Effect of Strain and Surface Proximity on the Acceptor Grouping in ZnO

According to the present knowledge, the level of zinc oxide conductivity is determined by donor and acceptor complexes involving native defects and hydrogen. In turn, recently published low-temperature cathodoluminescence images and scanning photoelectron microscopy results on ZnO and ZnO/N films indicate grouping of acceptor and donor complexes in different crystallites, but the origin of this phenomenon remains unclear. The density functional theory calculations on undoped ZnO presented here show that strain and surface proximity noticeably influence the formation energy of acceptor complexes, and therefore, these complexes can be more easily formed in crystallites providing appropriate strain. This effect may be responsible for the clustering of acceptor centers only in certain crystallites or near the surface. Low-temperature photoluminescence spectra confirm the strong dependence of acceptor luminescence on the structure of the ZnO film.


INTRODUCTION
The experimentally observed two types of photoelectron spectra (PES) coming from different crystallites in ZnO and ZnO/N suggest that the grouping of acceptor and donor complexes occurs in separate domains. 1 Density functional theory (DFT) calculations reveal that the complexes involving zinc vacancy (V Zn ), hydrogen (H x ), and, in the case of ZnO/N, also nitrogen modify the density of states (DOSs) of the valence band maximum (VBM).This phenomenon translates into the experimentally observed differences in PES between crystallites containing different acceptor-related complexes. 1ccording to a number of experimental and theoretical works, native defects and their complexes, often containing hydrogen, such as V Zn , V O , V Zn −nH (n = 2, 3), Zn i V O H, and others, determine ZnO conductivity as they introduce shallow and deep, donor and acceptor levels, 2−11 and the acceptor-related sample properties depend on a number of factors introduced by growth and/or annealing conditions. 12−15 For example, for ZnO/N it has been shown that both annealing medium and temperature influence acceptor-related cathodoluminescence intensity, which is higher under oxygen annealing. 15Generally, the reasons for donor and acceptor domains are not clear, but it might be due to the formation of defect clusters that require distortion of the crystal lattice.Hence, it can be assumed that microstrain plays a role here.
−20 For example, hydrostatic pressure-induced redistribution of native defects and the optoelectronic response have been indicated in ZnO rode-like nanocrystals. 216][17][18][19][20][21]26,27 In particular, the effect of substrateinduced strain in ZnO thin films on different substrates has been investigated by X-ray diffraction and photoluminescence measurements, and the excitonic peak positions are found to shift slightly toward the lower energy side with increasing uniaxial strain. 28 Alo, despite extensive theoretical studies of ZnO, research interest has mostly focused on the strain effects affecting the band gap and the electronic structure of pure ZnO, 18,29−33 the magnetic and electronic properties of the doped system, 30,34−36 or native defects under extremely high pressure.37 In refs 1 and 38, we have carried out some study of the electronic structure of Zn vacancy in ZnO.Here, using firstprinciples band structure calculations, we investigate the electronic band structure of ZnO/H, especially the electronic structure and formation energy of H interstitial, Zn vacancy, and V Zn H complex in ZnO as a function of different strain conditions.We model the observed acceptor domains as simple 0D nanocrystals with a passivated surface, i.e., quantum dots (QDs).Thus, we study here the surface proximity of these defects in QDs.Our results elucidate the effects of strain and surface proximity on the electronic structure and grouping of vacancy−hydrogen complexes.In particular, we demonstrate that strain leads to a decrease of the acceptor complex formation energy, so it might be responsible for the grouping of acceptors, which can only form in crystallites showing compressive strain or if they are close to the surface.In support of the DFT calculations, we present the results of photoluminescence measurements, which reveal considerably different acceptor luminescence for ZnO layers deposited on c− and a− oriented sapphires, i.e., showing a different crystallographic structure.

Computational Methods.
