A fast time-domain EM-TCAD coupled simulation framework via matrix exponential

Abstract

We present a fast time-domain multiphysics simulation framework that combines full-wave electromagnetism (EM) and carrier transport in semiconductor devices (TCAD). The proposed framework features a division of linear and nonlinear components in the EM-TCAD coupled system. The former is extracted and handled independently with high efficiency by a matrix exponential approach assisted with Krylov subspace method. The latter is treated by ordinary Newton's method yet with a much sparser Jacobian matrix that leads to substantial speedup in solving the linear system of equations. More convenient error management and adaptive control are also available through the linear and nonlinear decoupling.

A fast time‐domain EM–TCAD coupled simulation framework via matrix exponential with stiffness reduction

“…The division of linear and nonlinear components also facilitates error control and adaptive time stepping. • Slightly different from the judgment in [13], the benefit of MEXP, as demonstrated in the experiments, depends on the proportions of linear and nonlinear components in a more complex manner. The more linear components, the higher gain one can expect from solving a sparser matrix in the Newton's method, but at the cost of a (potentially) more expensive computation of the MEXP.…”

“…In this paper, we extend our previous work [13] by adding more technical details and insights. In particular, we prove the validity of regularizing the differential-algebraic equation (DAE) system to an ordinary differential equation (ODE) system via differentiating the Gauss's law in our EM-TCAD framework, which is a crucial step to enable the MEXP formula.…”

“…For more details of the equation formulation and solution scheme, we refer the readers to the conference publication [13].…”

“…The regularization technique reported in [13] relies on differentiating the Gauss's law with respect to the time variable that gives…”

“…To overcome the computational hurdle, we reported in a recent conference paper [13] a new solution technique based on the matrix exponential (MEXP) method. The idea is to decompose an EM-TCAD system into linear and nonlinear subsystems, corresponding roughly to the back-end and front-end structures in the problem of interest.…”