Ultimate photovoltage in perovskite oxide heterostructures with critical film thickness

One order larger photovoltage is obtained with critical thicknesses of La$_{0.9}$Sr$_{0.1}$MnO$_{3}$ films in both kinds of heterostructures of La$_{0.9}$Sr$_{0.1}$MnO$_{3}$/SrTiO$_{3}$ (0.8 wt {\%} Nb-doped) and La$_{0.9}$Sr$_{0.1}$MnO$_{3}$/Si fabricated at various oxygen pressures. Our self-consistent calculation reveals that the critical thickness of the La$_{0.9}$Sr$_{0.1}$MnO$_{3}$ film with the ultimate value of photovoltage is just the thickness of the depletion layer of La$_{0.9}$Sr$_{0.1}$MnO$_{3}$ in the $p-n$ heterostructures of La$_{0.9}$Sr$_{0.1}$MnO$_{3}$/SrTiO$_{3}$ (0.8 wt {\%} Nb-doped) and La$_{0.9}$Sr$_{0.1}$MnO$_{3}$/Si, respectively.