Origin and quantification of the ultimate carrier concentration limits in ${\mathrm{In}}_2{O}_3$ and Sn-doped ${\mathrm{In}}_2{O}_3$

The ultimate limits of the carrier concentrations in ${\mathrm{In}}_2{O}_3$ and Sn-doped ${\mathrm{In}}_2{O}_3$ 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 $3.35\mathrm{eV}$ above the valence band maximum are identified for ITO and ${\mathrm{In}}_2{O}_3$. The ultimate carrier concentrations achievable by Sn doping and by oxygen vacancies are estimated to be $1.8–1.9\times {10}^{21}{\mathrm{cm}}^{-3}$ and $6–7\times {10}^{20}{\mathrm{cm}}^{-3}$.