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Keywords:

  • band gap engineering;
  • dye-sensitized solar cells;
  • energy conversion;
  • photocatalysis;
  • photovoltaics

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

Long-term sustainable solar energy conversion relies on identifying economical and versatile semiconductor materials with appropriate band structures for photovoltaic and photocatalytic applications (e.g., band gaps of ∼1.5–2.0 eV). Nickel oxide (NiO) is an inexpensive yet highly promising candidate. Its charge-transfer character may lead to longer carrier lifetimes needed for higher efficiencies, and its conduction band edge is suitable for driving hydrogen evolution via water-splitting. However, NiO’s large band gap (∼4 eV) severely limits its use in practical applications. Our first-principles quantum mechanics calculations show band gaps dramatically decrease to ∼2.0 eV when NiO is alloyed with Li2O. We show that LixNi1−xO alloys (with x=0.125 and 0.25) are p-type semiconductors, contain states with no impurity levels in the gap and maintain NiO’s desirable charge-transfer character. Lastly, we show that the alloys have potential for photoelectrochemical applications, with band edges well-placed for photocatalytic hydrogen production and CO2 reduction, as well as in tandem dye-sensitized solar cells as a photocathode.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

Solar energy is a prime candidate for supplanting fossil fuels as a renewable and clean energy source. Engineering novel materials that efficiently convert sunlight to electricity and fuels drives much of the research on photovoltaic (PV), photocatalytic (PC), and dye-sensitized solar cell (DSSC) technologies.13 PV and PC technologies usually rely on semiconductors to absorb photons and generate electron–hole pairs.4, 5 Semiconductors with smaller band gaps absorb more sunlight and produce higher short-circuit currents (Isc), but the resulting charge carriers have less energy, leading to low open-circuit voltages (Voc).6 For PV applications, these competing effects lead to an optimal band gap of ∼1.5 eV.6 For PC applications, the band edges of the semiconductor should also be suitably placed to drive electrochemical reactions.5, 79

For instance, PC hydrogen production involves two half reactions (with potentials referenced to vacuum, based on the absolute potential of the standard hydrogen electrode (SHE)):10(1), (2)

  • equation image(1)
  • equation image(2)

Photo-generated holes drive oxidation when the valence band edge (VBE) lies sufficiently below the oxidation reaction’s potential (Figure 1 a). Likewise, excited electrons drive reduction when the conduction band edge (CBE) lies sufficiently above the reduction reaction’s potential. The necessity to overcome kinetic barriers and thermodynamic losses impose these constraints on the band edge positions and add ∼0.5 eV to the optimal band gap for PC water-splitting compared to PV.7, 8 Reduction of CO2 to form fuels or fuel precursors such as methane (CH4), methanol (H3COH) and formic acid (HCO2H) involves similar constraints on the CBE of the semiconductor. In these cases the CBE should lie well above the reduction potential of the CO2/CH4 (−4.04 V at pH=0), CO2/H3COH (−3.90 V at pH=0) and CO2/HCO2H (−3.67 V at pH=0) half reactions.9

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Figure 1. Schematic diagrams of necessary band alignment for (a) PC water-splitting and (b) tandem DSSCs. The dashed lines correspond to redox potentials. For DSSCs, the redox potential of I/I3 is used as an example. D1 and D2 refer to dye molecules at the photoanode and photocathode, respectively. D, D+ and D* correspond to the neutral, the singly ionized, and the excited dye molecules, respectively.

