Negative electron affinity from aluminium on the diamond (1 0 0) surface: a theoretical study

and experimental work has concentrated on elements that can provide a Abstract Density functional theory calculations were performed to model the adsorption of up to 1 monolayer (ML) of aluminium on the bare and O­terminated (1 0 0) diamond surface. Large adsorption energies of up to − 6.36 eV per atom are observed for the Al­adsorbed O­terminated diamond surface. Most adsorption sites give a negative electron affinity (NEA), with the largest NEAs − 1.47 eV on the bare surface (1 ML coverage) and − 1.36 eV on the O­terminated surface (0.25 ML coverage). The associated adsorption energies per Al atom for these sites are − 4.11 eV and − 5.24 eV, respectively. Thus, with suitably controlled coverage, Al on diamond shows promise as a thermally­stable surface for electron emission applications.


Introduction
The desirable bulk properties of diamond, coupled with its ability to form a negative electron affinity (NEA) surface is of technological interest for numerous electron emission appli cations including photodiodes [1], electron sources [2], sec ondary electron emission [3] and renewable energy generation [4]. Furthermore, low work function diamond devices have potential for surface transfer doping applications [5]. In a mat erial with an NEA, the conduction band minimum (CBM) is higher in energy than the surrounding vacuum, leading to vir tually barrierless electron emission when electrons are excited into the conduction band (figure 1). To form an NEA material, it is necessary to terminate the surface with atoms or groups of atoms that are electropositive relative to the bulk material, forming an electric dipole perpendicular to the surface with positive charge outermost. For diamond, simple H termination gives an NEA for each of the (1 0 0), (1 1 1) and (1 1 0) surfaces [6][7][8]. However, Hterminated diamond surfaces suffer from hydrogen desorption at elevated temperatures (≳700 °C) [9]. This makes Hterminated diamond unsuitable for hightemper ature applications, such as thermionic energy converters [4], and so there is an extensive search for alternatives with which to terminate diamond that provide high NEA whilst remaining stable at thermionic operating temperatures.
Previous experimental and computational studies of NEA surfaces on diamond include the use of group I and II metals [10][11][12][13] and firstrow transition metals (TMs) [14][15][16][17][18][19] as the electropositive species, with monolayer or submonolayer coverage on bare or oxidised diamond surfaces. Group I ele ments have long been known to exhibit NEA characteris tics on diamond, but larger adsorbed group I elements have low thermal stability which limits their usefulness at higher temper atures. For example, despite an extremely low work function of ~1.5 eV, the CsOterminated diamond surface loses Cs through desorption, and so the NEA is lost above ~400 °C [10]. Thus, recent computational and experimental work has concentrated on elements that can provide a more robust surface in addition to NEA, focusing on small group I and II metals, such as Li and Mg [20][21][22]. Experimental work with certain TMs shows NEA emerges from deposition of thin (<10 Å) layers onto bare or oxidised diamond surfaces [14][15][16][17]. The magnitude of the NEA varies with the TM and layer thickness. Computational work has also predicted NEA with various firstrow TMs, including Cu, Ni, Ti and Zn, on both bare and Oterminated diamond surfaces, with results sug gesting that carbideforming TMs give a larger NEA [18,23].
Aluminium on the diamond surface has thus far been omitted from NEA studies, even though Al forms a carbide and bonds sufficiently well to a diamond surface to act as either Ohmic or Schottky contacts for diamondbased devices [24]. Al 2 O 3 on diamond is a candidate material for device interfaces in MOSFETs [25] and MOSCAPs [26] and addi tionally for passivation of the ptype conductive surface found on Hterminated diamond that results from surface transfer doping [27]. However, these are typically thicker films than what is required to give NEA. In this work we show that up to 1 ML of aluminium on bare and Oterminated diamond has considerable potential for NEA devices.

