Residual resistance of 2D and 3D structures and Joule heat release

Abstract

We consider a residual resistance and Joule heat release in 2D nanostructures as well as inordinary 3D conductors. We assume that elastic scattering of conduction electrons bylattice defects is predominant. Within a rather intricate situation in such systems wediscuss in detail two cases. (1) The elastic scattering alone (i.e. without regardof inelastic mechanisms of scattering) leads to a transition of the mechanicalenergy (stored by the electrons under the action of an electric field) into heatin a traditional way. This process can be described by the Boltzmann equationwhere it is possible to do the configuration averaging over defect positions in theelectron–impurity collision term. The corresponding conditions are usually met inmetals. (2) The elastic scattering can be considered with the help of the standardelectron–impurity collision integral only in combination with some additionalaveraging procedure (possibly including inelastic scattering or some mechanisms ofelectron wavefunction phase destruction). This situation is typical for degeneratesemiconductors with a high concentration of dopants and conduction electrons.Quite often, heat release can be observed via transfer of heat to the lattice, i.e. via inelasticprocesses of electron–phonon collisions and can take place at distances much larger thanthe size of the device. However, a direct heating of the electron system can be registeredtoo by, for instance, local measurements of the current noise or direct measurement of anelectron distribution function.