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Title

Adhesion of electrodes on diamond (111) surface:A DFT study

Author(s)Ichibha, Tom; Hongo, Kenta; Motochi, I.; Makau,
N.W.; Amolo, G.O.; Maezono, Ryo

Citation

Diamond and Related Materials, 81: 168‑175

Issue Date

2017‑12‑13

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/15355

Rights© 2017 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY‑
NC‑ND license(http://creativecommons.org/licenses/by‑nc‑
nd/4.0/). Tom Ichibha, Kenta Hongo, I. Motochi,
N.W. Makau, G.O. Amolo, Ryo Maezono, Diamond andRelated Materials, 81, 2017, 168‑175.
DOI:10.1016/j.diamond.2017.12.008

Description

Japan Advanced Institute of Science and Technology

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Contents lists available at ScienceDirect

Diamond & Related Materials
journal homepage: www.elsevier.com/locate/diamond

Adhesion of electrodes on diamond (111) surface: A DFT studya,*

Tom Ichibha , Kenta Hongo

b,c,d

e

f

g

, I. Motochi , N.W. Makau , G.O. Amolo , Ryo Maezono

7baSchool of Materials Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
National Institute of Materials Science, Tsukuba, Ibaraki, Japand
PRESTO, JST, Kawaguchi, Saitama, Japane
Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, KenyafComputational Materials Science Group, Department of Physics, University of Eldoret, Eldoret, P.O. Box 1125-30100, Kenyag
Department of Physics and Space Science, The Technical University of Kenya, Nairobi, P.O. Box 52428-00200, Kenyabc

A R T I C L E I N F O

A B S T R A C T

Keywords:
Electrodes on diamond device
Surface termination
Power device

We explore possible candidates for metallic electrodes of diamond semiconductor from twenty kinds of metallic
sheets on oxygen- or hydrogen-terminated diamond (111) surface as well as pristine one. Their adhesion
strengths and electric characteristics of contacts (i.e. either Ohmic, Schottky or neither) are both considered as
ﬁgures of merit. The former is measured as work of separation, Wsep, obtained from density functional theory(DFT) simulations. The latter is inferred from DOS (density of states) analysis based on DFT, by checking whether
or not the in-gap peak disappears and if there is a large DOS around the Fermi level. We found that (1) Ti on
pristine surface has both the best Ohmic contact and fairly strong adhesion and (2) Ti and Cr on oxygenatedsurfaces have the strongest adhesion with good Schottky contact.

1. Introduction
Diamond is a promising candidate for the next-generation powerdevices, possessing a wider band gap by a factor of ﬁve and a higher
thermal conductivity by a factor of more than ten [1], compared with
Si [2,3]. These properties are key for the device robustness in its antivoltage and anti-thermal strengths which is required especially inpower semiconductor devices. Its higher electron mobility, 1.3 times ormore faster than Si, makes the device a very good candidate for use insignal processing with higher frequencies.
Nevertheless, diamond semiconductors have not been widely spread
yet in the practical situations. One of the primary reasons is the diﬃculty of synthesizing big diamond single crystals. Microwave plasma
assisted chemical vapor deposition (MPCVD) is often used for the synthesization [4–7], with which inch-size diamond (100) is established [6]. Another issue for diamond device is poor concentration ofcarriers in pristine diamond. To give large amounts of carrier density
especially for power devices, doping techniques are usually employed.
Boron has the lowest activation energy for doping, 0.37 eV, so thesynthesization of boron doped diamond (BDD), p-type semiconductor,
has been eagerly studied [8–12], and high carrier density doping,
1020 cm- 3, has already been established by applying high pressure [9].
Furthermore, the coexistence of high carrier density and high carrier*

