Thickness-dependent conductivity of nanometric semiconductor thin films

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 $\rho \sim \exp (const\mathrm{/}{L}^{1\mathrm{/}2})$ 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.