Defect engineering of the electronic transport through cuprous oxide interlayers

The electronic transport through Au–(Cu2O)n–Au junctions is investigated using first-principles calculations and the nonequilibrium Green’s function method. The effect of varying the thickness (i.e., n) is studied as well as that of point defects and anion substitution. For all Cu2O thicknesses the conductance is more enhanced by bulk-like (in contrast to near-interface) defects, with the exception of O vacancies and Cl substitutional defects. A similar transmission behavior results from Cu deficiency and N substitution, as well as from Cl substitution and N interstitials for thick Cu2O junctions. In agreement with recent experimental observations, it is found that N and Cl doping enhances the conductance. A Frenkel defect, i.e., a superposition of an O interstitial and O substitutional defect, leads to a remarkably high conductance. From the analysis of the defect formation energies, Cu vacancies are found to be particularly stable, in agreement with earlier experimental and theoretical work.

In order to provide insight into this question, we study in the following prototypical Au-(Cu 2 O) n -Au junctions including different kinds of defects such as vacancies (O or Cu), substitutional, interstitial (N or Cl) and Frenkel defects at different positions in the structures. We carefully optimize the atomic positions, in order to obtain physically relevant results. Note that in the main text our focus is on the optimized structures; but in most figures we include also the results for the unrelaxed structures for comparison, including some brief comments in order to highlight relevant changes due to relaxation. As is apparent from the results, the optimization of the structures strongly affects the electronic structure and transport properties such as the transmission coefficient and the conductance. Generally bulk defects are more effective for enhancing transport than near-interface defects. In order to increase the conductance we suggest that interstitial defects are more suitable than substitutional ones.
We note from the start that formally, one defect for the n = 4 junction corresponds to a defect concentration of 3.8%. We also wish to emphasize that the comparison of our model results with experimental data can only be qualitative, since the latter strongly depend on the method of preparation, as well as the concrete substratewhich we are, at least at present, not able to incorporate in a quantitative way.

Results
Using SIESTA 39 as electronic structure package, the transport properties are calculated by the SMEAGOL [40][41][42] code, which employs the nonequilibrium Green's functions method. Periodic boundary conditions are applied perpendicular to the [100] transport direction. The Perdew-Burke-Ernzerhof version 43 of the GGA is utilized for the exchange-correlation potential. Moreover, the energy cutoff is set to 250 Ry, and Monkhorst-Pack k-meshes of 15 × 15 × 25 points for the leads and 15 × 15 × 1 points for the transport calculations are used. Norm-conserving pseudopotentials are employed (fully nonlocal Kleinman-Bylander type 44 with double-zeta basis set). The pseudopotentials for the Cu, O and Cl atoms include nonlinear core corrections in the exchange correlation potential 45 . The basis set superposition error is corrected using the counterpoise procedure 46 .
A lattice strain of 4% is introduced by assuming an epitaxial interface, and therefore setting the Cu 2 O lattice constant to the Au value of 4.09 Å. All structural optimizations (relaxations) are based on the conjugate gradient method, converging the net force on each atom down to 0.04 eV/Å. The leads are modeled by two atomic layers of face centered cubic [001] Au; in addition, four Au layers on each side of the (Cu 2 O) n layer are included in the scattering region. We study Au-(Cu 2 O) n -Au junctions comprising n = 1 to 4 Cu 2 O unit cells, which corresponds to 3 to 9 atomic layers of Cu 2 O.
Comparison to previously published theoretical results on bulk Cu 2 O and Au shows good agreement with our calculations for the bulk materials 7 . The well-known fact that GGA underestimates the bulk band gap indeed is an issue of debate, but we take here the point of view that, since the band dispersions are qualitatively correctly described by first-principles calculations, a correct description of transport through small heterostructures can be expected, in particular, concerning the defect and doping dependence.
The pristine and defective heterojunctions under study are displayed in Fig. 1. We consider, in particular, defects at or near the interface (near-interface), as well as in the bulk (bulk-like). Concerning O, we study O vacancies near-interface, Fig. 1(c), and bulk-like, Fig. 1(d), and O interstitials near-interface, Fig. 1(e), and in the bulk (not presented in Fig. 1). Furthermore, Cu vacancies at the interface, Fig. 1(f), and in the bulk, Fig. 1(g), are addressed. For Frenkel defects, where an O atom is removed from a certain layer and inserted into another one, there are two possibilities, near-interface, Fig. 1(h), and bulk-like, Fig. 1(i). Finally, N and Cl substitutional and interstitial defects are also considered at different positions in the structure.
