3018
J. Phys. Chem. C 2008, 112, 3018-3026
Theoretical Study of the Thermodynamic and Kinetic Aspects of Terminated (111) Diamond Surfaces D. Petrini and K. Larsson* Department of Materials Chemistry, Angstrom Laboratory, Uppsala UniVersity, Box 538, SE-751 21 Uppsala, Sweden ReceiVed: October 2, 2007; In Final Form: December 4, 2007
Diamond surface susceptibility toward the degree and type of termination and reconstruction has been investigated theoretically by using density functional theory methods. The adsorption geometries and energies for H, O, and OH species adsorbed to diamond (111)-1 × 1 and (111)-2 × 1 surfaces under varying surface coverage were studied and compared with corresponding processes on the diamond (100)-2 × 1 surface. Furthermore, the energy barrier for the diamond (111)-1 × 1 to (111)-2 × 1 surface reconstruction for non-, H-, and O-terminated surfaces were also investigated using first-principle synchrotron transit methodologies. The results show that the adsorption energies for H, O, and OH are -4.53, -5.28, and -4.15 eV, respectively, for 100% terminated diamond (111)-1 × 1 surfaces and -3.29, -3.82, and -2.77 eV, respectively, for the diamond (111)-2 × 1 surfaces. Adsorption of O was found to be most energetically favorable in the on-top position on the 1 × 1 surface and in the bridge position on the 2 × 1 surface. The OH groups showed less-favorable adsorption energies in comparison to H and O. The calculations also show that the 1 × 1 surface configuration is energetically stable against transformation to the 2 × 1 configuration (of type Pandey chain) with a correspondingly small energy barrier; 0.32 eV. For this specific direction of surface reconstruction, significantly higher barriers were found for the H- and O-terminated diamond surfaces (58.4 and 44.0 eV, respectively). Plausible explanations for these observations are that the surface C-H and C-O bonds must be disrupted for the 2 × 1 (Pandey chain) reconstruction to occur.
Introduction Besides their well-known mechanical properties, diamond surfaces have very desirable properties that have been utilized in fields such as optics, electrochemistry, and electronics. These properties include thermal conductivity at room temperature (the most well-known property), output power capability, breakdown field, frequency bandwidth, large electrochemical potential window, and transparency of photon wavelengths greater than 220 nm. Thus, diamonds are well suited to be used as vacuum ultraviolet sensors,1 mirrors,2 field-effect transistors,3,4 and electrodes.5 When adding chemical inertness, radiation hardness, and a high degree of biocompatibility to the list of desirable diamond properties, diamond surfaces have been shown to perform as sensors capable of detecting things such as radiation in very harsh environments,6 pH,7,8 and certain neurotransmitters.9 The relative ease and economic aspects of chemical vapor deposition (CVD) manufacturing are also of major importance in the exploitation of diamonds in various applications. The asdeposited diamond surfaces are formed due to the inert character of the C-H bond, are hydrogen-terminated, and are chemically stable at intermediate temperatures. However, oxygen-terminated surfaces are particularly important because of their specific optical and electrical properties;9 therefore, a deeper understanding of various oxygen-termination reactions at diamond surfaces is of major importance. The low-index (111) surface plane is most frequently observed in CVD-grown polycrystalline diamonds. It can be represented as either the single or the triple dangling bonded * Corresponding author. E-mail:
[email protected].
