This study investigated the techniques for determining the elastic modulus and estimating the stress gradient of plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The experimentally determined elastic modulus was then used in a finite element beam model to compute the stress distribution inside the thin films using a commercial finite element analysis package. The computed beam displacement caused by a given stress gradient was compared with the displacement experimentally evaluated using optical interference microscopy. This comparison allows the stress gradient of the PECVD silicon nitride membrane introduced by the fabrication process to be evaluated

Antoszewski, J.

Dell, J. M.

Faraone, L.

Hu, X. Z.

Huang, H.

Liu, Yinong

Martyniuk, M.

Musca, C. A.

Nguyun, T.

Walmsley, B.

Winchester, K.

University of Queensland eSpace

SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
Evaluation Of Elastic Modulus And Stress Gradient Of PECVD 
Silicon Nitride Thin Films 
 
H. Huang1, K. Winchester2, J. Antoszewski2, T. Nguyun2, M. Martyniuk2, B. 
Walmsley1, Yinong Liu1, X.Z. Hu1, C.A. Musca2, J.M. Dell2, L. Faraone2 
1School of Mechanical Engineering, University of Western Australia, Australia 6009 
2School of Electrical, Electronic and Computer Engineering, University of Western Australia, Australia 6009 
 
 
 
ABSTRACT: This study investigated the techniques for determining the elastic modulus and estimating 
the stress gradient of plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The 
experimentally determined elastic modulus was then used in a finite element beam model to compute the 
stress distribution inside the thin films using a commercial finite element analysis package. The computed 
beam displacement caused by a given stress gradient was compared with the displacement experimentally 
evaluated using optical interference microscopy. This comparison allows the stress gradient of the PECVD 
silicon nitride membrane introduced by the fabrication process to be evaluated. 
 
1. INTRODUCTION 
In recent years PECVD silicon nitride (SiNx) has found increasing application as a structural 
material in microelectromechanical systems (MEMS), such as static membranes, tunable inductors 
and tunable MEMS Fabry-Pérot (FP) optical filters [Dell et al., 2002]. The advantage of PECVD 
SiNx is that it can be deposited at much lower temperatures than SiNx deposited by the more 
commonly used low-pressure chemical vapor deposition (LPCVD) method [Winchester and Dell, 
2001]. This is beneficial in fabricating devices that are temperature sensitive. However, evaluation 
and control of mechanical properties, such as elastic modulus and intrinsic stress, in thin films are 
critical to achieve required device performance and yield. 
SiNx thin films are used to construct tunable FP optical filters in this study. As illustrated in 
Figure 1(a), the PECVD SiNx thin film forms a membrane structure that is suspended on four pillar 
supporters via suspension arms. The membrane carries a mirror on its top surface, moving up and 
down under electrostatic force in response to a bias voltage applied between the membrane and the 
ground. Mechanical characteristics of the silicon nitride membrane, including the elastic modulus of 
the material, the intrinsic stress gradient through the thickness of the SiNx layer and the mechanical 
design of the structure, are thus of great significance in determining structural integrity and filter 
performance. Figure 1(b) shows the variation in the modeled response of the cross membrane 
structure in Figure 1(a) with the elastic modulus as a parameter. A change of modulus value from 
220 GPa, a typical value for bulk silicon nitride, to 150 GPa can result in a membrane displacement 
variation of ~50 nm at the applied bias of 1 V. The variation is significant when constructing a FP 
filter that is to operate over a specific spectral range. Of the same importance is the degree of any 
intrinsic stress gradient existing in the SiNx layer, which causes inherent deformation to the 
membrane and thus affects the optical performance of the filter. Therefore, it is essential to 
understand the properties of low-temperature deposited PECVD SiNx films if this material is to be 
successfully applied to MEMS devices.  
This paper reports on a nanoindentation investigation to determine the elastic modulus of 
PECVD SiNx thin films. The experimentally determined modulus was then used in a finite element 
cantilever beam model to estimate the intrinsic stress gradient resident in fabricated PECVD SiNx 
beams. By comparing the modeled beam deflection with the experimentally measured beam 
deflection, the stress gradient was then evaluated. Further verification of this method was carried 
out in a cross membrane structure. 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
   
