J. Phys. Chem. B 2002, 106, 2269-2276
2269
Electronic Properties of Structural Defects at the MgO (001) Surface Peter V. Sushko, Jacob L. Gavartin, and Alexander L. Shluger* Department of Physics and Astronomy, UniVersity College London, Gower Street, London WC1E 6BT, UK ReceiVed: July 31, 2001; In Final Form: NoVember 1, 2001
We have calculated the ionization energies, electron affinities, optical excitation energies, and relaxed electron and hole states at corners, kinks, and steps of the MgO (001) surface. The calculations are performed using an embedded cluster model and density functional theory and take into account the long-range surface polarization. The extent of localization of electronic states associated with specific structural defects at the surface is studied by the participation function method. The positions of energy levels of the surface sites with respect to the top of the surface valence band and the vacuum level are determined. The results demonstrate the existence of deep and shallow electron traps at steps, corners, and kinks of the MgO (001) surface, and establish direct correlation between common surface features and their spectroscopic and other electronic properties.
I. Introduction Understanding of the structure and electronic properties of defects at oxide surfaces is crucial for their applications as substrates, sensors, catalysts, and coatings. The role of surface steps, kinks, and vacancies in adsorption, dissociation, and reactions of gas-phase species at surfaces is well appreciated. More details of geometric structure of oxide surfaces are starting to emerge at nanoscopic scale due to recent advances in atomic force microscopy (AFM) and other surface-sensitive techniques (see, for example, refs 1-6). However, clear correlation between structural surface features and their electronic properties is still lacking. Although there is growing evidence that coordination of surface ions plays a crucial role in spectroscopic and chemical properties of oxide (and generally ionic) surfaces, to establish a direct correlation experimentally proved to be extremely difficult. These surface properties are important for many applications. Common examples include: surface charging after cleavage in a vacuum and under electron and photon irradiation;7 photocatalytical reactions at oxide surfaces,8,9 laser-induced desorption,10,11 leakage current at silicon-oxide interface,12 growth and properties of metal films and nanoparticles on oxides.13 Yet which particular surface features are excited at which photon energies, and the nature of electron and hole trapping sites largely remains unknown. Some basic questions include (i) optical absorption spectra and ionization energies of particular surface features, e.g., terraces, steps, corners, vacancies etc., and (ii) localization sites and properties of electron and holes produced at surfaces by irradiation, cleavage, polishing, and chemical or thermal treatment. Similar mystery surrounds the processes of charge and energy transfer between different surface features. These difficulties are partly due to the well-known problems of surface spectroscopy on insulators14 and partly due to the fact that electrons, holes, and excitons created by irradiation are mobile. For example, ionization of a surface terrace may result in formation of an electron paramagnetic resonance (EPR) active O- species at a surface kink or a corner (see, for example, discussion in refs 15-18). Therefore, optical spectroscopy and EPR of irradiated surfaces often deal not with the initial products but rather with stable species localized at defects and terminating surface sites.
Significant progress achieved on relatively simple cubic oxides provided some useful insights into the properties of surface features. In particular, the reduced ion coordination in these crystals leads to significant changes in the crystalline potential, which have been correlated with the chemical properties of the low-coordinated surface sites (see, for example, recent discussion19). The direct relation between excitation and luminescence energies and coordination of surface sites of powdered MgO and CaO has been proposed in a series of works in the seventies and eighties,15,20-24 and recently confirmed theoretically.25,26 These works demonstrated a dramatic dependence of excitation energies on the number of nearest neighbor cations surrounding surface oxygen ions. Extensive EPR studies show the existence of strongly localized hole and electron states at surfaces.15-17,27,28 There have been suggestions that electronically excited states and electrons produced at surface terraces can travel to less coordinated sites, such as kinks and corners.15,22 It has been shown that selective excitation or ionization of 3-coordinated sites creates stable species, such as O- ions observed by EPR.18 These results suggest a hierarchy of surface electronic states with different coordination and long-range environment, and charge transfer between these states. To build a complete model of surface electronic states even for one particular substance is a formidable task. Ideally, such a model should provide a direct correspondence between particular surface features, e.g., step edges, kinks, and corners, and their excitation and ionization energies, and electron and hole affinities, as well as their ability to trap electrons and holes. A complete picture would serve as a road map for our understanding of surface processes under electronic excitation. Several recent papers have been concerned with the surface electronic excitation of oxides in conjunction with photoinduced reactions (see, for example, refs 29-31). However, most previous theoretical studies (see, for example, recent review32 on MgO) have been focused on modeling adsorption of various species and did not address these issues. Recently metastable impact electron spectroscopy (MIES) combined with theoretical calculations allowed us to determine the position of the top of the MgO surface valence band with respect to the vacuum level.33 This provided a framework for building a map of excitation
10.1021/jp0129481 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/05/2002
2270 J. Phys. Chem. B, Vol. 106, No. 9, 2002
Figure 1. Surface features considered in this study: (a) corner; (b) step corner; (c) kink; (d) corner vacancy; (e) terrace vacancy; (f) step edge.
