1007.11 1006.62 1007.71 1007.41 1006.94 1007.16 1.09 0.42

3738-001 1034.43 1034.23 1034.61 1034.01 1034.8 1034.42 0.79 0.31

Run 2 Thickness in Nanomete rs for Fixed Index of Refraction, n =1.460

Wafer Serial Number

Center Top Bottom Left Right Average Nonuniformitv

Standard

Deviation

3723-001 5.06 5.07 5.05 5.04 5.08 5.06 0.04 0.02

3723-002 5.09 5.11 5.09 5.05 5.13 5.09 0.08 0.03 3722-001 7.60 7.60 7.59 7.62 7.59 7.60 0.03 0.01 3722-002 7.58 7.58 7.60 7.61 7.59 7.59 0.03 0.01 3721-001 10.51 10.51 10.51 10.48 10.55 10.51 0.07 0.02

3721-002 10.46 10.46 10.45 10.41 10.50 10.46 0.09 0.03 3365-003 49.73 49.72 49.77 49.77 49.71 49.74 0.06 0.03 3365-004 50.07 50.11 50.00 50.04 50.13 50.07 0.13 0.05 3718-001 98.96 98.96 98.99 98.94 99.15 99.00 0.21 0.09

3718-003 98.65 98.60 98.77 98.61 98.73 98.67 0.17 0.08

3562-005 1007.63 1007.09 1008.26 1007.80 1007.50 1007.66 1.17 0.43 3738-001 1034.62 1034.39 1034.93 1034.17 1034.94 1034.61 0.77 0.34

Sample Stability Baseline Determination

Upon receipt of the samples from VLSI Standards, NIST personnel began an extended series of

6
measurements using the NIST single-wavelength High-Accuracy Ellipsometer [3]. This instrument

employs the photometric, rotating analyzer ellipsometric method in which the reflected beam goes

through a rotating analyzer and the light intensity is measured by a silicon photodiode detector. The

measurements were all made in the center of each wafer. Twenty-five A,i|j pairs at a NIST

determined principal angle of incidence [11] and 16 A,\Jj pairs at the industry-common angle of

incidence of 70° were obtained on each sample between January 19, 1996 and February 28, 1996.

This provided information for the baseline analysis of sample stability. Samples were sufficiently

stable to proceed with the formal comparison.

Comparison of Ellipsometric Techniques (CNR RAE. and PA-RAE)

Measurements in this study were made using both four-zone averaged CNE at VLSI Standards Inc. and RAE at NIST. NIST also made use of Principal Angle-Rotating Analyzer Ellipsometry (PARAE) in which the principal angle of incidence for each sample is determined experimentally and is defined as that angle where the ellipsometric parameter A = 90°. For this condition, the ellipsometric

parameter ijj equals the polarizer azimuth angle. At these conditions, the reflected light is circularly

polarized, there is greater sensitivity to very small changes in the subject sample, and optimally

accurate data can be obtained for analysis.

CNE always uses a compensator, or quarter-wave plate (QWP), thus limiting its use to a single

wavelength. Manual null ellipsometry is time-consuming but can greatly reduce systematic errors due

to aberrations in the optical elements with appropriate zone averaging [12]. In general, though, the

RAE with one polarizer and analyzer has fewer optical aberrations than the CNE with its additional

QWP. Both RAE and CNE have regions of high measurement uncertainty in A. In the RAE,

measurement ambiguities occur when A = 0° or 180°. The linearity of the detector in the RAE is important especially for fully modulated signals. With the CNE, there are measurement ambiguities

when \Jj = 0° or 90°. These problems are further illustrated and discussed below.

Ellipsometry is based on the analysis of the relative change in polarization of light, polarized parallel,

p, and perpendicular, s, to the plane of incidence upon reflection from a surface. The Fresnel

reflection coefficients, i.e., the ratio of the reflected electric field vector to the incident electric field vector, is Rp for the parallel polarization and Rs for the perpendicular polarization. The complex ratio

of total reflection, p, which relates the measured ellipsometric parameters A and \|j to the material

parameters contained in Rp and Rs

, can be written as

p=-^=tan\|K? ,A (1)

A subsequent series of calculations ultimately results in the determination of thickness and refractive

index values for the film. CNE (Conventional Null Ellipsometry)

For CNE, the following equation governs the light intensity and is used to determine A and

7
I0 (\R

p

\ 2 + \R

s

\ 2)[1 -cos2\|/cosZ4 +sin2i|/sin(A -2P)sinZ4]

^CNE

=

~, ' (2)

where P and A are the Polarizer and Analyzer azimuth angles and I0 is the light intensity through the

polarizer with the compensator or quarter wave plate fixed at ±45° prior to the reflection of light

from the sample surface.

The intensity has a minimum which can be approached by independently rotating both the polarizer

and the analyzer to get the null conditions

^null 2 (3)

Anull^- (4)

Near null, P = PnM + bP, A = Anull +bA and |6P|, \6A | are «1; then the intensity near null for the

CNE can be expressed as

- I0(\Rf -\R

p

\ 2)[(bAf +(bPfsin

2 2^]

*CNE « • V5)

Thus, the intensity has a parabolic variation in bP and bA. These variations are independent of each

other. Equation (5) shows that ICNE is insensitive to bP and therefore A when i|r = 0° or 90° (sin

22i|/= 0).

RAE (Rotating Analyzer Elltpsometry)

The photometric method does not require a null measurement. The intensity varies with the

analyzer's azimuth, A:

I

0(\Rs \ 2sm2P+\R | 2 cos

2P)(l+acos2^+psmZ4)

!RAE=

£ E "

> (6)

where

8
tarvfy-taivlP

tan

2 i|/+tan2p' (7)

P

=

2tani|/tarLPcosA

(8) tan^+tan2 ?

The parameters a and p can be determined from a Fourier analysis of the modulating intensity of the

rotating analyzer signal. In the case of the NIST ellipsometer, the rotating analyzer is housed in an

optical encoder which provides the computer with an accurate read-out of its position for use in the

processing of the intensity signal.

Because most commercially available single-wavelength systems are utilized at the fixed angle of

incidence of 70°, NIST RAE measurements were made at this angle for a more direct comparison

between the two laboratories in this study. Unfortunately, for the samples with film thicknesses of

<10 nm, this results in a A value close enough to 180° where the reflected light is more linearly

polarized than is desirable for RAE analysis because of errors associated with detector nonlinearity.

PA-RAE (Principal Angle Rotating Analyzer Ellipsometry)

In this adaptation of the RAE method, the angle of incidence is set close to the principal angle, which

changes as a function of oxide thickness. The NIST Rotating Analyzer Ellipsometer has a nearly

continuous (±0.001°) step size for the angle of incidence. Utilizing this ac null method results in nearly circularly polarized light, which gives optimum measurement conditions [13].

In PA-RAE ellipsometry, P, which is the polarizer azimuth with respect to the plane of incidence, is set to iJj, while A is set to 90° by varying the angle of incidence to be close to the principal angle.

As seen in eqs (7) and (8), the ac null signal obtained in this method occurs when both a and P = 0. The advantage gained in utilizing the PA-RAE is that systematic errors related to photometry are

eliminated. The greatest disadvantage is that it is difficult and time-consuming to ensure accurate

setting of the angle of incidence. The NIST system was designed to minimize the former

disadvantage by the use of calibrated rotation stages [14].

The value of iJj at the principal angle of incidence for Si02 under 10 nm in thickness becomes close

enough to zero that there is an attenuation of the signal to the point where the amplifier gain

sensitivity must be increased, thus decreasing the signal-to-noise ratio. At 70° angle of incidence,

subsequent \|/ values are larger, allowing for greater intensity at the detector and a better signal-tonoise ratio than for PA-RAE at these thicknesses. The tradeoff is then that at 70° angle of incidence,

the value for A is close to 180° which indicates that, rather than circularly polarized light, it is nearly

linearly polarized, and far from optimum [13]. Again, when eqs (6), (7), and (8) are examined, the

optimum measurement conditions for photometric ellipsometry occur when a = P = 0 which

represents circularly polarized light.

9
Principal angle measurements were included in the experiment to provide what is believed to be the

most accurate data possible for analysis. These measurements also provided experimental information

for a comparison ofthe results of data obtained at the Principal Angle measurement angle traditionally

used by NIST in certifying the SRM 2530 series and the 70° angle readily accessible in the

commercial setting.

