Dc and ac conduction in n-InP and n-InSb in magnetic fields at very low temperatures

Abstract

Measurements of the longitudinal and transverse direct current (d.c.) magnetoresistance of n-type InP samples (carrier density from and the alternating current (a.c.) conductivity of n-type InSb samples (carrier density from have been made at temperatures T down to 0.04 K and in magnetic fields H up to 70 kG. For H=0, the InP samples were nonmetallic. At low temperatures, the conductivity is due to nearest neighbour hopping (NNH) which is followed by variable range hopping (VRH) at lower T as described by the first, and second terms in the expression. In the NNH regime, it is necessary to plot In (p/T) against T1 and this yields values of the activation energy much larger than the traditional In p versus T-1 plots In the VRH regime, Mott's law (x = 1/4) is obeyed. Values of To obtained by considering the temperature dependence of the pre-exponential factor are found to be much higher than if the temperature dependence of this factor is ignored. Good agreement between the theory and experiment is achieved in both NNH and VRH regions if an enhanced dielectric constant is used.Magnetoresistance measurements in both the NNH and VRH regimes are analysed using the theories of Shklovskii and Efros (1984) and reasonable agreement is obtained. The anisotropy of the magnetoresistance in the NNH agrees closely with the expected H2 dependence. In the VRH, In(p(H)/p(0)) varies as T-3/4 and H2 as expected for hopping with a constant density of states at the Fermi level.The InSb samples are metallic-like in zero magnetic field. High magnetic fields are applied to shrink the donor wavefunctions (to induce the metal-insulator transition) and to locate the samples on the insulator side where the measurements are carried out. The d.c. resistivity was measured and at low temperatures was of a VRH type with 1/4 x 1/2, and T0 being magnetic field dependent. Reasonable agreement with the theory is found at high fields.The real and imaginary parts of the a.c. conductivity were measured in the frequency range of 110-105 Hz. The real part of conductivity was found to vary as where s is approaching 1 at low temperatures and high fields but decreasing as T increases. At the lowest temperatures was independent of T but at higher T the temperature dependence is stronger than the linear dependence predicted by the simple pair approximation theory. Data are interpreted in terms of multiple hopping of electrons which becomes important at high temperatures and/or low frequencies. The scaling formula; has been applied to discuss the results for the real part of the conductivity, where and are normalized values and f is a universal function obtained by Summerfield (1985). The scaling parameter -log10A is found to be 3.0 +/- 0.2.The relative dielectric constant, due to donors, calculated from the capacitive part was found to be a decreasing function as the frequency is increased and/or the temperature is lowered. At very low temperatures, depending on the magnetic field, however, a temperature-independent, but frequency-dependent behaviour is observed. The lowest temperature value of the dielectric constant was found to diverge as the magnetic field is reduced towards the metal-insulator threshold value.