Introduction

As early as 1912, Baumbhauer observed the occurrence of various polytypes in silicon carbide crystals and, successively, SiC studies have been related to the phenomenon of polytypism (Verma and Krishna 1966; Pandey and Krishna 1983 and references therein). In recent years, the study of the main polytypes of SiC and their synthetic homologous have received renewed interest in the material science field due to their physical and electrical properties that enable SiC to be employed in high temperature, high power and high frequency electronic devices.

As high crystalline quality of SiC is necessary for device applications, the main focus of numerous studies has been the characterization of the grown-in structural defects that can damage device performance (Dudley et al. 2003 and references therein). Dislocations, micropipes, stacking faults and coalescence of different polytypes have been found to be typical “modifications” of the perfect crystal structure of SiC crystals (Agrosì et al. 2005; Tempesta et al. 2006) grown with PVT method (Tairov and Tsvetkov 1978).

Nowadays, the industrial growth of SiC crystals focuses primarily on the production of 6H and 4H SiC substrates for GaN-based optoelectronic devices. Although several improvements have been made to produce crystals with a very low defect density, the realization of these substrates still requires a further reduction of defects. Hence, in the material science field there is great interest in growing SiC crystals with a lower defect density and in characterizing defects.

All the aforementioned studies have aimed at producing the best materials for devices and have provided great advancements in basic research giving numerous interesting study samples. From a crystallographic point of view, several questions such as polytype stability, stacking fault and twinning formation, foreign polytype inclusions and interface between polytypes in syntactic coalescence need still to be resolved taking into account the low stacking fault energy that characterizes the most important SiC polytypes.

SiC polytypes differ among each other due to the unlike ordered stacking sequences of SiC double-layers. The SiC structure is based on a tetrahedron that consists of four atoms of Si (or C) at its corners bonded to a C (or Si) atom at the center of the tetrahedron. In the tetrahedron, a threefold axis may be taken as the c crystallographic axis. Two parallel planes, known as double-layers or bilayers, one consisting of only silicon atoms and the other of only carbon atoms, represent the basal plane normal to the threefold axis. The structural arrangement of the different SiC polytypes depends on the different stacking sequences of Si–C double-layers along the [0001] direction. The most common types can be described as alternative successive rotations of 0° and 180°, respectively, of one bilayer with respect to its neighbor. Different stacking of bilayers can also generate twins; however, to the best of our knowledge, the primary focus has been the study of twinning in the cubic polytype of SiC while the twins in hexagonal and rhombohedral polytypes of SiC have been rarely investigated. In particular, two studies (Thibault 1944; Van Loan 1967) investigated the twinning of the 15R SiC polytype and hypothesized the twin operation for this polytype as a 180° c-axis rotation. Although several studies have investigated the defect characterization of the most common SiC polytypes, such characterization, in cases where a syntactic coalescence of different polytypes and twins occurs, seem incomplete with results often very difficult to obtain. In some cases, a single technique may not be fully adequate to resolve the nature of foreign polytype inclusions or to distinguish inclusions of different polytypes from twin-lamellae. Actually, in our sample, a 6H slice, we had previously determined that a multi-analytical approach was essential in determining the presence of twin-related lamellae of the 15R polytype in syntactic coalescence and isooriented with 6H bulk (Agrosì et al. 2009). This work permitted the localization and identification of three lamellae of 15R SiC as well as the observation of a twin relationship existing between two of these, even if the twin law was only hypothesized.

The aim of this paper is to study the local stacking microstructure at the interface between the twin-related lamellae, to determine the real twin law and, eventually, to find the correlation between twinning and stacking fault formation in this polytype. The investigation uses High Resolution images (HRTEM) together with electron diffraction patterns and Bright Field (BF) images to shed light on the composite overlay of the stacking faults and the twinning found in our sample.

