Size effects in fluctuation spectra of many-valley semiconductors

Abstract

We present the results of theoretical investigation of inhomogeneous fluctuations in submicrometer active layers of many-valley semiconductors with equivalent valleys (Ge, Si type), where the layer dimension, $2d$, is comparable to or less than the intervalley diffusion relaxation length, ${L}_{\mathrm{iv}}.$ The study is based on the Boltzmann-Langevin kinetic equation. Boundary conditions for the fluctuations on the layer surfaces are derived. It is shown that for arbitrary orientations of the valley axes (crystal axes) with respect to the surfaces, the fluctuation spectra depend on the applied small electric field. Some physical phenomena are reported: unlike bulk samples, intravalley fluctuation processes cause the intervalley fluctuations in thin layers; the spectra of fluctuations depend on the layer thickness; with $2d\ensuremath{\lesssim}{L}_{\mathrm{iv}},$ a considerable suppression of the fluctuations arises for the fluctuation frequency $\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\tau}}_{\mathrm{iv}}^{\ensuremath{-}1}$, where ${\ensuremath{\tau}}_{\mathrm{iv}}$ is the characteristic intervalley relaxation time.