Energetic stability of isolated 3d transition metals in diamond

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Diluted magnetic semiconductors and defects in diamond

Introduction

Magnetic ordering in metals has been the backbone of information processing and storage devices for many years. A key milestone in this area was the discovery of the Giant Magneto Resistance (GMR) effect [108], in which the resistance to the flow of charge in thin films consisting of alternating ferromagnetic and non-magnetic metal layers was found to be strongly dependent on the applied magnetic field. At present, this change in resistance (called magneto-resistance) with the direction of magnetization is used in high volume information storage (e.g. computer hard disk reading heads, and MRAM chips) to sense changes in magnetic fields; whereas switching and retrieval is achieved separately by controlled flow of charge carriers [109].
The emerging field of spin-based electronics, called spintronics, seeks to achieve the complementary functions of magnetism and electronics within same material devices by exploiting the spin property of an electron instead of, or in addition to, its charge. This prospect has successfully been demonstrated by use of Diluted Magnetic Semiconductor (DMS) materials as one of the methods through which magnetism can be integrated with electronics, by doping of semiconductor materials with suitable magnetic impurities, such as transition metal atoms. As opposed to the metal-based GMR technology devices, semiconductor-based spintronic devices could in principle provide conventional electronics functionalities (e.g. amplification) and serve, in general, as information storage devices, amongst others.
DMS materials are standard semiconductors in which a small fraction of their constituent atoms has been replaced by magnetically ordering impurities (e.g. transition metal atoms) capable of providing both magnetic moments and spin polarised charge carriers in the semiconductor matrix. This integration results in a strong spin-dependent coupling between band and localized states, thus potentially serving as a possible means of injecting, controlling and detecting spin properties. However, current challenges towards practical implementation in spintronic devices include low Curie temperatures and lack of desirable spintronic properties [4] in the semiconductor materials which have so far been considered [3,104,110]. Although a lot of research efforts have been directed towards understanding and improving the mechanisms of spin transport in these semiconductor materials, there is still a need to find new DMS materials which may successfully be used in spintronic devices capable of operating at room temperature.

