Ostwald ripening of interstitial-type dislocation loops

JOURNAL OF APPLIED PHYSICS 100, 053521 共2006兲

Ostwald ripening of interstitial-type dislocation loops in 4H-silicon carbide P. O. Å. Perssona兲 and L. Hultman Thin Film Physics Division, Department of Physics, IFM, Linköping University, S-581 83 Linköping, Sweden

M. S. Janson and A. Hallén Royal Institute of Technology, Solid State Electronics, P.O. Box E229, S-164 40 Kista-Stockholm, Sweden

共Received 9 May 2006; accepted 27 June 2006; published online 14 September 2006兲 The annealing behavior of interstitial-type basal plane dislocation loops in Al ion implanted 4H-SiC is investigated. It is shown that the loops undergo a dynamical ripening process. For annealing below 1700 ° C the total area of dislocation loops increases, indicating that point defects are still available for accumulation, but for annealing times longer than 100 min at this temperature the value of the total loop area saturates. For longer annealing times, or higher temperatures, the dislocation loops are subjected to a conservative coarsening process, also known as Ostwald ripening. In this process the mean loop radius increases with increasing annealing time and temperature while the number of loops decreases. Meanwhile the summarized area of the loops stays constant. The observed ripening is suggested to occur by a mechanism, which involves coarsening by direct loop coalescence. Through this mechanism, loops on the same basal plane move towards each other until they coalesce into one, but loops on neighboring basal planes can only move until their loop edges meet 共in a basal plane projection兲 where they remain. Climb along the c axis is not favorable as shown by experimental results and is suggested to be caused by the atomic configuration of the loop. Upon continuous annealing, this results in a situation where the loops are confined in clusters. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2338142兴 INTRODUCTION

Silicon carbide 共SiC兲 has over the years become a mature material, suitable for electronic applications,1,2 due to progress in growth of both substrates and epilayers. For electronic device processing of planar devices, ion implantation may be used to introduce dopants into the material.3 The introduction of lattice damage is a negative consequence of the implantation process as vacancies, interstitials, and more complex clusters of these are formed when the implanted ions collide with the lattice atoms.4 The resulting crystalline quality of the implanted samples has been the subject of many studies, primarily by Rutherford backscattering spectroscopy 共RBS兲, where variables such as dose, dose rate, implantation energy, implantation temperature, and ion species were investigated.5–8 To electrically activate the implanted dopants, which predominantly occupy inactive interstitial sites after implantation, and to restore the damaged lattice, the sample is subjected to a thermal annealing process.9 For SiC this is typically carried out at 1500– 1700 ° C for approximately 30 min. After annealing, the implanted lattice undergoes a noticeable transition. From transmission electron microscopy 共TEM兲 images, it can be seen that the lattice is filled with dark spots with the highest density around the projected range of the implanted ions. Since the dark spots are uneven and diffuse they are recognized as lattice strain, originating from structural defects. These are well known from many material systems and are typically found in implanted and annealed or heavily irradiated samples. Upon closer examination by conventional a兲

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TEM the strain fields appear to be bean shaped with alternating dark/bright contrast, suggesting from classical electron microscopy studies that these defects are two-dimensional 共2D兲 planar defects. It is possible to extinguish the contrast of the defects by two-beam experiments, revealing that the defects are dislocation loops oriented in the c plane with a Burgers vector parallel to the c axis. The dislocation loop confines a two-dimensional cluster of interstitials that remain in the lattice after annealing. In SiC these defects have previously been investigated by Chen et al.10,11 for He implantation, and by Persson et al.12–14 and Ohno et al.15–17 for the implantation by donors and acceptors for device purposes. According to high-resolution cross sectional TEM studies, these loops are of interstitial type and in all reported cases residing in the close packed “knee” of the zigzag stacked SiC hexagonal polytypes 4H and 6H. Loops have also been reported on the close packed 共111兲 plane in implanted cubic SiC,18 but we suggest that for all other polytypes the loops prefer to nucleate in the plane with hexagonal symmetry, i.e., the knee of the ␣-polytypes due to lower nucleation barriers in stacking faults 共the SiC ␣-polytypes may be perceived as cubic with regularly occurring stacking faults兲. Electron energy loss spectroscopy 共EELS兲 studies have shown that the loops are not the result of clustering of the implanted ions, thus the loops are composed of SiC selfinterstitials. It was further shown that the amount of loops not only depends linearly on implantation dose but also on the type of implanted ion. If the SiC is implanted with an ion which upon electrical activation is known to replace Si in the lattice 共Al, B, Si兲, the SiC crystal will contain more and larger loops than a crystal, which has been implanted by an

