This thesis aims at investigating size dependence of properties of nanostructures from the point of view of a general scaling theory that smoothly connects properties of the bulk to that of nanostructures. Two different examples of a ``static'' and a ``dynamic'' property are considered in this study. The first example studied is of size dependence of coefficient of thermal expansion (CTE) which a static property of nanostructures. The CTE of nanobars and nanoslabs is studied using equilibrium molecular dynamics and dynamical matrix formulation in an electrically insulating medium. It is found that the fractional change in CTE from the bulk value scales inversely with the size of the nanostructures, thus, showing a simple description in terms of a scaling theory. In the second part, electron transport in carbon nanotube field effect transistors (CNTFETs) is studied using Landauer formalism. A CNTFET involves transport through a 1-d ballistic carbon nanotube channel with Schottky barriers (SB) at contacts which determines the transport characteristics. The CNT is modeled as a 1-d semiconductor having only two bands separated by an energy gap which depends inversely on tube diameter. After the contact is made, a self-consistent potential appears due to charge transfer between CNT and metal, which is calculated by solving Poisson equation. The electron transmission across the barriers is calculated using WKB approximation. Current and conductance are calculated using Landauer-Buttiker formula. Diameter dependence of properties like, conductance, threshold voltage, VON, etc. is calculated. It is found that there is no simple scaling for a property for small values of diameter. The scaling form is, however, found to be valid for larger diameters. Also, other calculated device characteristics are in close agreement with experiments. The model presented in this thesis is the first detailed study illustrating the applicability of the scaling approach to the properties of nanostructures. The static properties show scaling behavior, while ``dynamic'' properties derived from electronic response do not.

In this dissertation, we use finite element method together with other numerical techniques to study advanced electron devices. We study the radiation properties in electron waveguide structure with multi-step discontinuities and soft wall lateral confinement. Radiation mechanism and conditions are examined by numerical simulation of dispersion relations and transport properties. The study of geometry variations shows its significant impact on the radiation intensity and direction. In particular, the periodic corrugation structure exhibits strong directional radiation. This interesting feature may be useful to design a nano-scale transmitter, a communication device for future nano-scale system. Non-quasi-static effects in AC characteristics of carbon nanotube field-effect transistors are examined by solving a full time-dependent, open-boundary Schrödinger equation. The non-quasi-static characteristics, such as the finite channel charging time, and the dependence of small signal transconductance and gate capacitance on the frequency, are explored. The validity of the widely used quasi-static approximation is examined. The results show that the quasi-static approximation overestimates the transconductance and gate capacitance at high frequencies, but gives a more accurate value for the intrinsic cut-off frequency over a wide range of bias conditions. The influence of metal interconnect resistance on the performance of vertical and lateral power MOSFETs is studied. Vertical MOSFETs in a D2PAK and DirectFET package, and lateral MOSFETs in power IC and flip chip are investigated as the case studies. The impact of various layout patterns and material properties on RDS(on) will provide useful guidelines for practical vertical and lateral power MOSFETs design.