The Combined Inﬂuence of Dopant Species and Surface Termination on the Electronic Properties of Diamond Surfaces

: The combined e ﬀ ects of geometrical structure and chemical composition on the diamond surface electronic structures have been investigated in the present study by using high-level theoretical calculations. The e ﬀ ects of diamond surface planes [(111) vs. (100)], surface terminations (H, F, OH, O ontop , O bridge , vs. NH 2 ), and substitutional doping (B, N vs. P), were of the largest interest to study. As a measure of di ﬀ erent electronic structures, the bandgaps, work functions, and electron a ﬃ nities have been used. In addition to the e ﬀ ects by the doping elements, the di ﬀ erent diamond surface planes [(111) vs. (100)] were also observed to cause large di ﬀ erences in the electronic structures. With few exceptions, this was also the case for the surface termination species. For example, O ontop -termination was found to induce surface electron conductivities for all systems in the present study (except for a non-doped (100) surface). The other types of surface terminating species induced a reduction in bandgap values. The calculated bandgap ranges for the (111) surface were 3.4–5.7 (non-doping), and 0.9–5.3 (B-doping). For the (100) surface, the ranges were 0.9–5.3 (undoping) and 3.2–4.3 (B-doping). For almost all systems in the present investigation, it was found that photo-induced electron emission cannot take place. The only exception is the non-doped NH 2 -terminated diamond (111) surface, for which a direct photo-induced electron emission is possible.


Introduction
Diamond is a well-studied material with extraordinary properties. It has excellent mechanical, thermal, chemical, electrical, electrochemical, and optical properties (e.g., high hardness, low coefficient of friction, good wear resistance, low thermal expansion coefficient, high thermal conductivity, excellent chemical inertness, high charge carrier mobility, low background current, favorable optical transparency, etc.,). In addition, it shows quite unique electrochemical properties, such as a large electrochemical potential window, a low dielectric constant, controllable surface termination, and a high breakdown voltage [1]. However, the large band gap (5.4 eV) makes diamond an insulator, which thereby limits the usage of diamond for, e.g., electronic devices. However, it is possible to improve the diamond electronic properties substituting some C atoms with dopant elements. Another way is to terminate the diamond surfaces with specific atomic (or molecular) species. Hence, a change in the electron density, especially in the vicinity to the diamond surface, will induce the necessary electronic bandgap structure for, e.g., those applications where diamond is a plausible electrode material.
More generally, the properties of a crystalline solid surface depend on various factors, such as (i) number and distribution of binding atoms (i.e., for the atoms in the surface region), (ii) surface reconstructing and relaxation, (iii) type and degree of chemisorption to the surface, and (iv) elemental Package (CASTEP) software from BIOVIA [19][20][21]. More specifically, an ultrasoft pseudopotential [22] plane-wave approach was thereby used, which is based on the PBE (Perdew-Burke-Ernzerhof) [17] generalized gradient approximation (GGA) [19] of the exchange-correlation functional. Because of the presence of unpaired electrons in the systems, all calculations were based on spin polarized GGA (i.e., GGSA). In addition, the value of the energy cutoff for the plane wave basis set was set to 370.00 eV. Moreover, the Monkhorst-Pack scheme [23] was used for the k-point sampling of the Brillouin zone, which generated a uniform mesh of k points in reciprocal space. The 1 × 1 × 1 k-point, as well as the cut-off frequency of 370 eV, have earlier been tested and found adequate to use for the present type of system [24,25].
The CASTEP program, with the setting presented above, was also used in calculating the density difference when adding the terminating species to the non-terminated diamond surface (undoped or doped) (see Equation (1)): where ∆ρ is the density difference, and ρ(total), ρ(bare surface), and ρ(adsorbate layer) are the electron densities for the terminated surface, non-terminated surface, and complete adsorbate layer, respectively. The geometry-optimized structures were used for these single point calculations (i.e., with no geometry optimization). The results from these calculations show the re-positioning of electron density, being induced by surface termination. For example, weakening (or strengthening) of bonds will thereby be illuminated. Other examples are induced dipoles at the surface. The CASTEP program was also used in calculating electron bond populations and atomic charges, which are the two parameters that will give further insight into eventual bond weakening/strengthening (using electron bond populations) and dipole formations (using atomic charges). The assigned atomic charges were Mulliken charges since the alternative, the Hirsfield charges, often underestimates charges distributions in molecules [26]. In assigning the Mulliken atomic charges, as well as the bond population values, a projection of the plane wave states onto the localized basis was made by using a technique described by Sanchez-Portal et al. [23].
The electronic structure, including valence band maximum (VBM), conduction band minimum (CBM), bandgap and bandgap electronic states, were calculated using the software Atomistix Toolkit 2018.1 from Synopsys [27]. These DFT calculations were based on a spin-polarized generalized gradient approximation (GGSA) [17,20], using the PBE pseudopotential in addition to a linear combination of atomic orbitals (LCAO). Moreover, a Monkhorst-Pack k-point sampling of 5 × 5 × 1 was used in calculating both the electronics structures (i.e., DOS (Density Of State) spectra, band structures and fat-bandstructure). The fat-band structure is just another name of the projected band structure, which was used to visualize the contribution of different atoms to the band structures of the various model systems in the present study. Also, the density mech cut-off was set to 80 Ha (2176, 8 eV). The well-known problem with the DFT-calculations is the underestimation of bandgap values. The GGA-1/2 method [28] was therefore used in the present investigation. This method is a semi-empirical approach to correct the self-interaction error in local and semi-local exchange-correlation density functionals for extended systems. As such, it corrects the Kohn-Sham eigenvalues around the bottom of the conduction band and the top of the valence band. Test-calculations were performed by calculating the bandgap for bulk diamond, and to comparing these results with the experimentally obtained ones. The here presented method resulted in a bulk diamond bandgap of 5.6 eV, which is almost identical with the experimental one: 5.5 eV.
