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Deducing atomic models for point defects in diamond: The relevance of their mechanism of formation
Diamond & Related Materials 16 (2007) 216 – 219 www.elsevier.com/locate/diamond
Deducing atomic models for point defects in diamond: The relevance of their mechanism of formation J.M. Baker ⁎ Oxford Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom Received 29 November 2005; received in revised form 4 May 2006; accepted 9 May 2006 Available online 30 June 2006
Abstract There is often too little information about the properties of a point defect in diamond for one to be able to make an unambiguous assignment of an atomic model. One of the factors which is sometimes ignored in suggesting a complex atomic model is the route by which its constituents were assembled: the family tree of its generation. This general point is illustrated by considering some of the previously proposed multi-vacancy models for point defects (specifically EPR defects R7, R7a and R8) formed by annealing irradiated nominally defect-free diamond. As some of the inevitable precursors of the previously proposed models are not observed, alternative models are proposed. © 2006 Elsevier B.V. All rights reserved. Keywords: Diamond crystal; Annealing; Vacancy clusters; EPR point defects
1. Introduction This paper is stimulated by consideration of some of the models for vacancy clusters in diamond proposed by Iakoubovskii and Stesmans [1], but it has general relevance to the search for atomic models for some point defects in diamond. Early in the 20th century it was realised that the colour of many gemstones arises from isolated impurity atoms (often of transition metals) in the crystalline structure. The colour arises from electronic transitions between energy levels of the unpaired electrons in these point defects. Similar paramagnetic defects may be produced by radiation damage; e.g. F-centres in alkali halides [2]. The colouration of fancy coloured diamonds is produced by this type of paramagnetic point defect. About 50 years ago, another technique was invented, electron paramagnetic resonance (EPR) which gives detailed information about paramagnetic point defects [3]. Covalent crystals, like diamond [4], silicon [5] and quartz [6], exhibit a wide range of such defects related to substitutional and interstitial impurity atoms and vacancies and self-interstitials, or
⁎ Tel.: +44 1865 272336; fax: +44 1865 272400. E-mail address: [email protected]. 0925-9635/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2006.05.004
combinations of them, incorporated during growth, by post-growth diffusion and annealing or by radiation damage. Information about the atomic structure of such point defects may be deduced from EPR or from their optical spectrum in absorption, fluorescence or luminescence, which may contain narrow zero phonon lines (ZPL). The evidence which these spectra afford about the atomic structure (the model) of the defect is variable. EPR usually indicates the symmetry of the defect. The symmetry may also be determined from the effect of uniaxial stress along crystal symmetry directions on the ZPL. For S >1 /2, the fine structure parameter D determined by EPR may be interpreted in terms of interaction between constituent unpaired electron spins: in particular for S = 1 formed by dipolar interaction between two well separated unpaired electrons, the relative position of these electrons may be determined by assuming that they are point dipoles with S =1 /2. Hyperfine structure (HFS) in EPR, due to interaction between the spin S and neighbouring 13C nuclei indicates the number of equivalent C atoms, and gives information which may be interpreted in terms of their relative position. Theoretical modelling may also be used to deduce the stability of such defects. A complex point defect in diamond is a type of molecule, comprising impurities, vacancies or interstitials, locked in place by the surrounding lattice. One of the problems in discussing them is to understand how their constituent components were
J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
assembled. One may be able to show by modelling that a certain arrangement of constituents should be a stable defect; but that is not sufficient to show that it will exist, because it must be possible to make it. There must be a family tree of ancestors as constituents are added one by one, and each must have a long enough lifetime to be able to accept the next constituent. This does not rule out the possibility of unstable ancestors, but a sufficient number of them must be able to proceed to the next generation before they decay. This aspect has frequently not been considered when proposing a model for a defect. 