Hot-electron model in doped silicon thermistors

Non-ohmic behavior of doped silicon and germanium can be empirically explained using a hot-electron model, which is motivated by the hot-electron effect in metals at low temperatures. This model assumes that the thermal coupling between electrons and lattice at low temperatures is weaker than the coupling between electrons, so that the electric power applied to the electrons raises them to a higher temperature than the lattice. Although this model seems not suitable for semiconductors in the variable range-hopping regime, where the electrons are localized, it fits quite well the experimental data. To determine whether the hot-electron model in doped semiconductor is just an alternative way to parameterize the data or has some physical validity, we investigated the noise and the frequency-dependence of the impedance of doped silicon thermistors that arc used for low temperature thermal X-ray detectors. The measured excess white noise at low frequencies is consistent with the predicted thermodynamic fluctuations of energy between electron and phonon systems. The non-ohmic behavior shows a characteristic time that can be interpreted as a C/G time constant in the hot-electron model. By measuring this time constant, we get a hot-electron heat capacity C that agrees with the measured excess heat capacity of the implants. These support the assumption of a hot-electron system thermally separated from the lattice system.