mobility is generally not allowed because of the insulator transition of
BDD at high carrier density, 5 × 1020 cm- 3 [12]. Delta doping technique
has recently been reported to be a good solution [11,12].
Phosphorus doping has been applied for diamond (111), where
diamond becomes n-type semiconductor, diﬀerent from boron doping.
While high carrier density, 1020 cm- 3, is established [13,14], thegrowth of fairly large diamond (100) with good quality is quite challenging today [14]. Thus, phosphorus doping for diamond (100) has
been eagerly studied and also fairly high carrier density, around1018 cm- 3, is established [15].
Another important issue is electrode fabrication, namely about theestablishment of low contact resistance. Refractory metals (e.g. Ti, Mo,
W, Cr, and Ta) covered by noble metals, Au and Pt, are usually employed for electrodes [16–20]. Refractory metals form carbides after
annealing and noble metals prevent the corrosion of refractory metals [17]. Meyyappan et al. annealed Ti-W alloy and Cr both covered by
Au. They established the interdiﬀusion between Au and Ti-W or Cr
occurs and conﬁrmed such a tendency is more subdued for Cr [16].
Johnston et al. annealed Ti, Mo, W, and Ta covered by Au or Pt andestablished Pt signiﬁcantly prevents the interdiﬀusion [17]. Iacovangelo and Hoﬀ et al. studied trilayer electrode, Ti/Pt/Au, where Pt
works to prevent Ti from penetrating into the Au layer [18,19]. The
recent study by Msolli et al. has reported that a trilayer electrode, Ti/

Corresponding author.
E-mail address: s1720002@jaist.ac.jp (T. Ichibha).

https://doi.org/10.1016/j.diamond.2017.12.008
Received 25 August 2017; Received in revised form 5 December 2017; Accepted 6 December 2017
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T. Ichibha et al.

Fig. 1. Interface models: (a) unit cell of slab, (b) 4 × 4 × 1 supercells of slab, (c) parent surface (with terminations), and (d)metallic electrode layer. The large gray, small red, and small
yellow balls correspond to the metal, terminating atoms (hydrogen or oxygen), and carbon atoms, respectively. (For interpretation of the references to color in this ﬁgure legend, thereader is referred to the web version of this article.)

Ohmic contact, which agrees with the fact that Ti is typically used forrealizing Ohmic contact [16–20]. We further established that Cr has
higher adhesion strength than Ta and V, which were previously reported to have highest adhesion strengths [29]. In contrast, for theoxygenerated surface, it is found that (1) Ni has the best Schottky
contact and (2) Ti and Cr have highest adhesion strengths with good
Schottky contacts.
It is important to note that, while the computational works including ours have studied non-doped diamond, the doping of boron or
phosphorus signiﬁcantly aﬀects the electrode adhesion: It was reported
that boron doping reduces the contact resistance of Ti electrode [17].
The work by Teraji et al. conﬁrmed that this tendency is more pronounced with higher doping density for Au and Cu electrodes [33]. The
same tendency was also observed for phosphorus doping. Kato et al.
showed that heavy phosphorus doping results in an Ohmic contact of
the Ti electrode [13], and the contact resistance becomes lower, when
the dopant concentration becomes higher.
In this section, we have reviewed previous studies on the diamondsurfaces and made a brief explanation of our ﬁndings. The following
sections are organized as follows: Section 2 presents the surface models
and methodology. In Section 3, the results of the work are presented
and ﬁnally the conclusions drawn from the ﬁndings are given in
Section 4.

