Kelvin probe force microscopy study of the electrostatic system of the crystal surface of AuNi/GaN Schottky diodes

Using atomic-force-microscopy investigations of the electrostatic system of the crystal surface of AuNi/$n$–$n^+$-GaN planar Schottky diodes, it is shown that the electron work function for the surface of metal Schottky contacts depends on their linear size (diameter D). At $D>$ 120 $\mu$m, the work function of the central contact region approaches the work function $e\varphi_{\mathrm{Au}}\approx$ 5.40 eV of a continuous metallic gold film. A decrease in the diameter leads to a decrease in the work function to 5.34 eV at $D$ = 120 $\mu$m, 5.21 eV at $D$ = 40 $\mu$m, 5.18 eV at $D$ = 10 $\mu$m, and 5.14 eV at $D$ = 5 $\mu$m. The observed decrease in the work function with diameter is related to the increasing influence of the built-in periphery electrostatic field $\mathbf{E}_l$, which is determined by the area and perimeter of the Schottky contact. The fundamental differences between the thermodynamic and electrostatic systems of TiAlNiAu/$n^+$-GaN ohmic contacts, in contrast to analogous AuNi/$n$-GaN Schottky systems, are indicative of the absence of a Schottky barrier in them and the decisive role of the thermionic transport of mobile carriers.