Due to the contact between Au and Cu 2 O, the optimization changes the positions of the atoms at the interface and in the bulk of the Cu 2 O interlayer; for pristine junctions, e.g., the Au-Cu distance at the interface is reduced by about 4% due to relaxation. Defects, even those that are two layers away from the interface, alter the atomic positions further: in fact the additional shift of Cu towards Au at the interface is maximal for the cases (e), (g), and (h) in Fig. 1 (another 6%).
The defect formation energies give an indication which defects are more likely to be of experimental relevance than others; it is defined as the energy of the defective structure, minus the energy of the respective "constituents": where the subscript "total" refers to the respective total energies. For example, for an X vacancy, E total 0 is given by the total energy of the pristine structure, from which the energy of a single X atom is subtracted: total 0 total pristine X In particular, we determine E Cu from the Cu bulk energy, while we assume E O to be half the molecular energy. For a substitutional defect, where the atom X is replaced by the atom Y, we have The argumentation for interstitial and Frenkel defects proceeds similarly. The formation energies-as well as the respective conductances, to be discussed below-are given in Table 1. It is apparent that O interstitials are by far the most stable defects among those considered, followed by Cu vacancy bulk-like, N interstitial bulk-like, and bulk-like Frenkel defects. Generally bulk-like defects are more favorable than interfacial ones except for O vacancies, N interstitial and Cl substitutional defects. The stability of structures with Cu vacancies observed here was noticed in previous theoretical studies [47][48][49] , and was also seen experimentally 50-53 . Pristine junction. The projected density of states (PDOS) of the interfacial atoms for the pristine Au-Cu 2 O-Au heterojunction is shown in Fig. 2 (left). Broad Cu 3d and Au 5d states are apparent, as well as signs of Cu-Au hybridization, particularly at − 2 eV. Figure 2 (right) refers to the bulk-like O and Cu atoms in the center of the Cu 2 O region for n = 1 and n = 4. The enhanced Cu-O hybridization around − 1 eV is characteristic for the n = 1 case. Down to about − 5 eV we observe the expected dominance of Cu 3d states, the DOS structure being broader for n = 1.
The transmission coefficients and thickness (n) dependencies are shown in Fig. 3. For the optimized structure (right), T(E) reflects the shape of the DOS below the Fermi energy, E F , compare Fig. 2  near − 3 eV (due to the localized Cu levels), as well as the almost constant DOS above E F (due to the extended Cu states). We expect that the transmission at E F is dominated by Cu states, since Cu is located next to Au in the junctions studied. The corresponding conductance, G = G 0 T(E F ), is of the order of 0.15G 0 (for n = 1), where G 0 = 2e 2 /h denotes the conductance quantum (the factor 2 is due to the spin). Increasing n to 4, the conductance drops to 0.014G 0 .
Above E F , T(E) increases roughly linearly with energy due to the delocalized Cu 4s states. The transmission decreases with increasing thickness n. A transport gap of approximately 0.6 eV appears for the relaxed structure when increasing n to 4. For any thickness studied the heterojunction behaves as an n-type conductor. In the following, we omit the results for n = 3 since they are similar to those for n = 4.
O and Cu defects. First we discuss the role of O and Cu vacancies and O interstitial defects, cf. Fig. 1(c-g), as well as of Frenkel defects, which consist of an O vacancy and an O interstitial, cf. Fig. 1(h,i). Figure 4 shows T(E) for O vacancies (top part of the figure) and O interstitial defects (bottom part of the figure). In the following, we concentrate our discussion on the optimized structures (right). A major change of the  While for the unrelaxed system there is hardly any difference between n = 3 and 4, the transport gap appears for the relaxed structure only for n = 4. A pronounced transmission around − 7 eV appears for the relaxed structure for n = 3 and 4, due to significant contributions from Au-Cu interface states (which are absent in the case of n = 1). For energies far above E F , the transmission is somewhat reduced upon relaxation for n = 3 and 4. On the other hand, hardly any change due to the optimization process is observed for n = 1. transmission, compared to the pristine junction, is observable for both cases for n = 1, namely a shift of weight from the peak around − 3 eV towards E F , and an enhancement below − 5 eV. However, T(E) is more evenly distributed for an interstitial defect. In addition, T(E) is enhanced at the Fermi energy by vacancies due to contributions from Au and Cu states, as is apparent from the respective PDOS (not shown here). The conductance is 0.82G 0 , and thus considerably larger than in the pristine case.
