论文标题
无序媒体中的量子状态。 ii。空间电荷载体分布
Quantum states in disordered media. II. Spatial charge carrier distribution
论文作者
论文摘要
空间和温度依赖性电子分布$ n（\ mathbf r，t）$对于无序半导体的光电特性的理论描述至关重要。我们提出了两种强大的技术，可以访问$ n（\ mathbf r，t）$，而无需求解Schrödinger方程。首先，我们通过递归将哈密顿量应用于随机波函数（RWF）来得出非分类电子的密度。其次，我们从应用通用低通滤波器（ULF）到无序培养基中作用于电荷载体的随机电位，从而获得了依赖温度的有效电位。因此，在有效的潜力中，将完整的量子力学问题降低为$ n（\ mathbf r，t）$的准经典描述。我们通过与精确的量子机械溶液进行比较来验证两种方法。当我们比较RWF，ULF和LLT在升高的温度下与来自Schrödinger方程的精确解决方案的载体密度和迁移率的近似结果时，两种方法都优于广泛使用的定位景观理论（LLT）。
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.
