Phonon-Cyclotron Broadening of Stokes Scattering from Polar Semiconductors

Abstract

This is an investigation of the effects of electron-phonon coupling in polar semiconductors on the double-cyclotron Stokes scattering. The actual calculation is preceded by a representation of some general aspects of radiation scattering from the point of view of nonlinear susceptibilities. At the lowest temperatures and weak carrier concentrations, it is shown that for the Stokes line shift $\omega -{\omega }^{\prime }<(\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{c}-\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}{\omega }_0)$, a narrow line is expected, displaced below the double-cyclotron frequency $2{\omega }_c$ by a frequency shift or order $\alpha {\omega }_0$, where $\alpha$ is the Fröhlich polaron coupling constant. In the immediate vicinity of $\omega -{\omega }_0={\omega }_0$, a large discontinuous broadening is expected, which, with further field increase, falls off approximately as ${(2\mathrm{}{\omega }_c-{\omega }_0)}^{-\frac{1}{2}}$. The center of this line is displaced above $2{\omega }_c$ by an amount of order $\alpha {\omega }_0$.