1

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

2

Tunable Optical Grating for High Sensitivity Strain Sensing for

Semiconductor Materials

3

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

4

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

5

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.

6

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

7

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).

8

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.

9

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

10

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.

11

References

1. W. M. Choi, J. Song, D.-K. Khang, H. Jiang, Y. Huang and J. A. Rogers, Biaxially stretchable “wavy”

silicon nanomembranes. Nano Letters,pp. 1655-1663, 7. 2007.

2. D. Y. Khang, H. Q. Jiang, Y. Huang and J. A. Rogers, A stretchable form of single-crystal silicon for

high performance electronics on rubber substrate. Science, pp. 208-212, 311. 2006.

3. H.Q Jiang, Y.G. Sun, J. A. Rogers and Y. G. Huang, Mechanics of precisely controlled thin film

buckling on elastomeric substrate. Applied Physics Letters, pp.133119, 90. 2007.

4. K. M. Choi and J. A. Rogers, Journal of the American Chemical Society, pp.4060-4061, 125. 2003.

5. H. Jiang, D.-Y. Khang, J. Song, Y. Sun, Y. Huang and J. A. Rogesr, Proceedings of the National

Academy of Sciences of the United States of America, pp. 15607-15612, 104. 2007.

6. C. J. Yu, C. Masarapu, J. P. Rong, B. Q. Wei and H. Q. Jiang,Stretchable Supercapacitors based on

Buckled Single-Walled Carbon Nanotube Macro-Films, Advanced Materials. pp. 4793-4797, 21.

2009.

7. C. J. Yu, Z. Y. Wang, H. Y. Yu and H. Q. Jiang, A Stretchable Temperature Sensor Based on

Elastically Buckled Thin Film Devices on Elastomeric Substrates, Applied Physics Letters. pp.

141912-3. 95, 2009.

8. K. Efimenko, M. Rackaitis, E. Manias, A. Vaziri, L. Mahadevan and J. Genzer, Nested self-similar

wrinkling patterns in skins, Nat Mater. pp. 293-297. 4, 2005.

9. C. M. Stafford, C. Harrison, K. L. Beers, A. Karim, E. J. Amis, M. R. Vanlandingham, H. C. Kim, W.

Volksen, R. D. Miller and E. E. Simonyi, A buckling-based metrology for measuring the elastic

moduli of polymeric thin films, Nat Mater. pp. 545-550, 3. 2004.

10. J. L. Wilbur, R. J. Jackman, G. M. Whitesides, E. L. Cheung, L. K. Lee and M. G. Prentiss,

Elastomeric Optics, Chemistry of materials pp. 1380-1385, 8. 1996.

11. C. J. Yu, K. O'Brien, Y. H. Zhang, H. B. Yu and H. Q. Jiang, Tunable Optical Gratings Based on

Buckled Nano-Scale Thin Films on Transparent Elastomeric Substrates, Applied Physics Letter.

pp.04111, 96. 2010.

12. X. Y. Jiang, S. Takayama, X. P. Qian, E. Ostuni, H. K. Wu, N. Bowden, P. LeDuc, D. E. Ingber and G.

M. Whitesides, Controlling Mammalian Cell Spreading and Cytoskeletal Arrangement with

Conveniently Fabricated Continious Wavy Features on Poly(dimethylsiloxane) Langmuir. pp.

3273-3280, 18. 2002.

13. A.U. Manual, “Version 6.5, Hibbitt, Karlsson and Sorenson,” Inc., Pawtucket, RI (2004).

12

14. C.S. Selvanayagam, J.H. lau, X. Zhang, S. Seah, K. Vaidyanathan, and T. Chai, “Nonlinear thermal

stress/strain analyses of copper filled TSV (through silicon via) and their flip-chip microbumps,”

IEEE Transactions on Advanced Packaging. pp. 720-728, 32. 2009.

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

Scanning-moiré Method, Experimental Mechanics. pp. 112-116, 24. 1984.

16. H Jin, W-Y Lu, and J Korellis. Micro-scale deformation measurement using the digital image

correlation technique and scanning electron microscope imaging, The Journal of Strain Analysis.

pp. 719-727, 43. 2008.