Progress on Diluted Magnetic Semiconductors

The incorporation of transition metal impurities into non-magnetic host semiconductors started in the 1960s [111] and was aimed at combining the complementary properties of semiconductivity and ferromagnetism in single material systems. Among the most extensively studied ferromagnetic semiconductors were Eu doped Chalcogenides (e.g. EuSe, EuS, EuO) and Cr doped Chalcogenides (e.g. CdCr2Se4, CdCr2S4), but no practical application of these materials has been realized to date, mainly due to their low Curie temperatures and extreme difficulties in growing these crystals [112].
The next generation of DMSs began in the 1980s and focussed mainly on manganese doped II-VI and IV-VI heterostructures (e.g. Cd1-xMnxTe, Cd1-xMnxSe, Hg1-xMnxTe) [112] due to their ternary nature which offers the possibility of tuning their band gap [113] by changing the concentration of the magnetic ions. In addition, the cation valency of these materials closely matches that of common magnetic dopant ions like Mn which made them relatively easy to grow. Although many fundamental studies in these systems have been carried out [114,115], useful magnetic ordering phenomena for various transition metals has not been achieved yet at room temperature due to antiferromagnetic coupling of the transition metal spins with those of the host semiconductors [112]. On the other hand, p- type and n-type doping in II-VI ternaries is not easy to achieve, which made it relatively difficult to study their transport properties [111,116]. In addition, the solubility limits of the magnetic ions in these DMSs was also found to be generally small, and varied markedly from alloy to alloy [117]. However, these materials can be grown with relatively high concentration of free band carriers, and it was later demonstrated that their magnetic properties can be controlled by modifying their charge concentration [2]. But, lack of appropriate material technologies that would allow a high concentration of the magnetic impurities made these materials less attractive for technological applications [116].
Rapid progress on the research of DMS started in the 1990s following the successful epitaxial growth of Mn doped InAs and GaAs using non-equilibrium low temperature Molecular Beam Epitaxial (MBE) growth conditions [118-120]. This method made it possible to increase the concentration of magnetic impurity ions and substantially increase their electrical activity beyond thermal equilibrium solubility limits. Subsequently, various other semiconductors were studied in an attempt to increase their ferromagnetic transition temperature to more practical limits. Although progress in synthesizing and controlling the magnetic properties of DMSs was remarkable, the reported Curie temperatures were still far too low below room temperature to have any significant practical impact [121].
Recent studies on spintronics has focused on achieving practical magnetic ordering temperatures in many semiconductors, and tremendous progress has been made both in realizations of high quality epitaxial layers and on theory of magnetic ordering in DMS. As a result, several materials have theoretically been predicted to order ferromagnetically above room temperatures, but the ferromagnetic ordering properties of diamond are yet to be studied in detail. Although ferromagnetism has experimentally been reported in some of these materials, particularly in oxides [104], the results are unfortunately experimentally irreproducible, and are often due to spurious effects [122].
An important step in the search for high TC DMSs was the theoretical prediction of the relationship between the TC of a DMS and the properties of the host semiconductor for hole mediated ferromagnetism [121,123]. This result follows from the Zener model [124] of ferromagnetic interactions from which the spin-spin coupling may be assumed to be long range, allowing use of a mean field approximation [121,123,125]. In the presence of carriers, TC is determined by a competition between ferromagnetic (TAF) and antiferromagnetic (TAF) interactions, and can be expressed as [104]
The most direct dependence of TC on the host semiconductor’s physical properties comes from the density per unit volume of cation sites N0, which in turn has a reciprocal dependence on the host semiconductor’s lattice constant as . Refinements of the mean field solution of the Zener model for predicting TC take into account the effects of positional disorder [102,103], indirect exchange interactions [126], spatial inhomogenities and free carrier spin polarisation [127,128], but still the mean field approach and its variants has been found to produce reliable estimates of TC compared to experimental values for a wide range of materials [104]. Accordingly, semiconductor hosts with larger lattice constants have been predicted to have lowest TC, while hosts with smaller lattice constants have been predicted to have largest TC, well above room temperature, as illustrated in Figure 3.1 which makes diamond one of the most suitable material candidates for high temperature ferromagnetic ordering because of its small lattice constant (a0 = 3.567 Å [6]) compared to other semiconductors.
In addition, diamond is well known for its extreme properties (high electron and hole mobility, high breakdown field, excellent thermal conductivity, among others [19,20]). Thus achieving ferromagnetic ordering in diamond is expected to pave the way for spintronic devices with exceptional performance regarding high temperature, high power and high frequency applications.

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The potential of a diamond-based diluted magnetic semiconductor

Recent developments in techniques to grow high-purity single crystal synthetic diamonds have made diamond more attractive for solid state electronics [129]. Diamond, in its bulk as well as thin film forms, offers the opportunity not only to improve the operating performance of many existing technological systems, but also to develop a wide variety of new technologically advanced devices due to its combination of good optical, thermal, mechanical and electronic properties. Pure diamond is an electrical insulator, but when doped with suitable impurities can become an excellent semiconductor with superior performance regarding power efficiency, power density, and high frequency properties [130] thus making it an ideal material for active spintronic device applications. This prospect has attracted a lot of research activities in diamond aimed at finding suitable defects or impurities which may give rise to desirable electronic and spintronic applications.
An important property of diamond’s suitability for spintronic applications is its large band gap which may allow impurities to be excited without becoming ionized [129] at elevated temperatures (hence no “thermal run away” as in the case of Ge under laser irradiation [131]), thus allowing quantum spin states to retain their quantum coherence for usefully long times. Indeed, recent studies have shown that isotopically engineered CVD diamond has the longest room-temperature spin dephasing times ever observed in solid-state systems (T2=1.8 ms) [11], and diamond’s potential in quantum computing and spintronic applications has already been demonstrated at room temperature in the N-V centre [129], as well as in Cr [9] and Ni [10] related complexes in diamond.

