Ab initio study of electronic effects in the ZnO/TiO₂ core/shell interface: application in dye sensitized solar cells

Abstract

Core/shell structure of ZnO nanowires coated with a monolayer of TiO₂ is investigated using Density Functional Theory (DFT). The electronic states of the semiconductor is calculated and compared before and after coating of the TiO₂ monolayer on a ZnO [101̄ 0] surface. The effect of TiO₂ coating induce surface states changes and shifts the conduction and valence band edges to higher energies. Our results, in qualitative agreement with the experimental work of Matt Law et al. (J. Phys. Chem. B, 110, 22652), show an increase in open circuit voltage and a decrease in short circuit current in ZnO/TiO₂ core shell dye sensitized solar cells. Regarding the semiconductor density of states (DOS), TiO₂ coated ZnO have more conduction band acceptor states and lower electronic back recombination in agreement with experimental results. Surface dipoles are attributed to changes of the local density of states of the surface. This method can be used for more investigation of starting effects of semiconductor interface and helps the study of surface states and their physical origin in dye sensitized solar cells.

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Introduction

Dye sensitized solar cells (DSSCs) representing the third generation of solar cells, are environmentally friendly, of lower cost and have higher indoor efficiencies compared to conventional silicon solar cells.^1,2 Their commercialization started with coming into the market for indoor-use conditions and keyboard chargers. Generally, DSSC working electrode consists of mesoporous TiO₂ (or ZnO) structure coated on FTO substrate and dye molecules are adsorbed on the interface between semiconductor and electrolyte. The counter electrode is Pt coated FTO glass substrate. Incident photons excite the dye molecules; electrons of excited dyes are injected into the semiconductor and diffuse to the FTO, and its holes are injected to and diffused in the electrolyte. These holes also diffuse in the Pt layer which is regenerated by electrons of external circuit.²

One of the fundamental questions of DSSCs is the interface in semiconductor/dye/electrolyte² which has great influence on the electron injection and back recombination and its overall efficiency. The position of semiconductor energy levels which are determinant for the cell open circuit voltage (V_oc) and short circuit current density (J_sc) strongly depends on the interface properties and several research groups have investigated the changes of these energy levels both experimentally and theoretically.^3–11 The change in the position of semiconductor energy levels can occur by co-adsorbed molecules,^10,11 electrolyte ions^3,9 and by coating a thin insulator or semiconductor shell on the working electrode semiconductor.^4–8 Also the semiconductor density of states (DOS) and its distribution of traps affect the electron transport and recombination resulting in different cell V_oc and fill factor (FF).^2,12,13 Core/shell structures are among structures for decreasing the electronic recombination, and thereby, increasing the efficiency of DSSCs.^4–8 The properties of the shell affecting the DSSC performance, depend upon the physical separation of electrons and ions, the energy levels shifting, the creation of a barrier potential at interface, the passivity of the surface traps and the changes of the dye adsorption on the surface.^4–8 Matt Law et al. have introduced ZnO nanowire/TiO₂ shell as efficient DSSC with higher V_oc and FF and lower J_sc compared to bare ZnO nanowire based DSSCs.⁵ They explained the changes of J_sc by different injection rate of different shell thicknesses and increase of V_oc and FF by lower recombination rate and possible band shift. ZnO/TiO₂ core shell structures have been used as DSSC working electrode in different morphologies including nanowires and nanoparticles, also in ultraviolet detectors and photocatalysis.^14–18 In ZnO nanowire/TiO₂ core/shell based DSSCs a small decrease in J_sc and an increase in FF and V_oc of the cell have been reported.^5,14

There are ab initio studies of DSSC semiconductor electronic states and their contribution to the cell performance.^3,19–22 For the hetero-structured semiconductors in the DSSC, however, there are substantially less theoretical studies. Conesa have reported the position of conduction and valence bands in the anatase/wurtzite interface for the bulk TiO₂/ZnO slabs,²² but there is no discussion about mono-layer coating of the shell, surface dipoles changes and the way band positions can be related to DSSC performance in terms of device voltage, current and recombination current.

