用於延遲錯誤內建自我測試之高效能線性反饋位移暫存器選擇方法

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研究生：	陳申峰 Shen-Feng Chen
論文名稱：	用於延遲錯誤內建自我測試之高效能線性反饋位移暫存器選擇方法 High Quality LFSR selection for Delay Fault BIST
指導教授：	劉靖家 Jing-Jia Liou
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2005
畢業學年度：	94
語文別：	英文
論文頁數：	67
中文關鍵詞：	內建自我測試、線性反饋位移暫存器、測試、延遲、錯誤、轉換錯誤、路徑延遲錯誤
外文關鍵詞：	BIST, LFSR, testing, delay, fault, transition fault, path delay fault
相關次數：	點閱：3 下載：0
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假隨機測試樣本產生器(pseudo-random pattern generator)，例如線性反饋位移暫存器(Linear Feedback Shift Register, LFSR)，是用於內建自我測試(Build-in Self Test, BIST)最主要的部份。然而，對於線性反饋位移暫存器而言，不同的起始值(initial state)和不同的組態(configuration)，往往在錯誤涵蓋率(fault coverage)上造成很大的差異。截至目前為止，還沒有一個有效的方式可提供選擇出測試性較佳的線性反饋位移暫存器。我們發現，電路中不同的錯誤其被測試出來的機率也不同，根據這個觀點，我們提出了一個能加速搜尋的方法。我們用這個加速的方式，配合模擬降溫法(Simulated Annealing, SA)的搜尋演算法，可將我們的方法用於解決測試轉換錯誤(transition fault)及路徑延遲錯誤(path delay fault)。在我們的實驗結果中，對於電路s15850的轉換錯誤測試而言，以我們的方法選擇出一組線性反饋位移暫存器的組態，再配合15個不同的起始值，每個起始值都產生10k個測試樣本，便能有效的將錯誤涵率提升到99.71％，反觀隨機選擇的結果只達到96.77%。另外，對於s15850的路徑延遲錯誤，我們達到75.43%的錯誤涵蓋率，反觀隨機選擇的結果，僅達到48.42%而已。

The build-in test pattern generators such as linear feedback shift registers (LFSR’s) and cellular automata are used to generate pseudo-random patterns for circuit-under-test. They are both lowcost and realize the at-speed testing for the circuit, especially for testing delay faults in the circuit which requires that the test vectors be applied to the circuit at its intended operating speed. However, different configurations or different initial states of LFSR’s may yield significantly different fault coverages when used as a test pattern generator for a given circuit.
In this thesis, we develop a Simulated Annealing (SA) algorithm to select an effective LFSR for testing the transition faults and path delay faults of a circuit.
In our SA algorithm, we have to simulate a large amount of LFSR’s. Therefore, we develop a faster algorithm use to estimate the fault coverage. If the SA algorithm is used to search a better LFSR for transition fault, we propose a statistic method to estimate the transition fault coverage of the chosen LFSR. On the other hand, if the SA algorithm is used to search a better LFSR for a given path set, we also develop a logic simulator which can be used to estimate the path delay fault coverage.
Experimental results shows the search result of SA algorithm and the comparison between statistic method and fault simulation.

Introduction 10
1 Delay Testing Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1 Combinational Circuit Testing . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Sequential Circuit Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Delay Fault Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 Path Delay Fault Model . . . . . . . . . . . . . . . . . . . . . . 14
1.3.2 Transition Delay Fault Model . . . . . . . . . . . . . . . . . . . 14
2 Linear Feedback Shift Register . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Target Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 Performance Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 LFSR Limitation – Psdeudo Random Pattern Resistant Faults . . . . . . . 16
4 Overviow of the proposed searching process . . . . . . . . . . . . . . . . . . . . . 17
5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Previous work 19
1 Primitive LFSRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Learning Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Proposed Statistic Transition Fault Simulation algorithm 22
1 Overview of Proposed Statistic Transition Fault Simulation algorithm . . . . . . . 22
2 The Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 Transition Count and Sensitization . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Detection Probability and Estimated Fault Coverage . . . . . . . . . . . . 27
3 Experimental Results and Comparison . . . . . . . . . . . . . . . . . . . . . . . . 28
Path Delay Fault Simulator 30
1 Path classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.1 Robust testable path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.2 Non-robust testable path . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3 Functional sensitizable path . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4 Functional unsensitizable path . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Proposed Method to Select an LFSR for Path Delay Fault Testing . . . . . . . . . . 33
Simulated Annealing and Pattern Mapping algorithm 35
1 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1.1 An overview of Simulated Annealing Algorithm . . . . . . . . . . . . . . 35
1.2 Parameters and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2 Pattern Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 An overview of Pattern Mapping Algorithm. . . . . . . . . . . . . . . . . 41
Experimental Results 43
1 Search an LFSR for Transition Fault Testing . . . . . . . . . . . . . . . . . . . . . 43
1.1 Phase 1 – Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . 43
1.2 Phase 2 – Pattern Mapping. . . . . . . . . . . . . . . . . . . . . . . . . . 52
1.3 Comparison between proposed method and random selection . . . . . . . . 54
2 Search an LFSR for Path Delay Fault Testing . . . . . . . . . . . . . . . . . . . . 56
2.1 Phase 1 – Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . 56
2.2 Phase 2 – Pattern Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.3 Comparison between proposed method and random selection . . . . . . . . 61
Conclusions and Future Work 63
1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

                                

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