An improved transient algorithm for the simulation of a resonant tunneling diode

Naoufel Ben Abdallah (1) , A Faraj (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Shanghai Jiao Tong University [Shanghai]

A fast algorithm is proposed for the simulation of the transient evolution of a resonant tunneling diode by a multiscale approach. The problem is modeled by the time-dependent Schrödinger-Poisson system. By decomposing the wave function into a non resonant part and a resonant part, the fast algorithm is designed by combining standard finite difference method for the Schrödinger-Poisson equation with proper time-dependent and/or nonlinear transmission boundary condition. In addition, with a suitable interpolation of the non resonant one, an accurate and fast algorithm is presented for the computation of the resonant part via the projection method. With this two scale decomposition, the new numerical method can save the computational time significantly.

Mots clés: Nonlinear Schrödinger equation; numerical scheme; resonant tunneling diode; resonant states; time-dependent

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Naoufel Ben Abdallah, A Faraj. An improved transient algorithm for the simulation of a resonant tunneling diode. 2016. ⟨hal-00479989v4⟩