Non-linear transport and transient properties of semiconductors under high electric field

Abstract

The current in a semiconductor under a high electric field is studied by solving the Liouville equation. The formal theory is developed using the Stark ladder representation, and the infinite series of a perturbation expansion for the weak electron-phonon coupling is evaluated. The effect of an electric field on the scattering matrix is studied in terms of the self-energy due to higher-order scatterings. It is shown that the real part of the self-energy, as well as the imaginary part, has a role in the transport properties. The results are applied to the velocity overshoot and the ballistic effect in a short semiconductor device. It is found that the velocity overshoot is realised by the inelastic nature of the scattering while the ballistic effect arises from the variation of the self-energy with time or the correlation effect.