In this paper we investigate the electronic properties of ZnO surface with a mono-layer of TiO₂ coated on it and use our results to study the effects of core/shell DSSC qualitatively in comparison to the experimental data of ref. 5. The paper is organized as follows: In Sec. I we introduce the subject of ZnO/TiO₂ core/shell DSSC and in Sec. II we present the method of our calculations using the Kohn Sham formalism in the framework of density functional theory (KS-DFT). The results and discussions are presented in Sec. III. First the [101̄ 0] surface of ZnO has been studied. Then, we have studied the ZnO [101̄0] surface with TiO₂ coating, and have calculated the density of states (DOS), surface dipoles, electric fields, position of Fermi energy, surface charge and relaxed positions and compared our results to bare ZnO surface. Furthermore according to our theoretical results, we discuss the possible effects of the TiO₂ shell coating on our DSSC performance and its V_oc, J_sc and FF. Finally, in Sec. IV we talk about the concluding remarks.

Theoretical methods

First principle calculations were performed by Quantum ESPRESSO²³ package using density functional theory (DFT). Moreover, in this theory we have employed the Perdew–Burke–Ernzerhof pseudo-potential²⁴ along with the generalized gradient approximation (GGA) for exchange correlation functional. We employed ultra-soft pseudo-potential in which the Zn 1s/2s/2p, Ti 1s/2s/2p and O 1s electrons considered as core electrons and the rest of electrons considered as valence electrons. Coordinates of all atoms were relaxed by bfgs (Broyden–Fletcher–Goldfarb–Shanno) algorithm,²⁵ until the force acting on each atom is less than 0.002 Ry per a.u and we used the Davidson method for diagonalization of the Hamiltonian. The Kohn-Sham orbitals are expanded in a plane-wave basis set and the optimum cut-off energy for wave function and charge density are 30 and 320 Ry respectively. Self-consistency in total energy is achieved with a tolerance of less than 10⁻⁶ Ry. Brillouin zone sampling was carried out by a 4 × 1 × 2 Monkhorst-Pack grid for relaxation procedure, and by 5 × 2 × 3 Monkhorst-Pack grid for self-consistent procedures.

The unit cell of ZnO surface consists of 8 layers of 2 × 2 ZnO unit cells with the wurtzite structure (Fig. 1(a)). The super-cell is constructed from atomic coordinates and lattice constants obtained via the minimization of ZnO bulk energy. The vacuum layer is 10.0 Angstrom, i.e., it is chosen to be sufficiently large so that the interaction between adjacent cells is negligible. The ZnO/TiO₂ interface includes 8 layers of 2 × 2 ZnO unit cell plus 12 additional Ti and O atoms, forming a monolayer of TiO₂ on the ZnO slab (Fig. 1(b)). The lattice constants of ZnO surface (a = 3.23 Å, c = 5.21 Å) and TiO₂ rutile [100] surface (a = 2.95 Å, c = 4.60 Å) are roughly equal to their corresponding bulk values with differences of 7% and 11% respectively.

Fig. 1 Schematic representation of relaxed super-cells: (a) ZnO [101̄0] slab and (b) ZnO [101̄0] slab coated with a monolayer of TiO₂.

The experimental preparation of the coating has been done by atomic layer deposition with the rate of one-half mono-layer per cycle.²⁶ Therefore, because of lattice mismatch at the interface, the appearance of defects might be possible. For both ZnO and ZnO/TiO₂ slabs, the atomic coordinates of two bottom layers are fixed to the bulk coordinates and the other atoms were relaxed. The DOS of these two layers are subtracted from the total DOS to simulate the DOS of surface layers.

The structure is relaxed for several configurations with different positions of Ti and O atoms relative to ZnO surface atoms, all of which converge to the final positions where Ti atoms have moved closer to the oxygen surface atoms of ZnO slab and each Ti atom with its four adjacent O atoms forms a tetrapod (Fig. 1(b)).