2. The problem The defects which have been studied in diamond fall into four main groups in (1) natural diamond, (2) synthetic diamond asgrown in a variety of ways, (3) diamond irradiated by energetic particles, and (4) diamond of the first three categories which has been subsequently annealed. In groups 1–3 one cannot say much about the generation processes as several may proceed simultaneously before the sample is available for study. The fourth process is different, as by successively annealing to higher and higher temperature, the defects can be nudged gently over potential humps to be transformed step by step, or transformed by charge transfer from other sources. As this excitation is relatively gentle, it is likely that each step in a transformation from A to B is stable, or at least long-lived, so that it does not decay before the next step can be taken. An example of this sort of transformation is given by the defects formed by electron irradiation of nominally defect-free (type IIa) diamond at or below room temperature and subsequently annealed. This was first done by Lomer's group using
217
natural type IIa diamond [4,7], in which the effect of impurities is uncertain; but many of the defects found in that study (Fig. 1) were also present in a similar study of synthetic (HTHP) diamonds grown with nitrogen getters, where the purity is expected to be very high [1,8]. The defects fall into two broad groups: (a) those which anneal in and out below 600 °C, which are thought to be due to self-interstitials and their complexes, and (b) those which anneal in and out above 600 °C, where it is known that the vacancy becomes mobile. As by 600 °C it appears that all interstitials have disappeared, it is assumed that the defects present after annealing above 600 °C are vacancy clusters. In the discussion below, we use the symbol VN to represent a cluster of N vacancies, with a superscript to indicate its overall charge, and we consider the cluster in the following way. An isolated neutral vacancy has four C neighbours with dangling bonds. An adjacent vacancy removes one of these dangling bonds. Hence, in a continuous chain of vacancies, VN0 , each has two dangling bonds, except for the ends which have three each. We postulate that the dangling bonds reconstruct in pairs leaving two dangling bonds, one at each end of the chain. If the chain folds back on itself to become a continuous loop, each vacancy has two dangling bonds all of which reconstruct. If there are branching chains, the vacancy at each junction has only one dangling bond. The validity of these assumptions needs to be checked by computer modelling, but they do seem to have been confirmed for planar VN chains [9]. Using a combination of EPR and optical evidence, the identification of simple defects involving a vacancy V and a selfinterstitial I, such as V0 (GR1), V− (ND1) I0 (R2) and I20 (R1) is unambiguous and V20 (R4) is undisputed [10]. The problem with defects which anneal at higher temperatures is that there is too
Fig. 1. Isochronal annealing-in and annealing-out of EPR spectra [4,7].
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J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
little information about them to assign an unambiguous model. Most of the defects formed by electron irradiation of type IIa diamond followed by annealing above 600 °C have S = 1 and C2v symmetry, where (110) is a plane of reflection symmetry. These (R5, O1, R6, R10, R11, KUL11) have been plausibly attributed to VN chains with N = 3 to 8 lying in the (110) plane [1,11], as: (a) The orientation and magnitude of Dzz correspond to that calculated for dipolar interaction between two spins S = 1 / 2 at the ends of the chain. (b) Where it can be measured all have the same 13HFS from 4 or 8 nearby C atoms [1], suggesting that the electronic arrangement at either end of the chain is the same in all cases. (c) The concentration |VN0 | falls off in a sensible way as a function of N. The only slight worry is that, while C2v is the expected symmetry for odd N (Fig. 2(a)), for even N one would expect C2h symmetry (Fig. 2(b)). The assignment suggests that for the latter the departure from C2v symmetry is too small to be observable. These centres all anneal out at the same temperature, ∼1150 °C, which suggests a common mode of decay, such as that vacancies, or di-vacancies, just diffuse away from their ends. Some centres
Fig. 2. Illustrations of the defects discussed using, for easy comparison, the projection used in Fig. 5 of Ref. [1] to illustrate R7, R7a and R8 EPR centres (see (e)–(g)). They are projections on a plane close to (110) viewed from a direction close to the [110] direction with the [111] direction vertical on the page. Only vacancy sites are shown. The lines linking adjacent vacancies help the eye in visualising the structure and are in the position of C–C bonds of the defect-free structure. The un-terminated lines represent dangling bonds from a neighbouring carbon atom (not shown).
