Nanostructures were formed on diced specimens of several silicon carbide polytypes and silicon using electron beam lithography. A general introduction to nanostructure synthesis and electron beam lithography,are presented. A scanning electron microscope was retrofitted with a commercially available electron beam lithography package and an electrostatic beam blanker to permit nanoscale lithography to be performed. A process was first developed and optimized on silicon substrates to expose, poly-methyl-methacrylate (PMMA) resist with an electron beam to make nanoscale nickel masks for reactive ion etching. The masks consist of an array of nickel dots that range in size from 20 to 100 nm in diameter. Several nanoscale structures were then fabricated in silicon carbide using electron beam lithography. The structures produced are characterized by field emission Scanning Electron Microscopy.

An efficient numerical method for solving Schr&ouml / dinger&#039 / s and Poisson&#039 / s equations using a basis set of cubic B-splines is investigated. The method is applied to find both the wave functions and the corresponding eigenenergies of low-dimensional semiconductor structures. The computational efficiency of the method is explicitly shown by the multiresolution analysis, non-uniform grid construction and imposed boundary conditions by applying it to well-known single electron potentials. The method compares well with the results of analytical solutions and of the finite difference method.