ACM ISPD 16 A Compressivesensing based Testing Vehicle

ACM ISPD’ 16 A Compressive-sensing based Testing Vehicle for 3 D TSV Pre-bond and Post-bond Testing Data Hantao Huang 1, Hao Yu 1, Cheng Zhuo 2 and Fengbo Ren 3 1 Nanyang Technological University, Singapore 2 Intel Corporation, USA 3 Arizona State University, USA 1

Outline 1 Introduction 2 TSV I/O Test 3 Test Data Compression 4 Experiments 5 Conclusion 2

Data Analytics Challenge Data center for future big-data-oriented society: 1. Leaving data outside a nation will face serious cyber-security concern 2. Processing data inside a nation by traditional Gigascale systemat has 100 high. Gps cost Bandwidth with Space of 20, 000 sq. ft. Power of 68 MW and cost of 100 M-USD !!! 3

2. 5 D and 3 D Integration Memory/logic integrated on one common substrate by through-silicon interposer (TSI) I/O • Traditional 2 D integration is non-scalable for bandwidth • 3 D has best bandwidth scalability but poor thermal dissipation • 2. 5 D provides good scalability of bandwidth and also thermal 4

Challenges on 3 D-IC with TSVs [1] Lee, Hsien-Hsin S. , and Krishnendu Chakrabarty. "Test challenges for 3 D integrated circuits. " Design & Test of Computers, IEEE 26. 5 (2009): 26 -35. 5

Outline 1 Introduction 2 TSV I/O Test 3 Test Data Compression 4 Experiments 5 Conclusion 6

TSV I/O Test TSV Failure Mechanism • Pin holes in dielectric • Void due to TSV fabrication • Electron Migrations • TSV … Test Mechanism • TSV Test by probe in pre-bond phase • TSV elevator in postbond phase Limited Bandwidth for testing data: Only probe/elevator for data transfer 7

Pre-bond TSV Testing Fig. a gives a simple example to detect open, short and connected faults in TSV interconnection. Fig. b and c show the mismatch pitch of probe head is resolved by using scan-chain flip-flop (SF). In Fig. c only the top TSV has the I/O drive-ability, which means all the data is collected from other TSV SF by the top SF. Conceptual diagram for pre-bond TSV test 8

Post-bond TSV Testing Fig. right shows a conceptual post-bond testing diagram where built-in-self-test (BIST) circuit is shared between different TSV groups. The signal generated from BIST is scheduled and sent to router. Router will send the signal to TSV group driver for testing purposes by a sequence of digital bits similar as in the pre- 9

TSV Test Vehicles with Data Compression TSV Test Vehicles • Supported pre-bond die test, post-bond stack test and board level test • Test wrapper provides test access mechanism (TAM) and send/receive test data through I/O • Pad and TSV elevator provides data transfer, which has limited bandwidth • Test Data Compaction (TDC) provides data 10

Outline 1 Introduction 2 TSV I/O Test 3 Test Data Compression 4 Experiments 5 Conclusion 11

Previous Test Data Compressions Lossy Test Data Compression [1] XOR: Simple with high aliasing rate (detection failure) Multi-input Signature Register (MISR): good compression rate with low aliasing rate and no diagnostic information Lossless Test Data Compression [2] Length Run Coding: encoding runs of zeros using fixed length codes. Golomb Coding: encoding runs of zeros using a variable length code words Scan in 1 Scan in 2 Scan out Test Data compress ion Out 1 Out 2 Scan in n [1] Mc. Cluskey, E. J. , et al. "Test data compression. " Design & Test of Computers, IEEE 20. 2 (2003): 76 -87. [2] Chandra, Anshuman, and Krishnendu Chakrabarty. "System-on-a-chip test-data compression and decompression architectures based on Golomb codes. "Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on 20. 3 (2001): 355 -368. 12

New Problem Formulation The main proposed problem here is to fully utilize the compressive sensing to compress the TSV test data with high data compression rate under the given error probability while ensuring a lossless recovery. where Xr Є RN and Xe Є RN denote the received and expected signal through TSV for pre-bond test or scan chain for post-bond test and Y Є RM is the output result. Φ is the compressive sensing matrix. Efault Є RN is defective TSV index in the pre-bond test, while for the post-bond test, . Efault represents the error bits introduced by faulty ICs. 13

Sparsity Analysis of Test-data TSV Yield Analysis, overall probability of pre-bond have x defective TSV is Post-bond IC faulty-free probability estimated as Poisson distribution When defective error is sparse, signal difference Data here is defined: Yideal –Yactual (a) sparse data for yield (Ypre) of 95% (b) sparse data for yield (Ypre) of 99% 14

Sparse Test-Data Compression Efaulty • The scan chain output and the expected output from the probe pad are XORed to obtain the difference matrix, Efaulty , which is normally sparse with 1 to denote the error/failure. • Fig. above shows how to compress a sparse signal from N to M measurements. The compression rate is calculated as 1 -M/N. 15

