Detection of Cracks in Single-Crystalline Silicon Wafers Using Impact Testing

Transcription

1 University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School Detection of Cracks in Single-Crystalline Silicon Wafers Using Impact Testing Christina Hilmersson University of South Florida Follow this and additional works at: Part of the American Studies Commons, and the Mechanical Engineering Commons Scholar Commons Citation Hilmersson, Christina, "Detection of Cracks in Single-Crystalline Silicon Wafers Using Impact Testing" (26). Graduate Theses and Dissertations. This Thesis is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact

2 Detection of Cracks in Single-Crystalline Silicon Wafers Using Impact Testing by Christina Hilmersson A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Daniel P. Hess, Ph.D. Autar Kaw, Ph.D. Craig Lusk, Ph.D. Sergei Ostapenko, Ph.D. Date of Approval: March 29, 26 Keywords: audible, modes, frequency response, solar cells, vibration Copyright 26, Christina Hilmersson

3 Acknowledgement I would like to thank Dr. Daniel Hess for letting me work on this project, for being an outstanding adviser and helping me to complete this thesis. I also want to thank Dr. Sergei Ostapenko for his advice, support and for being in the committee. I like to thank William Dallas for making the cracks in the silicon wafers and scanning them in SAM. I would like to thank Dr. Autar Kaw and Dr. Craig Lusk for being on my committee and taking their time to read my thesis and give me excellent feedback. I would like to thank all the people in the Mechanical Engineering Department for their support, I especially like to thank Sue Britten for always being there for me. I would like to thank the University of South Florida for providing me with a first-rate education. I would like to thank all my family especially my parents, my sister and her family for all their support. I would also like to thank all my friends for always listening to me. I would really like to thank my roommate for putting up with me during the completion of this work. The work was supported by the National Renewable Energy Lab (NREL) Subcontract Nos. AAT and ZDO

4 Table of Contents List of Tables... iv List of Figures... vi Abstract...xii Chapter 1: Introduction and Background Overview Background Outline... 3 Chapter 2: Experimental Setup Introduction Sensors Analyzer Frequency response Test specimens Large crack wafer set Miscellaneous wafer set Small crack wafer set Setup Position of hammer and microphone Chapter 3: Test Matrix Introduction i

5 3.2 Randomization Test with large cracks Test with small cracks Tests of miscellaneous cracks Chapter 4: Test Results Introduction Sample frequency response data Extracted parameters Natural frequencies Large crack wafer set Miscellaneous wafer set Small crack wafer set Normalized frequencies Large crack wafer set Miscellaneous wafer set Small crack wafer set Peak magnitudes Large crack wafer set Miscellaneous wafer set Small crack wafer set Damping ratio Large crack wafer set Miscellaneous wafer set ii

6 4.7.3 Small crack wafer set Discussion Chapter 5: Conclusion and Recommendations Conclusions Recommendations References Appendices Appendix A : Run order... 5 Appendix B : Frequency response data Appendix C : Data from the large crack wafer set Appendix D : Data from the miscellaneous wafer set Appendix E : Data from the small crack wafer set Appendix F : Set up frequency response data iii

7 List of Tables Table 3.1 Run order for the large crack wafer set... 2 Table 3.2 Test number for the large crack wafer set Table 3.3 Large crack wafers Table 3.4 Small crack wafers Table 3.5 Miscellaneous wafers Table 4.1 Second mode frequency for large specimens Table 4.2 Second mode peak magnitude for the large crack wafer set Table 4.3 Second mode peak damping ratio for the large crack wafer set Table A.1 Test number for the small crack wafer set... 5 Table A.2 Run order for the small crack wafer set... 5 Table C.1 First mode natural frequency for large crack wafer set Table C.2 First mode normalized frequency for large crack wafer set Table C.3 Second mode natural frequency for large crack wafer set Table C.4 Second mode normalized frequency for large crack wafer set Table C.5 Third mode natural frequency for large crack wafer set Table C.6 Third mode normalized frequency for large crack wafer set Table C.7 Fourth mode natural frequency for large crack wafer set Table C.8 Fourth mode normalized frequency for large crack wafer set... 7 Table C.9 First mode peak magnitude for large crack wafer set Table C.1 Second mode peak magnitude for large crack wafer set iv

8 Table C.11 Third mode peak magnitude for large crack wafer set Table C.12 Fourth mode peak magnitude for large crack wafer set Table C.13 First mode damping ratio for large crack wafer set Table C.14 Second mode damping ratio for large crack wafer set Table C.15 Third mode damping ratio for large crack wafer set Table C.16 Fourth mode damping ratio for large crack wafer set Table D.1 First mode natural frequency for miscellaneous wafer set Table D.2 First mode normalized frequency for miscellaneous wafer set... 8 Table D.3 Second mode natural frequency for miscellaneous wafer set Table D.4 Second mode normalized frequency for miscellaneous wafer set Table D.5 Third mode natural frequency for miscellaneous wafer set Table D.6 Third mode normalized frequency for miscellaneous wafer set Table D.7 Fourth mode natural frequency for miscellaneous wafer set Table D.8 Fourth mode normalized frequency for miscellaneous wafer set Table D.9 First mode peak magnitude for miscellaneous wafer set Table D.1 Second mode peak magnitude for miscellaneous wafer set Table D.11 Third mode peak magnitude for miscellaneous wafer set Table D.12 Fourth mode peak magnitude for miscellaneous wafer set... 9 Table D.13 First mode damping ratio for miscellaneous wafer set Table D.14 Second mode damping ratio for miscellaneous wafer set Table D.15 Third mode damping ratio for miscellaneous wafer set Table D.16 Fourth mode damping ratio for miscellaneous wafer set v

