In this letter, we demonstrate high-performance AlGaN/GaN Schottky barrier diodes (SBDs) on Si substrate with a recessed-anode structure for reduced turn-on voltage Formula Omitted. The impact of the surface roughness after the recessed-anode formation on device characteristics is investigated. An improved surface condition can reduce the leakage current and enhance the breakdown voltage simultaneously. A low turn-on voltage of only 0.73 V can be obtained with a 50-nm recess depth. In addition, the different lengths of Schottky extension acting like a field plate are investigated. A high reverse breakdown voltage of 2070 V and a low specific ON-resistance of 3.8 Formula Omitted yield an excellent Balig's figure of merit of 1127 MW/cm2, which can be attributed to the low surface roughness of only 0.6 nm and also a proper Schottky extension of 2 Formula Omitted to alleviate the peak electric field intensity in the SBDs.