**4.1. Radii reduction and gradual healing**

6 Physics and Technology of Silicon Carbide Devices

4 mm

100 µm

trace the FPI boundaries.

1

**Figure 6.** SR phase-contrast image of MPs in the latest-to-grow wafer VI. Schematic of the wafer with black squares

respectively. One can see that the wafer I has higher density of pores. In addition, Figs. 3(a), (b) and (c) taken in SR X-rays and PL, respectively, show pores and FPIs in the wafer I located just outside the scope of the image in Fig. 2(c). The high resolution of Fig. 3(a) demonstrates that the groups of pores (marked by black and white arrows) consist of short tube-shaped or slit-like segments. The morphology of such pores was investigated and attributed to the elastic interaction between MPs and boundaries of FPIs, resulting in coalescence of MPs into larger pores elongated along the boundaries [11, 13]. FPIs were indeed observed on the same location, as revealed by the yellow PL images [28] of *n*-type 4*H*-SiC containing N and B in Fig. 3(b) and (c), recorded at 77 K. The comparison with the pore images in the optical micrographs taken prior to the excitation of PL (data not shown), indicates that the pores

A group of pores in Fig. 3(a) is partly displayed in the phase contrast image of Fig. 4. One pore from the group is marked by the arrow 2. Notice that the arrow 1 points to the group of MPs located at the place of interest in Fig. 2(c). The magnified image of the group is shown in the inset to Fig. 4. MPs appear as line segments, of which lengths are dependent on the wafer thickness, the miscut angle, and the sample tilting relative to the beam. The MPs run in different directions instead of lying parallel to the growth direction, similar to the observation described in an earlier paper [32]. In fact, the majority of MPs deviated from the growth direction and inclined toward one another or other defects in all six wafers studied. Interestingly, one can see that the sign of contrast changes per every MP as well as along its axis. For instance, a typical MP image with black edges and a white inside shows a reversal to light edges and a black inside, as is the case in the upper right corner of the inset of Fig. 4. The MP #3 from the group of three MPs and the MP #4 nearby demonstrate the features of black contrast. The effect was well explained by the simulation of MP images measured in a white SR beam [20]. At high angles between the MP axis and the beam, the section size of MP along the beam is small. At low angles, the section size increases, and the wave field

highlighting the locations of MPs is shown in the inset. MPs are located on the square #1.

#### *4.1.1. Micropipe ramification at the front of a growing crystal*

Ramification of MPs is accompanied by the partitioning of their Burgers vectors. According to the Frank rule [6], the equilibrium MP radius is proportional to the squared magnitude of its Burgers vector. As a result, ramification of MPs results in a decrease of their radii. The sketch of Fig. 7(a) represents a dislocated MP with the radius *r*<sup>0</sup> and the Burgers vector *b*<sup>0</sup> splitted into two smaller ones with the radii and the Burgers vectors *r*1, *r*<sup>2</sup> and *b*1, *b*2, respectively. A typical phase-contrast image of a ramified dislocation with a hollow core is shown in Fig. 7(b).

The ramification was modeled by Gutkin *et al.* to determine when a MP is favorable to split into a pair of MPs with smaller radii and Burgers vectors [7]. The angle between ramifying segments of the MP 'tree' was assumed to be small enough to consider these segments as a pair of parallel MPs. Also, it was assumed that the ramification required the repulsion of the ramifying segments. It is worth noting that the reverse process of the MP merging may follow the MP split. If the MPs formed by the split stay in contact, they are energetically favored to coalesce and produce a single MP. In this case, the split and following coalescence results only in a decrease in the MP radius. However the merging of the MP segments generated by the split does not occur if these segments, once formed, repulse each other. It was shown that the MPs may either repulse at any distance or repulse at distances *d* greater than the critical distance *dc* and attract each other at *d* < *dc*. The ramification of the MP segments (not followed by their coalescence) is possible if they repulse at any distance or the critical distance *dc* is small enough. The parameter region where the ramifying MP segments repulse at any distance is shown in Fig. 7(c). The system state diagram is depicted in the coordinate space (*b*1/*b*2, *r*1/*r*2). The upper and lower curves separate regions I and III, where the MPs attract each other at short distances while they repel each other at long distances, and the corresponding critical distance *hc* = *dc* -*r*<sup>1</sup> -*r*<sup>2</sup> between the MP free surfaces exists, from region II, where the MPs repulse at any distance. As is seen, an attraction area may exist for two same-sign MPs if *b*1/*b*<sup>2</sup> and *r*1/*r*<sup>2</sup> differ by more than 15%–25%. Ramification which does not require overcoming an energetic barrier is possible if the MPs are of the same sign, the radius of the original MP exceeds the equilibrium one, the total MP surface area reduces due to the ramification, and the radii of the ramifying MPs are approximately in the same ratio as the magnitudes of their dislocation Burgers vectors.

