First Principles Calculation Study on Surfaces and Water Interfaces of

Article pubs.acs.org/JPCC

First Principles Calculation Study on Surfaces and Water Interfaces of Boron-Doped Diamond Zdenek Futera,*,†,‡,§ Takeshi Watanabe,†,‡ Yasuaki Einaga,†,‡ and Yoshitaka Tateyama*,‡,§,∥,⊥ †

Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 333-0012, Japan § International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ∥ PRESTO, JST, 4-1-8 Honcho, Kawaguchi, Saitama 333-0012, Japan ⊥ Elements Strategy Initiative for Catalysts & Batteries, Kyoto University, Goryo-Ohara, Nishikyo-ku, Kyoto 615-8245, Japan ‡

S Supporting Information *

ABSTRACT: We investigated water interfaces of boron-doped diamond (BDD) terminated by hydrogen, oxygen, and hydroxyl groups by using density functional theory (DFT)-based molecular dynamics to elucidate the electrochemical behaviors of the asgrown and oxidized BDD electrodes. The reversible outer-sphere electron transfer on the as-grown electrode and the irreversibility on the oxidized electrode, observed in the experiment, are well explained by the BDD band position and subsurface band bending, which depend on the termination and interfacial dipoles. The reductive character of the H-terminated BDD is found, while the interface covered by the carbonyl oxygen is clearly oxidative. The redox character of the hydroxyl termination depends on the lateral hydrogen bonding network among the termination groups and is rather oxidative at the water interface. We also examined the preference of the boron position in the diamond and the stability of boron pairs and clusters. It is suggested that the wide distribution of the single boron dopants is crucial to the BDD conductivity, against the tendency of clustering. These results give novel atomistic aspects of the termination and the boron doping effects on the BDD electrodes, which is useful for further exploration of the efficient electrochemical applications of BDD.

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INTRODUCTION Diamond is a well-known material with outstanding mechanical and electronic properties suitable for applications in hightemperature and high-power electron devices. It is an insulator with a wide (indirect) band gap of 5.5 eV; nevertheless, the diamond surface exhibits significant p-type conductivity and negative electron affinity (NEA) when it is covered with chemisorbed hydrogen.1−7 However, the oxygen-terminated surfaces have a large positive electron affinity.3,7,8 These surface properties are the basis for diamond applications in fieldemission electronics.9−12 Later, boron-doped diamond (BDD) attracted the attention of the physics community as the first known covalent semiconductor that exhibits superconductivity when it is heavily doped.13−15 The superconductivity was found to be strongly dependent on the BDD surface orientation15,16 and the boron distribution in the material.17−19 The boron-doped diamond, the chemically very stable p-type semiconductor with an acceptor level 0.37 eV above the valence band (VB), was later recognized in electrochemistry and photoelectrochemistry as a promising electrode material.20−22 An extraordinarily wide potential window spanning −1.25 to 2.3 V vs SHE,23−25 much larger than in case of conventional © XXXX American Chemical Society

platinum, glassy carbon, or graphite electrodes, and low background currents are characteristic of the BDD electrodes.26−33 These properties make BDD effective for many important electrochemical applications such as water disinfection, wastewater treatment, accurate biosensors, pH detectors, and electrochemical synthesis.34−39 The origin of the wide potential window is not fully understood yet, although the chemical inertness and hydrophobicity of the diamond surface covered by the chemisorbed hydrogen are usually proposed as key factors.23 However, the hydrophilic oxidized BDD electrodes have been reported to exhibit a potential window comparable to or even wider than the as-grown electrodes that are covered with hydrogen,40−42 and thus the problem remains open. The electrochemical response of the BDD electrodes, that is, their current−potential characteristic, is dependent on the termination and active redox species. A significant change in the cyclic voltammogram (CV) was observed in the case of the surface-sensitive [FeReceived: June 18, 2014 Revised: August 28, 2014