and ionization energies and electron affinities of defects and common structural features at the MgO surface. In this paper we extend this work by including step edges, kinks, and corners, which are abundant at surfaces of cleaved and powdered samples. After calculating ionization energies and electron affinities we study localization and stability of electrons and holes at these surface features. This is important for our understanding of which surface features are likely to be (selectively) optically excited or ionized by which wavelength, and what will happen to the subsequently produced electrons and holes. In particular, we demonstrate that extra electrons can be easily trapped at three-coordinated surface magnesium sites and holes at three-coordinated oxygen sites, such as kinks and corners. The MgO (001) surface demonstrates a great variety of features that depend on its preparation.1,2 Our consideration is therefore inevitably based on simplified models, such as straight steps, normal corners, and simple kinks (see Figure 1a-c,f). However, even these simplest surface features are not trivial to model using quantum-mechanical methods. Out of the two principal possibilities, periodic34-36 and cluster models, in this paper we have chosen an embedded cluster model. In this model the electronic states are localized in a relatively small quantum cluster embedded in the surrounding lattice as discussed below. This is a good model for well-localized systems, such as vacancies or adsorbed molecules. However, the applicability of this model to the electron and hole states at surface steps or kinks is not known a priori. Therefore, we first investigate the extent of localization of the electronic states associated with specific structural defects at the surface using the participation function method.37,38 The localization length determines to what extent the results of our calculations depend on the cluster size and thus provides a basis for using an embedded cluster model to study the electronic properties of surface sites. In section III, we report the ionization energies (IP) and electron affinities (EA) of the low-coordinated surface sites shown in Figure 1. We determine the positions of the energy levels of the surface sites with respect to the top of the surface valence band and the vacuum level. Next we calculate the energies of electrons and holes at differently coordinated surface sites and discuss whether these defects can serve as electron and hole traps at the surface. Finally, the optical excitation energies of the step, corner, and kink sites are calculated and compared with the results of previous calculations. II. Analysis of Localization of Surface Electronic States Using Participation Function Approach MgO is a wide-gap ionic insulator, and its bulk and surface properties in the ground electronic state can be well described in the embedded cluster model.25,26,32,33,39 In ref 33 we have studied the dependence of the valence bandwidth and of the
Sushko et al. position of the top of the surface valence band of MgO with respect to the vacuum level as a function of the embedded cluster size and have demonstrated a rapid convergence of these properties. However, the excited states, such as extra electrons and holes or excitons, can be strongly delocalized and possibly have effective lengths much larger than any feasible quantum cluster size. Then the embedded cluster model may not be applicable any more. Therefore, before embarking on extensive ab initio calculations of these systems, it is useful to estimate whether characteristic localization length of these states is expected to be such that they can be treated in a cluster model. In this section we therefore calculate the local geometry and electronic structure of corners, kinks, and a step edge at the MgO (001) surface and characterize localization of their electronic states using a participation function approach. II.1. Details of Calculations. To characterize the electronic states associated with low-coordinated surface sites we use a finite nanocluster of rectangular shape, which includes 14 × 14 × 5 ions. In addition to corners and edges, which are already present in this cluster, one of the terraces was modified to accommodate steps, step corners, and kinks. The surface features studied for the localization of their electronic states are shown in Figure 1. To calculate the geometry of the nanocluster and the local geometries of the low-coordinated sites we used the classical technique with the shell model40 for oxygen ions and the rigid ion model for magnesium ions. All the ions interact via the interatomic potentials.41 The total energy of this system was minimized with respect to the positions of all ions using the GUESS code.33,42 As demonstrated in several previous studies (see, for example, refs 33, 34, 43), the relaxation of the surface