A higher-order accurate operator splitting spectral method for the Wigner–Poisson system

Abstract

An accurate description of 2-D quantum transport in a double-gate metal oxide semiconductor field effect transistor (dgMOSFET) requires a high-resolution solver for a coupled system of the 4-D Wigner equation and 2-D Poisson equation. In this paper, we propose an operator-splitting spectral method to evolve such Wigner–Poisson (WP) system in 4-D phase space with high accuracy. After the operator splitting of the Wigner equation, the resulting two sub-equations can be solved analytically with spectral approximation in phase space. Meanwhile, we adopt a Chebyshev spectral method to solve the Poisson equation. Spectral convergence in phase space and a fourth-order accuracy in time are both numerically verified. Finally, we apply the proposed solver to the simulation of a dgMOSFET, develop the steady states via long-time simulations and obtain numerically converged current–voltage (I–V) curves.