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TABLE I. Variation of fractional area and bound interstitials per dose. Annealing

Radius

Time Temperature Fractional Mean Sample Dose 共°C兲 area共%兲共nm兲 Maximum 共nm兲共1014 cm−2兲共min兲 1a 1b 1c 1d 2a 2b 2c 2d

2.6 2.6 2.6 2.6 5.2 5.2 5.2 5.2

8 30 120 480 240 240 240 240

1900 1900 1900 1900 1700 1800 1900 2000

4.0 4.4 4.8 5 13.1 14.3 14.5 15.1

3.2 3.3 5.2 6.2 5.1 6.2 7.5 9.9

11 13 15 22 16 20 26 31

ion replacing C 共C, N兲. Thus, what governs the fractional area and loop growth is the presence of excess Si interstitials.13 If there exists an excess amount of Si interstitials during the annealing process these interstitials tend to result in the formation of dislocation loops. It has been shown that at elevated annealing temperatures, typically above 1700 ° C, the mean radius of these loops increases while the density of loops decreases, keeping the total number of interstitials bound by loops constant.14 This dynamical behavior indicates a conservative coarsening according to 2D Ostwald ripening.17,19 Conservative ripening of dislocation loops has been observed and studied in detail for implanted Si by several researchers,20–22 but so far, the dynamics of the interstitial population and the formation of interstitial-type dislocation loops is not well understood for SiC. It is the purpose of this paper to extend the discussion by providing experimental results and suggest a model for the dislocation loop ripening based on coalescence of loops rather than exchange of point defects.

EXPERIMENT

The samples were prepared from epitaxial 4H-SiC layers, grown at Linköping University, on commercially available 共0001兲 substrates oriented 8° off the c axis, towards 具11-20典. Background nitrogen doping was in the low 1015 cm−3 range and the thickness of the epitaxial layer was 25 ␮m. Samples used in this study were implanted by 180 keV Al ions at 600 ° C. The implantations were performed normal to the surface to avoid channelling. Two doses were used: 2.6⫻ 1014 and 5.2⫻ 1014 cm−2. No amorphization is expected from these implantation conditions. To study the dynamics of the dislocation loops, experiments were performed by varying the annealing time and temperature, for the implanted samples according to Table I. The annealing conditions were chosen such that conservative 共steady state兲 ripening would occur. Conservative loop growth is not achieved unless given sufficiently high thermal budgets, i.e., high temperature annealing for extended periods of time. Short annealing times 共⬍10 min兲 requires annealing temperatures 艌1800 ° C and for typical processing temperatures 共⬃1700 ° C兲 ⬃2 h annealing is required. Thus,

for any lesser thermal budgets an equilibrium process is not to be expected.13 The lower dose sample was cut in four pieces and annealed isothermally at 1900 ° C for 8 min, 30 min, 2 h, and 8 h. The higher dose sample was annealed isochronally for 4 h at temperatures 1700, 1800, 1900, and 2000 ° C. Annealing was performed in an inductively heated Epigress furnace in an argon atmosphere. The experimental conditions for the samples are summarized in Table I. Plan-view samples for TEM were prepared by mechanical thinning and polishing from the back side. Low-angle 共4°兲 ion milling, in a BalTec RES 010 rapid ion etch operated at 8 kV, was used to make the samples electron transparent. A final polishing stage using low-energy ions at 2 kV was applied to remove the amorphous surface layer formed in the previous stage. The TEM investigations were carried out using a Philips CM 20 UT microscope, equipped with a LaB6 filament, operated at 200 keV for a point resolution of 1.9 Å. In order to correctly estimate the concentration of defects found in the crystal for each sample, the plan-view samples were photographed where the sample thickness was more than the depth at which the deepest defects are located. This was achieved by observing a saturation in the number of defects in the microscope as the sample thickness increased. For this purpose plan-view images are more reliable than cross sectional images, when measuring the outline and radius of dislocation loops. The mean radius of the loops in each sample was calculated by measuring the diameter of each loop in a photograph of a randomly selected area, typically 0.25 ␮m2. The associated radii were subsequently calculated and the mean radius obtained. The fractional area is defined as the total area on any picture covered by the present loops divided by the picture area A. The subsequent area for each loop is calculated assuming that they are circular, thus the fractional area is obtained, f=