structure significantly changes the ideal bulk termination geometry, especially at steps and kinks, and transforms it into a more rounded shape (see also discussion below). The electronic structure of the whole nanocluster was calculated using a semiempirical INDO method implemented in the SYMSYM computer code44,45 and the parametrization scheme described in refs 46, 47. The molecular orbitals and the corresponding one-electron energies were analyzed using the participation function approach described below. II.2. Participation Function Analysis. The participation function (PF) approach provides means for characterizing localization of the Hartree-Fock one-electron states. It is similar to that described in ref 38. In this section we outline the features of the PF approach essential for the present study. The orthonormal one-electron functions φ resulting from INDO calculation are expanded over Slater-type basis functions (χs) centered on each of the nanocluster ions (s): Natm ns
φi )
∑s ∑k asik χsk
where s runs through all atom s ) 1,..., Natm, and k through orbitals on each atom, the number of which is equal to ns. Using the coefficients asik of the expansion above, one can define atomic weights that would reflect qualitatively the delocalization of the one-electron state φi over atoms of the system ns
wsi )
∑k (asik)2
The participation function for each state i is defined as
Structural Defects at the MgO (001) Surface
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2271
Natm
Pi ) 1 +
∑s (wsi )2
In practical calculations it is more convenient to use an inverse ) 1/Pi. Using the same atomic participation function Pinv i weights wsi one can define an effective radius-vector Rieff for a state i
Rieff )
∑s wsi rs
where rs is the radius-vector of atom s, and the effective localization length Lieff is defined as Natm
Lieff )
∑s wsi |Rieff - rs|
If a one-electron state is predominantly localized on one atom, the corresponding atomic weight is close to unity while all other weights are negligible. Consequently, the inverse participation function Pinv ) 1/2 and the effective localization length Lieff ) 0. In the case of a completely delocalized state, all atomic weights are the same and equal to 1/Natm, and the inverse participation function is close to unity. The effective localization length is then close to the characteristic size of the system. Finally, we should note that definitions of participation function and localization length adopted in this paper are in fact not unique and rather provide a convenient framework for further analysis of the electronic states. II.3. Localization of Surface Electronic States. As already mentioned, the whole nanocluster of more than 800 ions, which accommodates the surface defects shown in Figure 1, was calculated using the INDO method. The results of these calculations and the participation function analysis can be summarized as follows. The density of one-electron states (DOS) exhibits tails at the top of the valence band and at the bottom of the conduction band (note that the one-electron states are smeared with Gaussians with an exponent equal 0.1 eV). These tails are about 1.0 eV long, depending on the concentration of low-coordinated surface sites. They are clearly seen in Figure 2 where we presented the DOS for the upper valence band only. The inverse participation function calculated for all states in the middle of the valence and conduction bands is associated with the bulk atoms and is very close to unity. This suggests that these states are delocalized. On the contrary, the inverse participation function for the states in the tails of the DOS is smaller than unity and for some states is close to 0.65, which corresponds to almost complete localization. Analysis of the corresponding canonical molecular orbitals suggests that most of these localized states are associated with 3-coordinated ions. This is supported by further analysis of effective localization lengths of electronic states also shown in Figure 2. One can clearly see that the bulk states in the middle of the valence band are delocalized and have effective localization lengths of the order of 10-14 Å, which correspond to the size of the nanocluster. The electronic states associated with nanocluster edges have even larger effective localization lengths. This reflects their delocalization over several edges. Finally, several highest occupied states, which are associated with 3-coordinated surface ions and have energies in the tails of the DOS, have small effective localization lengths of the order of 2-5 Å. Thus the results of the INDO calculations and the participation function analysis suggest that the electronic states associated
Figure 2. Density of electronic states (DOS) and localization lengths for electronic states in the nanocluster used to analyze the electron localization at surface defects.