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Band edge positions also play a significant role in DSSCs, another intriguing class of solar energy conversion devices. DSSCs have great potential for achieving high efficiencies when used in tandem structures (Figure 1 b).11, 12 In such cells, n-type and p-type semiconductor films act as photoanodes and photocathodes, respectively.11, 12 These semiconductor layers are coated with light-absorbing dyes, which are in contact with an electrolyte. At the photocathode, the photo-excited dye molecules (D*) donate electrons to the oxidized species in the electrolyte (process i in Figure 1 b), for example, I3 in an I/I3 redox system with a reduction potential of −4.72 V with respect to vacuum.13, 14 Hole transfer from the ionized dye (D+) to the valence band of the p-type semiconductor then regenerates the dye in its ground state (process ii in Figure 1 b). In a similar process, excited dye molecules donate electrons to the n-type semiconductor at the photoanode and then are regenerated in their ground state by an electron transfer from the electrolyte. Ultimately, the photocurrent of the device is limited by the electron transfer processes at the photoelectrode with the weaker photocurrent.12 This photoelectrode happens to be the photocathode in available DSSC devices.11, 12, 1416 This deficiency partly stems from the low rate of hole injection from the dye molecules to the VBE of the p-type semiconductor.17 To improve this rate, the VBE needs to lie sufficiently higher than the ground state of the dye molecule. In general, the position of the CBE is immaterial to the performance of the photocathode, as long as it lies higher than D*/D+ potential so as to prevent the loss of excited electrons of the dye to the semiconductor. However, direct electron transfer in n-type DSSCs from a hole conductor (which is used as an alternative to liquid electrolytes) to the semiconductor can contribute to Isc.18 Similarly, electron injection from the CBE of the p-type semiconductor to the electrolyte (process iii in Figure 1 b) might also contribute to Isc of a tandem DSSC if the semiconductor’s CBE lies sufficiently higher than the potential for the reduction reaction of the electrolyte. A critical component of engineering efficient PV and PC materials thus involves tuning band gaps and placing band edges appropriately.

Nickel(II) oxide (NiO) is an inexpensive semiconductor already being used in PV and PC applications.1922 It has a rock salt structure, with Ni2+ ions anti-ferromagnetically coupled in the [111] direction.23 The VBE and CBE of NiO have O 2p and Ni 3d character, respectively. This makes NiO a charge-transfer (CT) material. In contrast to Mott-Hubbard type semiconductors, where the VBE and CBE are both of Ni 3d character, the VBE and CBE of a CT material have different characters.23 The CT property might produce long carrier lifetimes,9, 24 making NiO appropriate for use as a semiconductor in p-type17, 19, 21, 2527 and tandem DSSCs.11, 12, 1416 Furthermore, its CBE is well positioned to drive PC hydrogen production,28 justifying its use as a water-splitting co-catalyst,22 and for CO2 reduction to produce fuels, such as CH4, H3COH, and HCO2H.28 Unfortunately, its large, indirect band gap (3.4–4.6 eV)23 has limited its functionality as a light absorber and its low VBE inhibits hole injection from dye molecules to NiO in DSSCs.17 Expanding NiO’s versatility in solar energy applications is then a matter of reducing NiO’s band gap while preserving its CT character, preserving its favorable CBE position for PC, and improving its VBE for DSSC applications.

Alloying is one route to engineer a material’s electronic and optical properties for specific purposes. For example, the alloy of gallium nitride (GaN) and zinc oxide (ZnO) has a lower band gap than both pure GaN and ZnO.29 Our group recently predicted that some transition-metal oxide alloys (MnxZn1−xO, FexZn1−xO, FexNi1−xO) have lower band gaps compared to the pure oxides.24, 30 Several metal oxides (e.g., ZnO, magnesium oxide (MgO) and lithium oxide (Li2O)), are highly miscible with NiO and form solid solutions, making them candidates for alloying.3133 Of these, Li2O is a particularly promising alloying partner, given that Li is an abundant and relatively inexpensive metal. Experiments show that NiO/Li2O alloys have the rock salt structure and are of the form LixNi1−xO up to at least x∼0.25.33, 34 This means that at these concentrations Li ions occupy cation sites (substituting Ni ions) and are not charge compensated by, for example, excess oxygen. Hence, with Li being a monovalent element, LixNi1−xO alloys (with x below 0.25) are p-type semiconductors35 suitable for the p-side of pn junctions in PVs, and for photocathodes in PCs and tandem DSSCs. Lastly, including Li suppresses the intrinsic vacancies in the NiO lattice structure36 that can deleteriously trap carriers. Experimental work over the past decades showed the appearance of empty states above the VBE and below the CBE of NiO when forming LixNi1−xO alloys.34, 37 These states were speculated to be impurity levels, since little increase in the conductivity upon alloying was observed. More recent studies have shown a dramatic increase in conductivity with increasing concentration of Li.35, 3840 However, these studies use a variety of experimental techniques to grow the alloy and measure a wide range of band gaps for LixNi1−xO alloys between 2.6 and 4 eV for x=0.25.3840 Thus the actual band gaps of these alloys are still a matter of debate. A more rigorous understanding of LixNi1−xO electronic structure is thus needed to determine its applicability in PVs and PCs.

