It is usual to define the electronic properties of microstructure of solid state devices in relation to the degree of freedom of mobile charge carriers, i. e. simple layered structures are referred as 2- dimensional (2D) systems, double confined structures or quantum wires and quantum balls are defined as 1-D and 0-D systems respectively. In general, these systems are referred to as Ultra-Low Dimensional Systems (ULDS). Current technology is based on the 2-D systems. However, advances in high resolution fine line lithography and crystal growth techniques indicate that microstructure on the scale of quantum wires and balls may be possible. The potential use of the artificial materials with 1-D or 0-D microstructures for computer memory and ultra-high device integration is considerable. Efficient device simulation algorithms are necessary for modeling the properties of the microstructure and indispensable to the introduction of this next generation of VLSI technology. This research project addresses the development of a robust, fast, and flexible algorithm to determine the relevant physical and microstructure parameters for optimal design and performance of devices of the Ultra-low Dimensional Systems. A team of young investigators composed of device physicists, numerical analyst, and computer scientist will be formed as an interdisciplinary group.