Calculated VBM values give information about the work functions of the studied model systems, and the calculated CBM values give information about the electron affinities. In addition, calculated electronic states in the bandgap give information about the possibility for photo-induced electron C 2020, 6, 22 4 of 24 emission. The work function is defined as the minimum energy needed to remove an electron from VBM to the vacuum outside the surface (see Equation (2)): where E(∞) is equal to zero, and E VBM is the energy of the VBM. Moreover, the electron affinity (EA) is defined as (see Equation (3)): where E(∞) is equal to zero, and E CBM is the energy of the CBM. The program Dmol3 [29,30] from BIOVIA was in the present study used for calculations of the valence band maximum, and thereby also the work function. A GGA method, which was based on a PBE non-local functional, was then applied. All electrons in the systems were included in these calculations, in addition to a DNP (double numerical potential) atomic orbital basis set. DNP is a polarized function with an angular momentum that is larger than that of the highest occupied orbital in the free atom. It gives a relatively more reliable description of the electronic structure of the systems under investigation [29].

Model Systems
The (111) and the 2 × 1-reconstructed (100) surfaces are the most frequently observed ones on the nano-diamond particles and nanocrystalline diamond. It has earlier been theoretically shown that it is possible to model (111) and (100) surfaces of nanodiamond particles of size larger than~2 nm by using 2D model slabs [31]. The diamond (111) and (100)-2 × 1 surfaces have therefore been chosen in studying the diamond surface electronic properties in the present study. The supercell model of the (111) surface include 6 C layers, with 16 C atoms in each layer. The corresponding (100) model include 7 C layers, with 16 C atoms in each layer. These model sizes have earlier been found large enough for the present type of study [32]. Moreover, the model surfaces are terminated with various types of species; H, F, OH, O, and NH 2 , respectively. All species are adsorbed in ontop positions (i.e., directly on a surface C atom), and O are also adsorbed on a bridge position (see Figure 1). The various positions of O are therefore denoted O ontop and O bridge . Moreover, in the doped diamond models, the dopant has substitutionally replaced a C atom in the lattice. It has earlier been shown that a dopant substitution within the second C layer will have the largest effect on the diamond surface electronic structure [32][33][34]. This position of any of the dopants B, N, or P, has therefore been chosen in the present study. In addition, the lower surface C atoms have been terminated with H atoms. The purpose with this choice was to saturate the radical C atoms on this lower surface. In addition, both the lower C atoms and their terminating H atoms were kept fixed in the geometry optimization calculations. The other atoms, in the model systems, could freely relax (see Section 2. Theoretical Methods). The reason for these geometrical constraints was to simulate a continuation into bulk diamond. Moreover, a large vacuum distance between the slabs was used (>15 Å) in order to avoid inter slab interactions. This is a distance that earlier has been tested and found adequate to use for the present types of systems [32]. the lower C atoms and their terminating H atoms were kept fixed in the geometry optimization calculations. The other atoms, in the model systems, could freely relax (see Section 2. Theoretical Methods). The reason for these geometrical constraints was to simulate a continuation into bulk diamond. Moreover, a large vacuum distance between the slabs was used (>15 Å) in order to avoid inter slab interactions. This is a distance that earlier has been tested and found adequate to use for the present types of systems [32].

Diamond Surface Termination
Despite the efficiency in upholding the cubic structure of the diamond surface, different types of surface termination species have been shown to change the properties of the diamond surface region (e.g., by inducing surface electronic conductivity and interfacial charge transfer properties). Another example of properties that may be affected by chemisorption is the field emission characteristics. The electronegativity of the chemisorbed species will thereby influence the emission current and threshold voltage [35]. The phenomena of diamond surface termination have experimentally also been observed to significantly influence the broad-band infrared reflectivity [36]. Hydrogen-terminated diamond surfaces have been found to be hydrophobic [37] and to show unique p-type surface electronic conductivity [38]. The oxygen atom is also one of the most used diamond surface terminators. Oxygen-terminated diamond surfaces generally show hydrophilic properties [39], as well as a positive electron affinity. The oxygen-termination can appear as a surface binding OH, O bridge , C ontop , or OOH groups. Different chemical routes are used to link functional groups to these O-group adsorbates. This procedure is usually performed in e.g., electroanalytical applications [40]. Fluorine-termination will, compared to H-termination, result in an even more hydrophobic diamond surface. In addition, F-terminated diamond surfaces exhibit exceptional electrochemical properties, such as a lower electrocatalytic activity, a wide electrochemical potential window, and low background current [41,42]. Nitrogen-terminated diamond surfaces are generally very chemically reactive and are thereby commonly used as an intermediate for further modification of the diamond surface (e.g., as a linker). For instance, a diamond surface that is terminated with amine (NH 2 ) can be modified to be used as a functionalized surface in biosensors [43].