Calculations based on the density-functional theory (DFT) within the generalized gradient approximation (GGA) 39,40 were performed using the QUANTUM-ESPRESSO package. 41On-site, Hubbard-like + U terms 41,42 were applied to the d(Zn) and p(O) orbitals as U Zn = 10 eV and U O = 7 eV, 1,43,44 reproducing to within 1% the experimental lattice parameters of wurtzite (w) ZnO (a 0 = 3.223 Å and c 0 = 5.24 Å), the experimentally established band gap, E g , at about 3.38 eV and the energy of the core d(Zn) level, centered about 7.5−8.4eV below the VBM. 45,46Figure S1 in Supporting Information shows the DOS of a perfect ZnO crystal calculated for the above + Us parameters.Ultrasoft atomic pseudopotentials 39 were employed, and the following valence orbitals were chosen: 3d 10 and 4s 2 for Zn, 2s 2 and 2p 4 for O, 2s 2 and 1s 1 for H.The plane wave basis with the kinetic energy cutoff of 40 Ry provided a good description of II−VI oxides.The Brillouin zone summations were performed using the Monkhorst−Pack scheme with a Γ point and 2 × 2 × 2 kpoints mesh. 47Ionic positions were optimized until the forces acting on ions were smaller than 0.02 eV/Å both in the bulk for the 128-atom supercell and QDs structures.The smearing width of 0.136 eV in the Methfessel−Paxton method was chosen to account for partial occupancies and to guarantee convergence and the lowest supercell total energy. 48e focused on two types of strain conditions: (1) the biaxial strain, i.e., in the xy-plan; and (2) the uniaxial strain applied along the c-axis direction.We defined the biaxial and uniaxial strains as ε xy = (a −a 0 )/a 0 × 100% and ε zz = (c − c 0 )/c 0 × 100%, respectively, where a 0 , c 0 and a, c are the lattice constants of the perfect single crystalline ZnO in its equilibrium and strained states, respectively.Thus, in the tensile and compressive cases, ε xy and ε zz are positive and negative values, respectively.For example, biaxial strain ranging from −4 to 4% was realized by compressing or stretching the material in the xy-plane, i.e., during the calculations, the lattice parameters were kept fixed at the specified strained a = b and c = c 0 and the internal coordinates of atoms were relaxed.
Additionally, considering the substrate clamping effect, we performed some calculations with fixed a = b for each strain, while relaxing the c-axis length; however, in both cases the results were qualitatively similar (see Supporting Information, Section S1, Figures S2−S8).
Approximately spherical Zn 84 H* 57 H** 57 O 84 QDs (a diameter of about 15 Å) containing 168 host atoms and 114 pseudo hydrogens were constructed using the bulk wurtzite crystal structure provided that no more than two dangling bonds were left on the surface, in agreement with our previous study 44 and other works. 49To isolate the QDs and avoid inter-QD interactions, a vacuum spacing of ∼15 Å was taken.Dangling bonds of Zn 2+ and O 2− ions on the uncompensated surface were passivated by pseudohydrogen atoms H* and H** with fractional charges, +1.5 and +0.5, respectively. 44,49,50The Zn− H* and O−H** bond distances were taken from optimized ZnH 4 and OH 4 tetrahedra.After relaxation, the length of Zn− H* is 1.6732 Å and that of O−H** is 0.98 Å.The finally optimized geometry of the undoped QD deviates from the initial bulk wurtzite structure.In the vicinity of Zn atoms in the QD center, the tetrahedral wurtzite C 3v symmetry is maintained.However, the optimized Zn−O bond lengths near the surface are about 1.5% shorter than those inside the QD (relaxed structure of the QD is shown in Figure S9, Supporting Information).We apply the U Zn = 10 eV and U O = 7 eV values to the QD calculations, 44 and we obtained E g as 4.4 eV that is in full agreement with the ZnO QDs experimental results. 51Figure S10 in Supporting Information shows the calculated DOS of QDs for above + Us parameters.
2.2.Synthesis of ZnO Thin Films.ZnO films investigated here were grown by atomic layer deposition (ALD) using diethylzinc and water precursors.The details of the growth process can be found elsewhere. 13About 120 nm thick films were deposited simultaneously on c-Al 2 O 3 and a-Al 2 O 3 substrates in the same ALD process.As previously shown, deposition on differently oriented sapphire substrates strongly influences orientation of ZnO films over a wide growth temperature range, especially for limited layer thicknesses. 15he studied layers were deposited at a temperature of 300 °C, which is high for the ZnO−ALD process, in order to get a high-intensity photoluminescence signal despite the limited layer thickness.Rapid thermal annealing (RTA, 800 °C, 3 min) in oxygen atmosphere was applied in order to further enhance layer quality and to facilitate the formation of zinc vacancies.As previously shown, ZnO samples grown by ALD have a high hydrogen content that after RTA was reported at the level of 10 19 /cm 3 . 12,15For this reason, hydrogen atoms are included in the theoretical calculations.
