Stationary equations for charge carriers in semiconductors including electron-hole scattering

Abstract

Under high-injection conditions, carrier transport through the semiconductor device is strongly affected by carrier-carrier interaction such as electron-hole scattering. An extended drift-diffusion model with drag current terms is presented, which can be motivated by the analysis of the Boltzmann equations incorporating electron-hole collision operators. In this paper an existence and uniqueness result for Hölder continuous weak solutions of the quasilinear system of—a priori degenerate—elliptic equations is proved. Numerical simulations of a forward biased pn-junction diode show that the electron-hole scattering lead to a diminution of the total current compared to the current without electron-hole collision terms. Finally, a formula for the total current depending on the applied voltage and the scattering parameter is derived from asymptotic analysis.

Keywords:

• Drift-diffusion model
• system of degenerate elliptic equations
• existence
• uniqueness
• semiconductors
• voltage-current charecteristics
• drift-diffusion model
• system of degenerate elliptic equations
• existence
• uniqueness
• semiconductors
• voltage-current characteristics