with 3-coordinated surface features are localized and their effective localization lengths are of the order of several Ångstroms. The one-electron states associated with steps, terraces, and these in the bulk are delocalized. Their effective localization lengths are of the same order of magnitude as the system size, e.g., step length or terrace area. It has been noted in several studies of localization of hole, electron, and exciton states in insulators (see, for example, refs 48-51) that the Hartree-Fock method tends to favor strong localization due to the lack of the electron correlation. Therefore, our HartreeFock-based INDO calculations are likely to result in underestimated effective localization lengths. Nevertheless, we believe that these predictions are qualitatively meaningful. They clearly suggest that the results of calculations of vertical ionization energies and electronic excitations of steps and terraces will depend more strongly on the size of the QM cluster than these for corners and kinks. Calculations of electron affinities may require even more extra care as description of a weakly bound extra electron may strongly depend on a method used.49-51 III. Structure and Electronic Properties of Surface Defect Sites III.1. Embedded Cluster Method. To calculate the electronic structure and properties of different surface sites we employed an embedded cluster model similar to that used in refs 26, 33, 42. In this model, a cluster of ions treated quantum- mechanically (QM cluster) is embedded in a large nanocluster of ions treated classically. This approach can be used to model properties of small nanoclusters produced, e.g., by chemical vapor deposition, as well as infinite solids. In the latter case, the nanocluster should be large enough so that the rest of the crystal would have negligible effect on the modeling of processes at the site of interest. The rectangular nanocluster used in the present study contains 20 × 20 × 20 ) 8000 ions, with the total charge and total dipole moment equal to zero. This provides correct variation of the electrostatic potential inside the nanocluster. The nanocluster is divided into two regions as shown in Figure 3: all ions in region I are relaxed in the course of the calculation, all ions in region II are kept fixed. Ions in region II are represented using the classical shell model40 and serve to produce correct electrostatic potential inside region I. Region I
2272 J. Phys. Chem. B, Vol. 106, No. 9, 2002
Sushko et al. TABLE 2: Parameters of the Local Geometry Relaxation and Values of the Electrostatic Potential for the 3-Coordinated Sitesa corner a,
Figure 3. Schematic representation of the embedded cluster model.
TABLE 1: Calculated Values of Ionization Energies and Electronic Affinities for Different Surface Sites (eV)a surface site
QM cluster + Interface
electron affinity ionization energy unrelaxed relaxed
Mg2+ corner Mg2+ step corner Mg2+ kink O2- corner O2- step corner O2- kink step edge surface terrace
Mg4O10Mg*15 Mg5O6Mg*12 Mg5O7Mg*17 Mg10O13Mg*15 Mg10O12Mg*20 Mg9O10Mg*17 Mg12O13Mg*22 Mg25O25Mg*37
7.0 7.3 7.5 6.0 5.7 5.3 6.4 6.5 [28]
0.0 0.6 1.1
0.6 (1.5)b 1.4 (2.5)b 2.0 (2.9)b
-0.1 -0.6
a Mg* in the cluster notations stands for Mg ions at the QM cluster interface (see Figure 3). The electron affinities for the step edge and terrace are given for the best basis set used in our calculations (see text for details). b Vertical ionization energies of relaxed 3-coordinated Mg+ sites.
is centered at the site of interest (shown as a step edge in Figure 3). It is further divided into three subregions: classical shell model ions (Figure 3), QM cluster, and a shell of the interface ions between them. The shell model ions provide a polarizable environment for a defect treated in the QM cluster. QM cluster and Interface region used in this work consist of three types of ions: (i) all electron O ions, (ii) all electron Mg ions, and (iii) interface Mg* ions. The latter have dual properties. Their interaction with the QM cluster is described using semi-local effective core pseudopotentials52 and they carry a single s-type Gaussian basis function. At the same time, they interact with other classical ions and between each other via classical shell model potentials. This interface is needed in order to prevent an artificial spreading of electronic states out of the QM cluster due to attraction of electrons to positive point charges in classical region. Thus, all O ions in the QM cluster are coordinated by either all-electron or effective core pseudopotential Mg* ions. To compare results, the calculations were made for QM clusters, which contained similar numbers of all-electron magnesium and oxygen ions. These clusters are listed in Table 1. We should note that QM clusters with the number of all-electron O ions much larger than that of Mg ions (such as Mg3O13Mg22* used in ref 33) have an excess number of electrons and lead to less accurate results than more stoichiometric clusters used in this work. This calculation scheme is implemented in a computer code GUESS,33,42 which interfaces the shell model based method with the Gaussian98 code.53 This interface allows us to calculate forces on quantum and classical ions and simultaneously optimize their positions using an effective energy minimization procedure, as described in refs 33, 42. The calculations were carried out using the density functional theory (DFT) and the B3LYP functional.54 The standard 6-31G basis set was used for all-electron ions in the QM cluster in most of the calculations. However, larger basis sets were used in several test calculations. The dependence of the results on the basis set for defects at the MgO(001) terrace has been addressed in ref 33.
