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

TL;DR

This paper investigates the metal-insulator transition in strongly compensated SrTiO$_3$ crystals and films, revealing a percolation-based transition that occurs at higher doping levels than traditional Mott criteria suggest, especially in thin films.

Contribution

It develops a percolation MIT theory for strongly compensated SrTiO$_3$ films and explains the discrepancy between Mott criterion predictions and experimental data.

Findings

Conductivity fits well with Drude model above critical concentration

MIT occurs at higher doping levels than Mott criterion predicts

Critical doping concentration increases as film thickness decreases

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 \times10^{20} $ cm$^{-3}$, at low temperatures. We obtain good fit of the conductivity data, $\sigma(n)$, by the Drude formula for $n \geq 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, $na_B^3 \simeq 0.02$, 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 $d \leq 130$ 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.