Effect of the Pekar mechanism on the phonon-drag thermopower inp-typeSi∕Si1−xGexheterostructures

Abstract

We examine the effect of the Pekar mechanism on the coupling of two-dimensional (2D) holes with 3D acoustic phonons in $p$-type $\mathrm{Si}∕{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ heterostructures by using the phonon-drag thermopower, ${S}^{g}$, as a probe. The origin of the Pekar coupling is due to the variation of the dielectric permittivity under strain in nanostructures characterized by strong confining electric fields. The hole-phonon interaction via the Pekar mechanism resembles that of piezoelectric coupling in polar materials and dominates over the deformation potential coupling at low temperatures. It is found that ${S}^{g}$ shows a ${T}^{4}$ temperature dependence at low $T$ (Bloch-Gruneisen regime) which is in good agreement with the experimental data reported recently by Possanzini et al. [Phys. Rev. B 69, 195306 (2004)]. We perform detailed calculations of ${S}^{g}$ by considering both a screened Pekar coupling and a screened deformation potential coupling in $p$-type $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ structures in the temperature range $0.25lTl6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The value of the deformation potential constant is taken to be $4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, in good agreement with previous studies. The strength of the Pekar coupling is determined by the magnitude of the surface electric field ${E}_{s}$. We treat ${E}_{s}$ as an adjustable parameter in our calculations and we find good agreement with all the experimental data of ${S}^{g}$, available at the moment, by using a value for ${E}_{s}$ of the order of ${10}^{9}\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{m}$. The possibility for the existence of such a large surface field in $\mathrm{Si}∕\mathrm{Si}\mathrm{Ge}$ is discussed.