9 List of Figures Figure 2.1 Large center crack wafer number Figure 2.2 Large center crack wafer number Figure 2.3 Large center crack wafer number Figure 2.4 Large center crack wafer number Figure 2.5 Large offset crack wafer number Figure 2.6 Large offset crack wafer number Figure 2.7 Large offset crack wafer number Figure 2.8 Large offset crack wafer number Figure 2.9 Large crack other direction wafer number Figure 2.1 Large crack other direction wafer number Figure 2.11 Large crack other direction wafer number Figure 2.12 Large crack other direction wafer number Figure 2.13 Miscellaneous wafer number Figure 2.14 Miscellaneous wafer number Figure 2.15 Miscellaneous wafer number Figure 2.16 Miscellaneous wafer number Figure 2.17 Miscellaneous wafer number Figure 2.18 Miscellaneous wafer number Figure 2.19 Miscellaneous wafer number Figure 2.2 Miscellaneous wafer number vi

10 Figure 2.21 Small crack wafer number Figure 2.22 Small crack wafer number Figure 2.23 Small crack wafer number Figure 2.24 Small crack wafer number Figure 2.25 Small crack wafer number Figure 2.26 Small crack wafer number Figure 2.27 Small crack wafer number Figure 2.28 Small crack wafer number Figure 2.29 Small crack wafer number Figure 2.3 Small crack wafer number Figure 2.31 Picture of the set up Figure 2.32 Position of hammer and microphone relative to wafer Figure 2.33 Hammer (x=83 mm, y=48 mm) Figure 2.34 Hammer (x=39 mm, y=6 mm) Figure 2.35 Hammer (x=53 mm, y=48 mm) Figure 4.1 Frequency response of crack-free wafer number Figure 4.2 Frequency response of large crack wafer number Figure 4.3 Second mode frequency for large specimens Figure 4.4 Second mode natural frequencies for miscellaneous wafer set Figure 4.5 Second mode normalized frequencies for miscellaneous wafer set. 36 Figure 4.6 Second mode peak magnitude for the large crack wafer set Figure 4.7 Second mode peak damping ratio for the large crack wafer set Figure B.1 Frequency response data of crack-free wafer number vii

11 Figure B.2 Frequency response data of crack-free wafer number Figure B.3 Frequency response data of crack-free wafer number Figure B.4 Frequency response data of crack-free wafer number Figure B.5 Frequency response data of cracked wafer number Figure B.6 Frequency response data of cracked wafer number 31 (Test 1) Figure B.7 Frequency response data of cracked wafer number 31 (Test 2) Figure B.8 Frequency response data of cracked wafer number 31 (Test 3) Figure B.9 Frequency response data of cracked wafer number Figure B.1 Frequency response data of cracked wafer number Figure B.11 Frequency response data of cracked wafer number Figure B.12 Frequency response data of cracked wafer number Figure B.13 Frequency response data of cracked wafer number Figure B.14 Frequency response data of cracked wafer number 27 (Test 1) Figure B.15 Frequency response data of cracked wafer number 27 (Test 2)... 6 Figure B.16 Frequency response data of cracked wafer number 27 (Test 3)... 6 Figure B.17 Frequency response data of cracked wafer number Figure B.18 Frequency response data of cracked wafer number Figure B.19 Frequency response data of cracked wafer number Figure B.2 Frequency response data of cracked wafer number Figure C.1 First mode natural frequency for large crack wafer set Figure C.2 First mode normalized frequency for large crack wafer set Figure C.3 Second mode natural frequency for large crack wafer set Figure C.4 Second mode normalized frequency for large crack wafer set viii

12 Figure C.5 Third mode natural frequency for large crack wafer set Figure C.6 Third mode normalized frequency for large crack wafer set Figure C.7 Fourth mode natural frequency for large crack wafer set Figure C.8 Fourth mode normalized frequency for large crack wafer set... 7 Figure C.9 First mode peak magnitude for large crack wafer set Figure C.1 Second mode peak magnitude for large crack wafer set Figure C.11 Third mode magnitude for large crack wafer set Figure C.12 Fourth mode peak magnitude for large crack wafer set Figure C.13 First mode damping ratio for large crack wafer set Figure C.14 Second mode damping ratio for large crack wafer set Figure C.15 Third mode damping ratio for large crack wafer set Figure C.16 Fourth mode damping ratio for large crack wafer set Figure D.1 First mode natural frequency for miscellaneous wafer set Figure D.2 First mode normalized frequency for miscellaneous wafer set... 8 Figure D.3 Second mode natural frequency for miscellaneous wafer set Figure D.4 Second mode normalized frequency for miscellaneous wafer set Figure D.5 Third mode natural frequency for miscellaneous wafer set Figure D.6 Third mode normalized frequency for miscellaneous wafer set Figure D.7 Fourth mode natural frequency for miscellaneous wafer set Figure D.8 Fourth mode normalized frequency for miscellaneous wafer set Figure D.9 First mode peak magnitude for miscellaneous wafer set Figure D.1 Second mode peak magnitude for miscellaneous wafer set Figure D.11 Third mode peak magnitude for miscellaneous wafer set ix

