Subcontract Report 

NREL/SR-520-44237 

November 2008 

Full Field Birefringence 

Measurement of Grown-In 

Stresses in Thin Silicon Sheet 

Final Technical Report 

2 January 2002 – 15 January 2008 

S. Danyluk 

Georgia Institute of Technology 

Atlanta, Georgia 

S. Ostapenko 

University of South Florida 

Tampa, Florida 
Full Field Birefringence 

Measurement of Grown-In 

Stresses in Thin Silicon Sheet 

Final Technical Report 

2 January 2002 – 15 January 2008 

S. Danyluk 

Georgia Institute of Technology 

Atlanta, Georgia 

S. Ostapenko 

University of South Florida 

Tampa, Florida 

NREL Technical Monitor: Fannie Posey Eddy 

Prepared under Subcontract No. AAT-2-31605-06 

Subcontract Report 

NREL/SR-520-44237 

November 2008 

National Renewable Energy Laboratory

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Contract No. DE-AC36-08-GO28308
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Executive Summary

This is the Final Report of the project, “Full Field Birefringence Measurements of 

Grown-in Stresses in Thin Silicon Sheet,” that has been conducted at the Georgia 

Institute of Technology by Steven Danyluk, a Professor in the George W. Woodruff 

School of Mechanical Engineering, and the University of South Florida by Sergei 

Ostapenko, an Associate Scientist in the Center for Microelectronics Research. 

The primary concern of this research has been to develop fundamental knowledge about 

residual stresses and microcracks and defects in silicon sheet. In the course of the work, 

the two groups developed new experimental techniques to obtain shear stresses and 

microcracks in sheet silicon. One of the techniques involves infrared photoelasticity, 

which measures the residual stress-induced birefringence. The residual stresses are 

related to the birefringence through the stress-optic coefficient described in this report. 

Anisotropy, thickness, and microstructure are some of the key parameters that effect 

birefringence, and these topics have been investigated as they relate to in-plane residual 

stresses. In the experimental system developed at Georgia Tech, the anisotropy thickness 

and microstructure were accounted for by the use of a four-point bending technique, and 

ultimately used to determine the principal stresses in silicon wafers. 

The work at the University of South Florida has focused on using acoustic techniques 

(resonance ultrasonic vibrations) to determine the existence of microcracks – usually 

edge cracks – in thin silicon wafers. This work has led to the development of hardware 

that can be used to screen wafers for edge defects. 

There have been numerous papers and reports written and these documents summarize 

the detailed technical elements of the work. These papers are listed in Appendix A of 

this report. There have been graduate students supported by this project and their names 

and other data regarding these are listed in Appendix B of this report. 

The key findings of our work may be summarized as follows: 

1. The polariscopy work has led to the development of a prototype non-contact, 

near-infrared light-transmission system for the inspection of thin, flat, large-area 

silicon wafers. Anisotropy, light scattering by thin wafers, influence of 

dislocations on stresses, and the extraction of principal in-plane stresses have been 

studied. This method is now ready for commercialization and in-line inspection 

of wafers at various stages of photovoltaic cell processing. 

2. The acoustic work has led to the development of a commercially viable system to 

inspect wafers for microcracks. Technical issues such as the influence of crack 

length on vibration frequencies of thin silicon wafers have been studied and 

solved. This method of crack detection has been commercialized by Dr. 

Ostapenko. 

The balance of this report summarizes some of the technical details. 

1 
A. Summary of the Polariscopy Study 

The Georgia Tech group has been working on developing a non-destructive, non-contact 

optical technique to measure the residual stress in thin silicon sheet. Figure A1 shows a 

schematic diagram of the polariscope system. Circularly polarized light, which is 

provided by the first polarizer and quarter waveplate, is used to illuminate the silicon 

sample. The residual stresses in the sample change the polarization state of the 

transmitted light, and the second wave plate and polarizer measure the change. A 

tungsten lamp with adjustable power up to 250W is used as the light source, and an 

infrared camera captures the images. In the camera, a band-pass infrared filter is used to 

pick a near-infrared wavelength center at 1150 nm with a bandwidth of 10 nm. 

Light source 

Polarizer 

1/4 waveplate 

Analyzer 

Silicon sample 

ρ

1/4 waveplate 

(α,θ)

Beam splitter

φ

β

Beam splitter

Figure A1: Setup of the residual stress polariscope

Camera 

The stress optic law can be used to obtain the maximum shear stresses in the beam if the 

stress- optic coefficient is known. The stress optic law is given as: 

( )δ

φθπ

λ

σσ

2 , 1 2 Ct =− (1) 

where C is the stress-optic coefficient, which is a function of θ (the principal stress 

orientation) and φ (the crystal-grain orientation); t is the thickness of the sample; λ is the 

wavelength of the light source; and σ1, σ2 are the two principal stresses. δ is the phase 

retardation that can be measured by the six-step phasing method. In this equation, δ is 

related to the in-plane residual stresses and the maximum sheer stress is then 

21 2 max σ −σ = τ (2) 

Equation (2) shows that only the absolute value of the difference in principal stresses is 

measured, and this value will be influenced by the crystal orientation, defect (dislocation) 

density, and thermal effects as a result of the infrared illumination. 

2 
A1. Goals and Objectives 

The goals and objectives of the residual stress work were to determine the influence of 

anisotropy on the stress-optic coefficient, develop a method for separation of the residual 

stress components, investigate the relationship between residual stress and dislocation 

density, and analyze the thermal effects on residual-stress measurements. 

A2. Summary of Approaches 

1. Calibration of anisotropic stress-optic coefficient 

The stress-optic coefficient, a parameter used in polariscopy, is orientation dependent, 

because light scattering will depend on the location of the atoms in the crystal structure. 

