The growth of AlGaN/GaN modulation-doped field-effect transistors (MODFETs) by ammonia-molecular-beam epitaxy on sapphire substrates is reported. C-doped GaN (2 μm thick) was used as the insulating buffer layer in the device structures. The MODFET structure was completed by the subsequent growth of 2000 Å of undoped GaN as the channel layer and 130 Å of AlxGa1-xN(0.1≤x≤0.3) as the donor barrier layer. Sheet carrier densities of up to 2×1013 cm-2 with mobility of ∼1000 cm2/V s have been achieved even without doping the AlxGa1-xN barrier, indicating a large piezoelectric effect and excellent interface quality. The MODFET layers grown exhibited a unique surface morphology showing very flat plateaus with rms roughness of 0.8 nm on the plateaus and rms roughness of 8 nm over a larger area. A 100-μm-wide device with a 1 μm gate length exhibited a maximum dc current drive of 0.9 A/mm, a peak transconductance of 160 mS/mm, a current gain cutoff frequency of 15.6 GHz, and a maximum oscillation frequency of 49.4 GHz. The high dc and rf performance is attributed to the high two-dimensional electron mobility, high sheet charge density, and insulating property of the C-doped GaN buffer.