AlN thin films were grown by an alternate supply of trimethyl aluminum (TMA) and ammonia, i.e., according to the processing scheme of the atomic layer epitaxy (ALE) technique. In contrast with the ideal ALE process, no saturation of the growth rate was observed with increasing TMA pulse time. In addition, with fixed pulse times the growth rate was strongly temperature dependent. These observations were interpreted in terms of a self-decomposition of TMA. Despite the absence of self-limitation, the films were uniform and showed good structural quality. The deposition temperatures were remarkably low, 325-425 degrees C, compared with CVD processes employing the same precursors. Time-of-flight elastic recoil detection analysis (TOF-ERDA) and nuclear resonance broadening (NRB) measurements indicated that the films contained hydrogen, carbon, and oxygen impurities.