Statistical Compact Model Extraction: A Neural Network Approach

Abstract

A technique for extracting statistical compact model parameters using artificial neural networks (ANNs) is proposed. ANNs can model a much higher degree of nonlinearity compared to existing quadratic polynomial models and, hence, can even be used in sub-100-nm technologies to model leakage current that exponentially depends on process parameters. Existing techniques cannot be extended to handle such exponential functions. Additionally, ANNs can handle multiple input multiple output relations very effectively. The concept applied to CMOS devices improves the efficiency and accuracy of model extraction. Results from the ANN match the ones obtained from SPICE simulators within 1%.Index Terms-Backward propagation of variance (BPV), compact model, extraction, neural, statistical. I. IntroductionAs semiconductor devices scale to 20 nm and below, process variations become more significant. Circuit designers need to use statistical or Monte Carlo (MC) models to assess the impact of process variation on circuit performance. The MC model specifies statistical distributions for model parameters (such as mobility and oxide thickness) that reproduce the measured or predicted distributions of performance parameters. The classic approach to determine the model parameter distribution is a time-consuming trial and error process of picking distributions and running MC until the resulting performance parameter distributions match the measured or specified result.The extraction is sped up by building an analytic model relating performance to model parameters, and in turn analytically relating the standard deviation of performance to that of model parameters. The measured target standard deviations are then back propagated to the model parameter variations through an optimization formulation. This is known as back propagation of variance (BPV). The methodology in [1] and [2] implements BPV efficiently but it only handles nonlinear relationships that can be adequately approximated using linear and quadratic terms. Principal component analysis (PCA) techniques similar to [3], although formulated to handle correlated process parameters, provide only linear relationships. These techniques work well if the degree of nonlinearity is not too high. This includes MOSFET parameters, such as Idlin, Idsat,

Statistical compact model extraction for skew‐normal distributions

“…Unfortunately, quadratic models fail to handle extreme non‐linearity like leakage currents. ANN can instead capture arbitrary non‐linearity very accurately and was adopted in [6]. Hence, we believe that the ANN is a very apt choice for the empirical model for the SCME problem in general.…”

“…2, are tunable parameters of ANN which are determined during the training phase as described in Algorithm 1 (see Fig. 3), similar to what is followed in [6]. Summary of Algorithm 1 (Fig.…”

“…Note that, like with any ANN application, the number of training and testing samples, number of hidden units and the testing error bound are heuristics and is application specific. We have found this specification to work very well across technologies [6].…”

“…Also the problem of SCME involves modelling multiple performance parameters simultaneously, some linear and others non‐linear. ANNs are adept at modelling multiple‐input–multiple‐output (MIMO) functions [6] with a combination of linear and non‐linear outputs and hence makes it an ideal choice for this problem.…”

Machine learning model for predicting threshold voltage by taper angle variation and word line position in 3D NAND flash memory

“…Machine learning (ML) is a good alternative to solving these problems. ML models are created through neural network algorithms (NNA) that analyze the relationship between inputs and outputs [10,11,12,13,14]. Its modeling process is less time consuming and shows high accuracy [15,16].…”