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

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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.