Capacitance-voltage profiling through graded heterojunctions: Theory and experiment

Abstract

Starting from the general equations for capacitance-voltage (CV) profiling through a graded heterojunction, we obtain numerical solutions to yield thermal-equilibrium energy-band diagrams, real electron profiles, and apparent electron profiles (i.e., the profile extracted from a CV measurement) for modulation-doped square, triangular, and parabolic potential wells. Room-temperature CV measurements are performed on parabolic potential wells grown by molecular beam epitaxy in the AlxGa1−xAs system, and the measured apparent electron profiles fitted to computer reconstructions whence the real electron distributions are deduced. These measurements reflect a uniform electron distribution in a parabolic well, with 3D electron density determined by well curvature. Data analysis also suggests the presence of a doping asymmetry in the modulation doping of the well. Appropriate corrections to growth conditions remove these asymmetries, as reflected in CV measurements. Besides its importance in the analysis of potential wells of different shapes, the theory presented is applicable to the determination of band offsets by the CV profiling technique where the unintentional grading of the band gap and/or doping in the neighborhood of the isotype abrupt heterojunction is known.