Lossless Compression and Recovery (I) The lossless recovery can be formulated as L 0 -norm minimization problem as below Where Efault is N dimensional sparse signal and Φ is the sensing matrix RMx. N and Y is the sparse representation data in low dimension RN (M<<N). The minimum sampled data is required (a) L 1 norm solution in 2 D example (b) L 2 norm solution in 2 D example Where K is the sparsity of the test data and can be estimated from the yield. 16

Lossless Compression and Recovery (II) OMP performs three functions: 1. Finding the most correlated column from the sensing matrix Φ by comparing simple dot multiplication. 2. Adding the largest correlated column to the selected column 3. Solving a L 2 norm minimization to generate the most fitted new signal. Above procedures will repeat K times to find Matching the expected signal Orthogonal Pursuit (OMP) complexity analysis at iteration t: • Atom searching: 2 nm • L 2 -norm minimization : mt^3+t^3/3 • Update: 2 mt Atom searching is the most time consuming due to the large n but 17

Testing flow for proposed testing vehicle 18

Outline 1 Introduction 2 TSV I/O Test 3 Test Data Compression 4 Experiments 5 Conclusion 19

Results and Comparison Pre-bond Test TSV No. Failure Prob. 0. 5% 4096 1% 0. . 5% 16384 1% 0. 5% 65536 1% Cluster Propo sed LR Coding GLC D=8 GLC D=16 α =0 89. 45% 81. 80% 76. 83% 79. 98% α =1 89. 70% 81. 14% 77. 29% 80. 18% α =2 89. 32% 81. 52% 76. 68% 79. 76% α =0 65. 29% 50. 99% 35. 57% 44. 38% α =1 65. 03% 50. 73% 35. 57% 43. 80% α =2 66. 48% 51. 52% 37. 16% 45. 85% α =0 89. 16% 80. 37% 75. 95% 79. 11% α =1 89. 23% 80. 15% 73. 99% 77. 28% α =2 89. 35% 80. 47% 75. 59% 78. 89% α =0 64. 80% 49. 42% 34. 08% 43. 49% α =1 64. 29% 46. 93% 29. 49% 38. 37% α =2 64. 86% 50. 62% 34. 51% 43. 84% α =0 89. 17% 79. 77% 73. 48% 76. 86% α =1 89. 21% 79. 73% 73. 09% 76. 63% α =2 89. 24% 79. 38% 73. 49% 76. 86% α =0 65. 32% 50. 03% 34. 27% 43. 35% α =1 64. 59% 48. 57% 34. 19% 43. 41% α =2 64. 88% 47. 08% 36. 68% 40. 21% • X-axis and Y-axis represent the location of TSV. The average failure probability is 20 % and due to the clustering effect, the failure probability can be as high as 81. 52% for the TSVs close to the center. • Compression rate is as high as 89. 45% 20

Results and Comparison • Post-bond Functional Test for ISCAS 85 benchmark in Verilog and Bench Matlab Error Output Prop LR GLC Probl. 5% 10% mark ( bits) osed Coding D=8 GLC D=16 c 499 1696 88. 15% 78. 22% 73. 01% 76. 42% c 432 196 88. 18% 77. 96% 76. 38% 78. 57% c 1908 2475 86. 89% 73. 69% 72. 83% 76. 34% c 2670 6300 82. 56% 73. 81% 69. 77% 73. 74% c 3540 1870 87. 76% 80. 55% 75. 75% 78. 72% c 5315 4674 81. 80% 75. 31% 71. 13% 74. 97% c 6288 416 85. 65% 81. 15% 82. 21% 84. 13% c 7552 7992 80. 30% 74. 27% 68. 26% 72. 19% c 499 1696 73. 82% 59. 53% 50. 17% 57. 17% c 432 196 82. 19% 68. 67% 63. 06% 66. 94% c 1908 2475 70. 57% 56. 00% 45. 86% 53. 27% c 2670 6300 61. 42% 55. 17% 44. 25% 51. 80% c 3540 1870 70. 82% 56. 56% 46. 24% 53. 76% c 5315 4674 63. 71$ 52. 38% 40. 88% 49. 14% c 6288 416 76. 06% 58. 51% 49. 83% 56. 49% c 7552 7992 60. 99% 54. 45% 43. 95% 51. 55% • Output data compression for prebond and post-bond TSV test via compressed sensing is discussed. • Experiment results with benchmarks have shown that 89. 70% pre-bond data compression rate can be achieved under 0. 5% error probability; and 21

Outline 1 Introduction 2 TSV I/O Test 3 Test Data Compression 4 Experiments 5 Conclusion 22

Conclusion • In this paper, the testing data compression is discussed for pre-bond and post-bond TSV testing via compressive-sensing based method. • By exploring the sparsity of the testing data, one can achieve on-chip data compression and lossless offchip data recovery. • The encoding for compression can be easily implemented on-chip using XOR and AND networks with significantly improved bandwidth for the output of the testing data. • Experiment results with benchmarks have shown: • 89. 70% pre-bond data compression rate can be achieved under 0. 5% failure probability; • 88. 18% post-bond data compression rate can be achieved with 5% failure probability. 23

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