Mechanism of the enhanced thermoelectric power in (111)-oriented n-type ${\mathrm{P}\mathrm{b}\mathrm{T}\mathrm{e}/\mathrm{P}\mathrm{b}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ multiple quantum wells

A theoretical investigation of the recently observed enhanced thermoelectric power S in (111)-oriented n-type $\mathrm{PbTe}/{\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ multiple-quantum-wells $(x\simeq 0.09)$ has been carried out, including both longitudinal acoustic phonon deformation potential scattering and polar optical phonon scattering of the two-dimensionally confined electrons in the quantum wells. An enhancement in S is observed experimentally and predicted theoretically, despite the lifting of the conduction band valley degeneracy, and an excellent agreement between the experimental and theoretical results has been obtained over a wide temperature range $(80\mathrm{}–400\hspace{0.5em}\mathrm{K}).\mathrm{}$ In the low temperature regime $\left(\sim 100\hspace{0.5em}\mathrm{K}\right),$ the polar optical phonons are found to be more effective in scattering carriers in the oblique L-point valleys than in scattering carriers in the longitudinal L-point valley, making the resulting S somewhat suppressed in this temperature regime. In the high temperature regime $(>~300\hspace{0.5em}\mathrm{K}),$ the polar optical phonon scattering generally contributes to increasing S due to the particular shape of the distribution function associated with it. It is emphasized that our theoretical model requires virtually no fitting parameters. The excellent agreement between the theoretical and experimental results suggests the validity of our model of enhanced thermoelectric figure of merit in two-dimensional structures and the reliability of the values of the parameters for the superlattice deduced from other independent measurements, such as Hall carrier concentrations and band energy gaps.