Model-Based Theoretical Prediction of the Electric Field Dependence of the Diffusion Coefficients of Various Semiconductor Wires

Abstract

This paper investigates how the diffusion coefficients of various semiconductor wires - namely Si, Ge, and 4H-SiC - are modulated by an external electric field assuming steady-state transport. This theoretical investigation consists of two steps. In the first step, we derive a model-based theoretical expression of the diffusion coefficient based on the continuity equation. Since this consideration is too simplified, in the second step, we perform Monte Carlo simulations to investigate how the electric field alters the electron occupation fraction of energy band valleys; for this, quantum mechanical scattering events during transport are calculated. Using these calculations, the electric field dependence of the diffusion coefficients of Ge and 4H-SiC wires with various cross-sectional areas is investigated because the conduction process of such materials is strongly ruled by the multi-valley transport of electrons. The obtained results reveal that the diffusion coefficient of Ge wires is constant when the electric field rises at 200 K and 400 K; but it rebounds under very high electric fields above 400 K due to the increase in the intrinsic carrier concentration. On the other hand, it is shown that the diffusion coefficient of 4H-SiC wires increases as the electric field rises in a low electric field range regardless of temperature, but it drops under high electric fields. Thus, it is considered that the theoretical models assumed for various semiconductor wires are useful in estimating the steady-state transport characteristics of scaled devices in a practical range of temperatures around room temperature.