Theory of thermoelectric cooling in semiconductor structures

Abstract

A new approach is suggested to explain the Peltier effect. This approach is based on the idea of the occurrence of induced thermal diffusion fluxes in any non-uniform medium through which a d.c. electric current flows, in particular in a structure composed of two different uniform semiconductors. These induced thermal diffusion fluxes arise to compensate for the change in thermal fluxes carried out by an electric current (drift thermal fluxes) during their driving through the junction in accordance with the general Le Châtelier-Braun principle. The occurrence of these thermal diffusion fluxes leads to temperature non-uniformity in the structure and, as a result, to the junction's cooling or heating. The general heat balance equations are obtained. It is shown that only two sources of heat exist: the Joule source of heat, and the Thomson source of heat. They have commensurable magnitudes in the problem considered. There is no Peltier's source of heating or cooling present. The new equation for the Thomson heat is obtained and its physical interpretation is made. New boundary conditions for the heat balance equation are derived. The analysis of these boundary conditions shows that the Peltier sources of heat are also absent at the junctions. It is shown that, in the general case, the thermoelectric cooling represents the superposition of two effects, the isothermal Peltier effect and the adiabatic Peltier effect. Both essentially depend on the junction surface thermal conductivity. The isothermal Peltier effect disappears in the limiting case of a very small surface thermal conductivity while the adiabatic Peltier effect disappears in the limiting case of a very large surface thermal conductivity. The dependence of thermoelectric cooling on the geometrical dimensions of the structure is discussed. It is shown that the thermoelectric cooling (heating) is a thermodynamically reversible process in the linear approximation of the electric current applied.