Mukherjee Atreyo, Vasileska Dragica, Akis John, Goldan Amir H
Department of Electrical Engineering, College of Engineering and Applied Sciences, Stony Brook University, Stony Brook, New York 11794, United States.
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, United States.
ACS Omega. 2021 Feb 5;6(7):4574-4581. doi: 10.1021/acsomega.0c04922. eCollection 2021 Feb 23.
Amorphous selenium lacks the structural long-range order present in crystalline solids. However, the stark similarity in the short-range order that exists across its allotropic forms, augmented with a shift to non-activated extended-state transport at high electric fields beyond the onset of impact ionization, allowed us to perform this theoretical study, which describes the high-field extended-state hole transport processes in amorphous selenium by modeling the band-transport lattice theory of its crystalline counterpart trigonal selenium. An in-house bulk Monte Carlo algorithm is employed to solve the semiclassical Boltzmann transport equation, providing microscopic insight to carrier trajectories and relaxation dynamics of these non-equilibrium "hot" holes in extended states. The extended-state hole-phonon interaction and the lack of long-range order in the amorphous phase is modeled as individual scattering processes, namely acoustic, polar and non-polar optical phonons, disorder and dipole scattering, and impact ionization gain, which is modeled using a power law Keldysh fit. We have used a non-parabolic approximation to the density functional theory calculated valence band density of states. To validate our transport model, we calculate and compare our time of flight mobility, impact ionization gain, ensemble energy and velocity, and high field hole energy distributions with experimental findings. We reached the conclusion that hot holes drift around in the direction perpendicular to the applied electric field and are subject to frequent acceleration/deceleration caused by the presence of high phonon, disorder, and impurity scattering. This leads to a certain determinism in the otherwise stochastic impact ionization phenomenon, as usually seen in elemental crystalline solids.
非晶态硒缺乏晶体固体中存在的结构长程有序性。然而，其各种同素异形体在短程有序性方面存在明显相似性，并且在高于碰撞电离起始点的高电场下向非激活扩展态输运转变，这使我们能够进行这项理论研究，该研究通过对其晶体对应物三角硒的带输运晶格理论进行建模，描述了非晶态硒中的高场扩展态空穴输运过程。采用内部开发的体蒙特卡罗算法来求解半经典玻尔兹曼输运方程，从而深入了解这些扩展态中非平衡“热”空穴的载流子轨迹和弛豫动力学。非晶相中的扩展态空穴 - 声子相互作用以及缺乏长程有序性被建模为单个散射过程，即声学、极性和非极性光学声子、无序和偶极子散射，以及碰撞电离增益，碰撞电离增益采用幂律凯尔迪什拟合进行建模。我们对密度泛函理论计算的价带态密度采用了非抛物线近似。为了验证我们的输运模型，我们计算并将飞行时间迁移率、碰撞电离增益、系综能量和速度以及高场空穴能量分布与实验结果进行比较。我们得出的结论是，热空穴在垂直于外加电场的方向上漂移，并由于高声子、无序和杂质散射的存在而频繁加速/减速。这导致了在元素晶体固体中通常所见的随机碰撞电离现象中存在一定的确定性。
