An analytic model for the MIS tunnel junction

A comprehensive analytic model describing current flow in the MIS tunnel junction under steady-state conditions is developed. The tunnel junction is viewed as imposing boundary conditions on the usual set of differential equations governing the electrostatic potential and carrier distributions within the semiconductor. These equations are then solved using the approximation techniques applied in conventional p-n junction theory. Full Fermi-Dirac statistics are used where necessary in the model, and surface states are treated using a Shockley-Read-Hall approach. In computing the band-to-metal tunnel currents, it is assumed that each valley in the conduction band and peak in the valence band can be assigned a single tunneling probability factor describing all transitions between that valley or peak and the metal. On making the above approximations, it is found that the state of the junction is described by two coupled nonlinear algebraic equations, which can be solved by routine iterative techniques. The model is applied to generate current-voltage characteristics for a minority-carrier AI-SiOx- pSi diode, operated both in the dark and as a solar cell, and for a negative barrier AI-SiOx-nSi contact exhibiting photocurrent multiplication. The results obtained are in good agreement with those predicted by more precise numerical methods.