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Record power density and high-efficiency operation with AlGaN-GaN high-electron mobility transistor (HEMT) devices have been achieved by adopting a field-plated gate-recessed structure. Devices grown on SiC substrate yielded very high power density (18.8 W/mm with 43% power-added efficiency (PAE) as well as high efficiency (74% with 6 W/mm) under single-tone continuous-wave testing at 4 GHz. Devices also showed excellent linearity characteristics when measured under two-tone continuous-wave signals at 4 GHz. When biased in deep-class AB (33 mA/mm, 3% Imax) device maintained a carrier to third-order intermodulation ratio of 30 dBc up to a power level of 2.4 W/mm with 53% PAE; increasing bias current to 66 mA/mm (6% Imax) allowed high linear operation (45 dBc) up to a power level of 1.4 W/mm with 38% PAE.