0.00
0.10
0.20
0.30
0.40
0.50
0.00 0.50 1.00 1.50 2.00
Applied Bias (V)
D
is
pl
ac
em
en
t (
µm
)
SiNx (E= 150 GPa) 
SiNx (E= 220 GPa)
 
Figure 1: (a) The FP filter consists of a top mirror, a SiNx layer and a ground mirror. The SiNx layer has a square 
membrane (with dimensions: 100 x 100 x 0.4 µm) supported at each corner by four arms (with dimensions: 100 x 20 
x 0.4 µm). There is a cavity (1.2 µm in length) between the membrane and the ground. (b) Boundary and finite 
element modeled membrane deflection is plotted as a function of applied voltage. 
2. EXPERIMENT 
SiNx thin films were deposited by PECVD at 125°C using SiH4/NH3/N2 precursors. The SiNx films 
for nanoindentation measurement were deposited on 300 µm thick silicon (Si) substrates. The film 
thicknesses were 350, 390 and 700 nm. The films were amorphous with a small volume fraction of 
porosity. Atomic force microscopy (AFM) showed smooth film surfaces with roughness less than 
10 nm. For micro-cantilever beams fabrication, the SiNx was deposited onto polyimide using the 
identical conditions to those made for nanoindentation, and then released in oxygen plasma. The 
beam deflection was measured using an optical microscope fitted with a green interference filter 
[Martyniuk et al. 2004]. 
Nanoindentation experiments were conducted using a HYSITRON TriboScope nanomechanical 
testing instrument. A Berkovich indenter with a tip radius of 100 nm was used. For each specimen, 
64 indents were performed with a load ranging from 50 µN to 9000 µN. Determination of elastic 
modulus was made from the initial part of the unloading-displacement curves [Oliver and Pharr, 
2004], over indenter penetration depths ranging from 20 nm to 200 nm. AFM was also used to 
confirm that the indents were well-formed over this penetration range. The elasticity modulus of the 
bilayer specimen was calculated by using Equation 1. 
                                               
EEE ieff
i
22 111 νν −+−=         (1) 
where Eeff is the effective modulus determined from the load-displacement curve, Ei and νi are the 
modulus and Poisson’s ratio of the diamond indenter, and E and ν are the modulus and Poisson’s 
ratio of the specimen.  Values of Ei = 1141 GPa, νi = 0.07 and ν = 0.27 were used in this study. 
Finite element modeling of stress gradient was conducted using commercial software 
CoventorWare™ Version 2003.1. For cantilever beam models, all the nodes at the fixed end of a 
beam were constrained in the directions of x, y and z axes. The cantilever beam models were 
meshed using the 27-node Manhattan Bricks. The cross membrane model used 1883 27-node 
Extruded Bricks, with the same boundary condition of no displacement along x, y and z axes 
applied to all the nodes at the fixed end of the arms. 
 