Impurities and point defects in diamond

Defects in semiconductor materials not only influence their electrical and optical properties, but also exhibit other important properties (such as magnetic ordering) which can be beneficial in enhancing semiconductor functionalities. In either case, the identification and control of defects and impurities in diamond (such as transition metals, dopants, self vacancies and other impurity-related complexes) is important in realizing diamond-based applications in electronic and spintronic devices. Defects in diamond have been studied using a wide range of experimental techniques, including Electron Paramagnetic Resonance (EPR) spectroscopy [132-136], photoluminescence (PL) spectroscopy [137,138], Raman spectroscopy [139] and Deep Level Transient spectroscopy (DLTS) [140,141], and a large number of impurities and defects have been found to exist in diamond; their type greatly depends on relative stability and concentration as determined by the history of diamond, in particular whether it is natural or synthetic [142]. A review of some important defects and impurities in diamond is given below.

Transition metal impurities

Most experimental and theoretical studies of transition metals in diamond are based on Ni and Co which are commonly used as ‘solvent catalysts’ during High Pressure-High Temperature (HPHT) growth of synthetic diamond. The precise form of these atoms in diamond has been under considerable discussion as initially it was thought that such ions were too large for inclusion into diamond. Although other transition metals such as Fe, Mn and Cu are also used during growth, only Ni [143,144] and Co [7,145] related defects have been identified positively as being incorporated into the diamond lattice. There is also unconfirmed evidence [146] for Cr, Mn, Cu and Fe, while incorporation of Ti and Zn has only been achieved by ion implantation, but not during crystal growth [147-149].
Theoretical studies have shown [146] that the electronic structure of transition metals in diamond is complicated by the presence of dangling bonds as well as the weak bonding between the 3d transition metal ion and carbon atoms in diamond it has been found that the key electronic states originate from combinations of the transition metal’s 3d electrons with the dangling bond states [7]. The resultant shift in energy due to interactions between the dangling bonds and the d orbitals determines the overall electronic structure and stability of a given charge state as well as the relative stabilities between different lattice sites in a particular charge state. In addition, the presence of other defects such as nitrogen and boron, which are the most dominant impurities in synthetic and natural diamonds (other fundamentaldefects in diamond include the vacancy and the self interstitial), have also been found to play a significant role in influencing the energetic stability of the different charge states [150].

Nickel

Nickel is the most commonly observed transition metal impurity in HP-HT diamond, and is mainly incorporated in the <111> growth sectors [151]. The observed properties of Ni-related centres are strongly affected by the presence of other impurities or defects (e.g. N, B or 52 vacancies) in diamond, and the lattice location or its charge state often depends on the concentration of these defects [152].
Experimentally, nickel related defects in diamond have been identified at various lattice sites and charge states, but there is less evidence for the presence of an interstitial species [152]. At the substitutional site, Ni-related defects have been identified in the negative charge sate with a Td symmetry and a spin of (labelled W8 [153] which has beencorrelated to a donor level at eV [154], and optical absorption peaks at 2.51 eV and 1.88 eV [154]) in diamonds containing nitrogen impurities. However, in cases where the nitrogen concentration is low (or where B is present), the W8 and its associated optical centres disappear, giving rise to other new EPR centres [152], such as NIRIM-1 (electrical levels at eV) and NIRIM-2 (absorption and luminescence 1.404 eV doublet) which have been attributed to T interstitial nickel in the positive charge state perturbed by a d vacancy [155] or a boron acceptor [156]. Numerous other optical Ni-related centres have been identified, many of which have been found to occur after subsequent heat treatments, suggesting aggregation particularly in nitrogen containing samples [157]. A class of EPR centres labelled NE1-NE9 have also been identified and attributed to Ni at a divacancy site in diamond containing nitrogen impurities at various concentrations [151].
The majority of these experimental observations of nickel features have been confirmed by theoretical calculations [151], though the assignment of to NIRIM centres have been predicted to be energetically unstable; the formation energy and mobility of the interstitial species suggest that nickel will be predominantly of the substitutional form [151]. Although the aggregation of Ni with other defects has theoretically been confirmed [158,159], indications that the NE group of centres are negatively charged in N containing diamond presents a possibility of other forms of the centre in p-type diamond, for example the Ni-V complex at eV which has been found to occur in B-doped diamond [159,160].