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dx.doi.org/10.1021/jp506046m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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(CN)6]3−/4− redox couple where the CV curve is changing from reversible to irreversible with surface oxidation.42 Furthermore, the presence of nondiamond sp2 carbon on the electrode surface reduces the potential window and leads to the larger background currents. Besides the termination effect, the concentration of the boron dopants is also an important factor influencing the electrochemical response of the BDD electrodes. Low-doped BDD with a boron concentration of 108 atoms/cm3 and a resistivity of 104 Ω·cm is a semiconductive material while semimetallic behavior with a resistivity reduced to 10−3 Ω·cm is known for the high doping of 1020 to 1021 B atoms/cm3.43 While the outer-sphere electron-transfer reactions proceed in a quasi-reversible manner on the heavily doped BDD electrodes, the inner-sphere reactions are strongly hindered.44 The potential window was observed to decrease with increasing boron doping.45 There are many experimental and some theoretical studies of the structure and electronic properties of bulk diamond,46,47 the reconstruction of clean diamond surfaces, and termination effects.48−61 Theoretical investigations of BDD until now mainly concerned the effects of the doping level and boron clustering.17−19,62−70 Also, the interaction of the boron dopant with hydrogen was taken into account.65,71−75 However, an explanation of the electrochemical behavior of BDD is still challenging from a computational point of view because of the great complexity of the semiconductor/electrolyte interface. In this work we investigate the water interfaces of the BDD electrodes under various conditions using large-scale DFT models and applying molecular dynamics (MD) to include finite temperate effects in the calculations. We explore several aspects that influence the structural and electronic properties of the interfaces, mainly the termination and the boron doping effects. Pairing and clustering of the boron dopants, their possible interaction with atomic hydrogen trapped in the diamond lattice, and the interaction with terminating groups are investigated here. Finally, we aligned the electronic states of the BDD surfaces and water interfaces to demonstrate the fundamental difference between the oxidized and reduced electrodes that is known from electrochemical measurements.

All calculations were performed with the CPMD plane-wave computational code.86 We used a diamond lattice constant of 3.59 Å, slightly longer than the experimentally measured 3.57 Å, to construct the models. This value, corresponding to a C−C bond length of 1.56 Å, was found to be optimum for our computational setting. A supercell with 256 carbon atoms was used for all models with fixed dimensions of 14.28×14.28×7.14 Å3 for the bulk, 10.154×10.154×43.080 Å 3 for the (100) surface, and 10.154×8.794×49.743 Å3 for the (111) surface model. The vertical z dimension of the surface supercells was chosen as 3 times the thickness of the diamond slab. The resulting space was left free for the vacuum surface calculations, and it was filled by 105 water molecules in the case of the water interface simulations. The number of water molecules was chosen to mimic the room-temperature density of water, and it was kept fixed in all of the models in order to make the structures energetically comparable. The boron doping was simulated by the substitution of an even number of carbon atoms in the diamond crystal lattice. Low-doped BDD was represented by 2 B atom dopants (∼0.8%), and 14 B atoms were used for highly doped samples (∼5.5%). The even number of boron atoms was used for computational reasons to avoid the necessity of demanding spin-polarized calculations. The position of the boron atoms was chosen to simulate BDD with either paired or homogeneously distributed dopants as discussed further in the text. To explore the termination effect, we prepared surface models fully covered with hydrogen (H), hydroxyl groups (OH), or oxygen (O) and surfaces terminated by a half-andhalf mixture of these atom groups. The terminations of the upper and lower surfaces of the diamond slab were identical in all models. We compared the stability of the individual surface structures on the basis of the formation energy concept.53,87 The formation energy for N surface sites (N = 32 in our case) is defined as follows:

COMPUTATIONAL DETAILS First principles calculations presented in this work are based on GGA DFT using the Becke−Lee−Yang−Parr (BLYP) exchange−correlation energy functional.76,77 Troullier Martins pseudopotentials78 in a Kleinman−Bylander representation79 were used for the core electrons, and the plane wave basis set was defined by a kinetic energy cutoff of 70 Ry. Brillouin zone integration of the bulk models was performed on a (2×2×2) Monkhorst−Pack grid80 while the surface supercells were sampled by the Γ point only, which was justified by the large scale of the supercells. The geometry of all of the bulk and vacuum surfaces was fully optimized by the GDIIS algorithm81,82 to the total energy minimum with gradient components of less than 4.0×10−4 a.u. For the water interface models, we performed Car−Parrinello molecular dynamics (MD)83 with a 5.0 a.u. time step and fictitious electron mass 500.0 a.u. Temperature was controlled with a Nose−Hover thermostat84,85 (with frequency 800 cm−1) at 298.15 K. The projected density of states (PDOS) was calculated on the optimized structures as well as on the MD samples. The final PDOS of the water interface models was constructed as an average of the PDOS from all of the samples.