Cr/Au, can be a better alternative to Ti/Pt/Au [20].
Based on the interest in the electrodes, a number of theoreticalworks have also studied the adhesion between diamond surfaces andseveral metals [21–31], but their exploration space has been limited
and hence there are still other possibilities of discovering more appropriate electrode metals for diamond surfaces. Pickett and
Erwin [21,23] have investigated, for the ﬁrst time, metal/diamond interfaces for electronic device applications using ﬁrst-principles localdensity functional approaches, inspired by the pioneering work on BN/
diamond interfaces by Lambrecht and Segall [22]. They modeled
nickel/diamond interfaces on both the (100) and (111) ideal surfaces
and computed their Schottky barrier heights and interface energies. It
was found that the tetrahedral arrangement leads to an Ohmic interface
with the interface energy of 0.97 eV per carbon atom, which suggeststhat the interface geometry plays a crucial role in its surface electronic
structure. Afterward, the Ohmic properties were veriﬁed by an experimental work [32] to support the above theory-driven prediction.
Recent works [28–31] examined material structure model and studied several metals. Guo et al. [28] treated 3 metals (Al, Cu, Ti) on
clean diamond (111)–(1 × 1) surface. Monachon et al. [31] treated 2
metals (Cu, Ni) on clean and hydrogen terminated diamond(111)–(1 × 1) surfaces. These two works evaluated the adhesion
strengths by calculating work of separation (Wsep), which represents theadhesion strengths between the metals and diamond surfaces. Whilethey treated the model of metallic electrodes as multi-layers of themetals, Motochi et al. [29] modeled the interfaces as periodic slabs
comprised of monolayer metallic electrodes and diamond slab with/without monolayer atomic terminations. They applied density functional theory (DFT) approaches to evaluate adsorption energy, Eads, anddensity of states (DOS) for their target systems. (Eads is notated as thesurface cohesive energy, Ecoh, in their work.) They concluded thattantalum and vanadium were the best metallic electrodes because they
showed highest Eads with surface metallic properties, i.e. no bandgaps.
In this study, we improved mainly the previous work by Motochi
et al. [29] in terms of the following three points: First, although theirwork gave a great insight into the possibility of the carbide forming
metals to form better electrodes, the number of metal samples was quite
limited. In contrast, the present study has systematically explored 20
kinds of metals for more desirable diamond electrodes. Second, we
adopted the metal/diamond structure model similar to the work by
Motochi et al. [29], but we paid more careful attention to the evaluation of adhesion for which we employed Wsep instead of Eads from thereason discussed in Section 2. Third, while they discussed only Ohmic
contacts, we evaluated Schottky contacts, too.
For pristine surface, our calculations conﬁrmed that Ti has the best

2. Model and methodology
Fig. 1 shows our slab model of interfaces between metallic electrodes and diamond surfaces. Although this ﬁgure explains the modelwith 4 × 4 × 1 super cell for the reader's convenience, all the calculations were conducted with a unit cell. We employed diamond (111)
surface as well as the recent theoretical works [29,34] because of its
potential applicability for excellent n-type semiconductor, due to theestablishment of high phosphorus doping density for the surface. We
considered hydrogen and oxygen terminations for the diamond surface
following the work by Motochi et al. [29]. Hydrogenated diamond isreported to have high carrier mobility [35] and vigorously applied tometal oxide semiconductor ﬁeld eﬀect (MOSFET) transistors [36,37].
The surface terminations by oxides are known as not only accelerating
carrier mobility [35] but also improving adhesion strengths of transition metal electrodes [29]. We employed the 20 metals, Mg, Al, Ti, V,
Cr, Ni, Cu, Zn, Zr, Nb, Mo, Pd, Ag, In, Hf, Ta, W, Pt, Au, and Pb with thethree kinds of terminations, which leads in total 60 interface systems
that were considered to explore desirable electrodes for power device
applications in total. We have performed DFT calculations with carefully chosen computational conditions as explained later in this section

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T. Ichibha et al.

the upper and lower ﬁve layers are identical. In order to take into account surface reconstructions, we optimized both the atomic positions
and lattice parameters (i.e., unit cell size) simultaneously within the
PBE-GGA method under the above condition. Our optimized geometries
reasonably agree with the experiment [42] as well as that by Motochi
et al. [29]. The number of the layers (Fig. 1) has been found to be large
enough to simulate the (111)–(1 × 1) surfaces because the geometry at
the ﬁfth layers from both sides is almost same as that of the bulk. The
optimized geometry was used to evaluate Eparent_surface . Erwin andPickett [43] pointed out that the dangling bonds of the (111)–(1 × 1)
surface are located at on-top sites. In the case of H- and O-terminations,
therefore, we placed the terminating atoms at an on-top site of theabove optimized (111)–(1 × 1) surface. Starting with initial atomic
conﬁgurations separated by their covalent radii [44], we ﬁxed thelattice parameters and reoptimized all the atomic positions and foundthat both the hydrogen and oxygen terminating atoms stay at the on-top
site with only a change in the vertical distance between the surface
carbon atom and the terminating atoms.
Secondly, since the on-top site may be thought of as being the most
preferable to electrode adhesion, we constructed the slab model by
putting metallic monolayers at the on-top site of the optimized(111)–(1 × 1) surface. Starting with initial atomic conﬁgurations separated by their covalent radii, we ﬁxed the lattice parameters andreoptimized all the atomic positions to get Eslab(x). Note that our unit
cell contains only one metallic atom on the surface. This means that we
ignore lattice mismatches at interfaces, but, as discussed in Section 3.4,
their inﬂuences for Wsep were found to be negligible. Similar to the notermination case, we placed metallic monolayers on the H- or O-terminating diamond surfaces and reoptimized the geometries.
Lastly, we considered the metallic monolayers (i.e., two dimensional
metallic sheets) without optimizing their geometries, which was used toevaluate Esheet(x). The errors due to omitting the optimizations arefound to be negligible as discussed later in Section 3.4. Since all the slab
systems are non-magnetic, we treated all the 2D sheets as being paramagnetic, irrespective of their actual magnetic states [45].