Table 1 Fine structure parameters for relevant EPR centres with S = 1, taken from Ref. [1] Centre
D1 (MHz)
D2 (MHz)
D3 (MHz)
Symmetry
R5 R7 R7a R8
−529.2(1.7) −392.2(1.4) −394.2(0.6) −336
245.0(1.7) 159.8(1.4) 191.2(0.6) 168
284.2(1.7) 229.3(1.4) 203.0(0.6) 168
C2v C1h C2v C2v
D1 is parallel to [011], and is taken to be negative, and D2 is parallel to [100], except for R7 where it is tilted by 15°.
remain after annealing at ∼1150 °C, indicating that they are more stable than VN0 , and it is the nature of some of these we wish to discuss, namely R7 [4,7], R7a [1] and R8 [4,7]. 3. Mechanisms of formation of defects It seems clear that clusters of vacancies must have been created by accumulation of individual migrating vacancies; or possibly vacancy pairs (R4), as such pairs could migrate as a unit by a shuffle mechanism. The latter is suggested by the relative concentration of the planar VN chains: the concentration |V4| is rather larger than one might expect relative to |V3| for accumulation of isolated vacancies. Hence, the steps to accumulate any particular cluster must involve precursors with the same arrangement of vacancies, less one or two adjacent vacancies, and as these precursors must have been relatively stable they should be observable as independent defects. For example, this is certainly so for the planar vacancy chains, VN0 , as all values of N occur up to N = 8, (R5 to KUL11) with the expected gradual decrease in concentration |VN0 | with increasing N. Conversely, a proposed model where the necessary precursors cannot be observed must be suspect, however stable the proposed model may appear to be. It is expected that vacancies migrate by jumping one step at a time along <111>. It is also known from modelling [9] that the V6 hexagonal ring (HR) is a very stable structure. However, it is not possible to form the V6 HR (Fig. 2(c)) from the observed V3 (R5) without going through the intermediate V4 or V5 part hexagonal ring (PHR) structure (Fig. 2(d)). There is no evidence of the EPR defects of C1 symmetry which would be formed by a planar VN chain tacking on an additional out of plane vacancy at one end. However, Ref. [9] suggests that the V4 PRH defects should have an S = 0 ground state, which might lead to a ZPL with low symmetry and which might have been missed. There are several centres which are more stable than the planar chains VN0 . Among these, Iakoubovskii and Stesmans [1] noted that there are several EPR centres (R7, R7a and R8) with S = 1 and D matrices similar to that of R5 (Table 1), and they suggest that all of these correspond to dangling bonds on carbon atoms separated by ∼0.5 nm along <110>. They are more stable than R5, so they are attributed to two closed ring structures with a common V−V−V chain: the vacancy at each end of this chain has three vacancy neighbours and so one dangling bond. Although these proposed structures, shown in Fig. 2(e)–(g), would be more stable than R5 and have similar D, they are much more complex, involving many more vacancies, and there is no evidence that any of many of the ancestors of these defects is formed. For example the simplest of
J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
the models, proposed for R7a, is V9 (Fig. 2(e)) which has been modelled by [9], and is predicted to have an S = 1 ground state, but so are the precursor defects V5, V7 and V8, none of which is observed, yet they are all predicted to be more stable than V3 (V6 is also more stable but has S = 0). The proposed models for R7 and R8 involve larger closed ring structures (Fig. 2(f) and (g) respectively), implying even more precursors, which are not observed. Hence, we seek alternative models for R7a, R7 and R8 which may be formed without precursors. 4. Alternative models We suggest that above 800 °C the di-vacancy is a much more common diffusing defect than the isolated vacancy, but when a di-vacancy approaches a larger VN cluster, first one vacancy moves into a site adjacent to VN, then the second vacancy may either follow it or move away. As R8 begins to appear as R5 reaches its peak, it is suggestive that R8 has either one or two vacancies attached to R5, i.e. either V4 or V5. V4 is either planar (O4) or of C1 symmetry, and probably S = 0, as there is no evidence of V4 of C3v symmetry with a tripod-like structure, formed by tacking a vacancy to the centre of V3 (which may suggest that there is low probability of tacking a migrating vacancy onto the side of a VN planar chain). So, is the part hexagonal ring (PHR) structure for V5 a possible model of R8? Modelling [9] shows it to have higher stability than R6 (V3), but this model of R8 has C1h symmetry, whereas experiment shows R8 to have C2v; however, D is axial about <110>, corresponding to pure dipolar interaction