Mixed conductivity and potential fluctuations in semi-insulating GaAs:Cr.

Abstract

Extensive investigations have been made on the electrical properties of semi-insulating (si) GaAs. However, most of the measurements were performed under dc conditions, and only very few data on the ac and high-frequency conductivity are available. Moreover data related to the thermopower of this material are practically nonexistent. On the other hand, almost all the theories assume implicitly that the semi-insulating crystal is microscopically homogeneous, i.e., free from potential fluctuations. In the case of chromium-doped si-GaAs showing a bipolar conduction, serious inconsistencies concerning galvanomagnetic data are observed. The most striking of them is the discrepancy between the theoretical and experimental values of the intrinsic carrier density ${n}_{i}$, and the disagreement between the signs of Hall and thermoprobe voltages. In this paper, we proceed to a new examination of the mixed conduction process, and derive complete expressions of the transport coefficients by taking into account the existence of long-range potential fluctuations, which play an essential role in semi-insulating (si) materials.It is shown that dc galvanomagnetic measurements are inadequate for the evaluation of the total carrier densities n,p in the conduction and in the valence bands. These densities can be determined only by measuring the high-frequency conductivity limit ${\ensuremath{\sigma}}_{\ensuremath{\infty}}$ and the thermoelectric power S versus temperature. Depending on the relative magnitudes of n and p and of the mobilities ${\ensuremath{\mu}}_{n}$,${\ensuremath{\mu}}_{p}$, the sign of S can be either positive or negative, while ${R}_{H}$ is nearly always negative. Original experimental data on the temperature dependence of dc and high-frequency conductivities ${\ensuremath{\sigma}}_{\mathrm{dc}}$ and ${\ensuremath{\sigma}}_{\ensuremath{\infty}}$, and of S, between 300 and 450 K are reported for six Cr-doped si-GaAs samples. These samples are n and p type and have mixed conductivity. The results are discussed on the basis of our model, which allows us to reach a complete and coherent understanding of the observed phenomena.In these samples, mixed conduction is due to the accumulation of packets of electrons in potential wells separated in space from packets of holes accumulated in potential hills. Therefore, models assuming a microscopically constant potential in the sample cannot realistically describe the physical state of the sample. On the contrary, by taking into account the existence of long-range potential fluctuations, all the discrepancies reported in the literature can be removed. Finally, the effect of annealing of an ``n-type'' sample is analyzed.