Sheet resistance of the TiAlNiAu thin-film metallization of ohmic contacts to nitride semiconductor structures

The relation between the geometry of the metric space of the thin-film TiAlNiAu metallic system surface and the geometry of the functional space of the sheet resistances $R_{sq}$ of this system is established. Based on the results obtained, the lateral size effect observed in the local approximation is described, which manifests itself in the dependence of the sheet resistance $R_{sq}$ of a TiAlNiAu metallic film on its lateral (in the $(x,y)$ plane) linear sizes. The dependence of the $R_{sq}$ value on the linear sizes is shown to be determined by the fractal geometry of the forming dendrites, specifically, by the power dependence of a variation in the linear sizes on the fractal dimension $D_f$. The obtained regularity is of great practical importance for accurate calculation of the $R_{sq}$ values of thin-film metal systems in designing discrete devices and integrated circuits and for controlling the technological processes of fabricating thin metallic films and systems based on them at the micrometer and nanometer scales.