between two dangling bonds in that direction, which is where the dangling bonds are in the V5 PHR model. So, the departure from C2v symmetry might be too small to be detected. V5 PHR could anneal out, not by evaporation of a vacancy, but by accruing another vacancy to form a very stable V6 hexagonal ring. As the concentration of V5 increases, it can take the role of precursor to larger VN defects. Where a di-vacancy attaches itself will depend upon the direction of the approach. It may form a V6 HR, S = 0, after which the second vacancy may not attach itself to the rather stable V6 ring. There is no EPR evidence for the predicted S = 1 ground state of V7, suggesting that it may not be formed by this route. There is an equal probability that a di-vacancy approaches V5 PHR from a different direction allowing it to form a V7 partial loop (Fig. 2 (h)), which is one short of a (presumably stable) V8 ring structure (Fig. 2(i)). This V7 also has a C−V−C−V−C structure with a dangling bond on each of the outer carbon atoms, which give S = 1 and D similar to R5. The probably stable V8 closed ring structure comprises all of the neighbouring sites to a Td interstitial site (4 nearest neighbours (nn) along <111> and 6 next nearest neighbours (nnn) along <100>) except for two along say [001]. That site has D2d symmetry about [001] and each vacancy has two dangling bonds which can re-construct to give S = 0 overall. There are two types of site formed by filling one of the vacancies with a carbon atom, depending upon whether it is one of the nn or nnn of the Td interstitial site
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which is filled. (Could this be the origin of equal concentration of R7 and R7a?) The V7 site described above has its carbon atom in a nnn site, giving a site of C2 symmetry about [001], with the dangling bonds on carbon atoms along [011], which is not inconsistent with the C2v symmetry of R7a, with the largest component of D along [011]. A carbon atom at a nn site would give a site of C1h symmetry (Fig. 2(j)), with the largest component of D along the <110> symmetry axis (R7 has such C1h symmetry). This latter site cannot be formed by attaching V2 to V5 PHR. However, the two V7 sites are interchangeable by moving the carbon atom to an adjacent vacancy, so if the two sites have similar stability, and this switch is easily driven at the annealing temperature, both sites should have similar concentration on cooling. This could explain why |R7,7a| takes off where |R8| reaches its peak, and why R7, R7a and R8 anneal out at much the same temperature (by acquiring an additional vacancy, or by expelling a mobile carbon interstitial). The validity of this argument depends upon (a) whether the pattern of re-bonding is energetically favourable, and (b) whether the V7 PR structures are stable against re-organisation or loss of a vacancy. These things need to be calculated by modelling. If these criteria are acceptable, these proposed structures are more logical than those suggested by Ref. [1], and they are free from the objection that there are no observed precursors. 5. Conclusions We suggest that the proposed models [1] for the EPR centres R7a (V9), R7 (V11) and R8 (V13), produced by isochronal annealing of irradiated type IIa diamond, although having the observed symmetry, are questionable as none of the inevitable precursor defects is observed. We propose that more probable models are V5 PHR (Fig. 2(d)) for R8 and two types of nearly complete ring V7 for R7 (Fig. 2(i)) and R7a (Fig. 2(j)). This proposal is speculative and needs confirming by detailed modelling of the proposed structures. References [1] K. Iakoubovskii, A. Stesmans, Phys. Status Solidi, A Appl. Res. 201 (2004) 2509. [2] J.H. Crawford, L.M. Slifkin (Eds.), Point Defects in Solids, vol. 1, Plenum Press, New York and London, 1972. [3] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford, 1970; J.A. Weil, J.R. Bolton, J.E. Wertz, Electron, Paramagnetic Resonance, Wiley, New York, 1994. [4] C.A.J. Ammerlaan, in: O. Madelung, M. Schultz (Eds.), Semiconductors, Impurities, Defects in Group IV Elements, III–V Compounds, Section 4.1 Diamond, Springer, Berlin, 1990. [5] C.A.J. Ammerlaan, in: O. Madelung, M. Schultz (Eds.), Semiconductors, Impurities, Defects in Group IV Elements, III–V Compounds, Section 4.2 Silicon, Springer, Berlin, 1990. [6] G. Pacchioni, et al., (Eds.), Defects in SiO2, Kluwer, 2000. [7] J.N. Lomer, A.M.A. Wild, Radiat. Effects 17 (1973) 37. [8] K. Iakoubovskii, A. Stesmans, Phys. Rev., B 66 (2002) 045406. [9] J.L.S. Hounsome, et al., Phys. Status Solidi, A Appl. Res. 202 (2005) 2182. [10] D.J. Twitchen, M.E. Newton, et al., Phys. Rev., B 59 (1999) 12900. [11] J.H.N. Loubser, J.A. van Wyk, Rep. Prog. Phys. 41 (1978) 1201.
