Hopping and correlated hopping studies of p-Ge at large uniaxial stresses and high magnetic fields

Abstract

The resistivity of p-Ge with different acceptor concentrations N _A has been measured at helium temperatures, at high stresses, and longitudinal and high magnetic fields. The ranges were: 15 K > T > 4.2 K, 10¹⁵ cm⁻³ < N _A < 4 × 10¹⁶ cm⁻³, H < 8 T, tensile stresses up to 6 × 10⁷ Pa and compressive stress up to 6 × 10⁸ Pa. All the data are in the regime of hopping transport. The data is conveniently presented in terms of the activation energy ε₃, and the pre-exponential ρ₃. The main experimental features are as follows. The activation energy plotted against uniaxial stress X exhibits a peak for both compressive and tensile stress (although tensile stress was not large enough to observe the peak clearly). Around the stress where this peak occurs, the pre-exponential ρ₃ begins to increase rather rapidly. Magnetic fields reduce the peak for compressive stress, and enhance the peak for tensile stress. At very high compressive stresses ρ₃ decreases with stress. For high concentrations, ε₃ also decreases with increasing stress at high stresses, but for low concentrations ε₃ is rather flat there.

We have developed a percolation theory for hopping transport through acceptor states which consist of an oblate and a prolate wavefunction, with an arbitrary energy splitting between these functions. Making this energy splitting depend on stress, and the size of the wavefunctions on magnetic field, we were able to reproduce most of the important experimental features, at least qualitatively. Some experimental features were not reproduced by the results of the percolation theory. These are mainly concentration-dependent features. Such features are in qualitative agreement with predictions for transport by correlated multi-electron hopping.

The important conclusions of our experiments are (1) we have a correct understanding of many features of the acceptor wavefunctions, (2) percolation theory provides a good description of one electron hopping transport, and (3) multi-electron hopping processes make an important contribution to hopping transport in p-Ge for concentrations above 3 × 10¹⁵ cm⁻³.