The Influence of Dopants on the Growth of Diamond by CVD

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2009

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 594

The Influence of Dopants on theGrowth of Diamond by CVD

TANGUY VAN REGEMORTER

ISSN 1651-6214ISBN 978-91-554-7396-9urn:nbn:se:uu:diva-9539

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A Bon Papa

“J'aime les papillons Car ils sont éphémères

Ils traversent notre ciel printanier En jetant mille couleurs

Et disparaissent”

J. de Rudder

List of Papers

This thesis is a summary based on the following papers, which are referredto in the text by their Roman numerals:

I. Effect of co-adsorbed dopants on diamond initial growthprocesses: CH3 adsorption

T. Van Regemorter, K. Larsson, J. Phys. Chem. A 2008, 112, 5429-5435

II. Effect of co-adsorbed dopants on initial diamond growthsteps: H abstraction from an adsorbed CH3

T. Van Regemorter, K. Larsson, Submitted to Diam. Rel. Mater.

III. A theoretical study of nitrogen-induced effects on diamondCVD growth

T. Van Regemorter, K. Larsson, Chemical. Vapor Deposition 2008, 14, 224-231

IV. Effect of Substitutional N on Important CVD DiamondGrowth Steps

T. Van Regemorter, K. Larsson, Submitted to J. Phys. Chem. A.

V. Effect of a NH co-adsorbate on the CH3 (or CH2) adsorptionto a surface step on diamond (100)

T. Van Regemorter, K. Larsson, Submitted to J. Phys. Chem. A.

Contents

1. Introduction ............................................................................................... 91.1 Diamond .............................................................................................. 91.2 Chemical Vapour Deposition ............................................................ 10

1.2.1 General ...................................................................................... 101.2.2 Growth mechanism ................................................................... 11

1.3 Impurities .......................................................................................... 151.3.1 Nitrogen ..................................................................................... 151.3.2 Boron ......................................................................................... 161.3.3 Phosphorous .............................................................................. 171.3.4 Sulphur ...................................................................................... 17

2. Computational methods and models ........................................................ 182.1 Ab initio approach ............................................................................. 182.2 Density Functional Theory ................................................................ 192.3 Basis sets ........................................................................................... 202.4 Surface models for diamond ............................................................. 202.5 Electronic analysis ............................................................................ 21

3. Results ..................................................................................................... 223.1 Introduction ....................................................................................... 223.2 Effect of atomic nitrogen .................................................................. 23

3.2.1 Effect of a co-adsorbed NHx species on the diamond surface .. 233.2.2 Effect of substitutional N .......................................................... 253.2.3 Effect of a NH co-adsorbate next to a surface step .................. 37

3.3 Effect of phosphorous, sulphur or boron atom ................................. 413.3.1 CH3 adsorption reaction ............................................................ 413.3.2 H abstraction reaction ................................................................ 43

4. Concluding remarks ................................................................................. 454.1 Effect of atomic nitrogen .................................................................. 454.2 Effect of phosphorous, sulphur or boron atom ................................. 46

5. Future works ............................................................................................ 47

6. Populärvetenskaplig sammanfattning ...................................................... 48

7. Acknowledgments ................................................................................... 50

8. References ............................................................................................... 52

Abbreviations

CVD Chemical Vapour DepositionDFT Density Functional TheoryBO Born-Oppenheimer ApproximationLDA Localized Density ApproximationGGA Generalized Gradient ApproximationLCAO Linear Combination of Atomic OrbitalHF Hartree-FockKS Kohn-ShamR Reactant P ProductI IntermediateTS Transition State

1. Introduction

1.1 DiamondThe exceptional properties of diamond makes it a major candidate for a

variety of applications [1–3]. For instance, its very high hardness coupledwith a high thermal conductivity, which enables to work at high tempera-tures (around 700°C), make diamond suitable for the machining of hard ma-terials. Additionally, diamond is chemically inert, what allows its use in ag-gressive environment (acidic, oxidizing, etc.). Its compatibility with humantissues opens up application possibilities in life science or bio-electronics[4]. Other properties like its transparency to UV and IR, low dielectric con-stant, low thermal expansion, high breakdown voltage, high carrier mobility,etc. makes diamond a promising material for applications in optics, electron-ic devices, etc. However, due its low natural abundance and the fact that itcan only be found as a gemstone, natural diamond is not appropriate for in-dustrial applications which requires thin films or the possibility to coat onanother material. The development of a controlled method for the growth ofsynthetic diamond on various substrates is then highly required.

Diamond is known to be only composed of carbon since Lavoisier [5], andlater Tennant [6], discovered it in 1772. It was later defined that, at normalpressure and temperature conditions (20°C and 1 atm.), graphite is the moststable allotrope of carbon and that the existence of diamond is only due tothe extremely large activation barrier that exists between the two forms [7].This metastability of diamond implies complications when it comes to syn-thesis. Two different main growth methods exist. The first one is based on ahigh pressure and high temperature technique (HPHT). With this method,graphite is placed in a press where the temperature and the pressure are in-creased until the point is reached when diamond is the most stable phase ofcarbon [8]. The first successful attempts to grow diamond with this methodwere performed by Liander and Lundblad in 1953 [9], followed by success-ful attempts from the General Electric Corporation in 1955 [10].

The other main growth method, called chemical vapour deposition (CVD),is based on a low pressure technique in which diamond, being a metastablephase, is deposited on a substrate. Diamond is then “trapped” on the surfaceby the use of precursors with high chemical potentials [8]. The first success-ful growth of diamond by using CVD was performed in the beginning of the1950s by Eversole, involving the activation of pure grade methane with hightemperature [11]. A few years later, Angus et al. confirmed the feasibility of

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the process by doing a careful analysis of the growth [12]. The addition of ahigh H2 concentration in the gas phase was then shown to significantly im-prove the growth process [13]. These initial successes in the growth of dia-mond at low pressure induced an increased interest for diamond due to itsextraordinary materials properties. In the mid-1970s, Derjagin and co-work-ers managed to synthesize diamond films on a non-diamond substrate at asignificant growth rate [14]. In the early 1980s, Setaka et al. described sever-al methods that may be useful for diamond deposition on non-diamond sub-strates [15].

1.2 Chemical Vapour Deposition

1.2.1 General

Diamond CVD growth is based on the activation of a H2/CH4 gas mixturecontaining high hydrogen concentration (> 90%) [16]. The gas phase activa-tion is commonly accomplished using either a microwave plasma or a hotfilament. The high electrons velocity in the plasma, or the high temperatureof the filament (about 2200°C), induces homolytic cleavages of the gaseousmolecules with the formation of radical and non-radical species (H, CH2,CH3, C2H2, etc.). These species react then with the growing surface through acomplex and dynamic chain of reaction steps (e.g., H abstraction, CH3 ad-sorption, CH2 insertion, etc.) which all together forms the diamond growthmechanism (see Figure 1).

Figure 1. Representation of the chemicalvapour deposition (CVD) process.

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The growth conditions with high H2 concentration have been establishedby Chauchan, Angus and Gardner in 1976, who observed that a large con-centration of radical H in the gas phase is essential for the etching ofgraphite otherwise formed on the diamond surface [13]. Using traditionalCVD growth methods, with more than 90% H2 in the gas phase, mono- orpoly-crystalline films will be formed depending on the type of substrate. Sin-gle crystalline diamond (SCD) thin films can be obtained with single crystaldiamond as substrate [17]. For the growth on another substrate like silicon,poly-crystalline (PCD) films are usually obtained [18]. Nano-crystalline dia-mond (NCD) films can also be grown in a hydrogen-rich atmosphere onnon-diamond substrates, with grain sizes between 30 and 100 nm (a high nu-cleation rate is required at the beginning of the growth process in order toform a complete film as fast as possible) [19,20]. Even ultra-nano crystallinediamond (UNCD) films can be grown, with nano-meter scale (around 15nm) particles. An Ar/CH4 mixture is then used without the addition of a largeamount of H2 [21,22]. Some more exotic methods using pulsed laser [23] orpulsed arc discharge [24] have also shown the possibility to grow diamondin a hydrogen-free environment.

1.2.2 Growth mechanism

Due to the large concentration of H radicals in the gas phase, the growingdiamond surface will in principle be completely saturated with hydrogenatoms. However, the gaseous H radical will also induce the formation of rad-ical carbons on the surface. The amount of surface radicals is defined by adynamic equilibrium between the H abstraction reaction, producing surfaceradicals and H2 molecules [1.1], and the H adsorption reaction, saturating thesurface radical carbons [1.2].

Cd-H + H• � Cd• + H2 [1.1]

and

Cd• + H• � Cd-H [1.2]

where Cd-H and Cd• represent the H-terminated and the radical carbon on the

diamond surface [25]. The inverse of reaction [1.1] has been shown to benegligible if the fraction of radical H in the gas phase is sufficiently high[26]. The heat of reaction for reaction [1.2] is usually that large that it willmake the reverse reaction (e.g., desorption of H) highly improbable. The bal-ance between the formation of surface C radicals and the recombination toC-H bonds, was calculated by Goodwin et al. to produce a concentration of

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surface carbon radicals, which is independent of gas phase composition dur-ing the growth [26].

While surface migration of adsorbed species is expected to take place in ageneral CVD process of thin films, diamond growth constitutes an excep-tion. The possibility for hydrogen migration on a flat (111) diamond surfaceshas been studied theoretically, and the calculated activation barrier has sug-gested this migration to be of no importance for the growth [27,28]. Hydro-gen migration between two neighbouring C-C dimers was also calculated tobe slow on the diamond (100)-2x1 surface [29,30]. However, H migrationfrom a mono-atomic step to a lower positioned terrace radical [31], or be-tween adsorbed species (e.g., CH3) and a neighbouring surface carbon[29,32], has been calculated to be fast. This type of migration is for diamond(100)-2x1 considered to be involved in the growth mechanism.

Following the abstraction of H from the growing diamond surface, an acti-vated carbon-containing growth precursor will be adsorbed on the newlyformed surface C radical. The gas phase composition has frequently beenstudied both experimentally and theoretically and it is generally acceptedthat the most abundant species within a traditional CVD set-up are CH3 andC2H2 [33–35]. The radical nature of CH3 makes it the most plausible candi-date as dominant diamond growth precursor [36]. This is supported by an ex-perimental work focusing on the relative importance of C2H2 vs. CH3 in thegrowth mechanism [37]. The main conclusion was that CH3 is most probablythe main growth precursor for both (100) and (111) surface orientations.

A CH3 adsorption on the diamond surface is generally assumed to be fol-lowed by a second H abstraction reaction to form an adsorbed CH2. The fol-lowing steps within the reaction mechanism will then become strongly de-pendent on the orientation of the diamond surface, out of which (100) and(111) are the most frequently observed. An H-terminated (111) surface isknown to remain unreconstructed, but the (100) plane is known to undergo a2x1 reconstruction (for both non-terminated and H-terminated surfaces)[38,39]. These experimental observations have been confirmed theoreticalby obtaining a larger stability for the reconstructed surface compared to theunreconstructed one [40,41]. The present work has focused on these two sur-faces; (111) and (100)-2x1 (see Figure 2). However, the (110) and (113) sur-

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Figure 2. Representation of the a) H-terminated (111) and b) 2x1 reconstructed H-terminated (100) diamond surface.

faces are also important for the growth of diamond films with, at the sametime, a good control of the morphology [42].

