Released film structures and method of measuring film properties

Released film structures are employed in measuring the mechanical properties of the film material. By measuring the deformation of thin film structures held under intrinsic tensile stress and then released, these mechanical properties can be accurately measured.

BACKGROUND 
This invention relates to a method of measuring the mechanical properties 
of films, and more particularly, to the measurement of thin films under 
tensile stress. 
Numerous methods have been developed to determine the mechanical properties 
of thin films. The importance of these methods has become well known with 
the development of integrated circuit fabrication, packaging techniques 
and the recent growth in solid state sensor applications. Determining 
these mechanical properties is necessary in assessing the large stresses 
in thin films as insulating layers, which can cause cracking and adhesive 
or cohesive failure, leading to component failure. Stress relaxation due 
to creep can also alter device performance in time. 
The ability to fabricate many micromechanical structures depends greatly on 
the mechanical characteristics of the material. Structures made of 
materials with tensile stress demonstrate significant performance 
deviation from the expected performance for the material with zero stress. 
For example, thin silicon diaphragm pressure sensors, in which the 
diaphragm is under tension, may exhibit such performance deviation. 
With the increasing application of polymer films to microelectronics, it is 
necessary to study the mechanical properties of these films. To fully 
characterize the mechanical properties of a thin polymeric film material, 
the stress, Young's Modulus and Poisson's ratio of the film, as well as 
ultimate strength of the film should be determined. 
Traditionally, the basic technique for measuring the stress in thin films 
has been to deposit the film of interest on a substrate and measure the 
stress-induced curvature of the substrate. See R. W. Hoffman, Physics of 
Nonmetal Thin Films, ed. Dupey and Cachard, Nato Advanced Study Institutes 
Service B, Vol. 14 Plenum Press, New York, 1976. The in-situ measurement 
of stress in polyimide films by this "wafer bending" technique was 
reported in P. Gelderman, C. Goldsmith, and F. Bedetti, "Measurement of 
Stresses Created during curing and Cured Polyimide Films," In K. L. 
Mittal, Ed., Polyimides, Plenum Press, New York, Vol. 2, 1984. The 
deflection or curvature of a beam supported at both ends, a cantilever 
beam, or a circular plate, can be measured optically by either a laser 
beam deflection system or by interferometric methods. The deflection can 
also be measured by capacitance changes or by mechanically probing the 
surface. See D. S. Campbell, "Mechanical properties of thin films," ed. L. 
I. Maissel and R. Gland, Handbook of Thin Film Technology, McGraw-Hill, 
New York, 1970. 
J. W. Beams has developed a method whereby a film is deposited on a 
substrate and a hole is drilled in the substrate without disturbing the 
film. If the stress in the film is compressive, the film will bow without 
further pressure. The deflection of the film due to this latent 
compressive stress can be measured optically. To measure tensile stress 
using the J. W. Beams approach requires the application of pressure to the 
film from an external source. See J. W. Beams, eds. C. A. Neugebauer, J. 
B. Newkirk, and D. A. Vermilyea, Structure and Properties of Thin Films, 
John Wiley & Sons, Inc., New York, 1954. 
These methods require the use of elaborate experimental instrumentation for 
curvature measurements, or they sacrifice accuracy and completeness to 
permit the use of simplified measurement methods. Reported in-situ 
measurement methods may rely on the buckling of microfabricated 
structures, which are most readily applicable to the measurement of the 
compressive stresses. See R. T. Howe and R. S. Muller, "Stress in 
Polycrystalline and amorphous silicon thin films," J. Appl. Phys. 
54,4674(1983); H. Guckel, T. Randazzo, and D. W. Burns, "A single 
technique for the determination of mechanical strain in thin films with 
applications to polysilicon," J. Appl. Phys. 57,1671(1985). 