Regardless of the method or the modeling algorithm used, it is of primary importance to remember

that any measurement uncertainties, both systematic and random, will propagate through the

calculations to the final result. This means that the total uncertainties associated with a derived

thickness and refractive index represent the accumulation ofuncertainties present at each intermediary

step, thus compounding those inherent in the mathematical code and in the measurement system itself.

Results and Discussion

While there was some indication of sample thickness change during the 6 months of the formal test, this observation was not found to be supported by most of the data acquired, and it must be

concluded that there was no sample drift within the level of reproducibility of the data accumulated.

During the four exchanges of the samples between the laboratories for the formal measurements,

there were instances indicating possible loss of statistical control. However, because there were only

four exchanges, there were insufficient total data to make sound statistical inference regarding

individual measurement sets. It was decided to include all data in the final analysis rather than reduce

the number of degrees of freedom through data elimination.

Comparison of A and i|j

The grand average values of A and i|/ experimentally obtained at an angle of incidence of 70° were compared for the four sample exchanges. Detailed tables of all individual measurements are given

in Appendix 3. It should be noted that A and \|/ are nonlinear functions of sample thickness,

wavelength, angle of incidence, polarizer azimuth, the properties of the optical elements in the

ellipsometer, and the sample alignment which can in turn cause errors in the angle of incidence. In

particular, sample alignment errors can be random or systematic and may account for some of the

differences observed between the laboratories for A and

The general results for the calculated differences in A and ijj in Tables 2 and 3 show differences in A approaching 0.3°, with the largest differences occurring for the thinnest oxides, while the

differences for l}/ are on the order of 0. 1 °

. Several modeling calculations were made to see whether

differences of these magnitudes could be explained by simple assumptions without going into detailed

considerations about aberrations in the optical components of the instruments, which is beyond the

intended scope of this comparison study.

10
Table 2: Measured values of A at AI = 70

A in Degrees

Sample

ID.

Nominal

Thickness (nm)

Mean Values Difference

VLSI-NIST

Expanded Unc.

VLSI NIST of Difference

3723-001 4.5 164.58 164.86 -0.28 0.35

3723-002 4.5 164.46 164.70 -0.23 0.36

3722-001 7.5 157.74 157.88 -0.14 0.23

3722-002 7.5 157.71 157.86 -0.15 0.21

3721-001 10 150.31 150.54 -0.23 * 0.14

3721-002 10 150.54 150.68 -0.14 0.15

3365-003 50 95.51 95.55 -0.04 0.05

3365-004 50 95.35 95.39 -0.04 0.09

3718-001 100 78.93 78.90 0.02 0.05

3718-003 100 78.90 78.85 0.05 0.07

3562-005 1000 -86.16 -86.19 0.04 0.16

3738-001 1000 -79.97 -80.07 0.10 * 0.04

* Denotes differences that are laraer. in absolute value, than their expanded uncertainties [Due to numerical roundoff, listed differences may differ in the last digit from what would be obtained by subtracting

the listed mean values.]

Table 3: Measured Values of \|r at AI = 70 °

i|r in Degrees

Sample

ID.

Nominal

Thickness (nm)

Mean Values Difference

VLSI-NIST

Expanded Unc.

VLSI NIST of Difference

3723-001 4.5 10.71 10.79 -0.08 * 0.05

3723-002 4.5 10.72 10.80 -0.08 * 0.04

3722-001 7.5 11.01 11.09 -0.08 * 0.04

3722-002 7.5 11.02 11.09 -0.08 * 0.04

3721-001 10 11.47 11.55 -0.07 * 0.04

3721-002 10 11.45 11.54 -0.09 * 0.05

3365-003 50 22.74 22.86 -0.12 * 0.09

3365-004 50 22.82 22.93 -0.11 * 0.08

3718-001 100 40.77 40.82 -0.06 0.10

3718-003 100 40.58 40.66 -0.08 0.11

3562-005 1000 62.34 61.99 0.34 * 0.14

3738-001 1000 39.87 39.94 -0.07 0.13

* Denotes differences that are larger, in absolute value, than their expanded uncertainties [Due to numerical roundoff listed differences may differ in the last digit from what would be obtained by subtracting

the listed mean values.]

11
Figures 1 and 2 result from simple model calculations and indicate how much A and ijx might change,

or be in error, as a function of oxide layer thickness, resulting from either of two simple sources of

variation that might have been encountered in this measurement sequence. Figure 1 shows how an

error ofjust 0.05° in the angle of incidence at a nominal angle setting of 70° would affect A and \jj as a function of thickness. Figure 2 shows the changes in A and l|r that would occur as a function

ofthickness resulting from just a 0. 1 nm increase in film thickness; this could result from any surface

contamination layer with an index of refraction similar to that of the Si02 , e.g., n = 1.3 to 1.6, and

could include less than a monolayer of moisture or organic contamination. Both examples show that

it is possible to incur offsets of about the magnitude seen in Tables 2 and 3 through some very simple

mechanisms.

0 10 20 30 40 50 60 70 80 90 10 Thickness (nm)

9-*

0 14 28 42 56 70 84 98

Thickness (nm)

Figure 1 . Change in A and ijf with a 0.05° change

from 70° in the angle of incidence for different Si02 film thicknesses.

Figure 2. Change in A and i|x with a 0. 1 nm change in the thickness of oxide film at 70° angle of incidence for

different film thicknesses.

A Values Measured By NIST and VLSI Standards at 70° Angle of Incidence

The measured values of A obtained by the two labs are compared in Table 2. In this table, the grand

mean values of A are shown for each of the 12 artifacts. For each artifact, the difference between

VLSI Standards and NIST is shown in the fifth column, along with the calculated expanded

uncertainty of the difference in the sixth column. The method of calculating the expanded

uncertainties for Tables 2 to 6 is described in Appendix A.

12
For films below about 50 nm in thickness, the VLSI Standards measured values of A tend to be lower

than the corresponding values forNTST. For the 100 nm and 1000 nm thicknesses, VLSI Standards'

measured As were higher than NIST's. In two cases, samples 3721-001 and 3738-001, the

differences were "statistically significant" in that the differences of the mean values were larger, in

absolute value, than the expanded uncertainty values (95% statistical confidence limits). The offsets

noted in this table are consistent with errors or offsets in the angle of incidence as illustrated in Figures 1 and 2 and described above. The experimental offsets in A have values that depend on

thickness in a manner very similar to that shown in Figure 2 due to a 0. 1 nm increase in film thickness.

While experimental results do not support evidence of an accumulation of organic contamination,

there is a possibility that variations in the atmospheric conditions (e.g., relative humidity) may cause

a small fluctuation in thickness.

y Values Measured By NIST and VLSI Standards at 70° Angle of Incidence

The measured values of i|/ obtained by the two labs are compared in Table 3. The table shows the

grand mean values of ij; for each of the 12 artifacts, and for each artifact, the difference between

VLSI Standards and NIST is shown, along with the calculated expanded uncertainty of the difference.

Except for artifact 3562-005, the values of \J/ obtained by VLSI Standards tend to be about 0.1°

lower than those obtained by NIST. These results are not simply explained by an assumption of a small difference in angle of incidence as shown in Figure 1. For thicknesses of 50 nm or less, the

differences are statistically significant in that the observed differences are larger, in absolute value,

than the corresponding expanded uncertainties (95% statistical confidence limits). However, for the

three thinnest film categories, < 10 nm, there is very little sensitivity of the calculated film thickness

to the value for i|r. In the exceptional case of the 1000 nm artifact 3562-005, the VLSI Standards

mean value is larger than the NIST mean by +0.34°. This reflects a distinctive physical property of

this artifact in that its nominal, calculated thickness of 1008 nm, a fourth cycle thickness, corresponds

to a first cycle thickness of -158 nm. This thickness has the distinction of falling on a part of the curve as depicted in Figure 3, where the slope of the polarizer azimuth angle versus thickness and,

hence, corresponding i|x value is extremely steep, causing a marked sensitivity to variations in the

measurements. It is in this area where any variation in instrumentation, optical components and their

housings, as well as variation in the actual measurements caused by individual alignment of the sample on the system would logically appear as a significant difference in the measured values reported by

the individual laboratories.

13
100 i

I I I I I I I I I I I I I I i I I

i

I I I I I I I I I I I

ooooooooooooooo

Thickness (nm)

Figure 3: i|/ Values at 70° Angle of Incidence

First Thickness Cycle

X = 632.8, nf = 1.460

Film Thickness and Modeling

The model and analysis used in the calculation of thickness and refractive index is as equally

important as the accuracy of the measurements themselves. The resultant data presented in the

preceding sections were examined in several different ways described below.

