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The performance of ultra-wide band gap materials like$\beta$-Ga$_\mathrm{2}$O$_\mathrm{3}$ is critically dependent on achieving highaverage electric fields within the active region of the device. In this report,we show that high-k gate dielectrics like BaTiO$_\mathrm{3}$ can provide anefficient field management strategy by improving the uniformity of electricfield profile in the gate-drain region of lateral field effect transistors.Using this strategy, we were able to achieve high average breakdown fields of1.5 MV/cm and 4 MV/cm at gate-drain spacing (L$_\mathrm{gd}$) of 6 um and 0.6um respectively in $\beta$-Ga$_\mathrm{2}$O$_\mathrm{3}$, at a high channelsheet charge density of 1.8x10$^\mathrm{13}$cm$^\mathrm{-2}$. The high sheetcharge density together with high breakdown field enabled a record power figureof merit (V$^\mathrm{2}$$_\mathrm{br}$/R$_\mathrm{on}$) of 376MW/cm$^\mathrm{2}$ at a gate-drain spacing of 3 um.

Electrostatic Engineering using Extreme Permittivity Materials for Ultra-wide Bandgap Semiconductor Transistors