Numerical Simulation of Advanced CMOS and Beyond CMOS Nanoscale Transistors

There is a growing consensus in the electron device community that the 32nm node could be the last technology node based on the conventional silicon planar MOSFET, due to the physical limitations of this technology. Several new approaches are under investigation in order to reach the requirement of the International Technology Roadmap for Semiconductors beyond the 32nm technology node; some studies are focused on new device architectures that allow a better control of the gate over the channel, while other ones propose to substitute silicon in the channel with high-mobility materials. The physics-based modeling of these new devices is extremely important because it is supposed to guide the electron device industry in the choice of the best device structures for the future technology nodes. In this context, the aim of this PhD thesis is to investigate two of these innovative technology options: the FinFET and the nanowires device architectures and the graphene based transistors. To this purpose, we developed several TCAD simulation tools based on advanced modeling techniques. In the first part of the thesis we developed a solver for the simulation of the electrostatics in the channel section of nanowires and FinFETs with realistic shape, based on an innovative numerical approach, the Pseudospectral method. Thanks to the remarkable accuracy of this approach (i.e. an exponential decrease of the approximating error with the number of discretization points), we were able to develop a very efficient simulator, which vastly outperforms solvers based on standard numerical approaches such as the finite differences. Moreover, we compared our approach with another innovative method, the Discrete Geometric Approach, in the simulation of the electrostatics of realistic devices. The second part of the PhD was focused on the simulation of graphene, the innovative material with very interesting physical properties discovered in 2004. First we developed a novel and general approach for the exact solution of the linearized Boltzmann transport equation; we applied the proposed method to the calculation of the graphene bilayer low-field mobility: the obtained results are quite consistent with the experimental values found in the literature. We also demonstrate that the most common approach used in the literature for the estimation of the low-field mobility (i.e. the Momentum Relaxation Time approach) introduces non negligible errors in the considered case. We thus developed also a semi-classical transport simulator based on the Monte Carlo approach for the modeling of the uniform transport in bilayer graphene. Our simulations showed that the saturation velocity in this material is much higher than in silicon; moreover, with respect to monolayer graphene, the saturation velocity is higher in bilayer graphene only at high carrier densities. Finally, we developed a semi-classical model for RF graphene FETs based on the Monte Carlo approach including a novel local model for band-to-band tunneling. The simulator, that was validated by comparison with full quantum results, improves the range of applications of semi-classical Monte Carlo models for graphene based transistors. Using this simulator we found that the band-to-band tunneling is responsible for the poor saturation of the current in GFETs transistors; moreover, we studied the effect of the scattering and of the gate length on the performance of this device and we found that the scattering has a non negligible influence on the main RF figures of merit even in short channel devices.