2.3.Photoluminescence Measurements.Photoluminescence (PL) spectra of ZnO samples were studied in the range of temperatures 5−100 K. Samples were mounted in an optical cryostat with a variable temperature exchange gas flow.Temperature stability during the experiment was kept at the level 0.05 K. Samples were excited by the third harmonic of a Nd 3+ YAG laser with a photon energy of 3.493 eV and a power density of 5 W/cm 2 .For detection of PL spectra, a spectrograph/monochromator with a 0.28 m grating equipped with a Hamamatsu C7042 thermoelectric charge-coupled device camera was used.

RESULTS AND DISCUSSION
We consider a bulk supercell and a QDs crystal containing various point defects, including interstitial hydrogen (H i ), Zn vacancy (V Zn ), and (V Zn −H) and (V Zn −H 2 ) complexes.Hydrogen interstitial is suggested to have a donor-like ground state in ZnO at a bond-center site, 1,52,53 and in this work, we compute H i in this configuration.Figure 1a shows optimized atomic structure for V Zn −H in the bulk ZnO.We also calculate the electronic structure of the V Zn and V Zn −H complexes at four different positions in the QD: near the QD center and at three midway sites.Below, we refer to these sites as c, m 1 , m 2 , and m 3 , respectively.The QD relaxed geometry and the precise placement of the vacancy sites are presented in Figure 1b.We do not consider the vacancy at m 4 sites because it is a surface site, and in this case the surface properties are strongly dependent on the passivation species.Thus, in all midway positions, likewise for the center site, the vacancy is surrounded by four O atom neighbors.The total energy of the H i interstitial was calculated for nine different positions in the QD (see Figure S11, Supporting Information).For each Zn at c−m 4 sites, hydrogen was introduced at the center of Zn−O bond in the xy-plane and at the bond along the c-axis.
The effect of strain conditions on the ZnO band gap and defect formation energy was investigated by calculating the total energies for the defective system and for pure ZnO under different ε xy and ε zz in the range between −4% compressive strain and 4% tensile strain, respectively.Figure 1c shows the effect of strain on the band gap value of pure ZnO at the Γ point.The E g curve versus strain follows a sublinear relationship regardless of the strain direction.With the increasing compressive (tensile) strain, the E g value increases (decreases) about 0.11 (0.13) and 0.06 (0.07) eV for ε xy and ε zz , respectively.The trend of the E g curve in our calculations is consistent with that in other reports. 29,31,35,36,54Interestingly, experiments have shown that the values of the ZnO band gap ought to be corrected according to the Burstein−Moss effect also based on the sublinear relationship. 33Under compressive (tensile) strain, the length of the Zn−O bond is shortened (elongated) (see Figure 1d), which leads to enhanced (diminished) overlapping of electron orbitals.Because both the VBM and the conduction band minimum (CBM) are antibonding states related to the d(Zn)−p(O) and s(Zn)− s(O) hybridization, respectively; thus, under compressive (tensile) strain, the VBM and the CBM are shifted down (up) with respect to the unstrained case.However, the shift of the VBM is higher, so we observe that the band gap widens (narrows). 18,55.1.Formation Energy under Strain.For all configurations, we calculate the defect formation energy E form as 56,57 = + where E tot (ZnO/D) and E tot (ZnO) are the total energy of the supercell with and without the defect (or complex), respectively; n i is a number with the + (−) sign corresponding to the removal (addition) of atoms, μ i is the variable chemical potential of atoms in the solid, q is the charge state of defect (or complex), ε F is the Fermi energy referenced to the VBM, ε VBM is the energy of the VBM of ZnO, determined in line with the algorithm in ref 57, and E* is the finite size supercell correction, including the potential alignment correction of the VBM and the image charge correction. 57We did not include E* in the QDs calculations.In line with our experiments, 1,15 the O-rich experimental conditions are considered.Thus, we calculate μ i as μ Zn = E tot (Zn bulk) + ΔH f (ZnO), μ O = E tot (O 2 )/2, and Here, E tot (Zn bulk), E tot (O 2 )/2, and E tot (H 2 )/2 are total energies per atom of the elemental solids.ΔH f is the enthalpy of formation per formula unit, which is negative for stable compounds.ΔH f at T = 0 K is obtained by considering the reaction of formation or decomposition of a crystalline from its components.The results of the calculations are shown in Figure 2 and Table 1.In particular, Figure 2a shows the defect formation energies obtained using eq 1 for conditions without strain.The numbers near the lines correspond to the defect charge states  (q), while the circle points represent the thermodynamic transition levels ε(q 1 /q 2 ) defined as the ε F at which the defect E form in the q 1 and q 2 states are equal. 57If the calculated ε(q 1 / q 2 ) lies in the band gap, we perceive it as a stable state, in contrast to the defect levels that are resonant and located below the VBM or above the CBM.
