Nanometer-scale test of the Tung model of Schottky-barrier height inhomogeneity

Abstract

Tung has shown [Phys. Rev. B 45, 13 509 (1992)] that a range of ``nonideal'' behaviors observed in metal/semiconductor (MS) Schottky diodes could be quantitatively explained by assuming that specific microscopic distributions of nanometer-sized ``patches'' of reduced barrier height exist at the MS interface. Here we report a simultaneous microscopic and macroscopic test of this model as applied to $\mathrm{metal}/6H\ensuremath{-}\mathrm{SiC}$ Schottky diodes, by (1) measuring the nm-scale barrier-height distribution (BHD) of particular Schottky diodes using ultrahigh vacuum (UHV) ballistic electron emission microscopy (BEEM), (2) extending the Tung model to calculate the expected nm-scale BHD for particular parameter values, and (3) quantitatively relating the measured nm-scale BHD of a particular Schottky diode to its macroscopic $I\ensuremath{-}V$ characteristic. Our studies indicate that (1) for relatively ideal diodes, both the microscopic and macroscopic behaviors are explained well by the Tung model with a large coverage (g5%) of shallow patches, (2) the measured BHDs are nearly identical for relatively ideal and highly nonideal diodes, and (3) a simple Tung model can account for highly nonideal behavior only by assuming an unphysical patch distribution in which the excess current is dominated by a few patches in the extreme tail of the patch distribution. Our measurements instead suggest that all the diodes contain a broad ``intrinsic'' distribution of shallow patches, while the large excess current in highly nonideal diodes is due to a few large defects of extrinsic origin. This last conclusion is consistent with a recent study by Skromme and co-workers [J. Electron. Mater. 29, 376 (2000)].