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Optimization of Test Strategies for System-in-Package Using Linear Programming

This research explores the application of linear programming to optimize test strategies for System-in-Package assemblies, considering cost and yield trade-offs. The approach involves analyzing defect levels, test methods, and component selection to minimize overall SIP costs. The study aims to find near-optimal solutions when exact optimization is challenging. Future work includes enhancing the efficiency of the approach and investigating variances between SIP and MCM test methodologies.

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Optimization of Test Strategies for System-in-Package Using Linear Programming

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  1. SIP Testing Speaker : Meng-Syue Jhan Advisor : Chun-Yao Wang 2007/09/04

  2. Outline • Introduction • Our Idea • Linear Programming • Example • Conclusion • Future Work

  3. Introduction • The system-in-package(SIP) consists of multiple chips stacked and connected within a package • The components can be manufactured separately, in different technologies, and then assembled

  4. Introduction • To produce high quality and cost effective, we require evaluation to determine the economics of the various solutions and the payback • We need to examine and understand the relationship between the cost parameters, the yield of the various components, and various test strategy parameters

  5. Outline • Introduction • Our Idea • Linear Programming • Example • Conclusion • Future Work

  6. Linear Programming • Linear programming is utilizing the math to analyst the problem of the resource distribution • A fraction in some situation is no meaning, and it has called Integer Programming

  7. Binary Linear Programming • In our problem, coefficients must be a binary number • Balas proposed branch and bound to solve binary integer programming problem in 1965

  8. How to Apply it to Our Problem • We explore the tradeoff between the defect level and cost • Given the objective function of the cost or defect level and constrains of our goal • Find the solution which meets all constrains

  9. Example • We have several choices among chips and testing methods, and want to minimize the cost of the overall SIP

  10. Example

  11. Example A B Testing Min Z = (5X1+7X2)+2(13X3+15X4)+10X5+15X6+20X7+30X8+W • 2 > X1+X2 ≧ 1 • 2 > X3+X4 ≧1 • 2 > X5+X6 ≧1 • 2 > X7+X8 ≧1 • 106(DL1+DL2) < 10000 • 104(DL1+DL2) = W Constrains of Dies Constrains of Testing Constrains of Defect Level

  12. Example Z = 8 X1=0 X1=1 hopeful hopeful X2=0 X2=1 X2=0 X2=1 Fathomed hopeful hopeful Fathomed X3=0 X3=1 X3=1 X3=0 hopeful hopeful hopeful hopeful X4=0 X4=1 X4=0 X4=1 X4=0 X4=1 X4=0 hopeful Fathomed hopeful Fathomed hopeful Fathomed hopeful 、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、、

  13. Example TEST TEST COST COST We find the optimal solution is (0,1,0,1,0,1,0,1) and Z = 174

  14. Conclusion • By this way, we can find the optimal solution between cost and yield • If no optimal solution could be found, our approach can find a solution near optimal but not satisfied constrains

  15. Future Work • Make our approach quicker • Find what is the variations between SIP and MCM in our approach

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