Magnetic field dependent impurity states in n-type InSb

Abstract

Hall effect measurements by Putley and other workers on n-type InSb in the temperature range 2-5 °K and in magnetic fields up to 15 kG have revealed a rapid increase in the Hall coefficient R with decreasing temperature, with an activation energy depending on magnetic field. In order to study more carefully the isolated donor levels as a function of magnetic field, the theory of the shielding of a charged centre by conduction electrons, in which the cylindrically symmetrical screening about the field direction is accounted for from the outset, is considered. We have then carried out variational calculations of the two lowest impurity levels, as a function of magnetic field. While the individual levels are appreciably changed by screening, the energy gap is very insensitive to the detailed choice of electron density over a wide range of densities and has its hydrogenic value to high accuracy. The magnitude of the observed activation energy accords well with this energy gap over a substantial range of magnetic fields. The model on which the Hall effect measurements are to be understood is then seen to be one in which the impurity states higher than the ground state are broadened by overlap and merge into a quasi-continuum with the InSb conduction band. The residual concentration dependence of the activation energy, as well as its magnetic field dependence, suggests that the measured activation energy will eventually reflect energy gaps between the ground and higher excited states of the donors as initially broadened impurity levels cease to conduct in higher fields.