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We report on the demonstration of metalorganic vapor phase epitaxy-regrown(MOVPE) ohmic contacts in an all MOVPE-grown $\beta$-Ga$_2$O$_3$metal-semiconductor field effect transistor (MESFET). The low-temperature(600$^{\circ}$C) heavy (n$^{+}$) Si-doped regrown layers exhibit extremely highconductivity with sheet resistance of 73 $\Omega$/$\square$ and record lowmetal/n$^{+}$-Ga$_2$O$_3$ contact resistance of 80 m$\Omega$.mm and specificcontact resistivity of 8.3$\times$10$^{-7}$ $\Omega$.cm$^{2}$ were achieved.The fabricated MESFETs exhibit a maximum drain-to-source current of 130 mA/mm,a high I$_{ON}$/I$_{OFF}$ of $>$10$^{10}$ with a high power FOM of 25MW/cm$^{2}$ were achieved without any field plates. Nanoparticle-assisted Ramanthermometry, thermal modeling, and infrared thermography were performed toassess the device self-heating under the high current and power conditions.This demonstration shows the promise of MOVPE technique for the realization ofhigh-performance lateral $\beta$-Ga$_2$O$_3$ devices and also highlights theneed for device-level thermal management.

130 mA/mm $\beta$-Ga$_2$O$_3$ MESFET with Low-Temperature MOVPE-Regrown Ohmic Contacts