Substitutional Doping of Diamond
The boron atom is one of the most used p-type dopants. B-doped diamond shows quite promising electrochemical properties, e.g., tunable electronic conductivity (depending on the boron-carrier concentration in the diamond lattice). Hence, boron-doped diamond (BDD) has been widely used for electronic applications. Nitrogen, as an n-type dopant, has also frequently been studied during the last decades [44][45][46][47][48]. However, the deep donor level of nitrogen (1.7 eV below the conduction band) limits the usage of nitrogen-doped diamond as an effective n-type semiconductor. Thus, phosphorous has C 2020, 6, 22 6 of 24 instead been introduced as a plausible n-type donor in diamond (111) [49]. Kato et al. produced this type of n-type diamond epilayer on (100)-oriented diamond surfaces [50]. Phosphorus, P, is nowadays the only well-established substitutional n-type donor [51]. n-type diamond heavily doped with P atoms, has recently been obtained with low electrical resistivity and low incorporation activation energy [52,53]. This makes phosphorus-doped diamond more promising for device applications, e.g., as an electron source for bipolar devices [54][55][56], as Schottky barrier diodes [57], and for thermionic emission applications [58].

General
The chemisorption of atoms (or molecules) to the diamond surface will lower the surface energy values, which will affect the chemical surface processes. It is also expected that the chemisorption (i.e., termination) of species to the surface will have a major effect on the properties of the surface (e.g., surface electronic properties). Despite the efficiency in upholding the cubic structure of the diamond surface, different types of surface termination species have been shown to change the properties of the diamond surface region (e.g., by inducing surface electronic conductivity and interfacial charge transfer properties). Another example of properties that may be affected by chemisorption is the field emission characteristics. The electronegativity of the chemisorbed species will thereby influence the emission current and threshold voltage [35]. The phenomena of diamond surface termination have experimentally also been observed to significantly influence the broad-band infrared reflectivity [36]. Hydrogen-terminated diamond surfaces have been found to be hydrophobic [37], and to show unique p-type surface electronic conductivity [38]. On the other hand, oxygen-terminated diamond surfaces generally show hydrophilic properties [37], and exhibit positive electron affinity [59]. In addition, OH-terminated surfaces can be formed during etching in a mixture of oxygen and water vapor [39]. Fluorine-termination will, compared to H-termination, result in even more strongly hydrophobic diamond surfaces, and have also recently been found to enhance the sp 3 characteristics of the diamond upper C layer (thereby improving the geometrical structure of this surface [60]). All these interesting properties of terminated diamond surfaces make it clear that surface termination is very important for especially those applications where diamond can be an electrode material.

Analysis of Calculated Electronic Structures for Undoped Diamond Surfaces
The electronic states around the bandgap for various terminated diamond (111) and (100) surfaces have been investigated in the present study by calculating the band structure, projected band structure (on specific atoms), and DOS spectra for the upper region of the diamond surfaces. For each model system, this upper region included the three upper C atomic layers, in addition to the terminating one. It is clear, from the analysis of the projected band structure, that the valence orbitals of the terminating species will form hybridization with the orbitals of the surface C atoms. This is the situation for all terminating species that have been investigated in the present study (H, F, OH, O(ontop), O(bridge), and NH 2 ), and for both types of diamond surface plane ((111) and (100)).
As can be seen in Tables 1 and 2, the electronic structures are much different for the (111) and (100)-2 × 1 surfaces. These differences can be exemplified by the bandgap (BG) values. The BG is bulklike for an F-terminated (111) surface, while it is much smaller for the (100)-2 × 1 surfaces (with a difference of 2.5 eV: 5.5 vs. 3.0 eV). The BG value is also bulk-like for the H-terminated (111) surface, with a somewhat smaller value for the corresponding (100)-2 × 1 surfaces (with a difference of 0. O bridge -termination on the (100)-2 × 1 surfaces was found to be 4.2 eV, which is almost identical to the BG value for NH 2 -termination to this surface plane.
The only exception to the dissimilarities between the two diamond surfaces is the situations with the O ontop -termination. Supercell models of these surfaces are shown in Figure 2. The BG values became as small as 0.5 eV [(111)] and 0.9 eV [(100)] [it is here very interesting to also note that the BG values for NH 2, O ontop , and OH-terminated diamond (100) surfaces are also very similar]. As can be seen in the DOS spectra in Figure 3a,b, the O ontop -terminated (111) surface can, however, be regarded as electronical conductive, while the O ontop -terminated (100) cannot. For the (111) surface, the E Fermi is positioned within the valence electron band, while the E Fermi for (100) is positioned within the bandgap. These differences in electronic properties have its origin in the difference in geometrical surface structures. For the (111) surface, the O ontop -termination will result in radical O adsorbates with covalent single bonds to the upper surface C atoms (see Figure 2a). This radical nature comes from the fact that O atoms have 6 valence electrons. The reactions between the O species and the radical surface C atoms on the diamond (111) surface, that lead to single bonded C-O formations, will therefore C 2020, 6, 22 8 of 24 result in radical O atoms. However, rather weak spin-densities could be found (see Figure 4a). This is most probably due to the withdrawal of electron density from the surface C atoms to the binding O atoms (induced by the large difference in electronegativity). This addition in electron density will contribute to partially paired electrons on the O adsorbates, thereby reducing the spin density within the terminating layer. Moreover, these partially unpaired electrons will form a broad and non-filled energy band which is a strong indication of surface electronic conductivity (see Figure 3a).  demonstrated by the spin-density map in Figure 4b, there is just a weak tendency for radical formation. Also, this observation is most probably due to the withdrawal of electron density from the surface C atoms to the binding O atoms. Moreover, the calculated C-O bond populations indicate much stronger covalent bonds. These values are of size 1.2, which is almost double the size when compared with the corresponding C-O bonds for the Oontop-terminated (111) surface (0.8). Hence, no unfilled energy band is expected to be formed for this type of surface.
