Generalized drift-diffusion for microscopic thermoelectricity

Abstract

Although thermoelectric elements increasingly incorporate nano-scale features in similar material systems as other micro-electronic devices, the former are described in the language of irreversible thermodynamics while devices such as heterojunction bipolar transistors and semiconductor lasers are often described with the drift-diffusion equations. We present a microscopic description of the thermoelectric effects using a generalization of the common drift-diffusion formulation of semi-classical transport. We then replicate these basic results in a commerical device simulation package to explore Peltier cooling at a basic p-n junction. This framework should enable the design of spatially-inhomogenenous thermoelectric elements and internally-cooled micro-electronic devices.