13 Figure D.12 Fourth mode peak magnitude for miscellaneous wafer set... 9 Figure D.13 First mode damping ratio for miscellaneous wafer set Figure D.14 Second mode damping ratio for miscellaneous wafer set Figure D.15 Third mode damping ratio for miscellaneous wafer set Figure D.16 Fourth mode damping ratio for miscellaneous wafer set Figure E.1 First mode natural frequency for small crack wafer set Figure E.2 First mode normalized frequency for small crack wafer set Figure E.3 Second mode natural frequency for small wafer set Figure E.4 Second mode normalized frequency for small crack wafer set Figure E.5 Third mode natural frequency for small crack wafer set Figure E.6 Third mode normalized frequency for small crack wafer set Figure E.7 Fourth mode natural frequency for small crack wafer set Figure E.8 Fourth mode normalized frequency for small crack wafer set Figure E.9 First mode peak magnitude for small crack wafer set Figure E.1 Second mode peak magnitude for small crack wafer set Figure E.11 Third mode peak magnitude for small crack wafer set... 1 Figure E.12 Fourth mode peak magnitude for small crack wafer set... 1 Figure E.13 First mode damping ratio for small crack wafer set Figure E.14 Second mode damping ratio for small crack wafer set Figure E.15 Third mode damping ratio for small crack wafer set Figure E.16 Fourth mode damping ratio for small crack wafer set Figure F.1 Hammer (x=33 mm, y=45 mm) Figure F.2 Hammer (x=43 mm, y=45 mm) x

14 Figure F.3 Hammer (x=38 mm, y=4 mm) Figure F.4 Hammer (x=38 mm, y=5 mm) xi

15 Detection of Cracks in Single-Crystalline Silicon Wafers Using Impact Testing Christina Hilmersson ABSTRACT This thesis is about detection of cracks in single-crystalline silicon wafers by using a vibration method in the form of an impact test. The goal to detect cracks from vibration measurements introduced by striking the silicon wafer with an impact hammer. Such a method would reduce costs in the production of solar cells. It is an inexpensive, relatively simple method which if commercialized could be used as an efficient in-line production quality test. A hammer is used as the actuator and a microphone as the response sensor. A signal analyzer is used to collect the data and to compute frequency response. Parameters of interest are audible natural frequencies, peak magnitudes, damping ratio and coherence. The data reveals that there are differences in frequency between the cracked silicon wafers and the non-cracked silicon wafers. The resonant peaks in the defective wafers were not as sharp (i.e., lightly damped) and occurred at lower frequencies (i.e., lower stiffness) with a lower magnitude and a higher damping ratio. These differences could be used to detect damaged product in a solar cell production line. xii

16 Chapter 1: Introduction and Background 1.1 Overview The renewable energy market is growing and so are the photovoltaic industries. The thought of using the sun s power for generation of electricity is not new. The concept dates back to the industrial revolution [1]. Crystalline Silicon is the most common material used in the photovoltaic market with over 95% market share [2]. The reason that the photovoltaic cell is not more widespread is cost, particularly cost of cell production. During crystal growth and processing of silicon wafers, imperfections (such as cracks, residual stresses and sub-surface damage) are introduced. Breakage during production due to defects is currently 6-15%, but the industry wants to get this down to 1% [2], the method used in this thesis to detect the cracks could help facilitate this goal. There is a need for fast in-line mechanical quality control methods to detect these imperfections during the production of silicon solar cells. This could reduce the further processing of defective products and reduce overall costs. This thesis focuses on vibration impact testing of wafers for crack detection. 1.2 Background During the production of the silicon cells, it is not uncommon that cracks and residual stresses are introduced. There currently exist some methods to detect residual stresses. These are X-ray diffraction, transmission electron 1

17 microscopy (TEM), micro-raman spectroscopy [3], scanning infrared polariscopy [4], resonance ultrasonic vibrations (RUV) [5] and audible vibration [6]. The cracks introduced are on a cleavage plane are almost closed and are not visible with the human eye. The critical lengths of such cracks is about 1 cm. At 1 cm or more, they propagate in processing from handling etc. The methods that have been used to detect cracks are scanning acoustic microscopy (SAM), ultrasound lock-in thermography, and millimeter wave [7]. More recently, resonance ultrasonic vibration (RUV) has been investigated to assess the presence or lack of cracks. Ultrasonic vibrations are applied to the wafers and the frequency spectra analyzed [8]. The SAM method of determining the presence of cracks is not feasible during mass production of photovoltaic cells since the time required to scan a 1 mm by 1 mm wafer is between 1 to 15 minutes. Additionally, the wafer has to be submerged in a water bath or covered with a water droplet. The SAM method, however, does allow for cracks as small as 5 to 1 microns to be detected. Ultrasound Lock-in Thermography can detect cracks with lengths as small as 1 microns. It takes 5-1 seconds to inspect a 1 mm by 1 mm wafer. The major disadvantage is still the time required to test the wafer. The Millimeter Wave method can be used to inspect a 1 mm by 1 mm wafer in as little as 3 to 5 seconds, but can only be employed for wafers before the metallization process. The crack length that can be detected is 4 microns and larger [7]. 2