Materials and methods

The sample used in this study was a \( (11\bar{2}0) \) slice cut from a 6H–SiC crystal grown at 2,200°C following the PVT method at the Berlin Institute of Crystal Growth (IKZ). The 6H crystal was grown on a 6H (0001) seed, 3.5° off-oriented toward \( \langle 11\bar{2}0\rangle \). During growth, the sample was nitrogen doped for a few minutes (Agrosì et al. 2009). Near the seed, the 6H slice showed three lamellae of 15R polytype. Among them, two lamellae were twin-related: a macro-lamella, labeled matrix-lamella (Lm), 0.6 mm thick and 20 mm long; and a micro-lamella, labeled twin-lamella (TL), 38 μm thick and 1.2 mm long, enclosed in Lm.

A fragment embedding the twin-lamella was extracted from a \( (11\bar{2}0) \) slice and was prepared for TEM observations.

TEM investigations were performed at the Dipartimento Geomineralogico of the University of Bari (Italy) with a Jeol JEM 2010 operating at 200 kV, a LaB6 source, a nominal point resolution of 2.0 Å, and a spherical aberration of 0.5 mm. The images were then recorded with a Gatan multiscan 794 CCD.

The fragment was glued onto a glass plate with the c-axis placed horizontally and then mechanically thinned down to approximately 30 μm in thickness. It was then removed from the plate and glued onto a 3 mm wide copper ring. A Gatan PIPS was used to achieve an electron transparency by ion milling the sample exactly crossing both the twin boundaries between the twin-related-lamellae. Finally, while a double tilt specimen holder maintained the sample, a carbon film was evaporated onto the thin foil to prevent electrostatic charging during the TEM observations.

To remove diffuse scattering noise, HRTEM images were processed using the Digital Micrograph program with the HRTEM filter by David Mitchel and based on the average background subtraction algorithm (Kilaas 1998). The NCEMSS program was used to interpret diffraction patterns of the selected area by means of simulations.

Results

TEM

Low Magnification (LM) image shows the TL lamella enclosed in the Lm lamella and allows the localization of the boundaries at the bottom (TBA) and at the top (TBB) of TL. Selected Area Electron Diffraction (SAED) patterns, taken above each lamella, reveal that both TL and Lm lamellae consist of the 15R polytype (Fig. 1). A number of straight dark lines corresponding to the projection of stacking faults on different (0001) planes are visible on the LM and Bright Field (BF) images (Figs. 1, 2a). Among the aforementioned lines, the real contact between the Lm/TL lamellae can be easily recognized by the sharp offset of Bragg contours (Fig. 2a). Locally, a higher magnification of this boundary reveals macro-steps that interrupt the interface continuity (Fig. 2b).

Fig. 1
figure 1

Low magnification image of the TL lamella embedded in the Lm lamella. The twin boundaries at the bottom, TBA, and at the top, TBB, of the TL lamella are shown. The inserted SAED pattern, taken above the delimited area of the TL lamella, corresponds to 15R polytype

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Fig. 2
figure 2

a Bright Field (BF) image of the TBB contact between the Lm and TL lamellae. b Lattice Fringe image of the region delimited by the dashed square in Fig. 2a. Macro-steps interrupt the interface continuity along the twin boundary

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SAED patterns, taken at precisely each twin boundary, show two identical diffraction patterns which are superimposed on one another by a twin operation, with a (0001) composition plane (Fig. 3). Upon comparing the electron diffraction pattern of the 15R polytype and the electron diffraction pattern in which the twinning appears, it can be observed that the diffraction spots belonging to the [000l]* and \( [ 3h\;0\;\bar{3}h\;l]^{*} \) rows are exactly superimposed and common to both individuals. Instead, the diffraction spots belonging to the \( [h\;0\;\bar{h}\;l]^{*} \) and \( [2h\;0\;\bar{2}h\;l]^{*} \) rows are paired.

