In‐Gap States in Electronic Structure of Nonpolar Surfaces of Insulating Metal Oxides

DOI: 10.1002/admi.201300131 which in principle can be used to identify the polarity of a surface, these include: electron counting model, [ 7 ] bond orbital model, [ 8 ] bond electron transfer model [ 9 ] and bound charge model. [ 10 ] Most of these models depend on the specifi cation of the chemical bonds, and the charge transfer through these bonds. However, it can be diffi cult to identify bonds in ionic oxides (e.g. BiVO 4 , SrTiO 3 ) because it is not always clear what should be the atom-atom distance cutoff to defi ne a bond. Besides, the possible surface reconstruction or relaxation can also make some of the above methods diffi cult to use. Here, we present an improved method to identify the polarity, which is more suitable for ionic systems. According to Tasker, [ 6 ] the surface of an ionic system can be classifi ed into three classes: those which do not have a net surface charge nor dipole moment, those with a surface dipole moment but no surface charge, and those that have a surface charge. While the fi rst two are defi ned as nonpolar surfaces, the last one is a polar surface. The polar surface is usually unstable for thick fi lms. In reality, its surface charges will often be neutralized by surface absorption (passivation) or reconstruction (in a way become nonpolar). Here, we will focus on nonpolar surfaces without passivation or reconstruction. According to our method, one fi rst needs to assign formal charges Z i to the ions in a crystal under consideration (e.g., Z i = –2 for O). In the next step, one constructs a slab with its surfaces parallel to the surface under consideration, and its thickness in the perpendicular zdirection being the same as the projected periodicity of the crystal to the z axis ( Figure 1 ). Then, this slab can be gradually moved in the zdirection. While it moves, the surface planes of the slab can cut through individual ions. We can assume the ion with Z i charge can be cut into two fractional charges α i ·Z F and (1–α i )·Z F below and above the slab surface plane, respectively (while the (1–α i )·Z F goes to the bottom of the slab). Now, obviously the total charge inside the slab must be zero, and one can calculate the zdirection dipole moment of the slab using all the atomic charges within the slab. When the slab cuts one ion into α i ·Z F and (1–α i )·Z F charges, its z -direction dipole moment will change with α i . One can always fi nd a position of the slab (a value of α i ) where the total z -direction dipole moment of the slab is zero. Now, one can sum over the charge left above the slab till the end of the surface. If the charge sum is zero, the surface is nonpolar, otherwise it is polar. In the case of a nonpolar surface, the zdirection dipole moment in the region above the slab will be the surface dipole moment defi ned in Tasker’s scheme. [ 6 ] The above method is easy to use and implement for routine analysis even for complex high index surfaces. Equipped with this procedure, we can now construct the nonpolar surfaces for a given oxide crystal. In this work, we will focus on closed shell semiconductor oxides with large band gaps. We will ignore the magnetic oxides and Mott insulators Oxide surfaces are important for many applications including energy storage, gas sensors, fuel cells, catalysis, and electronic devices. [ 1,2 ] Oxides are also used as insulating layers (e.g., in electronic devices), corrosion protection layers (e.g., for water splitting), batteries, thin fi lm transistors or dye-synthesized solar cells, and their interface or surface electronic states can signifi cantly infl uence the related carrier transports. Oxides are characterized by their complexity in crystal structures and the variability of their structures as functions of constitute metal elements. As a result, they often elude the study of trends in their properties. While the scientifi c community is actively searching for new oxides for different applications, there is an urgent need for understanding general trends in their properties to guide such searches. One example of such general understanding for bulk oxides is the Fermi pinning rule, and the observed diffi culty to dope large band gap oxides in p-type due to the appearance of oxygen vacancies. [ 3 ] However, there is still a lack of general understanding of the oxide surface electronic states, [ 4 ] in particular: under which conditions will the surface band gap state appear when there is no ligand passivation? Large volumes of literatures exist for individual oxide surface studies, [ 4–32 ] but little trend and not much systematic knowledge have emerged from such scattered studies. For main group semiconductors, it is generally understood that a surface termination without signifi cant reconstruction or surface ligand passivation will always create isolated surface in-gap states (IGS) within the bulk band gap due to the break of surface covalent bonds. [ 33,34 ] An electron counting rule and its relevance to the surface passivation of covalent bonding main group semiconductors has been established. [ 5 ] The existence of IGS is important for charge transfer from the bulk to the surface, hence will infl uence many applications. However, oxides can be viewed as between covalent and ionic bonding, and their properties can be very different from that of main group semiconductors. In this communication, through ab initio calculations, we found that, for all the d 0 transition metal oxide nonpolar surfaces considered here, none of them has IGS isolated states inside the band gap. We will discuss the reasons for this phenomenon, and hypothesize that this could be a general rule for d 0 transition metal oxides. We will start with a simple procedure to identify the polarity of a given general surface. There are already many models,