Exploring the Global Solution Space of a Simple Schrödinger-Poisson Problem
摘要
Quantum electron transport in nanostructures can be described by a coupled Schrödinger-Poisson system. For the simulation of IV-characteristics we need to solve the stationary system self-consistently with the bias as a varying parameter. We use a full Newton method and monitor the number of negative eigenvalues in the Jacobian in order to detect path switching during bias-stepping. Selected simulation examples demonstrate numerically that the solution to the Schrödinger-Poisson model at a fixed bias is in general not unique and the global solution structure of the continuation problem is non-trivial.