Electrical transport, electrothermal transport, and effective electron mass in single-crystalline In 2 O 3 films

A comprehensive study of the room-temperature electrical and electrothermal transport of single-crystalline indium oxide (In${}_{2}$O${}_{3}$) and indium tin oxide (ITO) films over a wide range of electron concentrations is reported. We measured the room-temperature Hall mobility ${\ensuremath{\mu}}_{H}$ and Seebeck coefficient $S$ of unintentionally doped and Sn-doped high-quality, plasma-assisted molecular-beam-epitaxy-grown In${}_{2}$O${}_{3}$ for volume Hall electron concentrations ${n}_{H}$ from $7\ifmmode\times\else\texttimes\fi{}{10}^{16}$ cm${}^{\ensuremath{-}3}$ (unintentionally doped) to $1\ifmmode\times\else\texttimes\fi{}{10}^{21}$ cm${}^{\ensuremath{-}3}$ (highly Sn-doped, ITO). The resulting empirical $S({n}_{H})$ relation can be directly used in other In${}_{2}$O${}_{3}$ samples to estimate the volume electron concentration from simple Seebeck coefficient measurements. The mobility and Seebeck coefficient were modeled by a numerical solution of the Boltzmann transport equation. Ionized impurity scattering and polar optical phonon scattering were found to be the dominant scattering mechanisms. Acoustic phonon scattering was found to be negligible. Fitting the temperature-dependent mobility above room temperature of an In${}_{2}$O${}_{3}$ film with high mobility allowed us to find the effective Debye temperature (${\ensuremath{\Theta}}_{D}=700$ K) and number of phonon modes (${N}_{\mathrm{OPML}}=1.33$) that best describe the polar optical phonon scattering. The modeling also yielded the Hall scattering factor ${r}_{H}$ as a function of electron concentration, which is not negligible (${r}_{H}\ensuremath{\approx}1.4$) at nondegenerate electron concentrations. Fitting the Hall-scattering-factor corrected concentration-dependent Seebeck coefficient $S(n)$ for nondegenerate samples to the numerical solution of the Boltzmann transport equation and to widely used, simplified equations allowed us to extract an effective electron mass of ${m}^{*}=(0.30\ifmmode\pm\else\textpm\fi{}0.03){m}_{e}$ (with free electron mass ${m}_{e}$). The modeled mobility and Seebeck coefficient based on polar optical phonon and ionized impurity scattering describes the experimental results very accurately up to electron concentrations of ${10}^{19}$ cm${}^{\ensuremath{-}3}$, and qualitatively explains a mobility plateau or local maximum around ${10}^{20}$ cm${}^{\ensuremath{-}3}$. Ionized impurity scattering with doubly charged donors best describes the mobility in our unintentionally doped films, consistent with oxygen vacancies as unintentional shallow donors, whereas singly charged donors best describe our Sn-doped films. Our modeling yields a (phonon-limited) maximum theoretical drift mobility and Hall mobility of $\ensuremath{\mu}=190$ cm${}^{2}$/Vs and ${\ensuremath{\mu}}_{H}=270$ cm${}^{2}$/V$\phantom{\rule{0.16em}{0ex}}$s, respectively. Simplified equations for the Seebeck coefficient describe the measured values in the nondegenerate regime using a Seebeck scattering parameter of $r=\ensuremath{-}0.55$ (which is consistent with the determined Debye temperature), and provide an estimate of the Seebeck coefficient to lower electron concentrations. The simplified equations fail to describe the Seebeck coefficient around the Mott transition (${n}_{\mathrm{Mott}}=5.5\ifmmode\times\else\texttimes\fi{}{10}^{18}$ cm${}^{\ensuremath{-}3}$) from nondegenerate to degenerate electron concentrations, whereas the numerical modeling accurately describes this region.