An Adaptively Segmented Forward Problem Based Non-Blind Deconvolution Technique for Analyzing SRAM Margin Variation Effects

Abstract

Abstract-This paper proposes an abnormal Vshaped-error-free non-blind deconvolution technique featuring an adaptively segmented forward-problem based iterative deconvolution (ASDCN) process. Unlike the algebraic based inverse operations, this eliminates any operations of differential and division by zero to successfully circumvent the issue on the abnormal V-shaped error. This effectiveness has been demonstrated for the first time with applying to a real analysis for the effects of the Random Telegraph Noise (RTN) and/or Random Dopant Fluctuation (RDF) on the overall SRAM margin variations. It has been shown that the proposed ASDCN technique can reduce its relative errors of RTN deconvolution by 10 13 to 10 15 fold, which are good enough for avoiding the abnormal ringing errors in the RTN deconvolution process. This enables to suppress the cdf error of the convolution of the RTN with the RDF (i.e., fail-bit-count error) to 1/10 10 error for the conventional algorithm.

Comparative study on deconvolution function dependencies of RTN/RDF effect estimation errors in analyzing sub-nm-scaled SRAM margins

“…Figure 3c shows the remaining issue of low-frequency ringing error (noise amplification) confronting the "deconvlucy" deconvolution process. This is due to the maximum likelihood iterations with gradient method [7][8][9][10][11]. As a result, the deconvoluted RTN distribution is significantly deviated from the expected curve (see Fig.…”

“…Figure 5b shows the RTN2 deconvolution result. Thanks to the proposed fitting function fmin-search forward problem based deconvolution (FminDCV) algorithm [10][11], the behavior of the RTN2 deconvolution process becomes smoothed and no ringing errors across the full range of x are exhibited at all unlike the MATLAB " built-in deconvolutionfunctions. However, the ordinary optimization problem attempts to prioritize more probability density populated zone around x=0 because those pdf dominate the overall cumulative density function (cdf).…”

“…"deconvlucy" (see Fig. 2d) uses Richardson-Lucy (R-L) algorithm [7][8][9][10][11] that is one of the most widely used deconvolution algorithms in the area of image processing although it has some shortcomings such as noise amplification [7][8][9][10][11]. This algorithm is based on maximizing the likelihood of the resulting g(x), as shown in Fig.…”

Errors in solving inverse problem for reversing RTN effects on VCCmin shift in SRAM reliability screening test designs

“…4(a)) is using long polynomial division to solve inverse problem. However, it has been reported that this induces the V-shaped ringing errors due to "division by zero" [8][9][10][11]. "deconvreg" and "deconvwnr" are using the regularized filter algorithm and Wiener filter algorithm, respectively (see Figs.…”

“…"deconvlucy" (see Fig. 4(e)) uses Richardson-Lucy (R-L) algorithm [7][8][9][10][11][12] that is one of the most widely used deconvolution algorithms in the area of image processing although it has some shortcomings such as noise amplification [7][8][9][10][11][12]. This algorithm is based on maximizing the likelihood of the resulting g(x), as shown in Fig.…”