From Figure 2b and Table 1, we observe that in the investigated range of strain values, the E form curve versus strain for hydrogen interstitial follows a sublinear relationship, and as the compressive strain increases from 0 to 4%, the E form decreases from 1.42 to 1.36 eV.In contrast, increasing tensile strain causes the E form of H 0 to increase from 1.42 to 1.45 eV.With the introduction of H into the host, the total number of electrons in the system increases, which induces compressive stress in the crystal lattice.This trend is similar to the results from ref 58, but it should be noted that in the latter case very small supercells were used, which translated into very high H concentrations.
The formation energy of both zinc vacancy and the (V Zn H) complex is not a monotonic function of the applied strain, and an increase of any strain leads to a decrease in E form but for the compressive strain the effect is stronger.In particular, the changes in E form are about 0.12 and 0.34 eV in the case of 4% compressive strain, for V Zn and (V Zn H), respectively.Similar variations in the formation energy for V Zn were observed in refs 35 and 59.In particular, ref 35 demonstrated for the first time that E form of zinc vacancy does not depend linearly on the strain due to the large structural relaxation around the vacancy.
The binding energy of the complexes, E b (V Zn H), was evaluated as the difference in the formation energy between the isolated constituents of the complex and the complex itself for a given Fermi level position.The positive E b values indicate the energetic preference for the defect complex to be formed.Results are shown in Table 1.In our simulations, the presence of H i is responsible for increased stability, i.e., a reduction of the formation energy of the V Zn point defect.E b = 3.42 eV for unstrained ZnO, and this value is increased by about 0.08 eV when the compressive strain increases to 4%.In contrast, the stability of the (V Zn H) complex decreases with increasing tensile strain.Figure 2a shows that the V Zn H 2 complex has the lowest E form = 0.26 eV and at the same time the highest E b = 2.66 eV with respect to V Zn H and H i .
From a very simple model, the E form decreases as the crystal is strained along the direction of strain induced by the defect. 35hus, from this point of view, if a defect gives rise to a reduction of the local crystal volume, the external compressive strain leads to a lower formation energy compared to that of the material without strain.The change in the total energy of point defects under strain is determined by the size of the defect-induced local volume change and can exhibit either parabolic or superlinear behaviors. 60However, it needs to be noted that both E form and electronic properties are affected by a lot of other factors such as defect electronic environment, 35 symmetry, spin properties, and surface proximity, just to name a few.In particular, for example, ref 38 indicated that interatomic distances (given by the lattice constant and atomic relaxations around the cation vacancy) determine both the defect electronic structure and the stability of spin-polarized states in a number of III−V and II−VI semiconductors.Introduction of hydrogen or V Zn into the lattice leads to large atomic perturbations.The increase in the energetic stability of vacancy and complexes with increasing strain can be explained by the distortion effects in the crystal structure due to the large atomic displacement during the relaxation process.Moreover, the observed structural distortions are complex; although the displacements of the second and further neighbors of defects are an order of magnitude smaller, the effect of atomic relaxations around the vacancy, involving not only the nearest but also more distant neighbors, cannot be neglected.The calculated relaxation energy is more than 1.5 eV for V Zn under 4% strain.