surface, but the nonreconstructed (1 × 1) single dangling bonded (111) surface has been shown to be the most stable.10 Several models for the rather complicated 2 × 1 reconstructions have been proposed, including the Chadi π-bonded molecule, π-bonded chain, and Seiwats single-chain model.11-13 However, it is settled that only the π-bonded chain, proposed by Pandey,14 is ascribed the 2 × 1 reconstruction observed for diamond (111) surfaces. The reconstruction has been verified theoretically, but the results are diversified considering whether the π-bonded chain is slightly buckled,12 dimerized,15 or unaltered.10,16 The reconstruction occurs at 1000 °C and close to the graphitization temperature for diamond.12 A proposed 2 × 2 π-bonded trimer has been shown to be highly unstable.10 Hydrogen- and nonterminated diamond (111) surfaces have been studied using first-principle,10,12,17 SLAB-MINDO,18 and ab initio molecular dynamics19 approaches. The undimerized and unbuckled chain model was shown to be the most stable form of the nonterminated surface reconstruction. A reaction barrier in the transition of the single bonded 1 × 1 to 2 × 1 Pandey chain reconstruction was calculated to be 1.81 eV per surface atom, thus substantially lower in energy compared to the adsorption energy for one hydrogen atom adsorbed to the surface.18 Because the adsorption energy of hydrogen is more favorable than the reconstruction energy, desorption of H is expected to take place after the process of surface reconstruction. The oxygenation of diamond (111) surfaces has been investigated to the same extent as the corresponding non- and hydrogen-terminated surfaces. One study of different oxygentermination scenarios was conducted using photoemission, LEED, and AES spectroscopy.20 The results demonstrated that
10.1021/jp709625a CCC: $40.75 © 2008 American Chemical Society Published on Web 02/02/2008
Terminated (111) Diamond Surfaces hydrogen atoms in the gas phase may replace oxygen on a (111)-2 × 1 reconstructed surface and convert it back into the 1 × 1 reconstruction. Oxygen atoms did not show the same reactivity in replacing H with O on a hydrogen-terminated surface. Oxidative etching on diamond (111) surfaces has been studied using dry oxygen, gas-phase oxygen/water vapor, and potassium nitrate liquid.21 In contrast to the diamond (100) surface, the (111) surface was very susceptible to etching due to the induced destabilization of the surface C atoms (following the divalent nature of the oxygen atoms).22 An X-ray scattering analysis of the structure of oxygen/water-etched diamond (111) surfaces has also been performed, demonstrating that the 1 × 1 surface was OH-terminated with an additional physisorbed water adlayer.23 The molecular oxygen adsorption (and desorption) processes on the diamond (111) surfaces have also been studied experimentally.24 Oxygen adsorption in on-top and bridge positions on a 2 × 1 reconstructed π-bonded chain were pointed out as the only plausible positions. The adsorption energies and geometries, as well as reconstructions of oxygen-terminated diamond surfaces, have been studied theoretically using planewave DFT.16,25 The results showed that the bridge and on-top oxygen will dominate the 2 × 1 reconstructed surface at low and high surface coverage, respectively.16,25 The Pandey chain was also lifted when the oxygen coverage was 100%; that is, all of the sites were carbonyl-terminated (CdO). Furthermore, to reach oxygen uptake above 50%, there was a need for thermal activation. Oxygen-terminated surfaces were also suggested to switch over to the OH-terminated 1 × 1 surfaces in the presence of atomic H.16 The purpose of the present study was to investigate the energetic stability of various oxygen-terminated diamond (111) surfaces using numerical orbital DFT techniques. The results included OH-, on-top O-, and bridge O-termination, as well as H-termination onto either a prehydrogenated or nonterminated diamond (111) surface. The surface coverage of all termination species varied from 0 to 100% in increments of 6%. In addition, the termination scenarios for the (111) surface were compared with a similar recently conducted study for diamond (100).26 Furthermore, kinetic considerations in the form of transitionstate searches were also included to investigate the origin of the temperature dependence of the 1 × 1 to 2 × 1 reconstruction. 2. Theoretical Approach 2.1. Methods. A density functional theory (DFT)27,28 method, available within the program Dmol3,29,30 was used for the energy and geometry calculations. A local numerical orbital basis set was generated as values on an atomic-centered spherical polar mesh, with a specific orbital cutoff of 3 Å. A doubling of the number of functions, together with an introduction of polarization p-functions (for hydrogen atoms) and d-functions (for nonhydrogen atoms), was used to get a more flexible basis set. The quality of the basis set is imperative for a good description of the system, especially when weaker bonds are present.29 All electrons in the system were treated in the same nonrelativistic nature because the atoms involved were light (C, H, and O). Thus, the electrons were not approximated by pseudopotentials. In order to study the periodicity of the surfaces, we used the Bloch theorem under symmetry unique Monkhorst-Pack31 generated k-points with a precise setting of 0.04 Å/k-point spacing, resulting in a total of 5 and 6 k-points for the diamond (111) and diamond (100) surface models, respectively. The exchange and correlation parts of the Hamiltonian were approximated using the Perdew-Wang (PW91) generalized gradient approximation (GGA). This, in contrast to the local