兺i␲r2i . A

共1兲

RESULTS

Figures 1 and 2 show the plan-view images of samples implanted by 2.6⫻ 1014 and 5.2⫻ 1014 cm−2, 180 keV Al ions, respectively, as they are imaged along 具0001典. The low dose samples were subjected to isothermal annealing at 1900 ° C with annealing time ranging from 8 min to 8 h. Those of the higher dose were subjected to isochronal annealing for 4 h each, at temperatures from 1700 to 2000 ° C. For the isothermally annealed samples in Fig. 1, it can be seen that the population of loops ranges in radii from a few nanometers to ⬃20 nm. Increasing annealing time reduces the concentration of loops while the maximum loop size increases. Similarly for the isochronally annealed samples in Fig. 2, loop size increases while the concentration decreases with increasing annealing temperature. The sample annealed at 2000 ° C for 4 h, shown in Fig. 2共d兲, is exceptional and a lower magnification is shown in Fig. 3. In this sample the


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FIG. 1. Plan-view TEM images of the low dose implanted sample subjected to the isothermal annealing after 8, 30, 120, and 480 min, respectively, at 1900 ° C. Each image is 500⫻ 550 nm2.

distribution of loops is not evenly distributed over a large area, but clustered in a “meshlike” distribution, leaving some areas completely free from loops while the clustered regions are crowded far beyond the density given by a random distribution. At the lower temperatures loops also begin to form clusters, but not as distinct as in this sample. Throughout Figs. 1–3 there can also be seen dark spots in the vicinity of the apparent rings. These are also dislocation loops which are suggested to reside closer to the entrance or exit surface and due to the extinction distance in SiC receive a different diffraction contrast compared to other loops. The radius of these have also been measured and included in the results. Histograms of the loop radii in each sample are presented in Fig. 4 for the low 共a兲 and high 共b兲 doses. As suggested by the previous images, the loop population in both the isothermal and isochronal sample series decreases, while maximum size increases, with increasing thermal budgets. Small loops are, however, the most commonly represented. The resulting fractional area, mean radius, and maxi-

FIG. 2. These images correspond to the high dose implanted isochronal series. Annealed at 1700, 1800, 1900, and 2000 ° C for 4 h, respectively. Similar to Fig. 1 the image areas are 500⫻ 550 nm2.

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FIG. 3. This image is a lower magnification of Fig. 2共d兲, showing dislocation loops arranged in a meshlike pattern.

mum radius for all samples are summarized in Table I. Furthermore, the evolution of fractional area and mean radius is shown in Fig. 5. As expected, the fractional area is conservative upon annealing for both the isothermal 共a兲共fractional area ⬃14%兲 and isochronal 共b兲共fractional area ⬃5%兲 series and there is an increase in mean radius in both series. The difference in fractional area is a direct consequence of the implanted dose.14 For the isothermal series, the mean radius

FIG. 4. Loop radius histograms for 共a兲 the isothermal series and 共b兲 the isochronal series.


