  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 high
conductivity with sheet resistance of 73 $\Omega$/$\square$ and a record
metal/n$^{+}$-Ga$_2$O$_3$ contact resistance of 0.08 $\Omega$.mm and specific
contact 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 25
MW/cm$^{2}$ were achieved without any field plates. Nanoparticle-assisted Raman
thermometry, thermal modeling, and infrared thermography were performed to
assess the device self-heating under the high current and power conditions.
This demonstration shows the promise of MOVPE technique for realization of high
performance lateral $\beta$-Ga$_2$O$_3$ devices and also highlights the need
for device-level thermal management.