leads to diminishing their average density. In particular, when the interacting pair of MPs has incomparable diameters or is located far (at the distance of more than about 5 average MP diameters) from other MPs, the coalescing MPs come directly to each other along the shortest way between them. In this case their behavior is governed by elastic interaction between them only. In some other cases, the ends of two MPs with opposite-sign Burgers vectors start to move around one another. One of the reasons for this is the action of neighboring MPs. The winding of MPs around each other results in coalescence of their subsurface segments. The

Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging

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35

Reactions of ramification, merging and twisting of MPs occur when MPs come in contact, touching each other by their surfaces. However, phase-contrast imaging shows that MPs which are not in a direct contact may have variable cross-sections. In our paper [12], we demonstrated the experimental evidence of two neighboring MPs reducing their diameters (approximately by half) one after another, at different distances from the surface of a grown crystal. This can be treated as an indirect proof of the contact-free reaction. Such an idea appeared when we studied the axial-cut slice of 4*H*-SiC boule with the orientation (11.0). MPs located almost parallel to the growth axis were nearly parallel to the sample surface. The sample was fixed on the holder with its surface perpendicular to the beam and rotated to achieve a horizontal position of MP axes. So the images were measured by using the more coherent vertical projection of the source. In the topography mode, the sample was tuned to obtain a symmetrical Laue pattern. An example of an indexed Laue pattern for the (11.0) sample orientation is displayed in Fig. 8(a). One can see many diffraction vectors **g** available

For few individual MPs, the distances between the edges modified along their axes showing that their cross-sections changed through the crystal. A good example is the MP pair shown in Fig. 8(b) and (c). An optical micrograph of Fig. 8(c) displays vertical lines of black contrast which are non-uniformly distributed over the sample area and uneven horizontal lines of light contrast. The former are attributed to MPs and the latter to layered inclusions of foreign polytypes (6*H* and 15*R*). We note that MPs agglomerate along the boundaries of the inclusions. The group of closely spaced MPs labeled as MP1 and MP2 is located distant from the other MPs. This particular group was examined in detail in synchrotron light. To indicate the positions of the MPs in figures 8 and 9, we used the features of non-variable contrast, namely, the morphological defect [visible in Fig. 8(c) to the left from the MP1] and

Fig. 9(a) and (b) demonstrate X-ray topographs of the MPs recorded in the 21.2 and 01.10 reflections, respectively. The white arrow indicates the MP1 located at a distance of 950 *µ*m from the mark (that is the morphological defect) shown in Fig. 8(c). The diagram in Fig. 9(c) represents the diffraction geometry. Synchrotron beam propagates along the surface normal [11.0], while the basal plane normal [00.1] lies perpendicular to the beam. We suspect that the dislocation Burgers vector **b** of the MP1 is parallel to [00.1]. The diffraction vectors **g**<sup>1</sup> = 21.2, and **<sup>g</sup>**<sup>2</sup> = 01.10 and the Burgers vector **<sup>b</sup>** [00.1] are projected onto the film. The angles between the projections, ∠**g**1, **<sup>b</sup>** and ∠**g**2, **<sup>b</sup>**, are also displayed. We note that, for a pure screw dislocation, its image is invisible when **g** · **b** = 0. In Fig. 9 one notices that the contrast increases with the decrease of the angle. The MP1 is invisible in the 21.2 topograph when <sup>∠</sup>**g**1, **<sup>b</sup>** = 78.8◦, as in Fig. 9(a), but discernible in the 01.10 reflection when <sup>∠</sup>**g**2, **<sup>b</sup>** = 20.6◦, as in Fig. 9(b). The contrast behavior indicates that the dislocation of the MP1 is of screw type.

the MP bundle located at a distance of 950 *µ*m and 1100 *µ*m, respectively.

examples of twisted configurations and the modeling can be found in a review [14].

