The atomic layer deposition (ALD) of aluminum oxide (Al2O3) from trimethylaluminium and water on silicon nitride was studied on as-received and HF-cleaned Si3N4 surfaces. In situ spectroscopic ellipsometry during ALD, X-ray photoelectron spectroscopy, X-ray reflectivity, and time-of-flight secondary ion mass spectrometry were used to elucidate the growth rate, the chemical composition, and the density of Al2O3. The effect of the substrate cleaning and of the growth temperature -varied in the 150–300 °C range- were analyzed by considering first-principles calculations of the early stages of the growth on both Si3N4 and SiO2 surfaces. Our work evidenced how not only complete ALD cycles but also complementary non-ALD reactions can account for the observed peculiarities related to the enhanced or inhibited growth rates on the Si3N4 surfaces as a function of temperature.