1.2.2.1 Growth mechanism on the (100)-2x1 surfaceFor the (100)-2x1 diamond surface, the most accepted growth mechanism

has been proposed by Garrison et al. [43], which has been further investigat-ed by Harris and Goodwin [44]. This growth mechanism, sketched inFigure 3, is composed of 4 steps following the formation of a surface C radi-cal by an H abstraction reaction. The adsorption of CH3 on the surface car-bon radical is followed by the formation of an adsorbed CH2, obtained bygas phase H abstraction from CH3. This CH2 adsorbate is thereafter consid-ered to be inserted within a surface carbon dimer by an opening of the dimer(with the formation of a double C-C bond) followed by the closing of thering through the formation of a new C-C bond. The last step, the ring-clos-ing, is calculated to have a large activation barrier and is generally consid-ered as the limiting step of the whole mechanism [45–47].

Within a classical growth process, the formation of a smooth surface is as-sociated with surface growth by a step-flow mechanism. This mechanismconsiders a growth species, initially adsorbed on a flat terrace, migrating to-wards a step edge where it gets finally incorporated within the crystal lattice.The step flow mechanism is generally considered to take place by the diffu-sion of the active carbon-containing species on the surface. For the diamondCVD growth, experimental evidence are generally obtained for a step flowgrowth mechanism under appropriate conditions [48–50]. From these obser-vations, the surface migration of carbonaceous species was initially consid-ered to occur on the diamond surface and the mechanism has been investi-

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Figure 3. Representation of the growth mechanism on (100)-2x1 surface proposedby Garrison.

gated theoretically [51,52]. The possible existence of the C migration on thesurface has been reiterated within two recent theoretical works [47,53].

However, the existence of a C surface migration is still under debate andanother mechanism has been proposed to explain the observed step flowgrowth process. It introduces the concept of “preferential etching” of an iso-lated CH2 species on a flat terrace, compared to the etching of CH2 adsorbednext to a step [54]. This etching mechanism has been proposed to occur withthe support of atomic H [54]. As mentioned by D'Evelyn et al., since the twomodels present their own limitations, both etching and short range migrationmight occur during the growth on the diamond surface [55].

The final phase of the growth mechanism is the incorporation of the car-bonaceous species into a surface step edge. The H-terminated (100)-2x1 dia-mond surface is observed experimentally as an alternation of mono-atomicSA and SB steps oriented towards the <110> directions, and delimiting ter-races of different heights [56]. From Chadi's definition, a step is called SA

when the dimerisation direction (or the dimer line) of the upper terrace isparallel to the step edge, and is called SB when the direction is perpendicular(see Figure 4) [57]. A step flow growth process is generally considered to oc-cur by extension of dimer rows and the dimer propagation of SB steps is ob-served to be faster than the SA step. SB steps also present more irregularitiesand even some extensions of single row dimer [58,59]. This obvious differ-ence in behaviour can be explained by the presence of an H at the SB stepwhich induces, by its removal, a radical carbon more stable than on the ter-race. Compared to SA steps where no radicals can be formed, the possible ex-istence of this radical makes SB steps more reactive towards the CH2 incor-poration [60–62].

1.2.2.2 Growth mechanism on the (111) surfaceThe (111) growth mechanism has also been largely studied theoretically

and various mechanisms have been proposed [63–66]. It has been calculatedthat a gaseous CH3 can either be adsorbed on a flat terrace or next to a stepedge followed by an H abstraction reaction to form an adsorbed CH2 species[36,67]. In this latter position, the adsorbed CH2 species can be incorporatedinto the lattice (in the presence of a carbon radical on the step) by the forma-

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Figure 4. Representation of step type a) A and b) B on the (100)-2x1:H reconstructeddiamond surface.

tion of a new C-C bond [68]. The possibility for surface migration of CH2

has been calculated to be feasible [69] but it has not been confirmed experi-mentally.

1.3 ImpuritiesAt room temperature, diamond is an insulator with a wide band-gap of

5.50 eV. Its exceptional properties, significant for electronic applications,have motivated many researchers to convert it into a conductor and semi-conductor material by the addition of impurities within the carbon lattice[70]. The most important dopants which can be substitutionally incorporatedinto the diamond lattice are N, P, S and B. Their incorporation feasibility andeffect on the diamond properties and diamond CVD growth will be dis-cussed in the following sections.

1.3.1 Nitrogen

A nitrogen atom, N, can easily replace carbon atom within the diamondlattice and the formation energy of a substitutional N defect has been calcu-lated to be low [71,72]. Its presence into the lattice induces a level in theband gap 1.7 eV below the conduction band. This electronic level is too lowfor using diamond as semi-conductor in devices at room temperature [73].The underlying reason to this low level is due to a structural reconstructionwhich takes place around the N dopant. The extra valence electron in N(compared to C) has been calculated to occupy the anti-bonding part of oneC-N bond which thereby becomes elongated [74–76].

In 1994, an important effect of N on the chemical vapour deposition pro-cess was observed for the first time. Locher et al. [77] and Jin and Mous-takas [78] observed that the presence of nitrogen in the gas phase willstrongly affect the growth rate and the final surface morphology. From hereon, it was observed that for a small N/C ratio the growth rate will be en-hanced and the surface morphology will exhibit a more pronounced <100>texture [79–81]. For larger N concentrations, the diamond film presents anano-structured morphology with a significant amount of sp2 carbons whichcan be explained by an increase of the secondary germination process[82,83]. The growth rate is also observed to decrease for a large N concen-tration in the gas phase.

Besides the large amount of experimental work performed on the effect ofN on diamond growth, only a few theoretical studies have been devoted tothis topic and the important effect of nitrogen is still not fully understood.Recently, Butler et al. proposed that the growth rate will increase on the dia-mond (111) surface with the help from CN species produced in the gas phase[66]. Within previous theoretical studies on the diamond growth mechanism,

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they suggested that the nucleation of a new carbon layer is the limiting stepfor the growth [84,85]. Their hypothesis is based on the fact that the creationof a new island, initiating the nucleation of a layer, requires the formation ofan adsorbed ethyl radical. Due to the presence of a terminal radical, the des-orption of this ethyl radical through a β-scission mechanism will competewith the formation of an island. They proposed that, since the CN speciesdoes not present a terminal radical, the desorption is less probable and thenucleation of a new carbon layer will take place more easily [66]. Whilst thisexplanation is interesting for the (111) surface orientation, it is difficult toapply it to another surface orientation where the presence of species withtwo carbon is less crucial, e.g., for the (100) surface orientation.

Frauenheim et al. proposed that the increased diamond (100) growth rateis induced by the presence of substitutional N within the diamond lattice. Itis well known from bulk studies that substitutional N will induce a latticedistortion due to the occupation of an anti-bonding C-N orbital by the“extra” electron in N (compared to C) [74–76]. When an empty, or partiallyempty, state is available in the band gap (e.g., originating from radical sur-face sites), it is observed that the “extra” nitrogen electron will easily betransferred towards this available state [86,87]. They especially observedthat the electron can be transferred into the anti-bonding orbital of a C-Cdimer bond which lengthens the bond and creates a possible adhesion site fora gaseous CH2. There is a weakness in this explanation since it implies theparticipation of gaseous CH2 presents in low concentration in the gas phase.

1.3.2 Boron

The boron atom, B, can also easily be substitutionally incorporated intothe diamond lattice since its presence has been found to be thermodynami-cally favoured [71]. It has been of a large interest to study since it will affectthe diamond properties differently depending on its concentration in the lat-tice. For a low boron concentration, the insulating diamond material is trans-formed into a p-type semi-conductor with a level 0.37 eV above the valenceband edge. For a high boron concentration, the diamond will even presentmetallic properties [88]. Boron doped diamond has even been reported to bea superconductor at temperature below 4K [89].

Due to the impact of boron on the diamond properties, it is of major inter-est to study its influence on the CVD growth process. While the diamondsurface morphology is observed to be affected by the presence of boron inthe gas phase [90], the growth rate is only slightly affected for low B con-centrations and is observed to decrease with an increase in boron concentra-tion [91]. To the knowledge of the author, the only theoretical work per-formed within this topic considers the B incorporation mechanism into thediamond lattice [92]. However, theoretical studies on the effect of boron onthe diamond growth process is missing.

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1.3.3 Phosphorous

The interest for phosphorous as a dopant has largely increased after thatKoizumi et al. managed to incorporate P into the diamond lattice, therebytransforming the insulator into an n-type semi-conductor (the level is 0.6 eVbelow the conduction band) [93]. This successful incorporation made thefirst diamond-based pn junction possible for a light-emitting diode [94]. It isthen of great interest to incorporate P into the diamond lattice but the largeradius difference between P and C makes the process thermodynamically un-favoured [71]. In contradiction to N, the “extra” valence electron within sub-stitutional P, compared to C, has been calculated to not induce an asymmet-ric bond elongations with the surrounding carbons [95]. It has been observedexperimentally that the presence of P in the gas phase induces an increase ingrowth rate but the number of experimental studies is rather limited and notheoretical studies have been found [96].

1.3.4 Sulphur

The incorporation of sulphur into the diamond lattice has also been widelyinvestigated since experimental studies have shown that diamond doped withsulphur by ion implantation methods presents a shallow donor level [97].This interesting observation has induced further investigations consideringthe incorporation of S into the lattice during the CVD growth process[96,98]. These studies have shown that the growth rate will generally de-crease in the presence of sulphur in the gas phase. Analysis of the gas phasechemistry during the growth, in the presence of sulphur, suggested a modifi-cation of the key growth species [99,100]. However, the effect of S on thesurface chemistry is still not fully understood [101].

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2. Computational methods and models

“Every attempt to employ mathematical methods in the study of chemicalquestions must be considered profoundly irrational and contrary to the spiritof chemistry. If mathematical analysis should ever hold a prominent place inchemistry – an aberration which is happily almost impossible – it would oc-casion a rapid and widespread degeneration of that science.”

Augustus Compte, French philosopher, 1798 – 1857; in Philosophie Positive, 1830 [102]

2.1 Ab initio approachThe description of many-particles systems (i.e., molecules or solids) can be

obtained by the resolution of the time-independent Schrödinger equation [2.1].

H� = E� [2.1]

where H is an operator called Hamiltonian which contains the kinetic andpotential energy operators, E is the total energy and � is the many-electronwave function. Unfortunately, the analytic solutions of this equation can onlybe found for H like atoms which posses only one electron (e.g., H, He+, etc.).For the more interesting cases, such as molecules or surfaces, exact solutionsare not available and approximations are required [103].

The total energy of a system is dependent on five contributions: the kinet-ic energy of each nucleus (TN) and electron (Te), the attraction between eachelectron and nucleus (VeN) and the internuclear and inter-electronic repulsionpotentials (Vee and VNN). The much lower mass of the electron compared tothe nuclei implies that they are much faster and can be considered as movingin the field of fixed nuclei. This is known as the Born-Oppenheimer (BO)approximation [104]. Within this approximation, the total wave function � isseparated into �e, describing the electronic behaviour, and �N, describing thebehaviours of the nuclei. The two part can now be solved separately.

