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Tunable Optical Grating for High Sensitivity Strain Sensing for
Semiconductor Material
George Chen
Arizona State University
Branch Counselor: Cihan Tepedelenlioglu
IEEE Number: 92186566
1005 East 8th Street Tempe, AZ 85281
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Tunable Optical Grating for High Sensitivity Strain Sensing for
Semiconductor Materials
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Table of Contents
Abstract………………………………………………………………………………………………………………..4
Introduction……………………………………………………………………………………………………..….4
The Grating……………………………….………………………………………………………………………….5
The Optical Setup…………………………………………………………………………………………………6
Finite Element Analysis…………………………………………………………………………………………7
Experimental Results……………………………………………………………………………………………8
Conclusion………………………………………………………………………………………………………….10
Acknowledgements…………………………………………………………………………………………….10
References………………………………………………………………………………………………………….11
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Abstract
In this paper, a novel strain sensing procedure using polydimethylsiloxane (PDMS) as an optical
grating is used to measure heat induced strain on different types of substrates. This paper will discuss
the methodology of using PDMS as a strain sensor. This is done by bonding the PDMS grating onto a
copper or silicon substrate, and then measuring the diffraction angle change due to thermal strain,
which is used to deduce the coefficient of thermal expansion (CTE). Thus far, measurements have been
completed that agree well with reference values.
Introduction
Wrinkling/buckling in a material is generally seen as a mechanical instability that is seen in a
negative light. However, recent research has led to many advancements in using buckled structures on
stiff thin films, including applications in: stretchable electronic devices1-7, microfluidics8, metrology
methods9, and tunable diffraction gratings8, 10, 11, 12 just to name a few.
Diffraction gratings are generally created in one of two ways. The first is through the use of a
ruling engine which uses a diamond-tipped tool to etch the lines. Another method that is often used is
laser interferometry which uses two lasers to create a holographic grating with sinusoidal grooves. In
this paper, a new grating manufacturing technique has been developed that is much simpler than the
aforementioned techniques. The method uses a soft substrate, and mechanically stretches it, before
treating it with oxygen plasma and depositing Au/Pd. When the tension is released, an optical grating is
formed. The simplicity of the manufacturing steps of the grating has another also causes it to be much
cheaper to produce.
The PDMS/Au gratings in this paper are used as a tunable strain sensor. The strain sensing in this
project is based off of an optical setup which is used to detect changes in the diffraction angle when a
laser is shined onto the surface of the grating after it has been attached to a substrate. Simulations have
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shown that this tunable grating along with the optical setup is expected to have high sensitivity in
measuring strain on various substrates such as copper and silicon.
The Grating
Figure 1(a) illustrates how the optical
grating is manufactured with the new
technique. The polydimethylsiloxane (PDMS) is
created by mixing the elastomer base with the
curing agent in a 10:1 ratio by weight. The
PDMS is then degassed and cured for three
hours at 80 ˚C. The PDMS is then mounted and
mechanically stretched on a linear stage. It is
then exposed to oxygen plasma (50 W) for one
minute before it is sputter coated with
approximately 10 nm of Au. After it is sputter
coated, the pre-strain from the mechanical stage is released which forms a buckled, sinusoidal pattern
on the surface of both the PDMS and the Au thin film. The wavelength of the wrinkling, d, can be
determined by the formula,
𝑑 = 2𝜋ℎ𝑓
(1+𝜀𝑝𝑟𝑒)[1+5𝜀𝑝𝑟𝑒
32(1+𝜀𝑝𝑟𝑒)]
1/3 [𝐸𝑓(1−𝑣𝑠
2)
3𝐸𝑠(1−𝑣𝑓2)
]1/3
(1)
where ℰpre is the strain applied by the linear stage, hf is the thickness of the Au film, E is Young’s
modulus, and v is Poisson’s ratio. The subscripts of s refer to the PDMS substrate while the f refers to
the Au. This formula shows that the by changing the amount of pre-strain ℰpre or the film thickness, hf,
the grating wavelength can be effectively tuned.