Fig. 3
figure 3

Portion of the SAED pattern, with inverted contrast, taken above the TBB boundary (left), compared with a simulation including a twin operation of 180°-rotation around [0001] (right). Note the geometrical match between them. Some diffraction spots indexes, as well as main reciprocal axes directions, either for the Lm lamella (in black, with “L” pedex) than for the TL lamella (in gray, with “t” pedex), are reported. The trace of the (0001) plane acts as a mirror plane. Only minor differences in the intensity distribution would distinguish the latter from the 180°-rotation around [0001] operation used for the simulation

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In order to determine the twin operation and to correctly index the paired spots, comparisons between experimental and simulated diffraction patterns were carried out introducing all the possible twin operations with the composition plane parallel to the (0001) plane. From a geometrical point of view, the different twin laws and the corresponding composite twin symmetries, which can be generated for any point group, can be predicted. For the 3m point group of the 15R polytype, either a center of symmetry or a reflection across the (0001) plane or across the \( \{ 10\bar{1}0\} \) equivalent planes and, as well as, a twofold rotation around either [0001] or the \( \langle 10\bar{1}0\rangle \) equivalent directions can be introduced as twin operations (Hahn and Klapper 2003). Tacking into account the composite symmetry derived from the combination of any aforementioned twin operations with the symmetry elements of the untwinned individual, three twin point groups will be generated: \( \bar{3^{\prime}}{{2^{\prime}/}}m, \) introducing the center of symmetry (twinning by syngonic merohedry), 6′mm′, introducing the twofold around [0001] and/or the coexisting mirrors across the \( \{ 10\bar{1}0\} \) planes, and, finally, \( \bar{6}^{\prime}m{{2^{\prime}}}, \) introducing the reflection across the (0001) plane and/or the coexisting twofold around the \( \langle 10\bar{1}0\rangle \) directions (Nespolo 2004, 2009). The last two twin groups belong to the twinning by reticular merohedry. The symmetry elements marked with prime correspond to those generated by the combination of any twin operation with the symmetry elements of the 3m point group. For brevity’s sake, only the twofold around [0001] and the reflection across the (0001) plane were, respectively, considered for the 6′mm′ and \( \bar{6}^{\prime}m{{2^{\prime}}} \) twin point groups. Consequently, the diffraction patterns were simulated introducing only the quoted twin operations.

The center of symmetry can be easily excluded as a twin operator because of the presence of pairs of spots in the experimental SAED patterns taken above the twin boundaries. Actually, the diffraction pattern of lattice twinned by syngonic merohedry is undistinguishable from that of a single untwinned individual. On the other hand, the crystal structures based on the hR lattice, having a hexagonal sublattice, are endemic candidates to twinning by reticular merohedry via the symmetry elements belonging to hexagonal point groups of the sublattice (Ferraris et al. 2008). Consequently, the twinning found in this paper can simply be due to a reflection through the rational plane (0001) or a 180°-rotation around [0001]. These twin operations may only be considered equivalent for centrosymmetric crystals where the \( \bar{3}m \) point group becomes a 6′/m′mm′ twin point group. Instead, the two operations are not equivalent for non-centrosimmetric structures, since they generate the aforementioned 6′mm′ or \( \bar{6}^{\prime}m{{2^{\prime}}} \) twin point groups.