For the electronic part of the wave function, Hartree proposed in 1928[105] to approximate the many-electron wave function as a product of singleparticles functions:

�e(r1,r2,...) = �1(r1) ... �2(r2) [2.2]

where each of the functions �i(ri) is a one-electron Schrödinger equation. Inorder to satisfy the Pauli principle, Slater and Fock proposed to include anon-local exchange term in the equation by describing the wave functionwith a single determinantal function (the Slater determinant) [106,107]. This

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iterative procedure is known as the Hartree-Fock (HF) method, also called“self-consistent” method.

Despite the beauty of the method, the use of a single configuration (or Slaterdeterminant) wave function leads to poor energy because it completely ne-glects correlation energy (defined as the difference between the energy calcu-lated with the HF method and the exact ground state energy within the BO ap-proximation) [108,109]. A better approximation, used in the configuration in-teraction (CI) method, can be obtained by including a linear combination ofmany other configurations. Despite the possibility to, in principle, obtain theexact wave function with this method, the important resources required by themethod makes it inapplicable for systems larger than few tens of atoms.

2.2 Density Functional TheoryOn an initial proposition from Thomas and Fermi, another approach de-

veloped by Hohenberg and Kohn in 1964 is using the density of electrons,n(r), to described the system instead of the wave function used in the HFmethod [110]. They demonstrated that the properties of a molecule in theground electronic state (e.g., the total energy E0) are determined by theground state electron density function (ρ0). In other words, the energy, E0, isa functional of ρ0. Unfortunately, while their theorem defines the functional,it does not explain how to find it [102]. In 1965, Kohn and Sham proposed amethod allowing to calculate the molecular properties from the electron den-sity [111]. Their first idea was to express the molecular energy as a sum ofterms:

E0[ρ(r)] = T[ρ(r)] + EeN [ρ(r)] + Eee [ρ(r)] [2.3]

where T is the kinetic energy and EeN and Eee are the nuclear-electron attrac-tion and the electron-electron repulsion, respectively. They introduced there-after the concept of a non-interacting reference system built from a set of or-bitals (i.e., one electron functions) called the Kohn-Sham (KS) orbitals, suchthat the major part of the kinetic energy can be computed to good accuracy.Since only EeN [ρ(r)] can be exactly defined in equation [2.3], they reformu-lated the equation as a deviation from the energy of an idealized system withnon interacting electrons. This deviation, called the exchange-correlationfunctional (Exc), is the problematic term of the DFT method which requiresthe use of approximations.

Many functionals of different kinds have been developed to approximatethis term, Exc. For this purpose, the electronic behaviour was first defined bya hypothetical uniform electron gas for which the form of Exc is known ex-actly, or at least with a very high accuracy. This approach is named the localdensity approximation (LDA). While it is a fairly good model for simplemetals such as sodium, LDA poorly describes systems with rapid changes in

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electron density (as for example in molecules). This initial approximationhas been improved by the addition of information about the gradient of thecharge density. It conducts to the method known as the general gradient ap-proximation (GGA). The far better results obtained with the GGA approxi-mation [112] lead to an increasing use of DFT methods that made possiblethe use of models containing more than 100 atoms.

The unknown Exc energy can be split into its exchange and correlationcontributions. Since the exchange energy part can be computed exactly witha Slater determinant, hybrid functionals have been developed. It contains afitted amount of exact exchange energy from the HF picture and an approxi-mate functional for the electron correlation part.

Within this work, the PW91 functional – Perdew-Wang [113] – has beenused in Papers I, II and III, the BLYP (a hybrid functional where the ex-change and correlation parts are generated by B88 [114] and LYP [115] re-spectively) in Papers IV and V and B3LYP (hybrid functional, where theelectron exchange part is described using the Becke three parameter hybridfunctional [116] and the electron correlation part is described by the LYPfunctional) in Paper IV.

2.3 Basis setsWithin the DFT formalism, the electronic density is described by the KS

orbitals. However, these orbitals are unknown and they have to be approxim-ated by a linear combination of basis functions, called basis set, using theLinear Combination of Atomic Orbital (LCAO) approach. In theory, an in-finite amount of basis functions is required but this is technically and prac-tically impossible. The bigger the basis set, the more flexible spatial space isallowed for the electrons and the better is the approximation. However, italso implies larger computer resources. Atom centred (or localized) basissets can be used for both isolated molecules and periodic systems like bulkmaterials, but plane wave basis sets can only be used for period models.

2.4 Surface models for diamondA surface can be seen as infinite in x- and y-directions and semi-finite in

z-direction. It can be represented by an infinite repetition of a unit-cell usingperiodic boundary conditions (PBC). The complicated part is the representa-tion of the semi-finite character in the z-direction, which can not be mod-elled easily. The surface is then represented by a slab with a finite thickness.For diamond, the lowest positioned carbon layer needs to be terminated withhydrogen atoms in order to saturate the otherwise radical carbons and also tosimulate bulk conditions. Since the unit-cell is also infinitely repeated in thez-direction, a vacuum layer needs to be set in order to avoid interactions be-

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tween the slabs. This method is used within CASTEP [118] and Dmol3 [119]programs from Accelrys, inc. Another way to model a surface is to constructa finite cluster. For diamond, the unsaturated carbon bonds also need to beterminated with H and the structure have to be partially frozen to avoid unre-alistic reconstruction of the surface. This method is used within Gaussian 03[120].

2.5 Electronic analysisThe electron density approximated with DFT methods gives access to

electronic properties such as atomic partial charge and bond population.These two properties need to be calculated in order to obtain a better under-standing of the structures and especially the reactivity of the surfaces. How-ever, the atomic charge and the bond order can not be experimentally mea-sured (it is not an observable). The problem is to define the meaning of “anatom in a molecule” [102]. Several methods have been proposed to definethis meaning. Three different methods have been used in this thesis, all ofwhich will be described below.

Mulliken defined a bond between two atoms by overlapping orbitals. Healso assumed that the electrons inherent to each atoms are obtained by shar-ing the electrons within the overlapping orbitals equally [121]. The method,known as Mulliken population analysis, presents some limitations; i) non-physical negative electronic populations for small magnitudes, ii) a signifi-cant sensitivity to the basis set used and iii) unreasonable charge distributionfor compounds presenting significant ionic character [122]. However, its usefor covalent materials like diamond gives a reasonable picture of the chargeevolutions, especially when studying trends for similar systems. This analyti-cal method is included within CASTEP software package [123].

The natural population analysis method, based on the construction of anorthonormal set of natural atomic orbitals (NAOs), proposed a solution tothe problems of the Mulliken method. The use of an orthonormal set of or-bitals has been shown to improve significantly the computed atomic chargesand bond populations [122]. This method is performed by the NBO (v3.1)program within Gaussian 03.

The Hirshfeld partitioned charges are defined via the electron deformationdensity. The deformation density is the difference between the electron densityof the atoms in the molecule and electron density for the isolated atoms [124].This analytical method is included in the DMol3 software package.

21

3. Results

“A surface is a form of matter with its own chemistry. In its structure andreactivity, it will bear resemblance to other forms of matter: bulk; discretemolecules in the gas phase and various aggregated states in solution. And itwill have differences.”

R. Hoffmann. [117]

3.1 IntroductionThe main focus of this work was to study theoretically the effect of a

dopant on reactions taking place on the diamond surface during the CVDgrowth process. As presented in the Introduction, the CVD growth mecha-nism is composed of many reaction steps making it difficult to study thedopant's effects on all of them. In order to understand how a dopant is affect-ing the growth process, some specific key reactions have been investigated.In a first approximation, the growth process is considered to occur through 3main steps: i) CH3 adsorption, ii) CH2 migration, and iii) final CH2 incorpo-ration into a step. The CH2 was assumed to be formed by H abstraction froman adsorbed CH3. During the migration of CH2 on the (100)-2x1 surface, anCH2 insertion into a carbon dimer is expected to occur. This may also be anisolated step with a resulting incorporation into the lattice. During all ofthese surface processes, the possibility for H to migrate from a surface C to aneighbouring adsorbed CH2 species must not be forgotten. It is worth men-tioning that the existence of these surface reaction growth steps are still un-der debate. For instance, the CH2 migration on the diamond surface duringgrowth has not been verified experimentally. The effect of N on all of theseindividual elementary reactions have in this work been theoretically investi-gated with the main purpose to outline plausible shift of rate determining re-action steps.

22

3.2 Effect of atomic nitrogen

3.2.1 Effect of a co-adsorbed NHx species on the diamond surface

Within Papers I and II, the effects of a co-adsorbed NHx (with x= 1 or 2)species on the CH3 adsorption process and the following H abstraction reac-tions have been theoretically investigated. The CH3 adsorption energies(ΔΕads) have been calculated using equation [3.1] :

ΔEads = Esurf-ads – (Esurf + Eads) [3.1]

where Esurf-ads is the total energy for the finally adsorbed surface and Esurf (orEads) is the total energy for the surface without adsorbate (or gaseousspecies). Energies for the H abstraction reaction (ΔEabs) have been calculatedusing equation [3.2] :

ΔEabs = (Esurf-CH2 + EH2) – (Esurf-CH3 + EH) [3.2]

where Esurf-CH2 and Esurf-CH3 are the total energies for optimized surface struc-tures with CH2 or CH3 adsorbed to it. EH2 and EH are the total energies forgaseous H2 and H, respectively.

For the (100)-2x1 surface orientation, the co-adsorbed dopant has beenplaced in three different positions (see Figures 5a, b and c) around the sur-face carbon on which the reaction take place (highlighted by a black circle).

23

Figure 5. Positions considered for NHx around the surface reactive carbon on the(100)-2x1 surface (a, b and c) and on the (111) surface (d).

For the (111) diamond surface, all the positions around the reactive surfacecarbon are equivalent due to symmetry and only one position for NHx couldbe considered (Figure 5d). The calculated energies in the presence of a co-adsorbed NHx are presented in Table 1. These energies are compared withthe reaction energies obtained without any dopant on the surface (i.e., the ad-sorption site is only surrounded by hydrogen).

Table 1. Reaction energies for the CH3 adsorption (ΔΕads) and the H abstraction reac-tions (ΔΕabs), with NHx (x= 1 or 2) as co-adsorbate and compared with a fully hydro-genated surface.

ΔEads (kJ/mol)Paper I (111)

(100)

Pos 1 Pos 2 Pos 3

H -317.7 -358.5

NH2 -290.7 -317.9 -330.0 -349.6

NH -301.5 -355.3 -375.2 -229.1

ΔEabs (kJ/mol)Paper II *** *** *** ***

H -21.4 -15.6

NH2 -33.6 -39.6 -36.8 -23.3

NH -319.3 -280.0 -300.2 -231.7

3.2.1.1 CH3 adsorption reactionIn the presence of NH2 on a neighbouring surface carbon, the CH3 adsorp-

tion is observed to be slightly disfavoured for both diamond (111) and (100)surfaces. When compared to the situation with only H surface neighbours,the decrease in adsorption energy induced by a neighbouring adsorbed NH2

is relatively low. This small negative effect on the adsorption energy can beexplained by sterical repulsions between the two co-adsorbates (NH2 andCH3) which destabilises the surface structure after the adsorption reactionand slightly disfavours the reaction (see Paper I). In the presence of the co-adsorbed NH in positions 1 and 2 on diamond (100) and on (111) (Figures5a, b, d), the CH3 adsorption is not significantly affected. However, whenNH is in position 3 (Figure 5c), the reaction is strongly energetically dis-favoured due to the formation of a new bond between the dopant and the re-active adsorption site (see Paper I).

