surface stabilization and electrochemical properties from ...171218/fulltext01.pdf · experimental...

ACTA

UNIVERSITATIS

UPSALIENSIS

UPPSALA

2007

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 380

Surface Stabilization andElectrochemical Properties from aTheoretical Perspective

DANIEL PETRINI

ISSN 1651-6214ISBN 978-91-554-7059-3urn:nbn:se:uu:diva-8372

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Till Mamma

"Ideas can not be fought except by means of better ideas. The battle consists not of opposing, but of exposing; not of denouncing, but of disproving; not of evading, but of boldly proclaiming a full, consistent and radical alternative." Ayn Rand

List of articles

I. A theoretical study of the thermodynamic and kinetic aspects of terminated (111) diamond surfaces D. Petrini, K. Larsson Accepted by The Journal of Physical Chemistry C

II. A Theoretical Study of the Energetic Stability and Geometry of Hydrogen- and Oxygen-Terminated Diamond (100) Surfaces D. Petrini, K. Larsson The Journal of Physical Chemistry C, 111, 2 (2006)

III. Structural and energetic consideration of H, F, S, Cl-terminated Diamond (100) and (111) surfaces: Quantum Mechanical Study D. Petrini, K. Larsson Submitted to The Journal of Physical Chemistry C

IV. Clean and Hydrogen-Terminated cubic Boron Nitride (100) sur-faces: A Quantum Mechanical Study D. Petrini, K. Larsson In manuscript

V. Electron-Transfer Doping on a (001) Surface of Diamond: Quantum Mechanical Study D. Petrini, K. Larsson The Journal of Physical Chemistry B, 109, 47 (2005)

VI. Electron transfer from a Diamond (100) Surface to an Atmos-pheric Water Adlayer: A Quantum Mechanical Study D. Petrini, K. Larsson The Journal of Physical Chemistry C, 111, 37 (2007)

VII. On the origin of the reactivity on the non-terminated (100), (110) and (111) diamond surfaces: an electronic structure DFT study D. Petrini, K. Larsson Submitted to The Journal of Physical Chemistry C

Contents

1. Introduction.................................................................................................9 1.1 Diamond .............................................................................................10

1.1.1 Surface functionalization ............................................................12 1.1.2 Induced p-type doping mechanism.............................................13

1.2 cubic Boron Nitride............................................................................18

2. Computational methods ............................................................................19 2.1 Quantum mechanics ...........................................................................19 2.2 DFT ....................................................................................................21 2.3 Computational approaches .................................................................24

2.3.1 Basis sets.....................................................................................24 2.3.2 Exchange and correlation functionals.........................................25 2.3.3 Transition state searches .............................................................26 2.3.4 Charge partitioning techniques ...................................................26 2.3.5 Chemical reactivity indications ..................................................28

3. Results.......................................................................................................29 3.1 Diamond and c-BN Surface properties ..............................................29

3.1.1 Energetic stability .......................................................................30 3.1.2 Hydrogen adsorption ..................................................................31 3.1.3 Oxygen adsorption......................................................................32 3.1.4 Hydroxyl adsorption ...................................................................33 3.1.4 Fluorine, sulfur and chlorine adsorption.....................................35 3.1.5 Cubic boron nitride .....................................................................37 3.1.6 Electronic structure.....................................................................39 3.1.7 Transition state searches .............................................................42

3.2 Indications of charge transfer .............................................................44 3.2.1 Population analysis .....................................................................45 3.2.2 Surface-adlayer interaction .........................................................48

4. Concluding remarks ..................................................................................51

Acknowledgements.......................................................................................55

5. Summary in Swedish ................................................................................57

7. References.................................................................................................61

Abbreviations DFT Density functional theory HSC High surface conductivity CVD Chemical vapor deposition FET Field effect transistor SCF Self consistent field LDA Local density approximation GGA Generalized gradient approximation TS Transition state FF Fukui function

9

1. Introduction

“You see things; and you say »why?« I dream things that never were; and I say »why not?«” The serpent to Eve, according to George Bernard Shaw The study of interfacial chemical reactions – surface reactions – began in the early 1800s with catalysis, tribology and electrochemistry investigations, and today surfaces lie in the forefront of chemistry research. A surface represents the interface between condensed matter (e.g., diamond) and the surroundings (e.g., air), and is involved in many chemical and physical processes. Typical surface applications are hard protective coatings, sensors, catalysis, inte-grated circuits and information processing and storage. Atomic resolution experimental surface studies are complicated due to the Angstrom (10-10 m) scale that represents typical surface dimensions. Nevertheless, surfaces may be modeled by using computational techniques whereby mechanisms, struc-tures, and other various properties can be determined at a molecular level with acceptable accuracy. The importance of surface science was recently recognized by the Noble committee in their scientific background descrip-tion of the 2007 Nobel Prize in chemistry: “Thus one can see the study of chemical reactions on surfaces as one route towards a deeper understanding of reactions in condensed phases in general.”

Two of the most exotic surfaces of today are diamond and cubic boron ni-tride, and they both show remarkable and similar properties: they are iso-electronic and their structures are based on FCC packing with half of the tetrahedral sites occupied. In addition, they are large band gap semi-conductors and both are extremely hard. Hence, these surfaces have a strong potential as coatings where their extreme capabilities are used for novel ap-plications. However, to predict and understand the experimental observa-tions for these surfaces, thus utilizing their full potential, more knowledge about, e.g., growth, structure, energetic stability and electronic structure are required. The purpose of this thesis is to study the geometries, mechanisms and electronic structures of diamond and cubic boron nitride surfaces, using quantum mechanic techniques. More specifically, two main subjects have been investigated: i) the properties of clean and terminated diamond and cubic boron nitride surfaces, and ii) the electron transfer from a diamond surface into a water-based adlayer. The latter is more specific and applica-

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tion oriented, whereas the former is more general with a contemporary re-search approach. The electron transfer is strongly dependent on the type of adsorbate terminating the surface. 1.1 Diamond Many of the extreme properties of diamond are due to the crystalline struc-ture, where the equivalent bonds between sp3 hybridized carbon atoms are responsible for heat conduction[1], optical brilliance, and the ability to with-stand large external pressures (i.e., diamond is the hardest material known). Other properties include low thermal expansion, IR-transparency and UV-reflectivity, chemically inertness and radiation hardness.[2-4] Moreover, some of diamonds´ electrical properties are also very good, e.g., breakdown voltage and carrier mobility, and the combination of semiconductor proper-ties of diamond are superior compared to most other semiconductors.[5-9] Diamond has successfully been used in ionic sensors, biosensors, transistors, electrochemical electrodes and UV mirrors.[10-15]

There are, however, areas where a deeper understanding of diamond sur-faces is needed to fully exploit its potential. For example, although p-type doping with e.g., boron is feasible, thermally activated n-type doping (using e.g., N, P, S impurities) is somewhat more complicated.[16-19] Bipolar tran-sistors, e.g. boron/nitrogen pn-junctions, have many drawbacks and do not utilize the full potential of diamond transistors. Nitrogen and phosphorous are deep donors, with low mobility which will affect the growth quality. Sulfur doping is not perfected, and some questions have risen about the ori-gin of conductivity.[19] On the other hand, unipolar carrier transport has been realized and been utilized in p-type channel field effect transistors and vertical Schottky diodes.[5, 20]Even if diamond is the hardest material known, it has limited use in tribological application regarding ferrous metals due to the increased solubility of carbon at elevated temperatures. Synthetic diamond films for applications, and contemporary research, became more readily available with the introduction of chemical vapor deposition (CVD) techniques. However, the growth process is not fully understood and, conse-quently, not perfected.[21]

The two most common CVD techniques for synthesizing diamond are hot-filament CVD[22], HFCVD, and microwave-plasma enhanced CVD, MPECVD[23]. HFCVD is a simple procedure with great upscale potential, but with the shortcoming of film quality and a more limited set of allowed precursor gases due to the degradation of the filament. MPECVD gives ex-cellent film quality and allows aggressive precursor gases (e.g., oxygen). The as-deposited (i.e., CVD-grown) diamond surfaces are hydrogen-terminated and rather chemically stable at intermediate temperatures due to the inert character of the C-H bonds. Terminating the diamond surface with

11

different species, e.g., oxygen or fluorine, has profound consequences for the surface electronic properties[24-27], structure[28, 29] and reactivity[30, 31]. Furthermore, also the electron affinity[24, 32-34], optical characteristics[35, 36], wetting capabilities[37], dipole moments and energetic stability are strongly dependent on the adsorbates present on the surface. In addition, the adsorption of non-carbon species has a profound effect during the CVD dia-mond growth process. The dominating gas phase species (often above 95%) during CVD growth of diamond is hydrogen, originally in the form of mo-lecular H2. One of the main functions of hydrogen is to uphold the sp3 hy-bridization of the top-most carbon atoms, i.e., to protect the growing dia-mond film from collapsing into a hexagonal structure (graphite). In addition, atomic hydrogen etches away graphite carbon and helps promote reactive sites for the adsorption of carbon-containing precursors.[38] Although the original carbon source is most often methane, CH4, many other carbon spe-cies have been shown to exist in the reaction chamber due to gasphase acti-vation; for example CH3, C2H2 and C2H4. The predominant growth species are generally assumed to be CH3; the bond enthalpy of the C-C bonds in C2Hx species are probably too large.[21, 39] However, ultra nano-crystalline diamond films (with fine grain-sizes) are synthesized using a hydrogen-poor gas mixture and the C2 dimer as main growth precursor.[40] Oxygen[41, 42] and fluorine[43-45] may also improve diamond film quality and growth rate, by introducing radicals and reactive surface sites. A ternary phase diagram of C-O-H have been constructed to obtain a general concept of diamond CVD growth.[46] Molecular chlorine readily dissociates into chlorine atoms, which may enhance growth rate by producing hydrogen atoms and by re-moving hydrogen from the surface.[47-49] The exact nature of the local (molecular level) structure, electronic configuration and energetic stability of the diamond surfaces are not known, despite the large number of experimen-tal studies available. This thesis is attempting to explain and predict some of the properties of the diamond surface. More specifically, the structure, ener-getic stability and reactivity of non-, hydrogen-, oxygen-, fluorine-, chlorine- and sulfur-terminated diamond (100), (110) and (111) surfaces have been studied.

As-grown hydrogen-terminated diamond films exhibit an unusual high electric conductivity compared to bulk diamond. This high surface conduc-tivity was discovered 1989[50], and this effect is very favorable to use in metal-on-semiconductor-FET (MESFET) applications where very low leak-age current and high breakdown voltages have been shown. Furthermore, diamond is expected to yield high power, high frequency and high efficiency transistors (important in, for example, future communication equipment).[51, 52] The origin of this strong decrease in surface restistivity is still under debate, where many models have been proposed. One of the models is the charge transfer doping mechanism where electrons are ejected into a wetting layer close to the surface.[53] It was first proposed as a hole accumulation

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layer formed by the presence of oxonium ions.[54] Another model is based on shallow acceptor states in the near-surface region.[55] Only the charge transfer doping model has been considered and studied within this thesis.

1.1.1 Surface functionalization The diamond (100) and (111) surfaces represent the most studied surfaces since these low index surfaces dominate as growth planes during chemical vapor deposition (CVD) of diamond. Because the carbon atoms within the top-most layers have a local bonding-configuration that differs greatly from that of the bulk, they may reconstruct (as most semiconductors do). Recon-struction is the rearrangement of the positions of the top-most atoms yielding a more energetically favorable configuration. The surface reconstruction reduces the relaxation effects to their bulk equivalents.[56] The 2x1-reconstruction of the diamond (100) surface is especially well known, and the most probable reconstruction of the (111) surface (occurring at higher temperatures) is the 2x1 �-bonded »Pandey« chain. The (100) and (111) surfaces, along with their reconstructions, are shown in Fig 1.1.