The zero-point energy EZPE is added to the total energy Etot of the fully optimized structure, and then the contributions from nC, nB, nH, and nO numbers of C, B, H, and O atoms are subtracted and normalized to the number of surface carbons N. The zero-point energy is approximated by

Ω=

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Etot + EZPE − nCμC − nBμB − nHμH − nOμO N

EZPE = nH′ e0H + nO′ e0O + nOHe0OH

(1)

(2)

Here, here n′H and n′O are the numbers of H and O atoms not included in the hydroxyl groups OH and eH0 , eO0 , and eOH 0 are the atomic ZPE energies calculated from the vibrational frequencies of methane (CH4), carbon dioxide (CO2) and orthocarbid acid (C(OH)4). The chemical potential of carbon, μC = −154.048 eV, was obtained from the bulk diamond calculation, and the chemical potentials of boron, μB = −75.143 eV, hydrogen, μH = −15.855 eV, and oxygen, μO = −432.557 eV, were determined by the total energies of the optimized B12 icosahedron and H2 and O2 molecules.

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RESULTS AND DISCUSSION Diamond Surfaces. First, we analyzed the structural stability of the vacuum (100) and (111) diamond surfaces

B



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without any termination adatoms or boron dopants to justify our computational setting. We compared the stability of the (1×1) bulk-terminated geometry with the (2×1) reconstructed structure that is known to be stable and energetically the most preferred on these surfaces.49,50,88−91 The graphitized sp2 (111) surface was also considered for the comparison of sp2 and sp3 surface carbon properties. Fully optimized structures of the clean surfaces are shown in Figure 1. The reconstruction is driven by existing dangling

Figure 2. Fully hydrogen-terminated surfaces in four different geometries: (a) (100)(1×1):H, (b) (100)(2×1):H, (c) (111) (1×1):H, and (d) (111)(2×1):H. For other termination types, see the SI.

reconstruction remains the most stable geometry of the (100) surface when it is terminated by monovalent H and OH. (Structures with two terminating atoms on one surface carbon that keep the (1×1) geometry are not favored because of steric repulsion.) However, the (111)(1×1) geometry is stable with carbonyl oxygen termination (energy differences and structures in Table 1 and SI). To compare the stabilities of both the clean and terminated surfaces, we calculated the formation energy, Ω, of all of the considered structures according to eq 1. The obtained values are listed in Table 2 and Table S2 in the SI. The values of Ω are

Figure 1. Bulk-terminated (1×1) and reconstructed (2×1) geometry of the optimized (100) and (111) surfaces: (a) (100)(1×1), (b) (100) (2×1), (c) (111)(1×1), (d) (111)(2×1), and (e) partially graphitized (111) with sp2 surface carbons.

Table 2. Formation Energies of the (111) and (100) Diamond Surfaces (eV)

bonds on the bulk-cut surfaces. A dimer chain (2×1) geometry is formed on the (100) surface stabilized by 1.39 eV/surface carbon (Table 1). This structure can be further stabilized by the

(100)

Table 1. Total Energy per Atom (a.u.) of the Clean and Terminated (100) and (111) Diamond Surfacesa (100)

(111)

type

(1×1)

(2×1)

(1×1)

(2×1)

(sp2)

clean H OH O

−5.65 −5.09 −6.18 −6.80

−5.65 −5.10 −6.18 −6.80

−5.65 −5.10 −6.18 −6.80

−5.66 −5.10 −6.18 −6.79

−5.66

(111)

type

(1×1)

(2×1)

(1×1)

(2×1)

clean H OH O

3.18 1.44 0.40 −0.03

1.85 0.38 −0.55 0.44

1.82 −0.04 −0.78 0.63

1.14 0.68 −0.17 1.49

based on μH and μO obtained from the single-molecule calculations, which correspond to the dilute ideal gas approximation. Under these conditions, oxidized surfaces covered with O or OH are clearly more stable than hydrogen-terminated ones. The formation energy, −0.025 eV, obtained for full oxygen coverage on the (100) surface is significantly lower than Ω of the hydrogenated one, 0.378 eV, where we compare the surfaces in their preferred geometries for each species, that is, (100)(1×1):O and (100)(2×1):H. In fact, the bridge position (Figure S7 in SI) is the most stable for full oxygen coverage with an even lower formation energy of −0.161 eV. A strong interaction of the carbon with oxygen is also pronounced on the (111) surface; nevertheless, here the hydroxyl coverage is the most stable because of its monovalent character that is compatible with single dangling bonds on the surface. We also considered mixtures of the terminating groups (Figure S8 in SI); however, these were not found to be the most stable structures. The structural stability discussed above is given by a rather special choice of the chemical potentials of H and O that are reasonable for vacuum surfaces. However, these are not quite appropriate for describing experimental conditions typical for the electrochemical applications. Therefore, we constructed phase diagrams of the (100) and (111) surface stabilities based on variations of μH and μO as they are shown in Figure 3 (details in the SI). From the diagrams it is obvious that several different surface structures can be stabilized by changing the

a

Relaxed bulk-terminated (1×1) structure, reconstructed (2×1), and graphitized (sp2) geometries are considered.

