Origin and quantification of the ultimate carrier concentration limits in In2O3 and Sn-doped In2O3

The ultimate limits of the carrier concentrations in ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ and Sn-doped ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ are derived from operando photoelectron spectroscopy of a solid oxide electrochemical cell with Y-doped ${\mathrm{ZrO}}_{2}$ as the oxygen electrolyte. It is demonstrated that the limits are determined by the transition of the oxygen vacancy to the neutral state and to the reduction of ${\mathrm{Sn}}^{4+}$ donors to ${\mathrm{Sn}}^{2+}$ electron traps, respectively. Maximum Fermi energies of 3.85 and $3.35\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ above the valence band maximum are identified for ITO and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$. The ultimate carrier concentrations achievable by Sn doping and by oxygen vacancies are estimated to be $1.8--1.9\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ and $6--7\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$.