SUMMARY OF THE INVENTION 
A released film structure is made by first depositing a film onto a 
substrate, thereby inducing some intrinsic tensile stress in the film. A 
portion of the film is then removed to form a structure, leaving a 
predetermined structure whose intrinsic stress is maintained by the 
adhesive force of the substrate so that the structure is held in place. By 
removing the substrate, preferably by a plasma etch, the film structure is 
released or suspended permitting deformation of the structure as a result 
of the film's intrinsic tensile stress. By measuring the displacement of 
the structure from its pre-release position, it is possible to determine 
certain mechanical properties of the film. Most notably, the ratio of the 
intrinsic stress N.sub.0, to Young's modulus E, of the film is easily 
calculated from the stress induced displacement for certain structures. 
Structures highly suitable for determining these mechanical properties 
include "T" shaped figures and fixed-end beams, as well as a rotating 
plate, which are illustrated in the drawings described below.

DETAILED DESCRIPTION OF THE INVENTION 
The preparation of a suitable substrate for deposition of the film whose 
properties are to be measured is outlined in FIG. 1. Crystalline silicon 
wafers have mechanical properties well suited for released structure 
fabrication. First, one side of the wafer 10 is doped to a thickness 11 
suitable for use as a substrate (FIG. 1A). A masking material 12 is then 
grown or deposited on both sides of the wafer. A window 13 is opened on 
the back masking by a standard negative photoresist lithography (FIGS. 
1B,C). The silicon substrate 10 exposed by the window is then etched 14 
with a solution that will penetrate to the doped layer 11 and stop (FIGS. 
1D,E). After mask removal, this doped silcon diaphragm serves as the 
removeable substrate 15 for released structure analysis of films. 
EXAMPLE 1 
The following illustrates the basic microfabrication technique for 
generating 3-5 micron thick silicon diaphragms used in released structure 
analysis. 
A silicon wafer is doped with boron at 1175.degree. C. The depth of the 
doping level can be adjusted by extending the deposition period, and by 
using an oxidizing ambient which improves boron diffusivity in silicon. A 
two-hour deposition yielded a 4.7 micron thick boron layer. Any thin 
backside doping is stripped with HF, or if more significant, by an 
SF.sub.6 plasma or a wet chemical isotropic etch. 
To avoid significant altering of the doping profile after deposition, a 
masking material is deposited on the surface. In this case, a thermal 
silicon dioxide was grown at 990.degree. C. Oxide thicknesses were 3100A, 
resulting from 15 minutes dry O.sub.2, 45 minutes steam at 95.degree. C., 
and 15 minutes dry O.sub.2. 
A square window is formed in the back oxide by standard negative 
photoresist lithography. This is followed by a hydrazine etch at 
118.degree. C. for about 4 hours to remove the silicon through the oxide 
layer window. This resulted in a 1.times.1 mm silicon diaphragm, 4.7 
microns thick, with a 2800 .ANG. thick SiO.sub.2 layer on top. 
The steps for fabricating releasable thin film structures is outlined in 
FIG. 2. First, a diaphragm of appropriate size and thickness is fabricated 
as shown in FIG. 1. The masking material 12 is removed, in particular 
where compressive stress tends to deform the diaphragm in the material 
(FIG. 2A). The film 20 being evaluated is then formed on or within the 
substrate and covered with a material 16 suitable for masking and 
patterning the material (FIG. 2B). In FIG. 2C the masking material 16 is 
given a pattern or structure, in this case, a "T" shape. FIG. 2D 
illustrates the removal of the thin film 20 exposed by the structured 
mask. The doped substrate 11 can now be seen through the patterned masking 
16 and film 20 layers. The masking layer 16 is then removed completely to 
permit the free suspension of the thin film when the underlying substrate 
15 adjacent the film structure is etched away. FIG. 2E shows the 
deformation of the "T" structure resulting from substrate removal. Due to 
the asymmetric nature of the structure, the transverse beam of the "T" 
deflects 17 as a result of the intrinsic tensile stress in the base of the 
"T". The displacement of the structure is easily measured because the 
initial position of the transverse beam can be identified by drawing a 
straight line between the two points of the top side of the transverse 
beam where it meets the main portion of the film. 
