Thin AlN films were grown in a Picosun R-200 atomic layer deposition (ALD) reactor on Si substrates. Trimethylaluminium (TMA) and NH3 were used as precursors; the substrates were cleaned in-situ by H-2 and N-2 plasma. The surface morphology of the films grown was studied in the temperature range 350 - 450 degrees C. The films crystalline structure was investigated by grazing incidence X-ray diffraction. The AN films were polycrystalline with a hexagonal wurtzite structure regardless of the substrate temperature. The results of scanning electron microscopy (SEM) revealed nanometer-sized crystallites, with the size increasing from 10 nm to 30 nm as the deposition temperature was increased. The results are promising in view of further studies of the properties of thin AN films.