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will be conserved. Loop annihilation under these circumstances can only take place through ripening in which the loops coalesce such that small loops disappear while larger loops grow, i.e., the loops are considered to be subjected to a conservative Ostwald ripening process.27 Conservative ripening trough 共A兲 loop growth by point defect diffusion through the bulk and 共B兲 loop coalescence through glide and climb are examples of mechanisms for Ostwald ripening. Point defect ripening of three-dimensional defects in bulk material has been thoroughly studied, as well as two-dimensional ripening on surfaces, although two-dimensional bulk ripening has been subjected to fewer investigations. Apart from the initial vacancy loops in quenched Al a number of studies have been undertaken for ion implanted Si.28–30 Most of these studies show, or suggest, bulk diffusion of point defects as the only ripening mechanism. Model A: Loop ripening through point defect diffusion

The theory of ripening through point defect diffusion is well described by other authors.32,33 To summarize their findings, the theory is developed from the loop growth rate equation, stating for the rate of change of the loop radius,

再

dr 2D 关兺riexp 共Gb/ri兲共⍀/kT兲兴 = dt b 兺ri

冎

− exp关共Gb/r兲共⍀/kT兲兴 , FIG. 5. Variation of the fractional area and loop mean radius for 共a兲 the isothermal series and 共b兲 the isochronal series.

increases rapidly at first and then more slowly whereas the isochronal series increases slowly, but slightly faster with higher temperature. DISCUSSION Models for Loop ripening

It is a well-known process that mobile point defects such as vacancies and interstitials, in concentrations higher than the thermal equilibrium, can form dislocation loops by clustering. The observations of vacancy loops were found in quenched aluminum.23 The elevated point defect concentration may be initiated by thermal quenching or by irradiation or implantation of energetic particles. A reduction in the total number of loops, by loop annihilation, is obtained through thermal annealing and was reported by Silcox and Whelan.24 Loop annihilation is driven by two competing processes, surface free energy and elastic energy minimization, and may occur through two mechanisms: 共1兲 long-range bulk diffusion by point defects to and from the loops and 共2兲 through short-range elastic forces acting on the loops25,26 such that the loops move by dislocation glide and climb. For both mechanisms, the loops will eventually annihilate if enough sinks are available for the defects. These sinks may, for instance, be surfaces, precipitates, grain boundaries, and other dislocations. Assuming that there are no such sinks available in a volume, the total amount of point defects in this volume

共2兲

for unfaulted loops. Here D is the interstitial diffusion coefficient, G is the shear modulus, and b the Burgers vector of the loop. Furthermore ⍀ is the atomic volume, typically ⬇b3, k is Boltzmann’s constant, and T is the applied temperature. Given the material constants, then for sufficiently large loop radii it is possible to rewrite Eq. 共1兲 by a MacLaurin expansion ex = 1 + x,

冋

册

1 dr 2DGb3 1 − . = dt kT rmean r

共3兲

Rewriting the growth rate can be successfully performed for dislocation loops in Al since these loops are large 共Ⰷ100 nm兲. For Si it has been suggested30 that Eq. 共4兲 is valid only for a loop radius larger than 20 nm. Because of the difference in shear modulus a sufficiently large loop radius for SiC must be on the order of five times larger, 100 nm, for Eq. 共4兲 to be valid 关condition 共i兲兴. Furthermore, it can be shown, using Eq. 共4兲, that the population must assume a distribution of radii such that the mean radius can never be smaller than half of the largest loop, rmean 艌 rmax / 2 关condition 共ii兲兴 and that the mean loop radius must evolve with the square root of time, rmean ⬃ 冑 t 关condition 共iii兲兴.32 Model B: Loop growth through loop coalescence

The other mechanism for loop growth, by loop coalescence, where the driving force is minimization of elastic energy, will now be discussed. Here, for a given loop, vacancies and interstitials diffuse through the dislocation core


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along the periphery of the loop rather than releasing the point defects into the bulk. It has been shown that diffusion along a dislocation line is energetically more favorable than bulk diffusion.34 When those point defects, diffusing through the dislocation core, prefer to move towards a particular side of the loop they are removed from the other side, effectively making the loop move. Because a smaller loop has fewer point defects to shuffle around the dislocation core, it moves faster than a larger loop. A loop influences other loops by a short-range force, which can be both attractive and repulsive, depending on the spatial orientation of the loops. This force is established by the introduced stress as the lattice bends to accommodate for the loop. If the force is attractive the loops will approach one another and eventually come close enough to coalesce and the elastic energy is reduced through a reduction in the total dislocation core length. If the loops exchange a repulsive force they will simply move away from each other until the force becomes too weak. Thus, in samples where ripening occurs through loop coalescence, we can expect to find loops approaching each other, rather than appear randomly distributed across the sample where they exchange point defects from a distance. The theory also shows that the mean radius increases with time approximately as r ⬃ t2/13.26 Observed radial evolution