chemisorption of monovalent termination atoms, as will be discussed below. The (111) surface can be stabilized by partial flattening (called relaxed (1×1) geometry here), graphitization, or (2×1) reconstruction known as Pandey chains.88 The chain reconstruction stabilized by 0.70 eV is the most stable here. Also the presence of the graphitized sp2 geometry, stabilized by 0.46 eV, is probable on the polycrystalline diamond surface. Although both (100) and (111) surfaces undergo significant structural changes, the third carbon double layer from the surface already resembles the bulk geometry (details in Supporting Information (SI)). Next, we explore the termination effect on the surface stability. We used hydrogen (H), hydroxyl (OH), and oxygen (O) for surface chemisorption as these are the most common atoms found on the diamond electrodes (structures in Figure 2 and SI). The (111) surface is stable in (1×1) geometry for all of the considered terminating groups. All of the dangling bonds are saturated by terminating atoms, and further reconstruction is not energetically favorable. On the contrary, (2×1) C



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Figure 3. Phase diagrams of the (100) and (111) surface stabilities based on the formation energy calculations. Solid vertical lines represent the chemical potential of H in the H2 molecule, and the vertical dotted lines show the μH in methane (CH4). Horizontal solid lines indicate the chemical potential of O in the O2 molecule, and horizontal dotted lines show the μO in carbon dioxide (CO2).

Figure 4. Plane-averaged electrostatic potential profiles (eV) of the clean and terminated (111) surfaces. The position of the surface carbon layer is used as the origin of the horizontal axis (z direction of the supercells). D



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chemical potentials. In an environment with lower μO, the hydrogenated surfaces are stable, as is typical for the diamond prepared by chemical vapor deposition (CVD). Lowering μH under these conditions leads to a stabilization of the clean unterminated surfaces in the reconstructed geometries. However, oxidized surfaces are preferred when the μO grows as it does on anodic electrodes in water. Looking at the position of μH obtained from H2 and CH4 and indicated in Figure 3, we see that the diamond surface in such an environment will most probably be covered by a mixture of H and OH atomic groups and the O in the bridge position on the (100) surface. Here, we investigate the electronic states of the surfaces. We calculated a projected density of states (PDOS) for each model and used the plane-averaged electrostatic potential to align these states to the vacuum level as demonstrated in Figure 4. The resulting position of the bulk band gap together with the surface valence band maximum (VBM) and the conduction band minimum (CBM) is shown in Figure 5. From the band alignment it is obvious that the termination of the surfaces has a large influence on the position of the electronic states compared to the clean diamond surface. While the hydrogen termination shifts the states closer to the vacuum level, states of the surface fully covered by carbonyl oxygen are shifted greatly in the opposite direction. The hydrogenated surfaces clearly

