**5.1. Generation of pores in early stage of SiC growth**

From our observations of FPIs, pores, MPs and their changes during the bulk SiC crystal growth described above, we suggest the formation mechanisms of defects as follows. The nucleation of FPIs in the initial stage is suggested as a basis of massive generation of full-core dislocations [26], pores and MPs [10, 11, 13, 31]. The bottom and lateral faces of growing FPIs are possibly the formation sites of interface dislocation structures to accommodate the misfit or misorientation of the matrix and FPI's crystalline lattices. The FPI boundaries are also able to serve as easy paths and sinks for vacancies which are nucleated at the growth front and migrate towards the crystal bulk. High densities of interface dislocations and vacancies thus formed possibly lead to coagulation of vacancies, forming slit-like pores along the FPI boundaries.

<sup>38</sup> Physics and Technology of Silicon Carbide Devices Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging 13 Characterization of Defects Evolution in Bulk SiC by Synchrotron X-Ray Imaging http://dx.doi.org/10.5772/52058 39

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

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 other mechanisms and do not contain any dislocation charge.

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

12 Physics and Technology of Silicon Carbide Devices

diameter of MP2 remains almost invariable.

**4.2. Annihilation of micropipes**

surface energy is the faster this process would be.

**5. Structural models of pore overgrowth**

**5.1. Generation of pores in early stage of SiC growth**

gradual healing.

boundaries.

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

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

MP merging may lead to the annihilation of initial MPs at the growing surface. We considered the motion of subsurface segments of MPs under the action of elastic forces due to their interaction and some effective friction [9]. The latter accounted for some extra surface energy related to the steps appearing on the pipe cylindrical surfaces during lateral displacements of the pipe segments. As a result, various reactions between the subsurface pipe segments were observed. In particular, it has been shown that the reaction of MP coalescence can lead to the annihilation of initial MPs. Some typical defect configurations in a 3D space are displayed in Fig. 11. They may be subdivided into planar and twisted pipe configurations. The planar configurations arise when the interacting pair of MPs is located far from other MPs; and the coalescing MPs come to each other along the shortest way [Fig 11(a)]. The twisted configurations like double spirals form if the interacting MPs are located within dense groups of other MPs. In this case, the coalescing MPs twist [Fig 11(b)]. When the magnitudes of Burgers vectors are the same, the initial defect configuration of a dipole is transformed into a new configuration of a semiloop [Fig. 11(c)]. As a result, we expect that the density of MPs would diminish during the crystal growth. The smaller the

From our observations of FPIs, pores, MPs and their changes during the bulk SiC crystal growth described above, we suggest the formation mechanisms of defects as follows. The nucleation of FPIs in the initial stage is suggested as a basis of massive generation of full-core dislocations [26], pores and MPs [10, 11, 13, 31]. The bottom and lateral faces of growing FPIs are possibly the formation sites of interface dislocation structures to accommodate the misfit or misorientation of the matrix and FPI's crystalline lattices. The FPI boundaries are also able to serve as easy paths and sinks for vacancies which are nucleated at the growth front and migrate towards the crystal bulk. High densities of interface dislocations and vacancies thus formed possibly lead to coagulation of vacancies, forming slit-like pores along the FPI 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 disappearance and its contribution to the increase in MP density.


*b*

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

http://dx.doi.org/10.5772/52058

41

(a) (b)

**Figure 14.** (a) The pore of a complex shape has equal number of up-steps and down-steps and first does not contain screw dislocation. (b) Pore overgrowth starts with a stepped bridge (S-bridge); if the large step compensates small steps around the two new pores, then no screw dislocations appear. (c) Pore overgrowth starts with a distorted bridge (D-bridge); there is no compensation of small steps around the two new pores, in which case a dislocation semi-loop arises: the edge segment of the semi-loop lies under the D-bridge, while two screw segments are within their new pores. These new pores become embryos of

These new pores can become embryos of dislocated MPs. It is worth noting that a similar mechanism for screw dislocation nucleation at foreign phase inclusions was first proposed by Chernov [4]. Dudley *et al.* experimentally observed and explained the nucleation of a pair of MPs at an inclusion in 4*H*-SiC [5]. In such a way, a pore elongated along the growth front and overgrown with the formation of many D-bridges can 'produce' many MPs of alternate dislocation signs of equal or different radii depending on the dislocation Burgers vectors.

