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

TL;DR

This paper introduces a high-accuracy spectral operator splitting method for solving the 4-D Wigner-Poisson system, enabling precise quantum transport simulations in semiconductor devices.

Contribution

It develops a novel spectral operator splitting approach with spectral convergence and fourth-order time accuracy for the Wigner-Poisson system.

Findings

Achieved spectral convergence in phase space.

Validated fourth-order temporal accuracy.

Successfully simulated I-V characteristics of dgMOSFETs.

Abstract

An accurate description of 2-D quantum transport in a double-gate metal oxide semiconductor filed effect transistor (dgMOSFET) requires a high-resolution solver to 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 system in 4-D phase space with high accuracy. After an 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 into simulating dgMOSFET, develop the steady states from long-time simulations and obtain numerically converged current-voltage (I-V) curves.