(a) (b)  The situation is completely different for the (100) surface. Adsorption of O species to ontop-positions on the 2 × 1-reconstructed (100) surface will induce a surface re-construction to the (100) surface ( Figure 2b). The original C-C bonds within the 2 × 1-reconstructed surface has thereby been disrupted, leaving surface radical C atoms with two "dangling bonds" each. The hereby formed unpaired C electrons can now pair with the unpaired electrons in the O ontop adsorbates, forming very strong C=O bonds. These surface regions are, therefore, not expected to be radical to its nature. As demonstrated by the spin-density map in Figure 4b, there is just a weak tendency for radical formation. Also, this observation is most probably due to the withdrawal of electron density from the surface C atoms to the binding O atoms. Moreover, the calculated C-O bond populations indicate much stronger covalent bonds. These values are of size 1.2, which is almost double the size when compared with the corresponding C-O bonds for the O ontop -terminated (111) surface (0.8). Hence, no unfilled energy band is expected to be formed for this type of surface.
Calculations of the valence band maxima (VBM) did also result in different numerical values for the two diamond surface planes. The absolute values of the VBMs are identical to the work functions, Φ experimentally shown to lower the ionization energy (i.e., the work function) to a value of 4.2 eV for the (100) surface [2]. This is a value that is very similar to the here presented calculated value of 3.9 eV.    Calculations of the valence band maxima (VBM) did also result in different numerical values for the two diamond surface planes. The absolute values of the VBMs are identical to the work functions, Φ experimentally shown to lower the ionization energy (i.e., the work function) to a value of 4.2 eV for the (100) surface [2]. This is a value that is very similar to the here presented calculated value of 3.9 eV.
From the calculated values of VBM's and BGs it was also possible to calculate the electron affinities (EAs) for the variously terminated diamond surfaces. As can be seen in Table 1 that H-and NH2-terminated diamond (111) surfaces show negative electron affinities (NEA), while F-and OHtermination result in positive electron affinities (PEAs). As expected, the situation was also here different for the diamond (100) surface (see Table 2). The H-, OH-, or NH2-terminated (100) surface show NEAs, while the others (F-, Obridge-, and Oontop-termination) will render PEAs. The electron affinities of H-and O-terminated diamond (100) surfaces have been experimentally estimated by using a combination of work function and photoemission experiments [59]. The obtained EA values were -1. The possibilities for photo-induced electron emission, by using visible light, has also been studied in the present investigation. The difference in surface properties between diamond (100) and From the calculated values of VBM's and BGs it was also possible to calculate the electron affinities (EAs) for the variously terminated diamond surfaces. As can be seen in Table 1 that Hand NH 2 -terminated diamond (111) surfaces show negative electron affinities (NEA), while F-and OHtermination result in positive electron affinities (PEAs). As expected, the situation was also here different for the diamond (100) surface (see Table 2). The H-, OH-, or The possibilities for photo-induced electron emission, by using visible light, has also been studied in the present investigation. The difference in surface properties between diamond (100) and (111) is also very clear here. As can be seen in Tables 1 and 2, and in Figures S1 and S5, it will only be possible to induce electron emission from the NH 2 -terminated (111) surface, and this can take place by a direct excitation of energy size 2.8 eV (i.e.,~443 nm). For the (100) surface, there is no possibility to emit electrons by using visible light.
The electroncially conductive O ontop -terminated diamond (100) surface is of no interest to study when considering electron affinities and photo-induced electron emission.

General
The growth process of boron-doped (B-doped) diamond material, with its extraordinary electrochemical properties, has earlier been well developed. It was then found that the B dopant will increase the electronic conductivity, as compared with intrinsic non-doped diamond [62]. Depending on the dopant concentrations, the diamond material will show a metallic-type conductivity [63,64], p-type semi-conductivity [65,66], or superconductivity [67,68]. The superconductivity property makes diamond very attractive for electronic applications.