18 The foundation behind the approach taken in this thesis is that impact on a cracked surface sounds different than impact on a non-cracked surface. An easy physical experiment is to tap a glass with a spoon and compare it to a glass which has a crack. One can hear the difference with a human ear. The same demonstration can be performed on silicon wafers. One can hear with the human ear which wafers are significantly cracked. These cracks are obviously large enough to be seen with your eye as well. It would be desirable to detect cracks that are not visible with the eye. In this thesis, an impact hammer is used to tap numerous silicon wafer specimens and the vibratory response is recorded by a microphone. The silicon wafers of interest are single crystalline silicon wafers grown by the Czochralski method [9]. This thesis assesses the use of an impact test method to detect cracks. This could be a relatively fast, inexpensive and nondestructive method that could be used for in-line quality testing. 1.3 Outline This thesis presents two different types of data: data from crack-free wafers and data from cracked wafers. In Chapter 2, a description of the setup as well as a description of each instrument used is given. The makeup of the test matrix is covered in Chapter 3. This includes wafer number, type of crack, crack length, wafer thickness and picture number. In Chapter 4, the results obtained are given. Finally, Chapter 5 presents the conclusion and future recommendations. 3

19 Chapter 2: Experimental Setup 2.1 Introduction This chapter presents the experimental setup and describes the sensors and the analyzer used. The specimens used are single-crystalline Czochralski (Cz) silicon wafers. Since the purpose is to detect cracks in wafers there are different types of specimens tested. In this research, the cracked specimens have been deliberately damaged with a diamond pin. In all, thirty different cracked specimens were made and tested. 2.2 Sensors An impact hammer and a sound level meter are the two sensors used in this experiment. The impact hammer, model PCB 84A17, is made by PCB Piezotronics Inc. The sensitivity of the impact hammer is 22.5 mv/n. The hammer s weight is 2.9 grams and the aluminum handle is 11.6 mm long, the hammer has a stainless steel head with a diameter of 6.3 mm and a red vinyl tip with a 2.5 mm diameter. The hammer is connected by a.18g1 coaxial cable, which is 3 m long, with a 5-44 connector terminating in a 1-32 connector that is connected with a BNC to the SigLab dynamic analyzer. The sound level meter used is a model 29 manufactured from Quest Technologies. The meter is set to measure sound pressure in the range of 6-12 db. The sensitivity of the sound level meter is 5V/12 db. The sound level 4

20 meter and the SigLab dynamic analyzer are connected from the ac output of the meter with a 6 ft shielded cable 1/8 plug to an RCA plug. The RCA plug is connected with a gold plated RCA to BNC adapter and connected with the female BNC connection of the analyzer. 2.3 Analyzer The analyzer is SigLab model 2-42 and is manufactured by DSP Technology Division. The SigLab has 4 input channels and 2 output channels. The impact hammer is connected to input channel 1 and the sound level meter is connected to input channel 3. The analyzer calculates the frequency response with the impact force as the input and the sound pressure as the output. A laptop is connected to the SigLab with a Slim SCSI PC card, the PC runs the SigLab software which is written in MatLab R12. In the SigLab software, the bandwidth is set to 1. khz and the record length is 8192, which gives a delta frequency of.313 Hz and a record time of.3 seconds. Also, the sensitivity of the hammer and the sensitivity of the sound level meter are included in the analyzer setup. The hammer sensitivity is set to 44.4 N/V for channel 1 and the sound pressure level sensitivity is set to 24 db/v for channel Frequency response The frequency response is computed with the impact force, F, (in units of Newtons) applied from the hammer as the input and the sound pressure level, S, (in units of db) from sound meter as the output. Time trace measurements of the 5

21 input and output are obtained. The measurements are windowed (i.e., box window for the input and exponential window for the response) and the Fast Fourier Transforms of the windowed time traces are computed. The measurements are repeated eight times,n, and then averaged. Power spectra (P FF (f),p SS (f)) and cross spectra (P SF (f)) are computed as [1,11] F ( f ) F ( f ) P FF ( f ) = n (1a) S( f ) S( f ) P SS ( f ) = n (1b) F ( f ) S( f ) P SF ( f ) = n (1c) where F(f) is the Fourier transform of F, S(f) is the Fourier transform of S and the is the complex conjugate. The frequency response is then computed as PSF ( f ) FR( f ) = (2) P ( f ) FF An m-file was written in Matlab to graph the magnitude (in units of db/n), phase (in units of degrees) and coherence (non-dimensional) versus frequency (Hertz). The coherence, γ 2 ( f ), is a function of frequency and is computed as 2 PSF ( f ) PSF ( f ) γ ( f ) = (3) P ( f ) P ( f ) FF SS Coherence is a number between and 1, where 1 means that all the output is caused by the input whereas a number of means that none of the output is caused by the input. 6

22 2.5 Test specimens The test specimens are single crystalline (1) Czochralski (Cz) silicon wafers. They are pseudo square (see specimen corners in Figure 2.1) with dimensions 127 x 127 mm. The thickness of the wafers were find by weighing each wafers and knowing that the density of the wafer is g/cm 3. Some of the specimens are crack-free and some of the specimens have cracks introduced in different orientations. The crack-free wafers are scanned in a Scanning Acoustic Microscopy (SAM) before and after testing to ensure that the wafers had not been damaged during the impact testing. Cracks are introduced in the wafers using a diamond pin and pressing carefully on the edge of the wafers with a light force (equivalent to the force used in writing). By doing this, the human ear can hear the wafer crack. To quantify the cracks, the wafers are scanned in the SAM before and after the impact testing. Since the cracks are not visible using optical methods the cracks images were created in the SAM. The wafers were placed under a water bath. A transducer (work as a transmitter and receiver) moves above the wafer and produced sound waves. These sound waves are at high frequencies and that is the reason why the wafer is in the water bath since the high frequencies do not propagate through air. Three different types of sets are presented in this thesis: the large crack wafer set, the miscellaneous crack wafer set and the small crack wafer set. First the small crack wafer set was investigated. Since the small crack wafer did not 7