*4.1.3. Correlated reduction in micropipe cross sections*

for the characterization of dislocations.

#### *4.1.2. Merging of micropipes*

Many morphologies of coalesced MPs were observed experimentally in SiC crystals by means of x-ray phase-contrast imaging. To explain these phenomena, a computer simulation of MP evolution was performed [9]. It has been shown that the reaction of MP coalescence gives rise to the generation of new MPs with smaller diameters and Burgers vectors, which again

**Figure 7.** (a) Initial MP with the radius *r*<sup>0</sup> and the Burgers vector *b*<sup>0</sup> splits into two parallel dislocated MPs 1 and 2 with the radii and the Burgers vectors *r*1, *r*<sup>2</sup> and *b*1, *b*2, respectively located at a distance *d* from each other. (b) SR phase-contrast image of a ramified configuration. Halos correspond to etch pits on the wafer surface. (c) The system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The curves separate parameter regions I and III, where both attraction area and unstable equilibrium position exist for two MPs, from parameter region II, where the MPs repulse at any distance.

leads to diminishing their average density. In particular, when the interacting pair of MPs has incomparable diameters or is located far (at the distance of more than about 5 average MP diameters) from other MPs, the coalescing MPs come directly to each other along the shortest way between them. In this case their behavior is governed by elastic interaction between them only. In some other cases, the ends of two MPs with opposite-sign Burgers vectors start to move around one another. One of the reasons for this is the action of neighboring MPs. The winding of MPs around each other results in coalescence of their subsurface segments. The examples of twisted configurations and the modeling can be found in a review [14].

#### *4.1.3. Correlated reduction in micropipe cross sections*

8 Physics and Technology of Silicon Carbide Devices

The ramification was modeled by Gutkin *et al.* to determine when a MP is favorable to split into a pair of MPs with smaller radii and Burgers vectors [7]. The angle between ramifying segments of the MP 'tree' was assumed to be small enough to consider these segments as a pair of parallel MPs. Also, it was assumed that the ramification required the repulsion of the ramifying segments. It is worth noting that the reverse process of the MP merging may follow the MP split. If the MPs formed by the split stay in contact, they are energetically favored to coalesce and produce a single MP. In this case, the split and following coalescence results only in a decrease in the MP radius. However the merging of the MP segments generated by the split does not occur if these segments, once formed, repulse each other. It was shown that the MPs may either repulse at any distance or repulse at distances *d* greater than the critical distance *dc* and attract each other at *d* < *dc*. The ramification of the MP segments (not followed by their coalescence) is possible if they repulse at any distance or the critical distance *dc* is small enough. The parameter region where the ramifying MP segments repulse at any distance is shown in Fig. 7(c). The system state diagram is depicted in the coordinate space (*b*1/*b*2, *r*1/*r*2). The upper and lower curves separate regions I and III, where the MPs attract each other at short distances while they repel each other at long distances, and the corresponding critical distance *hc* = *dc* -*r*<sup>1</sup> -*r*<sup>2</sup> between the MP free surfaces exists, from region II, where the MPs repulse at any distance. As is seen, an attraction area may exist for two same-sign MPs if *b*1/*b*<sup>2</sup> and *r*1/*r*<sup>2</sup> differ by more than 15%–25%. Ramification which does not require overcoming an energetic barrier is possible if the MPs are of the same sign, the radius of the original MP exceeds the equilibrium one, the total MP surface area reduces due to the ramification, and the radii of the ramifying MPs are approximately in the

Many morphologies of coalesced MPs were observed experimentally in SiC crystals by means of x-ray phase-contrast imaging. To explain these phenomena, a computer simulation of MP evolution was performed [9]. It has been shown that the reaction of MP coalescence gives rise to the generation of new MPs with smaller diameters and Burgers vectors, which again

