Hopping conduction in n-type indium antimonide below 1 k

Abstract

Measurements of the longitudinal and transverse resistivity of n-type indium antimonide in magnetic fields up to 40 kG and for temperatures down to 30 mK are described. The resistivity is given by the relation p1 exp (E ₁/kT) + p ₃ exp (E ₃/kT) + p ₀ exp (T ₀/T) ^x where for T > 1 K the first term, arising from the freeze-out of the electrons, is important; for 1 K T < 0·3 K the second term, associated with activated hopping, dominates; and for T < 0·3 variable-range hopping, given by the third term, is important. Expressions for x and T ₀ in the variable-range-hopping region have been derived assuming the density of states at the Fermi energy (a) is a constant and (b) varies with energy as C _ϵ ^2. Donor wavefunctions given either by Yafet, Keyes and Adams (1956) or by Hasegawa and Howard (1961) are considered in both cases. The best fit to the results is obtained with a constant density of states and Yafet, Keyes and Adams wavefunctions. The measured values of T ₀ are, however, much lower than the theoretical values and the magnetic field dependences of p ₀ and T ₀ differ appreciably from theory. It was also found that, in the activated hopping region, the activation energy E ₃ is below the theoretical value. It is suggested that both the activated and variable-range hopping are strongly affected by correlation effects but that, as the magnetic field increases, these effects are reduced and agreement between theory and experiment for p ₀ and T ₀ is approached. The measured ratio of transverse to longitudinal resistivity in the variable-range-hopping region is larger than expected theoretically and this is attributed to an anisotropy of the correlation effects.

It should be pointed out, however, that the experimental results could alternatively be described by the simple relation p ₁ exp (E ₁/kT) + p ₀ exp (T ₀/T)^1/2 in which the first term describes the freeze-out of the electrons down to 1 K and the second term agrees with experiment from 1 K to 30 mK. This term might arise from a quantitative theory of correlated hopping.