As a result, the density of pores (and full-core dislocations) decreases at this stage of crystal

The situation at the next stage of the crystal growth depends on whether new FPIs are generated or not. If generated, then the stages described above are repeated. However, though formed as explained in the intermediate stage, MPs can be attracted to FPIs and absorbed by their boundaries, producing extended pores there by agglomeration [10, 11]. If new FPIs are not nucleated, the processes of self-organization occur in the MPs ensemble: MPs elastically interact and react with each other as well as with full-core dislocations, as described in the section 4. As a result, some MPs annihilate or diminish their Burgers vectors and are finally healed. Otherwise they form separate dense groups of MPs which proceed to

Similar separate dense arrays of MPs are demonstrated in Figs. 5 and 6.

growth, while the density of MPs increases, as seen in Fig. 5.

**5.3. Evolution of defects in later stage**

grow with the crystal.

(c)

dislocated MPs.

*b*

**Figure 12.** Mechanism of MP nucleation through coagulation of vacancies at the cores of threading dislocations. (a) Pore at the boundary of FPI starts to dissolve by emitting vacancies which migrate to neighboring full-core threading dislocations. (b) Vacancies from pore and growth surface migrate along the dislocation cores, meet and coagulate, thus transforming full-core dislocations to MPs.

**Figure 13.** The pore of a convex shape has equal number of up-steps and down-steps and does not contain screw dislocation. (a) Open pore, (b) overgrown pore.

Third, if pores have complex shapes (like those represented in Figs. 2–4, they can produce dislocated MPs during their lateral overgrowth even without full-core dislocations as described below.

The surface regions around pores always contain surface steps. If the numbers of the steps up and down (let us call them up-steps and down-steps, respectively) are equal, there would be no screw dislocation inside the pore. Otherwise there should be a screw dislocation with a Burgers vector of the magnitude equal to the difference between the sum heights of up-steps and down-steps. Let us consider the first case as shown schematically in Fig. 13 and Fig. 14 for simple convex and complex pore shapes, respectively. If the pore shape is convex (say, circular or elliptical), its overgrowth can hardly lead to the formation of screw dislocations (Fig. 13). However, if the pore shape is complex with some concave fragments [Fig. 14(a)], one can expect that the pore starts to overgrow through a bridge between two opposite concave fragments in a narrow part of the pore [Figs. 14(b) or (c)]. This bridge can separate the initial pore into smaller ones. If the two new pores have different numbers of up-steps and down-steps on the growth surface, the difference can be compensated by large (or small) steps on the bridge [it is called S-bridge here, Fig. 14(b)] with no screw dislocations. Otherwise the bridge can have a smooth surface without steps and be distorted [it is called D-bridge here, Fig. 14(c)], forming a semi-loop of superdislocation. The edge segment of the semi-loop lies under the D-bridge, while the two screw segments are within their new pores.

**Figure 14.** (a) The pore of a complex shape has equal number of up-steps and down-steps and first does not contain screw dislocation. (b) Pore overgrowth starts with a stepped bridge (S-bridge); if the large step compensates small steps around the two new pores, then no screw dislocations appear. (c) Pore overgrowth starts with a distorted bridge (D-bridge); there is no compensation of small steps around the two new pores, in which case a dislocation semi-loop arises: the edge segment of the semi-loop lies under the D-bridge, while two screw segments are within their new pores. These new pores become embryos of dislocated MPs.

These new pores can become embryos of dislocated MPs. It is worth noting that a similar mechanism for screw dislocation nucleation at foreign phase inclusions was first proposed by Chernov [4]. Dudley *et al.* experimentally observed and explained the nucleation of a pair of MPs at an inclusion in 4*H*-SiC [5]. In such a way, a pore elongated along the growth front and overgrown with the formation of many D-bridges can 'produce' many MPs of alternate dislocation signs of equal or different radii depending on the dislocation Burgers vectors. Similar separate dense arrays of MPs are demonstrated in Figs. 5 and 6.

As a result, the density of pores (and full-core dislocations) decreases at this stage of crystal growth, while the density of MPs increases, as seen in Fig. 5.