Fig. 2. Partial contributions to DOS from each layer of the diamond slab. Only the ﬁrst
three layers contribute mainly to the surface state appearing between the bulk gap.
Energy as the horizontal axis is set with the Fermi energy at 0 eV.

and optimized the geometries using QUANTUM ESPRESSO [38] with PBEGGA [39] exchange-correlation functional and ultrasoft pseudopotentials [40] available therein.
Most of the preceding works have taken Wsep as the measure ofadhesion strength [24-26,28,31], which does not include the cohesiveenergies of the metallic sheets, diﬀerent from Eads [29]. We have veriﬁed whether or not our model can accurately simulate the interfaces interms of partial density of states (pDOS) at each of the diamond layers,which was not investigated in the previous study [29].
The expression for the work of separation is given by Eq. (1): [28]Wsep (x ) =1(Eparent_surface + 2⋅Esheet (x ) − Eslab (x )).
2Ω(1)Here, Ω is the surface area of unit cell, (i) Eparent_surface is the energy
per unit cell of the diamond slab with/without termination (parent
surface), (ii) Eslab(x) is the energy of the whole interface system (slab)
with the sheets of metal x, and (iii) Esheet(x) is the energy of the sheet ofmetal x (electrode). The factor 1/2 in Eq. (1) comes from the fact that
our slab model has interfaces on both sides. On the other hand, in thecase of the adsorption energy [29], Esheet(x) is replaced by the cohesiveenergy of the surface atoms from Wsep, which brings improper energy
gains for the evaluation of adhesion strengths.
Within the framework of the DFT approaches, all the three energies(i), (ii), and (iii) were computed under the conditions that
Eecutwfc = 90 Ry for the cutoﬀ energy of the orbital function expansion
and Eecutrho = 520 Ry to compensate for charges in the ultrasoft pseudopotential evaluation. The k-mesh size (discretization of Brillouinzone) of 14 × 14 × 1 was used for all the three energies. The MarzariVanderbilt smearing scheme [41] with δE = 0.02 Ry was applied to all
the systems. The above computational speciﬁcations were the best
choices for all the systems, but they were also very carefully chosensuch that all the evaluations of interface energy lie within the chemical
accuracy of ∼ 2 mRy/unit cell. Hereafter, we describe how to model
the metal-(terminating atom)-diamond interface system (slab) and its
subsystems (parent surface and metal) in order to evaluate the corresponding three energies in more detail.
First, we extracted a ten-layer diamond slab with an ideal(111)–(1 × 1) surface from the bulk structure. As conﬁrmed later in
Section 3.1, the number of layers is large enough to capture the change
in the electronic structure from surface to bulk. To construct the diamond surface, we chose a vacuum phase with dimension of 9.2 Å
subject to the periodic boundary condition (Fig. 1), which means that

3. Results and discussion
3.1. Number of diamond layers and metal layers
In order to check whether the number of diamond layers is large
enough to simulate the interfaces, we looked into pDOS contributions at
each diamond layer to the total DOS, as shown in Fig. 2. We found that
2p orbitals from the ﬁrst three layers mainly contribute to the surface
state appearing within the bulk gap. This corresponds to the fact thatany surface reconstruction occurs only within the ﬁrst two layers. Thisis consistent with previous studies by Pickett and Erwin [23,46]. We
note in Fig. 2 that the width of the in-gap peak, ∼2 eV, is a bit wider
than that usually expected for the surface state [47]. We also checked
the convergence of Wsep with increasing number of metal layers from
one to three. Here, we chose Ni electrode on pristine diamond surface
as a sample. We assumed the bulk structure for three layers of Ni, since
it is diﬃcult to determine the proper structure around the interface. The
diﬀerence of the adhesion strengths is only 7% between one and three
metallic layers, where the values of Wsep for the two cases are 5.20 J/
m2 and 5.63 J/m2 respectively. Therefore, we modeled the electrodes
with a single layer metal sheet.
3.2. Density of states
The DOS provides us with the useful insights for the electric properties of the interface systems: The DOS of diamond slab has a peak at'LDPRQG 5HODWHG0DWHULDOV  ²