The electric charge profile in the entire unit cell is obtained from our self-consistent calculations and also by integrating the local density of states of atomic orbitals, and by considering the contribution of nuclei and core electrons. The surface charge and surface dipoles can be calculated from the charge profile. Surface dipole electric fields and potentials were calculated according to the eqn (1) and (2), having in mind the first neighbour super-cell surface dipoles:

V(r) and E(r) denote potential and electric field at point r. ε is the permittivity of medium and P is the dipole moment. For calculating the work function, the bare potential of unit cell with extended vacuum layer is calculated and averaged over the entire volume of unit cell. The limiting value of bare potential at far distances is set to be the energy reference, i.e., the zero energy of vacuum.

Results and discussions

I. ZnO [101̄0] surface

Table 1 and Fig. 2 show the relaxation parameters of ZnO [101̄0] slab. The results are in good agreement with previous DFT calculations and experimental results.^27,28

Table 1 Calculated relaxation parameters of ZnO [101̄0] surface.

	Present work (Å)	Theory^a (Å)	Experimental^b (Å)
a Ref. 27. b Ref. 28.
Δ 1,2⊥	0.31	0.38	0.2
Δ 2,3⊥	0.12	0.13	0.0
d 1,2⊥	0.63	0.46	0.62
d 2,3⊥	2.01	2.01	—
Δ 1y	3.41	3.50	3.37
d 1y	2.82	2.76	2.41

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Fig. 2 The relaxation parameters for ZnO [101̄0] slab. The big and small spheres are representatives of Zn and O atoms.

Calculated Zn–O bond length for the surface atoms is 1.86 Å which has about 7% contraction relative to the corresponding bulk bond lengths, and the calculated tilt of Zn–O bond-angle of surface atoms was 10.1 degrees-being in agreement to previous results.^27,29,30 By calculating the Mulliken charges of atoms, the bond of relaxed surface atoms in comparison to inner layer atoms tend to show up their covalent nature. Comparison of relaxed and un-relaxed ZnO [101̄0] slab shows slight change of states at the top of valence band (VB) and at the bottom of the conduction band (CB) in agreement with ref. 30. Oxygen vacancies in ZnO lead to the presence of intra-gap states³¹ which could be responsible for trap states distribution present in DSSCs. Also in TiO₂ nanoparticles, uncoordinated Ti surface atoms leads to the unoccupied states 0.3–0.4 eV lower than CB.³² The calculated value of the work function of ZnO [101̄0] surface is −4.76 eV relative to vacuum which is in good agreement with the experimental result of −4.65 eV of Moormann et al.³⁴ Finally, our surface energy of [101̄0] surface, defined as the difference between the bulk and the slab energies is 1.27 J m⁻² which is comparable to 1.3 J m⁻² of ref. 30.

In our calculations, band gap of ZnO is underestimated (Fig. 3) which is a well known error for DFT based band structure calculations of wide band gap semiconductors.³³ But DFT can predict the work function, relaxation parameters and surface charges of the semiconductors well enough and comparable to experimental results.^{22,27,29–31,33} We have calculated the band gap of bare ZnO surface as 0.88 eV in agreement with ref. 27 and 41.

Fig. 3 Total DOS of bare and TiO₂ coated ZnO [101̄0] surface. The bar indicates the Fermi level of bare ZnO [101̄0] surface.

II. TiO₂ coated on ZnO [101̄0] surface

Fig. 3 shows the total density of states for the bare ZnO [101̄0] slab and the TiO₂ coated ZnO slab. After the coating, the CB and the VB are shifted to higher energies by approximately 210 meV. This way, we can qualitatively explain the experimentally verified results of decrease in short circuit current, J_sc, after TiO₂ coating on ZnO nanowire.⁵ When the CB of semiconductor is shifted upward, then the injection efficiency and short circuit current would decrease because of lower driving force for electron transfer between the excited dye and the semiconductor.^2,35 Since V_oc in DSSCs is the difference between Fermi energies of electrolyte and semiconductor, by shifting the CB and VB to higher energies, the Fermi level is shifted correspondingly and the V_oc of the cell will have the same increase.^2,11

These computational results are in qualitative agreement with the experimental data of Matt Law et al.⁵ They relate the increase of V_oc to the reduction of dark current, but for thinnest shell of 0.5 nm TiO₂, dark current reduction itself is not sufficient for explanation of their experimental data. Based on our calculations, the recombination resistance should also be enhanced after TiO₂ coating. However, it seems that our calculations are in good agreement with data of thinnest shell of ref. 5 in which increase of V_oc is due to both band shifts and dark current changes and it can explain the changes of injection rate and J_sc.

In order to examine the total DOS shifts, we have investigated the surface charge and surface dipole of the ZnO surface before and after the TiO₂ coating. After the coating of TiO₂ layer, some negative charge is transferred to the ZnO [101̄0] surface, causing the Zn–O bonds to show higher ionic nature and to decrease the magnitude of normal component of the surface dipole. This charge transfer and distribution of surface dipoles can be responsible for energy shifts of CB and VB of ZnO. Normal component of dipole moment to the ZnO surface decreases by the TiO₂ coating, resulting in the band shifts to the higher energies. Calculated normal component of surface dipole layer density is −107 and −84 nC m⁻¹ for bare and TiO₂ coated surfaces respectively. Considering the dielectric constant of wurtzite ZnO as 8, the resulting electric potential difference is 750 − 585 = 165 meV which is of the order of the calculated band shifts and could be, in part, responsible for the band shift. Zaban et al. (an experimental study) and Kusama et al. (a theoretical study) have used co-adsorbed molecules of different dipole moment and relate the CB shift of TiO₂ to the changes of the co-adsorbed molecule dipole moment, which is in agreement with our assumptions and results.^3,11

External electric fields of ZnO/TiO₂ core/shell surface dipoles is calculated at 2.0 nm distance from the surface, the average electric field was 15.0 mV nm⁻¹ which is in fair agreement with the measured electric fields of ref. 36 (23.0 mV nm⁻¹) causing Stark effect to occur in DSSCs.³⁶ Due to surface electric fields, energy levels of adsorbed dye will be splitted and its absorption spectra will be shifted (Stark effect). The order of magnitude of the calculated surface dipoles are the same as the experimental values. It should be emphasized that the presence of dye and electrolyte ions will affect the surface electric fields considerably. Consideration of electrolyte, thicker TiO₂ shells, attachment of dyes to TiO₂ coating on ZnO, and inclusion of defects due to lattice mismatch in an ab-initio study can increase the accuracy of our results of real DSSCs.

The local density of states (LDOS) of surface atoms and bulk, namely inner, atoms are plotted in Fig. 4. Also the calculated LDOS for the bare ZnO and the coated ZnO are shown in the figure. The effect of TiO₂ coating on the LDOS of surface and bulk atoms is obvious in the Fig. 4. Because of the changes in the surface electric fields, we expect that the LDOS of surface atoms change their shape and position but the LDOS of bulk atoms keep their shape and shift the position of peaks only. Moreover, comparison of the total DOS shifts and LDOS shifts of ZnO bulk atoms shows that the order of magnitude of the peak shifts are almost the same (for the bulk atoms, LDOS shifts due to coating are from 150 to 300 meV but for the surface atoms, it is hard to define the peak shifts because of changes in peak shape. For the surface atoms, different peaks have different shifts from 600 to 1000 eV (Fig. 4)). The nearest neighbour interacting atoms and chemical environment surrounding the bulk atoms, will not changed by the coating of TiO₂ and they just experience a shift induced by surface dipoles to the total DOS. But chemical environment of surface atoms will be changed by the coating, and we expect changes of peak shape as well as its position.

Fig. 4 Comparison of the LDOS of selected atomic orbitals for bare ZnO (solid curve) and coated ZnO (dotted curve): (a) Zn 3d surface atom, (b) Zn 3d bulk atom, (c) Zn 4s surface atom, (d) Zn 4s bulk atom, (e) O 2p surface atom, (f) O 2p bulk atom.

Fig. 5 shows a schematic representation of band positions and dipole layers for bare and TiO₂ coated on ZnO surface. V_oc1 and V_oc2 represent the open circuit voltage of bare and TiO₂ coated on ZnO nanowire based solar cells. Shift of TiO₂ coated ZnO energy levels toward higher energies due to the coating, leads to its higher open circuit voltage compared to bare ZnO surface.

Fig. 5 Qualitative representation of band positions and dipole layers for bare and TiO₂ coated on ZnO surface. V_oc1 and V_oc2 represent the open circuit voltage of bare and TiO₂ coated on ZnO nanowire based solar cells. Calculated normal component of surface dipole in vacuum is indicated.

Partial density of states (PDOS) of surface atoms is shown for bare ZnO surface and for the TiO₂ coated surface (Fig. 6). There is a small peak in the energy gap of TiO₂ coated on ZnO which belongs to the TiO₂ layer (Fig. 6). It seems that this intra-gap state is a consequence of configuration of oxygen and titanium uncoordinated surface atoms and could be changed for a thicker shell of TiO₂. This small peak introduces surface trap states in the gap which act as trapping centres.

Fig. 6 PDOS of interface atoms for bare ZnO slab and for TiO₂ coated ZnO slab.

Our results, in agreement with ref. 39 and 40, show that the DOS of acceptor states for the TiO₂ is much higher than ZnO which can result in higher injection efficiencies for TiO₂ compared to ZnO.^39,40

Surface recombination of electrons to the electrolyte acceptor states and electron injection from dye to the semiconductor can be described by the Marcus theory of electron transfer and strongly depends on the DOS of empty acceptor states and energy level difference of acceptor and donor states.^37,38 Distribution of traps affects the electronic transport and lifetimes.¹² For surface recombination, the TiO₂ coated surface has much larger DOS in the CB, and the injected electrons lie near the CB minimum, but for bare ZnO surface, electrons fill the low density CB states and may fill the higher energies above the CB minimum. Shifting the energy levels of ZnO slab to the higher energies by TiO₂ coating, results in a shift of intra-gap trap states and decrease the overlap of semiconductor exponential trap distribution by the density of acceptor states of electrolyte.¹¹ This fact results in higher electron lifetime of TiO₂ coated surface.³⁷

Concluding remarks

In summary, we have investigated the electronic states of ZnO/TiO₂ interface and have calculated the effect of TiO₂ shell coating on the semiconductor band structure of ZnO as well as the surface charge. TiO₂ shell changes the surface dipole distribution of ZnO nanowire causing a shift in the CB and VB of ZnO to higher energies. Calculated electric potential difference caused by surface dipole changes is in the order of the calculated band shifts and could be, in part, responsible for the band shift. This result is in qualitative agreement with the trend of experimental data of Matt Law et al. explaining the increase in V_oc and decrease of J_sc using a mono-layer of TiO₂ shell.⁵ Our results show that TiO₂ shell decreases the overlap of ZnO surface trap density of states with electrolyte density of acceptor states, and in this way it can reduce the surface recombination of semiconductor electrons to the electrolyte oxidized states and increase the filling factor of the cell.

External electric fields due to surface dipoles of TiO₂ coated on ZnO is calculated, and the average electric field is found to be 15.0 mV nm⁻¹ which is in fair agreement with the measured electric fields (23.0 mV nm⁻¹) causing the Stark effect in DSSCs. This method can be used for studying the semiconductor surface states in the core/shell DSSCs in terms of surface local DOS, surface dipoles and possible band shifts and estimation/provision of different shell and core materials for improving the DSSC performance.

Acknowledgements

We wish to thank R. Asgari, R. Imani and T. Edvinson for their helpful discussions. We are also grateful to the Institute of fundamental sciences (IPM), Tehran for allowing us to use their computational cluster facilities.

Notes and references

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