Unfortunately, simulations of diffraction patterns carried out introducing a reflection through the rational plane (0001) or by performing a 180°-rotation around [0001] produced undistinguishable results. In both cases, the diffraction spots corresponding to the [000l]* and \( [ 3h\;0\;\bar{3}h\;l]^{*} \) rows are exactly superimposed and common to both individuals whereas the parallel \( [h\;0\;\bar{h}\;l]^{*} \) and \( [2h\;0\;\bar{2}h\;l]^{*} \) rows appear to be paired because of the superposition of reflections with different diffraction intensity. The pairs of diffraction spots observed on the SAED patterns taken above the twin interfaces appear to be the result of a superposition of the reflections of one individual on the forbidden reflections of the other individual and viceversa. In fact, the twinned diffraction patterns will be caused by the superposition of hkil L reflections of the Lm lamella and the corresponding \( \overline{hk} il_{\text{t}} \) reflections of the TL lamella if the twin operation is a twofold rotation around [0001]. Instead, they will be due to hkil L and \( hki\bar{l}_{\text{t}} \) if a (0001) reflection occurs. For instance, considering the general condition h–k + l = 3n for reflections of the rhombohedral space group with reverse setting, the pairs of spots will be due to the superposition of the \( 10\bar{1}1_{\text{L}} \) reflection of the Lm lamella onto the corresponding forbidden \( \bar{1}011_{\text{t}} \) reflection of the TL lamella and the superposition of the forbidden \( 10\bar{1}2_{\text{L}} \) reflection onto the corresponding \( \bar{1}012_{\text{t}} \) reflection when a twofold rotation around [0001] occurs (Fig. 3). Similarly, considering the (0001) reflection as a twin operator, the pairs of spots are due to the superposition of the \( 10\bar{1}1_{\text{L}} \) reflection of the Lm lamella onto the corresponding forbidden \( 10\bar{1}\bar{1}_{\text{t}} \) reflection of the TL lamella and the superposition of the forbidden \( 10\bar{1}2_{\text{L}} \) reflection onto the corresponding \( 10\bar{1}\bar{2}_{\text{t}} \) reflection. Therefore, it can be concluded that the real twin law cannot be determined merely by analyzing SAED patterns.

HRTEM

High Resolution (HR) images were recorded on both the TBA and TBB twin interfaces of the TL lamella in order to reveal the fine micro-structural arrangement at the twin boundaries and to find further evidence of the actual twin law. Depending on which boundary was investigated, the microstructural arrangement displayed different features. In Fig. 4, the HRTEM image taken across the TBB boundary can be seen. The contrast varies from the top to the bottom of the image (i.e. across the twin boundary), and from the left to the right (i.e. along the twin boundary direction) due to either slight variations of thickness or changing experimental conditions (uneven illuminating conditions for the twin individuals or defocus differences due to specimen tilting inside the holder).

Fig. 4
figure 4

HRTEM image of the TBB twin boundary along the \( [11\bar{2}0] \) direction. White and gray filled circles emphasize the periodic alternating of the bilayers in one orientation followed by the subsequent bilayers 180°-rotated. The corresponding Zhdanov notation of stacking sequence is listed at right. The FFT inset at left shows that the sequence (32)/(33)/(23) produces a twinned pattern

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Focusing on the black lines between the rows of gray dots, it can be observed that the separation of the former corresponds to the c-repeat distance (12.6 Å) of the primitive oblique 2D cell of the 15R polytype, i.e. 1/3 the c parameter of the triple rhombohedral R3m cell (a = 3.07; c = 37.7 Å represented on the lower right of the image) which is conventionally used. The sequence of the 12.6 Å spacings is, however, interrupted at the right place of the twin boundary, where a larger spacing (15 Å) consistent with the one-cell thick 6H polytype, occurs. Then the sequence restarts and continues up to the end of the imaged field.

In addition to this, by observing the pairs of gray dots just below the dark lines mentioned above (or any other choice of dot pairs), a sequence of primitive 2D oblique cells can be traced. These cells are oriented differently from the top to the bottom of the image, i.e. they are twin-related through the one-cell thick 6H, which thus acts as a twin interface. As expected, here the cell is larger and rectangular in shape. The directions perpendicular to the long side of the oblique cells from the two twin-related individuals form an angle (~8°) which matches the one measured between the twin-related \( [10\bar{1}1]^{*} \) axes in Fig. 3. Exactly, the same pairs of spots observed in diffraction patterns can be reproduced by the Fast Fourier Transform (FFT) (inset Fig. 4) of the area containing the twin fault.

Finally, an analysis was attempted of the geometrical arrangement in a primitive cell of the five dots present in a repeat distance along c-axis. In spite of the contrast variations mentioned above, a (32) zig-zag pattern at the top of the image which switch to a (23) zig-zag pattern at the bottom, through a (33), one-cell thick 6H, can be observed. The twin boundary coincides with the interface between three bilayers in one orientation and the three successive 180°-rotated in the (33) sequence. Moreover, a well defined continuity of the two lattices along the twin interface, without breaking any bonds, can be seen.

