Circuit Analysis and Defect Characteristics Estimation Method Using Bimodal Defect-Centric Random Telegraph Noise Model

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Circuit Analysis and Defect Characteristics Estimation Method Using Bimodal Defect-Centric Random Telegraph Noise Model March 17, 2016 TAU 2017 Michitarou Yabuuchi (Renesas System Design Co., Ltd.

1 Circuit Analysis and Defect Characteristics Estimation Method Using Bimodal Defect-Centric Random Telegraph Noise Model March 17, 2016 TAU 2017 Michitarou Yabuuchi (Renesas System Design Co., Ltd.), Azusa Oshima, Takuya Komawaki, Ryo Kishida, Jun Furuta, Kazutoshi Kobayashi (Kyoto Inst. of Tech.), Pieter Weckx (KU Leuven, IMEC), Ben Kaczer (IMEC), Takashi Matsumoto (University of Tokyo), and Hidetoshi Onodera (Kyoto University) 1

2 σ σ Kyoto Inst. of Tech. Summary What is proposed? Defect parameter extraction method and RTN (random telegraph noise) prediction nm SiON Τ F F max Τ F F max Measurement result of frequency fluctuation distribution by RTN RTN Prediction by proposed method 2

3 Contents Introduction Measurement of RTN Parameter extraction method Result Conclusion 3

4 Variation on scaled process -65 nm process voltage temperature process voltage temperature RTN 40 nmscaling More significant in small area RTN affects the yields CMOS image sensor Flash, SRAM 4

5 V th Kyoto Inst. of Tech. RTN: Random Telegraph Noise Capture Emit t # of defect Gate area LW V th /defect + + Carier Si 5

6 Threshold voltage shift ΔV th by RTN Defect-centric distribution Avg. μ Vth = N η Std. dev. σ ΔVth = 2Nη 2 Τ 1 LW # of Defect N LW Poisson dist. ΔV th /defect η 1 LW Exponential dist. 6

7 RTN in high-k process ~65nm 40nm 28nm Unimodal model Bimodal model Each oxide layer has its parameters High-k layer (HK) :N HK, η HK Interface layer (IL) :N IL, η IL 7

8 CCDF N CCDF N Kyoto Inst. of Tech. Comparison : Unimodal vs Bimodal Unimodal model (N, η) Bimodal model (N HK, η HK, N IL, η IL ) ΔVth [ mv] ΔVth [ mv] SiO 2 or SiON thin HK/IL HKMG 8

9 Circuit-level RTN prediction N HK, η HK, N IL, η IL? Calculation by bimodal model of Defect-centric distribution Defect parameter Threshold voltage shift Circuit Netlist RTN w/ V th prediction Monte-Carlo circuit simulation 9

measurement data Proposed method N HK, η HK, N IL, η IL!

10 Purpose of this study Parameter extraction method for RTN characteristics of bimodal model of Defect-centric distribution RO measurement data Proposed method N HK, η HK, N IL, η IL! Defect parameter Threshold voltage shift Confirm w/ measured data Circuit Netlist RTN w/ V th prediction 10

11 Measurement circuit 40 nm HK/Poly-Si Process TEG x840 7-stage ring oscillator (RO) Count # of oscillation by using on-chip counter 11

12 Measurement method Conditions 9,024 times/ro V dd = 0.65 V Δt = 2.2 ms t total = 20 s Fmin Calculate ΔF F max = F max F min F max for each RO 12

13 Result of frequency fluctuation distribution by RTN Standard normal quantile Follow bimodal defect-centric distribution 840 ROs 8.61% Τ F F max 13

14 σ σ Kyoto Inst. of Tech. How to extract parameters Prior to the loop Sensitivity Analysis KS test (calculate object function) Optimize defect vector N HK3, η HK3, N IL3, η IL3 N HK2, η HK2, N IL2, η IL2 N HK1, η HK1, N IL1, η IL1 N HK0, η HK0, N IL0, η IL0 Measured data Τ F F max Prediction Τ F F max 14

15 Obtain threshold voltage shift Calculate ΔV th w/ defect characteristics By using defect-centric distribution N HK,i, η HK,i, N IL,i, η IL,i ΔV thp1 ΔV thp2 ΔV thp7 ΔV thn1 ΔV thn2 ΔV thn7 14 Tr. X 840 RO 15

16 Τ Kyoto Inst. of Tech. Convert ΔV th to frequency shift (1) Prior to the loop Analyze sensitivity ΔV th to FΤF max of MOSFET Simulation condition : same as measurement Shift ΔV th of single NMOS and PMOS k p F F max PMOS k n NMOS ΔV th [V] 16

17 Convert ΔV th to frequency shift (2) Calculate FΤF max with sensitivities k n, k p INV F INV,i ΤF max RO Τ F F max = F INV,i ΤF max = ΔV thp,i k p + ΔV thn,i k n X840 RO = prediction of FΤF max distribution 17

18 σ σ Kyoto Inst. of Tech. Calculation of object function Kolmogorov-Smirnov test for null hypothesis populations of two samples are the same. Sample #1:measured data Sample #2:prediction Τ F F max Τ F F max Object function p becomes larger when difference b/w two CDF plots becomes smaller. 18

19 Manipulation of defect vector Downhill simplex method Solution for optimization problem Maximize object function p p i N HK3, η HK3, N IL3, η IL3 N HK2, η HK2, N IL2, η IL2 N HK1, η HK1, N IL1, η IL1 N HK0, η HK0, N IL0, η IL0 p 0 p 1 p 2 Convergence condition p i > 0.99 or i MAX =

20 Standard Normal Quantile Kyoto Inst. of Tech. Prediction vs measurement data Prediction Measured Τ F F max 20

21 Conclusion RTN prediction method by using circuit simulation with bimodal defect-centric distribution Parameter extraction method for defect characteristics of bimodal model by measurement data Replicate circuit-level RTN effect by Monte- Carlo simulation 21

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