Learning to Solve Nonlinear Partial Differential Equation Systems To Accelerate MOSFET Simulation

Seungcheol Han, Jonghyun Choi, Sung-Min Hong

Keywords: Partial differential equation, nonlinear equation, Newton-Raphson method, convolutional neural network

Abstract: Semiconductor device simulation uses numerical analysis, where a set of coupled nonlinear partial differential equations is solved with the iterative Newton-Raphson method. Since an appropriate initial guess to start the Newton-Raphson method is not available, a solution of practical importance with desired boundary conditions cannot be trivially achieved. Instead, several solutions with intermediate boundary conditions should be calculated to address the nonlinearity and introducing intermediate boundary conditions significantly increases the computation time. In order to accelerate the semiconductor device simulation, we propose to use a neural network to learn an approximate solution for desired boundary conditions. With an initial solution sufficiently close to the final one by a trained neural network, computational cost to calculate several unnecessary solutions is significantly reduced. Specifically, a convolutional neural network for MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor), the most widely used semiconductor device, are trained in a supervised manner to compute the initial solution. Particularly, we propose to consider device grids with varying size and spacing and derive a compact expression of the solution based upon the electrostatic potential. We empirically show that the proposed method accelerates the simulation by more than 12 times. Results from the local linear regression and a fully-connected network are compared and extension to a complex two-dimensional domain is sketched.

One-sentence Summary: Learning a convolutional neural network to approximately solve nonlinear PDE systems to accelerate MOSFET simulation by more than 12x times.

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