Hopping conduction in n-type indium phosphide

Abstract

Abstract Measurements of the resistivity of three samples of n-InP with ND - NA =4·8, 5·9 and 7·8 × 1015cm−3 in magnetic fields up to 70 kG and for temperatures down to 60 mK are described. The theoretical resistivity in zero magnetic field is in good agreement with experiment for both nearest-neighbour and variable-range hopping, provided that an enhanced dielectric constant is used, which is required to reduce the theoretical hopping activation energy to the measured ε3. It is found that the temperature dependence of the pre-exponential factor is significant and that ε3 should be determined from In(p/T) against T −1 plots. This also applies to the determination of T 0 in the variable-range hopping region where a T −¼ dependence of resistivity is observed and for which the pre-exponential factor varies at T ½. The magnetoresistance in the weak-field limit for the nearest-neighbour-hopping region confirms previously reported measurements, and the anisotropy of the magnetoresistance agrees closely with the expected (H/4H c)2 dependence (H c = N ⅓ D ch/ae). In the weak-field variable-range-hopping region the magnetoresistance In [p (H)/p(O)] varies as T −¾ and H 2, as expected for hopping with a constant density of states at the Fermi level.