50 µm

**Figure 7.** (a) Initial MP with the radius *r*<sup>0</sup> and the Burgers vector *b*<sup>0</sup> splits into two parallel dislocated MPs 1 and 2 with the radii and the Burgers vectors *r*1, *r*<sup>2</sup> and *b*1, *b*2, respectively located at a distance *d* from each other. (b) SR phase-contrast image of a ramified configuration. Halos correspond to etch pits on the wafer surface. (c) The system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The curves separate parameter regions I and III, where both attraction area and unstable equilibrium

*r*1/*r*<sup>2</sup>

*b1*/*b2* 0 1 2 34 5

II I

III

same ratio as the magnitudes of their dislocation Burgers vectors.

*4.1.2. Merging of micropipes*

*b1*

**1**

*b0*

*r0*

*r1 b2 r2*

**2**

(a) (b) (c)

position exist for two MPs, from parameter region II, where the MPs repulse at any distance.

*d*

Reactions of ramification, merging and twisting of MPs occur when MPs come in contact, touching each other by their surfaces. However, phase-contrast imaging shows that MPs which are not in a direct contact may have variable cross-sections. In our paper [12], we demonstrated the experimental evidence of two neighboring MPs reducing their diameters (approximately by half) one after another, at different distances from the surface of a grown crystal. This can be treated as an indirect proof of the contact-free reaction. Such an idea appeared when we studied the axial-cut slice of 4*H*-SiC boule with the orientation (11.0). MPs located almost parallel to the growth axis were nearly parallel to the sample surface. The sample was fixed on the holder with its surface perpendicular to the beam and rotated to achieve a horizontal position of MP axes. So the images were measured by using the more coherent vertical projection of the source. In the topography mode, the sample was tuned to obtain a symmetrical Laue pattern. An example of an indexed Laue pattern for the (11.0) sample orientation is displayed in Fig. 8(a). One can see many diffraction vectors **g** available for the characterization of dislocations.

For few individual MPs, the distances between the edges modified along their axes showing that their cross-sections changed through the crystal. A good example is the MP pair shown in Fig. 8(b) and (c). An optical micrograph of Fig. 8(c) displays vertical lines of black contrast which are non-uniformly distributed over the sample area and uneven horizontal lines of light contrast. The former are attributed to MPs and the latter to layered inclusions of foreign polytypes (6*H* and 15*R*). We note that MPs agglomerate along the boundaries of the inclusions. The group of closely spaced MPs labeled as MP1 and MP2 is located distant from the other MPs. This particular group was examined in detail in synchrotron light. To indicate the positions of the MPs in figures 8 and 9, we used the features of non-variable contrast, namely, the morphological defect [visible in Fig. 8(c) to the left from the MP1] and the MP bundle located at a distance of 950 *µ*m and 1100 *µ*m, respectively.

Fig. 9(a) and (b) demonstrate X-ray topographs of the MPs recorded in the 21.2 and 01.10 reflections, respectively. The white arrow indicates the MP1 located at a distance of 950 *µ*m from the mark (that is the morphological defect) shown in Fig. 8(c). The diagram in Fig. 9(c) represents the diffraction geometry. Synchrotron beam propagates along the surface normal [11.0], while the basal plane normal [00.1] lies perpendicular to the beam. We suspect that the dislocation Burgers vector **b** of the MP1 is parallel to [00.1]. The diffraction vectors **g**<sup>1</sup> = 21.2, and **<sup>g</sup>**<sup>2</sup> = 01.10 and the Burgers vector **<sup>b</sup>** [00.1] are projected onto the film. The angles between the projections, ∠**g**1, **<sup>b</sup>** and ∠**g**2, **<sup>b</sup>**, are also displayed. We note that, for a pure screw dislocation, its image is invisible when **g** · **b** = 0. In Fig. 9 one notices that the contrast increases with the decrease of the angle. The MP1 is invisible in the 21.2 topograph when <sup>∠</sup>**g**1, **<sup>b</sup>** = 78.8◦, as in Fig. 9(a), but discernible in the 01.10 reflection when <sup>∠</sup>**g**2, **<sup>b</sup>** = 20.6◦, as in Fig. 9(b). The contrast behavior indicates that the dislocation of the MP1 is of screw type.