One-Layer Model, 70° Angle of Incidence and Principal Angle of Incidence

The one-layer, fixed refractive index model calculated using the individual algorithms employed by

VLSI Standards and by NIST was examined. This constitutes the most direct comparison between

the derived thickness values that would be produced by each lab, in isolation, for these artifacts. A

second comparison considers the results after recalculating the data acquired by VLSI Standards

using the NIST analysis program, MATN1. This was done specifically to begin to understand any

observed differences in calculated thickness due to the algorithm as opposed to instrument and/or

technique (CNE vs. RAE).

Table 4 shows a comparison of the calculated thickness values obtained by VLSI Standards and

NIST, using their own standard algorithm for the calculation. These values are graphically depicted

in Figure 4. In each case, the same set of fixed parameters was used for the calculation (refractive

indices of air, Si02

, and Si), together with the individual laboratory's measured values of A and ij;.

14
Table 4: Calculated Thickness (one-layer model, using own algorithms)

Thickness (nm)

Sample

I.D. Nominal

Thickness (nm)

Mean Values Difference

VLSI-NIST

Expanded Unc. VT ST of Difference V IjuX NTST ill J A

J

"xitx /Zj-UUI nm +. J J. lo c in nU.Uons n 17 U. 1 z

t. J J. 15 C 1 £. J.lO nu.un7/ n i "? "xin J /ZZ-UU1 nm 7 5 /. /I 1 .by n no u.uz n no

3777 nn? 7 S /.J 1.15 1 . /U n m nU.Uons

•377 J / Z J.-UU 1 .nm1

i n i n £i W.jo n ns nU.UOn^

J / Zl vuz 10.53 10.52 n m nU.UOns

3365-003 50 49.86 50.11 -0.26 * 0.11 3365-004 50 50.10 50.33 -0.23 * 0.12 3718-001 100 99.19 99.25 -0.06 0.18

3718-003 100 98.85 98.95 -0.11 0.19

3562-005 1000 1007.89 1008.09 -0.20 * 0.11 3738-001 1000 1034.83 1034.67 0.16 0.27

* Denotes differences that are lar°er, m absolute value, than their expanded uncertainties [Due to numerical roundoff', listed differences may differ in the last digitfrom what would be obtained by subtracting

the listed mean values.]

From this comparison, the mean thickness values for the artifacts < 10 nm, as well as the 100 nm film

artifacts, differ by an average of <0.1 nm. For the artifacts <10 nm, the VLSI Standards

measurements and calculations result in slightly larger thickness values than obtained by NIST, while

for 50 nm and 100 nm films, the situation is reversed with VLSI Standards calculations, resulting in lower thickness values than NIST. For the 50 nm artifacts, the VLSI Standards method results in thickness values that are lower than NIST's by about 0.25 nm, and the differences are statistically

significant in that they exceed the corresponding expanded uncertainties. The same applies to the

1000 nm artifact 3562-005, where the VLSI Standards' thickness is lower than NIST's by 0.2 nm.

Again, the difference is statistically significant, implying that it cannot plausibly be explained as a

result of random measurement error. However, it should be noted that the functional

agreement <0.2 nm for the 1000 nm samples in this study regardless of the algorithm used represents an agreement within such a small percentage (0.02%) ofthe total thickness, that it is adequate for this

thickness regime and the purposes of this study. No further calculations were done on the 1000 nm

films.

In interpreting determinations of "statistical significance," it is important to keep in mind that

statistical significance is not related to the practical importance of a quantity. The statistical significance of an observed difference only addresses the question of whether the observed value

differs from zero by more than its uncertainty. In informal terms, it addresses the question of whether

the uncertainty in a given experimental result is small enough to "prove" (at the 95% level of

confidence) that the long term systematic offset of the two measurement systems is something other

than exactly zero. Metrology experience indicates that, given enough experimentation, any two

measurement systems can be shown to have some nonzero amount of systematic offset . On the other

hand, a small number of experimental measurements, with large uncertainties, might fail to show

statistical significance for a difference that could be quite large. Thus, it is more meaningful to

15
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16
consider what can be said, on the basis of the present comparison, about the maximum possible size

of the (presumed non-zero) systematic offset between the two measurement systems studied.

In particular, it is of interest to consider what can be said, on the basis of Table 4, about the possible

size of the overall systematic offset between the VLSI Standards and NIST measurement systems.

Since the thicknesses in Table 4 were calculated by the algorithm that is routinely used in each

laboratory, the differences shown there reflect a realistic comparison of the calculated thicknesses that

would result from routine application of the current measurement systems, including data reduction

methods.

At the 95% confidence level, an upper limit to the long-term average difference, or systematic offset,

between the two measurement systems is given by the sum of the observed mean difference (in

absolute value), plus the expanded uncertainty in Table 4. This sum is 0.2 nm or less for all artifacts

having nominal film thicknesses of 10 nm or less. That is, the results shown in Table 4 show that the

systematic offset between the two measurement systems (including thickness calculation algorithms)

is less than or equal to 0.2 nm for film thicknesses of 10 nm or less. As a whole, one can say, at the

95% level of confidence, that the (absolute value of the) systematic offset is no greater than 0.37 nm

for artifacts with film thicknesses of 100 nm or less, and no greater than 0.43 nm for all artifacts

studied.

Principal Angle Measurements

The comparison of calculated thicknesses can be extended by incorporating the thickness values

obtained from the NIST principal angle measurements with the calculated thicknesses obtained from

the VLSI Standards and NIST 70° angle of incidence measurements. NIST has based the certified

values of the existing series of SRMs* on the measurements made at the Principal Angle of Incidence

based on work showing them to be the most accurate. Figure 4 shows the graphical comparison.

The error bars in the plot represent 95% statistical confidence limits, calculated from the reduced data

set consisting of four values of the mean thickness per exchange for each artifact and measurement

method. In the figure, artifacts for which the error bars for VLSI Standards and NIST 70° do not

overlap correspond to cases in Table 4 where the difference between the VLSI Standards and NIST

70° mean values show a statistically significant difference.

The differences in Table 4 reflect the combined effect of differences between the two laboratories'

measurement systems and also between two separate calculation algorithms. In order to focus on just

the differences due to the measurement systems, the film thickness values were recalculated, from

VLSI Standards' raw A and i|r data, using NIST's standard algorithm as embodied in the MAIN1

program. Because the MAIN1 algorithm is not written to converge on data taken on thicknesses

outside the first ellipsometric cycle (0 nm to 290 nm), this comparison was only carried out for the

100 nm and thinner films The results of this comparison are summarized below in Table 5.

17
Table 5: Calculated Thickness (one-layer model, both using MAIN1)

Thickness (nm)

Sample

I.D.

i\omindi

Thickness (nm)

Mean Values umerence

VLSI-NIST

Expanded Unc.

\/T V.LMCT XTTCT of Difference

3723-001 4.5 5.20 5.10 0.10 0.13 3723-002 4.5 5.24 5.16 0.08 0.13 3722-001 7.5 7.74 7.69 0.05 0.09

3722-002 7.5 7.76 7.70 0.06 0.08

3721-001 10 10.67 10.58 0.09 * 0.06

3721-002 10 10.58 10.52 0.06 0.06

3365-003 50 50.09 50.11 -0.02 0.08

3365-004 50 50.32 50.33 -0.01 0.12

3718-001 100 99.15 99.25 -0.10 0.17

3718-003 100 98.81 98.95 -0.14 0.19

* Denotes differences that are larger, in absolute value, than their expanded uncertainties

The comparison in Table 5 shows that the mean thickness values differ by 0.1 nm or less for all artifacts with film thickness less than or equal to 50 nm. In fact, a major difference between Tables

4 and 5 is that the 50 nm films showed the largest differences in Table 4 (where separate calculation

algorithms were used) and the smallest differences in Table 5 (where the same algorithm is used for

both measurement methods). In Table 5, the VLSI Standards measurement data produce higher

thickness values for the artifacts with the three thinnest films (less than or equal to 10 nm) and lower

thickness values for the thicker films (50 nm and 100 nm). The only statistically significant difference

in mean thickness values occurs for artifact 3721-001, with a 10 nm film, which was also the only

artifact to show statistically significant differences in both A and \Jj in Tables 2 and 3, respectively.