T. Ichibha et al.

Fig. 3. DOS of the parent surface and the metal sheets with Hydrogen, Oxygen, and no-terminations. Blue, red, and black lines correspond to Hydrogen, Oxygen, and no-terminations
respectively. The vertical dotted line represents Fermi energy. The DOS are classiﬁed into Ohmic and Schottky contacts respectively. (For interpretation of the references to color in thisﬁgure legend, the reader is referred to the web version of this article.)

Schottky contact, it determines how well electric double layers areformed. On the other hand, higher DOS at EF is more preferred for bothcontact types. On the contrary, tiny DOS at Fermi energy means that the
conductivity is signiﬁcantly low. The DOS of such cases are shown inAppendix A. According to this analysis, it is concluded that Ti on thepristine surface is especially good for Ohmic electrode, while Ni on
Oxygen or Hydrogen termination excellently realizes Schottky contact.

Fermi energy, EF. This in-gap peak corresponds to the localized surface
electronic state because such a peak is not observed in bulk diamond.
For interface systems, the appearance of the peak means the existenceof localized electronic state around the interface. It is considered thatsuch localized electronic states appear with the electrode having low
carrier mobility across the interface. Since these electronic states giverise to electric double layers that are the origin of electric rectiﬁcation,
in-gap peaks can be regarded as the sign of a Schottky contact, otherwise the electric contact nature is Ohmic. Fig. 3 shows the combinationsof electrode metals and surface terminations (no-term., H-term., and Oterm.), separating them into Ohmic and Schottky contacts respectively.
Another important observation is the DOS at EF. For Ohmic contact,
DOS at EF corresponds to the density of conduction electrons, while for3.3. Bonding natures and adhesion lengths
Fig. 4 shows the change in the bonding lengths during the lattice
relaxation starting oﬀ with the initial value taken as the sum of covalentradii of the atoms constituting the interface. There is a clear contrast

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T. Ichibha et al.

Fig. 4. Deviations of the adhesion lengths, dadh, from the initialvalues for the geometrical optimizations. The sum of the initialcovalent radii is shown to be unity. Open circles (closed triangles) correspond to the lengths between the termination elements and metallic elements (surface carbon atoms). No-term.
stands for no-termination while H-term. and O-term. stand forhydrogen- and oxygen-terminated surfaces respectively.

Fig. 5. Work of separation Wsep obtained from our PBE-GGA
simulations with the ultrasoft pseudopotentials. No-term. stands
for no-termination while H-term. and O-term. stand for hydrogen- and oxygen-terminated surfaces respectively.

the smaller numbering of groups (i.e., left hand side in the periodic
table) would be accounted for by the smaller electronegativities. The
diﬀerence of the negativities between the metallic elements and the
top-most atom on the surface (carbon or oxygen) gets larger when thenegativity of the metallic element itself gets smaller. The larger difference leads to the ionic bonding nature, and hence to the more pronounced contraction. The scenario is consistent with the fact that we
get more contractions by O-termination than no-termination because
oxygen has the larger electronegativity and hence gives a larger difference of electronegativity.