23 show significant differences, larger cracks were made. These exploratory larger cracks are presented in the miscellaneous wafer set. After analyzing the miscellaneous wafers, the larger crack set was made and are presented as the large crack wafer set Large crack wafer set The large cracks have crack lengths varying from 38 mm to 55 mm. Some of the cracks begin at the center of an edge of the specimen, others are offset from the center of the edge. Some have segmented cracks (meaning the cracks are not continuous; instead they have small cracks in sequence). If zooming in on the crack and use high resolution of the SAM image one can see that wafer numbers 39, 32, 36, 4, 6, 8 and 41 has segmented crack. Wafer numbers 48 and 33 are also segmented but the initial crack from the edge is longer than the others. Wafer number 27 initially had segmented crack but during the tests it became continuous and wafer numbers 31 and 35 have continuous cracks. The large center cracks are cracked in the center of an edge of the specimen and are numbered 39, 31, 35, 48. These crack lengths vary between 38.6 to 52.7 mm and are shown in Figures The large offset cracks are cracked offset from the center of an edge of the wafer are numbered 32, 4, 36, 27 (see Figures ). The length of these cracks are mm. 8

24 Figure 2.1 Large center crack wafer number 39 Figure 2.2 Large center crack wafer number 31 Figure 2.3 Large center crack wafer number 35 Figure 2.4 Large center crack wafer number 48 9

25 Figure 2.5 Large offset crack wafer number 32 Figure 2.6 Large offset crack wafer number 4 Figure 2.7 Large offset crack wafer number 36 Figure 2.8 Large offset crack wafer number 27 1

26 Figure 2.9 Large crack other direction wafer number 8 Figure 2.1 Large crack other direction wafer number 6 Figure 2.11 Large crack other direction wafer number 33 Figure 2.12 Large crack other direction wafer number 41 11

27 2.5.2 Miscellaneous wafer set The miscellaneous cracks were made to explore larger cracks so the cracks starts at different location of the edge of the wafers. The cracks are made in different directions and have various crack lengths. The crack lengths vary from 18.5 mm to 52.7 mm. Wafer numbers 45, 46, and 7 have segmented cracks (meaning the cracks are not continuous instead they have small cracks in sequence). Wafer number 11 is smaller than the other, wafer number 23, 25, 47, 8 have continued cracks. The SAM images of the miscellaneous wafers are shown in Figures Figure 2.13 Miscellaneous wafer number 11 Figure 2.14 Miscellaneous wafer number 23 Figure 2.15 Miscellaneous wafer number 25 Figure 2.16 Miscellaneous wafer number 45 12

28 Figure 2.17 Miscellaneous wafer number 46 Figure 2.18 Miscellaneous wafer number 7 Figure 2.19 Miscellaneous wafer number 47 Figure 2.2 Miscellaneous wafer number Small crack wafer set The small cracks have crack lengths from 2.3 to 7.6 mm. Some of the cracks are a single crack and others have a V-shape. Note that all cracks in this 13

29 work initiate at an edge of the wafer. For the V-shape cracks, the point of the V is at the wafer edge. The location of the small cracks are arbitrary. All the small crack specimens are shown in Figures 2.21 Figure 2.3. Figure 2.21 Small crack wafer number 21 Figure 2.22 Small crack wafer number 22 Figure 2.23 Small crack wafer number 23 Figure 2.24 Small crack wafer number 25 Figure 2.25 Small crack wafer number 26 Figure 2.26 Small crack wafer number 27 Figure 2.27 Small crack wafer number 29 Figure 2.28 Small crack wafer number 3 Figure 2.29 Small crack wafer number 31 Figure 2.3 Small crack wafer number 32 14

30 2.6 Setup The test setup is shown in Figure 2.31 The specimen is set on a piece of convoluted foam of dimensions 7 x 33 x 26.5 cm. The sound level meter is attached to a rigid fixture and the microphone is set at 1.2 cm above the specimen. The microphone is set perpendicular to the wafer. The impact hammer is connected to channel 1 of the SigLab analyzer and the sound level meter is connected to channel 3 of the SigLab analyzer. Figure 2.31 Picture of the set up 15

31 2.6.1 Position of hammer and microphone The horizontal position of the hammer and the sound level meter with respect to the specimen is shown in Figure Figure 2.32 Position of hammer and microphone relative to wafer all the units are in mm The decision on were to locate the hammer and microphone with respect to the wafer was made by keeping the hammer in the same place and moving the microphone, and then moving the hammer while keeping the microphone in the same location. Figures show the frequency response with the microphone located in the same position as Figure 2.32 and the hammer is changing position. Figure 2.33 shows one dominate audible mode at 6 Hz, 16

32 Figure 2.34 and Figure 2.34 show 4 dominated modes with different peak magnitudes. The hammer and microphone locations used and shown in Figure 2.32 gave the most response (magnitudes) for the four audible modes. Magnitude (db/n) Coherence Phase (deg) Frequency (Hz) Figure 2.33 Hammer (x=83 mm, y=48 mm) Magnitude (db/n) Coherence Phase (deg) Frequency (Hz) Figure 2.34 Hammer (x=39 mm, y=6 mm) 17

33 Coherence Magnitude (db/n) Phase (deg) Frequency (Hz) Figure 2.35 Hammer (x=53 mm, y=48 mm) After deciding the location of the hammer and microphone as shown in Figure 2.32 both the hammer and the microphone were moved ± 5 mm. These results show small variations in magnitude (see Appendix F, Figure F.1-F.4). 18