J. Phys. Chem. C, Vol. 112, No. 8, 2008 3019 density approximation (LDA), provides a much better energy evaluation32-35 because the LDA method tends to over-bind electrons in a molecule (or solid). Moreover, systems containing unpaired electrons require spin-unrestricted theoretical methods. Many of the adsorption processes within the present study involve unpaired electrons; therefore, it is largely based on spinpolarized calculations. Also, first-principle synchronous transit methods have been used in mapping a reaction pathway in order to find a transition state particularly for the 1 × 1 to 2 × 1 surface transformation with the following types of surface terminations: (i) nonterminated, (ii) 100% hydrogen-terminated, and (iii) 100% oxygen-terminated. At first, a maximum is located on the pathway between the reactant and the product (also known as linear synchronous transit, LST) followed by energy minimization in the conjugate gradient (CG) directions resulting in a more reliable transition state.36 After the CG minimization, a quadratic synchronous transit (QST) search is conducted. QST alternates searches for an energy maximum with constrained minimizations in order to refine the transition state (TS) to a high degree. The results are expected to be close to the results one should obtain by using the very accurate eigenvalue methods where searches are conducted for an energy maximum along one normal mode and a minimum along all other modes. A confirmation of the calculated TS was obtained using a NEB37 confirmation verification scheme, resulting in a plausible minimum energy path (MEP). 2.2. Diamond Surface Model. For a correct modeling of a diamond surface with its various chemical processes, a number of criteria must be fulfilled: (i) optimal geometry optimization, (ii) well-tested computational methodology (e.g., large enough basis set), and (iii) the surface itself must contain a sufficient number of atoms to minimize interaction effects originating from the periodic boundary condition. The number of carbon layers must also be sufficient to allow reconstruction and relaxation of the surface. Also, a large enough vacuum distance must be present to ensure minimum slab-slab interference. Test calculations showed that a vacuum thickness of ∼10 Å was adequate to use in the present study. An increase to 15 and 20 Å resulted in minimal change in the H adsorption energy (a decrease by approximately 1.0% and 1.1%, respectively). The diamond (111) surface was modeled using 10 carbon layers with 16 carbon atoms per layer, yielding a total of 160 atoms. The surface carbons were hydrogen-terminated with the purpose of removing dangling bonds and of maintaining the sp3 hybridization of the carbon atoms (i.e., a bulk-like situation). Figure 1 shows the final optimized diamond (111) surfaces with the single-bonded unreconstructed surface and the 2 × 1 undimerized and unbuckled π-bonded Pandey chain. The positions of the carbon atoms within the two bottom carbon layers (including the terminating H atoms) were fixed to simulate the structure of a bulk diamond. 3. Results 3.1. General. Oxygen has a profound impact on the growth and properties of diamond (111) and (100) surfaces. For example, oxygen affects CVD growth,38-40 counteracts induced p-type doping,41 and alters the optical properties and hydrophobic character.42 Also, the photon quantum yield of diamond will degrade because of the deterioration of the negative electron affinity (NEA) given by the oxygen termination.43 Induced p-type doping of the (100) surface has been shown to be lost upon oxygenation,44 whereas a smooth oxygenated (111) surface remains conductive.45 Furthermore, atomic oxygen may contribute to a favorable sp3 hybridization of carbon and to
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Petrini and Larsson En) runs from n ) 1-4, where n is the number of studied variables (H, OH, Oether , and Oketone adsorbates). Thus, eq 1 shows the total adsorption energy for all terminating species for a specific terminating scenario. The stability of all terminating systems has been related to a 100% H-terminated diamond surface. These relative stabilization energies, Estab, have been calculated using the following equation
Estab ) Eads - EΗ
Figure 1. Models of the (a) nonreconstructed and (b) undimerized, unbuckled 2 × 1 reconstructed diamond (111) surface.
