A quantum kinetic approach for modeling a two-band resonant tunneling diode

ABSTRACT. We present amathematical study of a two-band quantum kinetic transport model. The multiband model, derived in the envelope function theory, is designed to describe the dynamics in semiconductor devices when the interband conduction-valence transition cannot be neglected. The Wigner formulation consists of a four-by-four system, containing two effective mass Wigner equations (one for the electron in conduction band and one for the valence band) coupled by pseudo-differential operators arising from the electric field in the semiconductor. The existence and uniqueness of a solution to the initial value problem are proved in a L2-setting for sufficiently regular electric potentials. An extension of the single band splitting-scheme algorithm is presented to solve the one-dimensional system for a bounded domain. Finally, we show some numerical results concerning the simulation of an interband resonant diode. Keywords: Multiband transport, Wigner formulation, Interband resonant diode