Diamond & Related Materials 23 (2012) 10–17

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Diamond & Related Materials

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Metal–semiconductor ohmic contacts: An ab initio Density Functional Theory studyof the structural and electronic properties of metal–diamond (111)-(1×1) interfaces

I. Motochi ⁎, N.W. Makau, G.O. AmoloComputational Materials Science Group, Department of Physics, Chepkoilel University College, P.O. Box 1125-30100, Eldoret, Kenya

⁎ Corresponding author.E-mail address: ismotochi@gmail.com (I. Motochi).

0925-9635/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.diamond.2011.12.021

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 April 2011Received in revised form 15 November 2011Accepted 20 December 2011Available online 11 January 2012

Keywords:Diamond–metal interfacesAdsorptionOhmic contacts

Metal contacts on clean, hydrogenated and oxygenated diamond surfaces have been studied using ab initioDensity Functional Theory (DFT). Five metals, i.e., gold, titanium, tantalum, vanadium and palladium on thethree surfaces were considered. Gold and palladium were found to form weak bonds on clean, hydrogenatedor oxygenated diamond (111) surfaces compared to the other three metals. Bulk properties were also studiedfollowing the formation of the respective ohmic contacts on the three surfaces. The clean diamond surfacewas found to have surface states which were modified by oxygen but removed by hydrogen. Density of statesstudies revealed that all the investigated metals had an effect on the electrical properties of the diamond sur-face. A peak that was characteristic of diamond was observed at ≈−11.8 eV. For the clean diamond surfaceterminated with gold and palladium, states due to Au-2p orbitals were observed at −2.5 eV and≈−1.5 eV, while Pd-5s orbitals were located at ≈−1.7 eV and −0.5 eV on the same surface. Titanium, tan-talum and vanadium showed unique states at high binding energies of≈−38 eV for vanadium,≈−34 eV fortantalum and ≈−32.5 eV for titanium, which were thought to be responsible for their strong bonding.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Diamond is an electrical insulator at room temperature with a re-sistivity of 102 Ω cm and has a wide bandgap of 5.5 eV [1]. However,boron-doped diamond which is mainly produced by chemical vapordeposition (CVD) processes [2,3] or naturally occurring type IIb dia-mond which has boron as substitutional impurity is a p-type semi-conductor. Diamond as a material has unique electronic andstructural properties which make it an ideal candidate for use inhigh power, high frequency applications as well as in high tempera-ture and corrosive environments (harsh environments) [4].

Diamond doped with boron, nitrogen or other suitable dopants isusually conductive, finding many applications in the electronics in-dustry. The fabricated diamond electronic devices need to be con-nected to metallic conductors in the outer circuit. Development ofgood electrical contacts is key to the enhancement of better perfor-mance of the electronic device. Hewett et al. [4] have argued that con-tacts formed on diamond must satisfy the following requirements; avery low contact resistance, they must also be strongly adhesive, beable to withstand the harsh environments for which diamond devicesare intended and they should also be compatible with conventionaldevice processing techniques.

Compared to other semiconductors, diamond does not have a na-tive oxide, therefore the properties of metallization contacts on

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diamond are strongly dependent on the surface terminating species[5]. Techniques have already been developed to measure ohmic con-tact characteristics on naturally occurring p-type diamond (type IIb)that is adsorbed with some carbide forming metals [6]. Empirically,circular transmission line method (c-TLM) of Reeves [7] togetherwith an end resistance measurement has been used to study theproperties of Au, Au/Ti and Al/Ti on hydrogenated CVD diamond [5].The c-TLM is a commonly used method for wide band gap materialsand allows the sheet and contact resistances to be determined togeth-er with the transfer length of the test structure. The end resistancemeasurement allows both the bulk sheet resistivity and the sheet re-sistivity beneath the contact to be determined from c-TLMmeasurements.

This work seeks to provide a theoretical treatment to what is ob-served experimentally [6] with regard to the formation of ohmic con-tacts. In doing this, the study examines the atomic monolayer of Ti, Taand V on diamond, as well as a non-carbide forming metal, Au. Pd isalso studied in order to classify it later after its properties are com-pared with those of the other metals considered in this study.