Figure 1.1 The diamond surfaces of a) (100)-1x1, b) (111)-1x1, c) (100)-2x1 and d) (111)-2x1.

A clean, i.e., a non-terminated, semiconductor surface is usually very reac-tive due to the existence of dangling bonds, i.e., unpaired electrons on the non-terminated top-most atoms. The energy change of the system (the sur-face) when species are covalently bonded to the surface is called the chemi-sorption energy (also known as adsorption energy). This energy is usually negative and, hence, exothermic. Clean and hydrogen-terminated surfaces have been extensively studied using experimental[57-59] and theoretical[60-63] methods. This is due to the important role of hydrogen in the CVD

13

growth, as well as the stability of hydrogen-terminated surfaces. Oxygen species adsorbed onto the diamond surface are also of interest[32, 64-73] due to the omnipresent oxygen within the atmosphere, oxygen inclusion during growth, and the oxygen-induced surface property changes. Fluo-rine[74-76], chlorine[48, 77] and sulfur[78-80] have also generated some attention for their capability to improve synthesis, to include impurity doping or change surface characteristics. However, detailed studies regarding ad-sorption energies and structural geometries, as a function of termination coverage have not been presented. Many of the theoretical studies have been using different computational techniques or lack of periodic boundary condi-tions (i.e., cluster calculations). In addition, there have not been any compre-hensive studies of surface reactivity of clean diamond surfaces. Diamond surfaces with hydrogen, oxygen, fluorine, sulfur and chlorine chemisorbed onto the surface have here been studied in papers I, II, and III. Paper II fo-cuses on the surface geometry and energetic stability of diamond (100) sur-faces with varying amount of hydrogen- and oxygen-containing species ad-sorbed onto the surface. Furthermore, paper I complements the results in paper II by investigating the 1x1 and 2x1 reconstructions of the diamond (111) surface, and in addition expand the results with transition state searches. Paper III examines the diamond (100) and (111) surface (with their 1x1 and 2x1 reconstructions) with H, S, F and Cl as adsorption species. Paper IV analyses the reactivity of diamond (100) and (111) surfaces using in-detail electronic structures of the clean 1x1 and 2x1 surfaces.

1.1.2 Induced p-type doping mechanism Materials with a rather large band gap, separating the valence (occupied) band from the conduction (empty) bands, are termed semiconductors. Elec-trons need to be promoted to higher energy levels, e.g., by thermal excita-tions, to increase the conductivity and to be able to sustain an appreciable current. The intrinsic electronic conductivity of semiconductors is very low compared to metals. However, the success for electronic applications involv-ing semiconductors hinges on the doping process, where the foreign atoms that are incorporated into the semiconductor crystal either introduces empty electronic states close to the valence band edge (p-type doping) or occupied electronic states just below the conduction band edge (n-type doping). Al-though diamond has a very large band gap of 5.5 eV [81, 82] (compared to 1.12 eV for silicon), it was noticed by Landstrass and Ravi[50] that diamond surfaces may experience an induced p-type doping whereby the surface con-ductivity was raised many orders of magnitude.[57] The at room temperature fully activated charge carriers have a high sheet density (~1013 cm-2) and are temperature independent (120-400 K), and thus suitable for certain FET applications. Both low index surfaces, as well as polycrystalline surfaces, exhibit this effect.[83] It was later on shown that there are two prerequi-

14

sites[33, 53, 84] for this high surface conductivity: i) a predominantly hy-drogen-terminated surface, and ii) an omnipresent water-based adlayer con-taining reducible species. The vacuum level for a 2x1 reconstructed diamond (100) surface is lowered below the conduction band minimum when it is hydrogen-terminated (as shown in Fig. 1.2) which considerable lowers the ionization energy from 6.7 eV to 4.2 eV. This effect is termed »negative electron affinity« (termed Ea in Fig. 1.2). The other prerequisite for a high surface conductivity is that the diamond surface has to be introduced into normal atmosphere, i.e., the high conductivity can not be seen in vac-uum.[85]

Fig. 1.2 Simple energy-diagrams of the clean and H-terminated diamond surface.

One proposed mechanism responsible for the high surface conductivity (HSC) of diamond is the electron transfer doping whereby a reducible wet-ting adlayer physisorbed onto the diamond surface oxidizes the diamond surface and leave holes within the top-most diamond layers.[53, 84, 86] The chemical potential of the reducible adlayer must lie below the valence band maximum for the electron transfer to be favorable. The first reducible spe-cies considered was the oxonium ion, i.e., a protonated water molecule originating from the dissolved carbon dioxide of the atmosphere (yielding carbonic acid). The reduction reaction of the resulting oxonium ion is:

223 222 HOHeOH �� [1.1]

which is defined to have a reduction potential of 0 V vs. the standard hydro-gen electrode, SHE. Adjustment of this potential due to temperature, concen-trations and partial pressures other than the standard state of 293 K, 1 M and 1 bar, respectively, is done via Nernst equation:

15

��

��

��

red

ox

aa

nFRTEE ln0 [1.2]

where n is the number of electrons, R is the gas constant, T is the tempera-ture, F is Faradays constant, and a is the activity of the species being reduced or oxidized. The mapping of electrochemical reduction potential to chemical potential are done via the following formulas[87]:

PTnG

,��

� [1.3]

nFEG �� [1.4]

where � is the chemical potential and G is the Gibbs free energy. The (abso-lute) chemical potential for the equation 1.1 above has been determined to be approximately -4.5 eV.[88] Varying the pH and using the reduction potential for the common atmospheric species H+, O2 and O3 under normal partial pressure, in conjunction with equation 1.2, give intervals where the chemical potential (corresponding to an energy) lies below the diamond surface ioni-zation energy (shown in Fig. 1.3). Electron transfer from the diamond sur-face to this species should be spontaneous since the chemical potential lies below the diamond ionization energy. Oxygen (O2) is omnipresent in normal atmosphere and has the potential to oxidize the diamond surface at any pH, whereas for the oxonium ion it is only spontaneous below pH 6-7. In fact deoxygenized water adsorbed onto diamond surfaces shows less HSC com-pared to a normal adlayer.[85] The ozone (O3) reduction line has been in-cluded even though ozone is present at very small concentrations in the at-mosphere. The reason is that it has been shown to restore the HSC of an-nealed diamond surfaces.[89, 90]

16

Fig. 1.3 Range of pH values where the electron transfer from a diamond surface to H+, O2 or O3 is calculated to be energetically favorable.

A plausible model for this electron transfer is shown in Fig. 1.4 where elec-trons from the top-most carbon atoms are injected into the adlayer since the vacant orbitals of the oxonium ion (i.e., the lowest occupied orbitals, LUMO) lies below the highest occupied orbitals (HOMO) of the diamond surface. This process results in holes within the diamond surface, and con-tinues until the positive space charge balances the driving force of the verti-cal charge transfer. A semiconductor surface and at the surface unfilled en-ergy states must align their Fermi levels (defined as the energy of the elec-tronic state which has 50% probability of being occupied), called Fermi level pinning, i.e., the independence of the sample work function to bulk doping. The valence band must be bent upwards if charge transfers across this inter-face, as can be seen in Fig. 1.4.a.

17

Fig. 1.4 The induced p-type doping mechanism of the diamond surface where elec-trons are injected into a lower lying water adlayer, leaving holes within the top-most carbon atoms (denoted by the + signs). The initial (before contact, figure a) band structure indicates that there is a difference in the chemical potential (�) and the Fermi level. Electrons are spontaneously injected into the adlayer (b) due to lower available orbitals, whereby the Fermi level and the chemical potential meet (c) and the holes causes a band bending.

A termination of the diamond surface with oxygen will completely de-stroy[91] the HSC by rendering the surface a positive electron affinity, PEA. This may be utilized in making some areas of the surface conductive, whereas the others are non-conductive (this has been used for e.g., lithogra-phy[92]). Paper V studies the effect of the termination species on the elec-tron transfer doping mechanism. In particular, the number of electrons trans-ferred from an (100)-2x1 H-terminated surface into an acidic water adlayer under H, OH, and O-termination are studied using different techniques. In contrast, paper VI focuses on the effect of the species within the attached water adlayer. The tendency (and prerequisites) for charge transfer from an H-terminated (100)-2x1 surface into a rather large water-based adlayer, con-taining water, molecular oxygen, oxonium ion and ozone, is here especially studied.

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1.2 Cubic Boron Nitride Similar to diamond, cubic boron nitride (c-BN) features extreme hardness, high thermal conductivity, as well as a wide band gap. However, cubic boron nitride is a synthetic material and is not found in nature. Since boron and nitrogen have three and five valence electrons, respectively, it implies that BN species are iso-electronic with carbon, which has four valence electrons. In fact, all of the carbon phases (graphite, cubic diamond and hexagonal diamond (lonsdaleite)) have in boron nitride a corresponding structure; h-BN, c-BN and w-BN, respectively. Whereas diamond is sensible to reactions with ferrous elements and the n-type doping process is not readily available, c-BN does not exhibit these drawbacks. Hence, c-BN has a profound poten-tial as a protective coating and for applications like bipolar electronic de-vices. Conversely, the c-BN growth process presents a major obstacle com-pared to diamond. Harsh synthesis methods, including energetic ion bom-bardment, yields c-BN with incorporation of stresses and structural de-fects.[93-96] The generation of defects will give poor crystalline quality, small grain size, and high density of grain boundaries.[97, 98] Thus, a more gentle CVD growth is needed. Some of the prerequisites[99] for a successful growth has been presented: (i) stabilization of the c-BN surface during growth, (ii) sufficient high mobility of the precursor at temperatures in the stability range of c-BN, (iii) preferential etching of h-BN and other ‘‘non-c-BN phases’’, and (iv) preventing secondary nucleation of h-BN during growth of c-BN. Theoretical investigations have included the low-index c-BN surface planes with different reconstructions, and under hydrogen- or fluorine-termination[100-108].

Structural, energetic and reactivity considerations of the (100) plane of c-BN is presented within this thesis. Both the boron- and nitrogen-rich sur-faces have been studied. The motivation for studying the (100) plane is that it is one of the most common in the growth process.

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2. Computational methods

"Nature, to be commanded, must be obeyed." Ayn Rand explains one of four pillars of Objectivism: metaphysics - Objec-tive Reality The advent of quantum mechanics began with a series of unexplainable ex-perimental observations and the historically most important experiment was the black body radiation. Lord Rayleigh encapsulated at the end of the 1800 century two laws into the Rayleigh-Jeans law, which unintentionally caused the collapse of classical physics. The effect was named the ultraviolet catas-trophe. Max Planck solved the ultraviolet catastrophe with Planck’s Distri-bution law, by introducing statistical mechanics. He proposed that energy of radiation was quantized into bundles of energy, photons. This discreetness of energy is not seen in classical physics where all variables are continuous. Max Planck once said; “Experiments are the only means at our disposal; the rest is poetry, imagination”. Fortunately, both Werner Heisenberg and Er-win Schrödinger had a lot of imagination as they 1926 independently, and differently, began to illuminate the mysteries concerning quantum mechan-ics.