For the thicker Cu 2 O layer, n = 4, we consider O vacancies at the interface and in the center of the Cu 2 O region, see Fig. 1(c,d). The exact position of the vacancy plays only a minor role for T(E). As compared to the pristine junction, the transport gap at E F has closed, but the conductance is rather small, about 0.063G 0 and 0.035G 0 for the near-interface and bulk-like vacancy, respectively.
An O interstitial atom in a thin (n = 1) Cu 2 O interlayer results in a significant T(E) down to − 8 eV, see Fig. 4  (rightmost). Furthermore, the minimum of T(E) around E F is completely washed out, resulting in enhanced conductances of 0.41G 0 (near-interface) and 0.62G 0 (bulk-like). However, the enhancement is slightly less than what is observed for O vacancies. For the thick (n = 4) Cu 2 O layer the effect of an interstitial O atom strongly depends on its position: the conductance is considerably higher for the bulk-like than for the near-interface interstitial (0.11G 0 vs. 0.02G 0 ). This fact can be related to a strong contribution of p orbitals, which lead to a clearly visible peak in the O (bulk-like) PDOS at E F , even larger than the Cu (bulk-like) PDOS. For a near-interface interstitial, on the other hand, this peak is located near − 1 eV. Overall T(E) behaves similar to the pristine junction.  Fig. 1(c-e). The pronounced transport gap found for O vacancies (n = 4) before relaxation is filled due to structural optimization. On the other hand, there is hardly any relaxation effect for vacancies for n = 1, while it appears largest for O interstitial doping. The transmission at E F generally is higher when the atomic positions are optimized, and that bulk-like defects lead to a higher transmission than near-interface defects.

. Transmission coefficient for O vacancies (top) and interstitials (bottom), before (left) and after (right) structural optimization; compare
In Fig. 5 we show the transmission coefficients for Cu vacancies; we focus again the discussion on the optimized structures (right). As compared to the pristine junction, vacancies enhance T(E) below − 5 eV for n = 1. For an interfacial Cu vacancy the change in T(E) below E F can be related to the sensitivity of the d bands to disorder, and the Au(5d)-Cu(3d) orbital interaction at the interface 54 . The conductance is reduced (compared to the pristine junction) to 0.12G 0 (n = 1). For a bulk-like Cu vacancy an enhanced T(E) is visible between − 5 and − 4 eV due to contributions from Cu 3d bulk states, and the conductance is given by 0.52G 0 . An increase of the conductance due to Cu vacancies is in agreement with previous work on thin films 15 . Independent of its position, a Cu vacancy shifts the minimum of T(E) around E F to higher energy.
On the other hand, for a thick (n = 4) Cu 2 O layer, the gross shape of T(E) for Cu vacancies is very similar to the case of O vacancies. The conductance, however, is higher for the bulk-like than for the interfacial Cu vacancy (0.032G 0 vs. 0.026G 0 ). Note that the conduction type can be modified by Cu vacancies.  Fig. 1(f,g). While the overall behavior is similar before and after relaxation, one notes an increase around − 7 eV and a decrease for energies far above E F due to optimization. At E F , the transmission is higher for n = 1 compared to n = 4 and for a bulk-like compared to near-interface defects. Slightly above E F , a Cu bulk vacancy creates for n = 4 a strong transport gap, for both the relaxed and unrelaxed situation. The labels "near-interface" and "bulk-like" refer to (h) and (i) in Fig. 1, respectively. For n = 1, of course, there is only one type of Frenkel defect. Due to the optimization, there is a drastic change in the transmission in the energy range − 6 eV to E F . A pronounced peak near − 7 eV appears for all thicknesses. Again an increase of the transmission at E F is found for n = 1 and 4 due to relaxation, while the transmission above E F is reduced.
Scientific RepoRts | 6:27049 | DOI: 10.1038/srep27049 Turning to Fig. 6, we observe that a Frenkel defect modifies T(E) substantially for n = 1, leading to a very high conductance of 0.92G 0 . For n = 4 we consider the two Frenkel defect configurations shown in Fig. 1(h,i). We find no significant difference in T(E), and obtain essentially the same conductance (0.070 G 0 vs. 0.075G 0 ) for both of them. Roughly speaking, T(E) can be considered a combination of the effects of an O vacancy and an O interstitial.