2. Computational procedure

All the calculations in this work were performed using the Quan-tum-ESPRESSO computer code [8,9]. It is based on Density FunctionalTheory (DFT), plane waves and pseudopotentials (both ultrasoft andnorm-conserving). Conjugate gradient electronic minimization wasused in energy minimization. In this study, electron–ion interactionsare described using ultrasoft pseudopotentials. The exchange and

Table 1Calculated DFT–GGA parameters of bulk diamond together with their experimentalvalues and their % deviation with respect to the corresponding experimental values.

Parameter Calculated value Expt. value [Ref.] % deviation

Lattice constant, ao, (Å) 3.568 3.567 [1] 0.03C\C atom distance (Å) 1.540 1.540 [13] 0.00Bulk modulus (Mbar) 4.220 4.420 [1] −4.54Cohesive energy (eV/atom) 9.10 7.37 [14] 23.47

Table 2

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correlation energies were calculated with the Perdew–Burke–Ernzer-hof (PBE) form of the generalized gradient approximation (GGA)[10,11]. Geometry optimizations were performed by the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The structures were re-laxed to an accuracy better than 10−5 Ry in their total energies. Theplane wave cutoff energy was thoroughly tested and an optimizedvalue of 37 Ry was used for all calculations done in this work. Opti-mized k-points of 4×4×4 for bulk and 4×4×1 for surfaces wereused. The cell parameters were fixed at the experimental value ofthe bulk crystal during geometry optimizations while the total ener-gies were minimized with symmetries. Where the experimentalvalues were unavailable for the bond lengths, the atom–atom dis-tance was approximated as the sum of covalent radii of the elementsin question [12].

The diamond surface was modeled using carbon atoms made up offive bi-layers since this was representative of both the diamond's bulkand surface properties. The various terminating species wereadsorbed on both ends of the diamond slab for symmetry. The thick-ness of the slabs together with a sufficiently large vacuum spacing of≈10 Å (vacuum approximately equal to the size of the slab) ensuredthat there was no interaction between the replicas. For the surfacecalculations, atoms were allowed to relax in the x, y and z directions.

3. Results and discussions

The bulk properties of diamond were fully investigated, and theseshowed excellent agreement with other theoretical predictions andexperimental values as partly shown in Fig. 1 and summarized inTable 1.

Apart from bulk diamond, this study also considered the energet-ics of relaxed geometries of the C(111)-(1×1) surface with and with-out the adsorbed atoms. To do this effectively, it was essential toinitially establish the ground state energies of all the free atoms,since these were to be used in computing the cohesive energies. Inthis regard the energies of free hydrogen, oxygen, gold, titanium, tan-talum, palladium and vanadium atoms were calculated.

3.1. Structural changes of relaxed diamond (111)-(1×1) surface

As noted earlier, a five bi-layer C-atom slab was taken to representthe diamond surface. Apart from such a slab making the calculationsless expensive computationally, it was also representative of the dia-mond's bulk and surface properties. The three surfaces (clean, hydro-genated and oxygenated diamond surfaces) formed the parentsubstrates upon which the ohmic contact materials were to beadsorbed. Following system relaxation, bond length changes for thesurface, near surface and bulk regions were obtained, as well asbond angles using the Xcrysden program [15].

Our investigations revealed that, although most bulk bond lengthsand bond angles were closer to their corresponding experimentalvalues after relaxing, there appears to be an alternate contraction

3.568 Å

2.522 Å 1.540 Å

3.568 Å

109.470

109.470

3.568 Å

C

Fig. 1. Optimized structure of bulk diamond.

and expansion of bonds in the surface region in the case of theclean surface as seen in both Table 2 and Fig. 2.a, which suggests abulk symmetry breakdown. The topmost layer and the 1st and 2ndinterlayer bond lengths experienced the largest contraction of−3.57% and bulk bond length expansion of +9.09%, respectively.

The hydrogenated surface was found to be somewhat stabilized byremoving the alternate expansion and contraction of the C\C bondlengths (see Table 2 and Fig. 2.b), which was quite prominent in theclean diamond surface. Contractions of −0.45% of the bulk bondlength and expansion of +0.32% were typically observed.