Finally, we calculated the formation energy of the H interstitial V Zn and its complexes at different positions in the QDs.In contrast to the bulk crystal, in the case of QD, we obtained very close total energies for hydrogen geometries in the xy-plane and bond center along the c-axis.Moreover, in some configurations the energy in the latter case was lower than it was in the basal plane.We note that in all cases the position of hydrogen with respect to the QD center plays a dominant role.At the same time, the energy difference between the basal plane and the c-axis was less than 6 meV; hence in Table 1, we provide only values of the lowest energies of H located either in the center of the axial bond or along the c-bond.Interestingly, the calculated length of the relaxed H−O bond was about 0.96 Å in all configurations.We note that the same bond length, 0.96−0.98Å, was obtained for all bulk systems, both passivated H**−O on the QD surface and the one optimized for OH 4 tetrahedra. 44,49According to the results of Table 1, one can see that H-doping in the QD is energetically favorable compared to that in the bulk crystal.Moreover, the lowest E form value was obtained for H at a location near the QD surface (m 4 ).We calculated the average Zn−O bond lengths for Zn at the c−m 4 positions in the relaxed QD without defects.They are 1.9831, 1.9829, 1.9837, 1.9883, and 1.9653 Å for c, m 1 , m 2 , m 3 , and m 4 , respectively.The obtained values combined with the results from Table 1 give rise to the conclusion that as the length of the Zn−O bond decreases, the formation energy of H, which passivates this bond, decreases as well.The lowest E form value was obtained for H at the m 4 site.This agrees well with the bulk results, which demonstrate a reduction in formation energy under low compressive strain.Moreover, the above observation may explain why, in the QD calculations, H favors the Zn−O center along the c-axis in contrast to the bulk crystal.We obtained that in the relaxed QD structure, the Zn−O bond lengths parallel to the c-axis are shorter than those vertical to the c-axis.The formation energy of Zn vacancy at the c-site of the QD is approximately 0.7 eV lower than in bulk ZnO (see Table 1).Moreover, V Zn at this site is more favorable than that at the m 1 or m 2 sites.However, the lowest E form value was obtained for the m 3 site.Similarly, the formation energy of the (V Zn H) complex at these points of the QD is approximately 1 eV lower than that of bulk ZnO.A similar decrease in the formation energy of zinc vacancy and the (V Zn H) complex compared to the bulk calculations was also observed for the two-dimensional surface in ZnO. 61.2.Defect Electronic Structure under Strain.In bulk unstrained ZnO, the calculated ε(+1/ −1) level of H i is 3.31 eV and is resonant with the conduction band, which assumes a shallow donor level.Such a shallow level inevitably introduces a local deformation of the CBM around the defect.Figures S1  and S3 (see Supporting Information) show the DOS results for pure bulk ZnO and ZnO/H i .The VBM of both crystals is formed mostly from p(O) orbitals, while the CBM is built from s(Zn) and s(O) states.However, in the case of ZnO/H i , a significant contribution of the s(H) states to the CBM is also witnessed.
As in pure ZnO, the VBM and the CBM of ZnO/H i shift down or up with respect to the unstrained system under tensile or compressive strain, respectively.Figure 3 shows the calculated total DOS and the contribution of s(H) orbitals of unstrained ZnO/H i in comparison with the results under 4% tensile and −4% compressive strain conditions.We can see that under tensile strain, H states associated with the CBM move deeper into the gap with respect to the level of the unstrained system.The electronic structure is affected by atomic displacements around H (see Figure 3g−i).Interstitial hydrogen becomes the most stable when forming a bond with oxygen.The H−O bond length changes from 0.985 to 0.96 Å for different strain values ranging from 4% tensile to 4% compressive, respectively.In the latter case, we obtained the lowest E form .
Figure 4 shows the calculated DOSs for H i in the QD crystal.As for bulk ZnO calculations, H i states are associated with the conduction band states and are pinned to the CBM at all sites due to the shallow H i shallow character.H interstitial in the QD also forms a strong bond with oxygen atoms, giving rise to large structure relaxations of the surrounding atoms (Figure 4e−g).The average O−H bond length (0.96 Å) is slightly shorter than in the case of bulk ZnO (about 0.98 Å).The strength of the O−H bond is a key factor in stabilizing the defect configuration; therefore, for higher compressive strain, a further decrease in the formation energy can be expected.
