Numerical simulation study of inhomogeneous metal-semiconductor contact with discrete distribution of varying barrier heights patches

The Poisson's equation and the drift diffusion equations were solved by numerical simulation to calculate the potential and electron and hole concentrations inside the bulk semiconductor near the metal-semiconductor contact. The current density was then estimated from the calculated potential and electron-hole concentrations using the continuity equations. The current as a function of bias was calculated by imposing external bias through the boundary condition during the numerical simulation using silicon parameters to obtain the current-voltage characteristics of metal-semiconductor contact. From the simulated current-voltage characteristics the diode parameters were extracted by fitting the current-voltage data into the thermionic emission diffusion current equation. The simulations were performed for the inhomogeneous metal-semiconductor contact having randomly distributed patches of varying barrier heights. The patch size was varied to see its effect of the current-voltage characteristics and the derived apparent barrier parameters. The derived barrier parameters were analyzed to study the effect of inhomogeneities on the current-voltage characteristics on metal-semiconductor contact. The simulations were carried out for discrete distribution of barrier height patches at the metal-semiconductor contact. It is observed that the apparent barrier height of the inhomogeneous contact decreases and ideality factor increases with increasing the deviation of barrier heights in the distribution.