The alternate contraction and expansion of the surface bondlengths was, however, not quenched fully by oxygen adsorption onthe (111)-(1×1) surface (see Table 2 and Fig. 2.c).

In all these three cases, the bond length of the middle layer, i.e.,r5(C\C), which was the bond between the 5th and 6th carbon atomlayers from either side, compares well with the computed bulkbond length of 1.540 Å, confirming the fact that a five bi-layer slabwas indeed sufficient to represent both the surface and bulk regions.

3.2. Structural properties of diamond–metal interfaces

3.2.1. The C\metal, C\H\metal and C\O\metal bond lengthsThe surfaces were modeled in such a way that each had full mono-

layer termination of adsorbates (see Fig. 2.b and c) to avoid any influ-ence of dangling bonds which may otherwise affect the electricalconductivity of the surfaces. Full monolayer termination also main-tains the bulk-like structure and hence avoids any tendency of thesurface reconstructing as is the case with a clean C (111)-(2×1) [16].

It is worth noting that not much theoretical or even experimentalwork has been done in this area of forming ohmic contacts on dia-mond. As such, where no experimental or theoretical values wereavailable, the initial bond lengths were approximated by the sum ofthe covalent radii of the atoms forming the bond, using Eq. (1)

rcov ¼ ra þ rb; ð1Þ

where rcov is the interatomic distance of a molecule made up of ele-ments a and b whose covalent radii are ra and rb, respectively.

Bond lengths and their % changes [contraction (−) or expansion (+) in brackets] in re-laxed clean, hydrogenated and oxygenated (1×1) diamond surfaces. r(C\O) is the C\Obond length, r(C\H) is the C\H bond length while r1(C\C), r2(C\C) … are the C\C bondlengths between the first and second, second and third atomic layers, etc. The % bondlength changes are relative to the experimental C\C bond length of 1.540 Å, 1.36 Åfor a single C\O bond and 1.1 Å for a C\H bond.

Bond Relaxed bond lengthin clean surface(Å)

Relaxed bond length inhydrogenated surface(Å)

Relaxed bond length inoxygenated surface(Å)

r(C\H) 1.100 [00.00]r(C\O) 1.321 [−2.87]r1(C\C) 1.485 [−3.57] 1.533 [−0.45] 1.561 [+1.36]r2(C\C) 1.680 [+9.09] 1.545 [+0.32] 1.528 [−0.78]r3(C\C) 1.533 [−0.45] 1.542 [+0.13] 1.543 [+0.19]r4(C\C) 1.554 [+0.91] 1.540 [0.00] 1.537 [−0.19]r5(C\C) 1.540 [0.00] 1.542 [+0.13] 1.542 [+0.13]

Fig. 2. Relaxed (a), clean (b), hydrogenated and (c) oxygenated diamond (111)-(1×1) surface. The bond lengths are in Angstroms.

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The systems were then allowed to relax and structures for the(1×1) surface terminated with a non-carbide forming metal (Au)are shown in Fig. 3.a, for a clean, b for hydrogenated and c for oxygen-ated surface, respectively. The results obtained were recorded inTable 3. Surfaces for relaxed structures terminated with a carbideforming metal (Ta) are shown in Fig. 4.a, for a clean, b for hydrogenat-ed and c for oxygenated surface, respectively.

The presence of metal atoms on the three surfaces resulted insome changes on each one of them. In particular the C\metalbonds for all metal atoms showed significant bond elongation, withthe largest increase of ≈+11% occurring in the C\Au bond lengthand the shortest of 6.5% in the case of C\Ta (see top section ofTable 3). This was, however, not unexpected since gold is basicallyinert, and hence less reaction was expected at the interface.

The presence of hydrogen betweendiamond and themetals, had theeffect of elongating the bond lengths even further as seen in themiddlesection of Table 3. We attributed this to the fact that diamond surfacesare known to have high affinity for hydrogen adsorption. Thus, hydro-gen being monovalent, bonds strongly to carbon instead of the metaladsorbate. However, C\H bonding is non-stoichiometric, thereby leav-ing some charge density on carbon for bonding with the metals. Themetals then bond to the carbon through charge densities of the metalsand carbon atoms.