Method
Planewave density functional theory (DFT) calculations were carried out using the Cambridge Serial Total Energy Package (CASTEP) code [28]. The diamond slab consisted of 14 carbon layers, sufficient to represent bulk diamond at the centre. The slab is periodic in the x and y directions and termi nated on both sides by a 2 × 2 supercell of the (1 0 0) surface. The slab width was fixed at 5.05 Å × 5.05 Å with a vacuum gap of 20-25 Å separating repeating slabs, chosen such that the electrostatic potential had fully decayed in the vacuum. A basis set of plane waves with an energy cutoff of 700 eV, the Perdew-Burke-Ernzerhof (PBE) generalised gradient approximation (GGA) for the exchangecorrelation functional [29] and Vanderbilt pseudopotentials [30] were used in all calculations. Densityofstates calculations were calculated using the OptaDOS code [31] with adaptive broadening and DOS spacing of 0.07 eV. The Brillouin zone was sampled by a 6 × 6 × 1 Monkhorst-Pack kpoint grid [32] for energy mini misation steps and a 12 × 12 × 1 kpoint grid for DOS calcul ations. The energy of the slab was minimised with respect to all atomic positions. The tolerances for convergence of ionic forces and total energy were 0.05 eV Å −1 and 2 × 10 −5 eV/ atom, respectively.
The ionisation energy I was calculated using the method of Fall et al [33], shown in equation (1) as the difference between vacuum and valence band maximum (VBM) ener gies. The electron affinity (EA) χ is calculated by subtraction of the experimental band gap, E g , from the ionisation energy, as shown in equation (2).
E vac is the energy of the vacuum level, E VBM the valence band maximum, V slab the average slab potential, E VBM, bulk the valence band maximum calculated for bulk diamond, and V bulk the average potential energy in the bulk. The difference between E VBM, bulk and V bulk has been calculated previously [34]. The experimental value of the band gap, E g , of 5.47 eV was used because the GGA method underestimates the band gap of diamond [18]. The energy of adsorption E ads was calculated from the energy of the structure containing both diamond slab and adsorbates E total by subtraction of the diamond slab energy E slab with no adsorbate, and the energy of an isolated adsorbate atom E at multiplied by the number of adsorbate atoms N. This divided by the total number of adsorbate atoms gives the energy per adsorbate (equation (3)). A negative E ads indicates exothermic adsorption.
For validation purposes, calculations were initially per formed on the bare, H and Oterminated diamond surfaces, and compared with previous published calculations. Table 1 shows that calculated energies and bond lengths are in good agreement with previous work. Values for adsorption ener gies are the most variable as they are particularly sensitive to the computational parameters, such as functionals used and the basis set. For diamond, DFT calculations generally give larger electron affinities than those measured experimentally [35]. This is related not only to the approximations in the DFT method, but also uncertainty in the surface coverages achieved experimentally.

Geometry optimisation
In this work, we define one atom per surface unit cell as con stituting a monolayer (ML), and thus four atoms constitute 1 ML of the 2 × 2 supercell used here to represent the dia mond surface. Both the bare and the oxygenterminated sur face were considered.