3.2.1.2 H abstraction reactionFrom Table 1, the presence of a co-adsorbed NH2 is observed to affect

only marginally the H abstraction process for both diamond (111) and all po-sition on the (100) surface. Prior to the H abstraction reaction, both the CH3

species and the dopant in its fully hydrogenated form are co-adsorbed on the

24

diamond surface. As already observed for the CH3 adsorption reaction, asterical repulsion is present between the co-adsorbed species (NH2 and CH3).This repulsion is thereby destabilising the reactive diamond surface and,consequently, favouring energetically the following H abstraction reaction.This surface destabilisation prior to H abstraction appears to be the only phe-nomenon responsible for the abstraction energy differences compared to thevalues obtained without any co-adsorbed dopant. When NH is co-adsorbedwith CH3 on the diamond surfaces, the H abstraction reactions become ener-getically more favoured. This energetic difference is explained by the forma-tion of a new N-C bond between the two co-adsorbed species after the H be-ing abstracted.

3.2.2 Effect of substitutional N

3.2.2.1 Preliminary investigationThe lack of significant effect observed in the presence of a co-adsorbed

NHx species on the diamond surface motivated the reorientation of the re-search strategy. Frauenheim et al. proposed that substitutional N will catal-yse the surface reactivity through an electron transfer process but their studywas limited to only one position for N [87]. In addition, the alternativemechanism they proposed implies that CH2 would become the main gaseousgrowth species which is in contradiction with many experimental and theo-retical works describing CH3 as the main growth species. Within Paper III,the effects of a substitutional N, within the 1st and the 2nd carbon layers, onthe CH3 adsorption and the following H abstraction reactions were investi-gated for both (111) and (100)-2x1 surfaces. The different positions consid-ered for the substitutional N are presented in Figure 6.

25

Figure 6. Substitutional positions for N on the (100)-2x1 surface in the 1st (a) and the2nd (b) carbon layer and on the (111) surface in the 1st (c) and the 2nd (d) carbon layer.

The CH3 adsorption energies (ΔΕads) and the H abstraction reaction (ΔEabs)have been calculated using equations [3.1] and [3.2]. The calculated energiesare presented in Table 2.

Table 2. Reaction energies for the CH3 adsorption (ΔΕads) and the H abstraction reac-tions (ΔΕabs) in the presence of a substitutional N from Paper III.

ΔEads (kJ/mol)(111) (100)

Pos 1 Pos 2 Pos 1 Pos 2 Pos 3

No N -317.7 -358.5

NL1 -333.5 -319.7 -379.6 -373.6 -363.3

NL2 -125.5 -176.6 -237.3 -171.6 -212.1

ΔEabs (kJ/mol) *** *** *** *** ***

No N -21.4 -15.6

NL1 -10.6 -21.0 -7.9 -23.1 -53.2

NL2 -262.6 -154.7 -138.0 -180.5 -140.0

CH3 adsorptionA comparison between the calculated CH3 adsorption energies in the pres-

ence of N in the 1st carbon layer with the values obtained for the undoped sit-uation does not indicate pronounced dopant induced effect for either the(111) or (100)-2x1 surface orientation. The reaction energies are all rathersimilar to the values obtained with no substitutional N (see Table 2). When anitrogen atom replaces a carbon atom within the 2nd carbon layer, its 5 va-lence electrons is in contradiction with its fourfold coordination to the sur-rounding carbons. As observed in Table 2, its presence induces importantchanges in the CH3 adsorption and H abstraction reaction energies.

The CH3 adsorption is observed to be strongly disfavoured by the pres-ence of N in the 2nd carbon layer for both diamond (111) and (100) surfaces.The underlying cause to this observation is the different degrees and types ofsurface relaxation before and after the adsorption process. Prior to CH3 ad-sorption, the extra valence electron of nitrogen is, for both types of surfaces,transferred to the surface radical carbon forming a lone pair which stabilisesthe surface. However, when the CH3 species is adsorbed to the diamond sur-face, the possibility for an electron transfer decreases dramatically due to thelack of radical surface species. The system is thereby forced to relax by othermeans. For both surface orientations, an off-site movement of the nitrogen isobserved by the elongation of one C-N bond induced by the anti-bonding in-teraction between the N lone-pair orbital and the C dangling bond. This ef-fect is similar to the effect largely reported in literature for the diamond bulk[76,125,126]. Obviously, the energy gain from the off-site relaxation, withCH3 adsorbed on the surface, is smaller compared to the electron transferprocess, with a surface radical carbon.

26

H abstractionIn contrast to CH3 adsorption on diamond (111) and (100), the gas phase

abstraction of H from adsorbed CH3 species (creating adsorbed CH2) isstrongly favoured by the presence of a substitutional N (see Table 2). Theunderlying cause to this observation can again be described by the differentdegrees and types of surface relaxation before and after the reaction. Thelack of a surface radical with CH3 adsorbed to the surface discards the possi-bility for an electron transfer from N towards the surface. The system is thenin a rather unfavourable situation. However, with a radical CH2 adsorbed onthe surface, the system is observed to relax by either of two different mecha-nisms (both dependent on the N position). When N is in position 1 and 3 onthe (100) surface and in position 2 on the (111) surface, an electron is trans-ferred from N in the 2nd carbon layer to CH2, forming a paired electron whichwill stabilise the system. However, for N in position 2 on the (100) surfaceand in position 1 on the (111) surface, another relaxation mechanism is ob-served. In these positions, the dopant is in position β with respect to the radi-cal C in CH2 which allows the relaxation of the surface through a β-scissionrearrangement (i.e., one N-C bond is broken and the C-C bond, which con-nects CH2 to the surface, becomes double; see Figure 7). On the (111) sur-face, the surface structure with N in position 1, where the β-scission rear-rangement takes place, is calculated to be 108 kJ/mol more stable comparedto the surface with N in position 2. For the (100) surface, the energetic differ-ence between the surface with N in position 2, with the β-scission reconstruc-tion, and the surface with N in position 1, is calculated to be about 117 kJ/mol.

For the diamond (100)-2x1 surface, the electron transfer mechanism whichtake place for N in positions 1 and 3 was observed to induce a weak interac-tion between CH2 and the H adsorbed on the neighbouring surface C (see Pa-per III). This interaction induced the weakening of the C-C dimer where CH2

27

Figure 7. β-scission reconstruction with N in position 2 in the (100) surface (a) andwith N in position 1 on the (111) surface.

is adsorbed which will probably favour the following insertion within thedimer. However, this assumption needs further investigations to be confirmed.

The degradation of the surface morphology which occurs at high N con-centration was proposed to be correlated with the β-scission rearrangement.A higher N concentration in the bulk induces a higher probability for N to benext to a reactive site. The structural reorganisation that induces the forma-tion of a sp2 carbon will then have the possibility to occur more often and toinduce the formation of the nano-crystalline structure.

3.2.2.2 Further investigation on substitutional N effectThe observations in Paper III clearly indicated important effects of substi-

tutional N within the 2nd carbon on key elementary growth steps. It motivat-ed further investigations on other reaction steps that are important for theCVD growth on the (100)-2x1 surface (i.e., CH2 dimer insertion, H transferand CH2 migration). The goal is to observe if some specific effects like, forexample, the C-C dimer elongation (observed with N in the 2nd carbon layerin positions 1 and 3) will really enhance the CH2 insertion within the dimer.In addition, further substitutional positions have been considered by placingN within two other C layers (3rd and 4th), in complement to the 2nd carbonlayer (Paper IV). In total, 7 different N positions have been considered, outof which 3 are identical to the ones in Paper III for the 2nd carbon layer (seeFigure 8). In this way, not only the effect by the elemental N is looked for,

28

Figure 8. Representations of the N positions in the 2nd (a), 3rd (b) and 4th (c) carbon layer.For the 2nd carbon layer, the positions are labelled 1, 2 and 3 from right to left and for the3rd and the 4th carbon layer the N positions are labelled 1 and 2 from right to left.

but also the eventual tendency for a somewhat longer range effect. The sur-face with specific positions of N will be presented as: NLxPy, where x and yrepresent the positions of N in the yth position within the xth atomic layer.

The calculations were based on the density functional theory (DFT)method, using two different softwares: the program package DMol3 from Ac-celrys, Inc. [119] and the Gaussian 03 suite of programs [120]. The DMol3

program is working under periodic boundary conditions and uses localizednumerical basis sets, whilst Gaussian 03 is using cluster models and local-ized basis sets. Both of these DFT softwares have been used for calculatingreaction energies and thereby the thermodynamic driving force for the reac-tions to take place. However, a complete energetic reaction profile shouldalso contain kinetic information by including an estimation of the energeticbarriers for the reactions. These energies could here only be calculated byusing Gaussian 03. The reaction energies (ΔE) were calculated using the fol-lowing equation:

ΔE = Eprod – Ereact [3.3]

where Eprod and Ereact are the energies calculated for the product and the reac-tant surface structure, respectively. Similarly, the activation energies werecalculated with the following equation:

ΔE* = ETS – Ereact [3.4]

where ETS is the energy calculated for the transition state structure.

CH2 insertion into C-C dimerThe insertion reaction within a carbon dimer is generally described as oc-

curring in two steps: a) a dimer opening step which forms an intermediate“open-ring” structure, and b) a ring closing step [43,44]. However, the inter-

29

Figure 9. Mechanism describing the incorporation of an adsorbed CH2 into a carbondimer. R, P and TS denote the reactant, product and transition state structure of thereaction, respectively.

mediate “open-ring” structure has been calculated by Tamura et al. to have ashort life time [46]. The ring closing step of the reaction is assumed to be therate-determining due to its higher activation barrier and is therefore the onlyreaction step which is here presented and discussed (see Figure 9).

Table 3. Reaction energies (ΔE) and activation barriers (ΔE*) for CH2 incorporationinto the carbon dimer. The calculations have been performed with the programsDMol3 and Gaussian 03, both with and without N in the lattice at various positions.

Energies (kJ/mol) No Nitrogen NL2P1

NL2P2

NL2P3

NL3P1

NL3P2

NL4P1

NL4P2

ΔE (DMol3) -20 -14 85 -11 -56 -105 -28 -32

ΔE (Gaussian03) -37 -23 56 -39 -72 -139 -48 ---

ΔE* (Gaussian03) 107 251 355 80 208 178 214 ---

The calculated energetic profile for the CH2 insertion reaction, with N indifferent positions, are presented in Table 3. The reaction energy analysisshows that substitutional N affects the thermodynamic of the reaction in the2nd and 3rd carbon layers in position 2. This important variation can be ex-plained by the presence of a β-scission reconstruction. For NL2P2, the re-construction has already been observed taking place when CH2 is adsorbedon the surface and an important energetic stabilisation was observed (Figure10a). For the CH2 insertion reaction, it corresponds to the surface structureprior to the reaction which explains the negative effect on the reaction ener-gy (i.e., the reaction becomes disfavoured). For NL3P2, the β-scission takesplace after the insertion reaction (Figure 10b) that strongly stabilises the fi-

30

Figure 10. Representation of the β-scission reconstructions observed when a surfacecarbon radical is in β-position of N; (a) N in position 2 in the 2nd carbon layer withCH2 adsorbed on the surface, (b) N in position 2 in the 3rd carbon layer with CH2 in-serted in the carbon dimer.

nal surface structure with CH2 inserted into the C-C dimer. The reaction be-comes then strongly favoured.