Analysis of Calculated Electronic Structures for B-Doped Diamond Surfaces
The B-induced acceptor states for diamond (111) and (100) Tables 1 and 2). All of these BG values have been obtained from the DOS spectra (see Figures S2 and S6). The only exception to the dissimilarities between the two diamond surfaces is the situation with O ontop -termination. The BG values for this type of termination is as small as 0.4 eV [(111)] and 0.2 eV [(100)]. As can be seen in the DOS spectra in Figure 5a,b, both O ontop -terminated surface planes are electronically conductive. This is not the situation for non-doped diamond surfaces (see chapter 6.2. Analysis of Calculated Electronic Structures for Non-Doped Diamond Surfaces). The B-doped diamond (111) and (100) surfaces show similar results when compared with the non-doped surfaces. As can be seen in Figure 6a, Oontop-termination results in radical O adsorbates with covalent single bonds to the upper (111) surface C atoms. These unpaired electrons will also for B-doped (111) surfaces form a broad and non-filled energy band which is a strong indication of surface electronic conductivity (Figure 5a). Moreover, as was the situation with non-doped diamond (100), adsorption of O species to ontop-positions on the B-doped 2 × 1-reconstructed (100) surface was found to induce surface re-construction to (100)-1 × 1 (see Figure 6b). The B element has, compared to C, a smaller electronegativity value (2.04 vs. 2.55), and these values are both smaller than for O (3.44). There will therefore be a more pronounced transfer of electron charge from the B dopant toward the O adsorbates, which leads to larger spin densities at these surface atoms (as The B-doped diamond (111) and (100) surfaces show similar results when compared with the non-doped surfaces. As can be seen in Figure 6a, O ontop -termination results in radical O adsorbates with covalent single bonds to the upper (111) surface C atoms. These unpaired electrons will also for B-doped (111) surfaces form a broad and non-filled energy band which is a strong indication of surface electronic conductivity (Figure 5a). Moreover, as was the situation with non-doped diamond (100), adsorption of O species to ontop-positions on the B-doped 2 × 1-reconstructed (100) surface was found to induce surface re-construction to (100)-1 × 1 (see Figure 6b). The B element has, compared to C, a smaller electronegativity value (2.04 vs. 2.55), and these values are both smaller than for O (3.44). There will therefore be a more pronounced transfer of electron charge from the B dopant toward the O adsorbates, which leads to larger spin densities at these surface atoms (as compared with non-doped diamond (100)) (see Figures 4b and 6b). This spin density results in a non-filled valence energy band which is a strong indication of surface electronic conductivity ( Figure 5b). As is obvious from Figure 6a,b, the spins, being induced by the B dopant, result in spin-densities solely located within the terminating O layer. compared with non-doped diamond (100)) (see Figures 4b and 6b). This spin density results in a nonfilled valence energy band which is a strong indication of surface electronic conductivity ( Figure 5b). As is obvious from Figure 6a,b, the spins, being induced by the B dopant, result in spin-densities solely located within the terminating O layer. Calculations of the valence band maxima (VBM) did also, for p-type doping (using B), result in different numerical values for the two diamond surface planes. As can be seen in Table 1, the order of Φ for the (111) surface became NH2 < H < OH < Oontop = F, with the values 2.7, 3.2, 3.6, 5.3, and 5.3 eV, respectively. This order is, though, not identical to the order of BGs. However, it is identical to the order of VBMs for non-doped diamond (111), and also very similar when comparing numerical values. Moreover, the calculated order of Φ for the (100) surface became NH2 < H < OH < Obridge < Oontop < F, with the values 3.2, 3.4, 4.0, 4.7, 5.0, and 5.0 eV, respectively (see Table 2). There are obvious similarities between the two different diamond surface planes. They show an identical order of work function values, and the values for the different adsorbates are very similar when comparing diamond (111) with diamond (100). As can be seen in Tables 1 and 2, there  As can be seen in Table 1, H-and OH-terminated diamond (111) surfaces have negative electron affinities, while Oontop-and NH2-termination induce positive electron affinities. For F-termination, the electron affinity was equal to zero. The situation was, with one exception, similar for the diamond (100) surface (see Table 2). The H-, OH-, and NH2-terminated (100) surfaces show NEA values, while the others (F-, Obridge-, and Oontop-termination) render PEAs. Total photoyield spectroscopy measurements have shown that B-doped H-terminated polycrystalline diamond has an electron Calculations of the valence band maxima (VBM) did also, for p-type doping (using B), result in different numerical values for the two diamond surface planes. As can be seen in Table 1, the order of Φ for the (111) surface became NH 2 < H < OH < O ontop = F, with the values 2.7, 3.2, 3.6, 5.3, and 5.3 eV, respectively. This order is, though, not identical to the order of BGs. However, it is identical to the order of VBMs for non-doped diamond (111), and also very similar when comparing numerical values. Moreover, the calculated order of Φ for the (100) surface became NH 2 < H < OH < O bridge < O ontop < F, with the values 3.2, 3.4, 4.0, 4.7, 5.0, and 5.0 eV, respectively (see Table 2). There are obvious similarities between the two different diamond surface planes. They show an identical order of work function values, and the values for the different adsorbates are very similar when comparing diamond (111) with diamond (100). As can be seen in Tables 1 and 2, there  As can be seen in Table 1, H-and OH-terminated diamond (111) surfaces have negative electron affinities, while O ontop -and NH 2 -termination induce positive electron affinities. For F-termination, the electron affinity was equal to zero. The situation was, with one exception, similar for the diamond (100) surface (see Table 2). The H-, OH-, and NH 2 -terminated (100) surfaces show NEA values, while the others (F-, O bridge -, and O ontop -termination) render PEAs. Total photoyield spectroscopy measurements have shown that B-doped H-terminated polycrystalline diamond has an electron affinitiy of −1.0 eV [69]. Polycrystalline diamond surfaces are comprised of (111) and (100) surface planes, and the dominating plane depends on the experimental setup. As can be seen in Table 1, the calculated EA values for these planes are −0.3 eV and −0.6 eV, respectively. These results show similarities with the experiemental values (especially for the diamond (100) surface plane).
