Thermoelectric properties of n-type $\mathrm{PbTe}/{\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ quantum wells

A systematic theoretical analysis of electronic states and thermoelectric transport in $\mathrm{PbTe}/{\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ quantum well structures is presented, employing more realistic well model than has been used up to now. The carrier scattering both on optical and acoustical phonons is considered. The kinetic equations are solved using the variational method and taking into account the intersubband transitions. The electrical conductivity, thermopower (Seebeck coefficient) and thermoelectric power factor as functions of the well width are studied for quantum well (QW) structures with (100) and (111) crystallographic orientations and different carrier densities. It is found that the power factor is greater in (100) QW’s, but the more realistic the well model is the lower the power factor. The dependencies of the power factor on the carrier density are determined and analyzed. It is shown that when the potential barrier height grows but the carrier density remains constant, the power factor is decreased. However the latter may be increased by increasing the permissible carrier density. So the expected values of the power factor for QW’s with $U=250\mathrm{}\hspace{0.5em}\mathrm{meV},$ $d=20\mathrm{}\hspace{0.5em}\mathrm{\AA }\mathrm{},$ and $n=5\mathrm{}\times {10}^{19}\hspace{0.5em}{\mathrm{cm}}^{-3}$ are $175\hspace{0.5em}\mu {\mathrm{W}\mathrm{}\mathrm{cm}}^{-1}{\mathrm{K}}^{-2}$ in the case of (100) orientation and $108\hspace{0.5em}\mu {\mathrm{}\mathrm{Wcm}}^{-1}{\mathrm{K}}^{-2}$ for the (111) one. The comparison with the results of recent experiments is also presented.