We introduce a deep-recessed gate architecture in $beta$-Ga$_2$O$_3$ delta-doped field effect transistors for improvement in DC-RF dispersion and breakdown properties. The device design incorporates an unintentionally doped $beta$-Ga$_2$O$_3$ layer as the passivation dielectric. To fabricate the device, the deep-recess geometry was developed using BCl$_3$ plasma based etching at ~5 W RIE to ensure minimal plasma damage. Etch damage incurred with plasma etching was mitigated by annealing in vacuum at temperatures above 600 $deg$C. A gate-connected field-plate edge termination was implemented for efficient field management. Negligible surface dispersion with lower knee-walkout at high V$_mathrm{DS}$, and better breakdown characteristics compared to their unpassivated counterparts were achieved. A three terminal off-state breakdown voltage of 315 V, corresponding to an average breakdown field of 2.3 MV/cm was measured. The device breakdown was limited by the field-plate/passivation edge and presents scope for further improvement. This demonstration of epitaxially passivated field effect transistors is a significant step for $beta$-Ga$_2$O$_3$ technology since the structure simultaneously provides control of surface-related dispersion and excellent field management.
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