2.1 Quantum mechanics The time-independent Schrödinger equation specifies the energy of a system:

�� EH � [2.1]

Here H is an operator called the Hamiltonian. It operates on a function, �, the wave function. When an operator operates on a function, it usually yields another function. However, in the Schrödinger equation above it leaves the function (�) unchanged, except multiplied by a constant (E for energy). If such a relation exists, the function (�) is called an eigenfunction and the constant (E) is called an eigenvalue. The eigenfunction above is called the wave function, and it completely describes the system. »The system« could be e.g., an atom, a molecule or a surface. All properties of a system can be obtained if you have the appropriate operator and the wave function (e.g., the

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Hamiltonian operator, H, gives the total energy, E). The wave function has a real interpretation called the Born interpretation; the probability for a particle being found within a volume element, d�, at the point r, is proportional to

� � �� dr 2 [2.2]

Thus, the wave function is a probability density. The Hamiltonian of a non-relativistic, molecular system without external electrical or magnetic field is described by:

��

��

� ��

��

��

��

N

k

N

il ikl

lkN

i

N

ij ij

N

i

M

k ik

k

M

kk

k

N

ii

e

rZZe

re

rZe

mmH

1 1

2

1 1

2

1 1

2

1

22

1

22

221

221 ��

[2.3]

The five terms on the right side are (from the left): i) the electron kinetic energy, ii) the nucleus kinetic energy, iii) the electrostatic energy (whose expectation value are also known as the external potential), iv) the (repul-sive) electron-electron interaction, and vi) the (repulsive) nucleus-nucleus interaction, respectively. The constants are as follows: mx is the mass of particle x, and rx,y is the distance between particle x and y, Z is atomic num-ber of the nucleus, and e is the elementary charge (of an electron). The Ham-iltonian in Eq. 2.1 above may be simplified using the Born-Oppenheimer approximation that neglects the movements of the nuclei and reduces the second and fifth term in Eq. [2.3] to two constants. Hence, the second and fifth term of the Hamiltonian may be omitted, which yields:

� ��

��N

i

N

ij ij

N

i

M

k ik

kN

ii

ee r

erZe

mH

1 1

2

1 1

2

1

22

221 � [2.4]

which is called the electronic Hamiltonian. Thus, the Schrödinger equation, [2.1], may be simplified into:

�� ee EH � [2.5]

The total energy of the system may now be divided into one electronic and one nucleus part.

ne EEE �� [2.6]

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Solution of E.q. 2.5 is exceedingly difficult and analytical solutions exist only for one-electron systems, e.g., the hydrogen atom. However, an accept-able trial wave function may be tested with the variational principle, which states that the quality of a trial wave function is related to its associated en-ergy: the lower the better. The variational principle, in Diracs bracket nota-tion for the expectation value (E), is described by:

000ˆˆ �� HEEH trialtrialtrial �� [2.7]

Thus, a Hamiltonian operator working on any trial wave function gives higher or (at best) the same energy as the true ground state energy. Although searching through every possible wave function is not feasible, the principle may be used to search for the best solution within a finite and practicable subset of all wave functions. Thus, if the real ground state wave function is not included in this subset, which is very likely, it will lead to an approxima-tion of the wave function.

2.2 DFT As described above, minimizing the energy of a chemical system by varying a plausible wave function could yield results close to the true solution to the Schrödinger equation. One important approximation is the Hartree-Fock approach, which approximates the N-electron wave function with N one-electron wave functions and they are represented by a so-called Slater de-terminant. Thomas and Fermi proposed another approach to the solution by using the density as the central quantity rather than the wave function. They made crude approximations to the total energy dependence of the density, i.e., the mapping of the density to the energy. Coarse approximations were used for the kinetic energy, neglecting exchange and correlation effects. Consequently, it became unsuccessful for chemical applications.

In 1964 Hohenberg and Kohn published a paper which lay the ground-work of modern density functional theories, and where two theorems were presented.[109] The first theorem concluded that there cannot be two differ-ent external potentials (due to the electron-nucleus attraction, see E.q. 2.5) that give the same ground state density, i.e., the ground state density uniquely describes the external potential. Hence, the ground state density yields the Hamiltonian that gives the wave function. All ground-state proper-ties are therefore a functional of the electron density. A functional takes a function as input but the output is a number just like a regular function. The energy functional of a chemical system will look like this:

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� � � � � � � �0000 �� Neee EETE �� [2.8] where T is kinetic energy, and Eee is the potential energy due to electron-electron interaction (repulsive). ENe is the nucleus-electron attractive interac-tion, i.e., the external potential acting on the density. Separating the system dependent (the external potential acting on the density) and non-dependent components (the kinetic energy and electron-electron interaction) yields:

� � � � � � � �� eeext ETrdVrE �� 0000 [2.9]

� � � �00 �� HKext FrdVr ��

where FHK[�] is defined as the Hohenberg-Kohn functional. Finding the ex-act solution of equation 2.6 would be possible if the Hohenberg-Kohn func-tional were known. Some terms included within FHK[�] are known (i.e., the classical kinetic energy and the classical Coulomb electron-electron interac-tion) but the unknown (non classical) terms are the problem within the den-sity functional theory and these have to be approximated. The other theorem establishes a variational principle; of all the allowed densities, only the ground state density attains the minimum energy.

The implications of these two theorems are profound. The wave function, properties, ground and excited states, are encoded within the density. Kohn and Sham published 1965 an article which gave an insight into how to ap-proach the difficulties associated with the Hohenberg-Kohn functional de-scribed above.[110] They realized that a large part of the kinetic energy might be determined exactly if an orbital-based non-interacting system is introduced. The remainder is collected with other non-classical electron-electron interactions into the exchange-correlation energy, which yields the following energy expression:

� � � � � � � � � �� NeXCs EEJTE �� [2.10]

where the Ts is the exact kinetic energy of a non-interacting system, J is the electron-electron coulomb interaction, EXC is the exchange-correlation en-ergy, and ENe is the electron-nucleus interaction. The exchange-correlation energy is the only unknown term, which consists of the remainder of the kinetic energy and non-classical potential energies:

� � � � nclCXC ETE �� [2.11]

23

where Encl includes self-interaction, exchange and correlation effects. Kohn and Sham now introduced the concept of one-electron orbitals, �, termed Kohn-Sham orbitals. Expressed as a Slater determinant, these orbitals repre-sent the exact wave function to an artificial non-interacting reference system, �:

� � � � � ��

� � � � � �NNNN

N

N

S

xxx

xxxxxx

N�

��

��

��

��

��

��

��

��

21

22221

11211

!1

�� [2.12]

where N is the number of electrons. Furthermore, this non-interacting system is connected to a real, interacting system by varying an effective potential in the Hamiltonian so that the density exactly equals the ground state density. Applying the variational principle to Eq. 2.10 and 2.12 yields an equa-tion[111], for which the solution is the orbitals that minimize the corre-sponding energy:

� � iiieff rV ��

� �� 1

2

21 �

[2.13]

� � � � � � �� M

A A

AXCeff r

ZrVrdrrrV

112

12

21

��

� � [2.14]

Thus, the non-interacting system is related to a real system through the effec-tive potential, where the exchange-correlation potential is the only unknown. This potential is defined as the functional derivate of the energy:

�� XC

XCEV � [2.15]

If the exact form of the exchange-correlation potential was known, then the exact density would also be known. Eq. 2.13 must be solved iteratively and is known as the self-consistent field (SCF). A plausible input density is used in the optimization SCF procedure.

24

2.3 Computational approaches There are many different computational approaches to the solution of the DFT equations. Specific choices of e.g., basis sets, exchange-correlation functionals, and integration techniques must be made. Other properties, be-sides the energy, may be extracted once the charge density has been ob-tained. All of the calculations used in papers (I-IV, VI-VII) have utilized the Dmol3 code[112-114], whereas the CASTEP code[115] was used in paper V.

2.3.1 Basis sets The coefficients of the »basis set« functions are optimized in the SCF itera-tion scheme. Several different types of basis sets exist, e.g., plane waves, analytical- and numerical atom-centered functions. Atom-centered basis sets are perhaps more conceptually intuitive, whereas the plane waves are delo-calized and extends throughout the model space. The molecular orbitals used in CASTEP are built from the plane wave basis set:

� � � �� RGkiGii eCr ,� [2.16]

The Bloch theorem states that the electronic wave function can be expanded at each k-point of the reciprocal space as an (infinite) sum of plane waves. However, since an infinite number of plane waves are not feasible, the sum is truncated to include plane waves below a certain cut-off in the kinetic energy they represent. Plane waves associated with a small kinetic energy are more important to the overall charge density than those with large en-ergy. Dmol3 expands the molecular orbitals in terms of atomic basis func-tions via nuclei centered basis sets:

��

� ii c [2.17]

This expansion shifts the non-linear optimization problem into a linear prob-lem. The resulting equations can be solved using linear algebra where a more easily and efficient computer code may be used. In Dmol3, the basis func-tions are given numerically as values on an atomic-centered spherical-polar mesh, rather than as analytical functions (i.e., Gaussian orbitals). Throughout the calculations, the double numerical polarizable (DNP) basis set has been used. This includes a function for each occupied atomic orbital and a second set of valence orbitals (for greater flexibility towards bonding), as well as polarization d-functions for non-hydrogen atoms and p-functions for hydro-gen. These polarization functions are important for, e.g., hydrogen bonding. The size of the DNP basis set is comparable to the 6-31G** set, the latter

25

being a well-known basis set within the Hartree-Fock theory. However, the numerical basis set is much more accurate compared to a Gaussian basis set of the same size.[112] This basis set also minimizes an artificial energy low-ering effect called »basis set superposition error«. This error originates from the fact that the interaction energy between two species, formed by subtract-ing the sum of their individual energies from the combined energy, can yield an overestimation. The greater flexibility of a larger basis set, which the combination of the two species provides, lowers the energy. The basis sets within Dmol3 will exactly dissociate (within the DFT framework) a molecule to its constituent atoms. Therefore, weaker bonds will be calculated with pronounced precision when using DFT within the DMol3 program.

2.3.2 Exchange and correlation functionals The exchange-correlation functional is the only approximation made when solving the DFT equations shown above. However, there is no outlined route to improve (systematically) this functional. One approach to model the ex-change-correlation functional is called LDA, the local density approxima-tion, which constructs the exchange-correlation energy in the following way:

� � � � � �� rdrrrE CXLDAXC

�� [2.18]

The energy per electron of a uniform electron gas, , depends on the local density, �(r), and are termed X and C for the exchange and correlation part, respectively. These energies are weighted by �(r), i.e., for the probability that they will be found at that region of space. The exchange part is written:

� �3

343

!�� r

X

�

�� [2.19]

It is almost identical to the form that Slater proposed for the Hartree-Fock exchange. Several different implementations of the correlation energy have been proposed.[116, 117] The LDA level of quality often gives reasonable structures, but often overestimate bonds.[118-120] However, significant improvements are found if the gradient of the density is also considered. Hence, the variation of the density, in addition to the density at the point considered, often provides better energy evaluation and structure determina-tions. These are named the generalized gradient approximations, which con-tains a functional of both the density and gradient of the electron density:

� � � �� rdfEXC�),( �� [2.20]

26

The exact nature of this functional varies and there are many implementa-tions of this so called GGA theory, e.g., BLYP, PW91 and PBE.[119-121] These approximations may contain semi-empirically fitted values. Still, an-other class of exchange-correlation functional exists; the hybrid functionals, which contains the exact (Hartree-Fock) exchange energy determined from the Slater determinant, and the only approximations made are for the correla-tion part, e.g., B3LYP.[122] However, they are not necessarily better than GGA since the splitting of the exchange-correlation into two functionals is artificial. The expressions above are for the unrestricted case where the spins of the electrons are neglected. Differencing the spin-densities, �� and ��, yields the spin densities. Although the functional is not dependent on this separation, it will add larger flexibility due to the extra variables. In addition, all these exchange and correlation energies depend only on the density and the gradient of the density (GGA) at that point, and no long-range electron-electron correlation will take place. This implies that dispersion forces (i.e., induced dipole interactions) may not be seen.

