Thermoelectric Transport Coefficients of Cubic Crystals via K-Space Integration

Abstract

In cubic crystals the electrical and thermal conductivities and the absolute thermoelectric power can all be expressed in terms of the integral

$${K_O}\left( \varepsilon \right) = \frac{1}{{12{\pi ^3}{\hbar ^2}}}\sum\limits_q \smallint {\nabla _k}\varepsilon {\rm T}\left({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k} ,\varepsilon } \right)d{S_q}\left( \varepsilon \right)$$

(1)

and its first energy derivative at the Fermi surface.¹ Here q is the index of the constant-energy surface sheet and T(k̲,ε) is a generalized relaxation time function of the wavevector k̲ and the energy ε. The integrand of Eq. (1) is analytic everywhere; therefore it should be possible to calculate K_O (ε) with an empirical value of T or a function T(k,ε) derived from a model.