Levelized incomplete LU method and its application to semiconductor device simulation

In circuit simulation, the CPU time is spent in two parts: one is to transfer the circuit equation into the corresponding linear equation Ax = B, the other is to solve this matrix equation. In order to improve the simulation speed and apply our method to mixed-level device and circuit simulation, we propose to simplify the creation of the matrix equation by equivalent subcircuit, and speed up the simulation by levelized incomplete LU factorization. The levelized incomplete LU is used to solve Ax = B because it offers, the good convergence of the direct method and the high speed, small memory space of the iteration method. The Ax = B is obtained by transferring the Poisson equation and continuity equation into their equivalent circuits to simplify the mixed-level simulation. Finally, we will apply the above methods to the simulation of PN diodes and verify their performance on the simulation and design of semiconductor devices.