Deducing atomic models for point defects in diamond: The relevance of their mechanism of formation J.M. Baker ⁎ Oxford Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom Received 29 November 2005; received in revised form 4 May 2006; accepted 9 May 2006 Available online 30 June 2006
Abstract There is often too little information about the properties of a point defect in diamond for one to be able to make an unambiguous assignment of an atomic model. One of the factors which is sometimes ignored in suggesting a complex atomic model is the route by which its constituents were assembled: the family tree of its generation. This general point is illustrated by considering some of the previously proposed multi-vacancy models for point defects (specifically EPR defects R7, R7a and R8) formed by annealing irradiated nominally defect-free diamond. As some of the inevitable precursors of the previously proposed models are not observed, alternative models are proposed. © 2006 Elsevier B.V. All rights reserved. Keywords: Diamond crystal; Annealing; Vacancy clusters; EPR point defects
1. Introduction This paper is stimulated by consideration of some of the models for vacancy clusters in diamond proposed by Iakoubovskii and Stesmans [1], but it has general relevance to the search for atomic models for some point defects in diamond. Early in the 20th century it was realised that the colour of many gemstones arises from isolated impurity atoms (often of transition metals) in the crystalline structure. The colour arises from electronic transitions between energy levels of the unpaired electrons in these point defects. Similar paramagnetic defects may be produced by radiation damage; e.g. F-centres in alkali halides [2]. The colouration of fancy coloured diamonds is produced by this type of paramagnetic point defect. About 50 years ago, another technique was invented, electron paramagnetic resonance (EPR) which gives detailed information about paramagnetic point defects [3]. Covalent crystals, like diamond [4], silicon [5] and quartz [6], exhibit a wide range of such defects related to substitutional and interstitial impurity atoms and vacancies and self-interstitials, or
⁎ Tel.: +44 1865 272336; fax: +44 1865 272400. E-mail address: [email protected]. 0925-9635/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2006.05.004
combinations of them, incorporated during growth, by post-growth diffusion and annealing or by radiation damage. Information about the atomic structure of such point defects may be deduced from EPR or from their optical spectrum in absorption, fluorescence or luminescence, which may contain narrow zero phonon lines (ZPL). The evidence which these spectra afford about the atomic structure (the model) of the defect is variable. EPR usually indicates the symmetry of the defect. The symmetry may also be determined from the effect of uniaxial stress along crystal symmetry directions on the ZPL. For S >1 /2, the fine structure parameter D determined by EPR may be interpreted in terms of interaction between constituent unpaired electron spins: in particular for S = 1 formed by dipolar interaction between two well separated unpaired electrons, the relative position of these electrons may be determined by assuming that they are point dipoles with S =1 /2. Hyperfine structure (HFS) in EPR, due to interaction between the spin S and neighbouring 13C nuclei indicates the number of equivalent C atoms, and gives information which may be interpreted in terms of their relative position. Theoretical modelling may also be used to deduce the stability of such defects. A complex point defect in diamond is a type of molecule, comprising impurities, vacancies or interstitials, locked in place by the surrounding lattice. One of the problems in discussing them is to understand how their constituent components were
J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
assembled. One may be able to show by modelling that a certain arrangement of constituents should be a stable defect; but that is not sufficient to show that it will exist, because it must be possible to make it. There must be a family tree of ancestors as constituents are added one by one, and each must have a long enough lifetime to be able to accept the next constituent. This does not rule out the possibility of unstable ancestors, but a sufficient number of them must be able to proceed to the next generation before they decay. This aspect has frequently not been considered when proposing a model for a defect. 2. The problem The defects which have been studied in diamond fall into four main groups in (1) natural diamond, (2) synthetic diamond asgrown in a variety of ways, (3) diamond irradiated by energetic particles, and (4) diamond of the first three categories which has been subsequently annealed. In groups 1–3 one cannot say much about the generation processes as several may proceed simultaneously before the sample is available for study. The fourth process is different, as by successively annealing to higher and higher temperature, the defects can be nudged gently over potential humps to be transformed step by step, or transformed by charge transfer from other sources. As this excitation is relatively gentle, it is likely that each step in a transformation from A to B is stable, or at least long-lived, so that it does not decay before the next step can be taken. An example of this sort of transformation is given by the defects formed by electron irradiation of nominally defect-free (type IIa) diamond at or below room temperature and subsequently annealed. This was first done by Lomer's group using
