Dimension Effect on Intrinsic Carrier Concentration of Semiconductor Calculated from Density of State

Abstract

Dimension effect is an important effect to understand nanoscience and nanotechnology. In this work, dimension effect on intrinsic carrier concentration of semiconductor has been studied. The study is based on the calculation from the density of state at 3,2 1 and 0 dimensions at temperature k[subscript B]T <<E[subscript g]/2 where E[subscript g] is energy gap. Since the density of state at different dimension has different function, intrinsic carrier concentration calculated from density of state is expected to vary as a function of dimension. For 2,1 and 0 dimensions, the energy level are discrete outside the energy gap. Moreover, 1 and 0 dimensions also have degenerated state and the degeneracy has an effect on density of state. From the calculation, it has been found that the intrinsic carrier concentration of semiconductor depends on the dimension and is proportional to T [superscript D/2] exp (-E[subscript g] / 2K[subscript B]T) where D is a dimension.