Numerical analysis of Gaussian potential patches model depending on the substrate doping in inhomogeneous Schottky barrier diodes over a wide temperature range

The current-voltage (I-V-T) characteristics of an inhomogeneous n-type GaAs Schottky barrier diode have been investigated by numerical analysis using the modified thermionic emission (TE) current equation by Tung in the 40–320 K range at 40 K intervals. This total current (TC) equation consists of TE current and the patch current components. The patch current dominates through the low Schottky barrier height patches at low temperatures. From the I-V-T characteristics given for three different standard deviations $(σ)$ at each substrate doping value $N d$⁠, we have determined the temperatures at which the patch current begins to dominate. The starting temperature of the patch current has decreased as the $σ$ and $N d$ values decrease. It has been seen that the temperature at which the patch current component begins to dominate is about 120, 80, and 60 K for $σ 4$⁠, $σ 3$⁠, and $σ 2$ at $N d=1.0× 10 14 c m − 3$ or $N d=1.0× 10 15 c m − 3$⁠, respectively; 160, 120, and 80 K at $N d=5.0× 10 15 c m − 3$⁠; and 200, 160, and 80 K at $N d=1.0× 10 16 c m − 3$⁠, respectively. Moreover, for the substrate with high doping, it has been observed that the I-V curve of the patch current component or the TC shifts toward higher voltages than the expected position at low temperatures. Thus, from the I-V-T characteristics, it has appeared that Tung’s pinch-off model tends to be more applicable to lightly doped semiconductors. Moreover, the TC equation should be used at high temperatures because the I-V curves at high temperatures belong to the TE component, and the patch current expression without the TE component should be especially used for fit to the experimental curves at low temperatures.