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Han Zhao Advisor: Prof. Lei He TA: Fang Gong

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Presentation on theme: "Han Zhao Advisor: Prof. Lei He TA: Fang Gong"— Presentation transcript:

1 Han Zhao Advisor: Prof. Lei He TA: Fang Gong
Final Project Quadratic Response Surface + Importance Sampling Han Zhao Advisor: Prof. Lei He TA: Fang Gong

2 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

3 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

4 Quadratic Response Surface
Optimization problem x1 x2 x3 x4 Leff 1 Leff 2 Vth 1 Vth 2 Variable y Reading voltage Writing time Reading power Writing power Object function

5 Quadratic Response Surface
Central composite designs Circumscribed Inscribed Faced Center point Nominal parameters Star points Variation Generate 15+ samples Hspice simulation Linear regression to find coefficients

6 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

7 Reading Failure Model Polynomial function Optimal solutions
Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V) Vth 2 (x4) Voltage (y) 0.095 0.38 0.5 0.1632 0.105

8 Reading Failure Model compromise Lower part is optimal
Upper part is optimal

9 Writing Failure Model Polynomial function Optimal solutions
Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V) Vth 2 (x4) Time (y) (ps) 0.095 0.2 6.0412

10 Writing Failure Model consistent Right part is optimal

11 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

12 Optimal solutions for reading Optimal solutions for writing
Power Model Reading Writing Optimal solutions for reading Optimal solutions for writing Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V) Vth 2 (x4) Power (y) (mW) 0.105 0.095 0.31 0.5 0.0265 Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V) Vth 2 (x4) Power (y) (mW) 0.105 0.5 0.0522

13 Power Model

14 Area Model Total area Only depend on effective length
The optimal solution

15 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

16 Results Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V) Vth 2 (x4) Reading
voltage 0.095 0.38 0.5 0.105 Writing time 0.2 power 0.31 Writing power Optimal Consistent with results from QMC exhaustive search

17 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

18 Importance Sampling Motivation Method
Optimal design makes the yield rate approach infinitely to 1 To find the yield rate (approximately 1-1e-6), we should run Hspice about 1.4e9 times! The CPU runtime is too long to count Method Find failure regions with uniform distribution (5*sigma range) Sample quite a few points in that failing areas Calculate the equivalent yield rate with formulas

19 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

20 Results Failing regions Leff 1 (x1) (μm) Leff 2 (x2) Vth 1 (x3) (V)
Optimal 0.095 0.5 0.2 Reading failure 0.08 0.2617 0.198 Writing failure 0.096 0.106 0.525 0.273 Failing regions

21 Results Results Yield rate Samples CPU runtime Optimal 1 – 1e-6 1.4e9
Too long! Reading 1 – 5.78e-7 500 1 min Writing 1 – 2.83e-4

22 Outline Quadratic Response Surface Modeling Importance Sampling
Problem statement Reading & writing failure model Power & area model Results Importance Sampling Method Conclusions Future work

23 Conclusions Combine two methods to solve problem Future work
Quadratic response surface is used to find optimal designs Importance sampling is used to find the yield rates under the optimal designs Results are consistent with exhaustive search and meet all requirements (e.g., CPU runtime) Future work Improve response surface model to find more accurate results Propose more general methods to find coefficients in formulas of importance sampling

24 Acknowledgement Thanks for discussions, suggestions and helps!
TA: Fang Gong, Yiyu Shi Prof. Lei He Thanks for your attention!

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