NUMERICAL STUDY OF TRANSIENT WIGNER-POISSON MODEL FOR RTDs: NUMERICAL METHOD AND ITS APPLICATIONS*

作者：Jiang, Haiyan^*; Lu, Tiao; Yao, Wenqi; Zhang, Weitong

来源：SIAM Journal of Scientific Computing, 2023, 45(4): A1766-A1788.

DOI：10.1137/22M1502872

• sinc-Galerkin method
• semi-implicit time integration
• RTD simulation
• Wigner-Poisson equation

The system of transient Wigner-Poisson equations (TWPEs) is a common model to describe carrier transport in quantum devices. In this paper, we design a second-order semi implicit time integration scheme for TWPEs with the inflow boundary conditions, and a hybrid sinc-Galerkin/finite-difference method [H. Jiang, T. Lu, and W. Zhang, J. Comput. Appl. Math. , 409 (2022), 114152] is applied for the spatial discretization. The fully-discretized system is rigorously proved to be unconditionally L2-stable, and the computational cost is comparable with that of the second-order explicit Runge--Kutta scheme (ERK2). The numerical method is applied to study a double-barrier resonant tunneling diode (RTD), where representative characteristics of RTDs, including the resonant tunneling effect, bistability and the intrinsic high-frequency current oscillation, are simulated successfully.

• 单位
  北京理工大学; 北京大学