Zinc oxide crystallizes in two modifications: wurtzite with C4-6v symmetry (lattice parameters of hexagonal unit cell are a=3.250 A and c=5.207 A) and metastable sfalerite with Fm3m symmetry (a=4.280 A) [2]. In the former structure zinc atom is four-coordinated by oxygen atoms, which are placed inthe vertices of slightly distorted tetrahedron (nearest interatomic Zn-O distances are 1.992 A and 1.973 A).
The most stable nonpolar (1010) wurtzite surface can be produced by the cut along the plane described by hexagonal vectors a and c. The formation of the surface disturbs zinc tetrahedron coordination. A geometrical property of (1010) ZnO surface is a formation of Zn-O "dimmers" in the surface plane. Following relaxation of near-surface layers can affect both zinc and oxygen atoms of surface Zn-O bonds. A direction of surface relaxation for a crystal with ionic- covalent bonding is not obvious. From the analysis of LEED data it was predicted [3] that surface zinc atoms move downward at 0.4 A while oxygen atoms are not displaced from unrelaxed positions. However, the interpretation of LEED intensities is not unambiguous and depends on parameters used. Theoretical studies of (1010) ZnO surface predict different ways of its relaxation. Total energy minimization within "tight-binding" model shows either the absence of relaxation or the bond-conserving rotation of surface layer [4,5]. Both ab initio HF- crystalline [6] and LDA studies [7] give similar structures with movements downward both oxygen and zinc atoms and shortening the surface Zn-O bond. Although LDA and HF calculationspredict similar way of surface relaxation, the description of electronic structure in these approaches is different. Even for bulk ZnO crystal ab initio methods fail out in reproducing the forbidden energy gap: HF calculation (Eg=11.7 eV [8]) overestimates experimental value (3.45 eV [9]), and LDAcalculation predicts very small gap (Eg=0.23 eV [10]). Thus, the nature of surface electronic structure and the relaxed geometry for zinc oxide are open questions.
In this note we report the results of self-consistent band CNDO study of the bulk electronic structure of bulk zinc oxide in wurtzite modification and modeling the (1010) ZnO surface. The band theory approach based on CNDO LCAO approximation was considered in details [11] and applied to the investigation of the bulk electronic structure of oxide crystals [11,12]. The Bloch sums of 4sZn and 2s,2pO double-dzeta atomic functions [13] were used as a basis for crystalline orbitals. CNDO parametrization for oxygen atom was performed on the row of crystalline oxides in our previous studies [11]. Zinc atom parameters: the core (Uss=16 eV) and Coulomb (gammaAA=7 eV) integrals and bonding parameter (betaZn=1.3 eV) were chosen to reproduce the energy gap dEg=3.45 eV [9] and experimental DOS [14] of bulk zinc oxide. Integration over Brillouin zone was performed in 64 points; enlarging of pointsset doesn't change main characteristics of ZnO electronic structure. Calculated dispersion curves and density of states (DOS) for bulk zinc oxide are shown in fig. 1. Obtained value of Fermi level Ef=-5.3 eV is in a broad accordance with experimental data for a number of zinc-containing materials [15]. We found that valence band is formed by 2pO state and has width 3.4 eV. This value is slightly lower than experimental value 5.2 eV [14], but the later is broadened by electronic relaxation. We didn't find any significant differences in electronic structures of wurtzite and sfalerite modifications of zinc oxide, except small decreasing of forbidden energy gap from 3.5 eV to 3.2 eV. Main electronic properties of bulk zinc oxide are in a good agreement with results of previous theoretical works [4,10,16,17]. Nevertheless, a behavior of two lowest dispersion branches in the valence band along Gamma-M direction is in a discrepancy between calculated in previous studies and measured by ARPES [18] E(k). Our results reproduce this behavior in a good agreement with experimental data. We can conclude that CNDO method (which includes some part of interatomic correlation) gives more accurate description of electronic structure in upper valence band region.
To analyze the chemical bonding in ZnO crystal we used the local characteristics of the electronic structure, such as atomic charges Q, bonds orders W (Wiberg indexes) and atomic covalences C. Their definitions for a crystal have been done elsewhere [19]. For bulk zinc oxide we obtained that ionicity degree of Zn-O bonding is lower than that in ordinary s- metal oxides (Q(Zn)=1.72e, Q(O)=-1.72e, and W(Zn-O)= 0.11e). Calculated accordingly to [19] zinc covalence is 0.47 and total quantum chemical valence is 2.0.
