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

We present a mathematical 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 L ²‐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

Acknowledgments

The authors are grateful to Giovanni Borgioli and Chiara Manzini for many helpful discussions. This work was performed under the auspices of the National Group for Mathematical Physics of the Istituto Nazionale di Alta Matematica and was partly supported by the Italian Ministry of University (MIUR National Project “Mathematical Problems of Kinetic Theories,” COFIN2004).