For this comparison, differences attributable to the algorithm employed in calculating the thickness

are not found to be a significant contributor to measurement differences except for the 50 nm

samples. The differences arise because the measured A and i|j values do not fit the film substrate

model exactly, experimental errors exist, and the programs are calculating a "best fit" value for the

thickness based on their own algorithms. The algorithms used by VLSI Standards and NIST differ

in the functions used in minimization. The algorithm employed by NIST uses the sum of the squares

of the differences between the measured and modeled values of A and Constraints on the

minimization function include the fixed index of refraction of the Si02 layer. The results in Table 5 can be used to derive an upper bound for the systematic offset between the two measurement

systems, assuming that both were using the MATN1 algorithm for one-layer thickness calculations.

At the 95% confidence level, an upper bound for the systematic offset is obtained by adding the

(absolute) differences to their corresponding expanded uncertainties. This yields the statement that

the systematic offset is no larger (in absolute value) than 0.23 nm for nominal film thicknesses of

50 nm or less, and no larger than 0.3 1 nm for thicknesses of 100 nm or less. The results shown in Table 5 for a common data reduction algorithm are depicted graphically in Figure 5, together with

the corresponding PA measurements (as in Fig. 4).

18
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Comparison of CNE, RAE, and PA-RAE One-Layer Calculated Thickness

A direct comparison of the two thickness calculation algorithms can be made by comparing, for each

measured (A,i|j ) pair, the calculated thickness obtained from the VLSI Standards algorithm and that

obtained from MATNl. For each artifact, there are 20 measurements available for this comparison.

Figure 6 shows the 20 differences, obtained by subtracting the MAIN1 -calculated thickness from the

corresponding VLSI Standards-calculated thicknesses, for ten artifacts with film thicknesses up to

1 00 nm. The plot shows that the VLSI Standards algorithm gives thickness values that are uniformly

slightly lower than those obtained from MATNl for the artifacts with nominal thicknesses of 4.5 nm,

7.5 nm, and 10 nm. For the 50 nm artifacts, the difference between the two algorithms is greater,

with VLSI Standards producing results that average a little more than 0.25 nm below the MATNl

values. The variability of the differences is also larger for 50 nm thicknesses than for the others. The

sign of the differences reverses for the 100 nm films, with the VLSI Standards algorithm producing

slightly higher results than MATNl in that case.

4.5a 4.5b 7.5a 7.5b 10a 10b 50a 50b 100a 100b

Arifact ID, based on nominal film thickness

Figure 6. Comparison oftwo algorithms for calculating thicknesses, using the VLSI Standards (A,i|/) data. For each (A,iJ/) pair, both VLSI Standards' algorithm and NIST's MATNl algorithm were used

to calculate one-layer thickness values. The plot shows the differences, VLSI- MATNl, between the

resulting calculated values for the 20 measurements of each artifact. The artifacts are labeled by their

nominal thicknesses in the order shown in Table 4; for example, artifact 3723-001 is designated 4.5a,

and 3723-002 is 4.5b, etc.

20
Two-Layer Model, 70° Angle of Incidence and Principal Angle of Incidence

This comparison uses the data acquired and models a thickness and refractive index of the film based on a two-layer model. The two-layer model calculations were implemented using NIST's MATN1

computer program. This program generates values of film thickness, t

fi and interlayer thickness, t„ along with derived values of the refractive indexes for the film and the interlayer by doing a batch

analysis of all thicknesses. A two-layer model has been found to give a fit simultaneously to all samples that is much better than the one-layer model [2]. The one-layer model, when varying both

n and t, tends to give an index value that varies with film thickness. Table 6 gives a numerical

comparison ofthe two-layer thickness values obtained from the VLSI Standards and N1ST 70° A and

ijj data. In this table, two-layer thickness is defined as the sum of the film thickness and the interlayer

thickness obtained from the two-layer calculation: thickness = (/y + t

t). The grand average refractive

index ofthe Si02 for the collective NIST batches was calculated to be 1.464 with grand average

interlayer thickness, ti; of 0.91 nm with an interlayer refractive index, rij = 2.8. The corresponding

values for the collective VLSI Standards batches were calculated to be 1.464 and 0.95 nm,

respectively, and the interlayer refractive index, r^, of 2.8. By analyzing measurements made at the

principal angle of incidence along with the calculated thicknesses and comparing the results with

those obtained at the 70° angle of incidence from both laboratories, a perspective can be gained for

the degree of difference that the method and modeling can have on the final outcome as shown in Figure 7. The grand averages for the refractive index for the Si02 film, nf

, the interlayer thickness,

% and an interlayer refractive index, r\, calculated from the batches of principal angle data from NIST

are 1.464, 0.73 nm, and 2.8, respectively.

Table 6: Calculated Thickness (two-layer model)

Thickness (nm)

Sample

ID.

Nominal

Thickness (nm)

Mean Values Difference

VLSI-NIST

Expanded Unc.

of Difference VLSI NIST

3723-001 4.5 5.28 5.15 0.13 0.17

3723-002 4.5 5.32 5.21 0.11 0.17

3722-001 7.5 7.80 7.72 0.08 0.12

3722-002 7.5 7.82 7.73 0.09 0.13 3721-001 10 10.72 10.59 0.13 * 0.11 3721-002 10 10.62 10.53 0.09 0.10

3365-003 50 49.78 49.73 0.05 0.11 3365-004 50 50.01 49.95 0.06 0.11 3718-001 100 99.22 99.15 0.07 0.55 3718-003 100 98.87 98.84 0.03 0.54

* Denotes differences that are larger, in absolute value, than their expanded uncertainties

In this comparison, almost all the artifacts have mean differences of 0. 1 nm or less. Interestingly, the

thickness values obtained from the VLSI Standards data are all larger than the corresponding NIST

values. As was true in Table 5, the only artifact showing a statistically significant difference is 3721-001, with a 10 nm film, and for which the mean values for both A and i|j showed statistically

significant differences in Tables 2 and 3. It is not within the scope of this report to examine the

details of the two-layer model analysis, but the results are included for an illustration of the

21
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complexity of analyzing data from which film thickness values are calculated.

Conclusions

This CRADA was initiated to develop and test a two-laboratory measurement exchange procedure

by which traceability to NIST could be demonstrated for single-wavelength ellipsometry

measurements ofthin oxide films that are outside the thickness range supported by NIST SRMs. In keeping with the needs of the semiconductor industry, as described in the National Technical

Roadmap for Semiconductors (NTRS), the primary focus was to develop this capability in

the <10 nm thickness regime; a very thick oxide was included in the testing, however, to support

other applications. In addition, the two-laboratory measurement procedure itself was evaluated by

NIST for effectiveness as a possible protocol for providing NIST Traceable Reference Materials

(NTRMs) for future thin dielectric film standard artifacts, a logical extension of the NIST Standard

Reference Materials Program.

Comparisons of ellipsometric measurements from another laboratory with those from the NIST HighAccuracy Ellipsometer are most directly made in terms ofthe ellipsometric parameters A and This

gives a comparison of pure measurement equivalence without the added complexities introduced by

the choice of a structural model to fit the data or choice of error function to be minimized during the

fitting. CRADA measurements for the parameter A showed a small-to-moderate difference between

the instruments at VLSI Standards and NIST, although the differences were statistically significant

for only two of the 12 artifacts. The differences in A, as well as the associated expanded uncertainty

values, were the largest for the 4.5 nm, 7.5 nm and 10 nm films. The increased differences for the

thinnest films can be expected for several reasons: 1) A is a very sensitive function of change in film

thickness due to contamination or atmospheric (moisture) variations (Fig. 2), or due to instrumental

errors related to component alignment; and 2) there is a relatively greater difficulty in measuring these

films with RAE ellipsometry since their values for A are quite large indicating polarization

approaching linear, which is not an optimum measurement condition for photometric ellipsometry.

An upper 95% Confidence Limit for the between-laboratory difference in values can be calculated

from the difference in A values plus the expanded (2 o) uncertainty of the difference. The two-sample

average of this Confidence Limit is about 0.35° at 7.5 nm and about 0.60° at 4.5 nm; it is only about

0.17 at 1000 nm.

Differences found for although lower in magnitude than the differences in A, were statistically

significant for nine of the 12 artifacts. However, for the three thinnest film categories, the calculated

film thicknesses are almost entirely governed by the value of A. Therefore, differences found for i|j have little bearing on differences in calculated film thicknesses between the two laboratories.