As can be understood from the contents in Tables 1 and 2, as well as from the DOS spectra in Figure S2, there is no possibility to use visible light in a direct photo-induced emission of electrons from B-doped diamond surfaces [(111) or (100)].

General
The effects of substitutional doping by nitrogen, or phosphorous, have been thoroughly studied from an experimental point of view [70][71][72][73]. It is not only the changes in the electronic properties that have been observed, but these dopant elements can also have a great impact on the diamond surface morphology and growth rate when using chemical vapor deposition methods (CVD).
The N and P elements have one additional valence electron (i.e., 5 valence electrons in total) when compared with the C atom (with its four valence electrons). When replacing C atoms in the diamond lattice with N (or P) atoms, donor states will be formed in the diamond lattice [48]. One usually calls this type of doping elements for n-type dopants, and there is an n-type doping. These n-type dopants induce a donor state just below the CBM of diamond. The valence electrons that is occupying this bandgap state, will thereby get the possibility to become thermally excited to the conduction band. The n-type doped diamond has then become a semiconducting material, with the electronic conductivity governed by electrons that originate from the donor state in the bandgap.
However, in choosing a suitable donor (or acceptor) for diamond, one has to not only consider its donor (or acceptor) level but also its solubility and mode of incorporation (e.g., incorporation during growth by in-diffusion, or by ion implantation) [48]. Impurities have been shown to become introduced into diamond during CVD or HPHT growth [74,75]. In addition, a review article has reported on doping by implantation [71]. The resulting substitutional doping will, hence, depend not only on the solubility of the impurity, but will also depend on the kinetics of the growth. Kinetic trapping may be possible although the final n-(or p-) type doped product is thermodynamically unfavorable.

Analysis of Calculated Electronic Structures for n-Type Doped Diamond Surfaces
As was the situation with non-doped diamond surfaces, there are also for the n-type doped diamond (111) and (100) surfaces dissimilarities regarding the electronic structures in the energy region around the surface bandgaps (as can be seen in Tables 1 and 2). The calculated BG values for the (111) surface, were found to be very similar for the different termination scenarious. They were found to be in the range of 0.3 to 0.5 eV for the N-doped surfaces, and 0.3 to 1.0 eV for the P-doped surfaces. For the (100) surface, the calculated BG values for the N-doped surfaces were found to be in the range of 0.1 to 0.3 eV (with one exception), and to be in the range of 0.1 and 2.0 eV for the P-doped surfaces. As the exception, the BG value for an O bridge -terminated N-doped diamond (111) surface was found to be as large as 2.4 eV. Hence, the BG values for the (100) surface are more dissimiliar, as compared with the (111) surface. To be more specific, the order of BG values for the N-terminated (111)  Moreover, there are not only differences observed between the different diamond surface planes [i.e., (111) and (100)], but also between the N-and P-doped surfaces. As can be seen in Tables 1  and 2, the BG values for the N-and P-doped diamond (111) surfaces are very similar, but they differ appreciably for the diamond (100) surface. For this latter surface plane, the order of BG values, as well as several of the numerical values, are different when comparing the effects by the different n-type dopants. More specifically, termination by OH results in identical values, while termination by O ontop or O bridge gives values that are quite similar (less than 0.5 eV). Moreover, for H-, F-and NH 2 -termination, the difference in BG between N-and P-termination is as large as~1 eV.
Experimentally, an N-donor level~1.7 eV below the VBM has been observed for N-doped single-crystalline diamond [7,76]. Theoretically, the DOS spectra for bulk diamond does also show this feature (see Figures S3 and S7). However, the situation is completely different for the position of N in the second C layer (see Figures S4 and S8). The combined relaxation/reconstruction of the upper surface region has here resulted in an N donor level that is much closer to the VBM (See Tables 1  and 2). Moreover, field emission characterization of a heavily P-doped H-terminated diamond (111) surface have resulted in a P donor level~0.6 eV below the VBM [12]. As can be seen in Table 1, this is an experimental result that strongly supports our theoretical finding of 0.6 eV.
As was the situation with B-doped diamond (111) and (100) surfaces, the DOS calculations show that both N-and P-doped O ontop -terminated diamond (111) and (100) surfaces are electronically conductive. As compared with B-doping, substitutional doping with P was found to induce very similar geometrical structures [see Figure 2 (B-doping) and Figure 7 (P-doping)]. However, the spin-density was more pronounced when using P-doping ( Figure 8). The O ontop -termination resulted in radical O adsorbates with covalent single bonds to the upper (111) surface C atoms. These unpaired electrons did thereby form a broad and non-filled energy band, which is a strong indication of surface electronic conductivity (for all P dopant concentrations). In addition, the pronounced electron transfer from the P dopant toward the O adsorbate (induced by different electronegativity values) was observed to contribute to the non-filled valence energy band, and thereby to the surface electronic conductivity. Moreover, there are not only differences observed between the different diamond surface planes [i.e., (111) and (100)], but also between the N-and P-doped surfaces. As can be seen in Tables 1 and  2, the BG values for the N-and P-doped diamond (111) surfaces are very similar, but they differ appreciably for the diamond (100) surface. For this latter surface plane, the order of BG values, as well as several of the numerical values, are different when comparing the effects by the different ntype dopants. More specifically, termination by OH results in identical values, while termination by Oontop or Obridge gives values that are quite similar (less than 0.5 eV). Moreover, for H-, F-and NH2termination, the difference in BG between N-and P-termination is as large as ~1 eV.
