Metal-Insulator Transition in $n$-type bulk crystals and films of strongly compensated SrTiO${}_3$

Abstract

We start by analyzing experimental data of Spinelli [A. Spinelli, M. A. Torija, C. Liu, C. Jan, and C. Leighton, Phys. Rev. B 81, 155110 (2010)] for conductivity of $n$-type bulk crystals of SrTiO${}_3$ (STO) with broad electron concentration $n$ range of $4\times 10^{15}$ - $4\times 10^{20}$ cm${}^{-3}$, at low temperatures. We obtain good fit of the conductivity data, $\sigma (n)$, by the Drude formula for $n\ge n_c\simeq 3\times 10^{16}$ cm${}^{-3}$ assuming that used for doping insulating STO bulk crystals are strongly compensated and the total concentration of background charged impurities is $N=10^{19}$ cm${}^{-3}$. At $n<n_c$, 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 hydrogen-like donor state $a_B\simeq 700$ nm with which the Mott criterion of MIT for a weakly compensated semiconductor, $n{a}_B^3\simeq 0.02$, predicts $10^5$ times smaller $n_c$. We try to explain this discrepancy in the framework of the theory of the percolation MIT in a strongly compensated semiconductor with the same $N=10^{19}$ cm${}^{-3}$. 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 $d\le 130$ nm and calculate the critical MIT concentration $n_c(d)$. We find that, for doped STO films on insulating STO bulk crystals, $n_c(d)$ grows with decreasing $d$. Remarkably, STO films in a low dielectric constant environment have the same $n_c(d)$. 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.

7 pages, 2+1 figures. Published version with added Appendix on Metal-insulator transition in STO wires

References in corpus (4)

• Enhancement of Carrier Mobility in Semiconductor Nanostructures by Dielectric Engineering
• Intrinsic Mobility Limiting Mechanisms in Lanthanum-doped Strontium Titanate
• Atomically flat interface between a single-terminated LaAlO3 substrate and SrTiO3 thin film is insulating
• Disorder effects in topological insulator thin films

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