minimizinggraphite-likesp2 hybridizationduetoCOdesorption.46-48 The resulting termination scenario of an oxygenated diamond surface is expected to depend on a combination of factors including the type of oxygen species available, surface temperature, coadsorbates (with degree of surface coverage), as well as surface-level reconstruction.49-51 In the present study, surface energetic stabilities and adsorption energies for various degrees of hydrogen- and oxygen-terminations have been examined theoretically for diamond (111)-1 × 1 and (111)-2 × 1 reconstructed surfaces. These results have been compared with the corresponding results for the (100)-2 × 1 surface, as presented earlier.26 In addition, the authors have included some transition-state searches for the diamond (111)-1 × 1 to 2 × 1 transfer under (i) nonterminated, (ii) 100% H-terminated, and (iii) 100% O-terminated surface configurations. The choice of surfaces studied in the present investigation is motivated by the fact that low-index surfaces are dominating the polycrystalline CVD growth process, where the (111) and (100) surfaces are most highly represented with a quota dependent on temperature and pressure. The following equation has been used to calculate the adsorption energy associated with the chemisorption of the terminating species 4
Eads ) Esurface - EΟ -
∑ an‚En
(1)
n)1
where Esurface is the total energy of the surface, an is the number of a specific terminating species, En is the gas-phase energy of the adsorbing species (i.e., O, OH, and H), and EΟ is the total energy of a nonterminated diamond surface. The sum of (an‚
(2)
where Eads is the adsorption energy calculated using eq 1 and EH is the corresponding energy for H adsorbates. 3.2. Energetic Stability. The evolution in adsorption (and stabilization) energies when successively chemisorbing hydrogen and oxygen species on diamond (111)-1 × 1 and (111)-2 × 1 surfaces has been studied theoretically in the present investigation. The results have been obtained by starting with one initial surface configuration (e.g., the nonterminated (111)-2 × 1 surface) followed by a successive adsorption of a specific species. Each resulting surface adsorbate composition was accordingly geometry optimized and adsorption/stabilization energies were calculated using eqs 1 and 2. The respective energy profiles for OH-, Obridge-, and Oon-top-adsorption onto a (111)-1 × 1 and (111)-2 × 1 surface are described in Sections 3.2.1-3.2.3 below. 3.2.1. 1 × 1 Reconstructed Diamond (111) Surface. Starting with a 100% (θ ) 1) H-terminated diamond (111)-1 × 1 surface, the chemisorbed H atoms were successively replaced by atomic oxygen in the bridge or on-top position or were replaced by OH groups. The corresponding adsorption energies are shown in Figures 2 and 3. As can be seen in Figure 2, the replacement of hydrogen by on-top oxygen generally yields more favorable adsorption energies compared to a 100% H-terminated surface. The linearity of the adsorption energy curve indicates that oxygen adsorbs fairly easily in the on-top position without the presence of major diamond surface reconstructions and/or adsorbate-adsorbate repulsions, which would otherwise decrease the expected adsorption energy as the surface coverage increases. On the contrary, the replacement of two neighboring hydrogen atoms by one oxygen atom in a bridge position results in an energetically less-favorable situation. Hence, the adsorption energy of one oxygen atom cannot compensate for the loss of two hydrogen atoms. Moreover, the bridge position is highly unstable with respect to the adsorption of a second oxygen atom into a neighboring bridge position, resulting in two on-top oxygen atoms and two unsaturated carbon atoms. This type of oxygen migration was observed during the course of geometry optimization; thus, no energy barriers exist. As a result, for initial surface Obridge coverage of about 25% the resulting surface composition would involve only on-top oxygen and nonterminated surface sites. Also shown in Figures 2 and 3 are the recently calculated adsorption profiles for the 2 × 1 reconstructed diamond (100) surface.26 As demonstrated in Figure 2, the unfavorable situation with Obridge positions on the diamond (111)-1 × 1 surface resembles the behavior of the diamond (100)-2 × 1 surface. The only exception is that the bridged oxygen on the (100) surface is still geometrically stable but energetically unfavorable in relation to the corresponding H-termination situation. The Oon-top adsorbates will break the 2 × 1 reconstruction and convert the surface back to 1 × 1, resulting in a surface coverage of 75% or higher. Previously, on-top oxygen has been shown to be the final adsorbate structure for the diamond (111)-1 × 1 surface.16 However, those observations were accompanied by rather low oxygen binding energies of -4.27 eV as compared to the values of -5.28 and
Terminated (111) Diamond Surfaces
J. Phys. Chem. C, Vol. 112, No. 8, 2008 3021
Figure 2. An initially 100% H-terminated diamond (100)-2 × 1 or (111)-1 × 1 surface is successively oxygen-terminated by successively replacing the H adsorbates with O in either bridge or on-top positions.