For the other situations with N not being in the β-position relatively to thesurface radical (i.e., NL2P1, NL2P3, NL3P1, NL4P1 and NL4P2 in Table 3),the system can not relax through a β-scission mechanism. It is instead ob-served to relax through the transfer of an electron from N to the surface radicalcarbon, and thereby inducing the formation of an electron lone pair. This ef-fect, already observed with N in the 2nd carbon, is here confirmed to occur alsofor N positioned in the 3rd and 4th carbon layer. In these cases, the reaction en-ergies are generally observed as not strongly affected by the presence of N.

The activation barrier for the CH2 insertion reaction into the C-C dimerhas been estimated using Gaussian 03, and the resulting energies are present-ed in Table 3. With one exception, the CH2 insertion reaction is associatedwith a much larger activation barrier in the presence of substitutional N com-pared to the undoped situation (an increase within the range of 77 to 248 kJ/mol). For the situation with N in the 2nd carbon layer, position 3, the activa-tion barrier is lowered by 27 kJ/mol.

The large barrier calculated for N in the 2nd carbon layer position 2(NL2P2), of about 355 kJ/mol, is explained by the β-scission rearrangementthat strongly stabilises the surface prior to insertion. For N in the 3rd carbonlayer, position 2 (NL3P2), the β-scission rearrangement that takes place dur-ing the insertion reaction is not affecting the kinetics of the forward reaction.Despite the large decrease observed for the reaction energy, the activationbarrier is similar to the values obtained for the others N positions, when thereconstruction does not take place (i.e., the activation energy is about 178 kJ/mol for NL3P2 vs. 208 and 214 kJ/mol for, respectively, NL3P1 andNL4P1). It is important to emphasize the strong influence on surface reactiv-ity that surface structure stabilisation might induce. For N in position 2 in the2nd carbon layer, the large activation energy to overcome clearly shows howmuch the stabilisation of the initial structure will affect the reaction kinetics.

For all other N positions considered, where no β-scission rearrangementswere observed (i.e., NL2P1, NL2P3, NL3P1, NL4P1), the variations in acti-vation barriers are related to the stability of the transition structures only. Inthe presence of N, the more negative carbon surface, due to the presence ofthe transferred electron, will induce a stronger electrostatic repulsion be-tween the two carbon atoms which are involved in the new bond formation.The more intense electrostatic repulsion observed in the presence of N willinduce a destabilisation of the TS structure, which explains the higher activa-tion barriers. For N within the 2nd carbon layer in position 3, where N is di-rectly bonded to the surface C, the electronic charge appears to be less local-ized on the surface C within the transition structure thereby reducing theelectrostatic repulsion.

In conclusion, it appears that N in β-position of a surface radical C will in-duce the formation of an sp2 carbon species that strongly affects the dimer inser-

31

tion reaction energy and activation barrier. When N is not in β-position, the acti-vation barrier for the CH2 insertion into a C-C dimer is generally increased,thereby reducing the probability for the insertion reaction to take place.

CH2 migrationThe migration reaction of CH2 across dimer rows is based on the mecha-

nism proposed by Frenklach et al. [51], and is considered to occur in twosteps (see Figure 11). The 1st migration step (R � I) corresponds to the in-verse of the CH2 insertion reaction. The main difference is that, as a result ofthe reaction, the adsorbed radical CH2 is positioned very close to the neigh-bouring surface carbon radical. The proximity of these two C radicals in-duces a rapid formation of a new C-C bond that forms the finally bridgedstructure. This rapid formation constitutes the 2nd step (I � P) in the migra-tion process.

Table 4. Reaction energies (ΔE) and activation barriers (ΔE*) for the 1st (R1) and the2nd (R2) reaction step within the CH2 surface migration.

CH2 Migration(kJ/mol)

No Ni-trogen

NL2P1

NL2P2

NL2P3

NL3P1

NL3P2

NL4P1

NL4P2

DMol3ΔER1 28.1 20.1 -64.0 8.5 38.2 67.8 22.2 17.8

ΔER2 -106.5 30.7 92.8 -15.6 -8.7 -35.4 18.2 1.9

Gaus-sian

ΔER1 21.0 34.0 -49.4 32.0 51.9 117.2 35.9 ---

ΔER2 -92.7 49.3 108.8 -41.8 -5.3 -56.8 33.3 ---

ΔE*R1 139.9 154.2 251.1 125.0 188.6 273.9 182.6 ---

ΔE*R2 12.4 92.6 154.2 11.0 43.9 150.9 78.6 ---

32

Figure 11. CH2 migration reaction from an inserted position within a carbon dimertowards a bridged position between two C-C dimers. R, I and P represent the reac-tant, intermediate and product structures, respectively. TS1 and TS 2 represent thetwo transition states.

The calculated reaction and activation energies are presented in Table 4.For the first reaction step, the reaction energies are consistent with the valuescalculated for the dimer insertion reaction considering that migration is theforward and insertion is the inverse direction of the same reaction (ΔE=28kJ/mol and ΔE*=140 kJ/mol vs. ΔE=-20 and ΔE*=107 kJ/mol, where ΔEand ΔE* are the reaction energies and activation barriers, respectively). Thesimilarities between the reaction energies and the activation barriers indicatethat the presence of a neighbouring surface C radical is not affecting thisspecific reaction step (i.e., step 1). The following step (i.e., step 2) is energet-ically favoured by about -107 kJ/mol due to the formation of a new bondwithin the bridged structure. The very low activation barrier that has beencalculated for TS2 (of about 12 kJ/mol) indicates that the 2nd migration stepreaction will occur with a high probability.

In the presence of substitutional N, the reaction energy for the 1st migra-tion step is only affected when a β-scission rearrangement takes place, simi-larly to the CH2 insertion reaction. For N in the 2nd carbon layer, position 2,the reconstruction takes place after the first reaction step, which results in anadsorbed position of CH2 and an overall exothermic reaction (ΔE = -64kJ/mol). The situation is opposite for N in the 3rd carbon layer, position 2.For this situation, the β-scission reconstruction occurs with CH2 inserted intothe C-C dimer, resulting in an overall endothermic reaction (ΔE = 67 kJ/mol).

As can be seen in Table 4, the activation energies are observed to be onlyslightly affected by the presence of N in the 2nd carbon layer, positions 1 and3 (about 154 and 125 kJ/mol for NL2P1 and NL2P3). This is to be comparedwith a value of 140 kJ/mol for the undoped situation. For the other N posi-tions, the activation barriers are increased by the presence of the dopant;251, 189, 274 and 183 kJ/mol for NL2P2, NL3P1, NL3P2 and NL4P1, re-spectively.

By analysing the spin density on the two surface radicals, it was possibleto localize the radical C where N “extra” electron was preferentially trans-ferred, what could explain the activation energy differences (see Paper IV).With N in the 2nd carbon layer, position 1, N is directly bonded to the carbonradical within the dimer neighbouring the reaction site and the “extra” elec-tron from N is predominantly localized on the surface radical carbon directlyconnected to N. The reaction is thereby not affected by the presence of thedopant, and the activation barrier is similar in energy to the undoped situa-tion. With N in the 2nd carbon layer, position 2, the “extra” N electron is di-rectly transferred to the surface radical C involved in the first step of the mi-gration reaction. As a result for the TS structure, the C-C distance (represent-ed with a dashed line in Figure 11) will be increased due to electrostatic re-pulsions. The transition state structure will thereby be destabilised, what willfurthermore explain the higher activation barrier. With N in the 3rd and 4th

carbon layers, position 1, the “extra” electron from N will not be localized,but shared by both surface radical carbons. The reaction barrier becomes

33

higher due to an increase in electrostatic repulsion between the two C's in-volved in the bond breakage.

The reaction energies for the 2nd reaction step (i.e., the formation of abridged structure), presented in Table 4, show rather large energetic varia-tions induced by the presence of N within the surface. The reaction, whichpresents an energetic exothermic energy value of 108 kJ/mol for an undopedsituation, becomes less energetically favoured with N in the 2nd carbon layer,position 3 (by about 16 kJ/mol), and with N in the 3rd carbon layer, positions1 and 2 (by about 9 vs. 35 kJ/mol). On the other hand, N in the 2nd and the 4th

carbon layer, position 1 and 2, is observed to disfavour the 2nd step of the mi-gration reaction (an increase of about 31, 93, 18 and 2 kJ/mol for NL2P1,NL2P2, NL4P1 and NL4P2, respectively).

With N in the 2nd, or 3rd, carbon layer in position 2, the larger differencesin reaction energy can again be explained by the β-scission mechanism,which takes place before the reaction for the NL2P2 situation, and both be-fore and after the reaction for NL3P2. With N in the 3rd carbon layer, posi-tion 1, N is also in β-position with respect to the surface radical carbon afterthe reaction. A β-scission reconstruction is then observed taking place, wathinduces the stabilisation of the surface and, hence, an observed weakexothermicity of the reaction.

For N in the 2nd, 3rd and 4th carbon layer, position 1, the increase in activa-tion barrier can be explained by the presence of the “extra” N electron on thereactive surface carbon, onto which CH2 will bind. A resulting electrostaticrepulsion has been observed between the negatively charged C (in CH2) andthe surface carbon containing the electron lone pair. With N in the 2nd carbonlayer, position 3, a structural analysis of the surface indicates that the inter-mediate structure prior to the 2nd reaction step is “activated” due to the pres-ence of a substitutional N. The C-C dimer bond is longer compared to theother N positions (1.96 Å vs. 1.72 Å within NL2P1) and the C-CH2 bond be-comes shorter (1.43 Å vs. 1.48 Å within NL2P1). This surface destabilisationthat takes place before the reaction explains thereby the exothermicity of thereaction and the low activation barrier.

In conclusion, the study of the CH2 migration reaction shows that the ef-fect of a substitutional N within the 2nd carbon layer is very local. The“extra” electron from the substitutional N will only be transferred towardsthe closest surface carbon radical, and a second radical present on the surfacewill not be affected. If that surface carbon radical, to which the electron istransferred, is not involved in the reaction, the effect of N on this reactionwill be negligible. With N in the 3rd and 4th carbon layer, the “extra” electronfrom substitutional N is observed to be delocalized on both surface radicalswhich generally disfavours the CH2 migration reaction.