 
Ground
Top Mirror 
SiNx Layer 
(a) 
(b)
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
3. RESULTS AND DISCUSSION 
3.1 Nanoindentation 
Figure 2 shows the nanoindentation measurements of elastic modulus of the PECVD SiNx/Si 
bilayer specimens as a function of the indent contact depth. Also shown in the figure is the 
measurement of the elastic modulus of the Si substrate. It is seen that the measured moduli of all 
three specimens are less than that of the Si substrate and increased asymptotically to that of the Si 
substrate with increasing contact depth h. It is expected that for bilayer systems the measured 
modulus via indentation should eventually reach that of the substrate [Bhattacharya and Nix, 1988, 
Jung et al., 2004], which is 168 GPa in this case. However, the maximum load of the indenter used 
in our experiments is limited to 9000 µN, which is insufficient to see saturation of the modulus 
value.  
It is commonly believed that for a film/substrate bilayer system the elastic modulus of the film 
can be measured only if the ratio of indentation depth to film thickness is below a critical value, e.g. 
0.1. For this case, the data obtained at smaller contact depths, e.g. when h < 50 nm, appeared to be 
not reliable, mainly due to the size effect of the indentor tip [Wei et al. 2004], which had a nominal 
radius of 100 nm in this case. As shown in Figure 2, there appeared to be a plateau in the modulus 
value for each specimen when h is within the range of 50 to 80 nm, indicating that within this range 
of contact depth the effect of substrate on the measured modulus could be negligible. The plateau 
values are considered the true values of elastic modulus of the thin films. The determined modulus 
values for the films of 390 and 700 nm in thickness were ~100 GPa. The modulus for the film of 
350 nm was measured to be 108 GPa, slightly higher than the values for the two thicker films. The 
result indicated that for the SiNx/Si bilayer systems studied here the minimum film thickness for 
obtaining reliable film modulus was about 400 nm. This further suggested that a thicker film can 
provide more reliable estimation of the true film property. 
(a)
0
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100
150
200
250
0 50 100 150 200
h (nm)
El
as
tic
 M
od
ul
us
 (G
Pa
)
Pure Si
SiNx, 700nm
SiNx, 350nm
SiNx, 390nm
 
