This paper presents vertical (001) oriented $beta$-Ga$_2$O$_3$ field plated (FP) Schottky barrier diode (SBD) with a novel extreme permittivity dielectric field oxide. A thin drift layer of 1.7 $mu m$ was used to enable a punch-through (PT) field profile and very low differential specific on-resistance (R$_{on-sp}$) of 0.32 m$Omega$-cm$^{2}$. The extreme permittivity field plate oxide facilitated the lateral spread of the electric field profile beyond the field plate edge and enabled a breakdown voltage ($V_{br}$) of 687 V. The edge termination efficiency increases from 13.5 $%$ for non-field plated structure to 63 $%$ for high permittivity field plate structure. The surface breakdown electric field was extracted to be 5.45 MV/cm at the center of the anode region using TCAD simulations. The high permittivity field plated SBD demonstrated a record high Baliga figure of merit (BFOM) of 1.47 GW/cm$^{2}$ showing the potential of Ga$_2$O$_3$ power devices for multi-kilovolt class applications.
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