Åa
O site
Mg site
2.01
1.96
surface corner O site
Mg site
kink O site
Mg site
1.98 1.92 1.93 1.89 1.98 1.92 1.99 1.96 2.03 2.04 1.99 1.99 R, deg xy 92.14 100.62 91.70 100.11 95.78 104.56 xz 97.97 102.97 100.30 105.26 yz 97.97 102.97 94.26 99.39 d, Å 0.57 0.76 0.58 0.69 0.50 0.58 φsite, eV 15.72 -16.51 16.34 -15.14 16.49 -14.23 φnn, eV 19.62 (4) 20.95 (4) 21.72 (4) 20.95 (4) 22.32 (5) 21.81 (6) 22.31 (6) a The parameter a is the Mg-O distance at the 3-coordinated site, in Å; R is the O-Mg-O or Mg-O-Mg angle, where the middle ion is 3-coordinated; d is the displacement of a 3-coordinated ion from its ideal position after the geometry optimization in Å; φsite is the electrostatic potential on the terminating ions; φnn is the electrostatic potential at the nearest neighbors (oxygen ions) to the 3-coordinated Mg ion (numbers in brackets are coordination numbers of the oxygen ions), in eV. The bulk lattice constant is equal to 2.11 Å.
The calculations of optical excitation energies were carried out using the time-dependent DFT method implemented in the Gaussian98 package.53 III.2. Results of Calculations. (a) Structure of Surface Defects. The three types of 3-coordinated surface sites and a surface step edge considered in this study are shown in Figure 1. The cation- and anion-terminated 3-coordinated sites include (i) a corner terminated by three (001) terraces (called “corner” hereafter, Figure 1a), (ii) a corner at the (001) surface terrace formed by two monatomic steps (“step corner”, Figure 1b), and (iii) a 2 × 1 kink at the surface (“kink”, Figure 1c). The structure of these surface defects is characterized by strong relaxation from ideal geometries. The previous studies26,33,34,43 demonstrated that the relaxation of steps and corners tends to round these features by displacing the low-coordinated ions inside the surface. First, we discuss the geometric structure of 3-coordinated surface sites, which are important for further understanding of their electronic properties. As was shown in our recent work,33 the calculated geometry of the corner depends on the size of region I allowed to relax. Expansion of region I involves more ions and affects the relaxation energy. However, convergence of the corner ionization potential is less affected by displacements of ions far from it and is much faster. We checked that the radius of region I of 14 Å used in this work provides the convergence of the corner ionization potential. In Table 2 we compare the geometrical parameters of the three types of Mg and O 3-coordinated surface sites calculated for similar sizes of region I. One can clearly see that the relaxation with respect to the ideal geometry is very significant and it is larger for the Mg site than for the O site. The latter is manifested both in the overall displacement of an ion, d(relaxed - ideal) and in larger angles and smaller Mg-O distances. Comparison with relaxation of these features calculated using the classical shell model and interatomic potentials demonstrates that the difference in the relaxation of the O and Mg terminated features is due to the difference in ionic radii and polarizabilities, and more importantly due to electron density redistribution on surface features. The differences in the geometric relaxations are also manifested in the marked difference in the electrostatic potential on surface ions and in a trend for the three types of surface features also shown in Table 2. The values of electrostatic potential were
Structural Defects at the MgO (001) Surface
J. Phys. Chem. B, Vol. 106, No. 9, 2002 2273 TABLE 3: Character of Localization of the Electron Hole and Additional Electron on the Surface Sitesa hole localization, e surface site Mg2+
ions
corner all surface O Mg2+ step corner edge O terrace O Mg2+ kink edge O terrace O O2- corner corner O O2- step corner corner O O2- kink corner O step edge edge O
Figure 4. Energy diagram of ionization energies of surface oxygen vacancies and low-coordinated sites (see Figure 1). Neutral oxygen vacancies are denoted as F, single positively charged anion vacancies are denoted as F+ in correspondence with their notations as F centers. Va corresponds to a bare vacancy, which has a charge +2e with respect to the lattice.
