Reappraisal of Conduction and Hall Effect Due to Impurity Hubbard Bands in Weakly Compensated n‐GaAs

Abstract

A Hubbard-band model is used for analyzing the low-temperature data of Hall-effect measurements on weakly compensated n-GaAs samples with donor concentrations N D less than 10 16 cm À3 . In the model, not only the bottom Hubbard band formed from the neutral donor states but also the top Hubbard band formed from the negatively charged donor states is taken into account. Nearest-neighbor hopping (NNH) or Efros-Shklovskii (ES) variablerange hopping (VRH) is assumed for conduction in the bottom Hubbard band, depending on N D , while NNH is assumed for conduction in the top Hubbard band. For the sample with N D ¼ 1.3 Â 10 15 cm À3 , it is shown that the Hall mobility is dominated by NNH in the top Hubbard band in the temperature range of 4-15 K while it is dominated by NNH in the bottom Hubbard band below 3 K. For this sample, it is also shown that the absolute value of the Hall coefficient is dominated by the contribution from the top Hubbard band around its peak at 4.4 K. For the samples with N D in the range of 2.7-9 Â 10 15 cm À3 , on the other hand, it is shown that there hardly exists the temperature range in which the conduction in the top Hubbard band dominates.

Significant Effects of the D− Band on the Hall Coefficient and the Hall Mobility of n‐InP

“…In the previous studies of the author, the complicated behavior of the Hall coefficient R H ( T ) of elemental semiconductors of p‐Ge, n‐Ge, and n‐Si has been well described using a Hubbard‐band model. Furthermore, the existence of ε 2 conduction in n‐GaAs has been clarified in the previous study of the author …”

“…Analysis in the present study has been performed almost on the basis of the impurity‐Hubbard‐band model developed in the previous study of the author . In general, the temperature dependence of the conductivity of doped semiconductors can be expressed as…”

“…The tunneling processes of NNH and VRH can be treated as independent events when the system is in the insulator side of the metal–insulator (MI) transition in which the tunneling probabilities are small. As in the previous study, we assume Efros–Shklovskii (ES) VRH for the VRH conductivity.…”

“…According to Poklonski and Lopatin, the hopping conductivities are calculated as σ 2 = eN t μ 2 , σ 3 = eN b μ 3 , and σ VRH = eN b μ VRH , where and N b = are the effective concentrations of electrons hopping in the top and the bottom Hubbard bands, respectively. The concentrations of the positively, negatively, and neutally charged state of donors are, respectively, calculated as , , and using the charge‐state distribution functions f 1 , f −1 , and f 0 , which are defined in the previous study . In the calculation of the charge‐state distribution functions, we assume that the energy gap between the bottom and top Hubbard bands is calculated as U = E b − E t = 0.945 E b according to Poklonski et al, where E b and E t , respectively, denote the energy separations of the D 0 and D − states from the conduction‐band bottom, whereas U was connected to the activation energy E 2 of the hopping drift mobility in the D − band in the previous study …”

“…In case of NNH conduction, the Hall factor is shown to be expressed aswhere K H and I Hi are temperature‐independent constants. We assume that K H = 2/3 for both the top and bottom Hubbard bands in the present study as in the previous studies on n‐Ge and n‐GaAs …”