A back Laue X-ray diffraction system (at Oak Ridge National Laboratory) was used to 

determine the grain orientations in edge-defined film-fed growth (EFG) and cast silicon 

wafers and to find φ (2). Reference 1 describes some of the details of how the anisotropic 

stress-optic coefficient is obtained. Reference 2 describes a four-point bending technique 

used to introduce known in-plane stresses so as to calibrate the anisotropic stress-optic 

coefficients. In both cases, it is possible to extract the anisotropic stress-optic coefficient 

for single and polycrystalline silicon wafers. 

2. Method for stress separation 

Photoelasticity provides information on the principal shear stress and its orientation in the 

wafer. To obtain the full state of stress ( and ), stress separation must be used. 

Four-point bending, together with shear-difference technique, has been developed to 

determine stress separation. Four-point bending can tell whether the measured shear 

stress is positive or negative. The shear-difference technique is based on the direct 

integration of the equilibrium equations in the following finite-difference format: 

σσ yx , xy τ

∑ Δ

Δ

Δ = − x

y

boundary yx

xx

τ

σσ )( and/or ∑ Δ

Δ

Δ = − y

x

boundary yx

yy

τ

σσ )( (3) 

Using equations (1) and (3) and the basic stress transformation equations of mechanics, 

the full state of stress ( and ) can be calculated (Reference 3). σσ yx , xy τ

3. Relationship between residual stress and dislocation density 

To determine the relationship between dislocation density and residual stress, optical 

microscopy and image analysis were used, in addition to polariscope residual-stress 

measurements. EFG wafers were used for the dislocation-density experiment because 

their crystal structure is relatively constant and the surface relatively smooth. A Sopori 

etch was used to reveal etch pits on the surface of EFG wafers. Etch-pit density was 

assumed to be the same as the dislocation density. Wafers were also subjected to 

polariscopy to obtain the residual-stress maps, and the results of etch-pit density and 

residual stress were analyzed to find their relationship (4). 

3 
4. Analysis of thermal effect on residual stress measurement 

This task addressed measurement resolution and reliability issues associated with the 

infrared (IR) polariscope. In particular, the task was designed to systematically study the 

role of temperature rise in the silicon wafer due to IR light absorption on the residualstress output by the system. The nonuniform energy profile of the light source can 

produce a thermal gradient in the Si sample and, as a result, a thermal stress may be 

induced in the wafer, that will increase the system error. An ANSYS thermal model was 

built to calculate the temperature in the silicon wafer. This temperature profile was used 

as input to a structural model that calculated thermal stress. 

5. Relation of residual stresses to dislocation density 

There has been considerable discussion in the literature relating to the relationships of 

dislocation density to residual stresses and eventually to cell efficiencies. We have 

addressed this issue and a Georgia Tech student, Vicky Garcia, has published a thesis (5) 

that relates the residual stresses to electron-hole lifetime. There appears to be a linear 

correlation to these two parameters, as described in the thesis. 

A3. Key Findings 

The key findings of the residual stress work are as follows: 

The major preferential crystallographic orientation in cast wafers is (111) and near (111), 

but other orientations are (100), (210), (110), (144), (211), (321), and (431). The stressoptic coefficient varied with orientation and the variation between the maximum and 

minimum value. 

Full components of stresses have been obtained for several silicon beams. The maximum 

principal stress was found to be about 30 MPa for EFG wafers. 

A relationship was found between dislocation density and residual stress. The graph in 

Figure 2 shows the behavior of residual stress at high values of dislocation density. 

Equations are shown in the graph to quantify the relationship. There is an uncertainty in 

which stress relaxation occurs because since there are sources of residual stress other than 

dislocations. 

4 
Figure A2. Relationship between dislocation density and residual stress 

Thermal modeling shows that the polariscope system needs about 1 to 2 minutes to 

achieve steady-state. 

B. Summary of the Resonance Ultrasonic Vibration Study 

The Resonance Ultrasonic Vibrations (RUV) technique was adapted for non-destructive 

crack detection in full-size silicon wafers for solar cells [7]. Other experimental 

approaches targeting crack detection in PV silicon wafers and solar cells are described 

elsewhere. The RUV methodology relies on deviation of the frequency response curve of 

a wafer with a periphery crack versus regular non-cracked wafers. Crack detection is 

illustrated on a set of square-shaped production-grade Si wafers and confirmed by finite 

element analysis (FEA). The modeling is accomplished for the different modes of the 

resonance vibrations of a wafer with a periphery crack to assess the sensitivity of the 

RUV method relative to crack length and crack location. Crack-elongation experiments 

were performed using a specially designed tool. A statistical approach was proposed for 

crack detection in full-sized silicon wafers. 

B1. Goals and Objectives 

The goals and objectives of the crack detection work were to develop the methodology to 

detect resonance in thin silicon wafers, investigate the relationship between known crack 

sizes and ultrasonic signatures, and develop an experimental system that could be used by 

the PV community to inspect wafers. 

5 
B2. Summary of Approaches 

Ultrasonic vibrations are induced into an as-cut or processed silicon wafer of symmetrical 

geometry through a vacuum-coupled high-frequency piezoelectric transducer beneath the 

wafer as illustrated in Figure B1. A transducer frequency can be swept in the ultrasonic 

range from 20 kHz to 100 kHz. Standing longitudinal waves are set up at resonance 

frequencies with peak positions controlled primarily by the wafer’s geometry, size, and 

material’s elastic characteristics. The differing physical attributes of each Si wafer lead 

to altered resonance-mode shapes including peak position, peak bandwidth, and peak 

amplitude. The vibrations are detected using a broadband ultrasonic probe attached with a 

sensor-controlled force to the edge of the wafer. Stepper motors allow synchronized 

movement and precise positioning of the wafer and probe for RUV measurements. The 

entire system is computer controlled and programming devices are operated by 

Windows-based original software. The RUV unit may be integrated into an automatic 

belt-type solar cell production line or used as a stand-alone testing system for mechanical 

quality control. 

