Generalization of Thermal Conductivity and Lorenz Number to Hot-Carrier Conditions in Nondegenerate Semiconductors

We present a generalization to high-field transport of the carrier thermal conductivity and Lorenz number in nondegenerate semiconductors. The theory is based on the correlation-function formalism. In its range of validity, it provides exact values and predicts an anisotropic behavior of the above parameters with respect to the direction of the applied field. Calculations for the case of n-Si at 300 K evidence a dramatic decrease, more than 2 orders of magnitude, of the longitudinal values at the highest fields of $100\mathrm{kV}/\mathrm{cm}$.