Analysis of capacitance-voltage characteristics of ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$/Si quantum-well structures

The theoretical expressions of the capacitance-voltage (C-V) characteristics of a single quantum well are derived in different bias voltage regions based on solving analytically Poisson’s equation. A method to determine the parameters, including the doping concentrations in the well and the barrier, the location of the well, and the thickness of the cap layer, as well as the band offset at the heterointerface from an experimental C-V curve is presented. By carefully constructing a testing sample with the structure of the Al/(thin nitride layer)/Si/${\mathrm{Si}}_{0.67}$${\mathrm{Ge}}_{0.33}$/Si single quantum well, the measurement of a complete C-V curve in a wide voltage range is achieved. The structural parameters of the quantum well derived from the measured C-V curve agree well with the nominal values set by the experimental growth conditions. © 1996 The American Physical Society.