21.2

(a)

01.10

(b)

7.4 6.0 5.3 500 µm

950

11.0

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Distance, µm

1 3 2


1 3 2

11.0

Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging

21.2 **b**

**MP1**

**MP1**

parallel to [00.1], and the angles are ∠**g**1, **b** = 78.8◦ and ∠**g**2, **b** = 20.6◦.

4.2

2.5 2.1

100 150 200 250 300 350 400 450

3.9 3.7

(a) (b)

1.8 1.4

1.6

MP1

1.1

1.0

0.9

**Figure 10.** (a) Phase contrast image of micropipes MP1 and MP2 in the interval of 70–500 *µ*m along the pipe axes. The sample-to-detector distance is 10 cm. Variation in transverse cross-section sizes along the lines of MP1 (black squares) and MP2 (open squares) are shown in *µ*m. (b) The experimental (open circles) and simulated (curves 1–3) intensity profiles (the intensity in relative units via the distance across the MP image). The best agreement is achieved through a sequential adjustment in the pipe diameters perpendicular and parallel to the beam. The sample-scintillator distance is 45 cm. The transverse/longitudinal diameters are equal to 5.6/1.0 *<sup>µ</sup>*m (curve 1, fit = 1.92 × <sup>10</sup>−4). For comparison, curve 2 shows the best fit (8.12 × <sup>10</sup>−4) for the circular cross section 1.76/1.76 *<sup>µ</sup>*m, while curve 3 is given for the intermediate case 3.0/1.4 *<sup>µ</sup>*m (fit = 5.71 × <sup>10</sup>−4).

MP2

4.4 3.9

5.4 5.1 5.0

4.1

950

01.10

00.1

(c)

Intensity, r.u.

**Figure 9.** SR white beam topographs of MP1 and adjacent MPs obtained in the reflections **g**<sup>1</sup> = 21.2 (a) and **g**<sup>2</sup> = 01.10 (b). The position of MP1 is determined relative to the morphological defect shown in Fig. 8. Schematic diagram of the diffraction geometry (c). SR beam (a black arrow) propagates parallel to [11.0]. The dislocation Burgers vector **b** of MP1 is supposed

**Figure 8.** (a) Indexed Laue pattern for (11.0) 4*H*-SiC wafer (direction [00.1] horizontal) fixed perpendicular to SR beam. The sample-to-film distance is 130 mm. (b) SR phase-contrast image of the studied MPs, MP1 and MP2. (c) Optical micrograph (transmission) of MPs and foreign polytype inclusions. The distances from MP1 to the morphological defect (950) and the MPs bundle (1100) are shown in microns.

Phase contrast images of the MPs 1 and 2 were measured in a series at the distances from 5 to 45 cm from the sample to detector, increasing the distance every 5 cm. The image registered at the distance of 10 cm is shown in Fig. 10(a). To determine the characteristic sizes of the MP cross sections in different points along the MP axis, we applied the method of computer simulation [1, 19] of the measured intensity profiles. For every MP cross section under investigation, the computer program calculated many profiles for various possible section sizes on the base of Kirchhoff propagation to find the profile, which gives the best fit to the experimental profile. The parameters could be varied by user as well as via automatic procedures. One procedure calculated all points over a square net, while the other one looked for the best fit at every step and arrived at the best matching point. The coincidence allowed us to determine both the longitudinal (along the beam) and transverse (across the beam) sizes of the section [Fig. 10(b)].

