Thermodynamic theory of transport processes in semiconductors

Important energetic processes in semiconductors are analyzed from the point of view of equilibrium and irreversible thermodynamics. After carefully defining the necessary local variables and current densities, the continuity equations for particles, energy, and entropy are derived, leading to an expression for entropy generation. From this, the conjugate fluxes and affinities are directly obtained and the transport equations written using these quantities. The Onsager relations are applied to the kinetic coefficients defined in the transport equations and, after further manipulations, the experimental transport parameters may be found in terms of these quantities. Particular care is taken to ensure that the thermal conductivity is correctly defined. A new thermoinjection coefficient is found which describes the transport of heat by electrons and holes under conditions of zero total electric current and zero temperature gradient. The heat dissipation is derived in a number of different ways and compared with formula proposed by other authors. Expressions for the generation of useful external work using both photovoltaic and thermoelectric conversion are also found and related to the difference between free energy input and entropy generation. The equations presented form a suitable basis for the improved design of energy conversion devices. In two Appendixes, the thermodynamic methods used in the main text are compared with those based on the Boltzmann transport equations for electrons, holes, and phonons. Theoretical expressions are derived in these Appendixes for the kinetic coefficients. Issues relating to the definition of internal energy and chemical potential are analyzed in a third Appendix.