Oxygen, on the other hand brings a clear distinction between thestrongly bonding metals from the less adhesive ones. The strongly ad-hesive metals are those with many unpaired electrons in their d or-bitals. These include V, Ti and Ta, all of which had a contraction in

Fig. 3. Gold on (a) clean, (b) hydrogenated and (c) oxygenated

the metal\oxygen bond length (see the bottom section of Table 3),while gold and palladium (with filled d orbitals) had an increase inthe relaxed bond lengths compared to their approximated ones.This means that oxygen may thus be used to distinguish the carbideforming metals (e.g., Ti, Ta and V) from the non-carbide formingones (Au and Pd).

The percentage deviation in bond lengths for gold on hydrogenat-ed and oxygenated surfaces were almost similar (+58.56% and +50.95%, respectively), suggesting that the two elements, interfacingC and Au had an almost similar effect.

3.2.2. Cohesive energiesShortening or lengthening of a bond length can depict a bond's

strength or weakness due to the inverse relation between the bondlength and its strength. However, this alone cannot give the completepicture of the nature of bonding, and hence cohesive energies, Ecoh(x),of the ohmic contacts were also calculated using Eq. (2) for the differ-ent parent substrates

Ecoh xð Þ ¼ 1N

ESlab xð Þ−EParent−surf−N EAtom xð Þ½ �n o

; ð2Þ

where ESlab(x) is the total energy of the slab terminated with an atomof element x, EParent− surf is the total energy of the parent substrates(clean, hydrogenated or oxygenated surfaces), EAtom(x) is the total en-ergy of a free atom of element x and N is the number of element xatoms per surface unit cell; in these calculations N=2, since the

diamond (111) surface. The bond lengths are in Angstroms.

Table 3Calculated bond lengths (between bolded atoms) when ohmic contacts form on clean,hydrogenated and oxygenated diamond (111)(1×1) surfaces. The % change in bondlengths are given with respect to the approximated bond lengths, since no experimen-tal or theoretical data was available.

Adsorbingspecies

Approximated bond length(sum of covalent radii) (Å)

Relaxed bondlength (Å)

% change inbond length

C\Au 2.21 2.45 10.86C\Pd 2.08 2.24 7.69C\Ta 2.15 2.29 6.51C\Ti 2.13 2.31 8.45C\V 2.02 2.21 9.41C\H\Au 1.81 2.87 58.56C\H\Pd 1.68 2.92 73.81C\H\Ta 1.75 3.36 92.00C\H\Ti 1.73 3.43 98.27C\H\V 1.62 2.91 79.63C\O\Au 2.10 3.17 50.95C\O\Pd 1.97 2.39 21.32C\O\Ta 2.10 1.93 −8.10C\O\Ti 2.02 1.86 −8.60C\O\V 1.91 1.82 −4.71

Table 4Calculated PBE-GGA cohesive energies of the investigated elements on clean, hydroge-nated and oxygenated diamond surfaces.

Adsorbingspecies

Ecoh on cleandiamond surface(eV/atom)

Ecoh on hydrogenateddiamond surface(eV/atom)

Ecoh on oxygenateddiamond surface(eV/atom)

Hydrogen −4.264Oxygen −3.192Gold −2.000 −3.365 −1.939Palladium −3.250 −2.963 −3.032Titanium −5.582 −4.975 −6.261Tantalum −6.659 −6.012 −7.182Vanadium −6.577 −6.610 −7.785

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calculations were done for full monolayer coverages, as mentionedearlier. The results are shown in Table 4 and plotted in Fig. 5.