There are no other structural defects observed in the investigated volume that may act as sinks for loops or point defects. The epilayer is a single crystal and the loops are buried beneath the surface around the projected range of the implanted ions such that there is a loop-free zone between the loop region and the surface. Furthermore, the loops have not been found to spread out significantly along the c axis, i.e., appear closer to/further away from the surface for increased annealing time and/or temperature. We can therefore consider the ripening to occur within a closed volume. For Si on the other hand, loops near the surface have been concluded to be subjected to a nonconservative “Ostwald” ripening where point defects were captured by the surface.31 We have determined that the interstitial-type dislocation loops in the investigated samples become noticeably fewer and that the mean radius increases, for increased annealing time and/or temperature. Meanwhile the area covered by loops, or the total interstitial population associated to loops, is conserved. Figure 4 describes the change in the loop population during annealing. To facilitate the interpretation of changes in the population, Fig. 6 shows the related total area of loops associated with each radius. The area under each curve is proportional to the total amount of interstitials bound to loops in the associated sample. For both the isochronal and the isothermal series, the curves are shifted towards larger loop radii with increasing annealing time or temperature. Thus interstitials are transferred from smaller loops to larger indicating that the population is subjected to a conservative ripening process. According to Table I, the maximum radius in these samples is on the order of 30 nm. It has already been mentioned above that the minimum radius for condition 共i兲 to be

FIG. 6. Total area covered by respective radii for 共a兲 the isothermal and 共b兲 the isochronal series.

valid is the loop radii near 100 nm. Thus, even if it is concluded that interstitial-type dislocation loop ripening in SiC occurs by point defect diffusion, it will not be possible to establish that it occurs according to the theory. For Si it was postulated that the theory would be valid even for smaller radii than the critical radius,30 and we continue to investigate the possibility for the present samples. Table I reveals also that the maximum radius is typically three to four times larger than the mean radius in all samples, which is contrary to requirement 共ii兲. To determine the rate at which the mean radius evolves with time, a curve fit was applied to the isothermal series in Fig. 5 according to r = atb + C, as indicated in the figure, where a, b, and C are fitting constants. The best fit was found for b = 0.19. As a consequence, the mean loop radius does not evolve with the square root of time, which is requirement 共iii兲 for ripening by point defect diffusion. Assuming that 共i兲 is valid even for smaller radii it must be concluded that the exchange of point defects cannot be the mechanism through which the dislocation loops grow. However, if 共i兲 is not valid for small radii, it is still possible that ripening may occur via point defect diffusion since theory does not predict any growth rate for these radii. The theory for ripening through loop coalescence does not predict a distribution of loop sizes similar to what point defect ripening does, and hence there are no formal limits to a maximum or mean radius. However, in previously investigated profiles,26 the majority of loops are much smaller than the largest loop. This is comparable to Fig. 4, where the majority of loops are small, and the population extends in a


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tail towards much larger radii. It appears that this population distribution is more like those presented for loops in irradiated Al where ripening by glide and climb was concluded than in Si, where point defect ripening has been concluded. The ripening rate in Fig. 5, b = 0.19, is also close to the predicted rate for glide and climb, where b = 2 / 13= 0.154. This fact suggests elastic force interactions to be the mechanism for interstitial loop ripening in SiC. Observed loop distribution