Figure 3. Stabilization and adsorption energies for a successive replacement of H adsorbates with OH groups on diamond (100)-2 × 1 and (111)-1 × 1 surfaces.
-6.09 eV presented in this study from ref 51. The results in ref 16 indicate that the monovalent hydroxyl groups would rather bind to the surface. Calculated adsorption and stability curves for a successive substitution of H adsorbates with OH groups can be seen in Figure 3. The OH termination of the diamond (100)-2 × 1 and (111)-1 × 1 surfaces shows very similar energetic behavior in destabilizing the surface. Two competing effects can be identified here: (a) more strongly bonded OH atoms to the surface and (b) steric repulsion due to the rather bulky OH groups. The OH groups adsorbed onto the (111)-2 × 1 and (100)-1 × 1 surfaces show almost identical chemisorption energy values, but the stabilization energies for 100% terminated surfaces differ somewhat. As can be seen in Table 1, a 100% surface termination with OH destabilizes the (111)
surface more than the (100) surface (0.38 compared to 0.16 eV, respectively). This can be attributed to the fact that the 100% H-terminated diamond (111)-1 × 1 surface is energetically more stable than that of the (100)-2 × 1 surface and the stabilization energies for OH termination are related to those for the H termination. It has been shown in an earlier study that the diamond (110) surface is rather unstable in both its nonterminated and H-terminated forms with no sign of surface reconstruction.52 Furthermore, the exposure of a nonterminated diamond (100) surface to thermally activated oxygen has been studied by using spectroscopy and desorption techniques.53 Oxygen species adsorbed onto the surface were then assumed to be in the
3022 J. Phys. Chem. C, Vol. 112, No. 8, 2008
Petrini and Larsson
TABLE 1: Distances (in angstroms) of Nonterminated or Completely H-, O-, or OH-terminated Diamond (111)-1 × 1 and -2 × 1 Surfacesa surface
specific distance (Å)
reconstruction
adsorbate
2×1 2×1 2×1 2×1
clean H O OH
1×1 1×1 1×1 1×1
clean H O OH
a
C1-A
A-A
A-Aa
1.10 1.45 1.42 1.44
2.52 1.55 2.41 2.59
2.82 3.03 2.41 2.59
1.11 1.32 1.41 1.45
2.52 2.52 2.48 2.54
2.52 2.52 2.48 2.54
C1-C1
C1-C1a
C1-C2
C2-C2
C2-C2a
C1-C3
C2-C3
1.44 1.56 1.60 1.71 1.93 2.52 2.52 2.52 2.51 2.54
2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.52 2.51 2.54
1.54 1.60 1.55 1.58 1.60 1.50 1.54 1.57 1.55
1.56 1.54 1.57 1.59 1.60 2.52 2.52 2.52 2.52
3.67 3.62 3.65 3.62 3.64 2.52 2.52 2.52 2.52
2.37 2.59 2.50 2.58 2.62 2.48 2.51 2.58 2.52
1.62 1.57 1.59 1.57 1.61 1.65 1.56 1.53 1.55
The second-closest X-X distance.