Table 4 shows that the cohesive energies of clean and oxygenatedsurfaces are higher for most metals compared to their hydrogenatedcounterparts except for gold on hydrogenated surface, an observationthat is corroborated quite well by the observed bond lengths changes.Considering the hydrogenated surface, Pd had the lowest cohesiveenergy of −2.963 eV/atom while V had the highest value of−6.610 eV/atom. Overall, Ti, Ta and V had higher cohesive energies,implying stronger bonds. Such bonds can be attributed to the carbidesthat form between the metals and carbon. Tantalum and vanadiumhad higher cohesive energies compared to titanium on all the threesurfaces. It has been known that, gold is traditionally used to formohmic contacts [17]. However, this work showed that it has a low co-hesive energy of ≈−2.00 eV/atom on both clean and oxygenated di-amond surfaces and a slightly high cohesive energy of −3.365 eV/atom on hydrogenated surface. This suggests weaker adhesiveness,which is only comparable to that of palladium. This means that goldand palladium form ohmic contacts that can easily detach from thediamond electronic device. In fact, the low cohesive energies of goldconfirm the already observed phenomenon where gold easily peelsoff from other surfaces, an observation which is attributed to theinert nature of gold. Indeed, this work confirms the observations ofGluche et al. [18] who have reported destruction of the gold–diamondcontacts under high power conditions. Palladium had relatively low

Fig. 4. Tantalum on (a) clean, (b) hydrogenated and (c) oxygenate

cohesive energies, though slightly higher than gold on clean and oxy-genated diamond surfaces. This suggests that, palladium and gold canbe used interchangeably. For this reason, gold is suggested to be usedas a capping layer for the ohmic contacts to eliminate other atmo-spheric effects such as oxidation, though its binding on the respectivecarbide forming metals was not tested. Comparing the three surfacesterminated by a single metal at a time, we notice that the oxygenatedsurface generally forms stronger ohmic contacts, followed by theclean surface and least by the hydrogenated ones due to the reasonsalluded to before.

3.3. Electronic properties of parent surfaces

3.3.1. Density of states (DOS) for clean diamond surfaceAlthough different surfaces were considered in this work, the

clean surface formed the basis for all of them. It was thus necessaryto determine its density of states first, so that the effect of the adsor-bates could then be established. Fig. 6 shows the DOS and PDOS for aclean diamond surface which are constituted of broad valence bandsand a slightly narrow conduction band with some states at theFermi level i.e., at 0 eV. Olguín [19] has argued that when a surfaceis introduced on an infinite periodic system, the system becomessemi-infinite, with the boundary conditions dictating that the wavefunction has to be zero at the surface. The new boundary conditionsmanifest themselves in changes in the energy spectrum and in the oc-currence of new states. The valence bands had a band width of≈21.5 eV, a slight deviation from that observed by Zheng et al. [2]of 21.71 eV. This value also compares well with 21.0±1.0 eVobtained by Himpsel et al. [20]. The empty conduction bands whichwere narrower than the valence bands had a band width of≈11.5 eV. A band gap of 4.56 eV was obtained, though it was muchsmaller than the experimental value of 5.5 eV [1]. Hafner et al. [21],

d diamond (111) surface. The bond lengths are in Angstroms.

Cln_Surf H_Surf O_Surf

En

erg

y (e

V/a

tom

)

0

-8

-6

-4

-2

Au_contactsPd_contactsTi_contactsTa_contactsV_contacts

Fig. 5. Calculated cohesive energies of the different ohmic contacts (metal adsorbates)on clean, hydrogenated and oxygenated diamond surfaces; (Cln surf represents cleansurface, while H surf and O surf are for the contacts on hydrogenated and oxygenatedsurfaces, respectively). The lines are a guide to the eye.

DO

S (

Arb

.un

its)

Energy (eV)

Fig. 7. DOS for hydrogenated C(111)-(1×1) surface.

14 I. Motochi et al. / Diamond & Related Materials 23 (2012) 10–17

obtained a band gap of 4.25 eV using a first principle approach. Thedeviation observed between our computed value and the experimen-tal one was attributed to the well known fact that both local densityapproximation (LDA) and generalized gradient approximations(GGA) tend to underestimate the fundamental gap [22].

A state that was characteristic of diamond was observed at slightlyabove −11.8 eV, a value not very far from −12.5 eV obtained byDerry et al. [23] from DFT calculations, and very close to −12.0 eVobtained by Zheng et al. [2] from first principles, and −13.2 eVobtained by Reinke et al. [24] from their experiments. There was evi-dence of the presence of states in the band gap as mentioned before,and these were attributed to the presence of dangling bonds on theclean diamond surface. There was, however, no evidence of any sur-face state effect extending into the bulk. This explains the preserva-tion of diamond bulk structure as seen in Fig. 2.a where there wereminimal changes in bulk bond length and bond angles, for deeplying layers.