N and Cl doping. The effect of N substitutional and interstitial doping is addressed in Fig. 7. Clearly the onset of T(E) is related to the energetic positions of the N relative to the Cu states, and the high T(E) around − 6.5 eV is due to a strong overlap between them. Minima in T(E), for example near − 4 eV, coincide with minima in the Cu PDOS (not shown here). The shift of the minimum of T(E) around E F to higher energy is similar to the effect of a Cu vacancy. Conductance values of 0.40G 0 , 0.74G 0 , and 0.99G 0 are obtained for N substitution, near-interface N interstitial, and bulk-like N interstitial, respectively (n = 1). Substitution creates an excess hole, while an interstitial defect creates excess electrons. This explains why the conductance is higher for the interstitial than for the substitutional case. For bulk-like N interstitial there are more transmission channels than for the near-interface N interstitial at E F . Figure 7 also deals with N doping at different positions for n = 4. Comparing substitutional and interstitial doping, the overall energy dependence is quite similar (and similar to the pristine junction), except for subtle For the n = 1 heterojunction, besides the appearance of strong transmission around − 7 eV as discussed before, the shift of the extrema near the Fermi energy upon relaxation is remarkable, in particular, for N interstitial doping. The transmission is found to depend significantly on the location of the N interstitial only for the optimized case. For n = 4, it appears that transmission is slightly higher after relaxation for bulk-like doping (substitutional or interstitial) compared to near-interface doping.
differences near E F . As compared to the pristine junction, the transport gap is slightly reduced, and the conductance thus a little enhanced, similarly for bulk-like and near-interface substitution, to about 0.015G 0 . Turning to N interstitial defects (n = 4), Fig. 7 shows that the bulk-like position of the defect results in a slightly higher conductance than the near-interface position, 0.061G 0 vs. 0.031G 0 . Figure 8 addresses Cl doping. For n = 1 substitutional doping, we find close similarities to the pristine junction though the minimum near E F has shifted to lower energy, which is opposite to what is found for N doping. The conductance of about 0.34G 0 accordingly is higher than in the pristine junction, but lower than in the case of N doping. The shift of the minimum of T(E) to lower energy appears also for the Cl interstitial defect. A bulk-like Cl interstitial defect leads to a higher conductance (0.56G 0 ) than a near-interface Cl interstitial defect (0.32G 0 ).
Interestingly, see Fig. 8, for n = 4 we find again a shift of the minimum of T(E) near E F to higher energy (compared to the pristine case) for the bulk-like Cl substitutional defect. The conductances are given by 0.065G 0 and 0.043G 0 for near-interface and bulk-like substitution, respectively, which is considerably higher than for N substitution. In contrast to the other cases considered, the Cl bulk-like substitution has a lower conductance than the near-interface one. The overall results for Cl interstitials are similar to those for N interstitial defects, but with slightly smaller conductances (0.022G 0 for the near-interface, and 0.033G 0 for the bulk-like case). The calculated conductances for n = 4 are summarized in Table 1.

Discussion
Based on the density functional theory and the nonequilibrium Green's function approach, a comprehensive study of the electronic structure and transport properties of Au-(Cu 2 O) n -Au heterojunctions of different thickness, with different point defects, and with different kinds of anion doping of Cu 2 O has been carried out. As to be expected, the transmission decreases with increasing n. Compared to the pristine junction, we find for thin interlayers, n = 1, for O vacancies and for interstitial O, N, and Cl defects a drastic change of T(E) around the Fermi energy. Bulk-like defects are found to enhance the transport more effectively than near-interface defects-which appears reasonable since the system has a better chance to adjust to a bulk-like compared to a near-interface disturbance, thereby reducing scattering. Accordingly, we also find that for all cases considered the formation energy is lower for bulk-like than for interface or near-interface disturbances.
Experimentally it has been found that N and Cl doping enhances the conductance 16,17 , and that interstitial N defects are more effective than N substitution 18 . While this agrees with our findings, further work is needed to establish the connection between the present model studies and the actual experimental situation, where, in particular, the film thicknesses are much larger than in our model. Note that for Cl we observe the opposite trend: interstitial defects are less effective than substitution. In conclusion, our investigation provides indications on how to improve the electrical and photovoltaic properties of Cu 2 O contacted by two gold leads, namely by appropriate, preferably bulk-like defect engineering. Of course, it must be kept in mind that the detailed experimental conditions may not always be properly reflected by the idealized theoretical modelling.