217
natural type IIa diamond [4,7], in which the effect of impurities is uncertain; but many of the defects found in that study (Fig. 1) were also present in a similar study of synthetic (HTHP) diamonds grown with nitrogen getters, where the purity is expected to be very high [1,8]. The defects fall into two broad groups: (a) those which anneal in and out below 600 °C, which are thought to be due to self-interstitials and their complexes, and (b) those which anneal in and out above 600 °C, where it is known that the vacancy becomes mobile. As by 600 °C it appears that all interstitials have disappeared, it is assumed that the defects present after annealing above 600 °C are vacancy clusters. In the discussion below, we use the symbol VN to represent a cluster of N vacancies, with a superscript to indicate its overall charge, and we consider the cluster in the following way. An isolated neutral vacancy has four C neighbours with dangling bonds. An adjacent vacancy removes one of these dangling bonds. Hence, in a continuous chain of vacancies, VN0 , each has two dangling bonds, except for the ends which have three each. We postulate that the dangling bonds reconstruct in pairs leaving two dangling bonds, one at each end of the chain. If the chain folds back on itself to become a continuous loop, each vacancy has two dangling bonds all of which reconstruct. If there are branching chains, the vacancy at each junction has only one dangling bond. The validity of these assumptions needs to be checked by computer modelling, but they do seem to have been confirmed for planar VN chains [9]. Using a combination of EPR and optical evidence, the identification of simple defects involving a vacancy V and a selfinterstitial I, such as V0 (GR1), V− (ND1) I0 (R2) and I20 (R1) is unambiguous and V20 (R4) is undisputed [10]. The problem with defects which anneal at higher temperatures is that there is too
Fig. 1. Isochronal annealing-in and annealing-out of EPR spectra [4,7].
218
J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
little information about them to assign an unambiguous model. Most of the defects formed by electron irradiation of type IIa diamond followed by annealing above 600 °C have S = 1 and C2v symmetry, where (110) is a plane of reflection symmetry. These (R5, O1, R6, R10, R11, KUL11) have been plausibly attributed to VN chains with N = 3 to 8 lying in the (110) plane [1,11], as: (a) The orientation and magnitude of Dzz correspond to that calculated for dipolar interaction between two spins S = 1 / 2 at the ends of the chain. (b) Where it can be measured all have the same 13HFS from 4 or 8 nearby C atoms [1], suggesting that the electronic arrangement at either end of the chain is the same in all cases. (c) The concentration |VN0 | falls off in a sensible way as a function of N. The only slight worry is that, while C2v is the expected symmetry for odd N (Fig. 2(a)), for even N one would expect C2h symmetry (Fig. 2(b)). The assignment suggests that for the latter the departure from C2v symmetry is too small to be observable. These centres all anneal out at the same temperature, ∼1150 °C, which suggests a common mode of decay, such as that vacancies, or di-vacancies, just diffuse away from their ends. Some centres
Fig. 2. Illustrations of the defects discussed using, for easy comparison, the projection used in Fig. 5 of Ref. [1] to illustrate R7, R7a and R8 EPR centres (see (e)–(g)). They are projections on a plane close to (110) viewed from a direction close to the [110] direction with the [111] direction vertical on the page. Only vacancy sites are shown. The lines linking adjacent vacancies help the eye in visualising the structure and are in the position of C–C bonds of the defect-free structure. The un-terminated lines represent dangling bonds from a neighbouring carbon atom (not shown).
Table 1 Fine structure parameters for relevant EPR centres with S = 1, taken from Ref. [1] Centre
D1 (MHz)
D2 (MHz)
D3 (MHz)
Symmetry
R5 R7 R7a R8
−529.2(1.7) −392.2(1.4) −394.2(0.6) −336
245.0(1.7) 159.8(1.4) 191.2(0.6) 168
284.2(1.7) 229.3(1.4) 203.0(0.6) 168
C2v C1h C2v C2v
D1 is parallel to [011], and is taken to be negative, and D2 is parallel to [100], except for R7 where it is tilted by 15°.
