Hot electron temperature in InAs measured by tunneling

By preparing tunnel junctions with a superconducting film on the oxide layer on an InAs surface, we have observed directly the heating of the electron gas in the InAs when it is subjected to electric fields up to 300 mV/cm. We show that tunneling is a sensitive way of measuring the electron temperature up to values comparable to the energy gap of the superconductor (∼ 20 K) and, when compared to methods used previously, is particularly useful for small increases in electron temperature (< 10 K). Analysis of the data is carried out by making the assumption that the hot electron gas can be represented by a Fermi distribution at a temperature $T_e$ above the InAs lattice temperature. The consistency of the results supports the validity of this assumption, which has been made commonly in the past but not often investigated in detail experimentally. We find that $T_e$ measured by tunneling at a given electric field is higher than that determined from the Shubnikov-de Haas effect and mobility versus field and temperature measurements. To explain this discrepancy, we suggest that tunneling is sensitive to the surface electrons in InAs, namely, those in the accumulation layer. We speculate that these surface electrons are not in equilibrium with those in the bulk and can be considered as a separate system at a higher temperature than the bulk electrons at each field.