We start by analyzing experimental data of Spinelli et al. [Phys. Rev. B 81, 155110 (2010)] for the conductivity of $n$-type bulk crystals of ${\mathrm{SrTiO}}_3$ (STO) with broad electron concentration $n$ range of $4\times {10}^{15}$–$4\times {10}^{20}{\mathrm{cm}}^{-3}$, at low temperatures. We obtain a good fit of the conductivity data, $\sigma \left(n\right)$, by the Drude formula for $n\ge n_c\simeq 3\times {10}^{16}{\mathrm{cm}}^{-3}$ assuming that used for doping insulating STO bulk crystals are strongly compensated and the total concentration of background charged impurities is $N={10}^{19}{\mathrm{cm}}^{-3}$. 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 hydrogenlike 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 $N={10}^{19}{\mathrm{cm}}^{-3}$. 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 $n_c\left(d\right)$. We find that, for doped STO films on insulating STO bulk crystals, $n_c\left(d\right)$ grows with decreasing $d$. Remarkably, STO films in a low dielectric constant environment have the same $n_c\left(d\right)$. 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.

中文翻译：

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金属-绝缘体过渡Inn型块状晶体和强补偿SrTiO3薄膜

我们从分析Spinelli等人的实验数据开始。[物理 版本B 81，155110（2010）]对的导电性$ñ$型块状晶体 ${\mathrm{钛酸锶}}_3$ （STO）具有宽电子浓度 $ñ$ 范围 $4\times {10}^{15}$–$4\times {10}^{20}{\mathrm{厘米}}^{-3}$，在低温下。我们获得了良好的电导率数据拟合，$\sigma （ñ）$，由Drude公式得出 $ñ\ge {ñ}_C\simeq 3\times {10}^{16}{\mathrm{厘米}}^{-3}$ 假设用于掺杂绝缘STO块状晶体的元素得到了强烈补偿，且本底带电杂质的总浓度为 $ñ={10}^{19}{\mathrm{厘米}}^{-3}$。在$ñ<{ñ}_C$，电导率随着降低而崩溃 $ñ$而Drude理论的拟合失败了。我们认为，尽管氢原子供体态的玻尔半径非常大，但这仍是金属-绝缘体转变（MIT）${\mathrm{一种}}_{乙}\simeq 700$ nm，用于微补偿半导体的MIT的Mott准则， $ñ{\mathrm{一种}}_{乙}^3\simeq 0.02$，预测 ${10}^5$ 倍小 ${ñ}_C$。我们试图在渗流MIT理论的框架内解释这种差异，该渗流MIT具有相同的强补偿半导体。$ñ={10}^{19}{\mathrm{厘米}}^{-3}$。在本文的第二部分，我们针对强补偿半导体薄膜开发了渗滤MIT理论。我们将此理论应用于厚度为STO的掺杂STO薄膜$d\le 130$ nm并计算MIT的临界浓度 ${ñ}_C（d）$。我们发现，对于绝缘STO块状晶体上的掺杂STO膜，${ñ}_C（d）$ 随着减少而增长 $d$。值得注意的是，在低介电常数环境中的STO膜具有相同的${ñ}_C（d）$。这是由于电荷杂质电势的Rytova-Keldysh修饰而发生的，它允许大量薄膜电荷带电杂质贡献于随机电势。