EXAMPLE 2 
After constructing the oxide coated diaphragm of Example 1, first remove 
the oxide in HF. A commercially available polyimide is spin-coated onto 
the substrate-diaphragm using a vacuum spinning chuck at 4000 rpm for 2 
minutes. (Note that films whose properties are to be measured can also be 
deposited by spraying, spreading, painting, evaporating, sputtering, 
chemical vapor depositing (CVD), or by applying with any other suitable 
method.) This results in a film thickness of 2.5 microns. This layer is 
then baked at 135.degree. C. for 14 minutes. These coating and baking 
steps may be repeated to produce a film of desired thickness. In this 
case, 4 layers are applied, resulting in a 10 micron thick film which is 
then post-baked at 436.degree. C. for 45 minutes. 
To pattern the film, an aluminum layer of 2000 .ANG. is first evaporated 
onto the polyimide surface. The desired pattern is placed on the aluminum 
surface by a negative resist lithography. The aluminum pattern is first 
removed by a plasma etch. This reveals the surface of the polyimide 
through the patterned aluminum. The polyimide, as well as removal of the 
negative resist material, is accomplished by an O.sub.2 plasma etch. The 
aluminum layer is then removed using either a CCl.sub.4 plasma or a wet 
chemical etch, such as a Phosphoric-Acetic Nitric Acid solution. 
The final step is to release the structure by removing the silicon 
diaphragm. To remove a 4.7 micron thick diaphragm, a SF.sub.6 plasma etch 
is applied to the back of the diaphragm for 10 minutes. 
The "T" shape is particularly useful in measuring the ratio of residual 
stress to modulus. Large deflections are observed without creating large 
strains in the main body of the film surrounding the released structure. 
This guarantees that the film is in its linearly elastic domain. If the 
dimensions of the structure are selected appropriately, the Poisson's 
ratio for the film can also be extracted. 
In the discussion to follow, a simple analysis of the structure is 
performed by making appropriate assumptions, which can be verified later. 
FIG. 2E describes the parameters. This structure is modeled as a fixed-end 
beam or width 19, uniformly loaded in the center region by the center leg 
of width 18. The stress-induced shrinkage of this center leg creates the 
uniform load on the beam. To analyze this indeterminate structure, the 
force per unit length q on the boundary, is found in terms of the center 
deflection, d, (see deflection 17 of FIG. 2E) when the structure is 
released. 
The dimensions of the structure can be appropriately selected such that the 
deflection of the polyimide beam, d, is always less than 30% of the beam 
width, h. In this case, the beam deflections can be found by the well 
known application of small deflection theory and where the membrane 
stresses created as a result of the stretching of middle plane of the beam 
can be neglected. In this derivation, the effect of the residual tensile 
stress in the transverse beam is also neglected. 
The center deflection of a fixed-end beam under uniform load over a region 
in the center can be found by superposition of the deflections due to 
bending and shear as: 
EQU d=d.sub.b +d.sub.s, (1) 
where d is the total deflection and d.sub.b and d.sub.s are the 
contributions from bending and shear, respectively. The deflection at the 
center due to bending d.sub.b is given by: 
##EQU1## 
where 
EQU I=bh.sup.3 /12 (3) 
L is the length of the beam, b is the film thickness, W is the center leg 
width (18 in FIG. 2) and E is Young's Modulus. 
The component of the deflection due to shear, d.sub.s, given by 
##EQU2## 
where 
EQU A=bh (5) 
a.sub.s is the shear coefficient (which is equal to 1.5 for a beam with 
rectangular cross-section) and G is the modulus of elasticity in shear. 
The total deflection is: 
##EQU3## 
Note that shear forces aid deflection. 
However, q, is the load that is generated by stress-induced shrinkage of 
the center leg and is given as: 
##EQU4## 
where N.sub.0 is the residual tensile stress, L.sub.1 is the length of the 
center leg. In truth, this parameter is 
##EQU5## 
where L .sub.10 is the length of the presumably stress free transverse 
beam. However, this correction is of second order and is neglected here. 
