A General Purpose Semi-Classical Simulation Program for 2D Material Field Effect Transistors

二维材料作为misfet的传输层被深入研究，因为它们与硅相比具有优越的性能，不仅有助于扩展摩尔定律，而且还有助于提高模拟应用中晶体管的性能（例如毫米波放大器，传感器）。至少有700种不同的二维材料是已知的，目前正在研究，通常是纯理论手段。估计2 d的影响材料性能的晶体管数字和模拟应用程序的一个通用的半经典模拟程序会被开发,一方面可以基于从头开始的结果带结构和散射率的方法,另一方面可以模拟固定电流-电压特性,小信号参数和实际设备的瞬态行为,由quatum-transport难以模拟模型。假设晶体管宽度方向平移不变性的二维实空间泊松方程和电子/空穴片三维相空间（二维k空间和一维实空间）的玻尔兹曼方程将得到自洽解。二维k空间将被非结构化三角形网格离散化，第一布里渊区的不可约楔可以被完全镶嵌，从而可以处理一般的二维晶体类别和相应的对称性。离散玻尔兹曼方程将稳定由一个最近发展的方案，可以处理任意带结构和散射过程。包含价带和导带将使电子和空穴的模拟一致。代码应适当模块化，具有良好指定的接口，以便与其他模拟程序无缝交互，以计算波段结构和散射。此外，将实现均匀通道（长通道近似）的模式，以模拟更简单的模拟方法（例如漂移-扩散模型）所需的二维材料的基本传输特性（例如迁移率）。该程序的通用性将通过基于数值计算的带结构和散射模拟MoS2 MISFET的平稳、小信号和大信号行为来证明。与简单的输运参数（如迁移率）或漂移扩散模型相比，有了模拟器，就有可能以更高的精度预测二维材料场效应管的性能，并支持实验的设计和解释。

2D materials as transport layers for MISFETs are intensively investigated due to their superior properties compared to silicon that might help not only to extend Moore’s law, but also to push the performance of transistors in analog applications (e.g. amplifiers for mm-waves, sensors). At least seven hundred different 2D materials are known and currently investigated, often by purely theoretical means. To estimate the impact of the 2D materials on the performance of transistors for digital and analog applications a general-purpose semi-classical simulation program will be developed that on the one hand can be based on the results of ab initio methods for band structures and scattering rates and on the other hand can simulate the stationary I-V characteristics, small-signal parameters and transient behavior of realistic devices, which are difficult to simulate by quatum-transport models. The Poisson equation for a 2D real space assuming translation invariance in the width direction of the transistor and the Boltzmann equation with a 3D phase space (2D k-space and 1D real space) for the electron/hole sheet will be solved self-consistently. The 2D k-space will be discretized by an unstructured triangular grid with which the irreducible wedge of the first Brillouin zone can be completely tessellated making it possible to handle general 2D crystal classes and the corresponding symmetries. The discrete Boltzmann equation will be stabilized by a recently developed scheme that can handle arbitrary band structures and scattering processes. Inclusion of valance and conduction bands will enable the consistent simulation of electrons and holes. The code shall be properly modularized with well-specified interfaces to enable seamless interaction with other simulation programs for the calculation of band structures and scattering. Furthermore, a mode for a homogeneous channel (long channel approximation) will be implemented to simulate fundamental transport properties of the 2D material (e.g. mobility) required by simpler simulation approaches (e.g. drift- diffusion model). The versatility of the program will be demonstrated by simulating the stationary, small-signal and large signal behavior of a MoS2 MISFET based on a numerically calculated band structure and scattering. With the simulator it should be possible to predict the performance of 2D material FETs with a higher accuracy than by simple transport parameters (e.g. mobility) or drift-diffusion models and to support the design and interpretation of experiments.