Abstract

We investigate the one-dimensional electron gas (1DEG) interaction with three-dimensional (3D) acoustic phonons in a quantum wire (QWR) by calculating the temperature $T$ and electron concentration ${n}_{l}$ dependence of phonon drag thermopower ${S}^{g}$ and energy loss rate $P$ in the Bloch-Gruneisen regime taking account of static screening. Electron scattering by acoustic phonons through piezoelectric field and deformation potential is considered. At very low temperature, ${S}^{g}$ and $P$ are dominated by the contribution due to piezoelectric scattering. The contribution due to deformation potential becomes significant at relatively higher temperature. The power laws for $T$ and ${n}_{l}$ dependences of ${S}^{g}$ and $P$ are obtained. The screening affects weakly the power of $T$ and significantly the power of ${n}_{l}$. The interesting feature is that ${S}^{g}$ is reduced by a factor of ${({\ensuremath{\nu}}_{s}∕{\ensuremath{\nu}}_{F})}^{2}$, where ${\ensuremath{\nu}}_{s}$ is the sound velocity and ${\ensuremath{\nu}}_{F}$ is the Fermi velocity, compared to that in two-dimensional electron gas (2DEG). A qualitative comparison is made between the calculated and experimentally observed energy loss rate in etched InGaAs QWRs. Herring's law ${S}^{g}{\ensuremath{\mu}}_{p}\ensuremath{\sim}{T}^{\ensuremath{-}1}$ (${\ensuremath{\mu}}_{p}$ is the phonon limited mobility) is validated in QWR. Our results are compared with those in 2DEG.

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