We present β-Ga2O3 high-voltage Schottky barrier diodes (SBD) incorporating advanced electric field engineering approaches through the use of high-permittivity dielectrics. We present two approaches: 1) the lateral dielectric superjunction SBD, where the electric field within the drift layer is modified from triangular to rectangular profile, enhancing the breakdown voltage and enabling the use of higher drift layer doping to reduce on-resistance, and 2) the vertical high-k RESURF trench SBD, which leverages the reduced surface electric field effect (RESURF) to reduce the electric field at the metal-semiconductor junction and reverse leakage currents.A superjunction-like structure uses charge balance to push the VBR-Ron-sp trade-off beyond the material’s unipolar figure of merit. The lack of p-type doping in β-Ga2O3 makes the realization of such structures very difficult. However, field flattening can be achieved in β-Ga2O3 drift layers using a high permittivity material with appropriate choice of dielectric constant, device aspect ratio and semiconductor/dielectric width. An analytical model is discussed to highlight the device design strategy and experimental demonstration is reported in the lateral geometry. 500 nm of Si-doped Ga2O3 epitaxial layer with a sheet charge of 1.6×1013 cm-2 is grown using metal organic vapor phase epitaxy (MOVPE). Trenches with three different fin widths (WFin = 2, 5, 10 µm) were made and high-k dielectric BaTiO3 (BTO) with dielectric constant of 220 is deposited on the sample. A low specific on resistance of 1.65 mΩ-cm2 is observed for LAC = 5µm due to the high charge density epitaxial lateral Fins. For the SBD with LAC = 5µm and WFin = 5µm, a high average electric field of ~3 MV/cm (VBR/ LAC) is estimated across the entire length of the device. A very high Baliga's figure of merit (BFOM) of 1.35 GW/cm2 is observed for the RESURF SBD with LAC=5µm and WFin=2µm (VBR=1.49 kV and Ron-sp=1.65 mΩ-cm2), surpassing SiC unipolar FOM when considering just the conducting area.While superjunction-like structures effectively flatten the electric field inside the drift layer, high electric fields at the metal/semiconductor junction results in increased leakage current at large reverse bias, particularly in the case of vertical Schottky Barrier Diodes (SBDs). To circumvent this challenge, we present the approach of β-Ga2O3 Vertical Trench Schottky Barrier Diode (SBD) with a high-permittivity dielectric RESURF. The incorporation of a trench geometry, coupled with the high-permittivity dielectric RESURF, effectively reduces the surface electric field at the metal-semiconductor junction. This reduction facilitates the use of a lower work-function anode contact, further diminishing the turn-on voltage. The use of high-k dielectric also significantly reduces the dielectric leakage contribution to the overall reverse leakage of the diode. Large-area SBDs with areas of 1mm2 and 4mm2 exhibit pulsed forward current of 6A/20A and a catastrophic breakdown voltage of 1.74kV/1.4kV, surpassing other β-Ga2O3-based large-area power diodes, while small-area SBDs (200×200 µm2) do not exhibit catastrophic breakdown until 3kV. The large-area SBDs also demonstrate lower capacitance, stored charge, and stored energy compared to commercial SiC SBDs, indicating potential for superior switching performance. The combination of lower stored charge and a low forward voltage drop results in an excellent trade-off between conduction and switching power loss, yielding a QCVF figure of merit comparable to commercial bare die SiC SBDs. We demonstrate the potential of high permittivity dielectrics-based extreme field engineering to push the performance limits of β-Ga2O3 diodes for next-generation power electronics.We acknowledge funding from AFOSR MURI program (Dr. Ali Sayir) and Coherent/II-VI foundation.