The TBA twin boundary shows additional features when imaged in HR mode (Fig. 5), i.e. the presence of numerous stacking faults parallel to the (0001) plane. As before, a sequence of primitive oblique 2D cells can be traced across the boundary. This time, the rows of brighter dots are kept as markers. The primitive cells are all regularly spaced by roughly 12.6 Å. As in the previous case, their orientation is twin-related from the top to the bottom of the image. However, a definitive change can be interpreted here after ten cells. Within these ten cells (delimitated by arrows), short sequences of cells with quickly switching orientation occur. Using the Zhdanov notation, the dot arrangement throughout the sequence can be described equally as either a (23) sequence which finally passed to (32) after several “attempts” (left notation) or an interleaving of coupled (22) and (33) bilayers whose net result is to change the sequence order from (32), on at the top of the image, to (23) at the bottom (right notation).

Fig. 5
figure 5

HRTEM image of the TBA twin boundary along the \( [11\bar{2}0] \) direction. White and gray filled circles emphasize the periodic alternating of the bilayers in one orientation followed by the subsequent bilayers 180°-rotated. The corresponding Zhdanov notation of stacking sequence is listed at right

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At last, the FFT, which was calculated across the (33) plus (22) sequence, do not show any additional reflections of twinned individuals (Fig. 6). This finding indicates that the sequence introduces no twinning, only the 4H and 6H stacking faults, within the 15R. Consequently, it can be concluded that the coupled (33)/(22) sequence do not coincide with the twin interface but merely consists of a stacking faults, whereas the real twin interface consists of an isolated (33) sequence.

Fig. 6
figure 6

HRTEM image of a (33) plus (22) stacking faults in a (32)3 ordered matrix. White filled circles emphasize the periodic alternating of the bilayers in one orientation followed by the subsequent bilayers 180°-rotated. The corresponding Zhdanov notation of stacking sequence is listed at right. Note the FFT inset at left: the sequence (33)/(22) produces an untwinned pattern

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Discussion and conclusions

Twinning

The analysis of the SAED patterns, taken exactly above both the twin interfaces, indicates that the twin found in this study can be classified as a “Friedelian” reticular merohedric twinning. This type of twinning is characterized by specific parameters: n > 1 (twin index) and ω = 0 (obliquity) (Nespolo and Ferraris 2005). The twin index represents the ratio of the number of lattice nodes of the individual to the number of nodes restored by the twin operation and measures the degree of non overlapping of the lattices, whereas the obliquity measures the deviation from exact overlap. These parameters can be determined by the analysis of the twin lattice diffraction pattern that corresponds to the sublattice built solely on the common reflections (exactly overlapped). Since one node out of three is restored by the twin operation (the overlap between reflections from different domain affects one-third of the diffraction spots), the twin index is 3 (Fig. 3). Moreover, the precise overlapping of all the diffraction spots together with the explanation presented about the pairs of spots (see Results/TEM), confirms that the obliquity is zero (Fig. 3). On the other hand, this type of twinning by reticular merohedry, known also as “obverse–reverse” twinning (Herbst-Irmer and Sheldrick 2002; Hahn and Klapper 2003), is very common among rhombohedral (corundum, calcite) crystals. Moreover, it is well documented that the coincidence lattice (twin lattice) is a primitive hexagonal (hP) sublattice characterized by a triple volume for crystals with rhombohedral (hR) lattice (Hahn and Klapper 2003).

However, in our sample two different twin operations matched the observed features: a reflection through the rational (0001) plane, and the 180°-rotation around [0001]. Moreover, by examining only the SAED patterns, the corresponding \( \bar{6}^{\prime}m{{2^{\prime}}} \) and 6′mm′′ twin point groups are indistinguishable and consequently, the real twin law cannot be definitely established.

In the HR images, the fine microstructural arrangement at the twin interfaces can be seen and distinctions can be made between numerous adjoining stacking faults parallel to (0001) and the twin boundaries.