To study (1010) surface of ZnO we used the slab model with 4,8,12 layers (containing 8,16 and 24 formula units per unit cell in two-periodical slab, correspondently). We used mentioned local characteristics of surface electronic structure to estimate optimal slab width. We found that atomic charges and covalences depend weakly on the slab width, and even 4-layer slab in the "middle region" reproduces the local properties of atoms close to those in the bulk. For next study of surface relaxation we used the 8-layer slab. As one can see from Table, atoms in the second layer have atomic chargesand covalences, which are close to those in bulk ZnO. Deviation of electronic density within the first near-surface layer is essential: atomic charges are decreased and covalence of surface Zn-O bond is increased. However, the numerical value of total atomic valence, which depends on both ionic and covalent bonding [19], does not achieve the bulk value and equals to 1.92 for zinc atom.
To investigate the relaxation of (1010) surface we used different structural models proposed in experimental and theoretical studies. An accurate evaluation of the total energy within a semiempirical approach requires supplementary parametrization of core-core and core-electron interactions. To avoid this, we used a following "electronic" criterium to search for the optimal geometry of defect-containing crystal. As we found in our previous studies of complex crystals []containing an atom in fixed oxidation state, differences in coordination numbers or interatomic distances don't change of "integral" characteristics of electronic structure - atomic charges, covalences and valences. In other words, an atom conserves mentioned electronic properties in different crystal surrounding. Thus, we can expect, that relaxation of near-defect atoms must decrease a deviation of their electronic subsystem from unperturbed bulk values.
We have studied the electronic structure of relaxed ZnO surface using models proposed in [3,4-7]. Local properties of near-surface atoms are shown in Table. Calculated charges and covalences obtained in the geometry proposed in tight-binding study are close to correspondent values for unrelaxed surface and distinct from bulk values. One can see also that geometry proposed in LEED experiment shows increasing the covalent properties of surface anion under relaxation. It is connected with diminishing the Madelung potential on surface oxygen, while surface zinc moves down, and therefore with pushing up the oxygen-derived electronic surface states. Qualitatively, this behavior of surface states does not lead to a total energy minimization, thus we can join to authors of [6,7] that more accurate definition of experimental geometry is required. Upon reconstruction in HF and LDA geometry surface atoms move closer to neighbor atoms of opposite charge and become more ionic. We can conclude, that the direction of surface relaxation obtained in HF and LDA studies satisfy to the mentioned electronic criteria. The study of chemisorption (especially at the case of low coverage of surface) requires enlarging of unit cell to eliminate the mutual influence of adsorbed species. The ab initio methods fail out to describe such complicated systems, while semiempirical methods allow one to study the electronic structure of compounds with complex structure by small computer efforts. Investigations of chemisorption of CO on (1010) ZnO surface and adsorption induced postrelaxation of this surface within band-CNDO technique are in progress.
In conclusion, the bulk and surface (1010) electronic structure of zinc oxide has been studied by self-consistent band CNDO approach. Different models of surface relaxation were interpreted in terms of local properties of the electronic structure.
Acknowledgment: We thank Prof. I.V.Abarenkov and Dr. A.A.Tsyganenko for helpful discussions and Dr. I.I.Tupitsyn for developed computer codes for band-CNDO calculations. This work is supported by Russian Fundamental Research Foundation.
Table.
Local properties in bulk ZnO, unrelaxed and in different models of relaxed (1010) surface (I - LEED) [3], II-tight-binding [4], III-HF [6], IV-LDA [7]). Zn1,O1 - atoms of first surface layer, Zn2,O2 - atoms of second surface layer, Q(A) - charge on atom A, C(A)- covalency of atom A, W(A-B) -Wiberg index of bond A-B
-------------------!------------!-----------------!------------!----------- geom. Q(Zn1) Q(Zn2)!Q(O1) Q(O2)!W(Zn1 W(Zn1 W(Zn2!C(Zn1)C(Zn2)!C(O1) C(O2) used ! -O1) -O2) -O1) -------------------!------------!----------------!------------!----------- bulk 1.72 ! -1.72 ! 0.11 ! 0.47 ! 0.53 unrel. 1.49 1.73 !-1.54 -1.69 ! 0.45 0.13 0.10 ! 0.76 0.46 !0.79 0.59 I 1.67 1.69 !-1.54 -1.75 ! 0.30 0.10 0.18 ! 0.55 0.53 !0.84 0.48 II 1.50 1.70 !-1.40 -1.70 ! 0.51 0.09 0.15 ! 0.75 0.51 !1.01 0.58 III 1.63 1.75 !-1.64 -1.73 ! 0.32 0.12 0.11 ! 0.60 0.43 !0.66 0.51 IV 1.69 1.71 !-1.63 -1.76 ! 0.28 0.10 0.14 ! 0.52 0.49 !0.67 0.46 ----------------------------------------------------------------------------