Thermoelectric properties of a very-low-mobility two-dimensional electron gas.

Abstract

Experimental data on the thermoelectric coefficients of a very-low-mobility (\ensuremath{\mu}=0.13 ${\mathrm{m}}^{2}$/V s) two-dimensional electron gas in a GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum well are presented. The measurements span a temperature range of 1--200 K, and have been made in magnetic fields up to 8 T (at which point \ensuremath{\omega}\ensuremath{\tau}\ensuremath{\sim}1). As with high-mobility samples, phonon drag is found to be dominant at low temperatures, showing that the sample mobility is not relevant to this quantity. Data on the thermopower ${\mathit{S}}_{\mathit{x}\mathit{x}}$(B) and the Nernst-Ettingshausen coefficient ${\mathit{S}}_{\mathit{y}\mathit{x}}$(B) are compared with recent theoretical predictions. In the absence of magnetic field, B=0, the phonon mean free path (mfp) is initially determined from the measured thermal conductivity. Then the calculated value of ${\mathit{S}}_{\mathit{x}\mathit{x}}$(0) (thermopower in zero field) is in good agreement with measured values when T10 K but becomes up to an order of magnitude too small when T>20 K. To avoid this problem when B\ensuremath{\ne}0 the phonon mfp is redetermined from the measured values of ${\mathit{S}}_{\mathit{x}\mathit{x}}$(0) with the diffusion part subtracted. Then the calculated magnetothermopower \ensuremath{\Delta}${\mathit{S}}_{\mathit{x}\mathit{x}}$(B) is in good agreement with the data. The calculated drag contribution ${\mathit{S}}_{\mathit{y}\mathit{x}}^{\mathit{g}}$(B) to the Nernst-Ettingshausen coefficient ${\mathit{S}}_{\mathit{y}\mathit{x}}$(B), however, is only 5.4% of that measured. When the theoretical value of the contribution to ${\mathit{S}}_{\mathit{y}\mathit{x}}$(B) due to phonon drag is increased by a factor of (0.054${)}^{\mathrm{\ensuremath{-}}1}$=18.5 for all B and T, very good agreement with the data is again obtained over the whole regime investigated experimentally.