Modeling semiconductor heterojunctions in equilibrium

Computation of the equilibrium electrostatic potential and energy band diagram of semiconductor devices with nonuniform composition is considered. We first establish the relationship between the electrostatic potential and the energy band edges and then derive a Poisson-Boltzmann equation for the electrostatic potential. Although the equation is more general, we consider only the simple example of an abrupt heterojunction diode in detail. An analytical solution for doubly-intrinsic, abrupt heterojunctions is also presented. The modeling approach is then generalized to include Fermi-Dirac statistics for free carriers. We also discuss the application of the formulation to a variety of heterojunction devices (e.g. heavily doped silicon and gate-modulated devices).