In wurtzite ZnO, the V Zn �induced states can be considered as a combination of four dangling bonds of four O atoms surrounding the vacancy.H i is located at one of the four dangling sp 4 (O) bonds when V Zn is passivated by hydrogen.Four sp 4 (O) orbitals of oxygen neighbors combine into a singlet and a quasi triplet (a pair of doublet e t and singlet a t ) that are higher in energy.The quasi triplet is occupied with 4 or 5 electrons in the case of neutral V Zn or the complex, respectively.The electron−electron exchange interaction splits the e t and a t levels, setting them into spin-up (e t↑ , a t↑ ) and spindown (e t↓ , a t↓ ) states.Second, the two or one hole at the tripledegenerate state of V Zn or the V Zn H complex, respectively, induces the Jahn−Teller effect, which drives a strong nuclear reorganization and symmetry breaking.As a result, the quasi triplet splits into an occupied a t↓ singlet and an empty e t↓ doublet in the case of V Zn , and an occupied e t↓ doublet and an empty a t↓ singlet in the complex.For the Zn vacancy, these e t↓ and a t↓ states are reflected in the DOS results as depicted in Figure 5a.In particular, in bulk ZnO, the V Zn −a t↓ and e t↓ states are located about 2.25 and 2.5 eV above the VBM, respectively.The deep character of the zinc vacancy acceptor state is indicated by the calculated 0/−1 transition level, which was determined to be approximately 1.15 eV above the VBM (see Figure 2a), in agreement with the other first-principle calculations 2,7,62 and experiments. 63he creation of the vacancy or its complex is very sensitive to local atomic perturbations and structure. 1,2,62As was previously shown, the energetically lowest solution is due to the previous slight symmetry breaking and possible hole configurations. 1,2,62In the ground state, the density of spin polarization of the empty states of zinc vacancy and the complex demonstrates that each hole localizes onto a single sp 4 orbital of the nearest neighbor O ions, as shown in Figure 6a  for V Zn .The computation results for the nonground state show a very small Δ e−a splitting, i.e., the difference between e t↓ and a t↓ energies.This is a direct result of the delocalization error that occurs at lower energies due to dividing the holes between all the nearest neighboring O ions orbitals, 2,64 which is exemplified in Figure S8.Similar behavior of the vacancy wave functions was obtained within the LDA/GGA approximation. 38,62,64Taking the above considerations into account, we break the V Zn symmetry by the application of biaxial strain in the bulk crystal and surface proximity in the QD.The strain leads to additional lattice perturbations around the vacancy, which are reflected in its electronic structure and the shape of the spin polarization distribution, as depicted in Figures 5 and  6.In particular, in parallel to the increase of compressive strain from 0 to 4%, the splitting, i.e., the difference between e t↓ and a t↓ energies that is referred in Figure 5a,b as Δ e−a , increases from 0.25 to 4.7 eV.Moreover, a long tail can be observed in the spin density distribution, partly due to the resonance character of a t↓ , which is hybridized with the VBM exhibiting mostly the p-nature (see Figure 6a).The impact of surface on the electronic and spin structure of V Zn is further confirmed in Figures 5c−e and 6b−d, which show the DOSs and spin density distributions for different positions in the QD.As in the bulk case, here the wave functions of the empty vacancy states are also localized on two sp 4 dangling bonds, but one of these dangling bonds is directed along the c-axis (Figure 6b−  d).Generally, this description of the deep vacancy levels in the QD is consistent with the conclusions of bulk calculations because quantum confinement does not highly influence the localization of the levels that remain pinned to their energy, regardless of the nanocrystal size.