Comparison of values of A and \jr is the most direct way to evaluate the accuracy of another

laboratory's ellipsometer relative to the NIST instrument. However, acceptable values of the

differences and uncertainties for these parameters are not intuitive, and the relation between A and

ijj and calculated film thicknesses is nonlinear. Further, the customary user-desired output parameter

for the ellipsometric measurement of a thin film is the thickness of the film. Comparisons of the

calculated thickness values are therefore appropriate.

23
Using each laboratory's own algorithm and a single-layer model of the film gave average derived

thickness values that were consistently within 0.1 nm of each other for all films in the first ellipsometric period at 70° (0 nm to 283 nm thick) except for the 50 nm films, and averaged just

under 0.2 nm for the 1000 nm films. This result is generally satisfying since it represents less than a monolayer of Si02 . By using the same algorithm (MAIN1) to process the data with a one-layer

model (done for all but the 1000 nm films), the differences in the calculated thicknesses for the 50 nm

samples were greatly reduced. These changes are believed to be due principally to the extent of the

dependence of the calculated thickness of 50 nm films on both A and \|r and to the effect that the

algorithms used by the two laboratories differ in the error functions upon which they minimize when

determining thickness values that best fit the data

Single-layer model thicknesses from the 70° data at both laboratories were generally well supported

by comparison with the thicknesses from NIST principal angle measurements, with a lack of overlap

ofthe 95% confidence intervals occurring in only one instance, that being the NIST 70° and principal

angle data from one of the 10 nm films. This overall agreement is particularly satisfying because each

ofthe methods of ellipsometry employed has different sensitivities and potential errors related to the

optical components and the response of the photometer. Also, calculated thickness values from 70°

and principal angle ellipsometry should only agree exactly if the model being used for the

film/substrate system is known to be correct.

The assumption of using a fixed index of refraction relieves the large correlation of the index of

refraction, n, and thickness, t, that occurs when solving the ellipsometric equations for very thin films.

The precision in ^ resulting from the fit to data, becomes very high, but the values for 1 suffer a loss

of accuracy unless the chosen index value is known to be correct. Moreover, even if the index value

is chosen correctly, accurately measured values of A and i|j cannot be fitted exactly to the single-layer

model. This is because the evidence is that thermal oxides are nonideal, having an interface layer and

strain that are not accounted for in the single-layer model. Simply put, failure to account for them

in a single-layer model has a larger effect on the thickness calculated for the thinnest films. A singlelayer model with agreed-upon optical index values was chosen for the principal comparison of the

derived thicknesses in this study because of its simplicity.

The calculation ofthicknesses from a two-layer model, while believed to be physically more correct

and used for SRM certification, generally did not improve upon the single-layer comparison in this

study. This may indicate that the assumption of a common interlayer thickness, to be extracted during

simultaneous analysis of all artifacts, was not correct, perhaps due to the different lengths of time that were used for annealing the thick and thin films following oxide growth. In addition, NIST has had no prior experience including films <10 nm thick in the simultaneous fitting of a batch of samples to a two-layer model.

The best agreement in thickness values between the two laboratories results from the single-layer

model. However, because of the limited number of sample exchanges, simple thickness differences

are not the most appropriate expression of the results of the comparison. As noted in the case of the

comparison for A, the Upper 95% Confidence Limit (absolute difference plus expanded uncertainty)

for the between-laboratory differences is the preferred metric. For the 7.5 nm films, this Upper 95%

Confidence Limit on thickness difference is between 0. 1 1 nm and 0. 14 nm, depending on whether

24
individual algorithms, or a common algorithm, is used. For the 4.5 nm films, this Confidence Limit

increases to about 0.20 nm or 0.23 nm, again depending on algorithm used. For the 1000 nm films,

this Confidence Limit has an average value of 0.32 nm for the case of individual algorithms. Since the

expanded uncertainties are larger than the calculated average differences for these two films, it is not

statistically meaningful to use the calculated differences as scale offsets for VLSI Standards' results

with respect to NIST.

Both laboratories have long-term experience measuring artifacts in the 10 nm to 100 nm range, hence

the artifacts in this range served as a baseline for this study. A few simple conclusions can be drawn

from the results for these artifacts: 1) there are measurable, but generally statistically insignificant,

differences in A values between the labs; 2) these offsets vs. thickness follow a pattern that suggests

a specific mechanism to be the cause, but no clear explanation was found; 3) the differences in i|/ values were smaller, but generally statistically significant, and relatively independent of thickness; 4)

there is a very minor algorithm dependence (<0.05 nm) of the thickness for the 10 nm and 100 nm

films, but a more noticeable (~ 0.23 nm) for the 50 nm films; 5) simple thickness differences following

common-algorithm analysis appear acceptably small with no patterns detectable and only one

difference value that is statistically significant; and 6) expanded uncertainty values show room for

improvement of both the "within-laboratory" and "between-laboratory" components in future testing

of this type.

The differences and variations that were obtained in this study do not appear unreasonable

considering the 6-month duration, eight transcontinental shipments and lack of single-laboratory

environment control, as well as totally different types of instruments. In studying the data from the

experiment, certain unresolved ambiguities were observed. The possibility of such ambiguities was

the reason multiple artifact exchanges were required in order to better estimate the realistic uncertainty of the laboratory measurement exchange process. The study was planned for four to six

artifact exchanges, but only four were completed during the 6-month period. There were occasions

where the respective measurement systems may not have been in statistical control, as noted in Appendix 2, and there was some evidence of artifact drift seen in the NIST 70° data for the 4.5 nm

and 7.5 nm films, although this was not supported by the other measurements on the artifacts. In

future measurement exchanges of this type, the design should require six or more exchanges, which

would allow the possibility of data screening. Also, the current study was not optimized to detect

artifact instability. The use of control chart measurements made in coordination with the

intercomparison measurements, but on additional sets of artifacts retained by the individual

laboratories, should be added to any future studies.

In summary, the two-laboratory agreement for the 7.5 nm oxide films, as measured by the 95% Upper

Confidence Limits for the difference, is well within the NTRS manufacturing tolerance interval for

films at this thickness but not within the stringent precision-to-tolerance ratio for instrumentation used

for monitoring the production processes for these films.. In the case of the 4.5 nm films, the 95%

Upper Confidence Limit for the two-laboratory thickness difference is actually slightly larger than the

NTRS manufacturing tolerance interval. This indicates very clearly that additional work is needed

in order to tighten the agreement to levels commensurate with the needs of the semiconductor

industry as stated in the NTRS.

25
References

[I] The National Technology Roadmap for Semiconductors, Semiconductor Industry

Association, 1997, San Jose, CA.

[2] G. A. Candela, D. Chandler-Horowitz, J. F. Marchiando, D. B. Novotny, B. J. Belzer, and

M. C. Croarkin, StandardReference Materials. Preparation and Certification of SRM-2530,

Ellipsometric Parameters A and and Derived Thickness and Refractive Index of a Silicon

Dioxide Layer on Silicon, N1ST Special Publication 260-109 (October 1988).

[3] D. Chandler-Horowitz and G. A. Candela, An Ellipsometry System for High Accuracy

Metrology of Thin Films, SPIE 480, Integrated Circuit Metrology II, 2-8 (1984).

[4] N. V. Nguyen and C. A. Richter, Thickness Determination of Ultra-Thin Si02 Films on Si by

Spectroscopic Ellipsometry, in Silicon Nitride and Silicon Dioxide Thin Insulating Films,

Proceedings ofthe Conference, Vol. 97-10, M. J. Deen, W. D. Brown, K. B. Sundaram, and

S. I. Raider, Eds. (The Electrochemical Society, Inc., Pennington, New Jersey), pp 183-193.

[5] G. E. Jellison, Jr., The Calculation of Thin Film Parameters from Spectroscopic Ellipsometry

Data, Thin Solid Films 290-291, 40-45 (1996).

[6] J. Geist, A. R. Schaefer, J-F Song, Y. H. Wang, and E. F. Zalewski, An Accurate Value for

the Absorption Coefficient of Silicon at 633 nm, J. Res. Natl. Inst. Stand. Technol. 95, 549

(1990).

[7] J. M. Marchiando, Semiconductor Measurement Technology. A Software Program for

Aiding the Analysis ofEllipsometric Measurements, Simple Models, NIST Special Publication

400-83 (July 1989).