Al addition to the bare diamond surface
Upon geometry optimisation, the bare diamond surface recon structs to a (2 × 1) arrangement, forming dimer rows on the surface (figure 2). Between 1 and 4 Al atoms were added to both sides of the relaxed bare diamond slab, each atom    Table 2 displays the results for these surface arrangements for Al on the bare diamond surface, while the lowest energy positions for different surface coverages are shown in figure 3. For 0.25 and 0.5 ML coverage, the T4 site was found to be lowest in energy, while at 1 ML coverage the lowest energy configuration came from a parallelogram arrangement of Al atoms outside high symmetry sites, formed here by relaxation from the HH + T3 positions. This gave a hexagonal structure of Al atoms in the same plane, with Al-Al bond lengths of 2.52 Å in the y direction and 2.74-2.91 Å otherwise (figure 3(c)). This geometry is similar to that in the hexagonal (1 1 1) plane of bulk Al metal in which the Al-Al nearest neighbour distance is 2.86 Å; here Al-Al bonds are shorter because of epitaxial bonding of Al with the outermost carbon atoms.
The lengthening of the carbon dimer from 1.38 Å for the bare surface to between 1.63-1.85 Å suggests a change from a double to a very extended single bond. This is accompanied by a substantial reduction in Mulliken [42] bond population of the carbon dimer from 1.36 before Al addition to 0.52-0.78 after. The bond populations between Al and C atoms in the surface dimer lie between 0.02 and 0.67 and there is a correla tion with the magnitude of the adsorption energies. Mulliken population analysis shows Al gains a positive charge of up to 0.9e, 0.8e and 0.4e for 0.25, 0.5 and 1 ML, respectively. The majority of negative charge is located on carbon atoms in the dimer row. There is a noticeable distinction between Al at the 4coordinated HH and T3 sites and the 2coordinated HB and T4 sites. The bonding at the 4coordinate sites possess larger Mulliken charges but smaller Al-C dimer Mulliken bond popu lations and so we define the 4coordinate sites as 'ionic' and the 2coordinate sites as 'covalent'. Al preferentially bonds to the 2coordinate, more covalent sites, shown by larger E ads values.
EA is strongly affected by the positioning of the Al atoms, with covalent sites showing more negative EA. Most sites show an NEA ranging from −0.1 to almost −1.5 eV, but for 0.5 ML both the linear and (√2 × √2) arrangement for the HH + T3 configuration have positive EA. Comparing Al with the TMs studied by Tiwari et al [18,23] we find the EA of Al is, in general, more negative than those for Cu, Ni and V, and the variation with position smaller. Whilst they find Ti can possess a negative electron affinity larger than Al, for 0.5 and 1 ML coverages of Ti the most stable site has positive EA. Al has, generally, a larger adsorption energy than Cu, about the same as Ni, and smaller than V and Ti. The lowest energy adsorption sites for Al are different to these TMs-for the Aladsorbed bare surface T4 (covalent) sites are preferred over T3 (ionic) sites at <1 ML coverages. It is also worth noting that overall the magnitude of the adsorption energies for Al are smaller than the adsorption energy for H on the bare surface (table 1).

Al addition to the O-terminated surface
The clean Oterminated surface has two possible lowenergy configurations: the ether arrangement, where the oxygen bridges between two adjacent surface carbons, and the ketone arrangement, involving a C=O double bond normal to the sur face ( figure 4). These structures are similar in energy so both were considered for this study. In both cases, the unrecon structed (1 × 1) Oterminated surface has only two highsym metry positions for adsorbate atoms: the 4coordinate oxygen pedestal (OP) and 2coordinate oxygen bridge (OB) sites ( figure 4(c)). Additionally, Al was placed at the highsym metry sites of a (2 × 1) reconstructed Oterminated surface, which, while not stable for the clean surface, are stabilised by adsorbate addition. The procedure for addition of Al atoms for coverages above 0.25 ML was the same as described previ ously for (2 × 1) sites, and an analogous procedure was used for addition to the (1 × 1) surface. Table 3 shows results for Al addition to the (2 × 1) reconstructed surface and whether this final configuration is obtained starting from addition to either ether or ketone Oterminated diamond. The minimum energy structures are shown in figure 5. Al bonds only weakly to the ether Oterminated surfaces, with the OB site lower in energy than OP. The only reconstruction observed is when the Al-Al bond is perpendicular to dimer rows at 0.5 ML coverage. The 1 ML surface is not stable.
In contrast to the etherterminated surfaces, most config urations for the ketone Otermination relax into the (2 × 1) reconstructed surface. The weak ketone πbond is broken by the presence of Al, but not the strong ether σbond. The 0.25 ML OP ketone configuration moves to the T3 position, and Al atoms at 0.5 ML coverage in OP positions relax into either the HH, HH + T3 (linear) or HH + T3 (√2 × √2) positions depending on the original arrangement. The HB site for <1 ML addition only causes reconstruction of the dimer above which it lies. At 1 ML, Al atoms in the ketone OP and OB positions move into the HH + T4 and HB + T4 positions, respectively, although in the case of HH + T4, the Al atoms in the HH sites are at different heights above the surface. The T3 site is the lowest energy site for both 0.25 and 0.5 ML Mulliken charges on Al are up to 2.16e, 1.58e and 1.08e at 0.25, 0.5 and 1 ML coverages, respectively. The preferred sites for adsorption in these cases are the more ionic HH and T3 sites at <1 ML coverage. However, in general, the 'cova lent' sites have more negative EA than 'ionic' sites.
The electron affinity of the different Aladsorbed Oterminated diamond surfaces are less negative than for addi tion to the bare surface, with more positions showing positive EA. Adsorption energies are larger than for addition to the bare surface. Increased coverage leads to decreased adsorp tion energies, the reverse of the trend observed for adsorption to the bare surface. This is technologically useful for better control of surface coverage and discouragement of island for mation. The EA is less negative than observed by O'Donnell et al [20] for group I elements on Oterminated diamond, but adsorption energies are significantly higher. Compared with the transition metals studied by Tiwari et al [19], Al is most similar to Ti, with 0.25 ML coverage giving the largest NEA for both metals and comparable adsorption energies.