34 Chapter 3: Test Matrix 3.1 Introduction This chapter lists all the wafers that were tested in this study and how the run order was determined. Three different groups of cracked wafers are listed: large crack wafer group, small crack wafer group and miscellaneous wafer group. This miscellaneous wafer group was not tested as a set, but is included because it was used to explore larger cracks. 3.2 Randomization The order of the tests was randomized to eliminate bias error. All the wafers were tested three times each (8 impacts per test) and the test order is shown in Table 3.1 (for small crack tests see Table A.1). A table with the wafer number and test number (three tests per wafer) is also shown in Table 3.2 (for small crack tests see Table A.2). This table was used to define the random run order. The test order was determined by assigning each test a random number and sorting the random numbers. 19

35 Table 3.1 Run order for the large crack wafer set Run order Wafer number Test number Random Number in ascending order

36 Table 3.2 Test number for the large crack wafer set Wafer number Test Number Test with large cracks The large crack test set contains 16 specimens from which 12 specimens are cracked and the other 4 are crack-free. Table 3.3 shows the wafer number, type of crack, if segmented or continuous, the length of the crack, the thickness of the wafer and the figure number of the image. Table 3.3 Large crack wafers Wafer number Type of crack Segmented 21 Crack length [mm] Wafer thickness [μm] Photo Figure number 29 Crack Free Crack Free 35 N/A 34 Crack Free Crack Free 35 N/A 38 Crack Free Crack Free 36 N/A 47 Crack Free Crack Free 36 N/A 39 Center Crack Yes Center Crack No Center Crack No Center Crack Yes Offset Crack Yes Offset Crack Yes Offset Crack Yes Offset Crack No Offset Crack Yes Offset Crack Yes Offset Crack Yes Offset Crack Yes

37 3.4 Test with small cracks Thirty small crack wafers were tested. Twenty wafers were crack-free and ten wafers had cracks introduced to the wafers. Table 3.4 shows the wafer number, type of crack, the length of the crack, the thickness of the wafer and the figure number of the image. Table 3.4 Small crack wafers Wafer number Type of crack Crack length Wafer thickness Photo Figure [mm] [μm] number 11 Crack Free 294 N/A 12 Crack Free 294 N/A 13 Crack Free 294 N/A 14 Crack Free 292 N/A 15 Crack Free 291 N/A 18 Crack Free 291 N/A 19 Crack Free 291 N/A 2 Crack Free 292 N/A 33 Crack Free 294 N/A 34 Crack Free 294 N/A 35 Crack Free 294 N/A 36 Crack Free 294 N/A 37 Crack Free 294 N/A 38 Crack Free 293 N/A 39 Crack Free 294 N/A 4 Crack Free 294 N/A 41 Crack Free 294 N/A 42 Crack Free 293 N/A 43 Crack Free 294 N/A 44 Crack Free 293 N/A 21 V-shape Single V-shape V-shape V-shape V-shape Single V-shape V-shape Single Tests of miscellaneous cracks The tests from the miscellaneous cracks set were not performed in a totally randomized manner. The wafers were tested at different periods of time. 22

38 However, these tests are grouped put together for presentation. This set includes twelve wafers total: four are crack-free and eight wafers are cracked. Table 3.5 shows the wafer number, type of crack, if segmented or continuous, the length of the crack, the thickness of the wafer and the figure number of the image. Table 3.5 Miscellaneous wafers Wafer number Type of crack Segmented Crack length [mm] Wafer thickness [μm] Photo Figure number 2 Crack free Crack Free 35.6 N/A 42 Crack free Crack Free 293. N/A 49 Crack free Crack Free N/A 2 Crack free Crack Free N/A 11 Cracked No Cracked No Cracked No Cracked Yes Cracked Yes Cracked Yes Cracked No Cracked No

39 Chapter 4: Test Results 4.1 Introduction This chapter presents the test data and results. This includes frequency response data with four audible modes. The following parameters are extracted from these 4 modes: natural frequencies, peak magnitudes, damping ratios and coherence. 4.2 Sample frequency response data Typical frequency response data from a crack-free wafer is shown in Figure 4.1. The graph shows a range of frequencies from -1 Hz for coherence, magnitude and phase. Four dominant modes are found at the following frequencies: 42 Hz, 59 Hz, 84 Hz and 96 Hz. By comparing the frequency response data of a non-cracked wafer with a wafer with a large crack, as shown in Figure 4.2, one can still see four different modes but the frequencies are lower, the damping is larger (peaks not as sharp) and the peak magnitudes are lower. In the next section, these parameters are extracted from the frequency response data. 24

40 Magnitude (db/n) Coherence Phase (deg) Frequency (Hz) Figure 4.1 Frequency response of crack-free wafer number 29 Coherence Magnitude (db/n) Phase (deg) Frequency (Hz) Figure 4.2 Frequency response of large crack wafer number 35 25

41 The coherence ranges between and 1, and it measures the amount of output that is caused by the input. A coherence value of 1 means that 1% of the output is caused by the input. In Figure 4.1 and Figure 4.2 the coherence versus frequency is plotted. From these figures, one can see that the coherence is close to one around the four dominant modes. All the frequency response data from the large crack wafer set are presented in Figures B.1-B.2. The lowest coherence at some peaks is.9. The small crack wafer set is not included, since they did not show any change compared to the crack-free wafers when the cracks are less than 8 mm. However, the data was collected and the extracted parameters are presented in the next section and may be compared with the large crack wafer set and the miscellaneous wafer set. 4.3 Extracted parameters The following parameters are extracted from the four dominant modes in the frequency response data: natural frequencies, peak magnitudes and damping ratio. The data from the large-crack wafer set are shown in Tables C.1- C.16 and Figures C.1-C.16, the miscellaneous wafer set in Tables D.1-D.16 and Figures D.1-D.16, and the small crack wafer set in Figures E.1-E