[8] B. J. Belzer and D. L. Blackburn, Semiconductor Measurement Technology: The Results of

an Interlaboratory Study of Ellipsometric Measurements of Thin Silicon Dioxide on Silicon,

NIST Special Publication 400-99 (May 1997).

[9] There are currently conflicting sources for the optical constants of the silicon substrate used

in modeling the spectroscopic ellipsometry data. Until such time as a set of values is agreed

upon by the metrology community at large, between-laboratory comparisons of data obtained

by using spectroscopic ellipsometry have limited usefulness.

[10] E. D. Palik, ed., Handbook of Optical Constants of Solids, Academic Press Inc., New York,

719-763 (1985).

[II] D. Chandler-Horowitz and G. A. Candela, Principal Angle Spectroscopic Ellipsometry

Utilizing a Rotating Analyzer, Applied Optics 21, 2971-2977 (15 August 1982).

26
R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, paperback edition

(North-Holland Amsterdam, 1987).

R. W. Collins, Automatic Rotating Element Ellipsometers: Calibration, Operation, and Realtime Applications, Rev. Sci. Instrum, 61 (8), 2029-2062 (August 1990).

C. P. Reeve, The Calibration of Indexing Tables by Subdivision, NBSIR 75-750 (July 1975).

27
Appendix 1 . Calculation of Expanded Uncertainties

The expanded uncertainties in Tables 2 to 6 were calculated using the ISO method [Al .1]. In this case, the resulting expanded uncertainty coincides with a 95% statistical confidence interval for

the difference of the two means. The method of calculation is described as follows.

For each measurement method, NIST PA, NIST 70°, and VLSI Standards 70°, there were 20

measurements made on each artifact during the four exchanges, five measurements per exchange.

These 20 measurements were first reduced to the mean value per exchange, resulting in four mean

values. Next, the resulting four mean values were summarized by computing their mean and

standard deviation. For method i, let x denote the resulting mean value and let s. denote the

corresponding standard deviation. Note that s. has degrees of freedom equal to three since it is calculated from the deviations among four summary values. Also note that the quantity x; is equal to the grand mean of the 20 measurements, since the number of measurements per exchange

was constant (and equal to five).

The tabulated difference between two measurement methods, say i andj, is then given as

(x. - Xj), and the expanded uncertainty is calculated as U = kuc

, where

(

\ 2

f \

s.

1 +

S

J \ , v/4,

and where k is a factor from the Student-^ distribution for 95% confidence and degrees of

freedom v

eff given by the Satterthwaite formula [Al. 1, p. 64],

3 3

Reference

[Al. 1] Guide to the Expression of Uncertainty in Measurement, ISBN 92-67-10188-9, 1st Ed.

ISO, Geneva, Switzerland (1993). See also Taylor, B. N. and Kuyatt, C. E., Guidelines

for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST

Technical Note 1297, U.S. Government Printing Office, Washington, DC. (1994).

28
Appendix 2. Between- and Within-Exchange Variation in Ellipsometry Measurements

In the experiment design for this interlaboratory comparison, four exchanges of the artifacts and

five independent measurements per exchange were made on each artifact. It was decided to exchange the artifacts several times over a period of months based on the common experience

that laboratory measurement processes tend to exhibit greater variation over long time periods

than will be seen during a shorter period of a few days. That this proved true can be seen in the

accompanying Figures A2.1 to A2.4. In these figures, the A and i|j values from the NIST and

VLSI Standards measurement processes are plotted, for each artifact, against the time index 1 to

4, corresponding to the four artifact exchanges during the intercomparison.

For many of the measurement series associated with various artifacts, the shifts in the mean level

of the measurements that are visible to the eye can be shown to be statistically significant

differences by a formal statistical analysis of variance (ANOVA) procedure. The details of

exactly which measurement series show statistically significant differences between artifact

exchanges is not so important once it is accepted that the measurement processes involved have

the tendency to exhibit greater variability over long time periods than short time periods. It is important that any uncertainty analysis used should properly account for this behavior. The

uncertainty analysis procedure described in Appendix 1 was designed to ensure that both the

long-range and short-range variability of the NIST and VLSI Standards measurement processes

are properly represented in the uncertainty analyses presented in this report.

Study of the plots in Figures A2.1 to A2.4 shows that the NIST data for exchange 1 (July 1996)

and the VLSI Standards data for exchange 4 (December 1996) are somewhat anomalous,

compared to the other data. In the NIST data for exchange 1, and for the three thinnest films, the

values of A tend to be high relative to the other exchanges, while those for i|j tend to be relatively

low. In the VLSI Standards data for exchange 4, the variability of both the A and iJj data is noticeably larger than for the other time periods. These observations suggest that the

measurement systems may not have in strict statistical control during those respective time

periods.

The statistical design for this intercomparison included a provision for continuing without

modification the maintenance of control charts on the measurement systems at the two

laboratories. In both cases, this meant remeasuring NIST-certified thin film standards at regular

intervals, which turned out to be about once a month at VLSI Standards and about twice a month

at NIST. However, the schedule of control chart measurements was not specifically coordinated

with the intercomparison measurements in either laboratory, and the control chart measurements

would not have been effective for signaling out-of-control conditions that would affect the

intercomparison measurements.

A lesson learned from this experience, which should be applied in future comparisons of this

type, is that it would be better to design the study in a way that ensures that at least some relevant

control chart measurements (using artifacts in or near the size range of the intercomparison

artifacts) should be made in coordination (e.g., same day) with the intercomparison

measurements. This would allow the control chart measurements to be used to diagnose out-of29
control conditions in the measurement systems so that such conditions could be corrected before

the measurements are completed. This would likely have the effect of lowering the uncertainty

and increasing the quality of the results of the comparison.

30
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34
Appendix 3 . Thickness Values Using Regression Technique for Si02 Film on Silicon

Substrate

Spectroscopic ellipsometer results: Wavelength range: 300 to 800 nm Number of spectral points: 120

Beam size: 2x8 mm

Angle of incidence: (74.98 + 0.01) degrees

Refractive index used in modeling: Handbook of Optical Constants of Solids, E. D. Palik

RUN# 1 Thickness in nanometers using Regression technique

Serial No. center top bottom left right average nonuniformity std. dev. 3723-001 4.38 4.42 4.49 4.48 4.54 4.462 0.16 0.06

3723-002 4.54 4.56 4.58 4.49 4.44 4.522 0.14 0.06

3722-001 6.95 6.91 6.84 7.00 6.97 6.934 0.16 0.06

3722-002 6.86 6.92 6.97 7.00 7.01 6.952 0.15 0.06

3721-001 9.92 9.93 9.95 9.91 10.04 9.95 0.13 0.05 3721-002 9.92 9.93 9.94 9.88 9.92 9.918 0.06 0.02

3365-003 49.72 49.68 49.74 49.75 49.70 49.718 0.07 0.03 3365-004 50.04 50.09 49.98 50.00 50.07 50.036 0.11 0.05 3718-001 98.58 98.54 98.66 98.52 98.79 98.618 0.27 0.11 3718-003 98.38 98.34 98.50 98.27 98.34 98.366 0.23 0.08

3562-005 1009.21 1008.33 1008.59 1008.79 1008.67 1008.718 0.88 0.32

3738-001 1034.51 1034.58 1036.04 1034.72 1035.53 1035.076 1.53 0.68

RUN #2

Thickness in nanometers using Regression technique

Serial No. center top bottom left right average nonuniformity std. dev. 3723-001 4.59 4.59 4.60 4.57 4.63 4.596 0.06 0.02

3723-002 4.63 4.67 4.65 4.61 4.69 4.65 0.08 0.03 3722-001 7.10 7.13 7. 14 7.16 7.13 7.13 0.06 0.02

3722-002 7.11 7.16 7.14 7.13 7.06 7.12 0.1 0.04

3721-001 10.08 10.05 10.01 10.02 10.10 10.052 0.09 0.04

3721-002 9.96 9.98 9.99 9.99 10.07 9.998 0.11 0.04

3365-003 49.76 49.75 49.82 49.81 49.76 49.78 0.07 0.03 3365-004 50.08 50.13 50.04 50.06 50.13 50.088 0.09 0.04

