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 hundred micron 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$_{\thinspace }$der Waals Au/$p$-MoS$_{\mathrm{2\thinspace }}$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 room temperature of 300 K down to 120 K. We verified the gaussian thermionic model across two different types of $p$-MoS${}_2$ (geological bulk crystals and synthetic flux grown crystals), and finally compared the macroscopic Schottky barrier heights with the results of a nanoscopic technique, ballistic hole emission microscopy (BHEM). The results obtained using BHEM were consistent with the pristine Au/$p$-MoS${}_2$ 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 important 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 an important parameter to check for the validity of the transport model.

中文翻译：

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用于Au / MoS2肖特基势垒器件分析的高斯热电子发射模型

在金属/过渡金属二卤化硅（TMDC）界面处，肖特基势垒不均匀是可能的，这会影响器件性能。但是，很难解决界面不均匀性的分布问题，因为大多数技术在分析工具的光斑区域（例如，基于光电子的技术的斑点面积为数百微米平方）或整个设备的电流-电压平均值（$\mathrm{一世}-V）$测量。提取肖特基势垒高度的常用模型会忽略或无法解决此类不均匀性，这可能会导致提取不正确的肖特基势垒高度和Richardson常数，这与理论预期值相差一个数量级。在这里，我们证明了高斯修正的热电子发射模型最适合实验温度相关的电流-电压（$\mathrm{一世}-V-Ť）$van $ _ {\ thinspace} $ der Waals Au /的数据$p$-MoS $ _ {\ mathrm {2 \ thinspace}} $接口并允许从原始区域对缺陷区域的肖特基势垒高度进行反卷积。通过在宏观中包含高斯分布的肖特基势垒高度$\mathrm{一世}-V-Ť$ 分析表明，由缺陷引起的界面不均匀性可以消除卷积，并与从300 K到120 K的宽温度范围内对器件行为的影响密切相关。我们验证了两种不同类型的高斯热电子模型 $p$钼${}_2$（地质体晶体和合成助熔剂生长晶体），最后将宏观肖特基势垒高度与纳米技术，弹道空穴发射显微镜（BHEM）的结果进行了比较。使用BHEM获得的结果与原始Au /$p$钼${}_2$从高斯修正的热电子发射模型提取的肖特基势垒高度超过数百纳米。我们的发现表明，肖特基势垒不均匀性在分析$\mathrm{一世}-V-Ť$数据对于阐明缺陷（例如晶界，金属杂质等）的影响及其对器件性能的影响非常重要。我们还发现，有效的Richardson常数（一种材料比常数，通常仅被视为拟合常数）是检查运输模型有效性的重要参数。