Commercial on-axis wafers of 4H-SiC(0001) were etched in a standard reactor for chemical vapor deposition (CVD) using molecular hydrogen flux in order to improve the structure and morphology of the surface. The substrate temperature during etching was varied from 1400 to 1600° C. Characterization of the surface morphology was performed using optical and atomic force microscopy (AFM). Low-energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS) were also used to examine the surface structure and chemical composition of the samples. The sample of best quality was obtained for an etching temperature of 1400° C. Its surface is (√ 3x√ 3)R30° reconstructed and covered by an ordered "silicate" layer. Increasing the substrate temperature during etching to 1500° C leads to enhanced step-bunching and the formation of macro-terraces. At 1600° C distinct depressions appear on the surface, presumably from etching of structural defects such as screw dislocations. Subsequent annealing at 1000° C in ultra-high vacuum (UHV) removes the surface oxide and produces the (√ 3x√ 3)R30° surface phase of clean 4H-Sic(0001).