In finding q, the center leg stress-induced shrinkage is modeled as 
uniform across the width, W. In reality, due to the curvature in the beam, 
this is not the case. However, the length of the center leg is very large 
compared to the variation in shrinkage across the width and justifies the 
assumption. By substituting equation (7) into equation (6) the ratio of 
the stress to the modulus is related to the deflection, d, the dimensional 
parameters, and Poisson's ratio u as 
##EQU6## 
Note that the first term in the bracket in equation (9) is the contribution 
due to bending moment while the second term is the contribution due to 
shear. The bending term is approximately proportional to cubic ratio of 
the beam length to the beam width while the shear term is proportional to 
the first power of the same ratio. If the fixed-end beam is made slender 
(large ratio of the beam length, L to the beam width, h) the contribution 
of the shear component is negligible. This contribution, however, is large 
for stocky beams, which are beams for which the ratio of L to h is not 
large. For a ratio of length to width of the beam larger than 10, the 
shear component is less than 10%. In this case, the shear contribution is 
neglected to simplify equation (9) to: 
##EQU7## 
By fabricating a structure of appropriate dimensions on a silicon diaphragm 
and then removing the diaphragm to release the structure, the deflection d 
can be measured. Using equation (10), the ratio of the stress to the 
modulus can be calculated. In addition, if several beams with small ratios 
of length to width are fabricated on the same sample, equation (10) can be 
used to fit the data and extract the values of N.sub.o /E and u that best 
fit. 
EXAMPLE 3 
Two wafers were processed with BTDA-MDA/ODA (benzo phenonetetracarboxylic 
dianhydride-oxydianiline/metaphenylene diamine), a microelectronic grade 
polyimide of thicknesses 5.5 and 8.0 microns. Each wafer had several T 
structures with either slender of stocky beams. The deflections are 
measured with .+-.3 microns accuracy using an optical microscope. For the 
slender beam structures (ratio of the length to width of the beam above 
10), equation (10) was used to find the stress to modulus ratio. All the 
fabricated structures have a beam length, L, of 2048 microns. Table I 
presents the data, including the critical dimensions, for the wafer with 
5.5 micron thick film. The ratio of the stress to the modulus is 
0.011.+-.0.002. It is evident from equation (10) that the error in 
measuring d creates the uncertainty in the calculated stress to modulus 
ratio. In this work, the error in measuring the deflection, d, is at least 
10% (increasing for smaller deflections). This large measurement error 
translates into the error on the calculated stress to modulus ratio. The 
reason for the large measurement error is that measurements had to be 
taken at low magnification to be able to see the entire fixed-end beam 
portion in the field of view of the microscope. At higher magnification 
where the accuracy of the measurement increases, the entire beam is not in 
the field of view to provide a reference for measuring the deflection. 
TABLE I 
______________________________________ 
Data on Slender-Beam T Structures 
# W h L.sub.1 d 
##STR1## 
______________________________________ 
1 800 133 3027 35.0 0.0118 
2 800 133 4027 42.5 0.0108 
3 800 133 4027 40.5 0.0102 
4 800 166 4027 37.0 0.0097 
5 500 166 3027 30.0 0.0104 
6 500 166 3027 33.0 0.0116 
7 500 209 3027 30.0 0.0110 
______________________________________ 
(W, h, L.sub.1 and d are in microns) 
Note that as the length to width ratio for the beam is decreased to enhance 
the shear contributions, the percent uncertainty in the deflection 
measurements increase since the deflections decrease. One way to improve 
the deflection measurement is to put a straight strip 27 of the polyimide 
close to the front of the beam as shown in FIG. 3. This allows for going 
to high optical magnification since it is no longer necessary to have the 
whole beam in the field of view. However, it is unlikely that measurements 
with better than .+-.1 micron accuracy can be performed using an optical 
set up. A potential method is the use of diffractometry through the slit 
created by the strip and the deflected beam. This would improve the 
accuracy in measuring the deflection to fractions of a micron. 