exhibit a negative electron affinity, in agreement with known experimental facts. A similar, although less pronounced, effect can also be observed on surfaces covered by hydroxyl groups. We performed qualitative Mulliken population analysis of the calculated charge densities to explore charge transfer between termination atoms and the surface carbons. From the analysis we obtained an average charge of +0.13 a.u. per atomic H and −0.06 a.u. per carbonyl O. These results are in accordance with the concept of Pauling electronegativity: H < C < O. The largest surface charge was found on the oxygen in the hydroxyl group that attracts charge density not only from the surface carbon layer but also from the hydroxyl hydrogens. Charge on this oxygen was quantified to −0.30 a.u. However, the difference between the bulk and vacuum electrostatic potentials on this surface is sensitive to the orientation of the OH groups. In vacuum, the regular arrangement of the OH groups interacting between themselves by hydrogen bonding is energetically the most preferred. Such an arrangement places the electronic states of the surface between the clean and hydrogen-terminated types. However, if we partially disrupt the H-bonding network by mixing OH with H terminating groups in a half-and-half ratio, then the electronic states are lowered. We will show below that in water the interface where the structure is fluctuating and the regular pattern are no longer preserved and the electronic states are closer to the surface covered by the carbonyl oxygen. From now on, we focus on the (111) surface only as a representative model for electrochemical purposes. Boron Doping. Here we investigate the boron doping effect. We substituted an even number of carbon atoms, gradually from 2 to 14, with B dopants in the bulk supercell to simulate the transition from the low-doped (0.8%, 2 B atoms) to highly doped (5.5%, 14 B atoms) BDD. At low concentrations, the acceptor state was observed to be 0.29 eV above the VBM. This value is smaller than the experimentally measured 0.37 eV because of the known band gap underestimation in GGA. The Fermi energy level, located in the middle of the band gap in the undoped diamond, is now between the acceptor state and the VB edge as is typical for the p-type semiconductor. As the boron concentration increases, the number of the acceptor states is increasing as well. The whole band of these states is formed just above the VB (Figures S11 and S12 in the SI); the BDD becomes semimetallic. This behavior can be observed when the boron dopants are distributed homogeneously in the diamond lattice and do not interact covalently with one another. However, pairing and clustering of the boron atoms leads to energy stabilization of the structure as we found out by the formation energy comparison of different bulk structures. In our model doped with 14 B, the complete boron pairing into 7 B2 dimers and the formation of a 4 boron cluster with the pairing of all of the remaining borons (1 B4 5 B2) are the most stable structures. The latter was found to be 0.345 eV lower in formation energy than the homogeneous distribution (14 B1). However, larger than four-membered clusters leads to significant local deformations of the diamond lattice, with energies that are always found to be higher (details in the boron doping section of the SI). On the basis of these results, we also calculated band structures for low- and high-concentration models with paired boron dopants, that is, one or seven B2 pairs in the supercell. The acceptor states are shifted deeper into the band gap by boron pairing; they are almost 1 eV above the VBM and practically unoccupied, and no contribution to

Figure 5. Band alignment of the vacuum (100) and (111) surfaces. The bulk valence and conduction bands are shown by filled red and blue columns, respectively, and the positions of the surface valence band maximum (VBM) and conduction band minimum (CBM) are indicated by red and blue horizontal lines. E



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Figure 6. Schematic illustration of the B-doping effect on the (111)(1×1):H diamond surface. The valence band (VB) is represented by red, the conduction band (CB) by blue, and the boron states by magenta. Downward subsurface band bending on the surface caused by the B doping is indicated in the case of BDD.

conductivity is expected. These results are consistent with previous theoretical studies.17−19,70 The same effect was also observed in the (111)(1×1):H surface model. In the low-doping case, the hydrogentermination layer is positively polarized, the redistributed charge density is concentrated on the surface carbon double layer, and the energetically most stable location of the boron dopants is in the bulk region. When the dopant concentration increases, the boron atoms that do not prefer large cluster formation are distributed in the structure almost homogeneously, not only in the bulk but also in the subsurface region. We illustrated the changes in the electronic states connected with boron doping schematically in Figure 6, where the valence band and the conduction band edges are shown. The presence of positive holes h+, major charge carriers in BDD, in the bulk region and the surface dipole induced by terminating atoms leads to downward subsurface band bending on the vacuum surface. More acceptor states and holes are present in the highly doped BDD; however, the space region becomes very narrow in this case. The boron doping of diamond and the accompanying electronic changes discussed above might influence the stability of the BDD surfaces. Therefore, we recalculated the phase diagrams of (111) surfaces for low- and highly doped BDD. We consider only single, nonpaired dopants located in the bulk region (low-doped case) or in the bulk and subsurface regions (highly doped case). The resulting diagrams shown in Figure 7 remain qualitatively similar when compared to the undoped case (Figure 3). However, when the chemical potentials of both hydrogen and oxygen are very low, as in the vacuum surface experiments, then the graphitization rather than the (2×1) reconstruction of a clean surface is more stable after boron doping. With higher doping, the boron dopants are distributed throughout the whole sample, including the subsurface region, which causes a weaker adsorption of the terminating groups. Therefore, the region of the stable, clean surface is expanding with increasing boron doping. In practice, BDD is usually prepared by a chemical vapor deposition (CVD) technique with a relatively high concen-