Electronic structure
Projected densityofstates (PDOS) were computed to study the effect of metal adsorption on electronic structure. In each case, the bulk valence band maximum is set to zero, and states originating from different sets of atoms are offset for clarity. Bulk carbon atoms are taken from the middle of the diamond slab and are not expected to change. The PDOS for surface carbon atoms are taken from the dimer row. Figure 6 shows PDOS spectra for the clean oxygen free and (ether) Oterminated diamond surfaces. The extra states within the band gap for the bare surface originate from π and π* bonds of the dimer rows [23], and, similarly, Otermination also introduces interbandgap states from oxygen lone pairs [43].   Values of ionisation energy, I, electron affinity, χ, adsorption energy, E ads , and relevant bond lengths, d, calculated for the minimum energy positions at different surface coverages of Al on the bare diamond surface. The HH and T3 sites at 0.25 ML coverage were not energy minima and so are not included.

Coverage (ML)
Structure The PDOS spectra for the Aladsorbed diamond surfaces are displayed in figure 7. These were computed for the lowest energy structures in tables 2 and 3. The bulk carbon PDOS spectra are similar in all cases, as expected. Starting with addi tion to the bare surface, all coverages show mixing of Al and surface C states indicating covalent bonding. At 0.25 ML cov erage the broadness of the surface C DOS is due to there being two contributions to the DOS, as Al only interacts with one of the C dimers.
Turning to the PDOS for Al on the Oterminated surface, the aluminium DOS is considerably different from that of the bare surface due to the change from predominantly covalent to ionic bonding, consistent with the relative electronegativities of carbon and oxygen. The ionic bonding is most pronounced at 0.25 ML coverage where there are few occupied Al states near the valence band maximum. As the coverage increases, the 3s and 3p states of Al, unoccupied at 0.25 ML, move down in energy such that they become partially occupied. By 1 ML the Al DOS mixes with oxygen states indicating more cova lent character; with increasing Al coverage the effective posi tive charge on each Al decreases due to the finite capacity for the oxygen atoms to accept negative charge. This combination of ionic and covalent behaviour, and the different coordina tions of Al that are present are reflected by the complexity of the PDOS.

Conclusions
DFT calculations were performed on the adsorption of Al onto the (1 0 0) bare and Oterminated diamond surfaces. A notable structural difference from previous studies of the adsorption of other metals at the bare diamond surface is that the preferred coordination number of Al to carbon is two, and the bonding at such sites is appreciably cova lent in character. By contrast, on the Oterminated surface for <1 ML coverage, Al preferentially binds to sites where it is 4coordinate and the bonding is more ionic. Al-Al interactions are important structurally at larger coverages. At 1 ML coverage, following relaxation of Al on the bare surface, a hexagonal arrangement of Al is lowest in energy, whilst for 1 ML coverage on the Oterminated surface, Al-Al interactions force some Al atoms further from the surface. Al has relatively large adsorption energies of up to −4.11 and −6.36 eV on the bare and Oterminated surfaces, respec tively. NEAs are possible for up to 1 ML coverage; how ever, control of atomic position is required as positive EA is shown in certain configurations. The magnitude of both NEA and adsorption energies for Al is most similar to that of Ti, a carbideforming metal with comparable electronegativity. 0.25 ML coverage of Al on Oterminated diamond is pre dicted to have both NEA and stronger adsorption energies than Hterminated diamond regardless of adsorption site, and thus provides a possible route to a more temperaturestable surface termination. Work is currently underway to try and obtain an NEA value for Al on diamond experimentally.