Figure B1. (a) A schematic of the experimental RUV system; 

(b) mutual layout of the transducer, wafer, and probe in the RUV setup 

The transducer beneath the wafer serves as both a holding stage via the vacuum coupling 

with the wafer, as well as serving its primary purpose of inducing resonance vibrations in 

the form of standing waves into the wafer. The acoustic probe transmits the electrical 

signal to a computer-controlled lock-in amplifier allowing detection of mV-scale 

ultrasonic signals with sufficient signal-to-noise ratio. In our experiments, the wafer was 

excited with longitudinal vibrations and a peak resonance of vibrations was detected at 

specific frequencies controlled primarily by the wafer’s size and elastic properties. 

When performing RUV experiments with wafers of new sizes or geometries, fullspectrum measurements are conducted to locate the exact position of suitable resonance 

peaks. By exciting the wafers over a wide range of frequencies, we can define the natural 

resonance frequencies. These peaks are characterized by narrow bandwidth, large 

amplitude, and peak separation. Once the resonance peaks are located, further crack 

6 
analysis is possible on a set of similar wafers. By comparing resonance-peak properties, 

including frequency position, bandwidth, and amplitude, of wafers with similar 

geometries, crystal defects such as cracks or chips can be quickly detected. The RUV 

method is capable of fast, precise measurements within seconds. The interval includes 

wafer loading, data acquisition, analyses, and wafer unloading. This high-speed 

measurement makes the RUV system a potential candidate for in-line crack detection 

matching the throughput rate of the production line. Scanning Acoustic Microscopy 

(SAM) was used as a supporting method to visualize cracks with highest resolution of 10 

microns. SAM techniques are described elsewhere [8]. 

B3. RUV Mode Identification 

Specific resonance vibration modes were found by first measuring a full-spectrum 

frequency scan on the representative cast and Cz-Si wafers with an illustrative example 

presented in Figure B2 for a 156 mm x 156 mm cast Si wafer. RUV in square-shaped 

wafers of different accepted photovoltaic industry standard sizes were measured and their 

peak positions are summarized in Table 1. Each experimental peak represents a particular 

vibration mode that is compared with FEA results. FEA parameters for analysis include a 

size-specific mesh with square-shaped 1-mm or 2-mm individual elements. The silicon 

wafer is modeled as an isotropic thin plate with a Young’s modulus of 167 GPa, a 

Poisson ratio of 0.3, and a density of 2.3 x 103

 kg/m3. Free vibrations of the plate were 

calculated neglecting the effect of the transducer coupling and acoustic probe contact. 

Figure B2. Broad-range frequency scan of 

156mm x 156mm cast-Si wafer. Four individual 

RUV modes are shown. Inset zooms on the #1 

mode at ~30 kHz (points) with Lorentzian fit 

(solid line). 

Figure B2. Broad-range frequency scan of 

156mm x 156mm cast-Si wafer. Four individual 

RUV modes are shown. Inset zooms on the #1 

mode at ~30 kHz (points) with Lorentzian fit 

(solid line). 

Even in this simplified model, we found a close match of the experimental and calculated 

frequencies (Table 1) in wafers of different sizes. As expected, the resonance frequency 

of a specific mode (fres) shifts upward with reducing wafer size (a) and obeys a simple 

relation, such as fres ~ a

-1, which is illustrated in Figure B3 in the case of the four 

vibration modes numbered in Figure 2. 

7 
Table 1 Resonance-peak frequencies for four vibration modes in Si wafers of different 

sizes: (a) experimental data, (b) FEA calculations. Calculated frequencies are rounded to 

the last digit. 

 Mode # 

Wafer Size (mm) 

1 2 3 4 

 Peak Frequency (kHz) 

(a) (b) (a) (b) (a) (b) (a) (b) 

103 x 103 42.5 47.6 69.8 69.6 - 103.1 - 135.3 

125 x 125 37.3 39.3 57.4 57.4 83.8 84.9 - 111.5 

156 x 156 29.7 31.5 45.7 45.9 68.2 68.1 87.4 89.3 

In Figure B4 (a-d), we present FEA mode shapes for resonance vibrations indicated by 

arrows and numbers in Figure 2. The data closely follows the experimental and calculated 

resonance frequencies as seen in Table 1, so we are confident of this mode identification. 

To further verify this mode identification and to assure that FEA modeling matches the 

experimental data and provides correct representation of the vibration modes, we 

conducted an experiment to determine the mode shape from a series of amplitude 

measurements along a wafer’s edge. Once the peak vibration frequency of a specific 

mode was found, the mode shape was analyzed by conducting a single peak scan along 

one edge of the symmetrical wafer, noting the amplitude change from point to point that 

is consistent with peaks and nodes in the modal standing waveform. The resonance 

peaks were measured with a step size between 3 and 5 mm to construct a representative 

mode shape. The change in peak amplitude along the edge of the vibrating wafer was 

found to be similar to the mode shapes at the respective frequency as predicted by FEA. 

Some asymmetry of the experimental data can be attributed to angular distribution of the 

transducer’s vibrations. 

