A multistep pulsed-laser deposition (PLD) process is presented for epitaxial, nominally undoped ZnO thin films of total thickness of 1 to 2 μm on c-plane sapphire substrates. We obtain reproducibly high electron mobilities from 115 up to 155 cm2/V s at 300 K in a narrow carrier concentration range from 2 to 5×1016 cm-3. The key issue of the multistep PLD process is the insertion of 30-nm-thin ZnO relaxation layers deposited at reduced substrate temperature. The high-mobility samples show atomically flat surface structure with grain size of about 0.5–1 μm, whereas the surfaces of low-mobility films consist of clearly resolved hexagonally faceted columnar grains of only 200-nm size, as shown by atomic force microscopy. Structurally optimized PLD ZnO thin films show narrow high-resolution x-ray diffraction peak widths of the ZnO(0002) ω- and 2Θ-scans as low as 151 and 43 arcsec, respectively, and narrow photoluminescence linewidths of donor-bound excitons of 1.7 meV at 2 K. © 2003 American Institute of Physics.