Heat flow by phonons in Landauer - Datta - Lundstrom transport model for micro- and nanoelectronics

The Landauer - Datta - Lundstrom generalized transport model is applied to heat transfer by phonons. In both cases of electrons and phonons the Landauer approach generalized and extended by Datta and Lundstom gives correct quantitative description of transport processes for resistors of any dimension and size in ballistic, quasi-ballistic, and diffusive linear response regimes when there are differences in both voltage and temperature across the device. It is shown that the lattice thermal conductivity can be written in a form that is very similar to the electrical conductivity. Important differences between electrons and phonons are discussed.