Silicon carbide (SiC) and carbon nanotubes (CNTs) are two materials which have promising potential in electronics. Due to its large bandgap and large thermal conductivity, SiC is targeted as a potential material for use in high-power high-temperature electronics. Carbon nanotubes are at the forefront of current research in nanoelectronics, and field-effect nanotube transistors have already been developed in research laboratories. The small dimensions of these materials suggests their possible use in densely packed CNT-integrated circuits. Carbon nanotubes also appear to have very large electron mobilities, and may have applications in high-speed electronic devices.

 In this work the properties of the electronic structure and electron 

transport in silicon carbide and in semiconducting zig-zag carbon nanotubes are studied. For SiC, a new method to calculate the bulk band structure is developed. The conduction band minimum is found to lie at the $L$ and $M$ points in the Brillouin zones of 4H and 6H-SiC respectively. The quasi-2D band structure of hexagonal SiC is also determined for a number of lattice orientations. Electron transport in SiC is investigated in the bulk and at the SiC/oxide interface. The dependence of transport on the lattice temperature, applied field, and crystal orientation is studied.

 A methodology for semiclassical transport of electrons in 

semiconducting carbon nanotubes is also developed. Monte Carlo simulations predict large low-field mobilities (4000-13000 cm*cm/Vs) agreeing with experiments. The simulations also predict high electron drift velocities (500 km/s) and negative differential resistance.