between elongation or contraction of the adhesion lengths, dadh, after
optimization between the initial and optimized bond lengths (atomic
positions were optimized from their initial ones separated by thecovalent radii of atoms constituting the interfaces, as explained in
Section 2). The contrast might be attributed to the diﬀerent bonding
nature, such as ionic or covalent. In the case of no-termination, forinstance, Al (Ti) results in elongation (contraction) which is consistent
with the covalent (ionic) nature of the elements. Signiﬁcant elongations
for the hydrogen terminations compared with the oxygen terminations
and no-terminations might also be attributed to the fact that the diamond surface has only one dangling bond that hybridizes with thehydrogen 1s orbital and then there is no room for additional bonding
with the electrode metals. In the case of O-termination, The dadh became shorter [longer] for transition metals (Ti, Ta, V) [noble ones (Au,Pd)]. This contrast can be attributed to whether or not the d/f orbitalsof the valence shell are closed, i.e., the noble metals has closed shells,
while the transition metals possess open ones.1 The trend in the magnitude of the contraction can be explained to some extent in terms of
the electronegativity: the pronounced contraction by the elements with

3.4. Work of separation
Fig. 5 highlights the dependence of Wsep(x) on the metallic elements
x and the terminations (i.e. no-termination, O- and H-terminations),
evaluated from our PBE-GGA simulations with the ultrasoft pseudopotentials. It is found that the overall trend of Wsep(x) strongly depends on
the termination elements, reﬂecting their surface bonding natures. In
the case of the no-termination the Au electrode has the weakest adhesion as expected. Surprisingly, the Pd electrode is found to have aslightly stronger adhesion than Ti, a carbide forming metal. The group6 (Cr, Mo and W) basically have stronger adhesion than the othergroups. For any metal, the H-termination hinders the metal fromforming the electrodes because of no dangling bonds on the surface (see1
For Au, the partially occupied 6s orbital can contribute to the bonding with oxygen
atoms. However, it may be weak because s orbital has a spherical shape and may have lessoverlap with p orbital of oxygen than d/f orbitals.

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T. Ichibha et al.

constant as the diamond surface. We may estimate the energy loss dueto this artiﬁcial distortion. From the values of bulk modulus of metals
obtained in literature, we can roughly estimate the energy loss thatarises when the lattice of metallic sheets is distorted towards that of
diamond surface. Taking Birch-Murnaghan equation of state [48], we
estimate the loss being 0.377 J/m2 for Au, 0.015 J/m2 for Pd, 0.073 J/
m2 for Ti, 0.342 J/m2 for V, and 0.078 J/m2 for Ta. Such energy losses
are negligibly small compared with Wsep(x) of the metal sheets thatshow good adhesion.

Table 1Comparison of Wsep (J/m2) between our values and the previous theoretical works using
DFT (density functional theory) for several metals (Al, Cu, Ti, and Ni). The corresponding
adhesion lengths, dadh, are also given in parentheses. Note that the present metal/diamond interface models employ monolayer metallic sheets, while the previous ones did
multi-layer metallic sheets.

Al
Cu
Ti
Ni

This work

H. Guoet al. [28]C. Monachon
et al. [31]Y. Qi and L.G.
Hector [26]4.90 J/m2(2.09 Å)2.90 J/m2(2.06 Å)4.04 J/m2(2.18 Å)5.65 J/m2(1.92 Å)4.08 J/m2(1.86 Å)3.36 J/m2(2.09 Å)5.77 J/m2(1.94 Å)N/A

N/A

3.98 J/m2 (1.86 Å)

3.04 J/m2 (N/A)

N/A

N/A

N/A

5.00 J/m2(1.96 Å)N/A

4. Conclusion
We have conﬁrmed that Ti with pristine diamond surface has thebest Ohmic contact, which is consistent with the previous investigations [16–20], and established the combination of Cr and pristine diamond surface has higher adhesion strength than those of Ta or V andpristine diamond surface, which was reported previously to havehighest adhesion strength [29]. While Ni on oxygenated and hydrogenated diamond surfaces show the best Schottky contacts, their adhesion strengths are rather weak. On the other hand, Ti and Cr on
oxygenated diamond surface show the highest adhesion strengths, withgood Schottky contact. It is established that metal layers can hardly
attach to hydrogenated diamond surface, because there is no dangling
bond from hydrogen towards the metal. It is also observed that oxygenated surface weakens the adhesion strengths and increases the adhesion lengths, dadh, for noble metals (Pt, Au, and Pd), which implies dvalence orbitals (e.g. d z 2 ) are necessary for the metals to bond withsurface oxygens. For the other cases, it is found that the adhesion
lengths correlate weakly and negatively with the strength of bonding
ionic nature.

