First-principles calculations are performed to study the adsorption of oxygen at wurtzite AlN ͑0001͒ and ͑0001͒ surfaces as a function of oxygen coverage. We find that the adsorption of oxygen at the AlN ͑0001͒ surface has a larger binding energy than at the AlN ͑0001͒ surface. The hollow site ͑H3͒ is preferred for the ͑0001͒ surface, whereas the site directly above the Al sublayer and the H3 site are almost degenerate in energy for the ͑0001͒ surface. The trend of the adsorption energy as a function of the oxygen coverage for the AlN ͑0001͒ surface is similar to that of GaN, whereas for the AlN ͑0001͒ surface it is different from GaN. The asymmetry of the oxygen adsorption at the two surfaces is explained using the electron counting rule and the resulting surface electronic states.Surface study is an indispensable subdiscipline of materials research. 1 A microscopic determination of semiconductor surface structures is crucial in understanding its material properties and can provide important guidance to tune material properties during crystal growth. AlN is one of the IIInitride semiconductors, which has great potential for highpower, high-temperature UV photoelectronic devices. 2 Some work has been done in the past to study AlN surface properties, such as surface reconstruction, 3-7 surface band structure, 8 and surface phonons. 9,10 Oxygen is one of the most abundant unintended impurities incorporated in crystal lattice or adsorbed at surface in III-nitrides. Unlike in GaN where O behaves as a shallow donor, it acts as a deep center in AlN due to the wide band gap of AlN. 11 Experimental studies have also shown that O absorption at the AlN surface has effects on the surface roughness, 12 surface chemical stability, 13 surface contact with metal, 14 surface acoustic properties, 15,16 and thermal conductivity. 17 However, there is a lack of theoretical study of oxygen adsorption at the AlN surface. It is not clear where the stable oxygen absorption site is and what is the dependence of the stability and surface electronic structures on the surface polarity and coverage.In this work, we performed first-principles calculation to investigate the adsorption of oxygen at wurtzite AlN ͑0001͒ and ͑0001͒ surfaces, which are the two most common surfaces of all III-nitrides. We calculated the adsorption energies of various oxygen coverages at three possible adsorption sites. We show that the adsorption of oxygen at the Aladlayer-terminated ͑0001͒ surface is more exothermic than at the AlN ͑0001͒ surface. The hollow site ͑H3͒ is preferred for the ͑0001͒ surface, whereas the site directly above the sublayer ͑T4͒ and the H3 site are almost degenerate in energy for the ͑0001͒ surface. Electronic structure calculations show that the calculated results can be understood using simple electron counting rules applied to these semiconductor surfaces.The calculations are performed employing the general gradient approximation 18 within the first-principles densityfunctional theory. We used the plane wave basis and the Vanderbilt ultr...