Hot electron effects and dynamic behavior of gold doped germanium thin films as cryogenic phonon sensors

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Abstract
As a part of continuing development of thin film Ge 1−x Au x thermistors for ultralow mass highly sensitive cryogenicphonon sensors, the ac responsivity and hot electron effects have been explored. Responsivity as high as 1.6 nV/eV was achieved at 20 mK. A derivation is presented for the power index β=6 for electron-phonon heat exchange in variable range hoppingconductivity. Applying our previously developed optimization theory for bias-assisted tunneling,hot electron effects and bias-assisted tunneling were shown to account equally well for the nonlinear dc current–voltage characteristic. However, a model was developed for the thermal time constants of these devices which does predict a clear distinction between bias-assisted tunneling and the hot electron effects. Comparison of data with this model showed that bias-assisted tunneling rather than hot electron effects was the dominant finite-bias effect in the Ge 1−x Au x thin films.