3718-001 98.75 98.71 98.93 98.73 98.97 98.8182 0.259 0.12

3718-003 98.56 98.50 98.54 98.50 98.68 98.556 0.18 0.07

3562-005 1008.48 1008.25 1009.24 1008.76 1008.24 1008.594 1 0.42

3738-001 1036.65 1036.91 1037.23 1036.31 1037.35 1036.89 1.04 0.42

35
Table A2.1 NIST 70° Data

ALA \ 1 / r One-Layer Thickness Two-Layer Thickness Date Mean Std Dev Mean 1 viva11 Std Dev Mean Std Dev Mean Std Dev

3793-001 J / Zv J \J\J X Tul -96 165 IUJ. 161 X \J X 0V7 . X128Z. O XV/. 10 757 / 1 0\J ,\J0161U 4.994 0.046 4.999 0.046

"5723-001 ~) 1 \J\J X Sep-96 164.848 0.334 10.809 0.007 5.108 0.118 5.166 0.120

3723-001 Oct-96 164.732 0.190 10.801 0.003 5.145 0.066 5.207 0.069

3723-001 —' 1 Z. - ' Uv X Dec-96 164.684 0.117 10.801 0.019 5.166 0.042 5.228 0.042

3723-002 Jul-96 164.996 0.123 10.766 0.015 5.053 0.043 5.058 0.044

3723-002 Sep-96 164.733 0.264 10.808 0.003 5.148 0.093 5.207 0.095

3723-002 Oct-96 164.523 0.195 10.814 0.005 5.218 0.068 5.282 0.070

3723-002 Dec-96 164.544 0.132 10.815 0.017 5.216 0.047 5.278 0.047

3722-001 ^> / Z> Zs \J\J X Jul-96 1 58 087 0.028 11.060 0.013 7.613 0.010 7.598 0.010

^3722-001 / Z.Z. V/v J- Sen-96 157.879 0.192 1 1 099 0.006 7.693 0.073 7.735 0.073

J1799-001 / \J\J X 1 57 794 0 1 34 A1 A1. IvJ 101 0 004 7.725 0.051 7.766 0 051

1799-001 JL1 JS7/ . 779 / / z. 0 071 1 1 0Q9 0 014 7.733 0.027 7.777 0yj .\j0271 1799-009 Tnl-96 1 SR 049 0 039 1 1 060 0 01

1

7.630 0.015 7.615 0.015

1799-009 11 -J57/ . 866 OV7VJ 0 188 A11X . 1101\J X 0 01

1

7.698 0.071 7.739 0.071

3722-00? J / Z. Z. vVZ. Ort-Qfi 1 57 735 0 1 58 A1 A1 . lvJ 105 0 006 7.747 0.060 7.788 0.060

1799-009 1 57 786 0 105 A1 1A . A104vJ*T 0 01s 7.728 0.039 7.772 0.039

1791-001 J / Z, X "Uu 1 J Ul 1 50 667 0 026 1 1 S17 0 00Q 10.530 0.011 10.494 0.011

3721-001 J / z, A ~V/V7 1 1 50 540 0 140 1 1 SSI 0 007 10.582 0.057 10.606 0.056

3721-001 Oct-96 150.490 0 1 56 1 1 564 0.007 10.603 0.064 10.627 0.063

3721-001 Dec-96 150.465 0.057 11.554 0.008 10.613 0.023 10.639 0.023

3721-002 -J / Z. X V/ V/ z. Jul-96 150.81

1

0.085 11.508 0.015 10.471 0.035 10.436 0.034

3721-002 - 1

' J \J\J Sep-96 150 654 0.118 11.536 0.006 10.536 0.048 10.560 0.048

3721-002 J / Z. X V/ V/ z. Oct-96 150.631 0.122 11.552 0.006 10.546 0.050 10.570 0.050

3721-002 .. ' / Z- Jl v_/ v_/ z< Dec-96 150 X JV/.UZO 628 0.065 11.557 0.015 10.547 0.026 10.574 0.026

3365-003 Jul-96 95.541 0.052 22.840 0.042 50.110 0.045 49.635 0.044

3365-003 Sep-96 95.530 0.030 22.789 0.018 50.098 0.028 49.746 0.028

3365-003 Oct-96 95.550 0.009 22.883 0.023 50.122 0.019 49.779 0.019

3365-003 Dec-96 95.578 0.062 22.935 0.143 50.116 0.012 49.763 0.012

3365-004 Jul-96 95.390 0.044 22.921 0.043 50.328 0.033 49.849 0.033

3365-004 Sep-96 95.381 0.016 22.864 0.026 50.310 0.010 49.955 0.010

3365-004 Oct-96 95.401 0.022 22.969 0.022 50.340 0.037 49.994 0.036

3365-004 Dec-96 95.389 0.046 22.973 0.104 50.356 0.015 50.000 0.014

3718-001 Jul-96 78.905 0.030 40.733 0.043 99.090 0.078 98.653 0.080

3718-001 *J l A.KJ v v 1 Sep-96 78.913 0.029 40.868 0.022 99.335 0.038 99.332 0.039

3718-001 Oct-96y\j 78 917 0 030 40 85? 0 013 99.306 0.020 99.319 0.021

3718-001 Dpc-96 x-/*j\* y\> 78 884 0 043 40 840 0 049 99.280 0.083 99.284 0.087

3718-003 T11I-Q6 78 830 0 097 40 ^63 0 049 98.783 0.083 98.331 0.090

371 8-003 78/ 0.0870/ \j 0 03 1 40 71 1 0 011 99.047 0.020 99.037 0.021

371 8-003 Oct-96 78/ 0.08S7.7 / 0 018 40 689 0 003 9870.771 991 0 007 9870.770 998 0.007

-2718 00"? T)a^ Qfi. 78 847 0 041 zlO £8/1 0 077 98.994 0.137 98.991 0.142

3562-005 Jul-96 86.154 0.061 61.870 0.067 1008.186 0.038

3562-005 Sep-96 86.225 0.048 62.046 0.143 1008.049 0.108

3562-005 Oct-96 86.193 0.023 62.010 0.056 1008.081 0.036

3562-005 Dec-96 86.207 0.081 62.041 0.202 1008.057 0.141

3738-001 Jul-96 80.054 0.034 39.860 0.078 1034.843 0.157

3738-001 Sep-96 80.082 0.037 39.992 0.088 1034.578 0.174

3738-001 Oct-96 80.074 0.030 39.989 0.047 1034.583 0.093

3738-001 Dec-96 80.056 0.046 39.933 0.043 1034.695 0.088

36
Table A2.2 VLSI Standards, Inc. 70° Data

One-Layer Thick (VLSI)

Sample Date Mean ,StH Dev Mean StH Dev Mean Std Dev

One-Layer Thick (Mainl)