First principles theoretical methods can predict fundamental electronic properties of semiconductors (e.g., band gaps, positions of band edges, impurity formation, etc.). Theoretical modeling of LixNi1−xO alloys can help evaluate their promise for PV and PC applications. The theoretical description of the NiO electronic structure has been the subject of many studies over the past decades.23, 4146 Self-interaction error (SIE) causes standard Kohn–Sham density functional theory (KS-DFT)47 to fail for NiO by predicting it to be a conductor.44, 45 SIE stems from the inability of approximate DFT exchange-correlation (XC) functionals to properly treat the tightly-bound, open-shell Ni 3d electrons. The KS-DFT-based DFT+U method alleviates this problem by introducing Hartree–Fock (HF)-like average Coulomb (U) and exchange (J) terms to correct intra-atomic exchange interactions between Ni 3d electrons and hence, correct for SIE.43, 44 With an appropriate U–J value, this method predicts NiO to be a semiconductor,45 thereby describing ground state NiO quite well. Then, the non-self-consistent many-body Green’s function theory G0W048 as a perturbation correction to the one-electron wavefunctions and eigenvalues of DFT+U theory (DFT+U/G0W0) provides a quasiparticle (QP) gap directly comparable to photoemission (PE)/inverse photoemission (IPE) spectroscopy measurements. G0W0 as a perturbation correction to ground state theories has been quite successful when applied to a variety of transition-metal oxides including NiO.28, 30, 49, 50 Finally, the positions of the band edges relative to the vacuum level can then be determined using the QP gap and the position of the band gap center (BGC), where the latter can be calculated by DFT+U periodic slab calculations of the material’s work function.28, 51 Overall, the combination of DFT+U and G0W0 provides a powerful tool to evaluate the parameters most relevant to the application of LixNi1−xO in PVs and PCs.

Our first principles quantum mechanics calculations presented herein show that alloying NiO with Li2O results in an improved band gap for solar energy applications. Specifically, LixNi1−xO alloys with x=0.125 and x=0.25 have a considerably lower band gap than pure NiO. We find states that are devoid of impurity levels in the band gap and show that NiO’s favorable CT property is actually enhanced in the alloys. Using methodology developed in our group,28 we also calculate LixNi1−xO band edge positions and predict that their CBEs are still appropriate for driving the reduction half-reaction in PC water-splitting and CO2 reduction to form fuels. Furthermore, we will show that the VBEs of these alloys are much more favorable than pure NiO for accepting holes from the photo-excited dye molecules in the photocathode of tandem DSSCs.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

With the Perdew–Burke–Ernzerhof (PBE)52 functional treating XC and the ab initio U–J value of 3.8 for the Ni2+ ions, our DFT+U/G0W0 calculations confirm that NiO is a CT semiconductor with a gap of 3.6 eV28 (for details about the UJ calculations, conducted using a method developed in our group,53, 54 and more information about bulk calculations, see Supporting Information, Sections S1–S3). This value for the QP gap lies within the 3.4–4.6 eV23 experimental range of band gaps (vida infra). Likewise, PBE/G0W0 calculations on the anti-fluorite55 ground state structure of Li2O predict pure Li2O to be an insulator with a gap of 7.3 eV, also in excellent agreement with experimental range of 7.0–7.5 eV56 (for further details of the validation tests on the electronic and crystal structure of pure NiO and Li2O see Supporting Information, Section S4). These validation tests suggest that PBE+U/G0W0 can be trusted to accurately predict the electronic structure of LixNi1−xO alloys.