calculated using the fully optimized geometries and the charges on the quantum ions calculated using natural population analysis (NPA).55 The charges on the classical ions were equal to (2e (where e is the electron charge). First, we note that the electrostatic potentials on the O and Mg sites are different and demonstrate an opposite trend going from a simple corner to a kink. Second, the absolute values of the electrostatic potential on the 3-coordinated ions and the neighboring ions are also very different. These factors determine the ionization energies and electron affinities of these sites discussed below. (b) Ionization Energies of Surface Sites. The calculated ionization energies for a number of surface defects are summarized in Table 1 and schematically shown in Figure 4. Let us first consider the Mg terminated 3-coordinated surface sites. They all have three nearest neighbor oxygen ions, but the number of farther neighbors is different. The participation function analysis suggests that the electronic states associated with 3-coordinated sites should be localized. Therefore, we do not expect vertical ionization energies calculated for these sites to depend significantly on the cluster size. As one can see in Table 1, the ionization energies for these sites increase from 7.0 eV for the corner to 7.3 eV for the step corner and to 7.5 eV for the kink. The ionization energies for the O-terminated 3-coordinated sites show a reverse trend decreasing from the corner to the step corner and to the anion kink. (We note that the ionization energy for the O corner is by about 0.3 eV higher than that obtained in ref 33 due to a more stoichiometric cluster used in this work.) This tendency can be explained using the electrostatic potential data shown in Table 2. A relatively small electrostatic potential at an O corner site leads to electron delocalization. Hence the highest occupied electron state, which is ionized, is delocalized over the corner oxygen, and surrounding terrace and edge oxygen ions. This is reflected in the charge density distribution of the hole state after the vertical ionization shown in Table 3. This delocalized state has a lower kinetic energy than more localized states at the step corner and the kink and thus a higher ionization energy. On the other hand, the ionization of Mg terminated three-coordinated sites takes place from electronic states, which are delocalized over the oxygen ions on the edges and terrace sites of the quantum cluster (see Table 3 for the hole electron density distribution). As one can see in Table 2, the electrostatic potential on the edge ions increases as one goes from the simple corner to the kink geometry. This correlates with the increase in the ionization energy.
n×∆Q
electron localization, e ions
n×∆Q
∼ 0.1 corner Mg 1 × (-0.78) 2 × 0.14 corner Mg 1 × (-0.75) 3 × 0.18 1 ×0.13 corner Mg 1 × (-0.74) 2 ×0.24 1 ×0.36 1 × 0.68 1 × 0.51 3 × 0.15
a Only major contributions are shown. ∆Q is the charge difference between the initial and final states after ionization (hole localization) or addition of an extra electron to the system (electron localization) calculated using the natural population analysis; n is the number of ions experiencing significant charge redistribution.
Figure 5. Energy diagram of electron affinities of surface defects. All notations are as in Figure 4. Dashed and continuous lines correspond to unrelaxed and relaxed electron affinities, respectively.
According to our previous calculations25,33 and the participation function analysis discussed above, the states associated with the surface terrace and the step edge are expected to be delocalized. Consequently, we expect the calculated ionization energies to depend on the size of the QM cluster. In ref 33 we investigated this dependence for the terrace using a set of clusters of different surface area and found that the ionization energy gradually decreases as the size of the cluster increases. For our largest QM cluster and the 6-31G basis set we have obtained the ionization energy for a terrace of 6.5 eV, in good agreement with experimental data.33 This value can be compared with the ionization energy of 6.4 eV calculated for the step edge in this work. As expected, in this case the hole is equally delocalized over three anions located at the step edge (see Table 3). In our calculations for the terrace the electronic hole was delocalized over nine surface anions. Correspondingly, a cluster containing nine anions along the step is required to achieve similar delocalization of the hole at the step edge. This makes further investigation of the convergence of this value with respect to the cluster size too computationally demanding. Nevertheless, we note that the obtained value of 6.4 eV fits into the general tendency that the ionization potential decreases with coordination from about 6.5 eV for a terrace to about 6.0 eV for a corner and 5.3 eV for a kink (see also Figure 4). (c) Electron and Hole Affinities. The electron affinities (EAs) of different surface features are summarized in Table 1 and in Figure 5. First, we note that Mg-terminated 3-coordinated sites have quite large electron affinities. This result can be rationalized if one takes into account the large value of EA of free Mg2+
