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 [Karl-Michael E, Walter LE. IEEE Trans Comp Aided Des Integ Circ and Sys 1995;14:720.]. 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 [Leblebici Y, Unlu MS, Morkoc H, Kang SM. IEEE Int Symp Circ and Sys 1992;2:895; 1995;13:396.] 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.