Experimentally, an N-donor level ~1.7 eV below the VBM has been observed for N-doped singlecrystalline diamond [7,76]. Theoretically, the DOS spectra for bulk diamond does also show this feature (see Figures S3 and S7). However, the situation is completely different for the position of N in the second C layer (see Figures S4 and S8). The combined relaxation/reconstruction of the upper surface region has here resulted in an N donor level that is much closer to the VBM (See Tables 1 and  2). Moreover, field emission characterization of a heavily P-doped H-terminated diamond (111) surface have resulted in a P donor level ~0.6 eV below the VBM [12]. As can be seen in Table 1, this is an experimental result that strongly supports our theoretical finding of 0.6 eV.
As was the situation with B-doped diamond (111) and (100) surfaces, the DOS calculations show that both N-and P-doped Oontop-terminated diamond (111) and (100) surfaces are electronically conductive. As compared with B-doping, substitutional doping with P was found to induce very similar geometrical structures [see Figure 2 (B-doping) and Figure 7 (P-doping)]. However, the spindensity was more pronounced when using P-doping ( Figure 8). The Oontop-termination resulted in radical O adsorbates with covalent single bonds to the upper (111) surface C atoms. These unpaired electrons did thereby form a broad and non-filled energy band, which is a strong indication of surface electronic conductivity (for all P dopant concentrations). In addition, the pronounced electron transfer from the P dopant toward the O adsorbate (induced by different electronegativity values) was observed to contribute to the non-filled valence energy band, and thereby to the surface electronic conductivity.  The situation is different for the N-doped Oontop-terminated diamond (100) surface, since N is more electronegative than C: 3.04 vs. 2.55. As a consequence, the N dopant has the tendency to draw electrons from its binding C atoms, and it thereby counteracts the "neutralization" of the radical O adsorbates (i.e., that should otherwise take place by a de-reconstruction of the diamond (100)-2 × 1 The situation is different for the N-doped O ontop -terminated diamond (100) surface, since N is more electronegative than C: 3.04 vs. 2.55. As a consequence, the N dopant has the tendency to draw electrons from its binding C atoms, and it thereby counteracts the "neutralization" of the radical O adsorbates (i.e., that should otherwise take place by a de-reconstruction of the diamond (100)-2 × 1 surface). Hence, the N-doped diamond (100) surface is 2 × 1-reconstructed (see Figure 9). In addition, both diamond (111) and (100)-2 × 1 surfaces show surface conductivities, which is induced by the clear evidence of spin densities within the O adsorbate layers (see Figures 9 and 10). Except for non-doped diamond (100) surfaces, this was also the situation for all non-doping and doping situations in the present study.
C 2020, 6, x FOR PEER REVIEW 17 of 24 surface). Hence, the N-doped diamond (100) surface is 2 × 1-reconstructed (see Figure 9). In addition, both diamond (111) and (100)-2 × 1 surfaces show surface conductivities, which is induced by the clear evidence of spin densities within the O adsorbate layers (see Figures 9 and 10). Except for nondoped diamond (100) surfaces, this was also the situation for all non-doping and doping situations in the present study.
(a) (b)  The iso-surface value is 0.05 for both surface planes. The blue color shows the positive density, and the yellow color shows the negative density.
Like the situation with the BG values, the calculated valence band maxima (VBM) resulted in different numerical values for the two diamond surface planes. However, the results were very similar when comparing N-doped with P-doped diamond surfaces. As can be seen in Table 1, the order of Φ for the (111) surface became NH 2 < OH = H < O ontop < F for N-doping, and NH 2 < OH < H < O ontop < F for P-doping. These orders are almost identical, and of almost the same order when compared with the B-doped diamond (111) surface; NH 2 < H < OH < O ontop < F. Here, it is of a large interest to compare these Φ orders (i.e., for doped diamond) with the one obtained for non-doped diamond; NH 2 < OH < H < O ontop < F. It is thereby possible to draw the conclusion that substitutional doping by B, N, or P will not affect the order of work functions (at least not to any larger extent). Moreover, the corresponding values of Φ for N-doped (111) surfaces were 3.1, 4.6, 4.6, 5.4, and 5.9 eV. As can be seen in Table 1, these values are slightly larger than for B-doped diamond (111). Also, the corresponding values of Φ for P-doped (111) surfaces were 3.7, 4.8, 4.9, 5.4, and 6.1 eV. These are the values that are even larger than for N-doped diamond (111). A clear trend is thereby observed.