8 
Figure B4 FEA calculated mode shapes corresponding to peaks # 1-4 as seen in Figure 2. 

Two unique resonant modes were analyzed at about 30 and 45.6 kHz, which correspond 

to peaks #1 and #2, respectively (Figure B2), for a 156 mm x 156 mm square-shaped 

cast-silicon wafer. Figure B5 demonstrates the correlation between the amplitudes of the 

experimental data and theoretical FEA results. Experimental edge scans on other two 

vibration modes, #3 and #4, also show close relevance to calculated edge scans. The 

number of vibration nodes matches for both of the modes. However, an accurate fit of the 

experimental data is complicated due to a larger number of vibration periods for these 

high-frequency modes and limited spatial resolution of the probe. Good correlation 

between the experiment and the FEA modeling will serve as a guideline for crackinfluenced frequency-shifting behavior. 

Figure B5 Amplitude variation of the RUV mode along the wafer edge representing Peak 1 at 

30 kHz (left) and peak 2 at 45.6 KHz (right). (a) FEA modeling, (b) experimental data. 

B4. RUV Crack Detection [9]

Due to the fact that finding naturally occurring cracks with the precise position and length 

necessary for analysis is nearly impossible, cracks were intentionally introduced into the 

9 
(100)-oriented Cz-Si wafer. This was achieved by notching the wafer near the edge at 

the intended crack location with a diamond-tipped scribe. Consistently increasing the 

pressure until a cracking sound was heard usually achieved the desired results (Figure 6). 

Figure B6. SAM images present possible crackpropagation orientations a) single, b) dual, c) incorrectly 

formed branched crack, d) wafer with initial induced crack, 

and e) same wafer after successful elongation. 

Because of the possibility for crack propagation in either of two cleavage crystallographic 

<110> directions, the crack had to be coaxed to propagate in the required direction. This 

could generally be achieved by scratching (mm-length) the wafer surface along the 

intended propagation direction and then poking the wafer edge with the diamond scribe. 

Crack generation without initial directional forcing damage was often used due to its ease 

and lack of extra wafer damage from scribing. Single cracks typically appeared in either 

‘left’ or ‘right’ crystal directions or as dual cracks heading in both directions 

simultaneously from the point of pressurization. Crack elongation can be achieved by 

finding the tip of the initial crack and slightly pressurizing it with the diamond scribe; this 

can lead to crack “branching,” as illustrated in Figure B6c. To avoid this undesirable 

effect, a consistent crack elongation without ‘branching’ cracks can be achieved by 

precise pressurizing at the crack tip, as seen in Figures B6e and B6f. 

10 
Figure B7 Crack-detection run on a set of 125mm x 125mm cast 

wafers with the wafer #11 possessing 10 mm periphery crack 

identified by RUV parameter variations (1) peak position, (2) 

peak bandwidth, and (3) peak amplitude. 

We performed an RUV experiment on a set of identical (125 mm x 125 mm) productiongrade cast wafers with the results presented in Figure B7. This sequential RUV data 

collection and analysis is closely relevant to the solar cell testing routine targeting to 

reject mechanically unstable Si wafers in PV production. Three parameters of the RUV 

peak were analyzed: peak position, peak bandwidth, and peak amplitude. One of the 

wafers (# 11) was clearly an outlier inconsistent with the other wafers. Using SAM 

measurements, we confirmed that this wafer had a 10-mm periphery crack that was 

clearly observed in the RUV testing. 

11 
B5. Crack Elongation 

In Figure B8, we show a variation of the RUV f-scan of the resonance vibration peak at 

41.4 kHz (non-cracked wafer) caused by the 16-mm crack located on the wafer’s corner 

and the same wafer with the crack elongated up to 34 mm. The data are presented for 125 

mm x 125 mm Cz-Si wafer (#27a) with 220-micron thickness. This is the very first 

experimental justification on a gradual variation of the RUV peak parameters with crack 

length performed on the same Si wafer. For this study, we used a specially designed 

experimental apparatus that allowed the wafer with initial “seed” crack to be bent with 

constant computer-controlled bending speed and bending amplitude. The wafer was 

positioned in a clamping device with a single corner exposed. The device was clamped 

along a 45-degree angle relating to a crystallographic <110> direction. The alignment 

was achieved using a previously cleaved Cz-Si “dummy” wafer. With the wafer clamped 

in the machine along its edge, a stepper-motor-controlled rod exerted downward pressure 

at the exposed corner of the wafer. Slow stepping speeds of about 40 microns per second 

were used with maximum amplitude of the wafer’s exposed corner deflection varied from 

1 to 3 mm. In Figure B9, we present SAM images of the wafer part subjected to initial 

crack (a) and elongated crack (b). The effect of a crack elongation is quite substantial. It 

can be specified as a gradual downward peak shift, increase of the peak and width, and a 

strong reduction of the peak amplitude. These RUV signatures of the crack are consistent 

with previously observed data in Ref. [1]. 

41200 41400 41600

0

1

2

3

34mm

16 mm

no crack

Acoustic Amplitude [mV]

Frequency [Hz]

Figure B8: RUV scans on the same Cz-Si wafer (#27A) 

after two consecutive crack elongations. 

12 
(a) 

(b) 

Figure B9: Scanning Acoustic Microscopy images measured in the reflection ultrasonic 

beam mode at 75 MHz with 50 microns lateral resolution on the wafer #27a with crack 

length of (a) 16 mm and (b) 34 mm. Initial wafer (data not shown) had no crack longer than 

50 μm. 

10 mm 

B6. Cz-Si Wafers – Statistical Study 

Table 2: RUV statistics in as-cut Cz-Si wafers 

 

Mean 

Value Std.Dev % Std.Dev.