tration of atomic hydrogen in the reactive chamber during the growth process. Considering the trapping of this hydrogen in the diamond and BDD structures, we investigated its effect on the electronic structure and the interaction with the boron dopants. It is known that atomic H passivates the boron monomers (single atoms) in the BDD with a high thermal activation barrier of 2.5 eV.65,92−96 We can confirm this binding preference, and we also found that H can interact with the B2 pair in the diamond lattice and create the famous diborane structure where the B2 pair is bonded by two three-centered bonds mediated by interstitial hydrogens, B−Hi−B. The formation of this structure is stable not only in the bulk but also on the (111)(1×1):H surface. However, these structures do not provide any available acceptor level; therefore, they do not support the electrical conductivity of BDD. (See hydrogen in the diamond lattice part of the SI for details.) Water Interfaces. Finally, we investigate the BDD (111) (1×1) water interfaces. In the future, we will be working with the low-doped BDD model where the two single B atoms are located in the bulk region in order to explore the behavior of ptype semiconductor electrodes. We compare here interfaces fully covered with hydrogen, oxygen, and hydroxyl groups and their half-and-half mixtures. Clean nonterminated diamond geometry is not considered here because the diamond electrodes are expected to be terminated as we discussed above. In contrast to the vacuum surface models where we analyzed properties of the fully optimized structures, the interfaces involve the liquid water and thus the molecular dynamics (MD) is required. Therefore, we performed Car− Parrinello MD at room temperature and all the results that are presented here are averages from 20 MD samples. First of all, we explore the interaction between BDD and water, namely structure of the first hydration shell. In Figure 8, snapshots of all the considered interfaces are shown. It can be seen that there are no hydrogen bonds between (111)(1×1):H and the first hydration shell, the water molecules are oriented to the surface by oxygen atom and interact by the H−bonding among themselves. On the contrary, the BDD interface covered by carbonyl oxygens exhibits strong interaction with the first F



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Figure 7. Phase diagrams of the (111) surface stability of (a) low-doped BDD and (b) highly doped BDD. Solid vertical lines represent the chemical potential of H in the H2 molecule, and the dotted vertical lines show μH in methane (CH4). Solid horizontal lines indicate the chemical potential of O in the O2 molecule, and the dotted horizontal lines show μO in carbon dioxide (CO2).

hydration shell. The water molecules are oriented to the interface by their hydrogens and (111)(1×1):O···H(H2O) hydrogen bonds are clearly observable. Position of the water molecules also suggests that their dipole moments are interacting with dipole moment of the terminated BDD interface and thus kind of interfacial double layer is formed here. Indeed, the population analysis shows pronounced charge on the terminating oxygen, −0.21 a.u., comparing to the vacuum model. The hydroxyl termination is not interacting strongly with the first hydration shell because of the lateral H− bonding. To analyze the interfacial structure more quantitatively, we calculated radial and plane distribution function g(r) and g(z), respectively, for the distance between termination groups and water molecule oxygen and hydrogens. The function in distance range relevant for the interface is shown in Figure 9 where the considerable difference in behavior of H- and O-terminated interfaces is apparent. Significant peak at 1.75 Å in g(r) for (111)(1×1):O interface indicates well ordered first hydration layer and strong interaction between termination oxygen and water hydrogen. From the same peak in g(z) we see that the water is located perpendicular to the surface. No such structure

can be noticed in case of the hydrogen termination where the distance of water and termination H is greater than 2.0 Å. In case of the OH termination, weak interaction between the OH oxygen and the water molecule hydrogens is observable. However, the overall distribution resembles more the H termination behavior rather than the interfaces covered by carbonyl oxygen. The interaction become stronger when the termination OH groups are mixed with H and the lateral H− bonding between hydroxyls is partially disrupted. We can conclude that the H-terminated (111) interface exhibits hydrophobic behavior while the oxygenated BDD is clearly hydrophilic. The hydroxyl termination and OH, O mixture that is expected to be present on the oxidized BDD electrodes shows the hydrophilic tendency as well. The electronic structures of the individual BDD water interfaces were examined by the projected density of states (PDOS) calculations. These were aligned with respect to VBM of the bulk water, which provides a natural reference in these models. The PDOSs are plotted in Figure 10 together with the plane-averaged electrostatic potential profiles and the band alignment diagram. The H-terminated BDD interface has a VBM that is almost 3.0 eV above the water VBM. However, the G