Figure 4. A non-terminated 2 × 1 reconstructed diamond (111) surface is successively H-, O-, and OH-terminated with increments of one adsorbate. A comparison with H-termination on diamond (111)-1 × 1 and (100)-2 × 1 is included. The arrow identifies the H coverage where a (111)-1 × 1 and a (111)-2 × 1 surface have identical stabilization energies.
peroxide configuration. Other experimental studies suggest a bridge or on-top structure.24 3.2.2. Pandey Chain Diamond (111)-2 × 1 Reconstructed Surface. The surface reconstruction of the nonterminated diamond (111) surface was theoretically simulated by performing geometry optimization on an initial 1 × 1 surface. However, in order to obtain the generally observed 2 × 1 reconstruction of type Pandey chain, the surface geometry of the two topmost carbon layers must initially be somewhat perturbated toward the Pandey chain structure. Thus, the transformation from a 1 × 1 to a 2 × 1 geometrical reconstruction is associated with an activation energy barrier. In addition, the resulting surface 2 × 1 reconstruction was found to be energetically more stable than the 1 × 1 counterpart, as can be seen in Figure 4 for nonterminated surfaces. H-, O-, and OH-species were thereafter successively adsorbed onto the surface, starting from a nonterminated surface and thereafter increasing the number of adsorbates with increments of one. The left-hand axis in Figure 4 displays the relative stabilization energies (in comparison to a 100% hydrogenated surface) for various types of diamond surfaces studied, whereas the right-hand axis shows the total adsorption energies. For comparison, the hydrogen adsorption profiles for the (111)-1 × 1 and (100)-2 × 1 surfaces are also included in Figure 4. The reconstruction from 1 × 1 to 2 × 1
was found to lower the total energy of the nonterminated diamond (111) surface by 8.8 eV (or 0.55 eV per surface C) as can be seen in Figure 4. This is in close agreement with earlier observations (∼0.5 eV).12 When successively adsorbing H, O, or OH groups, the adsorption energies became, as expected, negatively charged. Adsorbed H atoms at lower surface concentrations (< 31%) did not demonstrate the capacity to largely alter the geometry of the surface. However, an H surface coverage above 31% yielded adsorption energies (and stabilization energies) unfavorable for the 2 × 1 reconstruction in comparison to the 1 × 1 surface. These results are consistent with other studies showing that a 100% H-terminated (111)-2 × 1 surface is energetically less-favorable than the 1 × 1 counterpart.16,17 Also, a small number of H adsorbates have been shown experimentally to induce the 1 × 1-to-2 × 1 reconstruction.54 The adsorption energy of H on an otherwise 100% H-terminated 1 × 1 (and 2 × 1) surface has in two different studies been calculated to -4.15 (-3.45)19 and -4.98 (-4.34) eV,16 respectively. The results obtained in the former study are more in agreement with the observations in the present study: -4.53 (-3.29) eV, whereas the results from the latter show a larger discrepancy. The calculations within the present study have furthermore shown that the adsorbed oxygen atoms prefer the bridge
Terminated (111) Diamond Surfaces
Figure 5. Structure of the (a) 50% and (b) 100% O-terminated Pandey chain structure of the 2 × 1 reconstructed diamond (111) surface. The carbon atoms of the Pandey chain are shown in white. The rest of the upper surface C atoms are shown in dark gray, and the oxygen atoms are shown in black.
positions within the Pandey chain. The resulting adsorption energies were more negative (i.e., energetically more preferable) for all surface coverage in comparison to the corresponding situation with hydrogen adsorbates. After all of the intrachain bridge sites had been occupied with O adsorbates (at 50% coverage), the next-coming oxygen atoms were adsorbed in a dimer manner, increasing the surface coverage until 100% were adsorbed. This dimerization resulted in a rotation of the two oxygen atoms in relation to the carbon atoms situated directly below. This situation, with adsorption to chain-chain bridge sites, is hence energetically somewhat less-favorable compared to the intrachain bridge positions. A reduced stability can therefore be observed as a slight decrease in the slope in Figure 4 at 50% O coverage. The geometrical structure of the 2 × 1 surface with a 50% or 100% oxygen surface coverage at bridge sites is shown in Figure 6. Other theoretical studies have also shown that oxygen adsorption is energetically favorable at lower surface coverage (
