# Electric Currents at Semiconductor Surfaces from the Perspective of Drift-Diffusion Equations

## TL;DR

This paper demonstrates that drift-diffusion equations can effectively model surface electric currents in semiconductors, clarifying the influence of key parameters and challenging the reliability of simplified conductivity models.

## Contribution

It introduces a comprehensive drift-diffusion framework for surface current analysis, highlighting the role of length parameters and the dominance of long-range modes.

## Key findings

- Long-ranged modes lead to two-dimensional currents.
- Surface behavior depends on few key parameters.
- Simplistic models are effective but may hinder accurate conductance reconstructions.

## Abstract

Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The current flow is calculated as a perturbation of an equilibrium solution depicting the space charge layer. We investigate the accumulation and inversion layers in great detail. Relying on numerical findings, we identify the proper length parameter, the relationship of which with the length of the space charge layer is not simple. If the length parameter is large enough, long-ranged modes dominate the Green's function of the current equation, leading to two-dimensional currents. In addition, we demonstrate that the surface behavior of the currents is ruled by only a few parameters. This explains the fact that simplistic conductivity models have proven effective but makes reconstructions of conductance profiles from surface currents rather questionable.