A comparative study of numerical and analytical methods of simulating inhomogeneous Schottky diode characteristics

The current-voltage characteristics of inhomogeneous Schottky diodes can be generated using either analytically solved equations for total current through all elementary diodes, or by numerical integration over the entire barrier height range. The simulation performed using these two methods yields current-voltage characteristics with different features. In this paper we have analysed the nature of elementary diodes representing a Gaussian distribution of barrier heights in inhomogeneous Schottky contact, and found that it is the constant series resistance considered for all elementary diodes in the distribution which makes the two methods yield current-voltage characteristics with different features. It apparently indicates that the two methods of analysing inhomogeneous Schottky contacts are inconsistent. It is shown that each elementary barrier in the distribution has a different series resistance associated with it, which has a direct correlation with its probability of occurrence in the distribution. Performing the numerical integration with varying series resistance yields current-voltage characteristics with features similar to those obtained by the analytical method. The analysis made in this paper confirms that the two methods of modelling inhomogeneous Schottky contacts yield consistent current-voltage characteristics.