2.3.3 Transition state searches Often in chemical reactions, there is activation energies associated with the reaction path connecting the reactant to the product. This energy barrier is called the activation energy and the corresponding structure is called the transition state. Finding the transition state within DFT may be conducted using first principle synchronous transit methods.[123] Confirmation of the transition state may also be conducted using nudge elastic band algo-rithms.[124] Various types of surface reconstruction of the diamond (111) surface (with different termination species) have been conducted using the LST/QST approach, and is presented in paper I.

2.3.4 Charge partitioning techniques Assigning charges to specific atoms within a molecule is totally artificial and a charge is described by Parr et al as a »noumenon« – an object of purely intellectual intuition.[125] Nevertheless, atomic charges may contribute to an enhanced understanding of results from calculations, and the charge con-cept are used within both inorganic and organic chemistry. A partitioning of the charge to individual atoms has been performed using two different meth-ods; Mulliken and Hirshfeld described below (see also paper V and VI). The variation in charge was used to analyze the electron transfer from the dia-mond surface to an attached adlayer.

Mulliken charges[126] are defined as the charge of the nuclei minus the summation of the coefficients (�) of a density matrix (P) and overlap matrix (S) belonging to atom A:

27

� ��"

��A

AM PSZq

[2.21]

where the density matrix (i.e., the charge-density bond-order matrix) and the overlap matrix are defined as

��i

ii ccP # # [2.22]

# # �S [2.23]

This procedure is, however, only viable for localized basis sets since e.g., plane waves provide no information regarding the localization of the elec-trons. Nevertheless, charge partitioning for delocalized basis sets, e.g., those used in CASTEP, can be performed using a projection of the plane waves states onto a localized basis (i.e., pseudo-atomic orbitals, generated from the pseudopotentials used in the electronic structure calculation).[127] The qual-ity of a plane wave projection onto a localized basis set is monitored by a spilling parameter, which are zero for a perfect projection and 1 for a com-plete orthogonal projection.

Hirshfeld partitioning scheme[128], also known as the Stockholder parti-tioning, is based relative to the deformation density. This partitioning scheme is defined as

� � � � � �� $

$$�� Rrrrd [2.24]

where �(r) is the density obtained by the SCF procedure, and the last term is the summation of all atomic densities where the atom � is located on coordi-nate (R). Partitioning the charge (q(�)) onto an atom (�) is done by integrat-ing the deformation density with a weight function via:

� � � � � �� rdrWrq d3

$�$ [2.25]

where the weight function (W) is described as the density fraction of atom � at point r:

� ��

�

%%%

$$$ �

�Rr

RrW [2.26]

28

Since the Hirshfeld partitioning only depends on the density it can be con-sidered one of the most theoretically sound partitioning methods, compara-ble to the Bader topological analysis (QTAIM charges) approach.[129]

2.3.5 Chemical reactivity indications Fukui introduced the frontier orbital reactivity concept 1952 (and earned the noble price 30 years later). This concept dealt with the role of the valence electrons, and their orbital distribution, in charge transfer mechanisms.[130, 131] Specifically, overlapping of the highest occupied orbital and the lowest unoccupied orbital were analyzed. Parr and Yang[132, 133] transferred this concept into the »Fukui function« which measures the charge density re-sponse of charge changes:

� � � �VN

rrf ��

��

[2.27]

Where N is the number of electrons, �(r) is the electron density and V(r) is the constant potential acting on an electron by all other electron and nuclei. Furthermore, three additional functions may be defined;

� � � ��

� � � ��

� � � �� &&&

'

&&&

(

)

��

��

�

��

�

��

��

��

rrf

rrN

f

rrN

f

NN

NN

NN

��

��

��

21

1

1

0

[2.28]

which is the finite difference approximation of Eq. 2.27 and corresponds to nucleophilic, electrophilic and radical attack, respectively. N is the charge added or withdrawn when calculating the charge density of the ions. Finding and relating reactive sites using Fukui orbitals (i.e., the mapping of Fukui functions onto a charge density isosurface) may be useful. It is a complement to other established methods when studying chemical reactivity; electrostatic potential (charge controlled) and the HOMO-LUMO concept.[134] Since the Fukui functions takes into account the relaxation of the orbitals they may give more accurate results sometimes named as Fukui function controlled reactivity.[135]

29

3. Results

“When I hear of Schrödinger's cat, I reach for my gun” Stephen Hawkins raillery over an interpretation problem of an appar-ent quantum mechanics paradox.

3.1 Diamond and c-BN Surface properties The chemisorption of oxygen species onto a diamond (100) and (111) sur-face has been studied in detail in papers I and II. Hydrogen adsorption has been studied in papers I, II, III and VII. Hydrogen and oxygen are impor-tant species in the diamond growth process, as described in Section 1.1. In addition, oxygen is omnipresent in the atmosphere and, thus, interacts with an exposed surface. Two forms of oxygen have been studied; atomic oxygen and hydroxyl, i.e., an OH-group. Atomic oxygen may adsorb onto the dia-mond surface in different configurations, e.g., on top or in bridge positions. OH-groups are probably involved in the initial oxygen adsorption.[136] It may, as an initial step, bind to steps and edges (i.e., defects) on the diamond surface. In proceeding steps, OH-groups may be converted into bridge or on-top oxygen at ideal, low-index surface areas. The chemisorption of fluorine, chlorine and sulfur, i.e., potential gasphase species in the reactor, on dia-mond (100) and (111) surfaces, have been studied in paper III. Some of the surface models used are shown in Fig. 3.1. Throughout the papers, a 16 sur-face atom area was used, except for paper II where 12 top-most carbon at-oms have been considered. The total number of carbon atoms ranges from 60 (paper II) to 160 (paper I). The cubic boron nitride (100) surface has alter-nating layers of boron and nitride, similar to the (111) surface. Paper VII examines both the nitrogen and boron side of the clean and hydrogen-terminated cubic boron nitride (100) surface. The adsorption energies, spe-cific geometries (i.e., bond angles and bond lengths) and electronic struc-tures were analyzed with the purpose to obtain a better understanding of: (i) the most probable species configuration on the terminated surfaces (e.g., the most favorable combination of oxygenic species and hydrogen, and specific binding position), (ii) energetic consideration of surface reconstruction and associated activation barriers, and iii) areas susceptible to electrophilic, radi-

30

cal and nucleophilic attack. Geometry optimization was used to yield a sur-face structure that minimizes the forces and energy gradients. Fukui orbitals, HOMO-LUMO and electrostatic potentials (see Section 2.3.7) were used to illuminate chemical reactivity.

Fig. 3.1 The studied surfaces where a) shows diamond (100)-1x1 (left) and (100)-2x1 (right) (paper III), b) shows diamond (111)-1x1 (left) and (111)-2x1 (right) (III), and c) shows c-BN:B (100)-2x1 (left) and c-BN:N (100)-2x1 (VII). The top-most atoms are for diamond shown in a whiter shade. For c-BN, nitrogen atoms are shown with a darker color compared to boron.

3.1.1 Energetic stability The adsorption energies for gaseous species, chemisorbed onto the surface at different surface coverage, have been studied in paper I and II. The results are presented in a plot where the adsorption and stabilization energies are shown over the whole range (0-100%) of surface coverage. The following equation has been used to calculate the adsorption energy associated with the chemisorption of the terminating species:

� *�� +n

nnsurfaceads EaEEE [3.1]

31

where Esurface is the total energy of the surface, an is the number of a specific terminating species, En is the gas-phase energy of the adsorbing species and E� is the total energy of a non-terminated diamond surface. The last term is the sum of the atomic energies of the species. The stabilization energy is here defined as the adsorption energy for all species on the diamond surface compared to the total adsorption energy for a 100% H-terminated surface. A surface configuration with negative relative stabilization energy is hence more favorable than the situation with a 100% H-terminated surface. The plots of the total adsorption energies of the species adsorbed onto the sur-faces, starting from 100% hydrogen coverage, can be seen in Figs 3.2-3.4. The plots show the successive adsorption energies as hydrogen are replaced with oxygen, or hydroxyl groups. Table 3.1 shows all of the calculated ad-sorption energies from papers 1-III. As can be seen in this table, reconstruc-tions of the non-terminated diamond (100) and (111) surfaces will lower the energy of the surfaces, and the 1x1-to-2x1 reconstruction of diamond (100) is the most favorable one (-1.85 vs. -0.55 eV for the Pandey chain). Another theoretical study has reported a value for the (111) surface that is close to -0.31 eV per surface atom.[61] Moreover, allowing the Pandey chain to relax, i.e., performing a geometry optimization of the ideal Pandey chain forma-tion, lowered the energy further by -0.20 eV. This difference between ideal and relaxed Pandey chain was attributed to the directional sp3 bonding of the carbon atoms. The large reconstruction energy of the diamond (100) surface is plausible since the top-most carbon atoms of the diamond (100)-1x1 sur-face have two unsaturated electrons and are, consequently, very reactive. In contrast to the (111) surface, there was no energy barriers associated with the 1x1-to-2x1 reconstruction for the (100) surface (see paper III).

3.1.2 Hydrogen adsorption A clean surface was the starting point for the hydrogen adsorption studies. As can be seen in Fig. 3.2, the clean (111)-2x1 surface is energetically more favorable than the corresponding 1x1 reconstruction. However, when 5/16 of the surface becomes H-terminated, both the partially H-terminated 1x1 and 2x1 surfaces show identical energies (indicated by an arrow in the figure). The (111)-1x1 is more favorable for a hydrogen coverage above 30%. In fact, a small number of hydrogen atoms on the diamond surface may recon-struct the (111)-2x1 to the 1x1 configuration.[29] A LEED pattern showed that 0.05 ML would effectively reconstruct the (111)-2x1 surface to the 1x1 reconstruction. The unfavorable adsorption energy for a 100% H-terminated (111)-2x1 is coherent with other DFT studies.[64, 137] A 100% hydrogen-terminated (111)-2x1 surface was shown to be stable towards reconstruction, but with lower adsorption energies compared to the 1x1 surface (+0.69 eV per H). This value is somewhat lower compared to ~+1.23 eV found in paper I and II. Hence, hydrogen stabilizes the carbon atoms of the Pandey chain

32

less compared to the 1x1 surface. A plausible explanation may be that the delocalized �-bonds of the Pandey chain are weakened. Hence, the electron configuration that stabilized the clean Pandey chain becomes perturbated. However, the value of the adsorption energy for hydrogen on the diamond (100) 1x1 surface is surprisingly high (-6.96 eV). Two hydrogen per carbon atom were chemisorbed onto the surface to saturate the two dangling bonds per surface carbon atom. Hence, hydrogen must be present on the (100)-1x1 surface to uphold the sp3 configuration and to prevent the 2x1 reconstruction. This dihydride configuration has been under much speculation[138-142], but it is generally accepted [143] that it does not occur during CVD growth conditions. Nevertheless, a very successful model attempting to describe growth mechanisms has been based on this dihydride configuration.[144] The very favorable adsorption energy for the dihydride surface configuration is probably not seen experimentally due to the favorable (and spontaneous) 2x1 reconstruction. Hence, two hydrogen atoms, per surface carbon, ad-sorbed onto the diamond (100)-1x1 surface is not realistic due to the faster reconstruction to the 2x1 surface. The adsorption energy for hydrogen on the (100)-2x1 surface (-4.30 eV) is in excellent agreement with experimental investigations.[70] The adsorption energy for H on an otherwise 100% H-terminated (111)-1x1 (and 2x1) surface has in two different studies been calculated to -4.15 (-3.45)[137] and -4.98 (-4.34)[64] eV, respectively. The results obtained in the former study (using molecular dynamics based on LDA) are more in agreement with the observations in the present thesis; -4.53 (-3.29) eV.

