Ab initio study of negative electron affinity from light metals on the oxygen-terminated diamond (1 1 1) surface

Recent computational work has shown that light metals adsorbed onto the oxygenated diamond (1 0 0) surface have the potential to give diamond a temperature-stable negative electron affinity (NEA). Here, we use density functional theory to study three of these metals, lithium, magnesium and aluminium, on the (1 1 1) surface. We show that all three of these metals adsorbed onto the ketone O-terminated diamond surface can possess a large NEA and adsorption energies above that of H-termination at monolayer (ML) or sub-ML coverages. Adsorption onto the ether O-terminated surface gives similarly large NEAs but lower adsorption energies. These results are promising for the development of novel NEA surfaces such as those required for thermionic devices.


Introduction
There has been considerable recent interest in obtaining a negative electron affinity (NEA) surface from diamond. An NEA, where the conduction band (CB) minimum is higher in energy than the vacuum energy, allows electrons located in the CB to escape to vacuum with little energy barrier, making NEA diamond an efficient source of electrons (figure 1). For example, electrons can be emitted by heating the diamond to temperatures around 800 °C (thermionic emission) [1], with applications in thermionic energy converters for solar power generation or waste heat scavenging [2][3][4]. Electrons can be emitted via field emission, for high-power switches, electron sources or flat-panel displays [5,6]. High secondary electron yields from NEA diamond have also been reported, for potential use in photomultipliers [7][8][9]. Alongside the NEA, the corresponding high energy of the valence band (VB) allows surface transfer doping from adsorbates [10]. The deposition of a material with a large positive electron affinity onto the diamond surface can induce a 2D hole gas in diamond and has been used to develop diamond-based electronic devices such as capacitors and field effect transistors [11][12][13].
Hydrogen termination has been the most widely studied NEA surface on diamond, with an electron affinity of −1.3 eV measured experimentally [14,15]. H-termination is unstable at elevated temperatures ( > ∼ 700 °C) [16]; this is problematic for thermionic emission applications which require these high temperatures to thermalise electrons into the CB. At these thermionic operating temperatures hydrogen desorbs from the diamond surface to create a bare surface with positive electron affinity. Therefore, work has focused on finding alternatives to H with which to terminate the diamond surface that retain NEA but are also stable at higher temperatures.
A diamond surface with NEA is believed to originate from termination with a more electropositive species than carbon, creating a dipole with positive charge outermost. Prior computational work has predicted an NEA from diamond terminated with group I metals and first-row transition metals (TMs) [17][18][19][20]. Experimentally, diamond exhibits an NEA upon deposition of thin layers of various TMs [21][22][23][24], or from termination with Si [25] or Ge [26]. Titanium deposition leads to an enhanced thermal stability over H-termination, and the higher emission temperature doubled the obtainable emission current density [27].
There has been particular focus on obtaining NEA from more complex metal-oxygen-diamond surface terminations. This is particularly desirable since typical metal-oxygen and carbon-oxygen bonds are stronger than metal-carbon bonds [28,29], increasing the thermal stability of the surface termination. Since the metal is already partially oxidised, there is less propensity for it to react further with oxygen, making these surfaces more air stable. Additionally, the partly ionic character of the metal-oxygen bond can enhance the surface dipole, producing a large NEA. One complication is that before the metal is deposited, the oxygen-terminated diamond surface can take several possible forms, with the two most stable involving the oxygen bonding either to a single carbon atom as a ketone (C=O), or bridging across two carbons as an ether (C-O-C).
The majority of research in this area has focused on the (1 0 0) surface, with experimental and computational studies including lithium [18,30,31], magnesium [31,32], aluminium [33], and various first-row TMs [34]. A computational study by O'Donnell et al [31] of metal-oxygen-diamond surfaces involving the group I elements showed that the adsorption energies of lighter metals are larger than those of heavier metals, and even though lighter metals are less electropositive, the NEA values are comparable. In contrast to the (1 0 0) surface, the (1 1 1) surface has been far less studied, even though it is the natural cleavage plane of diamond, a dominant growth surface in CVD diamond, and prevalent in nanodiamonds [35][36][37]. Experimental work with caesium has shown that the Cs-O-diamond termination is more thermally stable on the (1 1 1) surface, up to 500 °C compared with 400 °C for the (1 0 0) surface [38,39]. In this paper we consider adsorption of Li, Mg and Al each at 0.25, 0.5 and 1 monolayer (ML) coverages on the ether and ketone O-terminated (1 1 1) diamond surfaces. These three light metals exhibit promising NEA properties on (1 0 0) diamond and we now investigate their properties on the (1 1 1) surface.