The impact of strain on the electronic and spin structure of a complex is depicted in Figure 7a−d, which shows the DOSs for ZnO containing the V Zn H complex under 0, ε xy = 4%, ε xy = −4%, and ε zz = −4% strain, respectively.Figure 7a shows the total DOS of the complex without strain.It can be seen that the Jahn−Teller effect induces splitting of the quasi triplet into an occupied e t↓ doublet and an empty a t↓ singlet.The splitting Δ a−e , i.e., in this case the difference between the a t↓ and e t↓   energies is very large and depends on the strain value (see Figure 7).Δ a−e is 4.5, 5.0, 3.85, and 4.15 eV for ε xy = 0%, ε xy = 4%, ε xy = −4%, and ε zz = −4% strain, respectively.It is worth noting that for the unstrained case, a small atomic displacement was introduced before calculations.The obtained results are accompanied by the spin density calculations for the above configurations (Figure 7e 65,66 The shallow DAP emission band is located in the range 2.8−3.25 eV and is formed by the zero-phonon line and a number of intensive LOphonon replicas.In this study, we observe a spectacular difference in the NBE PL emission spectra of ZnO films grown on both substrates.In the case of the ZnO/c-Al 2 O 3 sample, the PL spectrum is dominated by excitonic emission of the D o X line with an energy of 3.369 eV (Figure 8b, bottom panel), which is accompanied by a weaker A o X line with an energy of 3.340 eV.In turn, the PL spectrum of the ZnO/a-Al 2 O 3 sample is dominated by acceptor-related emission with a DAP band at 3.26 eV with a well resolved LO-phonon replica at 3.18 eV accompanied by two narrow A o X and FA lines situated at 3.329 and 3.316 eV, respectively (see Figure S12 in Supporting Information), while the D o X line at the energy of 3.373 eV is much weaker (Figure 8b, upper panel).The PL peak energies and their interpretation are consistent with data previously reported for ZnO samples grown by ALD under similar conditions. 13,67s the ZnO/c-Al 2 O 3 and ZnO/a-Al 2 O 3 films were deposited together in the same ALD growth process, the differences between them can be caused only by their crystallographic structure.Thus, it might be expected that much more intensive acceptor luminescence observed for the ZnO/a-Al 2 O 3 film is related to the film orientation, strain in the layer, and/or the film microstructure.Analysis of the structural properties of both layers reveals the lattice parameter a = 3.258A for the ZnO/a-Al 2 O 3 film and c = 5.206A for ZnO/c-Al 2 O 3 films, which means that the first layer is subjected to tensile strain while the second one is almost relaxed.As was shown by DFT calculations, tensile strain reduces the formation energy of acceptor complexes, although this effect is stronger for compressive strain.On the other hand, in this case, we are dealing with biaxial strain, the effect of which is always more pronounced.Additional information is provided by calculation of the grain size, which in the case of ZnO/c-Al 2 O 3 is approximately 70 nm, i.e., much larger than for the ZnO/a- Al 2 O 3 film (40 nm).Thus, it can be concluded that both strain and surface proximity contribute to the intense acceptor luminescence of the ZnO/a-Al 2 O 3 film; however, theoretical calculations indicate that the latter effect is stronger.It is worth noting that such a significant influence of the crystallographic structure of the thin ZnO films on their shallow donor-and acceptor-related emission is shown for the first time.

CONCLUSIONS
In conclusion, we show the DFT results of a systematic analysis of the impact of different strain conditions and surface proximity on the electronic structure of zinc oxide and the formation energy of acceptor complexes that involve zinc vacancies (V Zn ) and/or −Hx groups.A wide range of strain conditions were considered: tensile and compressive strain, biaxial strain in a planar plane, and uniaxial strain along the caxis.We also considered the QDs crystal to study the importance of surface proximity.
It has been shown that strain noticeably affects the formation energy of acceptor complexes in zinc oxide.This effect might be responsible for the grouping of acceptors, which can be formed only in the crystallites showing compressive strain or near the surface.It was also shown that the presence of hydrogen is responsible for the increased stability, i.e., the reduction of formation energy of the (V Zn ) point defect, which can be further decreased by compressive strain.In support of the DFT results, the PL spectra reveal considerably different intensive acceptor luminescence for the ZnO samples with different crystallographic structures.
The obtained DFT results shed new light on abundant experimental reports showing that p-ZnO is much easier to obtain in nanostructures or thin films than in bulk ZnO.There are several reasons for this, such as easier formation of acceptor states and lowering their energy, as well as increased hydrogen incorporation in the near-surface layer.
Results for DOS of bulk and QD ZnO, DOS of ZnO/H, results of calculations with fixed a = b for each strain while relaxing the c-axis length, geometry of QD, calculated atomic configurations for the neutral vacancy and complex without previously breaking symmetry, and deconvolution of LT PL spectrum from the ZnO/a-Al 2 O 3 film (PDF)

Figure 1 .