Studying the ground state electronic structure of LixN1−xO can shed light on the qualitative nature of its band structure. We can also use PBE+U ground state calculations to screen for desirable states that merit examination with QP calculations. Our PBE+U calculations show a rather interesting combination of two different types of electronic structures for x=0.125. Figure 2 a and b show representative cases of these two electronic structures, corresponding to two of the unit cells considered. One of these cells contains 16 atoms and the other contains 32 atoms. The electronic structure of the 16-atom cell shows no impurity levels in the gap (Figure 2 a). This cell was derived from a special quasi-random structure (SQS) unit cell for the bulk at an alloying concentration of x=0.25 (for more details see the Computational Details Section). SQS cells mimic the correlation function of a random alloy solid solution.57, 58 The Li atoms are nearest metal cation neighbors to each other in the crystal structure resulting from this 16-atom cell. On the other hand, there are deep impurity levels in the band gap of the 32-atom cell (Figure 2 b), where Li atoms are next-nearest metal cation neighbors to each other. The source of these impurity levels is the formation of low-spin Ni3+ ions with magnetic moment 0.9 μB, as shown in the spin-density difference plot in Figure 2 d (compare this to Figure 2 c, in which all the Ni ions are high-spin Ni2+ with magnetic moments ∼1.5–1.6 μB). The site-projected density of states (pDOS) shows that the impurity levels in the gap of the 32-atom cell are mostly due to the presence of these low-spin Ni3+ ions (see the Supporting Information, Section S5 a). Recently, Chen and Harding also identified such impurity levels in Li0.125Ni0.875O and reached the same conclusion about their nature.59 But they only considered one unit cell structure and therefore did not find any other state devoid of Ni3+.

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Figure 2. The pDOS n(E) associated with Li0.125Ni0.875O PBE+U calculations on the (a) 16-atom and (b) 32-atom cells that differ in their relative placement of Li atoms. The relative positions of Li ions in a section of the crystal are shown in the insets of (a) and (b). Positive and negative n(E) correspond to the majority and minority spin states, respectively. This convention has been used in all other DOS plots. In the insets, Li, Ni (spin up), Ni (spin down) and O atoms are depicted by green, blue, gray and red colors, respectively. Empty states corresponding to free holes are clearly present at the edge of the valence band in (a). Deep impurity levels are prominent in the gap in (b). (c) and (d) show the spin-density difference plots (ρup-ρdown, where ρ is the electron density) for two representative planes that contain Ni ions in the 16-atom and 32-atom cells, respectively. The units are electrons per bohr3. Each Ni ion is labeled by its magnetic moment.

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Our calculations on other cells show two sets of states, each resembling one of the states presented in Figure 2 a and b (for the other cases studied and more information regarding impurity levels, see the Supporting Information, Section S5 a–c). The energy per atom of these states do not greatly differ from each other, with the maximum difference being ∼17 meV, which is even smaller than the thermal energy at room temperature (26 meV). Thus these different kinds of states will probably coexist in an actual random alloy. However, the macroscopic band gap of the alloy will be determined by the state with the lowest gap, which happens to correspond to the 16-atom SQS-derived cell. Additionally, the relative positions of the Li atoms in the 16-atom cell are very close to those of the anti-fluorite structure of Li2O, making the 16-atom cell a likely configuration at this high concentration. Another important feature of the state associated with the 16-atom cell is the strong O 2p character of the empty levels in the vicinity of the VBE. Unlike the 32-atom cell state in which the introduced holes are on Ni ions, the O 2p character of the holes in the 16-atom state is consistent with previous experimental and theoretical findings for this alloy.37, 60, 61 For these reasons we chose this cell as the representative cell for x=0.125 for determining the QP gap and evaluating the Li0.125N0.875O viability for solar energy conversion. Similar to the ground state of the 16-atom cell with x=0.125, calculations at x=0.25 on the SQS cell also show no impurity levels (see the Supporting Information, Section S5 b). We therefore went on to investigate the 16-atom, x=0.125 and the 16-atom, x=0.25 unit cells with G0W0 calculations to determine their QP gaps.