3.3.2. DOS for hydrogenated diamond surfaceThe computed DOS for hydrogenated diamond surface (Fig. 7)

showed that states within the band gap were removed followingthe adsorption of hydrogen. We can therefore propose that hydrogenstabilizes the diamond surface. This is in line with the findings ofKawarada [25]. This led to the diminishing of the energy band gapcompared to that of clean diamond surface of 4.56 eV. A number ofstudies [26] have shown that hydrogen adsorption leads to negative

DO

S (

Arb

.un

its)

Energy (eV)

Fig. 6. DOS for clean C(111)-(1×1) surface. The surface consists of ten atoms in a fivebilayer slab.

electron affinity of diamond surface, a fact closely associated withthe increased surface conductivity, due to the reduced band gap. A va-lence band width of ≈22.00 eV was established, which was almostdouble as wide as the corresponding conduction band of 10.9 eV.There was no evidence of the effect of the adsorbed hydrogen atomsextending deep into the bulk, except for new but diminished peakswhich were visible at −0.7 eV, and −1.8 eV below the Fermi leveldue to the H-1s states.

3.3.3. DOS for oxygenated diamond surfaceJust like the DOS for hydrogenated surfaces where the states in the

band gap were removed by hydrogen adsorption, the DOS for oxy-genated diamond surface was also modified by oxygen adsorptionas seen in Fig. 8, a fact corroborated by the findings of Derry et al.[23]. The states near the valence band maximum (surface states) ap-pear to merge with the valence band, hence making the Fermi level(0 eV) to fall within the valence band. Oxygen does not therefore ap-pear to stabilize the diamond surface as much as hydrogen does, sincesurface states that were not present in the case of hydrogenated sur-face are present. A band gap of 3.7 eV was obtained for oxygenatedsurface, a value which was larger than that of a hydrogenated surface.The widening of the band gap suggests that oxygen adsorption makesthe diamond surfaces to acquire positive electron affinity [26,27],hence altering the surface conductivity. Some new states were ob-served at −4.5 eV, −2.5 eV and −7.3 eV below the Fermi level.These were attributed to O-2p orbitals (see Fig. 8). Using Ultraviolet

DO

S (

Arb

.un

its)

Energy (eV)

Fig. 8. DOS for oxygenated C(111)-(1×1) surface.

Energy (eV)

DO

S (

Arb

.Un

its)

DOS for V on hydrogenated diamond surface

DOS for V on oxygenated diamond surface

Fig. 10. Density of states of vanadium on oxygenated diamond surface (top panel) andvanadium on hydrogenated surface (lower panel).

15I. Motochi et al. / Diamond & Related Materials 23 (2012) 10–17

Photoelectron Spectroscopy (UPS) on oxygenated C(111)-(1×1) sur-face, Loh et al. [28] reported observing similar features associatedwith O-2p centered at ≈−4 and −8.5 eV. The observed conductionband width of 14.5 eV was still narrow compared to the valenceband which was ≈22.0 eV wide. A fairly prominent and narrowstate was visible at the higher binding energies at −20.2 eV attribut-ed to O-2s states. Such a state has been observed at −21 eV and−22 eV by Derry et al. [23] using the FHI 98MD code and Feng-Binet al. [29] using Castep Code, respectively.

3.4. DOS after adsorbing metals on the parent surfaces

In this sectionwe present results on the DOS for the carbide formingmetals only, since we have already established that they form strongcontacts suitable for diamond based electronic applications, as observedby their relatively high cohesive energies on the different surfaces.

