In this work we study the Schottky barrier height (SBH) at the junction between $beta$-Ga$_2$O$_3$ and platinum, a system of great importance for the next generation of high-power and high-temperature electronic devices. Specifically, we obtain interfacial atomic structures at different orientations using our novel structure matching algorithm and compute their SBH using electronic structure calculations based on hybrid density functional theory. The orientation and strain of platinum are found to have little impact on the barrier height. In contrast, we find that decomposed water (H.OH), which could be present at the interface from Ga$_2$O$_3$ substrate preparation, has a strong influence on the SBH, in particular in the ($overline{2}$01) orientation. The SBH can range from $sim$2 eV for the pristine interface to nearly zero for the full H.OH coverage. This result suggests that SBH of $sim$2~eV can be achieved for the Ga$_2$O$_3$($overline{2}$01)/Pt junction using the substrate preparation methods that can reduce the amount of adsorbed water at the interface.
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