Figure 1.(a) Relaxed structure of V Zn H in the unstrained ZnO.(b) Relaxed structure of the QD.Purple and red balls represent Zn 2+ and O 2− ions, respectively.Smaller cyan balls denote pseudohydrogen atoms (H* and H**) employed for surface passivation.The numbers 1−5 denote, respectively, the Zn (or vacancy) sites: 1: c, 2: m 1 , 3: m 2 , 4: m 3 , and 5: m 4 .(c,d) Variations of the energy of the band gap (c) and average Zn−O bond length (d) under different strains for ZnO bulk.

Figure 2 .
Figure 2. (a) Defect formation energies of unstrained ZnO as functions of ε F .(b) Variation of the E form of V Zn , H i 0 and V ( H ) i Zn

Figure 3 .
Figure 3. (a−c) Total DOSs of ZnO/H i for unstrained and 4% tensile and compressive strained crystal, respectively.(d−f) Contribution (×10 times) of s(H) orbital for unstrained and 4% tensile and compressive strained crystal, respectively.Green dashed horizontal lines correspond to the VBM and CBM unstrained crystal.(g−i) Atomic configuration and the density of charge states of unstrained and 4% tensile and compressive strained crystal, respectively.Contours go from 0.0009 to 0.5 electron/Bohr 3 .

Figure 4 .
Figure 4. (a) Total DOS and (b−d) contributions of p(O), d(Zn), and s(H) orbitals of QD ZnO with H i at m 1 site.Horizontal dashed lines correspond to the VBM and CBM states.(e−g) Relaxed crystal structure of QD with H interstitial in the m 1 , m 2 , and m 4 configurations, respectively.

Figure 5 .
Figure 5. (a−e) Total (orange color) and the contribution of p(O) orbital (dark cyan color) spin-resolved DOS of ZnO containing a V Zn : (a,b) bulk under 0 and 4% compressive strain, respectively.(c−e) QD with vacancy at the m 1 , c, and m 3 sites, respectively.Left and right panels denote the spin-down and -up channels, respectively.

Figure 6 .
Figure 6.Calculated atomic configurations and isosurfaces of spin density corresponding to 0.05 electron/Bohr 3 for the neutral zinc vacancy: (a) in the bulk ZnO under 4% compressive strain, (b−d) in QD at c, m 1 , and m 3 positions, respectively.
−h).In particular, the results indicate that complex states are dominated by the localized and spinpolarized contributions of the sp4 orbitals of the nearest neighbor.The strong localization of the spin density on one O orbital is due to the fact that a t↓ is a deep state.Under compressive strain, the spin density of the complex is more delocalized, which can be observed as a long-range tail that involves p(O) orbitals of distant O ions, due to the strong p(O)−d(Zn) hybridization.It is to be noted that both p(O) and d(Zn) orbitals build the VBM, and under strain, p(O)− d(Zn) hybridization will increase.Atomic displacements around the defect complex under strain affect its electronic structure.After relaxation of the crystal structure in a supercell, the average O−O bond length is 3.195, 3.25, 3.16, and 3.18 Å for ε xy = 0%, ε xy = 4%, ε xy = −4% and ε zz = −4% strain, respectively.The change of the strain is accompanied by a strong change of the average O−O bond length around vacancy: 3.289, 3.55, 3.01, and 3.06 Å for ε xy = 0%, ε xy = 4%, ε xy = −4%, and ε zz = −4% strain, respectively.These changes include the Jahn−Teller perturbation that is also affected by the applied strain.3.3.Experimental Results.The X-ray diffractograms revealed a large difference in the crystallographic orientation of both ZnO films, which were grown in the same ALD process on c-and a-sapphire.The wurtzite-type crystal structure showed a strongly dominant [002] crystallographic direction for the ZnO/c-Al 2 O 3 layer, while a dominant [110] crystallographic direction was accompanied by a minor [002] for the ZnO/a-Al 2 O 3 layer (Figure 8a).Near-band edge (NBE) photoluminescence of zinc oxide has been the subject of fundamental research over the last 50 years.It has been studied in detail, and the nature of the emission lines is well established.It generally originates from excitonic emission transitions and donor−acceptor pair (DAP) recombination.Free exciton lines (X) are located in the range 3.376−3.387eV, donor-bound exciton lines D o X are located in the range 3.355−3.375eV, and acceptor-bound excitons A o X emit in the range 3.320−3.358eV.

Table 1 .
Defect Formation and Complex Binding Energies, in eV, in the Bulk under Biaxial Strain and at the Different Sites in the QD