As can be seen in Figs. 1 and 2 the loops are not randomly positioned. Already at low temperatures and short annealing times, the loops begin to form clusters where two or more loops are aligned by their edges in the c direction without overlapping. The observed phenomenon where loops align their edges on top of each other was previously reported14 and suggested to be a means of reducing total elastic energy of the lattice. For longer annealing times and higher temperatures more loops become associated to the two-dimensional clusters. The sample, which was subjected to the most severe annealing conditions in this investigation, is shown at a lower magnification in Fig. 3. In this picture loops are clearly distributed in clusters, leaving large volumes of the implanted part of the crystal free from loops. Loop clusters with free regions in between were previously reported for a cross sectional SiC sample35 annealed for 30 min at 2000 ° C. From a ripening point of view it seems extraordinary that the loops are positioned this close to each other without coalescing. Ripening by point defect diffusion does not require loops to be located near each other since the exchange of point defects occurs from a distance. Thus a random distribution of loops is more likely in the case of point defect diffusion. On the other hand, ripening by coalescence is a possible explanation for the clustering, assuming that the loops may glide along 共0001兲 but have difficulties in climbing along 具0001典, to conclude the coalescence. Glide is considered to occur as the dislocation slips across the close packed 共0001兲 plane whereas climb occurs in the perpendicular direction, which is along 具0001典.

FIG. 7. Examples of climb for 共a兲 a SiC bilayer, 共b兲 for a SiSi bilayer, and 共c兲 for a Si monolayer.

result from an excess of Si atoms, but whether a loop surrounds a Si monoplane, a Si–Si biplane, or a Si–C biplane has not yet been concluded.14 Should the loop consist of a Si–C biplane climb is possible according to Fig. 7共a兲, where a Si–C-containing loop is shifted upwards. This motion does not create any new defects and the coalescence between two such loops is shown schematically in Fig. 8共a兲关共i兲–共iii兲兴. If a climbing loop initially consists of a Si–Si biplane, according to Fig. 7共b兲, it forms a SiC antisite cluster in the

Suggested model for loop growth

Based on the observations described above, the following explanation for the ripening behavior is suggested: loops glide to approach one another and only loops located in the same basal plane can coalesce, thereby increasing the mean radius of the population. When two loops are aligned above each other without overlap on two adjacent basal planes, climb must commence in order for the two loops to coalesce. The experimental observations infer that this climb does not occur. Should the loops be able to climb, the spread along the c axis would increase and the surface would eventually capture and annihilate some of the loops causing a nonconservative ripening process. Since the loop area is conserved, this does not occur. The inability for the loops to climb along 具0001典 may be explained by the nature of the defect. With reference to Fig. 7 it is possible to make the following conclusions regarding the nature of the planar defects bounded by dislocation loops. The loops have already been shown to

FIG. 8. Coalescence of loops for 共a兲 two SiC bilayers forming a single SiC bilayer loop. In 共b兲 two SiSi bilayers cause the formation of two antisite clusters and a SiC bilayer loop. Finally, in 共c兲 two Si monolayers cause the formation of two inversion domains and a Si monolayer loop.


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size and shape of the original loop at the position where it starts to climb. Once the loop starts climbing it is transformed into a Si–C biplane, which continues to climb like the Si–C biplane described in Fig. 7共a兲. Should this climbing loop encounter a stationary Si–Si loop and coalesce, the resulting bilayer loop would consist of both Si–Si and Si–C, which seems unlikely. If two climbing loops resulting from this scenario encounter each other, the result would be a Si–C bilayer loop with two circular antisite layers in the vicinity, as described in Fig. 8共b兲关共i兲–共iii兲兴. Should the loop consist of a single Si plane, as in Fig. 7共c兲, the climbing loop will leave a trail of antisite defects 共both CSi and SiC兲 effectively forming an inversion domain. The remaining loop would be a Si single plane and the result from a coalescence of two such loops would be two inversion domains and a single Si loop, as shown in Fig. 8共c兲关共i兲–共iii兲兴. The presence of a dislocation causes the lattice to bend, resulting in a crystal with stored strain energy. This energy can be divided in two parts, Estrain = Ecore + Estrain .