Cobalt

Other than nickel, cobalt is the only other transition metal that has also been identified positively in HP-HT diamond [152,161]. Although the physical and chemical properties of cobalt and nickel are somewhat similar, the concentration of cobalt in diamond has been found to be relatively lower than that of nickel which explains why nickel is more readily detected in diamond compared to cobalt [161].
A number of photoluminescence (PL) peaks and EPR centres in HP-HT diamond grown with cobalt as a catalyst have been identified [152] in various charge states and lattice locations. As in the case of nickel, the observed properties of these centres are strongly affected by the presence of nitrogen in diamond samples. Among the EPR centres which have been linked to cobalt in diamond include a hyperfine structure attributed to interstitial cobalt in the double positive charge state [162] and other centres with a spin of (labelled O4, NLO2, and NWO1 [145]), whose microscopic models have theoretically been suggested [163] to be a cobalt atom at a divacancy site interacting with a nearby substitutional nitrogen atom in the negative charge state In addition, a PL peak at 2.367 eV with a level at 4.4 eV below the conduction band has been identified [152] and attributed to a complex of substitutional Co and nitrogen which, like in the case of nickel, indicates a likelihood of a family of cobalt-nitrogen defects forming after high temperature annealing.

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Manganese

A large class of diluted magnetic semiconductors are based on manganese doping [73]. However, theoretical predictions of ferromagnetic ordering of neutrally charged Mn in diamond have been predicted to be unlikely [73]. Efforts to find alternative transition metals which may order ferromagnetically in diamond have predicted ferromagnetic ordering in Co-doped diamond with a resultant moment of 0.4 µB per an impurity atom and ferromagnetic stabilization energy of 22 meV in the neutral charge state [164]. However, the magnetic ordering properties of Mn and Co in other charge states remain to be understood. In addition, relatively large magnetic moments and ferromagnetic stabilization energies are required in order to support significant spin polarisation at high Curie temperatures. Hence, there is need to find alternative transition metal ions which may successfully be considered in the search of a diamond-based DMS.

Other transition metals

Several theoretical [146,148,165] studies have been carried out on the 3d transition metal series in diamond, and have suggested that other transition metals should be present in diamond. While most of these studies have been directed towards investigating the electronic, electrical and structural properties corresponding to specific experimentally observed centres, as in the case of cobalt and nickel, no systematic studies have been carried out on their magnetic ordering properties which are better understood in other group IV semiconductors such as silicon [148,166,167] and germanium [168].

Dopants in diamond

Despite diamond’s potential in spin-based electronics, efficient n-type doping of diamond has remained a major challenge towards full utilization of diamond as a novel electronic material. The general factors that have been identified as possible limitations to successful doping in diamond include creation of energetically deep donor/acceptor levels, insufficient donor solubility and charge compensation [169]. While the issue of donor/acceptor levels and solubility may be circumvented by the choice of different dopant impurities or by changing growth conditions [79,170-173], charge compensation can be said to be the main factor limiting dopability in diamond [169]. However, continued research on alternative growth and doping approaches has shown promise in overcoming these difficulties.