The transverse diameters of MP1 and MP2 are presented in Fig. 10(a) versus the distance along the pipe axes increasing in the growth direction. It is seen that the transverse size of MP1 reduces from 7.4 to 2.1 *µ*m with growth. At the same time, the transverse size of the MP2 reduces from 4.1 to 1.6 *µ*m. In contrast, the longitudinal diameters remain almost the same as of the order of 0.8 *µ*m for the MP1 and 0.5 *µ*m for the MP2 (data not shown). In the correlated decrease of the MP1 and MP2 cross-section sizes in Fig. 10(a), several features are apparent. A remarkable decrease in the MP1 cross-section size occurs in the distance

<sup>36</sup> Physics and Technology of Silicon Carbide Devices Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging 11 Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging http://dx.doi.org/10.5772/52058 37

10 Physics and Technology of Silicon Carbide Devices


0-1.11

01.11

31.10

41.8 41.12



0-1.5 0-1.7

2-2.20 2-2.28

01.5 01.7

01.3

(c)

bundle (1100) are shown in microns.

beam) sizes of the section [Fig. 10(b)].

02.7 03.8

0-2.7

950 1100

MP2

Polytype inclusions

500 µm

200 µm

1100

MP1

**Figure 8.** (a) Indexed Laue pattern for (11.0) 4*H*-SiC wafer (direction [00.1] horizontal) fixed perpendicular to SR beam. The sample-to-film distance is 130 mm. (b) SR phase-contrast image of the studied MPs, MP1 and MP2. (c) Optical micrograph (transmission) of MPs and foreign polytype inclusions. The distances from MP1 to the morphological defect (950) and the MPs

Phase contrast images of the MPs 1 and 2 were measured in a series at the distances from 5 to 45 cm from the sample to detector, increasing the distance every 5 cm. The image registered at the distance of 10 cm is shown in Fig. 10(a). To determine the characteristic sizes of the MP cross sections in different points along the MP axis, we applied the method of computer simulation [1, 19] of the measured intensity profiles. For every MP cross section under investigation, the computer program calculated many profiles for various possible section sizes on the base of Kirchhoff propagation to find the profile, which gives the best fit to the experimental profile. The parameters could be varied by user as well as via automatic procedures. One procedure calculated all points over a square net, while the other one looked for the best fit at every step and arrived at the best matching point. The coincidence allowed us to determine both the longitudinal (along the beam) and transverse (across the

The transverse diameters of MP1 and MP2 are presented in Fig. 10(a) versus the distance along the pipe axes increasing in the growth direction. It is seen that the transverse size of MP1 reduces from 7.4 to 2.1 *µ*m with growth. At the same time, the transverse size of the MP2 reduces from 4.1 to 1.6 *µ*m. In contrast, the longitudinal diameters remain almost the same as of the order of 0.8 *µ*m for the MP1 and 0.5 *µ*m for the MP2 (data not shown). In the correlated decrease of the MP1 and MP2 cross-section sizes in Fig. 10(a), several features are apparent. A remarkable decrease in the MP1 cross-section size occurs in the distance

0-1.-3

0-2.-7

01.-3

02.-7

0-1.-5 0-1.-7

01.-5 01.-7

0-1.-11 2-2.-28 2-2.-20



01.-11

41.-4

31.-10


MP2

MP1

31.0 41.4

41.0

(a) (b)

**Figure 9.** SR white beam topographs of MP1 and adjacent MPs obtained in the reflections **g**<sup>1</sup> = 21.2 (a) and **g**<sup>2</sup> = 01.10 (b). The position of MP1 is determined relative to the morphological defect shown in Fig. 8. Schematic diagram of the diffraction geometry (c). SR beam (a black arrow) propagates parallel to [11.0]. The dislocation Burgers vector **b** of MP1 is supposed parallel to [00.1], and the angles are ∠**g**1, **b** = 78.8◦ and ∠**g**2, **b** = 20.6◦.

**Figure 10.** (a) Phase contrast image of micropipes MP1 and MP2 in the interval of 70–500 *µ*m along the pipe axes. The sample-to-detector distance is 10 cm. Variation in transverse cross-section sizes along the lines of MP1 (black squares) and MP2 (open squares) are shown in *µ*m. (b) The experimental (open circles) and simulated (curves 1–3) intensity profiles (the intensity in relative units via the distance across the MP image). The best agreement is achieved through a sequential adjustment in the pipe diameters perpendicular and parallel to the beam. The sample-scintillator distance is 45 cm. The transverse/longitudinal diameters are equal to 5.6/1.0 *<sup>µ</sup>*m (curve 1, fit = 1.92 × <sup>10</sup>−4). For comparison, curve 2 shows the best fit (8.12 × <sup>10</sup>−4) for the circular cross section 1.76/1.76 *<sup>µ</sup>*m, while curve 3 is given for the intermediate case 3.0/1.4 *<sup>µ</sup>*m (fit = 5.71 × <sup>10</sup>−4).

