High-performance AlGaN/GaN Schottky barrier diodes are fabricated on a composite AlGaN/AlN buffer layer with low screw-type and high edge-type dislocation densities. Without edge termination, the devices with 30-mu m anode-to-cathode spacing exhibit a high breakdown voltage (V(B)) of 3489 V, a low leakage current (I(R)) of less than 0.2 mu A at -2000 V, and a low specific on-resistance (R(on)) of 7.9 m Omega . cm(2), resulting in a figure of merit (V(B)(2)/R(on)) as high as 1.54 GW/cm(2). Their switching characteristics as revealed by the reverse-recovery transient waveform exhibit a short reverse-recovery time of 17 ns.