For the (100) surfaces, the Φ order is as follows: H = O bridge < NH 2 < OH < O ontop = F for N-doping, and H = O bridge < NH 2 < OH < O ontop < F for P-doping (see Table 2). These orders are also almost identical. However, the order of Φ values for B-doped diamond (100) surfaces is different; NH 2 < H < OH < O bridge < F < O ontop . This is also the situation for a non-doped diamond surface; NH 2 < H < O bridge < F < OH < O ontop . So it is again possible to state that the diamond (111) and (100) surface planes behave completely different with respect to electronic properties. Moreover, the corresponding values of Φ for the N-doped (100) surfaces were 3.7, 3.7, 3.8, 4.2, 5.3, and 5.3 eV. Also, the corresponding values of Φ for P-doped (100) surfaces were 4.0, 4.0, 4.1, 4.5, 5.3, and 5.5 eV. These values are thereby somewhat larger than for N-doped diamond (100), which in turn are, with one exception, somewhat larger than for B-doped diamond (100). As was the situation for diamond (111), one can also here see a clear trend. Like the situation with the BG values, the calculated valence band maxima (VBM) resulted in different numerical values for the two diamond surface planes. However, the results were very similar when comparing N-doped with P-doped diamond surfaces. As can be seen in Table 1, the order of Φ for the (111) surface became NH2 < OH = H < Oontop < F for N-doping, and NH2 < OH < H < Oontop < F for P-doping. These orders are almost identical, and of almost the same order when compared with the B-doped diamond (111) surface; NH2 < H < OH < Oontop < F. Here, it is of a large  As can be seen in Tables 1 and 2 and Figures S3, S4, S7, and S8, all variously terminated (111) and (100) surfaces display PEA values. In addition, there is no possibility to use visible light in photo-induced emission of electrons from either N-or P-doped diamond surface planes [(111) or (100)].

Summary and Conclusions
The combined effect of surface plane, termination, and doping, on the electronic structure of a diamond surface, has been studied in the present investigation by using theoretical DFT calculations. The bandgap values, work functions, electron affinities, as well as the probability for solar-induced photoemission of electrons, were of a special interest to study. The surface planes studied were (111) and (100). Moreover, the terminating species where H, F, OH, O ontop , O bridge , and NH 2. In addition, the diamond surfaces were either non-doped, n-type doped (with N or P), or p-type doped (with B).
With few exceptions, the electronic structures for non-doped diamond (111) and (100) surfaces were found to be quite different. In fact, this was the situation for all three measures of electronic structures: bandgap (BG) values, work functions, and electron affinities (EAs). However, there were also some similarities. The BG values for the OH-, O ontop -, O bridge -, and NH 2 -terminating species were for both surface types apparently smaller than for the H-and F-terminated surfaces. More specifically, the DOS-calculations showed that the O ontop -terminated (100) surface is electronic conducting. Furthermore, the H-and NH 2 -terminated (111) and (100) surfaces were found to have negative electron affinities (NEAs), while most of the other termination types resulted in positive electron affinities (PEAs). The OH-terminated (100) surface is an exception, which render a NEA value. Another dissimilarity worth mentioning is that it is possible to photo-induce electron emission (by solar light) from a NH 2 -terminated (111) surface, while this is not possible for the (100) counterpart (or for any of the other terminated surface types).
As was the situation with non-doped diamond surfaces, B-doped (111) and (100) also show completely different electronic structures. With one exception, it was found that B-doping will induce smaller BG values (i.e., as compared with non-doped diamond). Interestingly, there is no possibility for the B-doped diamond (111) and (100) surfaces to undertake photo-induced electron emission (by using visible light). B-doping was also found to induce smaller Φ values, and to increase the electron affinities to more positive values. Exceptions are the EA value for the OH-terminated (111) surface, and for the F-terminated (100) surface, which showed a decrease in values. In short, B-doped Hand OH-terminated (111) surfaces, as well as B-doped H-, OH-, and NH 2 -terminated (100) surfaces, showed negative electron affinities (NEAs). In addition, a B-doped F-terminated (111) surface showed an EA value of zero, while the other terminating situations showed PEAs.
The effect by N-dopants was completely different in that the diamond (111) and (100) surfaces showed very similar electronic properties (there is only one exception, and that is the situation with NH 2 -terminated surfaces). On the contrary, doping with P elements rendered quite dissimilar electronic structures. As expected, the BG values for the P-or N-doped surfaces where much smaller as compared with non-doped diamond. Moreover, the calculated BG values for N-doped diamond surfaces were somewhat smaller as compared with the corresponding P-doped surfaces. As a test, similar calculations were performed for N-doped bulk diamond. It was then observed that the BG value for a substitutional positioned N dopant was considerably smaller than for a substitutional positioned N dopant with a vacant neighboring site (i.e., an NV-site). As was the situation with B-doped diamond surfaces, there is no possibility for the N or P-doped diamond (111) and (100) surfaces to undertake photo-induced electron emission (by using visible light).
N-doping was also found to induce larger Φ values for the variously terminated (111) surface, and this was even more the situation for the corresponding P-doped surfaces. As expected, the EA values for both N-and P-doped surfaces [(111) and (100)] were found to be positive. When comparing the results of these two n-type dopant species, it was found that the EA values for H-and F-, termination were larger for the N-doping situations. The other terminating species (OH, O ontop , O bridge , and NH 2 ) were found to induce larger EA values for the P-doped surface.
In summary, it has been shown in the present study that it is not only the type of doping that is of large importance for the electronic structure of a diamond surface. Both the type of surface plane and the type of surface termination are of large importance for the final surface electronic properties.
Funding: This research was funded by the European Union's Horizon 2020 Program with grant number 665085.