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

作为MISFET的传输层的2D材料由于其与硅相比的上级特性而被深入研究，这可能不仅有助于扩展摩尔定律，而且还有助于推动模拟应用（例如，用于mm波的放大器、传感器）中的晶体管的性能。至少有700种不同的二维材料是已知的，目前正在研究，通常是通过纯理论的手段。为了估计2D材料对用于数字和模拟应用的晶体管性能的影响，将开发通用半经典模拟程序，该程序一方面可以基于能带结构和散射率的从头算方法的结果，另一方面可以模拟实际器件的稳态I-V特性、小信号参数和瞬态行为，这是很难用量子输运模型模拟的。假设在晶体管的宽度方向上的平移不变性的2D真实的空间的泊松方程和具有电子/空穴片的3D相空间（2D k空间和1D真实的空间）的玻尔兹曼方程将自洽地求解。2D k空间将通过非结构化三角形网格离散化，第一布里渊区的不可约楔形可以完全镶嵌，使得可以处理一般的2D晶体类和相应的对称性。离散玻尔兹曼方程将稳定最近开发的计划，可以处理任意的能带结构和散射过程。包含价带和导带将使电子和空穴的模拟能够一致。该代码应适当模块化，具有明确的接口，以便与其他模拟程序无缝交互，用于计算能带结构和散射。此外，将实施用于均匀沟道的模式（长沟道近似）以模拟由更简单的模拟方法（例如，漂移扩散模型）所需的2D材料的基本输运性质（例如，迁移率）。该程序的多功能性将通过模拟稳态，小信号和大信号行为的二硫化钼MISFET的基础上数值计算的能带结构和散射。使用模拟器，应该可以预测2D材料FET的性能，其精度比简单的传输参数（例如迁移率）或漂移扩散模型更高，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.