LOD-FDTD method for physical simulation of semiconductor devices

Abstract

Abstract-This paper describes a locally one-dimensional finitedifference time domain method for the two-dimensional timedependent simulation of semiconductor devices. This approach leads to significant reduction of the semiconductor simulation time. We can reach over 80% reduction in the simulation time by using this technique while maintaining the same degree of accuracy achieved using the conventional approach. As the first step in the performance investigation, we use the electrons flow equations in the absence of holes and recombination in this paper.

Global modeling of nonlinear circuits using the finite‐difference Laguerre time‐domain/alternative direction implicit finite‐difference time‐domain method with stability investigation

“…To remove the above CFL limit of time-step size, we presented here an implicit scheme. By applying the ADI principle [23,24], we have broken up the computation of (17) in the FDTD solution marching from the k th time-step to the (k + 1) th time-step into two computational sub-advancements: the advancement from the k th time-step to the (k + 1/2) th time-step and the advancement from the (k + 1/ 2) th time-step to the (k + 1) th time-step. For the first half-step, using the first-order upwind scheme for spatial derivatives,…”

“…The steady-state DC solution for electric fields, current densities, and the other transport parameters are obtained from the semiconductor model by solving Poisson's and hydrodynamic transport equations. The device is biased, and the DC parameter distributions (E, n, f, and J dc ) are obtained by solving (18)- (20), (24), (28), and (31) until reaching the steady state. This DC solution serves as the corresponding initial values inside the AD model.…”

“…To remove the above CFL limit of time‐step size, we presented here an implicit scheme. By applying the ADI principle , we have broken up the computation of (17) in the FDTD solution marching from the k th time‐step to the ( k + 1) th time‐step into two computational sub‐advancements: the advancement from the k th time‐step to the ( k + 1/2) th time‐step and the advancement from the ( k + 1/2) th time‐step to the ( k + 1) th time‐step. For the first half‐step, using the first‐order upwind scheme for spatial derivatives, and defining Yields the following equation: …”

Locally one-dimensional finite-difference time-domain scheme for the full-wave semiconductor device analysis

“…We propose to use the LOD-FDTD method, which eliminate the constraints of (9) as follows. By applying the LOD principle [13], the FDTD marching from the kth time-step to the (k + 1)th time-step is broken into two computational subadvancements: the advancement from the kth time-step to the (k + 1/2)th one and the advancement from the (k + 1/2)th time-step to the (k + 1)th one [14]. More specifically, two sub-steps are as follows.…”