3.1.3 Oxygen adsorption Oxygen atoms often stabilize a hydrogen-terminated surface, as indicated by the negative stabilization energies in Figs 3.2-3.4. In addition, due to the divalent nature of oxygen and its strong electronegativity value, it may break the C-C double bonds and induce a surface reconstruction. As presented in paper II, a high coverage of oxygen (in both the on-top and bridge positions) yielded a reconstruction of the (100)-2x1 surface into a bulk-equivalent 1x1 configuration. The most favorable position for oxygen on the (100) surface seems to be the bridge position which is supported by other experimental and theoretical studies.[72, 136, 145] In addition, the surface morphology will change and yield more oxygen in the on-top positions at elevated tem-peratures. An initial H-C-O-C-H surface configuration has been proposed as a plausible oxidation mechanism.[146] However, other studies have shown that the on-top position is more likely to occur, but with a rather small dif-ference in adsorption energy.[73] The reconstruction from (100)-2x1 to (100)-1x1 as observed in paper II, occurred spontaneously. This implies that no activation barrier can be present, since DFT is a 0K method. Conversely, no surface reconstruction was observed because of oxygen adsorption on the

33

(111)-2x1 surface. Hence, the fully oxygen-terminated (111)-2x1 to (111)-1x1 reconstruction is associated with an activation energy. Furthermore, the on-top and bridge oxygen atoms were not stable for the 2x1 and 1x1 recon-struction, respectively. An oxygen coverage above 50% on the (111)-2x1 surface resulted in a removal of the ether configuration and an introduction of rather strong O-O bonds. Although the total adsorption energy continued to decrease, the adsorption energy per species increased (i.e., became unfa-vorable) from -5.74 to -4.37 eV. In fact the adsorption energy per species of the eight oxygen atoms on the Pandey chain was found to be more favorable than for the situation with the 1x1 surface (-5.74 vs -5.68 eV), even though the resulting order of energies became reversed at 100% coverage (-4.37 eV vs -6.21 eV). In addition, experimental results have shown that CO desorp-tion from the (111)-2x1 surface involves 50% of the surface carbon, i.e., a 50% oxygen coverage was expected.[64]

3.1.4 Hydroxyl adsorption The adsorbed OH-groups showed both adsorbate-adsorbate interactions through hydrogen bonding (energy stabilization) and steric repulsion (energy de-stabilization). The hydrogen bonding is noticeable at low OH coverage, whereas steric-repulsion dominates at higher coverage. However, OH-groups may not induce a surface reconstruction due to the mono-valent character of the oxygen atom in the hydroxyl species. The amount of electrons that may be withdrawn, and reallocated, is larger for oxygen atoms compared to hy-droxyl groups. The destabilization of hydrogen-terminated surfaces due to hydroxyl group adsorption, is supported by an experimental study that re-ports small number of hydroxyl groups present on an oxygenated (100) sur-face.[136] Hydrogen bonding enthalpies of -0.15 eV were reported. The adsorption energies for the hydroxyl groups on the Pandey chain are unfa-vorable up to a 30% coverage. A severe weakening of the �-bond chain, as well as absence of hydrogen bonding, is probably responsible for this effect. A nine carbon cluster MP2-calculation on OH-terminated diamond (100) surfaces resulted in an adsorption energy of -3.28 eV per OH for a 100% surface coverage. This value is somewhat higher compared to -4.13 eV found in this thesis.[147] Another DFT study for the diamond (111) surface has reported on OH adsorption energies of -4.24 (-3.99) eV for the 1x1 (and 2x1) reconstruction. Hence, the adsorption energies are in good agreement for the 1x1 surface (0.09 eV difference), but the 2x1 Pandey chain shows much larger adsorption energies compared to the results presented herein.[64]

34

Fig 3.2 The adsorption profiles for the successive hydrogen replacements by oxygen (both bridged and on-top positioned) and OH groups. Left axis is the stabilization energy that relates the adsorption energy (right axis) to a 100% H-terminated sur-face.

Fig 3.3 The adsorption profiles for the successive hydrogen replacements by oxygen (both bridged and on-top positioned).

35

Fig 3.4 The adsorption profiles for the successive hydrogen replacements by OH-groups.

3.1.4 Fluorine, sulfur and chlorine adsorption The adsorption of hydrogen, fluorine, sulfur and chlorine onto diamond (100) and (111) in their most common surface reconstructions, 1x1 and 2x1, was studied in paper II. Only 100% terminated surfaces were considered, and the resulting adsorption energies are shown in Table 3.1. Fluorine is the termination species that most resembles hydrogen; mono-valent with a rather small covalent radius. Moreover, due to the strong anti-bonding occupancy of the electrons within the fluorine molecule, the F-F bond enthalpy is very low compared to Cl-Cl, 159 vs. 243 kJ/mol. Conversely, the bond enthalpy of HF is greater than for HCl (574 vs. 431 kJ/mol). Hence, fluorine mole-cules may more readily dissociate into atoms than chlorine molecules. The large HF bond enthalpy may induce a fluorine desorption process and, hence, yield additional radical sites for diamond growth precursors. Hence, fluorine may be involved both in the gas phase and on the surface in dia-mond growth. Fluorine has been found to be strongly adsorbed to all of the studied diamond surfaces (-5.53, -6.33, -4.56 and -4.56 eV for the (100)-1x1, (100)-2x1, (111)-1x1 and (111)-2x1 surfaces, respectively). Although the diamond (100)-1x1 surface has two unpaired electrons, two fluorine at-oms per carbon (difluoride configuration) atom was in paper III found to be highly unstable. Half of the fluorine-carbon bonds were severely weakened with C-F bond-lengths of more than 2 Å. The diamond (100)-1x1 surface reconstructs to a 2x4 pattern due to the mono-valent F, i.e., C-C bonds formed and F atoms were aligned in a perfect, bulk diamond equivalent, 1x1 pattern. Sterical repulsions between the adsorbed fluorine atoms as well as

36

the electron withdrawal power of fluorine, rendering underlying C-C bonds less rigid compared to e.g., monohydride (100)-2x1 surface, are plausible reasons for this reconstruction. Sulfur atoms could be adsorbed onto the surface, but showed small adsorption energies despite the divalent character of sulfur. Sulfur is probably too large for strong C-S bonds to occur, and steric S-S repulsions became pronounced. Noteworthy, the most favorable sulfur adsorption energies are observed at the (100) surface, and especially for the 2x1 surface reconstruction. This is expected due to the larger intrinsic reactivity of the (100) surface compared to the (111) surface. The larger adsorption energy for the (100)-2x1 surface reconstruction is probably influ-enced by the formation of sulfur-sulfur bonds on this surface. The geometry of the (100)-2x1 surface will probably allow a better orbital overlap com-pared to other surfaces, except for the Pandey chain, where comparable S-S bond lengths were found. However, the S-C bonds lengths present on the Pandey chain surface were found to be very long, and, thus, weak. Con-versely, a stable 100% coverage of chlorine could only be found for the Pandey chain. However, the adsorption energy is very weak (-0.18 eV) and desorption is expected at higher temperatures. Some chlorine was desorbed for the (100)-1x1 and (111)-1x1 surface as a result of geometry optimization. Hence, no adsorption energy for a full coverage could be obtained.

Table 3.1 The adsorption energies per species (and from which paper they origi-nate). All of the adsorption energies are related to their respective clean surface.

Surface Diamond c-BN

Species

100-1x1 100-2x1 111-1x1 111-2x1 100 B 100 N Clean* 0.00 -1.85V 0.00 -0.55III

-0.54V 0.00 -1.08VI

0.00

-1.38VI H -6.96V -4.30IV

-4.35V -4.53III -4.55V

-3.29III

-3.32V -4.49VI -5.03VI

OH ** -4.13IV -4.15III -2.77III ** ** Oon-top -5.95IV *** -5.56III *** ** ** Obridge -6.21IV -5.68IV *** -3.82III ** ** F -5.53V -4.49V -4.56V -4.02V ** ** S -3.32V -3.12V -2.61V -1.54V ** ** Cl *** *** *** -0.18V ** **

*Reconstruction energies compared to 1x1 surfaces. **No calculation has been per-formed. ***A stabile geometry could not be found.

As seen in Table 3.1, the general trend in adsorption energy strength is S < Cl < OH < H < F < O. Oxygen and fluorine atoms form very strong bonds

37

with the carbon atoms on the diamond surfaces. However, fluorine does not induce any larger reconstructions, except for the (100)-1x1 surface as de-scribed above. The adsorption energies for the OH-groups indicate that C-O bonds are more favorable than C-O-H bonds, despite potential hydrogen bonding. Sulfur atoms at 100% coverage generally bind very weakly to the (111) surfaces (-2.61 eV and -1.54 eV), compared to the (100) surfaces (-3.32 eV and -3.12 eV). As described above, chlorine shows no, or very little, tendency to cover the surface totally due to the size of the chlorine atom.

3.1.5 Cubic boron nitride Both the nitrogen- and boron-rich side of the clean and H-terminated cubic boron nitride (100) surface have been studied in paper VI. The clean c-BN (100)-1x1 surface may, just as the corresponding diamond surface, recon-struct. However, whereas the 2x1 surface dominates diamond reconstruction as seen in LEED measurements, c-BN (100) readily forms dimers in many plausible patterns: 2x1, 2x2 and two possible 2x4 configurations, as can be seen in Fig. 3.5 below. The energetic change (per top-most surface atom) due to reconstruction and hydrogen termination can be seen in Table 3.2.

Table 3.2 The energy change per top-most surface atom due to reconstruction and hydrogen adsorption on the nitrogen- or boron-rich surfaces. The energies for the hydrogen termination surfaces is the total adsorption energy divided by the number of surface sites.

Surface N-rich surface B-rich surface Clean 1x1 0.00 0.00 Clean 2x1 -1.38 -1.08 Clean 2x2 -0.60 -1.00 Clean 2x4 -1.25 -1.04 Clean 2x4 (3) -0.91 -1.05 1x1 100% H-terminated -5.03 -4.49 1x1 93% H-terminated -3.97 -3.48

Noteworthy, the nitrogen-rich surface favors the 2x1 reconstruction with an energy change of -1.38 eV, and disfavors alternating dimers. In fact, the least favorable surface reconstruction is the 2x2 configuration (-0.60 eV). The boron-rich side shows very similar reconstruction energies but the 2x1 sur-face configuration is slightly more favorable. Hence, the dimer formation for the boron-rich side is rather insensitive to either row formation or alternating dimers. Moreover, the c-BN (100)-1x1 surface under hydrogen termination showed a large adsorption energy of -5.03 and -4.49 eV for the nitrogen and boron rich surface, respectively. However, whereas partial hydrogen removal (~7%) on the diamond surface does not result in any larger reconstructions and/or adsorption energy changes as described in Section 3.1.2, this removal

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resulted in a local geometry change for the c-BN (100) surface. The non-terminated atom formed bonds with adjacent boron atoms. The resulting surface structure, as well as the deformation density of the newly formed B-B and N-N dimers, can be seen in Fig. 3.6. Evidently, the boron atoms form a rather strong bond. Furthermore, as shown in paper VI, this partial hydro-gen removal does not render the non-terminated boron atom particularly reactive to neither electrophilic nor nucleophilic attack. The nitrogen atoms form an N-N dimer but there is no N-N bonds formed, as may be seen in Fig. 3.6. N-B bonds below the dimer are much more affected: the surface does not become more reactive. The energy change is also largely affected by this hydrogen removal: the energy change increases by +1.01 and +1.06 eV for the boron and nitrogen rich side, respectively. The adsorption energy per hydrogen also (unfavorably) increases from -4.49 to -3.72 eV, and from -5.03 to -4.23 eV, for the boron- and nitrogen-rich, respectively.