 

Amplitude 0.47 0.09 19.1

 

Bandwidth 122.0 14.7 12.0

 

Peak 58616 71 0.12

 

To justify the applicability of the RUV method on processed silicon wafers and identify 

potential problems, we performed a statistical study using a set of 100 as-cut Cz-Si 

wafers (125 mm x 125 mm, nominal thickness 220 microns) that was initially measured 

with the RUV technique. This set then passed through consecutive solar cell production 

steps, which included 

surface texturing, 

centrifuge drying, 

diffusion, plasma and HF 

etching, anti-reflecting 

(AR) coating with SiN 

layer, metallization with 

front and back contacts, 

and contact stripes 

soldering. The processing 

was performed in 

commercial facilities of a solar cell producer. After each step, the entire set was returned 

and remeasured with the RUV technique. The objective of this study was to justify usage 

of the RUV system at different solar cell production steps. In Table 2, we present data of 

13 
the RUV statistics in as-cut wafers. It is clear that, compared to cast wafers, the standard 

deviation (S.D.) of all parameters is much smaller, confirming a high level of identity of 

the Cz wafers. Specifically, we observed the bandwidth S.D. of only 14.7 Hz compared 

to 33 Hz in cast and 171 Hz in EFG wafers. As a result, crack-detection sensitivity is 

highest in Cz-Si wafers, followed by cast and then by EFG. 

These data, along with variation of the standard deviation (not shown), document that 

RUV method sensitivity with respect to crack length is highest at the initial processing 

steps due to narrow statistical distribution and is lowest after contact stripe soldering. 

B7. Ruv System Stability and Accuracy: Fast Mode 

To explore stability and performance of the RUV system, we performed experiments by 

using RUV metrology with different cycling time by reducing measurement time down to 

a targeted 2.0 seconds per cycle. The entire RUV measurement cycle consisted of the 

consecutive steps: wafer loading from a home position on the transducer by vacuumcoupling the wafer and transducer, lifting the transducer with the wafer to a measuring 

position using computer-controlled Z-stage, contacting the wafer’s edge by ultrasonic 

probe using computer-controlled X-stage, data acquisition by measuring f-scan, 

Lorentzian fit of the experimental data, and wafer unloading to the home position. The 

duration of the measuring cycle can be varied by changing the number of data points per 

f-scan or lock-in amplifier integration time. In Figure B10, we show the frequency 

sweeps performed with different data points per f-scan (from 100 to 10) and cycling time 

from 12.4 seconds down to 2.0 seconds per cycle. We found that 2.0 seconds per wafer is 

an achievable throughput rate of the RUV system. Reduction of the data points per scan 

provides only a small variation of the f-scan parameters. Specifically, peak amplitude is 

reduced by 16%, peak bandwidth is reduced by 7 Hz (5%), and peak position is changed 

by 14 Hz. These variations are much smaller compared to typical standard deviations of 

corresponding distributions for any type of silicon-wafer technology. Therefore, a fast 2.0 

seconds cycle time was used in these experiments. 

Another practical aspect explored in this project is how a minimum cycle time of 2.0 

seconds depends on specific hardware parameters. In Figure B11, we show a dependence 

of the cycle time versus integration time-constant of different lock-in amplifiers used in 

this study. It is obvious that reduction of the acquisition time with the lock-in timeconstant provides speeding up of the entire process but leads to deterioration of 

signal/noise ratio. We noticed that various hardware systems respond differently to this 

parameter. According to the data in Figure B11, the lock-in amplifier #2 shows a superior 

performance reducing a cycling time below 2.0 seconds. This is a very encouraging result, 

proving that further acceleration of the RUV technique is possible with optimizing 

regime of the hardware and software. 

14 
45200 45300 45400 45500 45600

1

2

3

4

5

Acoustic Signal [mV]

Frequency [Hz]

 100 points, 12.4sec

 50 points, 6.9sec

 30 points, 4.6sec

 20 points, 3.5sec

 10 points, 2.0sec

0 20 40 60 80 100 120 140

1.6

2.0

2.4

2.8

3.2

3.6

4.0

2.0 seconds

 lock1

 lock2

 lock3

 lock4

Cycle time [sec]

time per point [msec]

Figure B10: RUV scans measured with 

different time. The shortest time is 2.0 sec 

per scan.

Figure B11: comparison of different lockin 

detectors for fast RUV scans. 

In Figure B12, we show a special experimental setting that essentially models a practical 

use of the RUV system in a solar cell production line. In this experiment, the same Si 

wafer was multiple measured by the RUV system in 

the same manner through an 

entire measuring cycle and data 

of individual measurements were 

compared and plotted after 

Lorentzian fit of the f-curve. 

Two runs each of 582 cycles 

were performed with the same 

cast-Si wafer. Though generally 

we found a consistency between 

these two runs, a slow variation 

of the RUV parameters is 

recorded. For instance, peak 

position is shifted upward by 

about 60 Hz, peak amplitude is 

reduced from 0.5 to 0.4 mV 

(20%), and bandwidth is 

essentially not changed. One 

technical problem was identified 

as a gradual variation of a 

vacuum coupling between the 

transducer and wafer. This effect 

has to be eliminated to assure 

higher stability of the RUV 

system as a production-grade in-line testing system. We documented that statistical 

variations of the data during each run are relatively small, showing a standard deviation 

of 0.06 mV for peak amplitude, 9-11 Hz for peak bandwidth, and 14 – 16 Hz for peak 

Figure B12: Two runs of the multiple RUV scans 

performed on the same cast silicon wafer measured 

consecutively 582 times per each run. Individual 

cycle time was 2.0 seconds with 1.0 second pause 

between the cycles. 