34

H transferThe reactant structure is here considered to be the adsorbed CH2 on an

otherwise H-terminated surface (R in Figure 12) and the product is an ad-sorbed CH3 with a neighbouring radical carbon (P in Figure 12). An H isconsidered to be transferred from a surface carbon towards the adsorbed CH2

species via a transition state structure (TS in Figure 12). An adsorbed CH2

species on the surface can, hence, undergo two different surface reactions;the reaction with a migrating H or the insertion into a C-C dimer. It is there-fore of greatest importance to also study the effect of substitutional N on thisH migration reaction mechanism.

Table 5. Reaction energies (ΔE) and activation barriers (ΔE*) for the H transfer reac-tion.

H transfer(kJ/mol)

No Ni-trogen

NL2P1

NL2P2

NL2P3

NL3P1

NL3P2

NL4P1

NL4P2

ΔE (DMol3) 9.9 -69.4 161.5 20.0 -17.0 16.8 -14.0 4.7

ΔE (Gaussian)

3.2 -86.7 169.5 55.3 -17.9 43.1 -16.3 ---

ΔE* (Gaus-sian)

90.2 4.7 186.5 77.9 33.7 68.6 34.0 ---

As can be seen in Table 5, there are major differences for the reaction en-ergies in the presence of substitutional N in specific positions. The reactionenergies vary from -69 to 161 kJ/mol, which is to be compared with 10kJ/mol for the undoped situation. Two major energetic effects are observed

35

Figure 12. Representation of the H transfer reaction with R, TS and P denoting reac-tant, transition state and product structures, respectively.

with N in the 2nd carbon layer, position 1 and 2. The H migration reaction isthen favoured by 69 kJ/mol and disfavoured by 161 kJ/mol, respectively. Forother positions of N, the reaction thermodynamic is only slightly affected bythe presence of N. The reaction is energetically favoured by 15 kJ/mol withN in the 3rd and 4th carbon layer, position 1, whilst it is somewhat dis-favoured (about 18 kJ/mol) with N in the 2nd carbon layer, position 3, and inthe 3rd carbon layer, position 2.

The more pronounced exothermic H migration with N in the 2nd carbonlayer, position 1, indicates that the situation with a CH3 adsorbate and aneighbouring surface radical C site is energetically more stable than a situa-tion with CH2 adsorbed on an otherwise fully H-terminated surface. This ob-servation can be explained by the fact that the substitutional N atom is di-rectly bonded to the surface C radical, thereby stabilising this specific struc-ture. This result shows that the surface structure is more stable with N direct-ly bonded to the surface radical C compared to the situation with N furtheraway. The smaller effects for the other N positions can also be explained bythe relative position of N. The fact that the H transfer reaction is stronglydisfavoured by N in carbon layer 2, position 2, can be explained by the β-scission rearrangement that strongly stabilises the surface structure with anadsorbed CH2.

The presence of substitutional N is observed to have a big effect on the ac-tivation energies (see Table 5). For most of the situations described, a de-crease in activation barrier for the H transfer reaction has been observed.This effect is obvious for N positioned within the 2nd carbon layer, position1, for which the activation energy is calculated to be around 5 kJ/mol (whichis a lowering in energy of about 85 kJ/mol). This very small barrier means inpractice that the adsorbed CH2 species will rapidly react with the neighbour-ing H species, thereby converting the adsorbate into CH3. It will then hinderthe C-C dimer insertion reaction for which an adsorbed CH2 is a prerequisite.An energetic decrease in activation barrier was also found for N in the 3rd

and 4th carbon layers, position 1. The calculated activation barriers for thesesituations are about 34 kJ/mol (a lowering of about 56 kJ/mol). This some-what smaller energetic decrease will also most probably speed-up the forma-tion of adsorbed CH3 species and hence negatively affects the growth pro-cess. For N in layer 2, position 3, and in layer 3, position 2, the activationbarrier for the H transfer reaction was found to be only slightly loweredcompared to the undoped situation (78 and 69 kJ/mol vs. 90 kJ/mol). How-ever, the inverse reaction (i.e., the H migration from the CH3 towards theneighbouring surface carbon) is interesting to consider since it is thermody-namically more favoured. For this inverse reaction, the activation barrier isfound to be much lower compared to the undoped surface (23 (26) kJ/molfor NL2P3 (NL3P2) vs. 87 kJ/mol). This decrease in activation energy im-plies that N in these specific positions will hinder the formation of adsorbedCH3 by H migration towards an adsorbed CH2. The large activation barrier

36

(187 kJ/mol) observed for N in layer 2, position 2, is explained by the β-scis-sion mechanism which strongly stabilises the adsorbed CH2 and thereby in-creases the activation energy.

These lowering in activation energies can be explained by an interaction be-tween the adsorbed CH2 and the neighbouring H adsorbate. The CH2 species,with an electron lone pair formed an electron transfer from the substitutional Ntowards CH2, was clearly observed interacting with the positively charged sur-face H atoms adsorbed on the neighbouring C-C dimer (see Paper IV).

In conclusion, substitutional N shows a very strong effect on H migrationfrom an adsorbed CH2 species to a nearby positioned surface radical C.

3.2.2.3 General conclusions on substitutional NThe limited size of the model used within this study corresponds to a high

substitutional N concentration. However, the aim with the present study wasnot to focus on the effect of N concentration but on the effect of a nearby po-sitioned N on the most important growth steps within the diamond synthesis.In the presence of N, the general increase in activation barriers and occur-rence of β-scission rearrangements, inducing the formation of C-C doublebonds, could be an explanation to the surface degradation and the decrease ingrowth rate observed experimentally. In addition, the fact that the electronictransfer from substitutional N towards an available surface state is rather lo-calized, what does not support the proposition of Frauenheim et al. wheresubstitutional N was considered as responsible for the catalytic effect ob-served experimentally.

3.2.3 Effect of a NH co-adsorbate next to a surface step

By studying the effect of substitutional N on the surface reactivity withinPapers III and IV, the catalytic effect of nitrogen on the diamond CVDgrowth could not be explained. For this purpose, the effect of a co-adsorbednitrogen species (NH) on the adsorption of CH3 (or CH2) next to a step edgeon the diamond (100)-2x1 surface has been investigated. The CH3 and CH2

adsorption energies (ΔΕads) were then calculated using the equation [3.1]. The reason for choosing the radical NH species as a co-adsorbate was in

part due to the fact that imines are known from organic synthesis to play asignificant role within radical reactions [127]. The formation of NH at thesurface is considered to be induced by an H abstraction reaction from an ad-sorbed NH2 species. In addition, NH2 has in Paper I been observed to inducesterical repulsions in the process of CH3 (or CH2) adsorption.

Two possible types of mono-atomic steps on the (100)-2x1 surface (SA andSB type; see Figure 4) have been considered. For both SA and SB steps on thediamond (100) surface, the NH co-adsorbate has been positioned at 3 differ-ent surface sites around the surface radical carbon onto which CH3 (or CH2)

37

will be adsorbed. These positions are labelled A1, A2 and A3 for the SA

stepped surface (see Figures 13a-c). Correspondingly, the positions for theSB stepped surface are labelled B1, B2 and B3 (see Figures 13d-f).

3.2.3.1 Stepped surface SA

CH3 adsorption reactionThe CH3 adsorption energies calculated for the SA stepped surfaces are

presented in Table 6. For the radical surfaces, prior to the CH3 adsorption re-actions, the presence of the radical co-adsorbate NH and the radical C ad-sorption site implies two possible electronic states for the system (a multi-plicity of 1 or 3). To calculate the CH3 adsorption energies, only the moststable surface structures are considered as reactant surfaces. The singlet elec-tronic state is considered for NH position A1, and the triplet state is consid-ered for A2 and A3.

Table 6. CH3 and CH2 adsorption energies calculated without any co-adsorbeddopant and for the three different NH positions (A1, A2 and A3) on the SA steppedsurface.

ΔEads (kJ/mol) No Dopant A1 A2 A3

CH3 -329.4 -303.8 -325.0 -323.6

CH2 -396.1 -637.7 -567.6 -583.2

From Table 6, it can be observed that the CH3 adsorption energy is not af-fected by the presence of a co-adsorbed NH species in position A2 or A3

38

Figure 13. The NH co-adsorbate in positions A1 (a), A2 (b) and A3 (c) on a SA

stepped surface, and in position B1 (d), B2 (e) and B3 (f) on a SB stepped surface.The surface radical C onto which the CH2 or CH3 adsorbs, is highlighted by a circle.

(-325 vs. -324 kJ/mol, to be compared with -329 kJ/mol for the situationwithout NH). With NH in position A1, the adsorption reaction appears to beslightly disfavoured (about 26 kJ/mol) compared to the adsorption on a fullyhydrogenated stepped surface. For NH in position A1 and A2, no significantinteraction could be observed between the radical dopant and the surfaceradical carbon, prior to CH3 adsorption, or the adsorbed CH3, after the reac-tion. This is consistent with the lack of adsorption energy changes in thepresence of NH. The situation is different when NH is placed in position A1,for which a favourable interaction on the surface between NH and the sur-face radical C, prior to adsorption, could be detected (see Paper V). A struc-tural analysis indicates that this interaction is causing a large elongation ofthe C-C dimer bond (1.97 Å for the singlet state vs. 1.76 Å for the tripletstate, where no N-C interaction was observed). For NH in position A2 andA3, a significant C-C elongation induced by the presence of the radical nitro-gen on the dimer could also be observed (1.74 and 1.70 Å vs. 1.64 for thedimer saturated with two H atoms).

CH2 adsorption reactionAs can be seen in Table 6, the CH2 adsorption energy is significantly

favoured by the presence of a co-adsorbed NH species (-638 (A1), -568 (A2)and -583 (A3) kJ/mol, to be compared with -396 kJ/mol for the situation withno NH co-adsorbate). The analysis of the radical surface prior to CH2 adsorp-tion, presented in the previous section, showed that a co-adsorbed NH is notstrongly affecting the surface energetic stability. The large energetic changesobserved are instead most probably originating from a surface stabilisationthat takes place after the adsorption reaction, as can be further analysed bystudying the surface structure after the CH2 adsorption. For all 3 NH positions,a new bond will strongly stabilise the final surface structure and, hence, ener-getically favour the adsorption reaction (see Paper V).

3.2.3.2 Stepped surface SB

CH3 adsorption reactionThe CH3 adsorption energies (ΔEads) calculated for the SB stepped diamond

(100) surfaces, are presented in Table 7. As was the situation for the SA

stepped surface, two possible electronic states are present for the radical sur-faces prior to the CH3 adsorption reactions; a multiplicity of either 1 or 3.Only the electronic state that gives the most stable surface structures willhere be considered as reactant surfaces. For the SB stepped surface, the tripletelectronic state is thereby considered for NH in position B1 and B2, and thesinglet state is considered for B3.

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Table 7. CH3 and CH2 adsorption energies calculated for the three different NH posi-tions (B1, B2 and B3) on the SB stepped surface.

