郭斯彥臺灣大學：電子工程學研究所彭志偉Peng, Chih-WeiChih-WeiPeng2007-11-272018-07-102007-11-272018-07-102004http://ntur.lib.ntu.edu.tw//handle/246246/57438高溫工作測試是用來測定高溫及高電壓對固態元件隨著時間變化的影響, 它是以加速的方式來模擬元件的工作條件, 而且主要是用來評估元件的可靠度。在此篇論文提出了一種模擬退火的演算法用來對於高溫工作測試的條件做最佳化, 我們的目標是要減少在硬體部份或是測試時間上面, 於高溫工作測試時所花的成本。並且我們也會對於可靠度的統計理論, 模擬退火演算法的由來及應用做一系列的探討。在我們的最佳化演算法裡, 必須計算較為精準的偏壓必v, 因為當最佳化過程中, 偏壓一旦改變, 不僅會影響到電壓加速因子, 同時也會影響到熱加速因子。因此我們利用曲線迴歸的方式來得到較為合理的加速因子及可靠度的計算, 並且, 對於曲線迴歸的模型選擇以及對不同模型所產生的適合度資料的統計分析會有詳盡的探討。在此篇論文, 我們也會介紹在不同的使用者設定的優先條件下程式執行的結果來驗證我們所提出方法的有效性。HTOL (High Temperature Operation Life) test is used to determine the effects of bias and temperature stress conditions on solid-state devices over time. It simulates the devices’ operating condition in an accelerated manner, and is primarily for device reliability evaluation. This paper addresses an SA (Simulated Annealing) method used for the HTOL test stress condition decision-making that is an optimization problem. The goal is to reduce the resources for the HTOL test, hardware or time, under reliability constraints. The theory of reliability statistic model and the SA algorithm are presented. In our optimization algorithm, we need to calculate the accurate HTOL stressed power for the next optimization loop since the Vs (Stressed Voltage) that is optimized will affect not only Afv (Voltage Acceleration Factor) but also Aft (Thermal Acceleration Factor). A curve-fitting algorithm is applied to get reasonable accelerated factors and reliability calculations. The model selection process and statistical analysis of fitted data by different models are also presented. Experimental results with different stress condition priorities and different user settings are given to demonstrate the effectiveness of our approach.誌謝………………………………………………………………………i 摘要…………………………………………………………………… ii ABSTRACT ………………………………………………………… iii TABLE OF CONTENTS ………………………………………………… iv LIST OF FIGURES……………………………………………………vii LIST OF TABLES…………………………………………………… ix CHAPTER 1 INTRODUCTION ………………………………………… 1 CHAPTER 2 RELIABILITY TESTS ……………………………………4 2.1. Purpose of Reliability Testing……………………… 4 2.2 Factors Affecting Reliability…………………………4 2.2.1 Design Phase ……………………………………… 4 2.2.2 Wafer Process ……………………………………… 5 2.2.3 Assembly Process ……………………………………… 6 2.2.4 Operation Environment ……………………………7 2.3 Reliability Tests ..…………………………………… 8 2.3.1 Wafer Level Reliability Tests ……………… 8 2.3.2 Product Level Reliability Tests ………………11 2.3.3 Reliability Failure Mechanisms ………………12 2.3.4 Procedure for reliability improvement through FA…13 CHAPTER 3 HTOL TEST …………………………………….…… 15 3.1 HTOL Facilities ……………………………………………15 3.1.1 HTOL test board ……………………………………… 15 3.1.2 HTOL test oven ……………………………………… 16 3.2 Reliability Statistic Models for HTOL ………………17 3.2.1 Accelerated Life Tests ……………………………… 17 3.2.1.1 Purpose of Accelerated Life Test ………………… 17 3.2.1.2 Temperature Acceleration ………………… 17 3.2.1.3 Voltage Acceleration ……………………… 20 3.2.2 Failure Rate Calculation …………………………… 22 3.2.2.1 Constant Failure Rate ……………………… 22 3.2.2.2 c2 Chi-square distribution ………………… 24 3.2.2.3 l, FIT, MTTF Calculation of HTOL test …………26 CHAPTER 4 Optimization Algorithms ……………………………29 4.1 Stress Condition Optimization Flow ………………… 29 4.2 Inverse Chi-square Random Variable by Approximation 30 4.3 Proposed SA-based Algorithm …………………………… 32 4.4 Curve Fit Algorithm for Ws Estimation………………… 34 4.4.1 Experimental Data Inputs …………………………… 35 4.4.2 Variables Affecting "Is" ……………………………… 35 4.4.3 Curve Fit Model Selection …………………………… 36 4.4.4 Parameters Estimated through Least Square Method 37 4.4.5 Residual Analysis ……………………………………… 39 4.4.6 R2 and R2(Adj) Analysis ……………………………… 41 4.4.7 Confidence