Section 3.3). In contrast, the O-termination results in quite diﬀerent
eﬀects on the adhesion. While it weakens the adhesion of the noble
metals (Pt, Au, Ag, Pd, and Cu), it strengthens that of some transition
metals (group-4,5,6), especially Ti and V. The combination of Ti andpristine diamond surface has both fairly high adhesion strength and thebest Ohmic contact, which is consistent with the fact that Ti is a typically used metal to realize Ohmic contact [16–20]. It is also reproduced
that the combinations of Ta and V with pristine diamond surface havehighest adhesion strengths with good Ohmic contacts [29]. In addition,
it is established that Cr on pristine diamond surface had a slightly
higher adhesion strength. While Ni on oxygenated and hydrogenateddiamond surfaces show the best Schottky contacts, their adhesion
strengths are rather weak. On the other hand, Ti and Cr on oxygenateddiamond surfaces show good Schottky contacts with the best adhesion
strengths.
Table 1 compares our numerical results of Wsep and dadh with thoseby previous studies [26,28,31] for Ni, Cu, Al, and Ti. Note that ourmetal/diamond interface models consider only monolayers, while theprevious ones adopt multi-layers. Despite such a diﬀerence, We foundthat our numerical results for Cu and Ni agree well with the previous
ones (their diﬀerences in Wsep and dadh lie within ∼ 0.6 J/m2 and ∼0.04 Å, respectively). On the other hand, our results overestimate dadhfor Al and Ti. Interestingly, the overestimation aﬀects Wsep in the opposite manner, i.e., Wsep increases (decreases) for Al (Ti). This may be
explained by the diﬀerent nature of the bonding, i.e., covalent for Al
and ionic for Ti as discussed in Section 3.3: Covalent bonds generally
tend to have longer bond lengths (e.g., sparse structure in diamondstructure) than ionic ones (e.g., NaCl structure). The optimal dadh for Al
would be longer than the previous ones and closer to ours, leading to astronger adhesion. On the other hand, our predicted dadh for Ti seems todeviate from the optimal one, leading to a weaker adhesion.
We note that the present work did not take explicitly into accountthe energy loss/gain by the lattice relaxation. The metallic ion is located just above the carbon atom in our slab model. This corresponds tothat the lattice of metallic sheet is forced to have the same lattice

Acknowledgments
The computations in this work have been performed using the facilities of the Center for Information Science in JAIST. This work was
supported by the Kenya National Council for Science and Technology(NCST, Now National Commission for Science, Technology andInnovation (NACOSTI)) Grant No. NCST/5/003/4th CALL/050, and theComputational Materials Sciences Group, Department of Physics,
University of Eldoret, Kenya. Authors, IM, NWM, and GOA wish toacknowledge the Center for High Performance Computing (CHPC) in
Cape Town South Africa for computational resources. KH is grateful forﬁnancial support from a KAKENHI grant (15K21023,17K17762), a
Grant-in-Aid for Scientiﬁc Research on Innovative Areas(16H06439),PRESTO (JPMJPR16NA) and the “Materials research by
Information Integration” Initiative (MI2I) project of the Support
Program for Starting Up Innovation Hub from Japan Science andTechnology Agency (JST). R.M. is grateful for ﬁnancial support fromTOKUYAMA Science Foundation,MEXT-KAKENHI grants17H05478,
the support by FLAGSHIP2020, MEXT for the computational resources,
Project Nos. hp170269 andhp170220 at K-computer.

Appendix A
In Fig. 6, we present the DOS for the combinations of metals and surface states which are neither Ohmic nor Schottky in the sense that tiny DOS
exist at the Fermi energy as mentioned in Section 3.2.

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T. Ichibha et al.

Fig. 6. DOS of the parent surface and the metal sheets with Hydrogen and no-terminations. They all correspond to a bonding conﬁguration that leads to neither Ohmic or Schottky
contact. Blue, red, and black lines correspond to Hydrogen, Oxygen, and no-terminations respectively. The vertical dotted line represents the Fermi energy. (For interpretation of thereferences to color in this ﬁgure legend, the reader is referred to the web version of this article.)High quality MPACVD diamond single crystal growth: high microwave power
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