Mean Std Dev

Two-Layer Thickness

Mean Std Dev

3723-001

3723-001

3723-001

3723-001

3723-002

3723-002

3723-002

3723-002

3722-001

3722-001

3722-001

3722-001

3722-002

3722-002

3722-002

3722-002

3721-001

3721-001

3721-001

3721-001

3721-002

3721-002

3721-002

3721-002

3365-003

3365-003

3365-003

3365-003

3365-004

3365-004

3365-004

3365-004

3718-001

3718-001

3718-001

3718-001

3718-003

3718-003

3718-003

3718-003

3562-005

3562-005

3562-005

3562-005

3738-001

3738-001

3738-001

3738-001

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

Jun-96

Aug-96

Oct-96

Dec-96

164.608

164.619

164.569

164.515

164.460

164.487

164.389

164.523

157.737

157.751

157.642

157.849

157.688

157.715

157.625

157.796

150.268

150.331

150.281

150.358

150.476

150.562

150.484

150.628

95.516

95.508

95.480

95.552

95.313

95.336

95.327

95.430

78.923

78.919

78.895

78.971

78.879

78.877

78.881

78.964

86.235

86.219

86.031

86.136

79.988

79.983

79.932

79.967

0.045

0.067

0.029

0.132

0.048

0.032

0.031

0.101

0.069

0.067

0.037

0.171

0.046

0.064

0.039

0.067

0.056

0.038

0.075

0.307

0.052

0.087

0.035

0.144

0.016

0.016

0.015

0.077

0.026

0.024

0.021

0.228

0.010

0.019

0.015

0.167

0.020

0.019

0.017

0.295

0.024

0.041

0.031

0.214

0.022

0.028

0.024

0.208

10.736

10.734

10.720

10.664

10.732

10.737

10.730

10.683

11.032

11.025

11.026

10.972

11.032

11.026

11.025

10.985

11.491 11.482

11.482

11.436

11.471 11.467

11.463

11.399

22.753

22.750

22.759

22.701

22.834

22.830

22.838

22.792

40.754

40.739

40.752

40.820

40.586

40.579

40.571

40.583

62.330

62.254

62.321

62.437

39.888

39.916

39.942

39.754

0.011

0.006

0.004

0.009

0.009

0.009

0.007

0.035

0.006

0.008

0.009

0.019

0.004

0.006

0.004

0.031

0.004

0.009

0.006

0.015

0.004

0.005

0.004

0.045

0.009

0.007

0.008

0.041

0.014

0.010

0.004

0.068

0.018

0.014

0.008

0.140

0.023

0.013

0.008

0.076

0.115

0.052

0.067

0.118

0.038

0.057

0.042

0.129

5.181

5.177

5.189

5.188

5.231

5.224

5.256

5.192

7.723

7.715

7.754

7.653

7.740

7.728

7.759

7.678

10.657

10.629

10.646

10.588

10.569

10.536

10.561

10.466

49.879

49.878

49.909

49.759

50.149

50.125

50.145

50.000

99.172

99.145

99.168

99.294

98.858

98.846

98.830

98.854

1007.893

1007.951

1007.911

1007.818

1034.807

1034.749

1034.700

1035.070

0.018

0.025

0.009

0.045

0.016

0.013

0.012

0.040

0.024

0.027

0.017

0.069

0.015

0.023

0.015

0.019

0.021

0.018

0.029

0.110

0.020

0.034

0.014

0.049

0.022

0.021

0.023

0.110

0.041

0.022

0.012

0.127

0.033

0.026

0.015

0.260

0.043

0.025

0.015

0.143

0.087

0.041

0.050

0.096

0.073

0.111

0.082

0.254

5.193

5.183

5.207

5.225

5.246

5.229

5.271

5.223

7.745

7.740

7.781

7.702

7.764

7.753

7.788

7.722

10.691

10.665

10.686

10.653

10.606

10.571

10.603

10.542

50.096

50.103

50.140

50.027

50.374

50.345

50.359

50.216

99.130

99.103

99.123

99.255

98.821

98.814

98.794

98.825

0.016

0.023

0.010

0.047

0.017

0.011

0.011

0.036

0.026

0.025

0.014

0.065

0.018

0.024

0.015

0.025

0.023

0.016

0.031

0.125

0.021

0.036

0.014

0.058

0.021

0.021

0.021

0.104

0.036

0.028

0.024

0.251

0.032

0.025

0.015

0.264

0.043

0.025

0.015

0.142

5.270

5.269

5.284

5.301

5.324

5.314

5.349

5.298

7.806

7.800

7.841

7.756

7.825

7.814

7.848

7.783

10.735

10.709

10.728

10.699

10.650

10.615

10.645

10.589

49.777

49.781

49.811

49.761

50.051

50.019

50.027

49.947

99.186

99.152

99.171

99.372

98.869

98.849

98.831

98.930

0.016

0.027

0.011

0.047

0.017

0.012

0.011

0.036

0.026

0.025

0.014

0.063

0.017

0.024

0.015

0.025

0.023

0.015

0.031

0.124

0.021

0.035

0.014

0.058

0.021

0.021

0.021

0.103

0.035

0.027

0.024

0.249

0.033

0.026

0.015

0.268

0.044

0.026

0.015

0.146

37
Table A2.3 NIST Principal Angle Data

A \\i One-Layer Thickness Two-Layer Thickness

Sample Date Mean Std Dev Mean Std Dev Mean StdDev Mean Std Dev

3723-001 Jul-96 89 763 0.372 3 018 0.015 5 210 0 279 5 092 0 285

3723-001 Sep-96 89 805 0.152 3 Oil 0.011 5 175 0 111 5 052 0 116

3723-001 Oct-96 89 675 0.079 3 013 0.010 5 274 0 062 5 255 0 064

3723-001 Dec-96 89 845 0.087 3 018 0.023 5 149 0 069 5 024 0 072

3723-002 Jul-96 90 040 0.448 3 045 0.017 5 171 0 326 5 056 0 334

3723-002 Sep-96 90 004 0.042 3 038 0.014 5 193 0 029 5 074 0 030

3723-002 Oct-96 89 937 0.106 3 053 0.012 5 250 0 075 5 229 0 078

3723-002 Dec-96 89 971 0.216 3 053 0.019 5 222 0 160 5 105 0 167

3722-001 Jul-96 89 971 0.254 4 407 0.018 7 716 0 197 7 607 0 196

3722-001 Sep-96 89 885 0.033 4 413 0.014 7 782 0 030 7 670 0 030

3722-001 Oct-96 89 935 0.026 4 415 0.009 7 748 0 024 7 685 0 021

3722-001 Dec-96 89 837 0.085 4 412 0.017 7 819 0 068 7 711 0 062

3722-002 Jul-96 89 926 0.242 4 416 0.020 7 753 0 189 7 644 0 189

3722-002 Sep-96 89 884 0.020 4 415 0.015 7 784 0 021 7 672 0 021

3722-002 Oct-96 89 903 0.013 4 424 0.010 7 773 0 012 7 713 0 012

3722-002 Dec-96 89 888 0.240 4 416 0.014 7 782 0 180 7 670 0 180

3721-001 Jul-96 89 930 0.200 5 958 0.020 10 642 0 160 10 533 0 159

3721-001 Sep-96 89 900 0.030 5 958 0.010 10 665 0 023 10 554 0 023

3721-001 Oct-96 89 914 0.107 5 971 0.016 10 659 0 085 10 568 0 084

3721-001 Dec-96 89 856 0.047 5 972 0.012 10 704 0 038 10 592 0 038

3721-002 Jul-96 89 764 0.267 5 931 0.018 10 597 0 211 10 487 0 211

3721-002 Sep-96 89 727 0.053 5 924 0.011 10 622 0 042 10 510 0 042

3721-002 Oct-96 89 742 0.033 5 942 0.015 10 618 0 030 10 527 0 030

3721-002 Dec-96 89 738 0.102 5 941 0.007 10 620 0 081 10 507 0 081

3365-003 Jul-96 89 938 0.066 22 789 0.044 50 144 0 057 49 777 0 057

3365-003 Sep-96 89 938 0.022 22 733 0.022 50 110 0 023 49 740 0 023

3365-003 Oct-96 89 946 0.010 22 833 0.025 50 162 0 012 49 665 0 012

3365-003 Dec-96 89 973 0.071 22 879 0.122 50 156 0 029 49 774 0 029

3365-004 Jul-96 89 938 0.047 22 875 0.045 50 381 0 037 50 Oil 0 037

3365-004 Sep-96 89 955 0.023 22 812 0.025 50 321 0 031 49 949 0 030

3365-004 Oct-96 89 962 0.026 22 920 0.015 50 379 0 040 49 878 0 040

3365-004 Dec-96 89 964 0.054 22 922 0.098 50 378 0 009 49 994 0 009

3718-001 Jul-96 90 015 0.031 40 938 0.038 99 049 0 064 99 014 0 066

3718-001 Sep-96 90 009 0.015 41 042 0.020 99 222 0 035 99 194 0 036

3718-001 Oct-96 89 996 0.026 41 046 0.007 99 226 0 009 98 806 0 009

3718-001 Dec-96 89 981 0.020 41 038 0.035 99 210 0 061 99 172 0 063

3718-003 Jul-96 89 934 0.035 40 754 0.046 98 730 0 075 98 683 0 079

3718-003 Sep-96 89 964 0.013 40 879 0.010 98 941 0 017 98 907 0 017

3718-003 Oct-96 89 932 0.015 40 868 0.009 98 918 0 015 98 491 0 016

3718-003 Dec-96 89 929 0.029 40 872 0.063 98 925 0 107 98 879 0 113

3562-005 Jul-96 89 795 0.049 53 048 0.056 1008 125 0 039

3562-005 Sep-96 89 853 0.034 53 202 0.113 1008 005 0 106

3562-005 Oct-96 89 811 0.014 53 198 0.050 1007 991 0 041

3562-005 Dec-96 89 826 0.074 53 230 0.146 1007 960 0 129

3738-001 Jul-96 89 963 0.055 34 327 0.059 1035 740 0 175

3738-001 Sep-96 89 990 0.045 34 448 0.073 1035 530 0 200

3738-001 Oct-96 89 .956 0.040 34 447 0.041 1035 478 0 123

3738-001 Dec-96 89 .983 0.023 34 406 0.031 1035 536 0 129

38


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