42 4.4 Natural frequencies Large crack wafer set The data from the second mode frequencies of the large crack wafer set are most representative and are shown in Table 4.1 (as well as in Appendix C). The first 4 specimens in the table are the crack-free wafers and the following 12 specimens have cracks as defined in Table 3.3 and shown in Figures In the crack-free wafers, the second mode frequency ranges from to Hz. For an individual crack-free wafer, the frequency deviation is less than.3 Hz, which is the frequency resolution of the measurements. The frequency deviation across all four crack-free wafers is 2.5 Hz. For the 12 large crack wafers, the second mode frequency ranges from to Hz and all the wafers are within 26.9 Hz. Six of the cracked wafers have frequencies that fall within the crack-free frequency range, two of the cracked wafers have slightly lower frequencies ( Hz) and four of the cracked wafers have significantly lower frequencies from to Hz. These 4 large crack specimens are numbered 31, 35, 48 and 27 and are italicized in Table 4.1. Comparing the italicized cracked wafers in Table 4.1 with Table 3.3, one sees that the continuous cracked wafers all show significant changes in frequency. 27

43 Table 4.1 Second mode frequency for large specimens Specimen number Test 1 [Hz] Test 2 [Hz] Test 3 [Hz] Mean [Hz] Test 1 Test 2 Test Frequency [Hz] Wafer Number Figure 4.3 Second mode frequency for large specimens The data in Table 4.1 is graphed in Figure 4.3. As seen in Figure 4.3 all the specimens have a low frequency deviation (less than.3 Hz), except large 28

44 crack wafer numbers 31, 48, and 27. Cracked wafer 31 has a deviation of 2.2 Hz, wafer number 48 has a deviation of 1.6 Hz, and wafer number 27 has a deviation of 16.9 Hz. By looking at the before and after images for wafer number 27(segmented) and wafer number 31(continuous), one can see that the cracks did elongate with testing (3 tests with 8 impacts each), thus reducing stiffness and frequency; however wafer number 48 (segment) did not show a notable change. Similar data for the first frequency mode are presented in Table C.1 and Figure C.1 (Appendix C). The crack-free wafers first mode frequency range is Hz. For an individual crack-free wafer the frequency deviation is less than.6 Hz. The frequency deviation across all four crack-free wafers is 1.9 Hz. For the 12 large crack wafers the first mode frequency range is Hz and all the wafers are within 31.6 Hz. Five of the cracked wafers have frequencies that fall within the crack-free frequency range, four of the cracked wafers have slightly lower frequencies ( Hz) and three of the cracked wafers have significant lower frequencies from to Hz. These 3 large crack specimens are numbered 31, 35 and 27. All the specimens have a frequency deviation of less than.6 Hz except large crack wafers numbered 31, 35, 48, and 27. Cracked wafer 31 has a deviation of 4.4 Hz, wafer number 35 has a deviation of.9 Hz, wafer number 48 has a deviation of 1.3 Hz, and wafer number 27 has a deviation of 1.6 Hz. 29

45 Table C.5 and Figure C.5 shows the third frequency mode. The crack-free wafers third mode frequency range is Hz. For an individual crackfree wafer the frequency deviation is less than.3 Hz. The frequency deviation across all four crack-free wafers is 3.8 Hz. For the 12 large crack wafers the third mode frequency range is Hz and all the wafers are within 3.9 Hz. Eight of the cracked wafers have frequencies that fall within the crack-free frequency range, one of the cracked wafers has slightly lower frequencies ( Hz) and three of the cracked wafers have significant lower frequencies from to 835 Hz. These three cracked specimens are numbered 31, 35, and 27. All the specimens have a frequency deviation less than.3 Hz except large crack wafers numbered 31, 35, 48, and 27. Cracked wafer 31 has a deviation of 13.4 Hz, wafer number 35 has a deviation of.6 Hz, wafer number 48 has a deviation of.9 Hz, and wafer number 27 has a deviation of 18.4 Hz. Table C.7 and Figure C.7 shows mode four. The crack-free wafers fourth mode frequency range is Hz. For an individual crack-free wafer the frequency deviation is less than.3 Hz. The frequency deviation across all four crack-free wafers is 4.1 Hz. For the 12 large crack wafers the fourth mode frequency range is Hz all the wafers are within 31.6 Hz. Five of the cracked wafers have frequencies that fall within the crack-free frequency range, three of the cracked wafers have slightly lower frequencies ( Hz) and four of the cracked 3

46 wafers have significant lower frequencies from Hz. These four cracked specimens are numbered 31, 35, 48 and 27. All the specimens have a frequency deviation less than.6 Hz except large crack wafer numbers 48, and 27. Cracked wafer number 48 has a deviation of 2.5 Hz and wafer number 27 has a deviation of 23.4 Hz Miscellaneous wafer set The data from the second mode frequencies of the miscellaneous crack wafer set are shown in Table D.3 and Figure D.3 (Appendix D). The first 4 specimens in the table are the crack-free wafers and the following 8 wafers have cracks as defined in Table 3.5 and shown in Figures The second mode frequency range for the crack-free wafers is from to Hz. For an individual crack-free wafer the frequency deviation is less than.3 Hz. The frequency deviation across all the crack-free wafers is 23.8 Hz. For the 8 cracked wafers the second mode frequency ranges from to Hz, all cracked wafers are within 38.4 Hz and the deviation within a wafer is less than 2.2 Hz. The deviation across the crack-free wafers are higher than found for the large crack specimens because these miscellaneous wafers have various thickness μm. This problem will be solved by normalizing in section 4.5. Data for the first mode is also shown in Table D.1 and Figure D.1, for the third mode Table D.5 and Figure D.5, and for the fourth mode in Table D.7 and Figure D.7. 31