Other structures that are well suited for measuring the mechanical 
properties of thin polyimide structures are shown in FIG. 4(A-H) both 
before and after release from the substrate. In FIG. 4A, the square 
polyimide plate in the center rotates after release FIG. 4B because of the 
stress-induced shrinkage of the four arms 29, acting as two pairs of 
couples. In FIG. 4C, the fixed end polyimide beam deflects due to 
stress-induced shrinkage of the five arms 30 (FIG. 4D), creating a uniform 
load over parts of the beam. In FIG. 4E, the square plate held by four 
legs 31 and a wide center arm deflects as shown in FIG. 4F due to the 
stress-induced shrinkage of the long center arm, pulling on the plate. 
FIG. 4G shows a fixed-end polyimide beam with an abrupt width-change at a 
selected point 28 along the axis of the beam. Upon release of the 
structure in FIG. 4H the width-change boundary is displaced due to force 
imbalance in the structure. The wide portion shrinks, stretching the 
thinner members until force balance is achieved. 
These fixed-end beam structures are particularly useful in studying the 
ratio of the intrinsic stress in the film to the modulus, the yield 
strain, and the ultimate strain at break. The analysis is simple and 
demonstrates how the above parameters can be measured. FIG. 5 describes 
the parameters. Since the whole structure is made of the same material 
with uniform thickness, b, the depth dimension is incorporated here by 
introducing forces per unit length. This automatically assumes that the 
stresses are uniform across the thickness of the film. All the parameters 
of the wide member are denoted with subscript 1 while the parameters of 
the thin members are denoted with subscript 2. 
This indeterminate structure is analyzed by assuming a displacement d (22 
in FIG. 5) after the structure is released. Then, the force, F.sub.1, 
acting on the boundary by the stress-induced shrinkage of the wide member 
is 
##EQU8## 
where E is the Young's modulus, N.sub.0 is the residual stress in the 
film, L.sub.1 is the initial length of the wide member, and W.sub.1 is the 
width of the wide member. The force, F.sub.2, acting on the boundary 
because of the stretching of thin members due to the shrinkage of the wide 
member is 
##EQU9## 
where L.sub.2 and W.sub.w are the length 23 and width 25 of the thin 
member. At equilibrium the two forces are equal. Setting equations (11) 
and (12), the result is 
##EQU10## 
For actual fabrication, the thin member is split into two or four thinner 
members placed at equal distances across the width of the boundary (FIG. 
4G and FIG. 6). This avoids the out of plane curling of the edges, that 
otherwise would be unsupported, and greatly improves the stability of the 
structure. However, the above analysis still applies as long as W.sub.2 is 
taken to be the total width of the thinner members. 
In the above analysis, L.sub.1 and L.sub.2 are the lengths of the members 
before releasing the structure. In truth, these should be the length of 
the members, L.sub.01 and L.sub.02, when the members are stress-free. For 
example, the relationship between L.sub.1 and L.sub.01 is: 
##EQU11## 
However, this correction is of second order and is neglected here. 
Equation (13) shows that by measuring the displacement d after the 
structure is released, the ratio of the stress to modulus can be 
determined. It is also clear that the strain in the thin arms, e is 
##EQU12## 
By appropriate selection of dimensions, the e can range from nearly zero 
to the ultimate strain at break. In this way, the beams can function like 
a tensile testing machine. The modulus can be studied as a function of 
strain since the residual stress is constant, to find the ultimate strain 
for the film. Coupled with stress measurements from load-deflection 
studies on polyimide membranes, the stress-strain curve can be determined. 
