In this paper, a manufacturing process was developed for fabricating high-quality AlGaN/GaN high electron mobility transistors (HEMTs) on silicon carbide (SiC) substrates. Various conditions and processing methods regarding the ohmic contact and pre-metal-deposition $BCl_3$ etching processes were evaluated in terms of the device performance. In order to obtain a good ohmic contact performance, we tested a Ti/Al/Ta/Au ohmic contact metallization scheme under different rapid thermal annealing (RTA) temperature and time. A $BCl_3$-based reactive-ion etching (RIE) method was performed before the ohmic metallization, since this approach was shown to produce a better ohmic contact compared to the as-fabricated HEMTs. A HEMT with a 0.5 ${mu}m$ gate length was fabricated using this novel manufacturing process, which exhibits a maximum drain current density of 720 mA/mm and a peak transconductance of 235 mS/mm. The X-band output power density was 6.4 W/mm with a 53% power added efficiency (PAE).