ΔEads (kJ/mol) No Dopant B1 B2 B3

CH3 -289.1 -265.1 -291.2 69.3

CH2 -378.7 -610.0 -570.3 -448.0

From Table 7, The CH3 adsorption energy is not significantly affected bythe presence of a co-adsorbed NH species in position B1 and B2 (-265 vs.-291 kJ/mol, to be compared with -289 kJ/mol for the situation with no NHadsorbates). However, the CH3 adsorption reaction becomes strongly dis-favoured with NH in position B3 (69 kJ/mol). For NH in position B2 andB3, the surface geometrical structure did not present any significant stabilis-ing interactions between the radical dopant and the surface radical carbonprior to adsorption. This was also the situation for the radical dopant and theadsorbed CH3 species (i.e., after the adsorption reaction).With NH in posi-tion B3, the analysis of the surface structure prior to CH3 adsorption showedthat a new bond is formed between N (in NH) and the surface radical carbon(see Paper V). It strongly stabilises the reactant surface structure and dis-favours the adsorption reaction.

CH2 adsorption reactionAs can be seen in Table 7, the CH2 adsorption reaction next to a SB step

edge is significantly favoured by the presence of a co-adsorbed NH species(-610, -570 and -448 kJ/mol for positions B1, B2 and B3, to be comparedwith -379 kJ/mol for the situations without NH). These large variations inadsorption energies can be explained by performing a structural analysis ofthe surface after the CH2 adsorption reaction. For NH in position B1, the ad-sorption reaction of CH2 is strongly favoured by the formation of a new bondbetween N (in NH) and C (in CH2). Similar to the effect observed for the SA

stepped surface, this bond formation strongly stabilises the final surfacestructure which hence energetically favours the adsorption reaction. WithNH in position B2, the positive effect observed on the CH2 adsorption reac-

40

Figure 14. Surface reconstruction observed with NH in position B2 and CH2 ad-sorbed next to a SB step edge.

tion is explained by the presence of a large surface reconstruction. As shownin Figure 14, an H atom is transferred from the SB step edge towards the CH2

adsorbate, forming an adsorbed CH3. One C-C bond within the step is there-after broken, inducing the formation of a new C-C bond and the C-N bondbecomes double. Finally, the large improvement in CH2 adsorption energyobserved for NH in position B3 is induced by the formation of a new bondwith the second carbon of the dimer, after the C-C bond breakage. Comparedto the fully hydrogenated surface, the formation of this new bond explainsthe significant adsorption energy improvement.

3.3 Effect of phosphorous, sulphur or boron atomWithin Papers I and II, the effects of a co-adsorbed PHx, SHx and BHx

(with x= 1 or 2 for B and P, and x= 0 or 1 for S) species on the CH3 adsorp-tion process, and the following H abstraction reactions, have been theoreti-cally investigated. The CH3 adsorption energies (ΔΕads) and H abstraction re-action (ΔEabs) have been calculated using equations [3.1] and [3.2]. For the(100)-2x1 surface orientation, the co-adsorbed dopant has been placed inthree different positions (see Figures 5a, b and c) around the surface carbononto which the reaction take place (highlighted by a black circle). For the(111) diamond surface, all the positions around the reactive surface carbonare equivalent due to symmetry and only one position could be considered(Figure 5d).

3.3.1 CH3 adsorption reaction

The calculated adsorption energies in the presence of a co-adsorbeddopant are presented in Table 8. These energies are compared with the ener-gies obtained when the reaction occurs without any dopant on the surface(i.e., the adsorption site is only surrounded by hydrogen).

From Table 8, it can be observed that the adsorption reaction is lessfavourable in the presence of a co-adsorbed PH2 or SH compared to the fullyhydrogenated surface [(111): 52 vs. 47 kJ/mol, and (100): (35-72) vs. (25-68)kJ/mol]. The CH3 adsorption reaction is disfavoured with BH2 in position 2and 3 on diamond (100) by 24 and 90 kJ/mol, respectively. However, thepresence of a neighbouring BH2 does not appreciably affect the reaction onthe (111) surface and in position 1 on the (100) surface.

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Table 8. CH3 adsorption energies in the presence of different adsorbed dopants (P, B and S) inboth their fully hydrogenated and radical forms.

ΔEAds (kJ/mol) (111) (100)

Pos 1 Pos 2 Pos 3

PH2 -266.0 -286.0 -298.9 -323.0

BH2 -325.1 -366.2 -334.3 -268.5

SH -270.6 -296.5 -305.6 -333.3

PH -218.3 -182.8 -195.7 -174.2

BH -230.5 -196.6 -291.0 -127.8

S -244.9 -243.1 -253.2 -221.9

H -317.7 -358.5

The negative effect on the CH3 adsorption energy induced by neighbour-ing PH2 or SH adsorbate is found to be due to sterical repulsions between theadsorbed CH3 and the co-adsorbed dopant (see Paper I). In comparison, aneighbouring BH2 affects the CH3 adsorption in a completely different way.For both diamond (111) and (100), the final surface structure (after CH3 ad-sorption) do not show any significant indication of sterical repulsions be-tween the co-adsorbed BH2 and CH3. For the (111) surface, no interactionscould be found between BH2 and the surface radical C, which explains thesimilar adsorption energy compared to the undoped surface. However, for aneighbouring adsorbed BH2 species on the (100) diamond surface, a stabilis-ing interaction could be found between B (in BH2) and the radical C on thesurface (see Paper I). From Table 8, it can be observed that this interactionis not significantly affecting the CH3 adsorption reaction energy for BH2 inposition 1 and 2 on the (100) surface. However, a drastic change can be ob-served with the dopant in position 3.

The adsorption energies presented in Table 8 show that, for both diamond(111) and (100) surfaces, the presence of PH, S or NH will always disfavourthe CH3 adsorption reaction. For all cases investigated, this reduction of ad-sorption energy is due to the formation of a new bond between the dopant andthe reactive adsorption site prior to CH3 adsorption, which thereby increasesthe surface stabilisation (see Paper I). The structural analysis of the surface af-ter CH3 adsorption did generally not show any significant interaction betweenthe dopant and the adsorbed CH3 species. The only exception is a specific re-arrangement observed for the (111) diamond surface and for the (100) dia-mond surface with the BH adsorbate in position 2. The analysis of the surfacestructure shows that an H atom is transferred from the adsorbed CH3 to theneighbouring BH species. Two new co-adsorbed species (CH2 and BH2) arepresent and a new C-B bond is thereby formed. The negative effect induced bythe bond formation between B (in BH) and the surface radical C prior to CH3

adsorption is thereby counteracted by this stabilisation. It results in an adsorp-tion reaction that is less energetically disfavoured

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3.3.2 H abstraction reaction

The calculated H abstraction energies from an adsorbed CH3 species in thepresence of a co-adsorbed dopant are presented in Table 9. These energiesare compared with the energies obtained when the reaction occurs withoutany dopant on the surface (i.e., the adsorption site is only surrounded by hy-drogen).

Table 9. H abstraction energies in the presence of different adsorbed dopants (P, Band S) in both their fully hydrogenated and radical forms.

ΔEabs (kJ/mol) (111) (100)

Pos 1 Pos 2 Pos 3

PH2 -101.8 -102.6 -98.2 -49.1

BH2 -95.2 -164.5 -176.0 -119.0

SH -52.4 -57.8 -47.4 -37.9

PH -340.3 -333.9 -329.6 -256.3

BH -318.8 -405.3 -255.6 -324.7

S -327.5 -288.1 -291.0 -211.6

H -21.4 -15.6

From Table 9, the presence of a co-adsorbed SH is observed to favour Habstraction slightly from an adsorbed CH3 for both diamond (111) and (100).However, the reaction becomes strongly favoured when PH2 or BH2 is co-ad-sorbed on a neighbouring surface carbon. This is the situation for both sur-face orientations and all dopant positions with one exception. For PH2 placedin position 3 on the (100) surface, the reaction energy is almost equivalent tothe value obtained in the presence of SH.

With SH or PH2 as a co-adsorbate, prior to the H abstraction reaction, ster-ical repulsions were observed between the CH3 adsorbate and the co-ad-sorbed dopant species (see Paper I). These repulsions are thereby destabilis-ing the reactive diamond surface and, consequently, favours energetically thefollowing H abstraction reaction. It was also observed that the presence ofBH2 is not interacting with the co-adsorbate CH3 and, hence, will not induceany destabilisation of the surface prior to abstraction (see Paper I). After theabstraction, no significant interaction between the co-adsorbed CH2 and SHspecies could be found (see Paper II). The positive effect by the dopant onthe abstraction energy is then only due to the sterical repulsion prior to thereaction. With PH2, the positive effect was shown to be induced by both sur-face sterical destabilisation (prior to the abstraction) and stabilisation (afterthe abstraction) (see Paper II). After the reaction, a stabilising interaction isobserved between P (in PH2) and C (in CH2) (see Paper II), which furtherfavours the abstraction reaction. This favourable interaction was not ob-

43

served for PH2 in position 3 on diamond (100), explaining that the reaction isless favoured in that case.

It is worth noticing that when PH2 or SH is adsorbed next to the resultingCH2 adsorbate with one H oriented towards the radical adsorbate, this H isfound to be transferred from the dopant to the carbonaceous co-adsorbate.This phenomenon is important since it results in a transformation backwardfrom CH2 to CH3, which may negatively affect the following growth steps.

In the presence of BH2 on the surface, the important improvement in H ab-straction reaction for both surface orientations and all positions considered isexplained by a bond formation between the B (in BH2) and C (in the ad-sorbed CH2) after the reaction (see Paper II). The final surface structure isthereby strongly stabilised and the abstraction enhanced.

For all dopant species and surface orientations studied, the abstraction en-ergies presented in Table 9 show that the presence of a co-adsorbed dopant inits radical form strongly favours the H abstraction process. For almost allcases, no significant interaction between the dopant and the adsorbed CH3,prior to the abstraction reaction, can be observed. One exception was ob-served for BH adsorbed on the (111) surface and in position 2 on the (100)surface. As described in Section 3.2.1, one H is transferred from CH3 to theneighbouring adsorbed BH, to finally result in two new co-adsorbates: CH2

and BH2. This pair of adsorbates form a new covalent bond which furtherstabilises the diamond surface. The energy gained by the H abstraction fromthis rearranged surface appears to be smaller compared to the two others sit-uations.

After the H abstraction reaction, an analysis of the surface structureshowed the presence of a new bond formation between the radical dopantand the neighbouring CH2 (see Paper II). The surface will thereby be sta-bilised and the reaction energetically favoured.

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4. Concluding remarks

Experimentally, the addition of a dopant species in the gas phase is knownto have strong effects on the CVD growth process – either accelerating or in-hibiting it. However, details of the key reactions involved in the CVDgrowth are difficult to extract from experiments only. This thesis investigat-ed theoretically the effects of dopants on reaction steps important for theCVD growth process of diamond using density functional theory. Thedopants studied were N, P, S and B out of which N was more specificallystudied.

4.1 Effect of atomic nitrogenWith a substitutional N positioned within the 2nd, 3rd or 4th carbon layer in

various sites, the reaction and activation energies were observed to bestrongly affected by the dopant through two different mechanisms. For N ina β position with respect to a radical C, a β-scission rearrangement, with theformation of sp2 carbons, took place. The presence of unsaturated carbon isgenerally considered to be responsible for defect formation during thegrowth. For the positions where this rearrangement could not take place, anelectron transfer from N to a surface radical C was observed to lead to theformation of a lone pair. In general, this electron transfer appeared to in-crease the reaction activation barriers which will negatively affect the reac-tion kinetics. The effects induced by substitutional N were thereby mostlycorrelated with the surface degradation and the decrease in growth rate ex-perimentally observed for high nitrogen concentration in the gas phase.