15 
position. These values are substantially lower than the similar parameter of the wafer’s 

statistical variations as presented in previous sections. 

Key Findings: 

The key findings of the resonance ultrasonic vibrations study are as follows:

• Vibration modes observed in the range from 20 to 100 kHz in silicon wafers of 

different standard size and geometry were identified. 

• Applicability of the RUV method for periphery crack detection in productiongrade cast wafers was justified.

• RUV method sensitivity was demonstrated using a crack-elongation study.

• Statistical analyses on the production-grade set of cast wafers to reject wafers 

with cracks was performed. 

• RUV methodology is applicable to all major Si wafer technologies used in solar 

cell production, such as single-crystal (Cz), cast, and ribbon (EFG). RUV method 

sensitivity is different for each type of Si materials due to the statistical 

distribution of the wafer’s characteristics. It is highest in Cz-Si, followed by cast 

and EFG. 

• The experimental RUV system (hardware and software) can match the 2.0 

seconds per wafer throughput rate in state-of-art solar cell production lines. This 

time can be further shortened by optimizing system hardware and programming 

options. 

Acknowledgements 

The Principal Investigators would like to thank NREL for support of this project and 

especially Rick Matson, Bushan Sopori,:and Fannie Posey-Eddy for providing guidance 

and encouragement over the years. Special thanks go to our industrial partners: Schott 

Solar, BP Solar, and Evergreen Solar. Juris Kalejs, John Wolgemuth, and Jack Hanoka 

provided wafers and encouragement during the work. 

References: 

1. He, S., Zheng, T., and Danyluk, S., “Analysis and Determination of the StressOptic Coefficients of Thin Single Crystal Silicon Samples,” J. Appl. Phy., 96, No. 

6, pp. 3103 (2004). 

2. Li, F., Garcia, V., and Danyluk, S., “Progress in the Determination of the Stress 

Optics Coefficient in Thin Polycrystalline Silicon Wafers,” Presented at the 17th

Workshop on Crystalline Silicon Solar Cells & Modules: Materials & Processes, 

Vail, CO, August 5-11, 2007. 

3. Li, F., and Danyluk, S., “Extraction of Principle Stresses from Polariscopy 

Measurements,” Presented at the 18th Workshop on Crystalline Silicon Solar Cells 

& Modules: Materials & Processes, Vail, CO, August 3-6, 2008. 

16 
4. He, S., Danyluk, S., and Ostapenko, S., “Residual Stress Characterization for 

Solar Cells by Infrared Polariscopy,” Presented at the DOE Solar Program 

Review, Denver, CO, October 25-28, 2004. 

5. Garcia, V., “Effect of Dislocation Density on Residual Stress in Polycrystalline 

Silicon Wafers,” Master’s Thesis, Georgia Institute of Technology, Atlanta, GA, 

Spring 2008. 

6. He, S., Danyluk, S., Tarasov, I., and Ostapenko, S. “Residual Stresses in 

Polycrystalline Silicon Sheet and Their Relation to Electron-hole Lifetime,” 

Applied Physics Letters, 89, No. 11, p. 111,909 (2006). 

7. Belyaev A, Polupan O, Dallas W, Ostapenko S, Hess, D., and Wohlgemuth J, 

“Crack Detection and Analyses using Resonance Ultrasonic Vibrations in FullSize Crystalline Silicon Wafers” Appl. Phys. Letters, 88 (2006) 111907. 

8. Rueland, E., Herguth, A., Trummer, A., Wansleben, S., and Fath, P., “Optical ucrack Detection in Combination with Stability Testing for In-line Inspection of 

Wafers and Cells,” Proceedings of 20th EU PVSEC Barcelona, 2005 pp. 3242 – 

3245. 

9. Trupke, T., Bardos, R. A., Abbott, M. D., Chen, F. W., Cotter, J. E., and Lorenz, 

A., “Fast Photoluminescence Imaging of Silicon Wafers,” Proceedings of 

WCPEC-4 (Hawaii, May 2006), in press. 

10. Fuyuki, T., Kondo, H., Yamazaki, T., Takahashi, Y., and Uraoka, Y., 

“Photographic Surveying of Minority Carrier Diffusion Length in Polycrystalline 

Silicon Cells by Electroluminescence,” Appl. Phys. Letters, 86, 262108 (2005). 

11. Rakotoniaina, J. P., Breitenstein, O., Al Rifai, M. H., Franke, D, and Schnieder A, 

“Detection of Cracks in Silicon Wafers and Solar Cells by Lock-in Ultrasound 

Thermography,” Proceedings of PV Solar Conference (Paris, June 2004), pp. 640-

643. 

12. Behnken, H., Apel, M., Franke, D., “Simulation of Mechanical Stress During 

Bending Tests for Crystalline Wafers,” 3rd World Conference on Photovoltaic 

Energy Conversion, 2003 Japan 

13. Sopori, B., Sheldon, P., Rupnowski, P., “Wafer Breakage Mechanism(s) and a 

Method for Screening ‘Problem Wafers’,” 16th Workshop on Crystalline Silicon 

Solar Cells and Modules, Denver, CO 2006 

14. Belyaev, A., Polupan. O., Ostapenko, O., Hess, D., and Kalejs, J. P., “Resonance 

Ultrasonic Vibration Diagnostics of Elastic Stress in Full-Size Silicon Wafers,” 

Semicond. Sci. Technology, 21, (2006), 2540260. 

15. Dallas, W., Polupan, O., and Ostapenko, S., “Resonance Ultrasonic Vibrations for 

Crack Detection in PV Wafers,” Meas. Sci. Technology, (2007) 18, 8520858. 

