Two-dimensional (2D) platinum diselenide (PtSe2) layers are a new class of near-atom-thick 2D crystals in a van der Waals-assembled structure similar to previously explored many other 2D transition-metal dichalcogenides (2D TMDs). They exhibit distinct advantages over conventional 2D TMDs for electronics and optoelectronics applications such as metallic-to-semiconducting transition, decently high carrier mobility, and low growth temperature. Despite such superiority, much of their electrical properties have remained mostly unexplored, leaving their full technological potential far from being realized. Herein, we report 2D/three-dimensional Schottky junction devices based on vertically aligned metallic 2D PtSe2 layers integrated on Si wafers. We directly grew 2D PtSe2 layers of controlled orientation and carrier transport characteristics via a low-temperature chemical vapor deposition process and investigated 2D PtSe2/Si Schottky junction properties. We unveiled a comprehensive set of material parameters, which decisively confirm the presence of excellent Schottky junctions, i.e., high-current rectification, small ideality factor, and temperature-dependent variation of Schottky barrier heights. Moreover, we observed strong photovoltaic effects in the 2D PtSe2/Si Schottky junction devices and extended them to realize flexible photovoltaic devices. This study is believed to significantly broaden the versatility of 2D PtSe2 layers in practical and futuristic electronic devices.