Irreversible Thermodynamics and Carrier Density Fluctuations in Semiconductors

The formalism of irreversible thermodynamics is applied to the kinetics of carrier transitions in semiconductors. The thermodynamic forces, the generalized resistances and admittance functions are introduced. It is shown that the thermodynamic forces which establish the regression of a perturbed state to equilibrium are the differences of the quasi-Fermi levels that have to be assigned to each group of carriers; the generalized resistances are simply related to the transition rates. It is then possible to write the kinetic equations for the rate of change of the various carrier concentrations in a unified form so that the dissipation-fluctuation theorem of Callen and Greene can be applied. The spectral density matrix of the spontaneous carrier fluctuations is immediately found from the admittance matrix. The results can be expressed in a closed form which is valid for nondegenerate as well as for degenerate semiconductors. An electrical network analog is also outlined. The theory is applied explicitly to electronic noise in extrinsic and near-intrinsic crystals with and without recombination centers. Finally, the close connection with statistical results obtained before is discussed and the complete agreement between the Einstein relation and the extended "$g-r$ theorem" for the variances is established.