Generalized steady state diode equation: The state equations approach

Abstract

The diode equation has been written as a set of state equations of the form e ̂ = f( e ̂ , x) where f(ê, x) is a non-linear function and ê is the state vector which comprises of electric field, quasi-Fermi levels and the currents as variables. These state equations are then solved using the techniques developed for dynamic nonlinear networks. The non-equilibrium conditions, as well as degeneracy is accounted for by the use of quasi-Fermi levels and the Fermi-Dirac integrals in the equations. The state equation formulation is especially useful in incorporating an accurate expression for the Fermi-Dirac integral in the case of degeneracy. We have used the convergent exponential power series for Fermi-Dirac integrals when Fermi level is within the band gap and numerical approximation for the case of high degeneracy. Current density and continuity equations, and the Poisson equation are coupled together into a single state equation. The splitting of the quasi-Fermi levels and the gradient of the current due to generation recombination are explicit in the equations. This method is also applied to heterojunctions. These results and further improvements in the methodology for solving these state equations are discussed.