n-type dopants

Trends in silicon suggest that potential n-type dopants in diamond are the group V elements of the periodic table (such as nitrogen and phosphorus). However, the only donor so far which is usually incorporated into diamond is phosphorus, but with a relatively deep donormlevel at eV [174].
Although many examples of electronic devices employing P-doped diamond have been demonstrated at high temperatures [151], there is need to develop shallower n-type dopants; much of the research efforts in determining the likely candidates are based on quantum mechanical modelling [151]. In particular, phosphorus’s high formation energy in diamond (~7 eV [175] in CVD diamond) leads to lower solubility and hence lower electron concentrations (up to 2 1019 cm−3 [176]) which make diffusion methods generally inappropriate. However, the use of plasma-enhanced CVD conditions has theoretically been predicted [169] (and validated by experiments [173]) as a successful method through which the solubility of phosphorus in diamond can be enhanced. An alternative approach which has also been considered is ion implantation, but implantation related complexes, e.g. vacancies and self interstitials have been found to act as compensation centres, resulting in deeper donor levels [177].
Nitrogen is abundant in natural diamonds and is easily incorporated into synthetic diamonds, but its deep donor level of eV [178] makes it inapplicable for room temperature electronic applications. In most synthetic and some rare natural diamonds (type 1b), nitrogen is incorporated in single substitutional form in the lattice, and both experimental and theoretical [23] data has shown that the nitrogen atom moves off-lattice along the <111> direction, resulting in a centre with C3v symmetry. The origin of the distortion has been shown [23] to originate from preferential formation of a lone-pair orbital on nitrogen and a dangling bond orbital on the unique carbon neighbour which forms bonding and anti-bonding orbitals due to sp3 hybridization.

p-type dopants

Unlike the difficulties experienced in n-type doping of diamond, p-type diamond is readily achieved by boron doping. Boron exists in natural type IIb diamond with an acceptor level of and has therefore been widely studied [179] as a p-type dopant in diamond. It is the most commonly used impurity for p-type conductivity in diamond and the results obtained are of good quality, so that limited data on other possible p-type dopants are available.
Although natural type IIb diamond is p-type due to substitutional boron impurities, its electron mobility and compensation ratio cannot be controlled effectively. Controlled p-type conductivity can be obtained by artificially grown diamond with the same activation energy as that of natural diamond. For example, results of highly conducting p-type diamond with an activation of up to 30% of the implanted boron atoms have been reported using high dose ion implantation [180,181]. In general, however, the doping efficiency obtained by implantation [180,181] of boron into diamond is fairly low, with hole mobilities not as high as in natural or boron doped CVD diamond, even after high temperature (>1400 K [180,181]) annealing. On the other hand, B-doped CVD diamond films have been grown with boron concentrations of up to [20,182], and even at low or medium concentrations the hole mobility can be as high as that of natural diamond, with a very high doping efficiency. It is worth noting that heavily B-doped diamond has a well-defined impurity band, but doping it more heavily makes it metallic, and this strongly B-doped material is a superconductor [183,184].

Contents
Abstract
Acknowledgement
List of Publications
Contents
1. Introduction 
1.1 Overview
1.2 Properties of diamond
1.3 Thesis outline
2. Theoretical background 
2.1 Quantum Mechanical Modelling
2.2 Density Functional Theory
2.3 Geometry optimization
2.4 Formation energy
2.5 Computational methodology
3. Diluted magnetic semiconductors and defects in diamond 
3.1 Introduction
3.2 Progress on Diluted Magnetic Semiconductors
3.3 The potential of a diamond-based diluted magnetic semiconductor
3.4 Impurities and point defects in diamond
4. Energetic stability of isolated 3d transition metals in diamond 
4.1 Introduction
4.2 Formation energy
4.3 Charge transition levels
5. Electronic structure, spin and symmetry of 3d transition metals in diamond 
5.1 Introduction
5.2 Results and discussions
5.3 Comparison with previous models
6. Magnetic ordering of 3d transition metals in diamond 
6.1 Introduction
6.2 Theoretical approach
6.3 Spin population and spin density distribution
6.4 Magnetic states and magnetic stabilization
6.5 Half-metallic ferromagnetic ordering in Fe-doped diamond
7. Summary and conclusions 
8. References and Bibliography
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