Research Initiation Grant: An Efficient and Comprehensive Transport Model for Semiconductor Device Analysis

电子传输的影响主导着半导体器件的行为。这项研究的主要目标是开发一个全面的、物理上准确的、适用于有效的数值评估的输运模型。该模型将整合两种表征电子传输的方法：勒让德多项式技术和能量传输方法。除了确定电流密度和电势外，当完全实现时，该模型将允许快速计算整个器件的电子分布函数。最初的研究将集中在用勒让德多项式数值求解齐次玻尔兹曼输运方程，同时考虑声子散射、一个非抛物线导带和碰撞电离的影响。然后，该模型将用于计算MOSFET中的电离产生的电流。接下来，将介绍几种导带的影响。最后，用福克-普朗克公式考虑了非线性电子-电子散射的影响。通过计算能量平衡方程来确定与空间相关的平均电子能量，从而得到空间相关性。空间相关的分布函数将由能量平衡方程和齐次玻尔兹曼方程的同时解来确定。这项研究将有助于更好地理解影响亚微米器件运行的物理现象，非常适合在CAD中应用。

Effects of electron transport dominate semiconductor device behavior. The main objective of the proposed research is to develop a comprehensive, physically accurate transport model, which is suitable for efficient numerical evaluation. The model will integrate two approaches for characterizing electron transport: the Legendre polynomial technique, and the energy transport method. In addition to determining current densities and electric potentials, when fully realized, the model will allow for rapid calculation of the electron distribution function throughout a device. Initial studies will focus on numerically solving the homogeneous Boltzmann transport equation, using Legendre polynomials, while incorporating the effects of phonon scattering, one non-parabolic conduction band, and impact ionization. The model will then be used to calculate currents generated by ionization in MOSFETs. Next, the effect of several conduction bands will be introduced. Finally, the effect of nonlinear electron-electron scattering will be accounted for by using Fokker Plank formulation. Spatial dependence will be obtained by evaluating the energy balance equation to determine the space-dependent average electron energy. The space-dependent distribution function will then be determined by simultaneous solutions of the energy balance equation and the homogeneous Boltzmann equation. This study will facilitate a better understanding of the physical phenomena which affect submicron device operation, and is well suited for applications in CAD.