共4兲

For an edge dislocation the core energy term is very uncertain, however, it is typically only 10%–20% of the strain energy,36 as such we only consider the strain energy. The total strain energy for a circular dislocation loop with a Burgers vector normal to the plane of the loop is given by Estrain = 2␲R

Gb2 关ln共4R/r0兲 − 1兴, 4␲共1 − ␯兲

共5兲

where G is the shear modulus, b is the Burgers vector, ␯ is Poisson’s ratio, R is the outer radius of the dislocation loop, and r0 is the inner dislocation core radius 共usually taken to be equal to the Burgers vector兲. Using for 4H-SiC, G = 185 GPa, b = 2.5 Å, ␯ = 0.167, and r0 = b, we can calculate the strain energy. For the loop configuration in Figs. 7共a兲 and 8共a兲, the process is straightforward. Every reduction in total dislocation line length reduces the strain energy stored in the crystal. Accordingly, given a Si–C bilayer configuration, loop coalescence through climb will commence. However, because there is no experimental indication of coalescence through climb, it is unlikely that the loops are composed of Si–C biplanes. Given the Si–Si bilayer situation in Fig. 8共b兲, the loops must initially produce the two antisite clusters according to Fig. 7共b兲 and then coalesce in a similar fashion as in Fig. 8共a兲. As long as the energy to produce the antisite clusters is less than the energy gained through the reduction in dislocation length the coalescence is possible. To estimate the cost of producing the antisite clusters we assume an energy of 4 eV per antisite37–39 and a basal plane density of 3 at./ nm2, resulting in a cluster formation energy of 12␲R2 eV for each cluster. The antisite cost will increase rapidly due to the R2 dependence whereas the strain energy increases near linearly with R. A comparison is shown in Fig. 9. According to this graph, the cost of forming antisite clusters is always larger than the gain in strain energy, which suggests that climb cannot occur given the Si–Si bilayer configuration which is

FIG. 9. Comparison between the formation energy of two antisite clusters 共upper curve兲 and the strain energy gain 共lower兲 upon coalescence of two loops.

in line with the experimental observation. It should be noted, however, that the continuum theory used to describe the strain energy of a dislocation loop breaks down when the loop size approaches atomic dimensions, which makes an estimate difficult for the smallest loops. Knowing that the Si–Si configuration is unable to climb, it is even more unlikely to imagine loop coalescence of the Si monolayer loops. To form two inversion domains is indeed costly. The most frequently reported mechanism for dislocation loop ripening in most materials is without doubt point defect diffusion. Few investigations have previously concluded glide and climb as the mechanism for ripening in any material and in those few cases it has been in single component systems such as Al. Distribution profiles, similar to the present, were reported for unfaulted prismatic dislocation loops30 in Si, whereas faulted Frank loops, in the same samples, were concluded to exhibit profiles which were in reasonable agreement with point defect diffusion ripening. Previously, two papers17,19 have been published, attempting to explain the ripening phenomenon in SiC with bulk diffusion. However, none of these papers present a detailed investigation of the ripening phenomenon in SiC and, furthermore, one of these investigations was also conducted in a temperature regime where a conservative ripening process is not established.17 In light of the present results, ripening by elastic force interactions resulting in coalescence of loops through glide along the basal planes, rather than a minimization of surface energy through point defect diffusion, must be considered as the likely mechanism for dislocation loops in SiC. Finally, the most likely composition of the dislocation loops must be a Si bi- or monolayer, since climb is not observed. CONCLUSION

The ripening dynamics of interstitial-type dislocation loops resulting from Al ion implantation in 4H-SiC have


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been investigated for SiC. It has been shown that at sufficiently long annealing times and/or high annealing temperatures, the dislocation loops follow a conservative coarsening process where large loops grow at the expense of smaller loops and that the mean radius r increases as a function of time as r ⬃ t0.2. Together with other observations of the mean and maximum loop radii, and also the clustering of loops for the most severe annealing conditions, it is concluded that the ripening mechanism is loop coalescence by glide where interactions of elastic forces act as the driving force. Based on our observations we propose the following model for the loop evolution. The loops glide on the 共0001兲 basal planes towards each other, attracted by a reduction in elastic energy, until further glide is not energetically favorable and they remain with edges aligned on top of each other in the c direction without overlapping. For sufficient annealing times and/or temperatures this results in a situation where some areas will be completely empty of loops separated by a three-dimensional network of loops. Loops in the same basal planes can still coalesce but loops on neighboring planes do not coalesce because climb is not initiated after glide ceases. This behavior is suggested to be the result of the Si nature of the loops. 1

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