Thickness-dependent conductivity of nanometric semiconductor thin films

TL;DR

This paper presents a quantum confinement-based theory explaining the exponential increase in resistivity of nanometric semiconductor thin films as their thickness decreases, aligning well with experimental observations.

Contribution

It introduces a new physical model for thickness-dependent conductivity in semiconductor thin films, surpassing classical surface scattering explanations.

Findings

Resistivity increases exponentially as film thickness decreases.

The model accurately reproduces experimental resistivity data for Si thin films.

Surface scattering alone cannot explain resistivity behavior below 10 nm.

Abstract

The miniaturization of electronic devices has led to the prominence, in technological applications, of semiconductor thin films that are only a few nanometers thick. In spite of intense research, the thickness-dependent resistivity or conductivity of semiconductor thin films is not understood at a fundamental physical level. We develop a theory based on quantum confinement which yields the dependence of the concentration of intrinsic carriers on the film thickness. The theory predicts that the resistivity $\rho$, in the 1-10 nm thickness range, increases exponentially as $\rho \sim \exp(const/L^{1/2})$ upon decreasing the film thickness $L$. This law is able to reproduce the remarkable increase in resistivity observed experimentally in Si thin films, whereas the effect of surface scattering (Fuchs-Sondheimer theory) alone cannot explain the data when the film thickness is lower than 10 nm.