remain after annealing at ∼1150 °C, indicating that they are more stable than VN0 , and it is the nature of some of these we wish to discuss, namely R7 [4,7], R7a [1] and R8 [4,7]. 3. Mechanisms of formation of defects It seems clear that clusters of vacancies must have been created by accumulation of individual migrating vacancies; or possibly vacancy pairs (R4), as such pairs could migrate as a unit by a shuffle mechanism. The latter is suggested by the relative concentration of the planar VN chains: the concentration |V4| is rather larger than one might expect relative to |V3| for accumulation of isolated vacancies. Hence, the steps to accumulate any particular cluster must involve precursors with the same arrangement of vacancies, less one or two adjacent vacancies, and as these precursors must have been relatively stable they should be observable as independent defects. For example, this is certainly so for the planar vacancy chains, VN0 , as all values of N occur up to N = 8, (R5 to KUL11) with the expected gradual decrease in concentration |VN0 | with increasing N. Conversely, a proposed model where the necessary precursors cannot be observed must be suspect, however stable the proposed model may appear to be. It is expected that vacancies migrate by jumping one step at a time along <111>. It is also known from modelling [9] that the V6 hexagonal ring (HR) is a very stable structure. However, it is not possible to form the V6 HR (Fig. 2(c)) from the observed V3 (R5) without going through the intermediate V4 or V5 part hexagonal ring (PHR) structure (Fig. 2(d)). There is no evidence of the EPR defects of C1 symmetry which would be formed by a planar VN chain tacking on an additional out of plane vacancy at one end. However, Ref. [9] suggests that the V4 PRH defects should have an S = 0 ground state, which might lead to a ZPL with low symmetry and which might have been missed. There are several centres which are more stable than the planar chains VN0 . Among these, Iakoubovskii and Stesmans [1] noted that there are several EPR centres (R7, R7a and R8) with S = 1 and D matrices similar to that of R5 (Table 1), and they suggest that all of these correspond to dangling bonds on carbon atoms separated by ∼0.5 nm along <110>. They are more stable than R5, so they are attributed to two closed ring structures with a common V−V−V chain: the vacancy at each end of this chain has three vacancy neighbours and so one dangling bond. Although these proposed structures, shown in Fig. 2(e)–(g), would be more stable than R5 and have similar D, they are much more complex, involving many more vacancies, and there is no evidence that any of many of the ancestors of these defects is formed. For example the simplest of
J.M. Baker / Diamond & Related Materials 16 (2007) 216–219
the models, proposed for R7a, is V9 (Fig. 2(e)) which has been modelled by [9], and is predicted to have an S = 1 ground state, but so are the precursor defects V5, V7 and V8, none of which is observed, yet they are all predicted to be more stable than V3 (V6 is also more stable but has S = 0). The proposed models for R7 and R8 involve larger closed ring structures (Fig. 2(f) and (g) respectively), implying even more precursors, which are not observed. Hence, we seek alternative models for R7a, R7 and R8 which may be formed without precursors. 4. Alternative models We suggest that above 800 °C the di-vacancy is a much more common diffusing defect than the isolated vacancy, but when a di-vacancy approaches a larger VN cluster, first one vacancy moves into a site adjacent to VN, then the second vacancy may either follow it or move away. As R8 begins to appear as R5 reaches its peak, it is suggestive that R8 has either one or two vacancies attached to R5, i.e. either V4 or V5. V4 is either planar (O4) or of C1 symmetry, and probably S = 0, as there is no evidence of V4 of C3v symmetry with a tripod-like structure, formed by tacking a vacancy to the centre of V3 (which may suggest that there is low probability of tacking a migrating vacancy onto the side of a VN planar chain). So, is the part hexagonal ring (PHR) structure for V5 a possible model of R8? Modelling [9] shows it to have higher stability than R6 (V3), but this model of R8 has C1h symmetry, whereas experiment shows R8 to have C2v; however, D is axial about <110>, corresponding to pure dipolar interaction between two dangling bonds in that direction, which is where the dangling bonds are in the V5 PHR model. So, the departure from C2v symmetry might be too small to be detected. V5 PHR could anneal out, not