Figure 3 shows the G0W0 pDOS for pure NiO, the 16-atom SQS-derived Li0.125Ni0.875O, and the 16-atom SQS Li0.25Ni0.75O bulk unit cells. The two alloys both have QP gaps, defined as the difference between the VBE and CBE, of ∼2.0 eV. Like pure NiO, these two gaps are both indirect. An indirect band gap could have a detrimental effect on light absorption; however, it could also act as an obstacle against carrier recombination (for more details about the indirect QP gaps of NiO and its alloys see the Supporting Information, Section S6). The QP gaps of both alloys are substantially lower than that of pure NiO (3.6 eV), and they both imply that these two alloys will absorb light in the visible region of the solar spectrum and in the optimal range for PC water-splitting applications. The highest occupied levels (Fermi levels) for both of the alloys lie within the valence bands (∼0.5 and 0.4 eV below the VBE for x=0.125 and 0.25, respectively), making the levels in the vicinity of the VBE empty at zero temperature. At room temperature, however, some of these levels will become occupied up to ∼0.1 eV above the Fermi level. Overall, the absorption is predicted to be strongest above ∼2.4 eV. The two alloys have very similar QP gaps, suggesting the reduction in the gap with increasing Li content plateaus somewhere around the two concentrations we studied. Such behavior has also been seen in other examples of transition-metal oxide alloys.24 This lack of change could even be beneficial, since it shows that small changes in the concentration will probably not affect light absorption much. Two effects account for the reduction in the band gap. First, heavy doping of semiconductors typically leads to gap narrowing, albeit only by ∼0.1 eV.62, 63 Second and more importantly, Li states are clearly present in the vicinity of the VBE and, to a lesser extent, the CBE of the alloys (Figure 3 b and c insets). Li/Ni/O hybridization thus broadens the peaks and narrows the gap. The O 2p peaks in the vicinity of the VBE and also the conduction bands are considerably broader in the alloys. The former enhances the presence of O 2p states at the VBE, while the latter leads to a higher range of available empty energy levels in the conduction band that can host excited electrons. In agreement with previous findings,37, 60, 61 O 2p states at the VBE show the alloys retain the CT property of NiO despite the alloys’ narrowed gaps and markedly different electronic structures. Lastly, the alloys are p-type since they introduce holes into the valence band, evident from the empty states immediately below the VBE. These features all point to the great potential of these alloys for significant light absorption.

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Figure 3. The G0W0 pDOS n(E) of LixNi1−xO for (a) pure NiO, that is, x=0, (b) x=0.125 and (c) x=0.25. The black and red arrows indicate the positions of the VBE and CBE, respectively, with respect to vacuum for each case. The dashed vertical line shows the highest occupied electronic state while the solid blue vertical lines indicate the redox potentials for water-splitting half reactions, I/I3 and CO2 reduction reactions producing methane, methanol, and formic acid at pH=9.9 (the pHpzc of NiO). The insets show a more detailed picture of the VBE and the CBE by zooming in closer to the edges.

