Numerical Investigation on the Convergence of Self-Consistent Schrödinger-Poisson Equations in Semiconductor Device Transport Simulation.

Semiconductor devices at the nanoscale with low-dimensional materials as channels exhibit quantum transport characteristics, thereby their electrical simulation relies on the self-consistent solution of the Schrödinger-Poisson equations. While the non-equilibrium Green's function (NEGF) method is widely used for solving this quantum many-body problem, its high computational cost and convergence challenges with the Poisson equation significantly limit its applicability. In this study, we investigate the stability of the NEGF method coupled with various forms of the Poisson equation, encompassing linear, analytical nonlinear, and numerical nonlinear forms Our focus lies on simulating carbon nanotube field-effect transistors (CNTFETs) under two distinct doping scenarios: electrostatic doping and ion implantation doping. The numerical experiments reveal that nonlinear formulas outperform linear counterpart. The numerical one demonstrates superior stability, particularly evident under high bias and ion implantation doping conditions. Additionally, we investigate different approaches for presolving potential, leveraging solutions from the Laplace equation and a piecewise guessing method tailored to each doping mode. These methods effectively reduce the number of iterations required for convergence.