Figure 1: (a) Schematic of the fabrication process for PDMS/Au grating. (b) Optical microscopy image and (c) Atomic force microscopy (AFM) images of wrinkling profile of PDMS/Au grating surface. (d) Wrinkling wavelength distribution at ten different spots over a surface area of 100×100μm2. The wrinkling wavelength remains largely constant over this surface area, in good agreement with the calculated wavelength value by Eq. (1). The error bars are one standard deviation of the data, which is taken as the experimental uncertainty of the measurement.
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In figure 1(b), an optical microscope slide of the PDMS grating is shown with hf = 10 nm and
ℰpre=15%. This results in a wavelength of 1.22 µm which is given as 1.20 µm for equation 1, when the
parameters are set as: Ef = 80 GPa, Es = 2 MPa, vf=.3, and vs=.49.11 Figure 1(c) shows the atomic force
microscope (AFM) 2D and line-scan images which demonstrates the uniformity of the buckling pattern
on a small area. This was done several times across the sample to ensure uniformity of the entire
sample. This can be seen in figure 1d which shows the uniformity measured at 10 different locations
with an area of 100x100 µm2.
The Optical Setup
In order to test the strain using the grating mentioned
previously, it was necessary to create an optical setup
that operated on the principles of optical diffraction.
As seen in figure 2, a laser light source is used to shine
onto the grating which diffracts the laser light into the
photo detector. The grating itself is attached to
substrates such as silicon or copper, and a minute change in strain of the underlying substrate causes a
larger change in the displacement produced by the grating as measured by the photo detector. By
analyzing the displacement of the peak laser beam position, the strain of the underlying substrate can
be extracted. The use of a diffraction grating is quite common in optics and can be explained by the
equation,
𝑑0 sin 𝜃 = 𝑚𝜆 (2)
where is the diffraction angle, d0 is the initial grating wavelength, and is the laser source wavelength,
and m is the order of diffraction. Figure 2 also shows a geometric relationship between the horizontal
position L and the vertical position y, which can be related by the equation: tan = 𝑦
𝐿 . When thermal or
mechanical strain is introduced to the underlying substrate, the grating wavelength changes from d0 to
Figure 2: Optical Setup for Strain Measurement
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d(=d0+Δd) which causes the diffraction angle, , to shift by Δ , which results in a change in the vertical
position y by Δy, which is also linearly dependent on Δd:
3/2 3/2
2 2 2 22
0 02 2
0 0
1 1
L Ly d A
m md d
d d
(3)
Here the strain on the substrate is denoted by ε which is equal to Δd / d0 and is directly proportional to
Δy by the magnification factor A (generally 1x107 µm).
The laser light source seen in figure 2 is a 633nm He-Ne laser with a 21mW output power.
Although the figure shows two optical lenses that are used to reduce the laser spot size from 700µm to
200µm, there are several components between the laser and grating that aren’t shown, such as the
optical chopper. The optical chopper is used to improve the signal to noise ratio and beam splitters are
also implemented to provide a reference signal into the auto-balanced photo detector. The photo
detector then compares the reference signal with the diffracted beam to further improve the signal to
noise ratio to increase the sensitivity of the optical setup.
Finite Element Analysis Simulation
In order to verify that the surface of the PDMS
grating will exhibit the strain of the underlying
substrate, finite element analysis (FEA)
simulations were done to test this theory. To
complete this, Abaqus13 Unified FEA was used.
The simulation results for this can be seen in
figure 3. Figure 3(a) shows the schematic of the
PDMS attached to the Si substrate. Figure
3(b)(i) shows an L/h ratio of 1 and the strain at Figure 3: (a) The schematic of the PDMS grating attached to a silicon substrate (b)(i-iv) Strain contours in the horizontal direction for different ratios of PDMS length(L) to a constant thickness of (h=100µm).
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the top of the PDMS is about two orders of magnitude higher than the strain at the top surface of the
silicon substrate. Figure 3(b)(ii, iii, and iv) show L/h ratios of 3, 10, and 30 respectively. It can be seen
from these simulation results that a small L/h ratio causes the surface of the PDMS to exhibit the strain
on the PDMS itself and not the silicon. However, with a higher L/h ratio, the strain from the underlying
silicon is clearly reflected on more and more of the surface of the PDMS grating. In fact, at an L/h ratio of
30, the strain of the underlying silicon is reflected on more than 80% of the total surface of the PDMS
grating. Since the laser spot is shined onto the center of the PDMS grating during testing, the detected
strain εPDMS reflects the actual strain εSi of the underlying substrate. Figure 4(a) shows the ratio of εPDMS to
εSi as a function of L/h for the
PDMS grating on the Si substrate.
