Electron-phonon scattering in carrier transport of the ternary chalcopyrites AgIn X 2 ( X = S , Se , Te )

Ternary chalcopyrites $(X = \mathrm{S},\mathrm{Se},\mathrm{Te})$ have attracted much attention due to their potential application in thermoelectrics and photovoltaics. Due to different fabricating techniques, experiment results on the carrier transport vary widely and the underlying mechanism of carrier scattering is still unclear. Based on the Boltzmann transport equation, we investigated the carrier transport properties of the ternary chalcopyrites by first-principles calculation plus Hubbard $U$. The calculation results of band gaps and the dielectric constants are close to the experiment results. It is found that the chalcopyrites have large electron mobilities, i.e., ${\ensuremath{\mu}}_e$ (300 K) of 266.7, 475.8, and $1319.7 {\mathrm{cm}}²/\mathrm{Vs}$ for ${\mathrm{AgInS}}₂, {\mathrm{AgInSe}}₂$, and ${\mathrm{AgInTe}}₂$ respectively. In contrast, the hole mobility ${\ensuremath{\mu}}_h$(300 K) takes 18.2, 51.8, and $77.8 {\mathrm{cm}}²/\mathrm{Vs}$ for three chalcopyrites, respectively. Calculation on the mode-resolved scattering rates reveals that the predominant carrier scattering is attributed to the ${B}₂⁽³⁾$ mode, which relates to the longitudinal off-center motion of In relative to the tetrahedron ${\mathrm{InX}}₄$. The mobility decays as $\ensuremath{\mu}\ensuremath{\propto}{T}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ takes $0.89\ensuremath{\sim}1.03$ for ${\ensuremath{\mu}}_e$ and $1.13\ensuremath{\sim}1.88$ for ${\ensuremath{\mu}}_h$. The impurity scattering effect has also been studied by considering two kinds of substitutional defects, ${\mathrm{In}}_{\mathrm{Ag}}$ and ${\mathrm{Ag}}_{\mathrm{In}}$, which lead the chalcopyrites to be $n$ or $p$ type, accordingly. The impurities ${\mathrm{In}}_{\mathrm{Ag}}$ can suppress the electron mobilities to half values when the density reaches ${10}¹⁷\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ while the impurities ${\mathrm{Ag}}_{\mathrm{In}}$ only moderately decreases the hole mobilities. The distinct suppression of carrier mobilities owes to the difference of the Born effective charges for two kinds of impurities. Our calculation reveals that the predominant carrier scattering of ${B}₂⁽³⁾$ can be attributed to its largest magnitude of electron-phonon matrix elements compared to other phonon modes.