NUMBER AND DENSITY-OF-STATES IN QUANTUM SEMICONDUCTOR STRUCTURES

Pushed by the semiconductor industry to achieve greater speed and func tionality, device dimensions are becoming sufficiently small to exhibi t prominent quantum mechanical effects, In addition, devices are now b eing developed that utilize these quantum effects, The number and dens ity of states are fundamentally important in the operation of any quan tum device. Traditionally in a classroom setting, one dimensional (1-D ), two-dimensional (2-D), and three-dimensional (3-D) continuum approx imations are presented to analyze the quantum wire, well, and box, res pectively, As shown in this paper, the exact number and density of sta tes can be straightforwardly calculated by students for real semicondu ctor quantum structures. These results clearly illustrate the overall true 3-D form of each of these structures, These correct calculations also reveal an overestimation in the number of states when using the c ontinuum approximations.