Interval Analysis ……………………42 4.4.7.1 95% confidence interval of b estimation …………43 4.4.7.2 95% confidence interval of "Is" estimation ……43 CHAPTER 5 Experiment Results and Discussion …………… 44 5.1 Curve Fit Results and Analysis ………………… 44 5.1.1 Experiment Environment …………………………… 44 5.1.2 Experiment Data Inputs ………………………………45 5.1.3 Curve Fit Model Selection …………………………… 54 5.1.3.1 Graph Comparison …………………………………… 54 5.1.3.2 R2 and R2(Adj) Comparison ………………………… 63 5.1.3.3 Residual Analysis for the Selected Model………… 64 5.1.3.4 Confidence Interval Analysis …………………66 5.1.3.5 3D Graph of the Curve Fitting …………… 67 5.2 Optimization Results and Analysis …………………68 5.2.1 Probability to Move during SA …………………68 5.2.2 SA Results and Comparisons …………………………… 69 CHAPTER 6 Conclusions …………………………………………71 References………………………………………………… …… 72 LIST OF FIGURES Figure 1-1 Reliability bath tube curve Figure 2-1 EM failure illustration and failure mechanism Figure 2-2 Test structure of EM Figure 2-3 Illustration of HCI Figure 2-4 Illustration of TDDB Figure 2-5 Procedure of reliability improvement through FA Figure 3-1 Illustration of HTOL board Figure 3-2 HTOL test oven overview (From KYEC corp.) Figure 3-3 Relationship between lifetime and temperature Figure 3-4 Relationship between activation energy and acceleration coefficient Figure 3-5 Relationship between temperature and acceleration coefficient using activation energy as parameter Figure 3-6 Example of constant electric field test of thin oxide film Figure 3-7 (a) Exponential cumulative distribution; (b) Exponential probability density; (c) Exponential hazard function Figure 3-8 Plots of Chi-square PDF by different DF Figure 3-9 Plots of Chi-square CDF by different DF Figure 4-1 The HTOL stress condition optimization flow Figure 4-2 Algorithm for the approximate inverse Chi-square value Figure 4-3 Algorithm for the approximate inverse Normal distribution value Figure 4-4 SA Algorithm Pseudo Code Figure 4-5 Initial Temperature pseudo code Figure 4-6 Curve Fit Flow and analysis for the Ws generation Figure 4-7 Response Curve Surface Figure 4-8 Random distributed regressive model Figure 4-9 2nd order shaped regressive model Figure 4-10 The outlier drops out of 3s Figure 5-1 The "Is" to Tah plots Figure 5-2 The "Is" to Vs plots Figure 5-3 The "Is" to Tah plots and the regressive curve with linear terms of Tah and Vs Figure 5-4 The "Is" to Tah plots and the regressive curve with quadric terms but without mutual term of Tah and Vs Figure 5-5 The "Is" to Tah plots and the regressive curve with quadric terms and the mutual term of Tah and Vs Figure 5-6 The "Is" to Tah plots and the regressive curve with cube terms of Tah and Vs Figure 5-7 The "Is" to Tah residual plots Figure 5-8 3D graph of the curve fit Figure 5-9 Possibility to move during SA LIST OF TABLES Table 2-1 Industrial reliability test specifications Table 2-2 Failure mechanisms of reliability tests Table 3-1 Major components and functions of HTOL oven Table 5-1 Hardware environment of the curve fitting experiment Table 5-2 Software environment of the curve fitting experiment Table 5-3 The current measurement under different Tah and Vs applied to the DUTs Table 5-4 The R2 and R2(Adj) comparison table of various regressive models Table 5-5 The confidence interval of the b parameters Table 5-6 The confidence interval of the "Is" Table 5-7 Environment of the SA experiment Table 5-8 Optimization results of different priority sets2090816 bytesapplication/pdfen-US單位時間失敗率卡方分配模擬回火演算法平均失效時間高溫工作生命週期曲線搓合Curve FitChi-square distributionFIT RateSA AlgorithmMTTFHTOLthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/57438/1/ntu-93-P91943002-1.pdf