by evaporation of a vacancy, but by accruing another vacancy to form a very stable V6 hexagonal ring. As the concentration of V5 increases, it can take the role of precursor to larger VN defects. Where a di-vacancy attaches itself will depend upon the direction of the approach. It may form a V6 HR, S = 0, after which the second vacancy may not attach itself to the rather stable V6 ring. There is no EPR evidence for the predicted S = 1 ground state of V7, suggesting that it may not be formed by this route. There is an equal probability that a di-vacancy approaches V5 PHR from a different direction allowing it to form a V7 partial loop (Fig. 2 (h)), which is one short of a (presumably stable) V8 ring structure (Fig. 2(i)). This V7 also has a C−V−C−V−C structure with a dangling bond on each of the outer carbon atoms, which give S = 1 and D similar to R5. The probably stable V8 closed ring structure comprises all of the neighbouring sites to a Td interstitial site (4 nearest neighbours (nn) along <111> and 6 next nearest neighbours (nnn) along <100>) except for two along say [001]. That site has D2d symmetry about [001] and each vacancy has two dangling bonds which can re-construct to give S = 0 overall. There are two types of site formed by filling one of the vacancies with a carbon atom, depending upon whether it is one of the nn or nnn of the Td interstitial site
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which is filled. (Could this be the origin of equal concentration of R7 and R7a?) The V7 site described above has its carbon atom in a nnn site, giving a site of C2 symmetry about [001], with the dangling bonds on carbon atoms along [011], which is not inconsistent with the C2v symmetry of R7a, with the largest component of D along [011]. A carbon atom at a nn site would give a site of C1h symmetry (Fig. 2(j)), with the largest component of D along the <110> symmetry axis (R7 has such C1h symmetry). This latter site cannot be formed by attaching V2 to V5 PHR. However, the two V7 sites are interchangeable by moving the carbon atom to an adjacent vacancy, so if the two sites have similar stability, and this switch is easily driven at the annealing temperature, both sites should have similar concentration on cooling. This could explain why |R7,7a| takes off where |R8| reaches its peak, and why R7, R7a and R8 anneal out at much the same temperature (by acquiring an additional vacancy, or by expelling a mobile carbon interstitial). The validity of this argument depends upon (a) whether the pattern of re-bonding is energetically favourable, and (b) whether the V7 PR structures are stable against re-organisation or loss of a vacancy. These things need to be calculated by modelling. If these criteria are acceptable, these proposed structures are more logical than those suggested by Ref. [1], and they are free from the objection that there are no observed precursors. 5. Conclusions We suggest that the proposed models [1] for the EPR centres R7a (V9), R7 (V11) and R8 (V13), produced by isochronal annealing of irradiated type IIa diamond, although having the observed symmetry, are questionable as none of the inevitable precursor defects is observed. We propose that more probable models are V5 PHR (Fig. 2(d)) for R8 and two types of nearly complete ring V7 for R7 (Fig. 2(i)) and R7a (Fig. 2(j)). This proposal is speculative and needs confirming by detailed modelling of the proposed structures. References [1] K. Iakoubovskii, A. Stesmans, Phys. Status Solidi, A Appl. Res. 201 (2004) 2509. [2] J.H. Crawford, L.M. Slifkin (Eds.), Point Defects in Solids, vol. 1, Plenum Press, New York and London, 1972. [3] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon Press, Oxford, 1970; J.A. Weil, J.R. Bolton, J.E. Wertz, Electron, Paramagnetic Resonance, Wiley, New York, 1994. [4] C.A.J. Ammerlaan, in: O. Madelung, M. Schultz (Eds.), Semiconductors, Impurities, Defects in Group IV Elements, III–V Compounds, Section 4.1 Diamond, Springer, Berlin, 1990. [5] C.A.J. Ammerlaan, in: O. Madelung, M. Schultz (Eds.), Semiconductors, Impurities, Defects in Group IV Elements, III–V Compounds, Section 4.2 Silicon, Springer, Berlin, 1990. [6] G. Pacchioni, et al., (Eds.), Defects in SiO2, Kluwer, 2000. [7] J.N. Lomer, A.M.A. Wild, Radiat. Effects 17 (1973) 37. [8] K. Iakoubovskii, A. Stesmans, Phys. Rev., B 66 (2002) 045406. [9] J.L.S. Hounsome, et al., Phys. Status Solidi, A Appl. Res. 202 (2005) 2182. [10] D.J. Twitchen, M.E. Newton, et al., Phys. Rev., B 59 (1999) 12900. [11] J.H.N. Loubser, J.A. van Wyk, Rep. Prog. Phys. 41 (1978) 1201.