Energy Conversion And Coupled Transport Processes

Abstract

Abstract The collision of carriers may cause both energy and momentum transfer among them. Energy conversion processes must involve energy exchange between at least two different carriers. For example, Joule heating is due to the relaxation of energy from electrons to phonons, and thermal radiation from a solid results from the conversion of the energy of phonons or electrons in the solid into photons. The exchange of energy among electrons, phonons, and photons can in principle be determined by evaluating the collision integral in the Boltzmann equation. Discussions in the previous two chapters are based on the relaxation time approximation, which is strictly valid only for elastic scattering processes that do not involve energy exchange among carriers. The relaxation time approximation, however, is often used even for inelastic collision without rigorous justification. Traditionally, the constitutive equations obtained from the relaxation time approximation are used in combination with the energy conservation law to describe energy exchange processes. For example, in heat conduction processes involving Joule heating, one combines the Fourier law with the first law of thermodynamics to derive the heat conduction equation that determines the temperature distribution. Joule heating is included in the conservation law without consideration of how electrons deliver their energy to the lattice systems. This approach is adequate in most macro scale processes and in systems in which electrons and phonons are close to equilibrium and heat generation occurs over a region much larger than the carrier mean free path, but can fail when these conditions are not satisfied.