Giant thermopower and figure of merit of semiconducting polaronic nanolayers

Polarons—electrons coupled with lattice vibrations—play a key role in transport and optical properties of many semiconductors. Here, we calculate the energy spectrum and thermopower of Fröhlich polarons confined to a potential well as a function of the well thickness. We show that the polaron mass enhancement in $2+ϵ$ dimensions explains a giant thermoelectric power recently observed in doped semiconducting nanolayers (multiple quantum wells) and propose a route for enhancing the performance of thermoelectric energy nanoconverters by increasing their figure of merit by more than one order of magnitude.

Figure 1

(Color online) (a) Normalized polaron level shift $E_{pn}/\alpha \hslash \omega$ and (b) the relative polaron mass renormalization $\left(1-m/m_n^{\ast }\right)/\alpha$ for a number of subbands $n$ and different nanolayer thickness $t$ in the crossover region. A sudden increase in the shift and in the mass for sufficiently thick nanolayers $\left(t>2\right)$ and high-energy subbands is due to a breakdown of the perturbation expansion.

Figure 2

(Color online) (a) Polaron mass $m^{\ast }/m$ of the lowest subband and (b) Seebeck coefficient $S$ in the crossover region for a few coupling constants $\alpha$ and $\hslash \omega =0.05\text{meV}$, $T=300\text{K}$, $m=m_e$, and $n_p=1.66\times {10}^{20}{\text{cm}}^{-3}$ (solid lines) as the functions of the nanolayer thickness $d$ [inset in (a)]. Symbols correspond to the experimental mass measured optically in Ref. 14 and to the experimental Seebeck coefficient measured in Ref. 10.