Theory of thermoelectric effects when the temperature approximation is incorrect

TL;DR

This paper develops a new theory for thermoelectric effects in submicron semiconductors that accounts for non-Maxwellian electron distributions when traditional temperature approximations are invalid.

Contribution

It introduces a theoretical framework that models thermoelectric phenomena without relying on electron temperature or chemical potential, considering rapid surface energy relaxation.

Findings

The theory applies to conditions where surface relaxation dominates electron-electron collisions.

It demonstrates the inadequacy of Maxwellian assumptions in certain thermoelectric regimes.

Provides a non-Maxwellian distribution model for accurate thermoelectric analysis.

Abstract

The flow of a thermoelectric current through a semiconductor of submicron dimensions is analyzed. The rate of surface relaxation of the energy is assumed to be much higher than the rate of electron-electron collisions. Under these conditions, it is incorrect to describe the electron gas by means of a Maxwellian distribution and thus to describe the thermoelectric effects in terms of an electron temperature and a chemical potential. A theory is derived for these effects. This theory does not include the latter parameters and is based on a non-Maxwellian distribution which is spatially nonuniform in terms of energy.