2274 J. Phys. Chem. B, Vol. 106, No. 9, 2002 ion (the experimental value of EA is 15.03 eV and it is equal to 15.4 eV in our calculations). In the bulk of MgO crystal, this electron affinity is practically eliminated by the Madelung potential. However, the Madelung potential decreases rapidly as the Mg coordination decreases, and at the Mg corner and other 3-coordinated sites it becomes comparable to the EA for a free ion (see Table 2). The trapped electron is almost entirely localized at the terminating Mg ion, which thus becomes close to Mg+ (see Table 3). The calculated relaxed electron affinities of 3-coordinated Mg sites of 1-2 eV demonstrate that they can serve as electron traps. This conclusion is supported by the vertical ionization energies also presented in Table 1. The character of relaxation of 3-coordinated Mg sites on trapping an electron depends on a particular configuration. The Mg ion at a corner moves along the (111) axis away from the three nearest oxygen ions. The Mg ion at a step corner is displaced along the (001) axis (almost perpendicular to the surface terrace) away from the surface. Finally, the Mg ion at a kink moves approximately along the (111) axis away from the surface. This outward displacement of Mg ions is caused by the reduced Coulomb interaction with the nanocluster ions. Naturally, the question arises as to whether the Mg-terminated 3-coordinated sites can trap a second electron. Our calculations predict negative values for the second electron affinity for corner sites. We have also calculated the vertical electron affinity of the step edge and examined its dependence on expansion of the basis set. The EA calculated using the 6-31G basis set was -0.5 eV. As we extended the basis set to 6-311G and then to 6-311+G for O ions and to 6-311G for Mg ions, the EA increased gradually to -0.4 eV, -0.2 eV, and reached -0.1 eV for our largest basis set. In all three cases the additional electron was delocalized over 4-coordinated Mg ions along the step. This result can be compared to our previous calculations of EA on the surface terrace33 using the same method and basis sets. The largest value of EA for the surface terrace was -0.56 eV. In other words, our results predict negative affinity in both cases and suggest that at a step it is larger than at a surface terrace. Both energies are most probably overestimated due to the small number of atoms in the quantum cluster. We were unable to calculate the relaxed EA for the step because the relaxation led to an artificial localization of the additional electron at the boundary of the QM cluster. Similar to the issue of electron ionization, one can also ask how stable are trapped holes or O- species with respect to delocalization into the valence band. Or, in other words, how much energy it will cost for an electron from the valence band to become trapped onto a low-coordinated O- ion. To address this question we calculated vertical excitation energies for electrons from the valence band into the unoccupied state of relaxed holes localized at 3-coordinated anion sites (Figure 1ac) using the TD-DFT method. We note that the lowest energies correspond to the electron (hole) transfer between the states localized on the 3-coordinated O ion itself (within its 2p electronic shell). They determine the values of g-tensor and are not discussed here. The higher excited states correspond to the hole transfer from a defect state and delocalization over the step and terrace O ions of the same coordination. These excitations start from about 1.0 eV for a corner, 1.2 eV for a step corner, and 1.5 eV for a kink (see Table 4) and represent the vertical electron affinity of these surface defects. The relatively small electron affinities suggest that holes can be easily delocalized at higher temperatures. For example, the O- species observed
Sushko et al. TABLE 4: Absorption Energies (TD-DFT) for Surface Terrace, Step Edge, and Anion Terminated 3-Coordinated Sites, eVa optical absorption surface site
this work
experiment
terrace step edge O2- corner O2- step corner O2- kink 2 × 1
5.3 4.8 3.6 3.7 3.7
6.6 [14], 6.2 [47] 5.8 [14] 4.6 [14]
hole excitation
1.0 1.2 1.5
a Hole excitation corresponds to transfer of the electronic hole from its localized state at an oxygen-terminated site into a delocalized state in the valence band (see text for details).