16. Li, F., Garcia, V., and Danyluk, S., “Full Field Stress Measurements in Thin 

Silicon Sheet,” IEEE 4th World Conference on Photovoltaic Energy Conversion, 

(IEEE Cat. No. 06CH37747), 2006, p. 4. 

17. Li, F., Garcia, V., Danyluk, S., Ostapenko, S., Kalejs, J., and Yates, D., “In-plane 

Residual Stress and Its Relationship to Dislocation Density in Polycrystalline 

(EFG) Silicon Sheet,” IEEE 4th World Conference on Photovoltaic Energy 

Conversion, (IEEE Cat. No. 06CH37747), 2006, p. 4. 

17 
Appendix A 

Listing of Reports and Papers Published 

2002

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of January 2 – March 31, 2002. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of April 1 – June 30, 2002. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of July 1 – September 30, 2002. 

Ostapenko, S.2, He, S.,1 and Belyaev, A.2, “Full Field Birefringence Measurements of 

Grown-in Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, 

GA, 2

University of South Florida, Tampa, FL, Trip Report for 12th Workshop on 

Crystalline Silicon Solar Cells and Processes, Breckenridge, CO, August 11-14, 2002. 

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Annual Report for period of January 2 – December 31, 2002. 

2003

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of January 1 – March 31, 2003. 

Danyluk, S., He, S., and Zheng, T., “Error Analysis of a Circularly Polarized PhaseStepping Polariscope,” Georgia Institute of Technology, Atlanta, GA, Trip Report for 

the NCPV and Solar Program Review Meeting, Denver, CO, March 24-26, 2003. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, 

“Development of an Infrared Residual Stress Polariscope for Solar Cells Inspection,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Trip Report for the NCPV and Solar Program Review Meeting, Denver, CO, 

March 24-26, 2003. 

18 
Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of April 1 – June 30, 2003. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of July 1 – September 30, 2003. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Annual Report for period of January 2 – December 31, 2003. 

2004

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of January 1 – March 31, 2004. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of April 1 – June 30, 2004. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of July 1 – September 30, 2004. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of October 1 – December 31, 2004. 

Danyluk, S.1

, Ostapenko, S.2, He, S.,1 “Residual Stress Characterization for Solar Cells 

by Infrared Polariscopy,” 1Georgia Institute of Technology, Atlanta, GA, 2University 

of South Florida, Tampa, FL, Trip Report for the DOE Solar Program Review 

Meeting, Denver, CO, October 25-28, 2004. 

19 
2005

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Li, F. 1, Tarasov, I.2, Dallas, W.2, and Belyaev, A.2, 

“Full Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of January 1 – March 31, 2005. 

Danyluk, S.1

, Ostapenko, S.2, He, S.1, Li, F.1, Tarasov, I.2, Dallas, W.2, and Belyaev, A.2, 

“Full Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of April 1 – June 30, 2005. 

Danyluk, S.1

, Ostapenko, S.2, He, S.1, Li, F.1, Tarasov, I.2, Dallas, W.2, and Belyaev, A.2, 

“Full Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of July 1 – September 30, 2005. 

Danyluk, S.1, Ostapenko, S.2, He, S.,1 and Li, F.1, “Residual Stresses in Thin 

Multicrystalline Silicon Measured by Near Infrared Polariscopy,” 1Georgia Institute 

of Technology, Atlanta, GA, 2

University of South Florida, Tampa, FL, Poster 

presented at the 15th Workshop on Crystalline Silicon Solar Cells and Modules, Vail 

Cascade Resort and Spa, Vail, CO, August 7-10, 2005. 

Danyluk, S.1, Ostapenko, S.2, and He, S.,1 “Residual Stress Characterization for Solar 

Cells by Infrared Polariscopy,” 1

Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Trip Report for the DOE Solar Program 

Review, Denver, CO, November 6-9, 2005. 

Danyluk, S.1, Ostapenko, S.2, He, S.,1 Tarasov, I.2, Lulu, S.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of October 1 – December 31, 2005. 

2006

Danyluk, S.1

, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of January 1 – March 31, 2006. 

Danyluk, S.1

, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, and Belyaev, A.2, “Full 

Field Birefringence Measurements of Grown-in Stresses in Thin Silicon Sheet,” 

1

Georgia Institute of Technology, Atlanta, GA, 2University of South Florida, Tampa, 

FL, Quarterly Report for period of April 1 – June 30, 2006. 

20 
Danyluk, S., Melkote, Li, F., and Garcia, V., “Full Field Birefringence Measurements of 

Grown-in Stresses in Thin Silicon Sheet,” Georgia Institute of Technology, Atlanta, 

GA, PowerPoint Presentation presented at the 16th Workshop on Crystalline Silicon 

Solar Cells and Modules: Materials & Processes, Denver, CO, August 6-9, 2006. 

Danyluk, S.1

, Ostapenko, S.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Quarterly Report for period of July 1 – 

September 30, 2006. 

Danyluk, S.1

, Ostapenko, S.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Quarterly Report for period of October 1 – 

December 31, 2006. 

2007

Danyluk, S.1, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, Polupan, O.2, and 

Monastyrskyi, A.2

, “Full Field Birefringence Measurements of Grown-in Stresses in 

Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 2University of 

South Florida, Tampa, FL, Quarterly Report for period of January 1 – March 31, 2007. 

Danyluk, S.1, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, Chornokur, G.2, Polupan, 

O.2

, and Monastyrskyi, A.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Quarterly Report for period of April 1 - 

June 30, 2007. 

Danyluk, S.1

, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, Polupan, O.2, and 

Monastyrskyi, A.2, “Full Field Birefringence Measurements of Grown-in Stresses in 

Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 2University of 

South Florida, Tampa, FL, Quarterly Report for period of January 1 – March 31, 2007. 

