An analytical model for conduction and valence band edge profiles of bandgap graded and displaced heterojunctions

Abstract

An analytical model for conduction and valence band edge profiles applicable for a wide variety of p–n heterojunction devices is presented by analytically solving the Poisson equation, taking the displacement of p–n junction relative to material junction as well as spatial variation of permittivity into account. The model is applicable for abrupt and compositionally (linearly and parabolically) graded systems. Unlike other analytical models, the present model considers the variation of the built-in potential depending on the positions of the depletion edges in the graded region. A displacement of the p–n junction into the wide bandgap semiconductor is shown to cause strong barriers in the conduction band and the width and height of the barrier increase with the amount of displacement. Displacement into narrow bandgap semiconductors is found to cause dips in the conduction band, the depths of which increase with the amount of displacement. The developed analytical expressions are particularly suitable for circuit simulation purposes as well as for the design of heterojunction devices like heterojunction bipolar transistors (HBT).