Metal-insulator transition in n -type bulk crystals and films of strongly compensated SrTiO3

We start by analyzing experimental data of Spinelli et al. [Phys. Rev. B 81, 155110 (2010)PRBMDO1098-012110.1103/PhysRevB.81.155110] for the conductivity of n-type bulk crystals of SrTiO3 (STO) with broad electron concentration n range of 4×1015-4×1020cm-3, at low temperatures. We obtain a good fit of the conductivity data, σ(n), by the Drude formula for n≥nc≃3×1016cm-3 assuming that used for doping insulating STO bulk crystals are strongly compensated and the total concentration of background charged impurities is N=1019cm-3. At n<nc, the conductivity collapses with decreasing n and the Drude theory fit fails. We argue that this is the metal-insulator transition (MIT) in spite of the very large Bohr radius of hydrogenlike donor state aB≃700 nm with which the Mott criterion of MIT for a weakly compensated semiconductor, naB3≃0.02, predicts 105 times smaller nc. We try to explain this discrepancy in the framework of the theory of the percolation MIT in a strongly compensated semiconductor with the same N=1019cm-3. In the second part of this paper, we develop the percolation MIT theory for films of strongly compensated semiconductors. We apply this theory to doped STO films with thickness d≤130 nm and calculate the critical MIT concentration nc(d). We find that, for doped STO films on insulating STO bulk crystals, nc(d) grows with decreasing d. Remarkably, STO films in a low dielectric constant environment have the same nc(d). This happens due to the Rytova-Keldysh modification of a charge impurity potential which allows a larger number of the film charged impurities to contribute to the random potential.