interval from 74 to 132 *µ*m while the transverse diameter of MP2 drastically decreases later in the distance interval from 314 to 345 *µ*m. In addition, a rapid decrease of the transverse diameter of MP1 happens in the distance interval from 393 to 458 *µ*m when the transverse diameter of MP2 remains almost invariable.

The radii reduction of both MPs was explained by a contact-free reaction between them [12, 14]. We suppose that the MP1 and MP2 contain superscrew dislocations with opposite Burgers vectors **b**<sup>1</sup> and **b**2. In case of a contact-free interaction micropipe MP1 emits a full-core dislocation half-loop, which expands by gliding, reaches the surface of micropipe MP2, and reacts with its dislocation. The corresponding dislocation reactions are described by equations: **b**<sup>1</sup> - **b**<sup>0</sup> = **b**<sup>3</sup> and **b**<sup>2</sup> + **b**<sup>0</sup> = **b**4, where **b**<sup>3</sup> and **b**<sup>4</sup> are new Burgers vectors of micropipes MP1 and MP2, respectively. Strong reduction in the radii can lead to their gradual healing.

*z*

520

*y*

<sup>60</sup> *<sup>x</sup>*

**b**=+3

560

600

100

140

other mechanisms and do not contain any dislocation charge.

disappearance and its contribution to the increase in MP density.

**5.2. Generation of MPs in the intermediate stage**

embryos of new MPs [Fig. 12(b)].

described earlier [21].

**b**=-3 200

100

*z*

0

(a) (b) (c)

depend on the growth rate. SR phase-contrast image of semi-loops resulting from macropipes twisting (c).

**Figure 11.** Coalescence of MPs with equal magnitudes of Burgers vectors results in the annihilation of the subsurface MP segments (a, b). The coalescing MPs come to each other along the shortest way (a) or twist (b). The Burgers vectors are shown in units of *c*, which is the lattice parameter in the growth direction. The coordinates *x* and *y* are given in units of *Gc*2/(8*π*2*γ*), where *G* is the shear modulus and *γ* is the specific surface energy. The length of MPs (along the *z* axes) is in arbitrary units that

Another possible mechanism of pore formation is the attraction and agglomeration of MPs at FPI boundaries [10, 11, 13], for instance, resulting in the majority of pores observed at the boundaries of FPIs (Fig. 3). By effectively accommodating both the dilatation and orientation misfits between FPI and matrix, these pores in early stages can attract additional random full-core dislocations and MPs from neighboring regions (Fig. 4), as earlier described in detail [13]. In such a way, the interface pores can extend along FPI boundaries and accumulate dislocation charge that is the resulting Burgers vector of all the dislocations absorbed by the pore. Of course, one can not exclude the presence of the pores that have been formed by the

When the FPIs stop to grow and become overgrown by the matrix, there is no reason for the pore formation as misfit defects. The disappearance of pores started to occur at this point, as seen in Figs. 2 and 5. We suggest three possible mechanisms that can explain the

First, pores can dissolve through emission of vacancies, which migrate to full-core threading dislocations on the FPI/matrix interface [15, 26] and are absorbed by them, as illustrated in Fig. 12. These dislocations can reach the growth front and proceed to grow with it [Fig. 12(a)]. At the dislocation core, these vacancies are coagulated with the vacancies that migrate from the growth front along the dislocation cores, thus forming

Second, the pores can be overgrown by the lateral growth of the crystal and, if they contain dislocations with large Burgers vectors, can transform to MPs by the mechanism

200 <sup>100</sup> *<sup>x</sup>* <sup>300</sup>

**b**=+2

<sup>400</sup> *<sup>y</sup>*

30 µm

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**b**=-2

Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging