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The viability of these alloys for PC and DSSC applications ultimately hinges on the positions of the VBE and CBE with respect to the vacuum level. Our band edge calculations reveal that the Li0.125Ni0.875O and Li0.25Ni0.75O alloys’ VBE (CBE) is shifted up (down) compared to the corresponding values for pure NiO (arrows in Figure 3). The position of the inner peaks do not change substantially upon alloying, indicating the robustness of our evaluation of the energies with respect to vacuum. The CBEs of both these alloys lie 0.90 eV above the redox potential of the H2/H+ reduction reaction at pH=9.9, the point of zero charge (pHpzc) for NiO64(Figure 3 b and c). pHpzc is the pH at which the surface of the semiconductor is neutral. As for CO2 reduction, the CBE of Li0.125Ni0.875O and Li0.25Ni0.75O alloys remains above the redox potential of CO2/CH4, CO2/H3COH and CO2/HCO2H half reactions by 0.66 eV, 0.52 eV and 0.29 eV, respectively. Hence, the photo-generated electrons should capably drive H2/H+, CO2/CH4 and CO2/H3COH reactions thermodynamically and kinetically by providing ample over-potential. With the help of an external bias, the excited electrons from the CBE of the alloys could also drive CO2/HCO2H. For example, PC hydrogen production from water on hematite electrode surfaces has been achieved with an external bias.65 Overall, both Li0.125Ni0.875O and Li0.25Ni0.75O look to be highly promising as co-catalysts for hydrogen production in PC water-splitting and CO2 reduction.

For NiO-based tandem DSSC photocathodes, the VBE position is the crucial parameter. Our calculations show that the VBEs of Li0.125Ni0.875O and Li0.25Ni0.75O alloys lie considerably higher than the VBE of pure NiO (Figure 3). Yet the VBE remains below the I/I3 redox potential, enabling the establishment of VOC at the photocathode (∼0.2 V). Note that this voltage is much smaller than the voltage at which Li ions are extracted from the crystal structure of some other NiO/Li2O alloys (∼3.6 V).66 Therefore, it is unlikely that Li ions are extracted from the host NiO structure of Li0.125Ni0.875O and Li0.25Ni0.75O upon being connected to a circuit. Overall, the VBE of these alloys much more capably accepts holes from the dye molecules, compared to NiO’s VBE. The contribution of alloying does not end here. The lower band gap of Li0.125Ni0.875O and Li0.25Ni0.75O enables them to absorb some of the sunlight that the dye might fail to absorb. The CBE of these alloys lies more than 1.2 eV higher than the redox potential of a common electrolyte such as an I/I3 redox system. Hence, some of the photo-generated electrons in the conduction band of the oxide could directly contribute to the electrochemical reaction in the electrolyte. Such a contribution is desired when LixNi1−xO light absorption does not deleteriously affect the amount of available light that can be absorbed by the dye molecules. This implies that LixNi1−xO alloys should be incorporated in tandem DSSCs as a back electrode. In other words, in an optimal design for a tandem DSSC with LixNi1−xO alloys as a photocathode, the light must enter the device through the transparent n-type semiconductor of the photoanode and be absorbed by the dye molecules. The photocathode can then absorb the light that the dye layers have failed to absorb. Overall, the Li0.125Ni0.875O and Li0.25Ni0.75O alloys can improve the efficiency of NiO-based DSSCs by contributing to light absorption as well as enhancing dye to VBE hole injection.

Conclusions

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

We have shown that the band gap of the p-type LixNi1−xO alloys with x=0.125 and x=0.25 lies very close (∼2.0 eV) to the optimal band gap for PC applications, which requires visible light absorption. These alloys should dramatically increase light absorption compared to pure NiO, which has a large band gap of ∼3.4–4.6 eV that only absorbs a tiny fraction of the solar spectrum. Alloying allows a much larger fraction of sunlight to be absorbed while retaining the potentially electron–hole-pair-lifetime-extending CT properties and an optimal CBE for PC water-splitting and CO2 reduction found in pure NiO. Moreover, the VBEs of these alloys are placed favorably for accepting photo-generated holes from dye molecules in the photocathode of tandem DSSCs. The lower band gap of these alloys can further aid light-absorption if used as a back electrode in tandem DSSCs. We have thus provided the initial evidence that alloying NiO with Li2O can be expected to make NiO a versatile material for light absorption, charge transport, and redox chemistry in both PV and PC applications.