Fig 3.5 Four plausible reconstruction patterns of the c-BN (100)-1x1 surface: 2x1, 2x4, 2x4(3) and 2x2.

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Fig. 3.6 The 100% and 93% H-terminated c-BN (100)-1x1 boron- and nitrogen-rich surfaces (top) along with the deformation density slice through the non-terminated atom (bottom). Figure a) and b) shows the boron-rich side, whereas c) and d) shows the nitrogen rich side.

3.1.6 Electronic structure Some electronic properties of the top most carbon atoms of clean diamond (100), (110) and (100) surfaces have been studied in paper IV. Electrostatic potential maps, electron deformation densities, Fukui function and frontier orbitals of the top-most carbon atoms were analyzed to determine the reac-tivity of these surfaces. The reactivity of a surface has a profound impact on, for example, surface functionalization, growth mechanisms, local bonding and adsorption preferences. Thus, an understanding of reactivity may con-tribute to the prediction and explanation of successful growth precursors and reconstruction-induced adsorption behavior. The electrostatic potential estimates the interaction of a positive test charge experienced at the isosurface. Hence, negative values of the electrostatic potential could indicate a location susceptible to electrophilic (electron with-drawing) attack. This closely resembles the electrophilic Fukui function, but the Fukui function also measures the response of the charge density in den-sity changes. Hence, the orbital relaxation is taken into account. The Fukui functions are more flexible than the electrostatic potential, but the areas sus-ceptible to electrophilic attack, as determined by Fukui functions and elec-trostatic potential, often coincide. Frontier orbitals are often involved in chemical reactions, since these are most accessible for forming covalent bonds and electron transfer reactions. The distribution of the HOMO on the density isosurface should correspond to the sites of electrophilic attack reac-

40

tivity as predicted by the electrostatic potential and Fukui function, whereas distribution of the LUMO and the nucleophilic Fukui function should corre-spond. Double bonds may have a large charge density, but they may be rather non-reactive nevertheless. Hence, the electrostatic potential may erro-neously predict sites prone to electrophilic attack at those double bonded sites. Fig. 3.7 shows the Fukui orbitals mapped onto a charge density isosur-face. The electrostatic potential is shown in Fig. 3.8. The contributions of the Kohn-Sham orbitals HOMO and LUMO to the charge density are shown in Fig. 3.9.

Fig 3.7 Three Fukui functions (f-, f+ and f0) for the diamond (111)-1x1 [a], (111)-2x1 [b], (110)-1x1 [c], (100)-1x1 [d] and (100)-2x1 [e] surfaces. The Fukui func-tions correspond to the electrophilic, nucleophilic and radical susceptibility charac-ter, respectively.

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Fig 3.8 Electrostatic potential of the charge density isosurface of the diamond (111)-1x1 [a], (111)-2x1 [b], (110) [c], (100)-1x1 [d] and (100)-2x1 [e]

Fig 3.9 The mapping of the HOMO and LUMO orbital onto the electron density of the clean diamond (111)-1x1 [a], (111)-2x1 [b], (110)-1x1 [c], (100)-1x1 [d] and (100)-2x1 [e] surfaces.

As can be seen in Fig. 3.7-3.9, the sites susceptible to electrophilic attack, i.e., as predicted by Fukui function, electrostatic potential (and the location of the HOMO), correlates well. In general, the reactive sites are located

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above the top-most carbon atoms under 1x1 reconstruction. These atoms are susceptible to both electrophilic and nucleophilic (as well as radical attack) due to the radical character of the dangling bonds. Surface reconstruction often changes this behavior. For the (111)-2x1 reconstruction, the Pandey chain carbon atoms alternate the electrophilic and nucleophilic attack for every atoms along the chain. There is a perfect match between the f- and HOMO, as well as the f+ and LUMO as can be seen in Figs. 3.7.b and 3.9.b. In addition, the location of the f- and the electrostatic potential coincide for the diamond (100)-2x1 surface. The location of the HOMO is shifted per-pendicular to the C-C dimer direction. A plausible explanation is that the orbitals that contribute to this bond are lower in energy compared to the HOMO. The location predicted by f+ and LUMO is very good; there is a nodal plane between the C-C dimer, and, hence, less reactivity towards nu-cleophilic species. The number of nodal planes determines the orbital bond-ing character by the fact that a small number of nodes implies constructive interference and a more bonding character. Conversely, many nodal planes denote a more anti-bonding character due to destructive interference. In fact, the diamond (111)-2x1 and (100)-2x1 surfaces separate the bonding charac-ter of the HOMO and LUMO by the number of nodal planes. The diamond (100)-1x1 HOMO has a very unfavorable number of nodal planes. Hence, this orbital should be associated with a high orbital energy, and may explain the reactivity of this clean surface (i.e., the high hydrogen adsorption energy and the 1x1-to-2x1 reconstruction energy). However, there are some dis-crepancies; the HOMO and LUMO of the diamond (111)-1x1 surface does not provide any information about surface reactivity. Moreover, the reactive sites on the (110)-1x1 surface is more confined around the surface atoms in the Fukui functions, compared to the electrostatic potential and the HOMO and LUMO which predicts the whole carbon chain to be reactive. With re-spect to the orbital relaxation considered within the Fukui concept, f-, f+ and f0 are probably more accurate compared to Kohn-Sham orbitals or the elec-trostatic potential.[135] Many of the hydrogen and oxygen adsorption re-sults correspond well to the reactivity study within paper IV. Examples of this are; (i) the bond-geometry of the hydrogen, hydroxyl and bridge oxygen on the diamond (100)-2x1 and (111)-2x1 surfaces, (ii) the strong preference for on-top oxygen on the (111)-1x1 surface, and (iii) the specific 1x1-to-2x1 reconstruction for diamond (100).

3.1.7 Transition state searches Although one surface reconstruction is energetically favorable, it may be associated with large activation barriers. Thus, the transition between reac-tant and product can be kinetically hindered, regardless of overall exother-

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mic reaction energy. Transition state searches attempt to find this activation barrier. In paper I, transition state searches have been conducted for the dia-mond (111) surface. The 1x1-to-2x1 reconstruction of a i) clean, ii) 100% H-terminated and iii) O-terminated surface have been studied using LST/QST/CG tools described in Section 2.3.3. The results are shown in Fig. 3.10. Evidently, the clean 1x1-to-2x1 reconstruction has a small activation barrier, whereas the oxygen- and hydrogen-terminated surfaces show much larger activation barriers. The high activation energies associated with the O- and H-terminated surfaces are plausible since several C-H and C-O bonds must be broken to obtain the 2x1 Pandey chain: only half of the top-most carbon atoms of the 1x1-and-2x1 surfaces are identical. Thus, one-half of the top-most C-O or C-H bonds remain on the surface, whereas the second half must be broken for the Pandey chain reconstruction to occur. However, for the clean surface it is only the delocalization of the C-C bonds (i.e., electron redistribution not associated with bond breaking) that accounts for the acti-vation energy. One-half of the carbon atoms that belong to the second carbon layer must be lifted, but no bonds need to be directly broken. As shown in one experimental study, oxygen may be adsorbed onto a 2x1 surface, and does not break the 2x1 reconstruction.[148] LEED, AES and photoemission data showed C-O bonds present on the surface. Hence, both the full monolayer and the half monolayer show large activation energies toward 2x1-to-1x1 reconstructions; oxygen effectively protects the 2x1 reconstruc-tion by increasing the activation energy considerably. However, adsorbed hydrogen at small concentrations converts the surface back to the 1x1 con-figuration.[75] Furthermore, hydrogen may replace oxygen and induce a 2x1-to-1x1 reconstruction. As indicated in Figs. 3.7 and 3.9, it is possible that hydrogen adsorbs on the nucleophilic sites, i.e., on every alternating carbon atom along the Pandey chain. This may induce an easier 2x1-to-1x1 reconstruction; there is no C-H bond that needs to be broken. In fact, this H-adsorption may even yield the reconstruction spontaneously. Oxygen may not bind in the ketone position on the (111) Pandey chain, as described ear-lier, and, thus, effectively hinders the reposition (i.e., reconstruction) of the top-most carbon atoms by forming C-O-C bonds.

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Fig 3.10 The minimum energy paths connecting reactants and products and the resulting transition states. The transition state of the 1x1-to-2x1 reconstruction of the clean diamond (111) surface, as well as a 100% H- and a 100% O-terminated sur-face is shown.

3.2 Indications of charge transfer One of the proposed models for the increase in surface conductivity »the induced p-type doping mechanism« has been studied within this thesis. The interaction between a diamond (100) 2x1 surface and a water-based adlayer was investigated in papers V and VI. Paper V analyzes the charge transfer to an adlayer consisting of two water molecules and two oxonium ions by per-forming a charge partitioning analysis, partial density of states as well as analyzed geometrical changes. Four different H-terminated surfaces were considered: i) a 100% H-terminated, and H-terminated surfaces with ii) one OH-group replacing one hydrogen, iii) one oxygen atom replacing one hy-drogen (oxygen in the on-top (ketone) position), and iv) one oxygen atom replacing two hydrogen atoms (oxygen in the bridge (ether) position). The adlayer of the fully H-terminated surface slab is presented in Fig. 3.11.a. The arrow shows where the oxygen species was chemisorbed on the diamond surface. Paper VI focuses on the degree of charge transfer from the diamond surface to the attached adlayer, and the thermodynamic driving force behind it. A 100% H-terminated surface and an adlayer consisting of eleven species were then considered. The adlayer consisted mainly of water molecules, with

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the inclusion of oxonium ions, molecular oxygen or ozone, or a combination thereof. The following adlayer configurations were studied: (i) 11 H2O, (ii) 10 H2O+1 H3O+, (iii) 10 H2O+1 O2, (iv) 10 H2O+1 O3, (v) 9 H2O+1 O2 1 H3O+, and (vii) 9 H2O+1 O3+1 H3O+. In addition, the relative positions nor-mal to the surface (i.e., the surface-to-species distance) of non-water species (i.e., the oxonium ion, oxygen molecule and the ozone molecule) was shifted in order to investigate the effect of distance (to the surface) on the charge transfer. Hence, the starting point of geometry optimization for adlayer (v) above was a) the oxygen molecule close to the surface and the oxonium ion further away, and b) vice versa. Fig. 3.11.b shows the surface with an ad-layer containing nine water molecules, one oxonium ion and one ozone molecule.

Fig. 3.11 The diamond (100)-2x1 surface with an attached adlayer: a) shows the diamond surface with two water molecules and two oxonium ions used in paper V, whereas b) shows a eleven species adlayer attached to an 100% H-terminated sur-face (used in paper VI).