The microstructural arrangement of the twin boundaries consists of a (23) pattern that switched to (32) (see the right notation of Fig. 5) with coherent interface. From a geometrical point of view, in the HRTEM images of Figs. 4, 5 the (0001) compositional plane could coincide with the twin plane because the (23) sequence appears “reflected” onto the successive (32) sequence. Nevertheless, since individual Si and C atoms and even the SiC bilayer polarity cannot be established from these HR images, in order to define the real twin law some structural considerations about the polarity of the 15R SiC polytype must be made. Actually, the structure of the most common silicon carbide polytypes can be described by identifying the different stacking sequences of Si–C double-layers that are based on alternating successive rotations of 0° and 180° along the [0001] direction. These structures are acentric and are based on a Si–C4 (C–Si4) tetrahedron stacked to form polar frameworks in which all the tetrahedra have an apex outside of the layer plane. The piling-up of the polar SiC tetrahedron can only be parallel, whereas a (0001) reflection will produce an antiparallel orientation of tetrahedra with subsequent violation of its polarity (Fig. 7b). Indeed, for the non-centrosymmetric and the polar structures of SiC (Wyckoff 1963) a (0001) twinning could be achieved only by means of incoherency at the interface (interpenetrative twinning). Since the HR images show a coherent interface with a perfect structural match at and near the composition surface, the real twin operation must be a 180°-rotation around the [0001] direction, in accordance with the previous studies of Thibault (1944) and Van Loan (1967).

Fig. 7
figure 7

Schematic representation of different stacking sequences with the corresponding Zhdanov notation listed at right: a (23)3 perfect sequence of 15R polytype; b twinning by (0001) reflection with antiparallel orientation of tetrahedra. Note the violation of the polarity; c twinning by the 180° rotation of the whole (23)3 sequence. Note that the obtained sequence is different with respect to that imaged in HRTEM: three and two bilayers, respectively, under and on the twin boundary, generate the sequence of five bilayers in the same orientation; d real twin law. TB twin boundary; e (22)/(33) stacking faults. SP slip plane

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The 180°-rotation around [0001] is the common twin operation relating SiC bilayers in all main polytypes of SiC (Jepps and Page 1983). However, the inversion of the sequence (23) in (32) cannot be simply justified by the 180°-rotation around [0001]: the stacking sequence obtained by the 180° rotation of the whole (23)3 consists of five bilayers in the same orientation and thus will be different with respect to that in the HRTEM images (Fig. 7c). On the contrary, the stacking sequence will match that which was experimentally observed if the rotation is visualized in terms of bilayers rather than considering the rotation of the whole sequence of the 15R polytype (Fig. 7d). This type of operation produces the insertion of (33), a one-cell thick 6H like sequence, while preserving the nearest-neighbor geometric relationship between adjacent SiC bilayers and their polarity. Accordingly, successive stacking sequences will be twinned. On the other hand, the one-cell thick 6H like sequence, may be also considered a cubic SiC twin having a 180°-rotation around [111] ([0001] in a hexagonal system) of two successive series of three bilayers.

Defects and growth mechanism

Stacking faults, twinning and macrosteps on the twin boundaries represent the growth defects found in the twin-related lamellae of a 15R polytype enclosed in a 6H SiC sample. The stacking faults observed in the HRTEM images can be described as follows. The stacking sequence of the perfect structure of a 15R polytype consists of the periodic alternating of three bilayers in one orientation followed by the 180°-rotation around [0001] of two bilayers (23/23/23 ecc…) (Fig. 7a). This sequence is locally interrupted by the stacking of the coupled (22) and (33) bilayers, whereas the successive stacking sequence remains unmodified (23/23/23). The FFT calculated across the (33) plus (22) bilayers shows no twinning. The interleaving of the (22) and (33) bilayers can be explained by imaging a 180°-rotation around [0001] of a single bilayer along a slip plane, as shown in Fig. 7e). Nevertheless, the rotation of some bilayers rather than the rotation of the entire sequence of the 15R polytype was also mentioned in the discussion about the twinning. Hence, it follows that the formation of both, stacking faults and twins, should rely on similar processes. On the other hand, in crystals affected by polytypism where the structural motif of any polytype can be described with the periodic juxtaposition of “modules”/layers obtained by varying the relative orientation and/or position of adjacent modules, the relationship between the formation mechanism of twinning and stacking faults is reasonable. In fact, in layered structures, the formation of the stacking faults and twins during crystal growth can be ascribed to the incorrect addition of a new layer. Nevertheless, in the stacking faults this “accident” is followed immediately by subsequent layers that “correct” the mistake and obey the original stacking rule (Baronnet 1997). Instead, in the twins the subsequent layers do not restored the original stacking rule and a twinned structure results.

