C-V Profiling of Delta Layers in Silicon by Quantum and Classical Approaches

The resolution of the capacitance-voltage profiling technique is known to be limited by the Debye length for classical structures. When very narrow layers exist in the sample quantum effects become important and the spatial extent of the electron (or hole) wave function can become a limiting factor. In this paper the interpretation of C-V profiles of structures containing delta-doped layers is discussed, concentrating on n-type layers in silicon. C-V profiles are calculated for a range of structures by solving Poisson´s equation in one dimension, and results obtained from this classical model are compared with the electron wave function width as calculated from Schrödinger´s equation.