3.2.1 Population analysis The most straightforward way to determine if charges (electrons) have been transferred across the diamond-adlayer interface is to analyze the charges within the adlayer and surface. The resulting charge transfer is shown in

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Table 3.3. Both paper V and VI have used the Mulliken formalism, and pa-per VI includes the Hirshfeld partitioning scheme (see section 2.3.4). The CASTEP program was used in paper V. However, that code did not have support for Hirshfeld analysis. Partial electron transfer is indeed detected for surfaces with H- and OH-termination (paper V), whereas the chemisorbed oxygen atom effectively hinders the process. This trend in electron transfer was earlier observed for diamond (100)-2x1 at a different pH level.[149, 150] When the adlayer consisted of water only, no electron transfer was obtained. In addition, a study conducted on a diamond cluster also reports electron transfer into reducible species.[151] For example, CO3H was shown to have a LUMO below the diamond valence band maximum, and thus the adsorbate is susceptible for electron transfer. However, other mechanisms for electron transfer were not ruled out. A variation of the adlayer (i.e., its chemical composition and spatial distribution) using a more realistic water cluster with more correct oxonium-water interactions, e.g., allowing hydra-tion shells and Grotthuss movements, was used in paper VI. The charge transfer into that type of adlayer can be seen in the lower part of Table 3.3. An adlayer containing only water molecules did not exhibit any electron transfer. However, exchanging one of the molecules with oxonium, oxygen or ozone yielded a reduction of the total adlayer charge, i.e., electrons were transferred. The largest degree of electron transfer is observed when either oxygen or ozone are combined with the oxonium ion. This is expected from thermodynamic considerations: the electrochemical reduction potential of oxygen and ozone is pH dependent. Thus, oxonium ion and oxygen, or ozone, enhances the oxidizing power of the adlayer more than a simple summation of the individual values. Evidently, from Table 3.3 it is shown that the electron transfer will be more pronounced if the species closest to the surface is the species with the strongest oxidizing power. Hence, there is a rather large distance dependence of the transfer of electrons, as expected. The effect of pH on surface conductivity has realized diamond based pH sensors.[10] However, oxygen terminated areas was needed for an apprecia-ble change in conductivity due to pH change. In addition, varying the pH by 10 units only changed the corresponding conductivity by a factor of two.[27] It was speculated that chemical equilibrium was never reached in extended electrolytes (compared to a thin attached atmospheric adlayer). Furthermore, de-oxygenized water could not increase conductivity to any appreciable amount.[85] The charge transfer doping was very recently given support in an article in Science magazine where the authors used the large surface area of diamond powder to measure pH changes due to electron transfer.[152] They also concluded that oxygen was indeed responsible for this induced p-type doping. The similarity in the calculated Mulliken and Hirshfeld charge values (paper VI) further strengthens the results, since it is no appreciable dependence in charge partitioning for the methods used. Thus, there is not artificial charge transfer due to e.g., drawback from Mulliken charge parti-

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tioning. Plausible explanations to the deviation between the absolute values of the Mulliken charges in paper V and VI are; i) different levels of DFT, ii) more realistic adlayer with hydration shells (paper VI), and iii) the oxonium ions were closer to the surface.

Table 3.3 The charge reduction of the adlayer (i.e., the amount of electrons trans-ferred). Both variations in the surface (paper V) and adlayer (paper VI) configura-tion have been studied. The adlayer species studied in paper VI are separated by comma. The species that is closer to the surface is shown to the left, whereas the species furthest away is in the middle.

Charge transfer, [e-] Study Surface Adlayer Mulliken Hirshfeld

100% H 1.80 * 92% H 8% OH 1.90 * 84% H 8% Ob 0.01 *

pape

r V

92% H 8% Ok

2 H2O and 2 H3O+

0.00 * 11 H2O 0.00 -0.01 1 H3O+,1 H2O, 9 H2O 0.13 0.19 1 O2, 1 H2O, 9 H2O 0.33 0.31 1 O3, 1 H2O, 9 H2O 0.46 0.40 1 O2, 1 H3O+, 9 H2O 0.66 0.64 1 O3, 1 H3O+, 9 H2O 0.70 0.67 1 H2O, 1 H3O+, 9 H2O 0.08 0.13 1 H2O, 1 O2, 9 H2O 0.26 0.25 1 H2O, 1 O3, 9 H2O 0.26 0.22 1 H3O+, 1 O2, 9 H2O 0.47 0.50

pape

r VI

100% H

1 H3O+, 1 O3, 9 H2O 0.44 0.48 *Not supported by the CASTEP program.

The relation between the electron transfer and the corresponding difference in chemical potential of the surface and adlayer is discussed in paper VI. It is calculated from the standard reduction potentials using Eq. 1.2-1.4 and using common partial pressures found in normal atmosphere. The degree of elec-tron transfer calculated for six top-most adlayers (paper VI) as presented in Table 3.3, are shown in Fig. 3.12 below. As can be seen, there is a correla-tion between the amount of charge transfer and the diamond-adlayer poten-tial difference. The water-only adlayer showed no sign of charge transfer. Moreover, water-only adlayers should not induce a charge transfer due to the

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fact that the potential difference is below zero (calculated using the thermo-dynamic equations).

Fig. 3.12 The correlation between the chemical potential difference (right axis) and electron transfer (left axis) from an H-terminated diamond (100) 2x1 surface into an adlayer consisting of nine water molecules and I) 2H2O, II) 1 H3O+ +1 H2O, III) 1O2 +1H2O, IV) 1O3 +1H2O, V) 1O2 +1H3O+, and VI) 1O2 +1H3O+.

3.2.2 Surface-adlayer interaction A prerequisite for the electron transfer was in papers V and VI found to be an energetic overlap of the surface HOMO (i.e., upper edge of the diamond surface valence band and the LUMO of the adlayer). Hence, the energy of the surface HOMO must be similar to the LUMO of the adlayer, for the charge transfer to be thermodynamically feasible. The partial density of states (pDOS) of (i) the non-attached surface, (ii) the adlayer and (iii) the adlayer interacting with the surface, have been carefully analyzed. As can be seen in Fig. 3.12, there is a HOMO-LUMO overlap for the adlayer system with nine water molecules, one molecular oxygen and one oxonium ion. The Fermi level is positioned at the highest occupied energy state. These over-laps are not seen for systems were there is no electron transfer.

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Fig. 3.13 The density of states plots of the diamond surface and the adlayer being reduced. There is an orbital overlap between the HOMO of the surface (positioned just below the Fermi-level) and the LUMO of the adlayer.

Calculated adhesion energies of the water adlayer attached to the diamond surfaces will indicate the strengths of the adlayer-surface interactions. Sub-tracting the single point energy for the surface and the adlayer separately (and using the same geometry) from the surface interacting with the adlayer, will yield surface-adlayer adhesion energy strengths as presented in paper VI. As can be seen in Fig. 3.14, there is an obvious correlation between the degree of electron transfer and the adhesion energy. Adlayer systems show-ing the strongest interactions also yielded the largest degree of electron transfer. This type of electron transfer is of an adiabatic character, i.e. origi-nating from adlayer-surface atomic overlap. The possibility for adiabaticity will increase with i) shorter adlayer-surface distances, and ii) correspond-ingly stronger bonds. The present calculated adlayer adhesion energies range from ~20 kcal/mol to ~100 kcal/mol for a system with four molecular spe-cies situated closest to the surface. Hence, the adhesion bond energy per interacting molecule is within the range 5-20 kcal/mol, which indicates bond strengths similar to hydrogen bonds.

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Fig. 3.14 Correlation of adsorption energy and electron transfer for the 11 different adlayer systems studied in paper VI.

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4. Concluding remarks

“To succeed in the world, it is much more necessary to possess the penetra-tion to discern who is a fool, than to discover who is a clever man.” Charles M. de Talleyrand

This thesis presents density functional theory studies for various surface mechanisms on the low-index diamond and cubic boron nitride surfaces. The aim has been to gain a more thorough knowledge about common surface mechanisms including adsorption energies, surface reactive sites, electronic structure and the origin of diamond high surface conductivity. Non-terminated diamond surfaces are very reactive due to unsaturated carbon atoms, but their reactivity will change as they reconstruct to lower their en-ergy. Adsorption of (gas phase) species is most often exothermic and, hence, favorable. Hydrogen is a very important growth species and oxygen (some-times also included during growth) is omnipresent in the atmosphere and strongly affects surfaces. Fluorine and chlorine are important precursor addi-tions, due to the possibility of lower growth (substrate) temperature and bet-ter film quality. The high surface conductivity of diamond, i.e., a large band gap material, is puzzling and may be utilized in electronic applications. This effect is observed on H-terminated diamond surfaces in the presence of an atmosphere. Cubic boron nitride is a very interesting material with many similarities with diamond, but there are major problems associated with c-BN thin film growth. More specifically, to reduce film stress and improve e.g., substrate adhesion and film quality, a gentle CVD growth is required, but not found. The (100) c-BN surface, a plausible growth direction, has been investigated for most favorable surface reconstruction, hydrogen ad-sorption energies and hydrogen induced reactivity. The main conclusions are:

, Clean diamond surfaces are very reactive, and this reactivity may be evaluated using DFT calculated electronic structure properties e.g., Fukui functions, electrostatic potential and Kohn-Sham orbi-tals. The diamond (111)-2x1 Pandey chain structure shows alter-nating sites which are reactive to electrophilic and nucleophilic attack, respectively. The unreconstructed diamond surfaces exhib-its a large representation of occupied orbitals close to the Fermi level. The reconstruction leads to a separation of the HOMO-

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LUMO gap, which renders the surface less reactive. The surface is nevertheless susceptible to adsorption of e.g., hydrogen and oxygen atoms. It is possible to obtain, a priori, specific bonding characteristics of adsorbed species using these reactivity indica-tors on clean surfaces.

, Hydrogen stabilizes all of the studied surfaces, but the unrecon-structed surfaces exhibits the largest adsorption energies. The di-hydride formation of the diamond (100)-1x1 surface was found to be very favorable. However, it is probably not observed due to the reconstruction into the monohydride (100)-2x1 surface. The (111)-2x1 surface exhibits the least favorable hydrogen adsorp-tion energies. It was speculated that hydrogen occupies every al-ternating carbon atoms and thus induce an easy reconstruction back into the 1x1 surface.

, Hydroxyl groups, however, show somewhat lower adsorption en-ergy compared to hydrogen, being dependent on degree og sur-face coverage. Two effects were noticed: (i) Sterical hinders (un-favorable) due to the rather bulky OH group, and (ii) hydrogen bonding (favorable) from the weak O-H···O bonding amongst the hydroxyl species. Sterical hinders become more dominant than hydrogen bonding at higher OH coverage.

, Oxygen binds very strongly to the diamond surface and seems, whenever possible, to favor the bridge position. Bridge position was observed for the diamond (100)-2x1, (100)-1x1 and (111)-2x1 surfaces. Oxygen may also induce a 2x1-to-1x1 reconstruc-tion on the diamond (100) surface.

, The adsorption energy for both hydrogen and oxygen indicates small adsorbate-adsorbate interactions.

, Fluorine atoms show adsorption energies intermediate to those of hydrogen and oxygen. Although fluorine is more electronegative compared to oxygen, it may only accept one electron and hence may not form double bonds (except for perhaps boron). A 100% F-terminated diamond (100)-1x1 surface reconstructs into a 2x4 surface pattern. Fluorine adsorption energies for the diamond (111) surfaces was found to be identical.

, A full surface coverage of sulfur was found to be possible, but as-sociated with rather low adsorption energies. Furthermore, the strongest C-S bonds were observed for the diamond (100)-1x1 surface due to the double unsaturated top-most carbon atoms. Significant S-S bonding occurs on the diamond (100)-2x1 sur-face.

, Chlorine could not reach full surface coverage, except for the Pandey chain (-0.18 eV). Instead, chlorine atoms were abstracted and (gas phase) Cl2 molecules formed.