3.4.1. DOS for carbide forming metals on clean diamond surfaceThe DOS for these metals (Ti, Ta and V) showed similar character-

istics to each other (see Fig. 9 for Ti on clean surface and Fig. 10) for Von H- and O-terminated surfaces, respectively. These metals removedthe energy band gap completely, hence rendering the diamond sur-face to exhibit a metallic character. It was also established that apartfrom the usual broad valence and narrow conduction bands onclean diamond surface, there were new states at high binding ener-gies (see middle panel of Fig. 11 for Ta on clean diamond surface).These states occurred at ≈−37.5 eV for vanadium (not shownhere), ≈−34 eV for tantalum (middle panel of Fig. 11) and≈−32 eV for titanium adsorbed on clean diamond (see Fig. 9), re-spectively. In the case of titanium on clean diamond surface, thesestates were due to Ti-2p orbitals. The d orbitals were observed tohave their effect mostly around the Fermi level, resulting in peaks at≈−0.4 eV and other peaks which manifest themselves as surfacestates just above the Fermi level. The states at high binding energiesmay explain the high cohesive energies observed for these metals.The conduction band was slightly wider as compared to that of theclean diamond surface thereby enhancing conductivity. The surfacestates observed on clean diamond surface were diminished, implyingthat the metals facilitate easy flow of charge carriers from the semi-conductor to the metal and vice versa. There were no significantchanges in the valence bands except for some new states appearingjust below the Fermi level in all the three cases. For instance therewere nice and well defined peaks at ≈−2.3 eV for tantalum,≈−1.32 eV for vanadium and at ≈2.0 eV for titanium on clean dia-mond (111)-(1×1) (see Fig. 9 for the Ti case) surface attributed toTa-4s, V-4s and Ti-4s orbitals, respectively.

DO

S (

Arb

.un

its)

Energy (eV)

Fig. 9. DOS for titanium on clean diamond surface.

3.4.2. Carbide forming metals on hydrogenated diamond surfaceHydrogen is one of the major terminating species in CVD grown

diamond. Just like for the clean surface where the DOS of the adsor-bates is compared with those of a clean surface, the DOS of themetal adsorbates is also compared with those of the hydrogenatedsurfaces. The middle panel of Fig. 12 shows the DOS for tantalum onthe hydrogenated surface, where the valence and conduction bandshad similar characteristics to those previously observed on the cleansurface i.e., wide valence bands and much narrower conductionbands joined by diminished states around 0 eV.

As can be seen from the middle panel of Fig. 12, when a carbideforming metal is adsorbed on hydrogenated diamond, the conductionband reduced in width to ≈10 eV when measured from the Fermilevel, while the valence band showed an increase, giving the widestbandwidth of ≈24 eV compared to that of the clean surface (21 eV).There was no energy gap, indicating the metallic nature of the surface.For hydrogen terminated surfaces, tantalum, titanium and vanadiumhad surface states at 0.6 eV, 0.8 eV and 0.26 eV, respectively, abovethe Fermi level attributed to d orbitals of the respective metals.There were new states formed just below the Fermi level in all thethree cases, with tantalum terminated surfaces showing states at−3.5 eV, and−0.5 eV due to Ta-5d orbitals while for titanium termi-nated surface, they were seen at −1.94 eV, and −0.51 eV due to Ti-3d orbitals. Similar states were also seen in the case of vanadium onhydrogenated surface at −1.0 and 0.5 eV due to V-3d orbitals (notshown here). The states observed at high binding energies when

DOS for clean diamond surface

DOS for Ta on clean diamond surface

DOS for Au on clean diamond surface

Energy (eV)

DO

S (

Arb

.Un

its)

Fig. 11. Comparison of DOS for tantalum and gold on clean diamond surface with thatof the clean surface.

DO

S (

Arb

.Un

its)

Energy (eV)

DOS of hydrogenated diamond surface

DOS of Ta on hydrogenated diamond surface

DOS of Au on hydrogenated diamond surface

Fig. 12. DOS for gold and tantalum on hydrogenated surface compared to their hydro-genated diamond surface.

DOS for oxygenated diamond surface

DOS for Ta on oxygenated diamond surface

DOS for Au on oxygenated diamond surface

Energy (eV)

DO

S (

Arb

.Un

its)

Fig. 13. DOS for gold and tantalum on oxygenated surface compared to their oxygenat-ed diamond surface.