at room temperature by EPR in MgO powders16 can be eliminated by thermal treatment. (d) Optical Absorption Energies. To complete this study and to compare the results using different methods, we have calculated the optical absorption energies for the terrace, step edge, anion corner, anion kink, and anion step corner using the TD-DFT method. The results of these calculations are summarized in Table 4. They were obtained in the following way. First, the excitation energies of the first 15 excited states were calculated for each of the defect sites. Then, the natural population analysis was performed for each excited state. This allowed us to separate excitations associated with each particular defect site, e.g., excitation of the surface corner site from that of the surface terrace close to it. The obtained excitation energies were then smeared out using Gaussian functions and weighted with the corresponding oscillator strengths. The positions of the lowest energy maxima in thus obtained spectra are presented in Table 4 together with the experimental energies. One can see that TD-DFT systematically underestimates the excitation energies. But the qualitative tendency is in good agreement with the experimental values22,56 and with the results of our previous calculations using the Hartree-Fock method,26 and shows a strong dependence on oxygen coordination. The step corner and kink have almost identical transition energies and similar oscillator strength. As has been demonstrated in refs 25, 26, the relaxed excitons are strongly localized at 3-coordinated sites and delocalized over step edges and terraces. We should note that our method gives also several other maxima. For the corner and kink sites they correspond to transitions into higher excited states inside the cluster, in particular into the states localized at step edges and terraces. Energies of these transitions depend on the cluster size and cover the whole range between about 4 and 6.5 eV. Their contribution into real spectrum depends on the concentration of particular surface features, i.e., on sample preparation. Nevertheless, they correspond very well to the photon energy interval covered by the broad excitation spectra of photoluminescence of MgO powders discussed in refs 15, 20, 21, 24. IV. Discussion Elucidation of the mechanisms and particular sites for electron and hole trapping at oxide surfaces is important for our understanding of many surface applications, for example, sample charging after cleavage and irradiation; formation and properties of chemically active species; leakage current in microelectronic devices; creation of flash memory devices; mechanisms of tribology. One of the main universal parameters of insulators used so far is the band gap. However, creation of nanoparticles and growth of thin oxide films requires a much richer set of parameters, which could characterize properties of particular
Structural Defects at the MgO (001) Surface surface features. For example, an interesting trend in the electron binding energy with the cluster size has recently been demonstrated for small MgO clusters and is described in ref 57. In this study we have considered a set of these parameters on the example of the MgO (001) surface. The results of our calculations demonstrate that extra electrons and holes are likely to be delocalized at terraces and step edges, and localized at 3-coordinated terminating sites, such as kinks and corners. They also have lower energies at these sites, which suggests that, if produced at terraces and steps, electrons and holes will tend to move to kinks and corners. Our results demonstrate that a real surface may possess both deep and shallow electron traps. Deep traps with electron affinities of more than 2 eV include anion vacancies at terraces, steps, and corner sites. However, there are a number of electron traps with electron affinities within the range of 1-2 eV. The demonstrated existence of these traps is important for our understanding of the mechanisms of surface charging and photoinduced surface processes. In particular, it suggests that shallow electron traps may serve as transient states for electron trapping in photoinduced processes, creating electron-hole pairs. More generally, these results establish, to the best of our knowledge, the first example of direct correlation between common surface features and their spectroscopic and other electronic properties. This map of surface electronic states can be expanded, as when more details of the surface atomic structure will emerge. Using the technique described above, similar maps can be produced for other surfaces (see, for example, ref 58). The immediate applications of these results include: photoinduced surface reactions, as they show which surface features can be directly excited or ionized at which photon energies; surface charging, as they pinpoint some of the surface charge traps; properties of the metal/MgO interface, as they show the energies of defect states with respect to the metal Fermi level. In particular, if the Fermi level of the metal substrate is lower than 3.5 eV, which is most often the case, electrons from neutral oxygen vacancies, F centers (see Figures 4, 5) can tunnel into metal and these centers are unlikely to be stable. This applies to most other electron traps, except single positively charged anion vacancies, F+ centers. On the other hand, bare anion vacancies at 3-coordinated sites are very deep electron traps and are likely to trap electrons from metal. Finally, we would like to note that accurate treatment of adsorption on ionic substrates requires correct representation of relative ionization energies and electron affinities of a surface and an adsorbed species. Although the accuracy of these molecular properties is relatively easy to control, that of surface calculations depends on the embedding scheme and usually is not checked at all. The results of this work provide initial benchmarks for ionization energies and electron affinities of surface features, which can be used for testing these properties in modeling adsorption and photoinduced reactions at surfaces. Acknowledgment. We acknowledge the support by the Divisions of Chemical Sciences of the Office of Basic Energy Sciences. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under contract No. DE-AC06-76RLO 1830. A.L.S. and J.L.G. would like to thank the Leverhulme Trust for finanical support. We are grateful to O. Diwald, A. Foster, E. Kno¨zinger, G. Pacchioni, and M. Sterrer for valuable discussions. References and Notes (1) Abriou, D.; Creuzet, F.; Jupille, J. Surf. Sci. 1996, 352, 499. (2) Robach, O.; Renaud, G.;Barbier, A. Surf. Sci. 1998, 401, 227.
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