Energy transport in highly disordered conductors

Measurements of the electron-phonon resistance in a dirty conductor are made at temperatures below 1K. These experiments consist of heating the electrons out of equilibrium with their surroundings by a small amount and measuring the resulting temperature rise using the resistance of the sample as a thermometer. These measurements are made possible by the use of an ac heating technique, where the response of the sample at three times the excitation frequency is used to determine the thermal resistance out of the electron gas. The samples are formed by ion implantation of arsenic into silicon to form thin layers of very heavily doped semiconductors. The doses used to fabricate the samples studied range from 2.5x1014 cm-2 to 1016 cm-2. Partial compensation by an additional implant of boron is employed to further disorder one of the samples. The samples are characterized by Rutherford backscattering, sheet resistance, and Hall measurements. Magnetoconductance measurements are also made, in order to determine the phase-breaking rates in these samples. The thermal time constant extracted from the heating measurement displays a similar temperature dependence in all the samples, τ ∼ T-3.4. No sign of cross-over behavior is observed. This is a stronger temperature dependence than is predicted for the clean limit of the electron-phonon interaction, as one would expect, since the thermal phonon wavelength in silicon is much larger than the elastic mean free path in all the samples. However, in the dirty limit, theory predicts that τe-p∼T-4. In addition, the magnitude of the thermal time constant measured in this work is orders of magnitude smaller than is predicted by theory. This is presumably due to effects of disorder, small kfl, which are not taken into account by present theories of the electron-phonon interaction