We report a vertical β-Ga₂O₃ Schottky Barrier Diode (SBD) with BaTiO3 as field plate oxide on low doped thick epitaxial layer exhibiting 2.1 kV breakdown voltage. A thick drift layer of 11 μm with a low effective doping concentration of 8×10¹⁵ cm⁻³ is used to achieve high breakdown voltage. Using the high-k dielectric with dielectric constant of 248, the breakdown voltage increases from 816V for the non-field-plated SBD to 2152V (>2x improvement) for the field-plated SBD without compromising the on-state performance. The diode dimensions are varied to analyze the effect of edge high-field related leakage with reverse bias and also the effect of current spreading during forward operation. Very uniform distribution of breakdown voltages of 2152V±20V are observed for the diode diameters from 50 μm to 300 μm for the field-plated SBDs. The on and off state power losses are also analyzed and compared with the non-field-plated devices and the switching losses are estimated analytically.