Theory of thermoelectric power factor in quantum well and quantum wire superlattices

Calculations are presented for thermoelectric transport in quantum well and quantum wire superlattices, using (i), the full superlattice electronic band structure in (ii) a multisubband inelastic Boltzmann equation for carrier-phonon scattering. The transport direction is taken to be in the quantum well planes and along quantum wires. It is demonstrated that these two features are needed to give a quantitative treatment of the power factor P in superlattice systems. Results are given for PbTe and for GaAs quantum well and quantum wire superlattices, including the dependence of P on growth direction and on potential offset. For both quantum well and quantum wire superlattices, the dependence of P on potential offset $V_0$ is found to be qualitatively weaker than in previous work based on the constant relaxation time approximation for carrier scattering. These weaker dependences on $V_0$ are traced mainly to the enhancement of the electron-phonon scattering rates upon confinement. These results give a different picture of the effects of confinement on P suggesting, for example, that increased confinement in superlattices does not lead to significantly higher P and that free-standing structures, such as free-standing quantum wires, may be particularly attractive for thermoelectric applications.