Method
Density functional theory (DFT) calculations were performed using the plane-wave CASTEP code [40] on a diamond slab consisting of 14 carbon layers. In all calculations, the diamond slab surfaces were 2 × 2 supercells of the primitive (1 1 1) surface cell, and periodic in two dimensions. Lattice vectors parallel to the surface were both fixed to 5.05 Å, and the angle between them was fixed to 120°. Terminations were applied to both the top and bottom surfaces to prevent any charge imbalance across the slab. A vacuum gap of approximately 20-25 Å separated repeating slabs to ensure no interaction between surfaces. A basis set of plane waves with an energy cut-off of 700 eV, the Perdew-Burke-Ernzerhof (PBE) generalised gradient approximation (GGA) for the exchange-correlation functional [41] and Vanderbilt pseudopotentials [42] were used in all calculations. Density-of-states spectra were computed using the OptaDOS code [43] with adaptive broadening and DOS spacing of 0.07 eV. The Brillouin zone was sampled by a 6 × 6 × 1 Monkhorst-Pack k-point grid [44] for energy minimisation steps and a 12 × 12 × 1 k-point grid for DOS calculations. The validation of these computational param eters has been shown previously [33].
Calculations of ionisation energies, I, were adapted from the method of Fall et al [45] in which the energy of the valence band maximum (VBM) of the slab, E VBM , is determined from the addition of the average electrostatic potential of the slab, V slab , to the difference between the VBM position in bulk diamond, E VBM, bulk , and the average electrostatic potential of bulk diamond, V bulk . This energy is then subtracted from the vacuum energy, E vac , as shown by equation (1).
The electron affinity, χ, is calculated from the subtraction of the band gap of diamond, E g , from the ionisation energy (equation (2)). The experimental value for bulk diamond is used since the GGA method underestimates the band gap of diamond [19].
The adsorption energy, E ads , was calculated by subtraction from the total energy of slab plus adsorbates, E total , the slab  energy with no adsorbate, E slab , and the number, N, of isolated adsorbate atoms of energy, E at . This is divided by the total number of adsorbate atoms to give energy per adsorbate (equation (3)). A negative E ads indicates exothermic adsorption.

Surface structures
Initially, the adsorption energy and electron affinity were calculated for the hydrogen-terminated (1 1 1) surface for comparison with subsequent terminations. The H-terminated surface is lowest in energy with no reconstruction, in agreement with experiment [46]. The calculated adsorption energy is −3.79 eV, which is smaller than the value of −4.89 eV obtained by Loh et al [47]. The adsorption energy is taken with respect to the energy of an unterminated (1 1 1) surface with (2 × 1) reconstruction, where surface carbons form a zig-zag π-bonded 'Pandey' chain along the surface [48]. The calculated electron affinity of H-termination is −2.2 eV, in good agreement with other computational work [49,50]. This is larger than the experimental value of −1.3 eV; it is not uncommon for DFT to overestimate the magnitude of the electron affinity of diamond. This difference may be due to approximations inherent to DFT, or because of defective experimental surfaces. Unlike on the (1 0 0) surface, where ketone and ether oxygen terminations can be present simultaneously, on the (1 1 1) surface the extent of O coverage is believed to affect how O is bonded to diamond; the ketone can form 1 ML coverage, but the maximum ether coverage is 0.5 ML due to the way oxygen bonds with the surface [47]. It has been argued that steric repulsion between oxygen atoms may limit the total surface coverage of oxygen to 0.5 ML for the (1 1 1) surface experimentally [51], but a similar argument for the (1 0 0) surface was strongly disputed by Zheng et al [52] and calcul ations of adsorption energies suggest 1 ML coverage is possible [39,47].
We define 1 ML of metal addition as one adsorbate per surface unit cell, so four adsorbates comprise 1 ML of the 2 × 2 diamond supercell used in these calculations. For addition to both ether and ketone O-terminated (1 1 1) surfaces, sites for metal addition are chosen that maximise the metal-oxygen (M-O) coordination number. Coverages of 0.25, 0.5 and 1 ML are studied, representing 1, 2 and 4 metal atoms, respectively, added to the diamond surface 2 × 2 supercell.

