Overview

A formal theory for the flow of charge and heat will be developed in this chapter. Applications of the theory will also be explored, experimental techniques discussed, and results surveyed. Our goal is to extend Ohm s law, J= ? , to include temperature gradients and to develop an analogous expression for the heat current, J _Q. The final result has the form

(4.1a)

(4.1b)

We might have expected to associate applied electric fields with electric currents and temperature gradients with heat currents, but electrons transport both charge and heat, so the two flows are coupled. Our goal is to derive eqs (4.1) from the BTE and to relate the coefficients, L _ij, to the semiconductor s material properties.

The theoretical treatment is based on a number of simplifying assumptions. First, conduction by electrons is assumed (but a corresponding set of equations for holes could be readily developed). We also assume that the applied fields are low, so that the currents are proportional to the driving forces (the electric field and the temperature gradient). Finally, we assume the relaxation time approximation and spherical, parabolic energy bands which makes it easy to solve the BTE.

When the band structure is complex or when the RTA doesn't apply, the BTE is difficult to solve, but the form of the resulting current equations is unchanged. We can view the coupled current equations, (4.1a) and (4.1b), as phenomenological relations describing low-field transport in any semiconductor, but the coefficients, L _ij ,