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different situation comparing the band position of the vacuum surfaces where the character of the fully hydroxylated surface is rather similar to that of the H-terminated one. This phenomenon is caused by the lateral H bonding of the hydroxyl groups on the (111) diamond surface that has a suitable lattice constant for this type of interaction. Nevertheless, the lateral H bonding is disrupted on the interface where the OH groups interact with water. However, the BDD interfaces with the carbonyl oxygen interact with water by charge transfer as discussed above. In this case, the VB edge is close to the water VBM. These suggest that the H-terminated interface has reductive character and the interfaces with the carbonyl oxygen exhibit oxidative properties. Furthermore, the chemisorbed oxygen and hydrogen induce different surface states in the diamond band gap. The hydrogen states are located just below the CBM. Because of the high position in energy, they are not expected to contribute to electron transfer to the interface. On the contrary, the surface states introduced by oxygen span the VB edge and appear in the lower part of the band gap. However, as can be noticed in Figure 10, these states are relatively well localized; therefore, we do not expect that they fully mediate the electron transfer from the [Fe(CN)6]3−/4− redox couple. Also, we assume band-edge pinning rather than Fermi-level pinning that is usually associated with delocalized surface states. The oxygen states on the OH-terminated interfaces are saturated by the interaction with hydrogen, and they are not located deep in the band gap. The states are located in the diamond valence band, whose position is higher in this case than on the interfaces with the carbonyl oxygen. The BDD band position with respect to the water reference can explain the electron-transfer behavior between the BDD electrode and the aqueous [Fe(CN)6]3−/4− redox couple

Figure 8. Water interface structure of BDD fully covered by (a) H-, (b) O-, and (c) OH-termination groups and their half-and-half mixtures: (d) O, H, (e) OH, H, and (f) OH, O. Geometries are snapshots from MD trajectories.

energy difference decreases to 1.7 eV for the interface with the termination of the half-and-half OH, H mixture. The VBM of the BDD interface fully covered by OH groups was found to be even lower, 1.4 eV above the water VBM. This is a qualitatively

Figure 9. Radial distribution function g(r) and plane distribution function g(z) showing the average distance between BDD-termination hydrogen and water oxygen (red color) and between termination oxygen and water hydrogens (blue color). The functions are plotted for interfaces fully covered with H, O, and OH termination groups and their half-and-half mixtures (O, H; OH, H; and OH, O). H



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Figure 10. Projected density of electronic states of the BDD water interfaces with different termination groups aligned with the bulk water VBM (left part of the figure; states from different parts of the system are resolved by colors: gray = bulk carbon, magenta = boron, red = termination oxygen, blue = termination hydrogen, green = bulk water, and turquoise = interfacial water), plane-averaged electrostatic potential profiles (right upper part), and schematic band alignment (right lower part). The magenta dotted line in the band scheme shows the position of the [Fe(CN)6]3−/4− redox couple.

observed in the experiment. The water VBM with respect to the vacuum level is known to be significantly underestimated in BLYP calculations, located at −6.40 eV.97 Thus, the redox free energy of the [Fe(CN)6]3−/4− couple, Eredox = −4.80 V when we assume −4.44 eV to be the position of the standard hydrogen electrode (SHE) (0.36 V vs SHE), can be placed 1.6 eV above this water reference as it is shown in Figure 10. As can be seen, the VBM position of the H-terminated BDD is substantially higher than the redox couple energy level. Because the low-doped BDD is a p-type semiconductor, there is the downward band bending in the space charge region near the interface. Assuming that the band edges are pinned on the water interface, the subsurface band bending is significantly suppressed when the bulk VBM is shifted down by applying a bias potential to align the BDD Fermi level EF with Eredox. This situation is shown in the upper panel of Figure 11. As a result, the electron transfer from and to the redox couple can easily occur. This corresponds to the reversible reduction/oxidation of the aqueous [Fe(CN)6]3−/4− redox couple through the Hterminated BDD, observed in the cyclic voltammetry. On the contrary, the position of the oxidized BDD Fermi level is lower than Eredox, and thus the upward bias has to be applied to align these two energy levels. Following the same arguments as above, we see that the bias application leads to the enhancement of the downward subsurface band bending in the BDD space charge layer, as shown in the lower panel of Figure 11. Therefore, the depletion layer of holes appears near the interface. This layer is practically insulating, and thus almost no positive charge carriers are located near the interface. The electric potential drop across the BDD space charge region

Figure 11. Electronic bands on the as-grown, H-terminated BDD interface (blue frame) and on the oxidized BDD interface (red frame). Low-doped BDD behaving as a p-type semiconductor is considered here. Left-hand-side diagrams show the position of the Fermi level (EF) with respect to the aqueous [Fe(CN)6]3−/4− redox couple free energy (Eredox) before applying the bias potential. The situation with the positive bias on BDD:H and the negative bias on BDD:OH,O is shown on the right-hand side. In this case, the subsurface band bending is suppressed on BDD:H but enhanced on BDD:OH,O as a result of the band edge pinning.

