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

Experimental data on the thermoelectric coefficients of a very-low-mobility (μ=0.13 ${\mathrm{m}}^2$/V s) two-dimensional electron gas in a GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Al}}_{\mathit{x}}$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 ωτ∼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 T20 K. To avoid this problem when B≠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 Δ${\mathit{S}}_{\mathit{x}\mathit{x}}$(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${)}^{\mathrm{-}1}$=18.5 for all B and T, very good agreement with the data is again obtained over the whole regime investigated experimentally.