16 I. Motochi et al. / Diamond & Related Materials 23 (2012) 10–17

carbide forming metals adsorb on clean diamond surface were alsoobserved on the hydrogenated surface at approximately the same en-ergies they were previously established (i.e., at ≈−37.5 eV for V,≈−34 eV for Ta and ≈−32 eV for Ti, attributed to 2p orbitals of therespective metals).

3.4.3. Carbide forming metals on oxygenated diamond surfaceThese metals had high cohesive energies when adsorbed on oxy-

genated diamond surfaces, hence stronger bonding, a phenomenonwhich was attributed to states at high binding energies (see the mid-dle panel of Fig. 13). The states at high binding energies were at ap-proximately the same position as they were when these metalswere adsorbed on clean surfaces (see the middle panel of Fig. 11)and on hydrogenated surface (see middle panel of Fig. 12). Thesestates were therefore not affected by the oxygen or the hydrogen in-terfacing the metal and diamond.

The valence band width of an oxygenated diamond surface termi-nated with tantalum was 23.2 eV which was wider than that of theclean surface (21 eV) but narrower than on a hydrogenated surface,(24 eV). The conduction bandwidth was ≈12 eV (see Fig. 13),which was a bit wider than that of the hydrogenated diamond surface(11 eV) (see Fig. 12) and equal to that of the clean surface (seeFig. 11). The band gap was totally eliminated upon the adsorption ofTi, Ta and V on the oxygenated diamond (111) surface, making thesurface to exhibit metallic character. New states occurred at 1.79 eVabove the Fermi level in the case of a tantalum terminated surface,2.0 eV (see top panel of Fig. 10) above the Fermi level in the vanadi-um terminated surface and of 1.5 eV above the Fermi level in the tita-nium terminated surface. Just like for the carbide forming metals onclean and hydrogenated diamond surfaces, new states were onlyseen close to the Fermi level attributed to the d orbitals of the respec-tive metals.

4. Conclusions

The study has revealed a clear correlation between C\metal,C\H\metal and C\O\metal bond lengths and cohesive energies.A shorter bond length between atoms resulted in stronger bonds,hence a correspondingly high cohesive energy. Similarly, a longbond length as evidenced in the case of gold on all substrates was apointer to weak bonding. This was further confirmed by the low co-hesive energies of gold on diamond which was a result of their inert-ness, and hence the adherence and mechanical integrity of pure gold–diamond contacts are generally poor. The states responsible for thestrong bonding in the case of Ti, Ta and V (at high binding energies)were absent in the case of Au and Pd. In spite of this, they still had

expanded conduction bands just like in the case of Ti, Ta and V. Vana-dium, tantalum and titanium had shorter bond lengths especially onthe oxygenated surface and hence the reason for the higher cohesiveenergies among the metal contacts investigated. These characteristicsfit in well with diamond electronic devices that are often used or areenvisaged to be used under harsh environments.

Indeed cohesive energies of the different metals on the three pri-mary surfaces (clean, hydrogenated and oxygenated surfaces)showed that gold bonds weakly on all of the surfaces compared tothe other metals. Just like gold, palladium also showed a ratherweak bonding on all the three surfaces. Though Pd is not a noblemetal to exhibit inert behavior, this phenomenon may be attributedto its chemistry of having filled d orbitals. The known carbide formingmetals on the other hand had strong bonds formed between them asconfirmed by their high cohesive energies.

The best metals according to this study, for use as ohmic contactsin diamond-based electronics are therefore proposed to be tantalumand vanadium due to their strong adherence properties. They also re-move the band gap on the three surfaces, giving the surfaces a metal-lic property which is necessary for smooth transfer of charge carriersacross the metal diamond interface. These adhere more to the oxy-genated surface, followed by the clean surface and least of all on thehydrogenated surface.

Acknowledgments

The authors are highly indebted to INFM/Democritos NationalSimulation Center, ICTP, ICMR and the Addis Ababa University forjointly inducting them to the use of Quantum-ESPRESSO packageused in this work. The Computational Materials Science Group ofChepkoilel University College is thanked for their positive criticism,assistance and constructive discussions. The Department of Physics,Chepkoilel University College is also appreciated for its sponsorship.The Kenya Government through the National Council for Scienceand Technology (NCST) is highly thanked for providing support inthe form of a research grant.

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