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becomes significant. As a result, the irreversible electrochemical response is expected. In fact, such electrochemical behavior was observed for the oxidized, low-doped BDD electrodes.98 Note that some experimental measurements suggest that the Fermi level pinning rather than the band edge pinning might occur on the oxidized BDD interface.98,99 However, the mediation of electron transfer by the localized oxygen surface states is not clear. The Fermi level could be pinned by the surface states of the graphitized sp2 carbon that can be induced on the electrode surface during anodic treatment.100 Concentration of the boron dopant can be also important here. With the increase of the boron doping, the band of acceptor states is formed above the valence band and the depletion layer becomes narrower. This acceptor band, whose position coincides with the oxygen surface states, can then lead to the Fermi level pinning. In practice, one can expect mixing of the band edge pinning and the Fermi level pinning behavior on the oxidized BDD electrodes, with the ratio depending on the above-mentioned factors. The reversibility of the electron transfer for the [Fe(CN)6]3−/4− redox couple can be also influenced by the charge of the terminating atoms on the interface. The oxidized electrodes are covered by the negatively charged oxygen that repels the considered anion electrostatically. Therefore, we can expect a relatively larger overpotential. However, the as-grown BDD electrodes covered by the positively charged hydrogen attract the iron anion, which may contribute to the reversibility. It is also suggested that the hydrophilicity and hydrophobicity have no direct influence on the reversibility because the hydrophobic H-terminated BDD is reversible and the hydrophilic oxidized BDD electrode is irreversible. Although these factors may play some minor roles, the outer-sphere electron transfer between the BDD interface and the aqueous redox couple is mainly governed by the band position and bending scheme discussed above.

BDD, they can possibly represent active sites for electrode reactions. Finally, we showed that on the BDD water interfaces the termination influences not only the position of the electronic states but also the hydrophobic/hydrophilic character of the BDD. The as-grown hydrogen-terminated BDD was found to be reductive and hydrophobic while the interfaces where the carbonyl oxygen is adsorbed on the surface are clearly oxidative and hydrophilic. On the basis of these results, we elucidated the origin of different electrochemical behaviors between the asgrown and oxidized BDD electrodes. We demonstrated the mechanism of reversibility and irreversibility of the interfacial electron transfer by the different amounts of subsurface band bending in the low-doped BDD space charge region that is caused by the termination difference. These insights into the structure, stability, and electronic states of the BDD interfaces, obtained in this work, will be very useful for the further efficient applications of BDD in electrochemistry.

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ASSOCIATED CONTENT

S Supporting Information *

Geometry, structure, and stability of clean and terminated diamond surfaces; boron doping effect illustrated by the density of states; stability of boron clusters; structure, stability, and density of states of hydrogen interacting with bulk BDD; and stability, band alignment, and density of states of BDD surfaces. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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CONCLUSIONS Several aspects important to understanding the electrochemical response of the boron-doped diamond electrodes are discussed in this article on the basis of the large-scale DFT calculations of the BDD surfaces and the water interfaces. From the experimental measurements, it is known that the character of BDD termination is one of the key factors influencing the interfacial electron transfer. To address this problem, we examined electronic states of the clean and terminated diamond surfaces. From the band alignment, we clearly observed an upward band shift leading to the negative electron affinity in the case of hydrogen termination while the opposite effect is typical for the surfaces where the carbonyl oxygen is present. This behavior results from the opposite surface dipole of these structures, and we observed it also on the water interfaces. Besides the termination effect, the boron doping effect was investigated here as well. We observed the different character of the low- and highly doped BDD, which corresponds to semiconductive and semimetallic behavior known from the experimental measurements. Interestingly, we showed that the spatial distribution of the boron dopants in the diamond structure influences the BDD electronic states considerably. The boron pairing and the B-pair interaction with hydrogen were found to be stable not only in the bulk BDD but also on the hydrogen-terminated surface. Though such surface impurities do not contribute to the electric conductivity of

ACKNOWLEDGMENTS This work was partially supported by KAKENHI 20540384 and 23340089 as well as by the Strategic Programs for Innovative Research (SPIRE), MEXT, and the Computational Materials Science Initiative (CMSI), Japan. The calculations in this work were carried out at the supercomputer center in the NIMS, ISSP, and ITC (Oalkleaf-FX) in the University of Tokyo, Kyushu University as well as the K computer at the RIKEN AICS through the HPCI Systems Research Projects.

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First Principles Calculation Study on Surfaces and Water Interfaces of

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