掺杂半导体中的安德森局域化
Anderson localization in doped semiconductors
AI总结：
本文基于安德森局域化和 Ioffe-Regel-Mott 判据，通过建立并求解载流子屏蔽带电掺杂剂无序的积分方程，给出了掺杂半导体金属-绝缘体转变的临界密度。
摘要：
我们从理论上考虑了体半导体中掺杂诱导的绝缘体到金属转变问题，通过获得作为补偿函数的转变密度，假设该转变是由 Ioffe-Regel-Mott（IRM）判据控制的安德森局域化转变。我们计算了高掺杂金属侧的平均自由程，该平均自由程来源于载流子被电离掺杂剂散射，我们将电离掺杂剂建模为淬灭的随机带电杂质。带电掺杂剂的库仑无序被载流子自身屏蔽，从而得到一个局域化积分方程，该方程由依赖于密度的平均自由程等于费米波数的倒数所定义，正如 IRM 判据所规定的那样。通过近似解析地和精确数值地求解该积分方程，我们为掺杂诱导的金属-绝缘体转变提供了局域化临界密度的详细结果。
英文摘要：
We theoretically consider the problem of doping induced insulator to metal transition in bulk semiconductors by obtaining the transition density as a function of compensation, assuming that the transition is an Anderson localization transition controlled by the Ioffe-Regel-Mott (IRM) criterion. We calculate the mean free path, on the highly doped metallic side, arising from carrier scattering by the ionized dopants, which we model as quenched random charged impurities. The Coulomb disorder of the charged dopants is screened by the carriers themselves, leading to an integral equation for localization, defined by the density-dependent mean free path being equal to the inverse of the Fermi wave number, as dictated by the IRM criterion. Solving this integral equation approximately analytically and exactly numerically, we provide detailed results for the localization critical density for the doping induced metal-insulator transition.
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