In order to explain the origin of the stacking faults and the twin found in our sample, it is necessary to consider the growth mechanism. The sample was grown by PVT method under nitrogen doping, on the 6H (0001) seed 3.5° off-oriented toward \( [11\bar{2}0] \) (Agrosì et al. 2009). The off-orientation of the seed promoted a step formation. The growth mechanism was achieved by adding material to the self-perpetuating steps formed at the sites of a single or multiple cooperating screw dislocations and a lateral step flow (Agrosì et al. 2009). When the steps were too high, the danger of step bunching increased, macro-steps formed and local super-saturation changes occurred resulting in stacking fault and foreign polytype formation. A crystal growing with such mechanism will necessarily possess planar defects that depend on the layer sequence of exposed macro-steps (Pandey et al. 1982; Pandey and Krishna 1983; Baronnet 1997 and references therein). On the other hand, the formation of the microstructural arrangement found on the twin boundaries may also be explained by the aforementioned growth mechanism. In previous studies concerning the origin of polytypism, among the most probable series of structures predicted on the basis of the theoretical screw dislocation ledges exposed in a perfect 15R polytype, with a single low-energy fault configuration, a (23)n (32)m sequence, with n and m integer numbers, was also found (Krishna and Verma 1965; Pandey and Krishna 1983). Hence, it can be concluded that the (23)/(32) twin sequence is not only geometrically and structurally consistent but also energetically favored.

Some considerations can be also made about the formation energies of the planar defects found in our sample. In the literature, several studies concerning interaction energies between the ith neighbor SiC bilayers have been carried out. Among them is a theoretical study of extended planar defects, affecting the main SiC polytypes, which were created without breaking any bond. In this work, at least five stacking faults in 15R SiC were found and the corresponding formation energies were calculated (Iwata et al. 2002, 2003). The authors established that stacking fault energies in which the 180°-rotation of a single bilayer occur [for example (1112)], were considerably higher and could be justified only in the cases of heavily doped samples, whereas the faults with (33)/(22) and (22)/(33) sequence were found to be the most energetically favored.

It is well known that the probability and frequency of twin formation is governed by the (hkl) stacking fault energy which is the energy of the (hkl) twin boundary (Hahn and Klapper 2003). Hence, it can be concluded that both the twin and the stacking faults found in our sample are energetically favored. Nevertheless, we found the presence of only one twin micro-lamella, whereas stacking faults largely affected the 15R lamellae (Agrosì et al. 2009). This fact suggests that the formation energy of the two planar defects is different and an increase of energy may be necessary for twin formation. On the other hand, the growth process of twins is generally favored by different factors, such as the incorporation of impurities on the surface and fluctuations in thermodynamic conditions (Nespolo and Ferraris 2004). In the studied sample, the twin-lamella TL was located above the dark green stripes corresponding to the incorporation of nitrogen which occurred in the earlier growth stages (Agrosì et al. 2009). Thus, it may be concluded that the twin formation is related to the nitrogen doping. The local increase of dopant content in the growth surface may have modified the velocity of the steps, determining step bunching and the formation of macrosteps by the coalescence of multiple SiC growth steps (Papaioannou et al. 1998). Hence, the presence of macrosteps has played an important role in the growth of the twin-lamella.