Thin AlN films were grown using a Beneq TFS-200 ALD reactor. TMA (trimethylaluminium) and NH3 were used as precursors. The substrate temperature was 330 °C, the ALD cycles, 550. The TMA and NH3 doses (pulses) lasted 180 ms and 90 ms, followed by 2-s and 9-s nitrogen gas purge, respectively. In order to study the morphological evolution of the thin AlN films, substrates providing different surface kinetics were used: Si-face and C-face of 4°-off axis and on-axis 4H-SiC, and graphene grown on 4H-SiC by sublimation. As revealed by atomic force microscopy (AFM), the lowest RMS surface roughness of about 0.8 nm was exhibited by the AlN film deposited on Si-face on-axis 4H-SiC due to its higher surface energy which provides for better film nucleation. The chemical composition and bonding states were investigated by X-ray photoelectron spectroscopy (XPS). The existence of AlN is justified by the presence of the XPS peaks of Al 2p and N 1s at about 73.3 eV and 396.6 eV, respectively. These results are promising in view of further studies of thin AlN films properties for application in surface acoustic wave devices (SAW).