Distortion of charge distribution due to internal electric fields described by the drift-diffusion semiconductor model

TL;DR

This paper analyzes the Debye--Hueckel drift-diffusion equation to describe how internal electric fields distort charge distribution and symmetry, providing explicit functions for electric field effects and nonlinear density shifts.

Contribution

It offers a detailed mathematical characterization of electric field influence on charge density, including symmetry distortion and nonlinear shifts, extending previous models.

Findings

Explicit functions for electric field and charge density effects

Demonstrates symmetry distortion and scale shifts due to electric fields

Captures stronger nonlinearity than previous logarithmic shift models

Abstract

In this paper, the initial value problem for the Debye--Hueckel drift-diffusion equation is studied. This equation was introduced as a model describing plasma behavior and is also known as a simulation model of MOSFET, and so its solution describes charge density. It is well-known that, if the initial density is localized, then the density is adjusted to be radially symmetric due to the linear diffusion. Consequently, the electric field is also governed by a radially symmetric potential, and its effects are expected to act radially symmetrically. The main result express the electric field and its effect on the charge density as concrete functions. It also denotes the distortion of symmetry and the shift of scale on the density due to the internal electric field. Unlike the historical paper via Escobedo and Zuazua and the followers, the main result captures stronger nonlinearity than the logarithmic shift.