Electron-phonon scattering and Joule heating in copper at extreme cold temperatures

A quantum mechanical model has been used to calculate the full electron-phonon scattering rates in pure copper at extreme cold temperatures. The proposed model uses Fermi's Golden rule, specific to each scattering mechanism and wave vector state, providing more accuracy and more details than the widely used empirical third power rule for scattering rates. The empirical third power rule is actually only valid in the low-temperature limit. The results are in good agreement with existing experimental data and theoretical calculations with the assumption that the wave vector of a phonon is much larger than the wave vector of an electron (q ≫ k) and three-dimensional density of states converted to one-dimensional density of states to reduce calculation burden by orders of magnitude. The energy generated by Joule heating is calculated using the proposed model and compared with the experimental data from the literatures. Although the results presented are specific to copper, the method is directly applicable to other metals. In addition, the proposed model can be used to study the thermal properties of copper wires in high temperature superconductor power cable applications.