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, Electron transfer from a diamond surface into an adlayer is de-pendent on both the adlayer species, as well as surface terminator. Oxonium was reduced by the charge transfer. This effect was even more pronounced with oxygen- and ozone-containing adlay-ers. The charge transfer follows thermodynamic trends fairly well. Chemisorbed oxygen effectively hinders this transfer of charge. A chemisorbed OH-group also exhibits an electron trans-fer. Prerequisites for this electron transfer is; i) surface-adlayer orbital overlap, ii) a reducible species within the adlayer and iii) mainly hydrogen-terminated surfaces. In addition, this thesis gives support to a proposed model »the charge transfer doping« believed responsible for the high surface conductivity of dia-mond.

, The 2x1 reconstruction of the clean (boron and nitrogen rich) c-BN (100)-1x1 surfaces was found to be the most (energetically) favorable compared to 2x2, and two 2x4 formations also studied. However, whereas the nitrogen rich surface more strongly fa-vored the 2x1 (row) dimer formation, the boron rich side show similar reconstruction energies. Hydrogen adsorption on both the boron and nitrogen side stabilizes the 1x1 surface configuration, and show large adsorption energies. However, a partial hydrogen removal largely alters the local geometry with the formation of B-B and N-N bonds of the boron and nitrogen rich sides, respec-tively.

Although the electron transfer observed in papers V and VI supports charge transfer as the model for the induced p-type doping model, no other model has been investigated. Hence, the results give an indication of charge transfer from the surface to a reducible adlayer, but do not rule out any other mecha-nisms. It is possible that a combination of factors determines the surface conductivity, e.g., sub-surface, hydrogen induced, electronic states.

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Acknowledgements

“Don’t worry honey; there is plenty of more where that came from” Homer Simpson tries to encourage Lisa after an oil tanker run aground off the Canada coast. First, I would like to thank my supervisor, Professor Karin Larsson, for the encouragement and relentless appreciation she has showed over the years. In addition, my second supervisor, Professor Jan-Otto Carlsson – head of department, is acknowledged for his support on this project. The present colleagues within our research group, Anna Pallas and Tanguy van Regemorter, as well as the former, Igor Arvidsson, Henna Ruuska and Tobias Törndal, have been invaluable for fruitful theoretical chemistry pon-derings. Professor Leif Nyholm is acknowledged for his electrochemistry expertise, as well as his patience answering my many questions. Perti Knuutila – you are invaluable in the undergraduate laboratory. Jonas Ekshult – thanks for all the great laboratory things we did together, as well as the rewarding thoughts about chemistry, politics and George Co-stanza. Those cobalt tetra-, penta- and hexaammines were more elusive than we ever thought, right? Wendy Haglund – thanks for all the nice discussions as well as badminton games. … Rolle, Roger, Björn J and P, Jann, Erik H – thanks for all the memorable moments. Thank you very much Lena Rolander for helping us with the kids, amongst many other things.

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Gunvor och Nisse, Saimi och Reino, Timo och Mia, Hasse och Ingrid J – tack för alla härliga sommarlov (plus allt annat)! I have the deepest gratitude towards my father, Hanno Lindroth, sister, Jes-sica Lindroth and late mother, Lillemor Lindroth. I love you my wonderful kids, Stella, Hjalmar and Teodor! You make it all worthwhile – although one might wonder at 04.15 am. Zzz… Above all – thank you my lovely wife Isabel! I truly, genuinely love you.

Daniel Petrini, Uppsala, 2007-12-05

“Dear god, we paid for this food ourselves – so thanks for nothing.” Bart says the Simpson’s grace.

(Fibonacci)

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5. Summary in Swedish

“Om en nordbo säger: ’detta går icke’, ja då har man slagit i granit” Tommy Segerstedt om arbetsmoral och strävsamhet Diamantföretaget De Beers lanserade 1947 en reklamslogan ”A Diamond is forever” – diamanter är eviga - med syftet att uttrycka att diamanter är varak-tiga och därmed minimera andramarknaden. Det är sant att diamant är ett oerhört hårt material (det hårdaste), men det är faktiskt endast metastabilt. Grafit som är en annan struktur av kol är faktiskt mera stabilt. Omvandlingen från diamant till grafit tar dock väldigt lång tid. Ytan på en diamant är dess-utom reaktiv – där sker många processer som förändrar ytans funktionalitet väsentligt. Diamant brinner och bildar koldioxid vid ~1000 grader Celsius.

Ett ämne som liknar diamant är kubisk bornitrid (c-BN). Diamant före-kommer naturligt men c-BN är ett syntetiskt material. Bor (B) och kväve (N) är kols grannar i den andra radens grundämnen i periodiska systemet. Därför har kubisk bornitrid samma struktur som diamant och många egenskaper som liknar diamant. Till exempel så är båda oerhört hårda material, har hög värmeledningsförmåga (diamant har den högsta vid rumstemperatur) och är halvledare med ett stort bandgap. Dessa egenskaper gör att diamant och ku-bisk bornitrid har en stor potential att kunna användas i till exempel transis-torer, sensorer, skyddande filmer och som värmeledare. Vidare har de bra optiska egenskaper så som hög transparens från UV till bortom IR. De tål också höga stråldoser och är i det närmaste biokompatibla. Ett materials funktionalitet påverkas ofta av dess yta, och därför är det ofta önskvärt att belägga ett substrat med en tunn film.

Diamantfilmer kan tillverkas relativt enkelt med en »chemical vapour de-position« (CVD) teknik i en reaktor innehållande huvudsakligen metan (<5%) och vätgas (~95%). Reaktiva radikaler som bildas genom t.ex. värme eller mikrovågor reagerar kemiskt på den varma ytan som ska beläggas. Ofta kan syre också ingå i processen för att öka filmkvalitet eller tillväxthastighet. Kubisk bornitrid är svårare att syntetisera. Antingen så användes »physical vapour deposition« (PVD) tekniker eller CVD. Men båda metoderna innebär (för c-BN) högenergetiska jon-bombardemang med dålig filmkvalitet och höga spänningar i filmen som följd. Vidare så blir vidhäftningsförmågan mellan film och substrat ganska dålig. En mera varsam CVD teknik behövs för att göra kubisk bornitrid attraktivt på en större skala än idag.

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Ytmekanismer är svåra att analysera p.g.a. den dimension som representerar individuella atomer, dvs. ner till Ångströmskala, 10-10 m. Med hjälp av dato-rer kan man approximera de kvantmekaniska ekvationer som beskriver elek-tronerna inom de atomer som bygger upp molekyler och ytor. Om elektro-nerna approximeras med stor noggrannhet så kan många egenskaper hos t.ex. en yta beräknas. Dessa beräkningar kan leda till att man förstår experi-mentella data. Den teori som användes i alla vetenskapliga artiklar i den här avhandlingen kallas DFT, density function theory. DFT är en Nobelprisbelö-nad, robust metod som med stor noggrannhet kan beräkna ytors struktur, stabilitet och egenskaper. Den här avhandlingen syftar till att öka förståelsen inom två områden av diamant: i) egenskaper hos rena, väte-, syre-, fluor-, svavel- samt klor-terminerade ytor och ii) elektronöverföring från en väte-terminerad (100) yta till ett vattenlager precis ovanför ytan. Det förstnämnda är mera grundforskningsbetonat och syftar till att bland annat ge svar på följande frågor: vilken yta är mest stabil och hur ser denna yta ut? Det har betydelse för tillväxt samt även för de ytor som utsätts för normal atmosfär; syre finns ju överallt. Resultaten i denna avhandling visar att väte och fluor stabiliserar den yta de binder till. Syre binder starkt och i flera konfigurationer; olika positioner med olika bindningsstyrkor. Syre kan också få de översta atomerna att förflytta sig i relation till atomlägena inne i materialet (bulkpositionerna), vilket kallas rekonstruktion. Väte och syre uppvisar inga större skillnader i bindningsstyrka beroende på täckningsgrad. OH-grupper som påverkas av två effekter; vätebinding och steriska hinder. Vätebindning sker mellan grundämnena F, O, N och väte och sänker syste-mets energi. Steriska hinder innebär att OH-grupperna storlek påverkas av varandra och är en repulsiv effekt.

Studierna av elektronöverföringen är intressanta då man har sett att en väte-terminerad diamantytas annars så låga elektriska ledningsförmåga (det är egentligen en isolator) ökar markant vid närvaro av normal atmosfär. Två betingelser för att få denna effekt har experimentallt fastställts: (i) ytan måste vara väte-terminerad och (ii) ytan måste vara i kontakt med en atmosfär. En av de föreslagna modellerna baseras på överföring av laddning (elektroner) mellan yta och omgivning. Modellen förenar halvledarfysik och elektrokemi samt även ytkemi. Kortfattat kan den beskrivas som att väteatomerna på diamantytan sänker tröskeln för att elektroner ska kunna fly från ytan. Sam-tidigt ska det finnas vattenmolekyler med inslag av H+ (dvs. en proton som gör vattnet surt) och syre, strax ovanför ytan. Då finns det energinivåer utan-för diamantytan som ligger lägre än hos vissa elektroner i ytan. Det betyder att elektroner kan överföras spontant. Kvar i diamantytan lämnas hål, dvs. avsaknad av elektroner, och dessa hål kan nu leda en ström. Hålledning har liknats med bubblor i kolsyrad dryck: bubblorna (hålen) rör sig uppåt, men samtidigt rör sig vätskan (elektronerna) nedåt. Denna dopningsprocess på diamantytan kan användas för att tillverka sensorer och transistorer, men de bakomliggande vetenskapliga orsakerna är inte fullständigt bevisade. Det

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finns en stor kontrovers om vilken modell som bäst beskriver effekten. Fig. 6.1 är en vy över hur en diamantyta med ett tillhörande vattenlager kan se ut. I två artiklar i denna avhandling visar resultaten på att elektronöverföring sker till ett vattenbaserat adlager, men att det krävs syre, ozon eller H+. Störst effekt får man om syre eller ozon kombineras med H+. Detta stämmer väl överens med vad som förväntas inom elektrokemin. Endast vatten ger ingen elektronöverföring. I en annan artikel påvisades yttermineringens inverkan; syre hindrade elektronöverföringen. Syrets inverkan på konduktiviteten har bevisats experimentellt. Vidare så krävdes det ett överlapp mellan adlagrets och ytans orbitaler för att detta skulle ske.

Fig. 6.1 Ett vattenlager som omger en väte-terminerad diamantyta. Om förhållandet är gynnsamt så överförs elektroner spontant från diamantytan till vattenlagret och reducerar det. Kvar lämnas då hål i diamant filmen, och dessa hål kan leda en elekt-risk ström.

Även rena och väte-terminerade kubisk bornitrid (100) ytor har undersökts. Denna yta har antingen bor eller kväve atomer längst uppe. En ren, icke-terminerad kubisk bornitrid (100)-1x1 yta kommer att rekonstruera till ett 2x1 ytmönster, precis som diamant. Väte som adsorberats på en (100)-1x1 yta binder starkt och upprätthåller det bulklika 1x1 mönstret. Om en vakans i väte-termineringen uppstår, förändras dock den lokala geometrin avsevärt

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och ytan destabiliseras. Detta kan också ha betydelse för ytreaktiviteten, och för möjligheterna att realisera en varsam CVD tillväxt. Mera beräkningar måste dock göras för att fullt ut förstå denna yta. Resultaten som har genere-rats inom denna avhandling är en liten del, och bland de första teoretiska, för att bättre förstå ytreaktiviteten, strukturen och de mest gynnsamma tillstån-den på kubisk bornitride. Syftet är att kunna styra tillväxten mot mera högk-valitiva och funktionella tunna filmer.

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