Appearance of effective surface conductivity - an experimental and analytic study

TL;DR

This study investigates how surface conductivity in p-type doped germanium varies with distance, revealing a surface-bulk transition and providing an analytical formula to quantify effective surface conductivity at different scales.

Contribution

It introduces an analytical integral formula for effective surface conductivity as a function of distance, supported by experimental measurements and classical current flow analysis.

Findings

Surface conductivity varies systematically with distance from the source.

At small distances, measured surface conductivity differs from the bulk value.

At large distances, surface conductivity approaches the bulk conductivity.

Abstract

Surface conductance measurements on p-type doped germanium show a small but systematic change to the surface conductivity at different length scales. This effect is independent of the structure of the surface states. We interpret this phenomenon as a manifestation of conductivity changes beneath the surface. This hypothesis is confirmed by an analysis of the classical current flow equation. We derive an integral formula for calculating of the effective surface conductivity as a function of the distance from a point source. Furthermore we derive asymptotic values of the surface conductivity at small and large distances. The actual surface conductivity can only be sampled close to the current source. At large distances, the conductivity measured on the surface corresponds to the bulk value.