47 4.4.3 Small crack wafer set The second mode frequencies for the small crack wafer set are shown in Figure E.3. The first 2 specimens in the Table 3.4 are the crack-free wafers and the following 1 wafers have cracks as defined in Table 3.4 and shown in Figures The crack-free wafers second mode frequencies range from to Hz. For an individual crack-free wafer the frequency deviation is less than.6 Hz, the frequency deviation across all twenty crack-free wafers is 7.8 Hz. For the 1 small crack wafers the second frequency mode ranges from 565 to Hz and all are within 7.5 Hz. The deviation in an individual wafer is less than.3 Hz. Note that the ranges are very similar to the crack-free wafers and that the cracks are small less than 8 mm. Data for the first mode is presented in Figure E.1, for the third mode in Figure E.5, and for the fourth mode in Figure E Normalized frequencies Some of the wafers were found to have slightly different thickness. Since natural frequency is directly proportional to the thickness to the three-halves power, the frequencies are normalized with respect to the thickness of the wafers by f f norm = (4) 3/ 2 h 32

48 where f norm is the normalized frequency, f is the measured natural frequency (in Hz) and h is the thickness of the wafer (in μm) [12]. The normalization is necessary for the miscellaneous wafer set since the thickness varied and also to compare the three different type of sets Large crack wafer set The normalized frequencies for the second mode (presented in Table C.4 and Figure C.4) of the large crack wafer set did not show a large difference from section since the thickness range of these wafers are similar μm. The crack-free wafers second mode normalized frequency ranges from.8 to.1 Hz/ μm 3 / 2. For an individual crack-free wafer, the frequency deviation is less than.1 Hz/ μm 3 / 2. The frequency deviation across all four crack-free wafers is.2 Hz/ μm 3 / 2. For the 12 large crack wafers, the second mode normalized frequency ranges from.162 to.1111 Hz/ μm 3/ 2 and all the wafers are within.49 Hz/ μm 3 / 2. Four of the cracked wafers have normalized frequencies that fall within the crack-free normalized frequency range, four of the cracked wafers have slightly lower normalized frequencies ( Hz/ μm 3 / 2 ) and four of the cracked wafers have significantly lower normalized frequencies from Hz/ μm 3 / 2. These 4 large crack specimens are numbered 31, 35, 48 and 27. All the specimens have a frequency deviation of less than.1 Hz/ μm 3/ 2 except large crack wafer numbers 31, 48, and

49 Cracked wafer 31 has a deviation of.4 Hz/ μm 3 / 2, wafer number 48 has a deviation of.3 Hz/ μm 3 / 2, and wafer number 27 has a deviation of.32 Hz/ μm 3 / 2. Since the thickness for the large crack wafer set does not vary significantly, the normalization of the first, third and fourth frequency modes are not discussed in this section but are presented in Appendix C for completeness. Data for the first mode in Table C.2 and Figure C.2, for the second mode in Table C.4 and Figure C.4, for the third mode in Table C.6 and Figure C.6, and for the fourth mode in Table C.8 and Figure C Miscellaneous wafer set The miscellaneous wafers second mode frequencies are graphed in Figure 4.4 and the normalized second mode frequencies are graphed in Figure 4.5. In Figure 4.4 wafer numbers 42, 49, 2, 23, 7,47, 8 had significantly lower frequencies than the other 5 wafers. The reason that the frequencies are lower is not because of any cracks instead it is because the thickness of the wafers varied from μm. The crack-free wafers second mode normalized frequency ranges from.111 to.1135 Hz/ μm 3 / 2. For an individual crack-free wafer, the normalized frequency deviation is less than.1 Hz/ μm 3 / 2. The normalized frequency deviation across all four crack-free wafers is.25 Hz/ μm 3 / 2. 34

50 For the 12 large crack wafers, the second mode normalized frequency ranges from.143 to.1129 Hz/ μm 3/ 2 and all the wafers are within.86 Hz/ μm 3 / 2. Three of the cracked wafers have normalized frequencies that fall within the crack-free normalized frequency range, four of the cracked wafers have slightly lower normalized frequencies ( Hz/ μm 3 / 2 ) and one (number 23) of the cracked wafers has significantly lower normalized frequencies from Hz/ μm 3 / 2. All the specimens have a normalized frequency deviation of less than.2 Hz/ μm 3/ 2 except large crack wafer numbers 23 and 47 they have a deviation of.4 Hz/ μm 3 / 2. Data for mode 1 are provided in Table D.2 and Figure D.2, for mode 3 in Table D.6 and Figure D.6, and for mode 4 in Table D.8 and Figure D.8. 35

51 Frequency [Hz] Test 1 Test Wafer Number Figure 4.4 Second mode natural frequencies for miscellaneous wafer set.114 Test 1 Test 2 Normalized frequency [Hz/ μm 3/2 ] Wafer number Figure 4.5 Second mode normalized frequencies for miscellaneous wafer set 36