Danyluk, S.1

, Ostapenko, S.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Trip Report for the Materials Research 

Society Spring Meeting, San Francisco, CA, April 9-13, 2007. 

Danyluk, S.1

, Ostapenko, S.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Trip Report for the Materials Research 

Society Spring Meeting, San Francisco, CA, April 9-13, 2007. 

Danyluk, S.1, Ostapenko, S.2, Li, F.1, Dallas, W.2, Polupan, O.2, Wohlgemuth, J.3, 

“Residual Stress Measurements Using Polariscopy and Crack Detection and Analysis 

Using Resonance Ultrasonic Vibrations in Crystalline Silicon Wafers,” 1

Georgia 

21 
Institute of Technology, Atlanta, GA, 2

University of South Florida, Tampa, FL, 3BP 

Solar International Inc., Frederick, MD, Trip Report for the DOE Solar Program 

Review, Denver, CO, April 17-19, 2007. 

Danyluk, S.1, Ostapenko, S.2, Li, F.1, Garcia, V.1, Dallas, W.2, Polupan, O.2, Chornokur, 

G.2, and Monastyrskyi, A.2, “Full Field Birefringence Measurements of Grown-in 

Stresses in Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 

2

University of South Florida, Tampa, FL, Quarterly Report for period of July 1 – 

September 30, 2007. 

2008

Danyluk, S.1, Ostapenko, S.2, Li, F.1, Dallas, W.2, Polupan, O.2, Chornokur, G.2, and 

Monastyrskyi, A.2

, “Full Field Birefringence Measurements of Grown-in Stresses in 

Thin Silicon Sheet,” 1Georgia Institute of Technology, Atlanta, GA, 2University of 

South Florida, Tampa, FL, Quarterly Report for period of October 1, 2007 – May 31, 

2008. 

Danyluk, S., Li, F., “Li, F., and Danyluk, S., “Extraction of Principle Stresses from 

Polariscopy Measurements,” Presented at the 18th Workshop on Crystalline Silicon 

Solar Cells & Modules: Materials & Processes, Vail, CO, August 3-6, 2008. 

22 
23 

Appendix B 

Students Trained Under the Program 

Student Name Thesis Title Graduation 

Date/Degree 

Current 

Employment 

Georgia Tech 

Shijiang He Near Infrared Photoelasticity of 

Polycrystalline Silicon and it’s 

Relation to In-Plane Residual 

Stress 

Fall 2005/PhD Intel 

Victoria Garcia Effect of Dislocation Density on 

Residual Stress in 

Polycrystalline Silicon Wafers 

Spring 2008/MS NASA, 

Huntsville, AL 

Fang Li TBD Summer 2009/PhD Georgia 

Institute of 

Technology 

University of South Florida 

Igor Tarasov Scanning Photoluminescence in 

PV Silicon Wafers 

2004/PhD SDI 

Anton Belyaev Stress Diagnostics and Crack 

Detection in Full-Size Si Wafers 

using Resonance Ultrasonic 

Vibrations 

2005/PhD SDI 

William Dallas Resonance Ultrasonic Vibrations 

for Crack Detection in Si Wafers 

for Solar Cells 

2006 /MS 

Andrii 

Monastyrskyi 

RUV Technique for In-Line 

Crack Detection in PV Silicon 

Wafers and Solar Cells 

2008/MS 

Christina 

Hilmerson 

Detection of Cracks in SingleCrystalline Si Wafers using 

Impact Testing 

2006/MS 

Oleg Polupan None 2007/Bachelor 
F1146-E(09/2007) 

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1. REPORT DATE (DD-MM-YYYY)

November 2008 

2. REPORT TYPE

Subcontract Report 

3. DATES COVERED (From - To)

2 January 2002 - 15 January 2008 

4. TITLE AND SUBTITLE

Full Field Birefringence Measurement of Grown-In Stresses in Thin 

Silicon Sheet: Final Technical Report, 2 January 2002 - 15 January 

2008 

5a. CONTRACT NUMBER

DE-AC36-08-GO28308 

5b. GRANT NUMBER

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6. AUTHOR(S)

S. Danyluk and S. Ostapenko 

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NREL/SR-520-44237 

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PVA72501 

5f. WORK UNIT NUMBER

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Georgia Institute of Technology, Atlanta, Georgia 30332-0403 

University of South Florida, Tampa, Florida 33620 

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AAT-2-31605-06 

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14. ABSTRACT (Maximum 200 Words)

The primary concern of this research was to develop fundamental knowledge about residual stresses and microcracks 

and defects in silicon sheet. During the work, two groups developed new experimental techniques to obtain shear 

stresses and microcracks in sheet silicon. One technique involves infrared photoelasticity, which measures the residual 

stress-induced birefringence. The residual stresses are related to the birefringence through the stress-optic coefficient 

described in this report. Anisotropy, thickness, and microstructure are some of the key parameters that affect 

birefringence, and these topics were investigated as they relate to in-plane residual stresses. In the experimental 

system developed at Georgia Tech, the anisotropy thickness and microstructure were accounted for by using a fourpoint bending technique, and were ultimately used to determine the principal stresses in silicon wafers. The work at the 

University of South Florida focused on using acoustic techniques (resonance ultrasonic vibrations) to determine the 

existence of microcracks – usually edge cracks – in thin silicon wafers. 

15. SUBJECT TERMS

PV; full-field birefringence; residual stress; silicon sheet; infrared photoelasticity; silicon wafer; crack detection; 

resonance ultrasonic vibration; 

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