With NHx (x= 1 or 2) adsorbed on the surface, the observed effects on theCH3 adsorption and the following H were small and could hardly explain theinfluence of nitrogen on the diamond CVD growth, observed experimentally.

The effect of a co-adsorbed nitrogen species (NH) on the adsorption ofCH3 (or CH2) next to a SA (or SB) step edge on the diamond (100)-2x1 sur-face was then investigated. The NH species was observed to significantly af-fect, in specific positions, both the CH3 and CH2 adsorption reaction energieswhen adjacent to a SB step edge. However, from these results only, generalconclusions on a possible effect of NH on the diamond growth process aredelicate to formulate.

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It is worth mentioning that an adsorbed NH was observed to significantlyincrease the bond length of the connected C-C dimer. This effect might havea strong influence on the growth mechanism on a (100)-2x1 diamond surfacethorough some alternative reactions not considered in this work.

4.2 Effect of phosphorous, sulphur or boron atomA preliminary investigation on the effect of P, S and B was performed by

studying their influence as fully hydrogenated and radical co-adsorbate onthe CH3 adsorption and H abstraction reactions.

With a co-adsorbed SH, the adsorption reaction was observed to be dis-favoured and the H abstraction favoured compared to the reaction on an un-doped surface which can be explained by sterical repulsion effects.

In the presence of PH2, sterical repulsions were similarly affecting the CH3

adsorption reaction as compared to SH, but the H abstraction reaction wasmore favoured due to the presence of a weak CH2-PH2 stabilising interactionafter the reaction.

It is worth mentioning that an H transfer from a co-adsorbed SH (or PH2)dopant to CH2, leading to CH3 formation, was observed to be energeticallyfavoured. The surface concentration of the highly reactive CH2 species couldthen be affected by the presence of the co-adsorbed dopant which should dis-turb the following growth steps.

With BH2 co-adsorbed on the surface, the adsorption reaction was alsodisfavoured compared to the adsorption on the undoped surface. No stericalinteractions were observed but an interaction between B and the radical sur-face carbon stabilises the reactant surface for subsequent CH3 adsorption.The H abstraction reaction appeared to be favoured by the formation of astrong B-C bond between BH2 and CH2 after the H abstraction.

With the dopants in their radical forms, the H abstraction reaction was ex-tremely energetically favoured compared to the undoped surface due to theformation of a strong XHy-CH2 bond (X = P, S or B and y = 0 or 1), therebystabilising the diamond surface significantly.

In conclusion, an adsorbed boron or phosphorus appears to have a signifi-cant influence on the CH3 adsorption and H abstraction reactions but their ef-fect on the diamond growth mechanism could not be clearly defined. Thesulphur presented a rather limited effect on the two reactions studied, whatcould hardly be correlated with the decrease in growth rate observed experi-mentally.

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5. Future works

From these observations, ideas for further investigations can be proposed.First, it would be interesting to analyse the effect of a substitutional N onspecific reaction steps on the (111) surface. This surface orientation is gener-ally considered to be more quickly degraded in the presence of a high nitro-gen concentration. It would then be interesting to compare the effects in-duced by substitutional N for both surface orientations in order to check if itcan be confirmed theoretically.

Within Paper V, the adsorbed NH radical was observed to increase thebond length of the C-C dimer on the surface. This bond weakening mighthave significant effects on the growth mechanism for the (100)-2x1 surfaceorientation. It would then also be of a great interest to investigate if this ad-sorbed NH radical could be responsible for the catalytic effect of N on thegrowth rate observed experimentally.

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6. Populärvetenskaplig sammanfattning

Diamant är mest känd som en exceptionell och dyrbar ädelsten. Det ärbland annat på grund av dess ovanliga ljusbrytning, vilket gör den mycketattraktiv som smycke. En annan utmärkande egenskap som diamant ärvälkänd för är dess extrema hårdhet, vilket är en av de högsta för ett naturligtmaterial. I och med industrialiseringen har forskning på nya typiska materialkommit att initieras. Industrierna var till att börja med endast intresserade avdiamant för dess extrema hårdhet, men med tiden har många andraexceptionella egenskaper kommit att belysas. Därmed har mängdenpotentiellt viktiga industriella tillämpningar börjat öka drastiskt. Tillexempel har diamant uppvisat en betydande kemisk resistant under extremaförhållanden. Det har även konstaterats att diamant uppvisar en högkompatibilitet mot mänsklig vävnad, därför har diamant kommit att betraktassom en perfekt kandidat för många bio-elektroniska applikationer. Dessaunika egenskaper, och andra som inte här är nämnda, har medfört ett ökatintresse för diamant. Den största nackdelen med detta material är emellertiddiamantsyntes av tillräckligt god kvalitet och med möjlighet till detaljeradprocess-styrning är svårt att uppnå. För högteknologiska tillämpningar ärmöjligheten till kontroll och styrning av syntesprocessen av ytterstabetydelse för de slutliga resultaten i jakten på att skräddarsy diamant förspecifika tillämpning.

Att syntetisera diamant med specifik geometri och/eller med möjlighetenatt deponera tunna diamant-filmer på en annan typ av material, kan uppnåsgenom att använda en metod som består i att växa diamant från gasfas.Eftersom diamant är helt uppbyggt av kol, kan metan (CH4) i en blandningmed vätgas (H2) vara lämplig som gasblandning vid diamant-beläggning påönskat substrat. Med hjälp av gasfas-aktivering vid något högre temperaturkan man sedan uppnå en ytkemisk kontroll, och därigenom kunna styratillväxten. Denna teknik, som kallas ”Chemical Vapour Depostion” (CVD),utnyttjar olika aktiveringsmetoder; glödtråd, värme, plasma eller laser. Manskulle därmed i teorin kunna växa högkvalitativ diamant på många olikatyper av underlag. Kravet är dock att detta underlag (substrat) skall tåla entemperatur upp till ca 1000°C. Emellertid är denna tillväxtprocess bådemycket komplex och dynamisk, vilket innebär en ansenlig mängdkonkurrerande delreaktioner på ytan. Kunskap om dessa delreaktioner (och

48

hur de interagerar med varandra) innebär att man kan få bättre kontroll avden totala tillväxt-processen.

Det vore önskvärt att kunna analysera en växande diamantyta undertillväxt (in situ), men det har i alla fall under årens lopp utvecklatskarakteriseringsmetoder för att analyseras diamantytor utanförtillväxtkammaren. Vad som har visat sig vara oerhört svårt (i vissa fall tilloch med omöjligt) är att analysera ytan, med dess sammansättning ochkemiska processer, på atomär nivå. Under de senaste decennierna harlyckligtvis både datorer och kvantmekaniska beräknings-program kommit attgenomgå en mer eller mindre lavinartad utveckling. Dessa hjälpmedel gördet möjligt att använda bl. a. kvantmekaniska beräkningar som ett viktigtverktyg (som komplement till syntes och karakterisering) när man sökerinformation om ytreaktioner (vid t.ex. tillväxt) på atomär nivå. Dennainformation kan sedan användas för att i) förklara experimentellaobservationer, ii) designa experimentella uppsättningar, samt iii) ersättaexperiment där dessa ej kan genomföras.

I denna avhandling har teoretiska metoder använts för att undersökaeffekten av ett dop-ämne (dvs en icke-kolatom som N, P, B och S) påtillväxtprocess en hos diamant. Experimentellt har man visat att förekomstenav dessa dop-ämnen har en betydande inverkan på tillväxtens kemiskaprocess. Som exempel kan nämnas att stora mängder kväve i gasfasen harbefunnits försämra både ytmorfologin hos diamant samt desstillväxthastighet. Det är internationellt av stort intresse att försöka förståvarför sådana effekter äger rum. Denna avhandling tar upp effekten av ettdopämne på några noggrant utvalda nyckelprocesser inom diamant-tillväxten. De teoretiska beräkningarna har här visat att dopämnet N påverkardessa viktiga tillväxtsteg på ett negativt sätt, både vad gäller tillväxthastighetoch morfologi. Mer specifikt fann vi att N bara påverkade tillväxten negativtnär det befann sig inbäddat under ytan. De i denna avhandling erhållnaresultaten kan förklara tidigare gjorda experimentella observationer. De treövriga dopämnena (P, B och S) har här också visats ha ett intressantinflytande på två specifika reaktions-steg, men ett direkt samband medexperimentella observationer var svårare att uppnå.

49

7. Acknowledgments

First of all, I would like to thanks my supervisor Professor Karin Larssonfor her guidance and encouragements during all my PhD time.

I am also very thankful to Professor Jan-Otto Carlsson for his support andfor the stimulating environment within the department.

Professor Josh Thomas, Professor Kristina Endström and Dr TorbjörnGustafsson thank you for the possibilities you gave me to develop myknowledge on batteries and fuel cells in many occasions and various places.

The administrative part and the research of apartments would have beenhell without Eva Larsson, Gunilla Lindh and Katarina Israelsson. Thank youfor all the help !

Katrin, Emilie, Anti and Jaanus, it is impossible to express all my grati-tude for all you have done for me. It was such a great time, Thank you !

I would like also to specially thanks Erik Lindahl for the discovery of thewild part of Sweden, the long discussions on any kind of winter sports, etc.and Oscar for the introduction to the Swedish gastronomy. Of course, I amalso very thankful to Erik Lewin, Erika, Anna Fallberg, Wendy, Daniel Petri-ni, Kinson, Gabi, Jussi, David Raymand, Tomas, and all the people from theDepartment of Materials Chemistry for creating a such enjoyable researchenvironment. It was a real pleasure to meet you all for work or extra workactivities !

All the conferences would not have been the same without all theDRIVERs. Rosaria, Zoya, Andrada, Hadwig, Bianca, Wenying, Michele,Wojciech, Fabio, Ovidiu and Alexander, thank you so much for all the greattime and the interesting discussions. I am also very thankful to all the seniorsfor the time they spend increasing our knowledge in the diamond field.

I take the opportunity to acknowledge the Financial support form the Eu-ropean Project RTN DRIVE within the 6th Framework Program (no. MRTN-CT-2004-512224).

Xavier, je ne saurais trop te remercier pour ton soutient quasi quotidien aucours de ces 4 années passées en Suède. Merci pour tout !

Guillaume, Sophie, Guerric, Sarah, Ben, Yoann, Dimitri, Stefano, Denis,Nath, Seb, Murielle et tous les autres, je vous remercie pour votre insatiableenvie de faire la fête dès que je posais les pieds en Belgique ! Ce fut desmoments exceptionnels. Et Hélène, merci pour la relecture !

50

Un tout grand merci également à mes parents, bonne-maman, grand-maman, Diane, Gautier, Valéry, Louise, Margot, et tout le reste de la famillepour vos encouragement et votre soutien durant ces 4 années.

Sandrine, ton amour m'a toujours encouragé à aller de l'avant et àpersévérer même dans les moments les plus rudes. Merci pour tous ces bonmoments en Belgique, en Suède, en Espagne ... Et pour ceux à venir !

Uppsala – 21 January 2009

51

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The Influence of Dopants on the Growth of Diamond by CVD

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