These results show that when the
L/h ratio exceeds 20, the εPDMS
reflects the εSi with only a 5%
margin of error. Figure 4(b) shows
that this L/h ratio is independent of temperature which implies that the strain measurement can be
made without worrying about the temperature since the strain measurements that are made are
completed by introducing thermal strain. The L/h ratios were taken into consideration when
manufacturing the PDMS gratings used in the experiments. These simulation results show that the
current setup should be able to successfully measure the strain on various substrates using the PDMS
grating.
Experimental Results
To verify the strain sensing capabilities of the optical setup, three different configurations of
PDMS on various substrates were tested that had coefficients of thermal expansions (CTE’s) spanning
three orders of magnitude. The first test was completed on free standing PDMS, the second tested
Figure 4 :(a) εpdms/εSi and εpdms as a function of L/h. (b) Phase diagram of εpdms/εSi.
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PDMS on a copper substrate, and the third tested PDMS on a silicon substrate. The thermal strain was
induced through the use of a heating cartridge that is controlled by a thermal couple to create a
feedback system to control the temperature. Several calibrations were done to calibrate the system to
within a degree of accuracy, while the temperature was ramped from room temperature (22°C) to 65°C.
Figure 5: Measured CTE results for (a) free standing PDMS, (b) PDMS on a Copper substrate, and (c) PDMS on a silicon substrate. A schematic of the heating setup is inset.
In figure 5(a) it can be seen that the measured CTE is 274 parts per million per degree Celcius
(ppm/°C) for free standing PDMS. The PDMS had a portion of it hanging off the edge of the Cu block and
that is where the laser spot size was shined to analyze the diffraction peaks. The results show good
linearity and are quite close to a reference value of 265 ppm/°C which was obtained from a commercial
thermal-mechanical analysis tool (Q400 from TA instruments under an expansion mode of 10mN force).
In figure 5(b) the results for PDMS on a copper substrate is shown, and the measured CTE is 18.2
ppm/°C. In this test, the PDMS was directly attached to the copper substrate with the use of double
sided adhesive tape which explains why the linearity of the test is not as good since the bonding quality
may have been an issue when the temperature is raised. The measured CTE of 18.2 ppm/°C is consistent
with the accepted CTE value of Cu which is 17.5 ppm/°C14.
In figure 5(c), the result for PDMS bonded to a silicon substrate is shown with a measured CTE of
2.7 ppm/°C. Unlike the previous two, the PDMS and Si had excellent bonding due to a surface treatment
of oxygen plasma on the Si to form a SiO2 bond between the PDMS and Si. The commercially accepted
CTE value for Si is 2.6 ppm/°C, and the measured value of 2.7 ppm/°C is indeed very close to that
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reference value. The data here also shows very good correlation which is attributed to the better
bonding quality between the Si and the PDMS grating compared to the PDMS attached to copper. The
ability to measure the CTE of Si demonstrates the high strain sensitivity of this technique since the
displacement within the silicon is on the order of 10-5 meters with a 200µm laser spot.
Conclusion
In conclusion, PDMS gratings fabricated through buckled thin films were successfully used to
detect micro strains in various substrates that spanned coefficients of thermal expansion across several
magnitudes. An optical setup is optimized to amplify the small strain signal so that it can be accurately
measured. The use of this PDMS grating does require an L/h aspect ratio of 20-30 for the strain of the
underlying substrate to be reflected on the surface of the PDMS strain grating. This novel strain
detection method that can be coupled with 1-D and 2-D scanning capabilities to rival that of both Moiré
Interferometry15 as well as Digital image correlation (DIC)16, in terms of the spatial resolution as well as
the in plane displacement. Future work lies in further improving the optical setup as well as automating
the entire strain measurement process.
Acknowledgements
I acknowledge the support from Intel Corporation through the university consortium Connection One. I
would like to thank the Fulton Undergraduate Research Initiative (FURI) program at the University for
providing part of the funding for this project. Lastly I would like to acknowledge Hanshuang Liang, Teng
Ma, Dr. Hongbin Yu, and Dr. Hangqing Jiang for mentoring me.
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