Such a curve is schematically illustrated in FIG. 10, in which S.sub.1 and 
e.sub.1 are the stress and strain of the films as fabricated. Known 
methods of stress analysis, such as the cantilever beam yield only S.sub.1 
and e.sub.1 for a particular film. By varying the dimensions of the 
structures, the strain can be varied over a range of values e.sub.2, 
e.sub.3 including the ultimate strain at break e.sub.4. This aspect of the 
invention arises due to the redistribution of stress that occurs upon 
release of the structure. For example, by varying the width of the narrow 
beams, the structure will deform differently upon release yielding a 
different strain e. 
EXAMPLE 4 
Two wafers were processed, with polyimide film thickness of 5.5 microns for 
the first sample and 8.5 microns for the second. Beams with various 
dimensions were fabricated on each sample. Table II shows the data on six 
beams that were fabricated on the wafer with 5.5 micron polyimide film. 
The deflections were measured with .+-.3 microns accuracy. 
TABLE II 
______________________________________ 
Data on Fixed-end Beam Structures 
L.sub.1 
L.sub.2 W.sub.1 
W.sub.2 d 
##STR2## 
______________________________________ 
1535 505 690 2 .times. 45 
13.0 0.0136 
1535 505 690 2 .times. 45 
13.0 0.0136 
1535 505 690 4 .times. 20 
14.0 0.0140 
2510 505 590 2 .times. 95 
11.5 0.0151 
2510 505 690 2 .times. 95 
12.0 0.0156 
2510 505 690 4 .times. 45 
12.0 0.0149 
______________________________________ 
(L.sub.1, L.sub.2, W.sub.1, W.sub.2, and d are in microns) 
The stress to modulus ratio for these samples is 0.0145.+-.0.002, somewhat 
higher than expected. There are two explanations: first, the stress in the 
polyimide film of this wafer is higher than normally observed. Second the 
film could have yielded since the strains are high, on the order of 4%. On 
the wafer with the thinner film, when the strain, e.sub.2, exceeded 4.5%, 
the members completely failed. On the wafer with the thicker polyimide 
film, although the film cracked above 4.5% strain, it did not break until 
8% strain was reached. Ratio of the stress to modulus calculated from 
measurements on this sample are also in agreement with the above results 
for strains close to 4.5%. The ratio increased for higher strains, which 
is attributed to the cracking of the film, acting like the film is 
yielding. In a thin film, cracks are fatal while in the thicker film the 
cracks provide partial relaxation of the stress in the member. Even though 
there is not enough data for a firm conclusion, it may be assumed that the 
film is yielding at strains close to 4%. To confirm this, the stress to 
modulus ratio has to be determined for this film at lower strains. This 
can be done by either adjusting the dimensions of the structures or 
putting T structures on the sample. 
FIG. 6 shows a SEM photograph of a typical fabricated beam on the 5.5 
micron thick polyimide sample. The dimensions are 1500 microns long by 490 
microns wide, changing to 80 microns wide (20 microns for each member) for 
a length of 505 microns. FIG. 7 is the magnified view of the boundary in 
the FIG. 6. The white line marks where the width-change boundary was 
located before the structure was released. The displacement in this case 
is 14 microns. 
FIG. 8 is a SEM photograph showing a rotated plate after release that is 
held by four orthogonal arms. 
FIG. 9 is a magnified view of the plate. 
In summary, beam dimensions were chosen to study a variety of polyimide 
chemistries with BTDA-ODA/MPDA being the first to try. This polyimide 
develops failure signs at strains above 4.5% and fails at above 8% strain 
(for 8.5 micron thick film). The ultimate strains for BTDA-ODA/MPDA 
polyimide were thought to be above 10%. The fixed-end beam structures are 
appropriate for studying both the stress to modulus ratio at high strains 
and the ultimate strain of thin films under tension have been introduced. 
These structures can be used in-situ with accurate control on the 
dimensions and axial loading of the beam. The film can be viewed in-situ 
as strained with optical and scanning electron microscopes, revealing 
failure signs such as cracking. 
While the invention has been particularly shown and described with 
reference to preferred embodiments thereof, it will be understood by those 
skilled in the art that various changes in form and details may be made 
without departing from the spirit and scope of the invention as defined in 
the appended claims.