Figure 2: Elastic moduli of SiNx/Si bilayer systems and Si substrate are plotted as a function of indenter contact 
depth, h. 
3.2 Evaluation of intrinsic stress gradient 
Intrinsic stresses can be easily generated during processing of low-temperature deposited SiNx films. 
The evaluation of intrinsic stresses in thin films is essential in order to realize the required 
performance and reliability of any MEMS device where thin films are used. A typical method to 
assess the internal stresses is to measure the stress-induced substrate curvature using an optical 
setup. From the measured curvature, the average stress in a thin film can be estimated using the 
Stoney formula [Stoney, 1909]. X-ray diffraction (XRD) methods have also been utilized to 
measure the stress residing in thin films [Zhang et al., 1999]. In this method, the shift of the {100} 
a
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
crystal plane diffraction peak of the substrate caused by internal strain is detected by XRD. The 
stress was then calculated by multiplying the strain with the elastic modulus. The method is 
effective only if stress in thin films is sufficiently high that the induced substrate strain can be 
detected by XRD. The estimated stress is that in the near interface layer between the film and the 
substrate. 
To date, there does not appear to have been reported any reliable methods that are able to 
measure stress gradient through thickness (i.e. along z-axis) in thin films. In this study, a method 
that utilizes both experimental and numerical results for evaluating the stress gradient in SiNx films 
was investigated. In this method, a cantilever beam of 200 µm in length, 20 µm in width and 500 
nm in thickness was fabricated using low-temperature PECVD of the SiNx film followed by oxygen 
plasma sacrificial layer removal. Upon the release, the beam was deflected under the influence of 
the internal stress gradient in the thin film. The beam profile was measured along the length using 
an interference microscope, with the results shown in Figure 3(a) as solid symbols. A finite element 
model of the cantilever beam was then built. With the assumption that the stress gradient was the 
dominant factor to cause the beam deflection, the beam profiles were numerically obtained by 
employing different values of linear plane stress gradient along the z-axis. The best fit of the 
computed beam profile to the measured data gave an estimate of the stress gradient in this thin film. 
The computed beam profile under a stress gradient of 275 MPa/µm was found to be the best 
estimation, which was also plotted in Figure 3(a). To further test the reliability of this method, 
cantilever beams with different lengths were fabricated using the same processing conditions as 
those used to obtain the data in Figure 3(a). Their corresponding FEM models were also built. This 
time, the stress gradient of 275 MPa/µm estimated earlier was used in all the models and the beam 
deflections were thus computed. The comparison between the measured and computed tip 
deflections, shown in Figure 3(b), indicates a good agreement between the finite element modeling 
and the experimental data. Minor differences could be due to the assumption of a linear distribution 
of the stress gradient in the films and the beam dimensional error from the fabrication.  
The method was also used to evaluate the stress gradient in a Fabry-Perot SiNx membrane 
structure fabricated using the low-temperature PECVD SiNx and an oxygen plasma release process. 
The stress gradient value of 275 MPa/µm was again used in the cross membrane FEM model to 
compute its resultant deformation. As shown in Figure 4(a), the computed deformation along z-axis 
at the center of the membrane is -469 nm (i.e. bowing downwards) and the deformation along the 
edge of the membrane is +532 nm (i.e. extending upwards). The PECVD fabricated cross 
membrane structure, that has the same dimensions as those in Figure 4(a), has a deformation of 
about -500 nm at the center and a deformation of about 500 nm along the edge, estimated using its 
interference pattern shown in Figure 4(b). The deformation values determined experimentally and 
numerically are in reasonably good agreement. Careful comparison of the two images in Figure 5 
shows that their deformation patterns are rather similar. The differences in deformation values could 
be attributed to the complexity of the cross membrane structure being modeled, as well as the 
dimensional inaccuracy caused by the fabrication. The MEMS fabrication might produce a 
dimensional inaccuracy of several percent and a certain level of non-uniformity in membrane 
thickness, which was not considered in the finite element model. In future studies the FFM model 
will be refined to allow improved stress gradient evaluation. 
4. CONCLUSIONS 
The nanoindentation technique was found to be an effective method to measure elastic modulus of 
low-temperature deposited PECVD SiNx thin films. The accuracy of this method relies on the 
proper interpretation to indentation results. This study has demonstrated that the effect of the 
substrate must be removed to obtain a reliable modulus values for the thin films considered here. 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
(a) (b)
By comparing cantilever beam deformations predicted by finite element modeling with the 
experimentally determined beam deflection results, the intrinsic stress gradient in the thin films can 
be estimated. Experimental verification with the cross membrane structure indicates that this 
method is reliable. However, model refinement is needed to achieve a more accurate estimation of 
stress gradient. 
0
10
20
30
40
50
0 50 100 150 200
Position Along Beam Length (µm)
D
ef
le
ct
io
n 
( µm
)
Measurement
Simulation
 
Figure 3: (a) Measured and computed deflection profile of a cantilever beam. Beam is 200 µm in length, 20 µm in 
width and 300 nm in thickness. (b) Comparison between measured and computed tip deflections of cantilever 
beams with various lengths under a stress gradient of 275 MPa/µm. E = 100 GPa was used in the modelling. 
 
 
Figure 4: (a) Deformation contour map of the modelled membrane structure was obtained under a stress gradient of 275 
MPa/µm. E = 100 GPa was used in the modelling. The square membrane has an edge length of 100 µm and a thickness 
of 400 nm which is supported at its corners by four arms. The arm dimensions are 20 µm in length and 10 µm in width. 
(b) PECVD fabricated cross membrane structure using deposition temperature of 125 oC in a SiH4/NH3/N2 atmosphere 
followed by the oxygen plasma releasing. Each interference fringe indicates a deformation of 250 nm. 
ACKNOWLEDGEMENTS 
This project is financially supported by DARPA/MTO under grant number BAA02-20.  
REFERENCES 
Bhattacharya, A K and Nix W D: Analysis of elastic and plastic deformation associated with indentation 
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SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
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Evaluation Of Elastic Modulus And Stress Gradient Of PECVD Silicon Nitride Thin Films

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Evaluation Of Elastic Modulus And Stress Gradient Of PECVD Silicon Nitride Thin Films

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