abstract: Moore's law has been the most important driving force for the tremendous progress of semiconductor industry. With time the transistors which form the fundamental building block of any integrated circuit have been shrinking in size leading to smaller and faster electronic devices.As the devices scale down thermal effects and the short channel effects become the important deciding factors in determining transistor architecture.SOI (Silicon on Insulator) devices have been excellent alternative to planar MOSFET for ultimate CMOS scaling since they mitigate short channel effects. Hence as a part of thesis we tried to study the benefits of the SOI technology especially for lower technology nodes when the channel thickness reduces down to sub 10nm regime. This work tries to explore the effects of structural confinement due to reduced channel thickness on the electrostatic behavior of DG SOI MOSFET. DG SOI MOSFET form the Qfinfet which is an alternative to existing Finfet structure. Qfinfet was proposed and patented by the Finscale Inc for sub 10nm technology nodes. As part of MS Thesis we developed electrostatic simulator for DG SOI devices by implementing the self consistent full band Schrodinger Poisson solver. We used the Empirical Pseudopotential method in conjunction with supercell approach to solve the Schrodinger Equation. EPM was chosen because it has few empirical parameters which give us good accuracy for experimental results. Also EPM is computationally less expensive as compared to the atomistic methods like DFT(Density functional theory) and NEGF (Non-equilibrium Green's function). In our workwe considered two crystallographic orientations of Si,namely [100] and [110]. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016

abstract: The quest to find efficient algorithms to numerically solve differential equations isubiquitous in all branches of computational science. A natural approach to address this problem is to try all possible algorithms to solve the differential equation and choose the one that is satisfactory to one's needs. However, the vast variety of algorithms in place makes this an extremely time consuming task. Additionally, even after choosing the algorithm to be used, the style of programming is not guaranteed to result in the most efficient algorithm. This thesis attempts to address the same problem but pertinent to the field of computational nanoelectronics, by using PETSc linear solver and SLEPc eigenvalue solver packages to efficiently solve Schrödinger and Poisson equations self-consistently. In this work, quasi 1D nanowire fabricated in the GaN material system is considered as a prototypical example. Special attention is placed on the proper description of the heterostructure device, the polarization charges and accurate treatment of the free surfaces. Simulation results are presented for the conduction band profiles, the electron density and the energy eigenvalues/eigenvectors of the occupied sub-bands for this quasi 1D nanowire. The simulation results suggest that the solver is very efficient and can be successfully used for the analysis of any device with two dimensional confinement. The tool is ported on www.nanoHUB.org and as such is freely available. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020