Gaussian Thermionic Emission Model for Analysis of Au/MoS2 Schottky-Barrier Devices

Schottky-barrier inhomogeneities are expected at the metal-transition-metal-dichalcogenide (TMDC) interface and this can impact device performance. However, it is difficult to account for the distribution of interface inhomogeneity as most techniques average over the spot area of the analytical tool (e.g., few hun-dred micrometers squared for photoelectron-based techniques), or the entire device measured for electrical current-voltage (I-V) measurements. Commonly used models to extract Schottky-barrier heights neglect or fail to account for such inhomogeneities, which can lead to the extraction of incorrect Schottky-barrier heights and Richardson constants that are orders of magnitude away from theoretically expected values. Here, we show that a Gaussian-modified thermionic emission model gives the best fit to experimental temperature-dependent current-voltage (I-V-T) data of van der Waals Au/p-MoS2 interfaces and allow the deconvolution of the Schottky-barrier heights of the defective regions from the pristine region. By the inclusion of a Gaussian-distributed Schottky-barrier height in the macroscopic I-V-T analysis, we demonstrate that interface inhomogeneities due to defects are deconvoluted and well correlated to the impact on the device behavior across a wide temperature range from a room temperature of 300 K down to 120 K. We verify the Gaussian thermionic model across two different types of p-MoS2 (geological bulk crystals and synthetic flux-grown crystals), and finally compare the macroscopic Schottky-barrier heights with the results of a nanoscopic technique, ballistic hole emission microscopy (BHEM). The results obtained using BHEM are consistent with the pristine Au/p-MoS2 Schottky-barrier height extracted from the Gaussian modified thermionic emission model over hundreds of nanometers. Our findings show that the inclusion of Schottky-barrier inhomogeneities in the analysis of I-V-T data is useful to elucidate the impact of defects (e.g., grain boundaries, metallic impurities, etc.) and hence their influence on device behavior. We also find that the effective Richardson constant, a material-specific constant typically treated as merely a fitting constant, is a useful parameter to check for the validity of the transport model.