Recent studies show disordered materials such as amorphous silicon (a-Si), in spite of their low mobility, can efficiently amplify photocurrent via carrier multiplication process. Detectors with a thin (~40nm) a-Si multiplication layer has demonstrated single photon sensitivity at high speed under room temperature. It is believed that the abundance of bandtail states that cause low mobility of the amorphous materials actually contribute to the detector’s superior performance because carrier impact ionization involving these states, which can be modeled by donor-acceptor pairs (DAPs), relax the k-selection rule of the many-body carrier multiplication process. Our paper presents a theoretical framework to calculate the carrier multiplication process in a-Si or other disordered materials involving DAPs. Our analysis also establishes the relations between detector characteristics and key parameters such as the density of band tail states, layer thickness, and applied electric field. DAP assisted carrier multiplication rate is computed first. Carrier multiplication coefficients for electrons and holes under given applied field are then calculated using a trial distribution function that satisfies both the continuity equation and the energy balance equation. Our analysis shows that thinner a-Si gives rise to higher multiplication efficiency than thicker a-Si because of its higher carrier kinetic energy when the layer thickness is shorter than the length of energy relaxation by phonon scattering. Using the calculated carrier multiplication coefficients, voltage dependent gain of the device is computed and the results agree well with the measured results of a-Si cycling excitation process (CEP) detectors.

中文翻译：

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非晶硅中的缺陷辅助载流子倍增

最近的研究表明，无序材料如非晶硅 (a-Si) 尽管迁移率低，但可以通过载流子倍增过程有效地放大光电流。具有薄 (~40nm) a-Si 倍增层的探测器在室温下高速表现出单光子灵敏度。据信，导致非晶材料迁移率低的大量带尾态实际上有助于探测器的优越性能，因为涉及这些态的载流子碰撞电离，可以通过施主 - 受主对 (DAP) 建模，放松 k 选择多体载波乘法规则。我们的论文提出了一个理论框架来计算 a-Si 或其他涉及 DAP 的无序材料中的载流子倍增过程。我们的分析还建立了探测器特性与关键参数（如带尾态密度、层厚度和外加电场）之间的关系。首先计算 DAP 辅助载波倍增率。然后使用满足连续性方程和能量平衡方程的试验分布函数计算给定外加场下电子和空穴的载流子倍增系数。我们的分析表明，当层厚度小于声子散射的能量弛豫长度时，较薄的 a-Si 比较厚的 a-Si 产生更高的倍增效率，因为它具有更高的载流子动能。使用计算的载波乘法系数，