Metal addition to the ether surface
The ether oxygenated (1 1 1) diamond surface retains the (2 × 1) reconstructed Pandey chain structure observed for the bare surface [47]. Oxygen atoms bridge two C atoms in the upper Pandey chain at 0.5 ML coverage. Figure 2 shows the ether surface with the sites considered for metal addition shown in the plan view. Table 1 shows results for Li, Mg and Al adsorption at different sites and coverages to the ether O-terminated (1 1 1) surface, and figure 3 shows the sites with the largest calculated NEA. For each metal, one C-O bond from each ether breaks at sub-ML coverages, allowing a M-O bond to form. There is little difference between adsorption energies at 0.25 and 0.5 ML coverage. Al has the largest adsorption energy while Li and Mg have similar, lower energies; only the adsorption energy of Al is larger than that of H-termination. At 1 ML both C-O bonds break and oxygen atoms are incorporated into the metal layer. This is a different result to that in previously reported computational work for Li at 1 ML [53,54], and possible reasons for this are discussed later.
During energy minimisation, a small amount of atomic rearrangement occurs; after the ether bond breaks oxygen and metal atoms move slightly from their initial positions. For metal atoms at the L site, only Li remains 2-coordinate to O atoms in one Pandey chain, while Mg and Al are instead 2-coordinate to O atoms across two Pandey chains (e.g. Al in figure 3(c)). As the C-O bonds break, adjacent C atoms form a C=C double bond; Mulliken population analysis [55] shows an increase in the C-C bond population from 0.82 before adsorbate addition to ~1.4 after. Bond populations confirm there is no bonding between metal and surface C atoms. Mulliken charges of the metals give an idea of the degree of

Metal addition to the ketone surface
The ketone oxygenated (1 1 1) diamond surface also retains the (2 × 1) reconstruction [47], although the C=O doublebond breaks one of the C-C bonds of the upper Pandey chain, resulting in the elongated hexagonal pattern observable in the plan view (figure 4). In this configuration, O atoms have 1 ML coverage. Adsorbed metals can be 3-coordinate to O and are either located above the upper or the lower Pandey chain. Table 2

Electronic structure
Partial density-of-states (PDOS) spectra were computed to analyse contributions to the electronic structure from individual atoms or groups of atoms. These were computed for the ketone O-terminated (1 1 1) surface, as it has the most promising NEA properties. Shown in figure 6 is the PDOS spectrum for the adsorbate-free ketone surface. The spectrum has the VBM set to zero, and different groups of atoms are offset for clarity. Bulk carbon atoms are chosen from the centre of the diamond slab and indicate the position of the band gap of bulk  diamond. Surface carbon atoms are those in the upper Pandey chain. The peaks for the surface C and the O atoms overlap, indicative of covalent bonding. There are additional peaks for the O atoms in the VB and within the band gap region of the bulk diamond, originating from lone pairs. This is similar to that observed for oxygen on the (1 0 0) surface [50]. Figure 7 shows PDOS spectra for ketone surfaces with adsorbed metals, taken for the lowest energy structures at 0.25 and 0.5 ML coverages given in table 2. 1 ML coverage is not shown as it is associated with lower adsorption energies. In Turning to the metal DOS, Li has little contribution to the DOS except at energies ~4 eV above the VBM at 0.25 ML coverage, moving down in energy to be just above the Fermi level at 0.5 ML coverage. The position of the Li DOS above the Fermi level shows that these 2s states are unoccupied and so charge transfer has occurred. The behaviours of the DOS for Mg and Al, meanwhile, are similar to one another, although with different peak shapes. At 0.25 ML coverage, the metal DOS lie just above the Fermi level, while at 0.5 ML coverage these DOS move down in energy to be partly above and partly below the Fermi level. The metal states change from being unoccupied to partially occupied, associated with the smaller positive charge, and with an electron affinity less   negative at 0.5 ML coverage. Each of the metal DOS display largely ionic behaviour as there is little interaction between the metal and the oxygen states.

