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arXiv 2212.00643cond-mat.dis-nncond-mat.mtrl-sci
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无序介质中的量子态。II。空间载流子分布

Quantum states in disordered media. II. Spatial charge carrier distribution

A. V. Nenashev, S. D. Baranovskii, K. Meerholz, F. Gebhard

摘要:

空间和温度相关的电子分布$n(\mathbf r,T)$是无序半导体光电性质理论描述的基础。我们提出了两个强大的技术来访问$n(\mathbf r,T)$没有解决薛定谔方程。首先,我们通过将哈密顿量递归地应用于随机波函数(RWF),导出了非简并电子的密度。其次,我们通过对作用于无序介质中载流子的随机势应用通用低通滤波器(ULF),得到了一个与温度有关的有效势。由此,整个量子力学问题被简化为有效势场中$n(\mathbf r,T)$的准经典描述。我们通过与精确的量子力学解的比较,数值验证了这两种方法。这两种方法被证明优于广泛使用的本地化景观理论(LLT)时,我们比较我们的近似结果的载流子密度和迁移率在升高的温度下得到的RWF,ULF,和LLT与那些从精确解的薛定谔方程。

英文摘要:

The space- and temperature-dependent electron distribution $n(\mathbf r,T)$ is essential for the theoretical description of the opto-electronic properties of disordered semiconductors. We present two powerful techniques to access $n(\mathbf r,T)$ without solving the Schrödinger equation. First, we derive the density for non-degenerate electrons by applying the Hamiltonian recursively to random wave functions (RWF). Second, we obtain a temperature-dependent effective potential from the application of a universal low-pass filter (ULF) to the random potential acting on the charge carriers in disordered media. Thereby, the full quantum-mechanical problem is reduced to the quasi-classical description of $n(\mathbf r,T)$ in an effective potential. We numerically verify both approaches by comparison with the exact quantum-mechanical solution. Both approaches prove superior to the widely used localization landscape theory (LLT) when we compare our approximate results for the charge carrier density and mobility at elevated temperatures obtained by RWF, ULF, and LLT with those from the exact solution of the Schrödinger equation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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