Algorithms for Solving Electronic Continuity Equation in Numerical Simulation of Semiconductor Devices

For solving the discretized electronic continuity equation, two aspects of work are carried out. Firstly, the matrix of the discretized linear system is analyzed, and three types of characteristics of the matrix are obtained. Secondly, based on the characteristics of the matrix, the discretized electronic continuity equation is solved by preconditioned Krylov subspace methods, and the effectiveness of several types of preconditioned methods is compared and analyzed. The results show that the algebraic multigrid (AMG) preconditioned Krylov subspace method is very effective for solving discretized electronic continuity equations. A large-scale parallel scalability test of the AMG preconditioned Krylov subspace method for solving discretized electronic continuity equations is carried out, and the selection of three key algorithm parameters in the AMG method is compared and analyzed.