Discussion
A comparison of the different oxygen terminations reveals that each metal is more strongly bound to the ketone than to the ether surface. This is not unexpected, as the coordination number to oxygen is greater for metals on the ketone surface. The formation of a strained C=C bond on the upper Pandey chain of the ether surface may also be a contributing factor for the low adsorption energy. Adsorption on the ketone varies more with coverage than on the ether surface, consistent with the larger ionic interaction between the metal and the ketone, which is due to the higher coordination number. Electron affinities, meanwhile, are broadly similar for the metal-adsorbed ether and ketone surfaces. As the ketone surface has twice the number of O atoms, one might expect that the ketone electron affinities should be less negative. However, on the ketone surface the metal atoms are more ionised than on the ether surface. This larger surface dipole appears to negate the effect of doubling the number of O atoms, leading to similar values for the electron affinity.
The Li adsorption behaviour reported here for the ether surface differs somewhat from the work of O'Donnell et al [53]. In particular, we find no stable surface at 1 ML coverage due to incorporation of O into the metal layer, whereas O'Donnell et al report a local minimum where each Li is 2-coordinate to oxygen. It is possible that different computational parameters or convergence criteria contribute to these differences. Alternatively, the larger surface supercell used here gives additional freedom of movement to the atoms. A comparison of the Li-adsorbed ketone surfaces with those in [53] shows the NEAs and adsorption energies are in good agreement and show the same trends.
The adsorption energies for each metal on the ketone (1 1 1) surface are comparable to the (1 0 0) surface for the same coverages [18,31,33]. However, the situations which maximise NEA differ; Li and Mg have a slightly larger NEA on (1 0 0) and at higher coverages compared to those on (1 1 1), while Al has larger NEA on (1 1 1) at the same coverage as (1 0 0). Two factors are likely to affect the differences in the adsorption energy and NEA between the (1 0 0) and (1 1 1) surfaces. First, the M-O coordination number is 3 for (1 1 1) and 4 for (1 0 0). The increased coordination number leads to a more positively charged metal adsorbate, affecting the M-O dipole. Second, the coordination geometries of the adsorbates are different. For an adsorbate at the same height above the carbon layer, the M-O bond length on (1 1 1) will be smaller. A comparison shows the M-O bond lengths on the (1 1 1) surface are generally slightly smaller than on the (1 0 0) surface [31,33].

Conclusions
DFT calculations have been used to study the adsorption of up to 1 ML of Li, Mg and Al onto the ether or ketone oxygenterminated diamond (1 1 1) surfaces. Adsorption more readily occurs on the ether (1 1 1) surface than the corresponding (1 0 0) surface [33], although with all three metals 1 ML coverage results in the transfer of O atoms from the surface and into the metal layer, breaking all the C-O bonds. For sub-ML coverages large NEAs are predicted.
We find that the metal-adsorbed ketone (1 1 1) surfaces have the largest adsorption energies, which are comparable to those of the corresponding metal-adsorbed (1 0 0) surfaces [31,33]. Al has the largest adsorption energy, then Li, then Mg, but all are larger than for hydrogen-termination. Adsorption energies decrease with increasing coverage, which is beneficial for avoiding island formation of the metal. Large NEAs are observed at 0.5 ML Li and 0.25 ML Mg and Al coverages, but electron affinities become more positive as coverage increases. Li has the most negative NEA, then Mg, then Al. The results here show the potential for NEA devices using CVD diamond. Li is the most favourable for experimental work that prioritises a large NEA, while Al is preferable for work prioritising high thermal stability, although careful control of coverage is required.