Computational Details

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

We performed our DFT+U and DFT+U/G0W0 calculations using VASP version 5.2.2.67, 68 To find the equilibrium geometries and the ground state electronic structures, we ran spin-polarized PBE+U calculations using the PBE generalized gradient approximation (GGA)52 as our XC functional on different unit cells, corresponding to pure and alloyed cases. (For further computational details and more information about bulk calculations, see Supporting Information Sections S2 and S3). Non-self-consistent G0W0 calculations were then performed on the optimized PBE+U geometries as a perturbation correction to PBE+U one-electron wavefunctions and eigenvalues.

For pure NiO, we used a 4-atom rhombohedral cell, with the Ni ions anti-ferromagnetically coupled in the [111] direction, as observed experimentally.23 To find the ground state electronic structure of anti-fluorite Li2O,55 we performed PBE calculations on a 3-atom unit cell. We used a SQS57, 58 unit cell for the bulk at an alloying concentration of x=0.25, in which the periodic 16-atom cell contained two Li and six Ni ions, along with eight oxygen ions, while preserving the antiferromagnetic ordering of the Ni ions in NiO. However, for x=0.125 we could not find an SQS cell with 32 atoms or less. Cells that contain more than 32 atoms are computationally prohibitive for our eventual G0W0 calculations. Therefore, we used the x=0.25 16-atom SQS cell with one less Li ion (i.e., one more Ni ion) along with four different 32-atom ordered cells to model the crystal structure for x=0.125. These cells differ in how Li ions are placed relative to each other. As in x=0.25, all x=0.125 cases are set to preserve the magnetic ordering of pure NiO (for details about these unit cells, see Supporting Information, Sections S2 and S5 a).

The VBE and CBE positions are the key parameters for determining the applicability of LixNi1−xO alloys in PC and DSSC applications. However, the position of the band edges with respect to vacuum cannot be determined using bulk DFT calculations. Band energies from periodic DFT calculations are shifted due to contributions from pseudopotentials that represent the nucleus and core electrons.69 This prompted us to develop a procedure to evaluate absolute band energies with respect to the vacuum level, including the VBE and CBE.28 Using this approach, we determined the BGC position with respect to vacuum by performing DFT+U calculations on periodically replicated slabs that are cleaved from the bulk unit cells along the (100) plane (the lowest energy surface of the rock salt crystal structure of NiO) and separated by a sufficiently large vacuum layer above their surface (for details see Supporting Information, Section S7). We found in our previous work that calculating the BGC with respect to vacuum has several advantages, including computational efficiency and better agreement with experiment, compared to calculating the VBE.28 After establishing the BGC position, we use the QP gap to specify the position of the VBE and CBE, which should correspond to the experimental VBE and CBE at pHpzc. We chose this method to predict the VBEs and CBEs of NiO alloys because we previously showed that it provides a better agreement with experiment for transition-metal oxide band edges when compared to other computational methods28 (for a detailed comparison between the experimental and theoretical values of the VBE for NiO, see the Supporting Information, Section S8). To verify the solubility of Li in NiO at high concentrations (up to 25 %), formation energies of the considered alloys were calculated in oxygen-rich conditions using PBE+U (for details, see the Supporting Information, Section S9).

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

E.A.C. thanks the U.S. Department of Energy, Basic Energy Sciences and the Air Force Office of Scientific Research for funding this project. A portion of the research was performed using EMSL, a national scientific user facility sponsored by the Department of Energy’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Research leading to these results also received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n° [254227] to M.C.T.

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Results and Discussion
  5. Conclusions
  6. Computational Details
  7. Acknowledgements
  8. Supporting Information

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