Electrostatic and electrical transport analysis of nanomaterials and numerical methods development

The nanotechnology today is continuously boosting the application of nanostructured materials in the development and innovation of electronic devices, such as Nano -- Electromechanical Systems (NEMS), electrical transistors, thermoelectric devices, and solar cells. Due to the size miniaturization, quantum mechanical effects play important roles in the performance of such devices. To correctly capture the quantum mechanical effects and understand how these effects influence the electrostatic and electrical transport properties of nanomaterials, efficient and accurate computational models are highly desirable. Currently, the commonly used model for electrostatic analysis of nanoscale devices is based on self -- consistent solution of the effective -- mass Schroedinger equation coupled with the Poisson equation. However, a major drawback of this model is its inefficiency to simulate systems with large Degrees of Freedom (DOFs). To reduce the computational cost, in this thesis, two Component Mode Synthesis (CMS) approaches, namely the fixed -- interface CMS and the free -- interface CMS, are incorporated into the Schroedinger -- Poisson model to speed up the electrostatic analysis in nanostructures. The new model is employed to analyze the quantum electrostatics in both nanowires and FinFETs. Numerical results demonstrate the superior computational performance in terms of efficiency and accuracy.;In addition to the electrostatic analysis, carrier transport in nanostructures with perturbation from quantum effects also merits careful consideration. Among the computational models developed for quantum mechanical carrier transport analysis, the Non -- Equilibrium Green ' s Function (NEGF) coupled with Poisson equation has gained vast application in both ballistic and diffusive transport analysis of nanodevices. In this thesis, the NEGF model is expanded to include mechanical strain and carrier scattering effects. Two important multiphysics systems are investigated in this work. We first study the effect of mechanical strain on the electrical conductivity of Si/Si 1 - x Ge x nanocomposite thin films. The strain effect on the bandstructures of nano -- thin films is modeled by a degenerate two -- band k · p theory. The strain induced bandstructure variation is then incorporated in the NEGF -- Poisson model. The results introduce new perspectives on electrical transport in strained nano -- thin films, which provides useful guidance in the design of flexible electronics. Secondly, nanoporous Si as an efficient thermoelectric material is studied. The Seebeck coefficient and electrical conductivity of nanoporous Si are computed by using the NEGF -- Poisson model with scatterings modeled by Buttiker probes. The phonon thermal conductivity is obtained by using a Boltzmann Transport Equation (BTE) model while the electron thermal conductivity is captured by the Wiedemann -- Franz law. The thermoelectric figure of merit of nanoporous Si is computed for different doping density, porosities, temperature and pore size. An optimal combination of the material design parameters is explored and the result proves that nanoporous Si has better thermoelectric properties than its bulk counterpart.;In the electrical transport analysis of nanomaterials, we found that the standard NEGF -- Poisson model using the Finite Difference (FD) method has a high computational cost, and is inapplicable to devices with irregular geometries. To overcome these difficulties, an accelerated Finite Element Contact Block Reduction (FECBR) method is developed in this thesis. The performance of the accelerated FECBR is evaluated through the simulation of two types of electronic devices: taper -- shaped DG -- MOSFETs and DG -- MOSFETs with Si/SiO 2 interface roughness. Numerical results show that the accelerated FECBR can be applied to model ballistic carrier transport in devices with multiple leads, arbitrary geometry and complex potential profile. The accelerated FECBR significantly improves the flexibility and efficiency of electrical transport analysis of nanomaterials and nanodevices.