CHAPTER FIVE
5.3 Crystal Defects in SiC
5.3.1. Introduction
The main crystal defects found in epitaxially grown 3C-SiC are stacking faults with their accompanying partial dislocations, twins and inversion domain boundaries.
In a TEM study by Jacob et al. (2000) on epitaxially grown 3C-SiC on Si(001) a high density of planar defects lying on {111} planes was found. Defects included stacking faults and microtwins and the authors suggested that the defects were introduced during the growth process to accommodate the large lattice and thermal mismatches between the crystals.
Similar findings were reported by Stoemenos et al. (2004) in a TEM study on 300µm thick freestanding 3C-SiC. Microtwins, stacking faults and inversion domain boundaries were observed and their presence attributed to the same reasons as above.
Powell et al. (1987) in an extensive microscopy study on 3C-SiC found microtwins, stacking faults and also misfit dislocations accommodating the lattice mismatch. They presented possible mechanisms for the nucleation and growth of the defects and these will be discussed in Sections 5.3.2 and 5.3.3.
Furthermore Pirouz et al. (1987), Ho et al. (1999) and Nagasawa et al. (2002) all studying epitaxially grown 3C-SiC on Si (001) found microtwins and stacking faults as the predominant defects in the SiC and attributed their presence to lattice and thermal mismatch.
5.3.2 Accomodation of Misfit and Interfacial Twinning
The mechanism for the accommodation of misfit during growth and its relationship to interfacial twinning has been thoroughly explained by Powell et al. (1987). The total misfit, f, between an epilayer and substrate is accommodated by the elastic strain, ε, of planes in the regions of good register and by interfacial dislocations, δ. The spacing of misfit dislocations with Burgers vector b would be S = b/δ. The Si/SiC system has a lattice mismatch of about 20% (f ≈ 0.2). Assuming that the entire misfit is accommodated by misfit dislocations, f = δ and S ≈ 5b. Thus an array of edge misfit dislocations in SiC parallel to the interface with b = a/2 [110] at a spacing of S ≈ 5d110 would accommodate all the misfit.
Furthermore it is also frequently observed that where misfit dislocations become irregular, twinning occurs. The twins nucleate at the interface due to coherency accommodate the lattice mismatch having strength 2a/2 according to Frank’s rule.
A shear type dislocation gliding on the (111) plane for example with b = a/2 [101]
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will have an edge component along the [110]
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direction of half the strength of the pure edge with 2a/4. Thus the shear type dislocation is only half as efficient as the edge misfit dislocation in accommodating the misfit. On the other hand partial dislocations of the type a/6 [121]
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or a/6 [211]
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gliding on a (111) plane will also have an edge component with strength 2a/4 and is just as efficient as the shear type dislocation in misfit accommodation. Furthermore a twin as discussed above may be considered
as the propagation of a number of partials with the width of the twin determined by the number n of the partials. Such a system can be considered having Burgers vector equal to that of a superdislocation with b = na/6[121]
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having strength n 2a/4. Thus a twin formed by glide of these partials is much more efficient in mismatch accommodation than the edge misfit and shear dislocations.
It is necessary to consider the lattice mismatch in the [110]
at a spacing of 5d {110} orthogonal to the first array would satisfy the mismatch strain along this direction also. The strength of the edge component of an a/6[121] twin needs to be six (111) layers thick to be able to accommodate the mismatch along the [110]
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direction as efficiently as an edge misfit dislocation having b = a/2[110]
_ _
. In another publication Powell et al. (1987) presented high resolution TEM results of misfit dislocations present at the SiC/Si interface. They found the dislocations occur on average every four lattice fringes.
5.3.3. Mechanisms for the Formation of Stacking Faults
The mechanism of formation of stacking faults in SiC is still widely debated. It is obvious that the driving force behind the process is the low stacking fault energy in SiC but the exact process of formation of the SFs during growth seems not to be as a result of one thing but rather a combination of different processes during growth. The possible mechanisms are discussed by Powell et al. (1987) and Pirouz et al. (1987).
(a) Firstly if it is assumed that the process of growth of the material occurs through the formation of discrete nuclei on the substrate surface, it can be envisioned that some of the nuclei may be deposited on incorrect sites forming surfaces of mismatch boundary. When the correctly deposited islands meet the incorrectly deposited islands an inverted pyramid of stacking fault could result growing on the inclined {111} faces with its {001} base at the interface. Using a simple geometric consideration (depicted in (e)) it can be shown that depending on the nature of the dislocations at the
intersection of the fault, the faces of the pyramid would either be all of the same nature or alternatively intrinsic and extrinsic faults. It can also be shown that the measurement of the width of the fault at the surface of the foil enables one to measure the point of nucleation.
(b) It is possible for interfacial stacking faults to have formed during the cooling stages due to the lattice mismatch between the substrate and film. In this case, the stacking fault would nucleate at the interface during the cooling stages and subsequently propagate into the bulk by glide of partial dislocations. However the activation energy of dislocation motion in SiC is very high and it is unlikely that the stacking fault nucleated would propagate throughout the bulk of the layer. Thus the faults are limited to a region close to the interface with the bonding partial dislocations parallel to the interface.
(c) The next possibility is the spontaneous generation of dislocations at the interface as soon as the epitaxial layer begins to grow. Conditions on the interface such as contamination, roughness, moderate stresses would enhance the generation at lower temperatures of growth. According to Booker et al. (1978) the dislocations always form in pairs and once the dislocations are generated they split into two Shockley partials bounding a ribbon of stacking fault between them.
(d) The fourth possibility is that dislocation loops are generated within the bulk of the material presumably during the cooling stages by the stresses caused by the thermal mismatch between the substrate and film. Following this, the glide dislocations would split up into Shockley partials bounding wide ribbons of stacking fault between them since the stacking fault energy in SiC is very low. The interaction between partials gliding on different {111} planes would give rise to intersecting faults.
Fig. 5.2 A schematic diagram of the fault on the (111) planning assuming that it has nucleated at point O. W1 and W2 are the widths of the fault on the top and bottom of the foil respectively.
(e) The last possibility is that stacking faults arise during the growth of the film due to incorrect deposition of some nuclei on the surface of the growing film. This could be as a result of a rapid deposition rate, inhomogeneities in the film or impurities in the carrier gas. Furthermore diffusion rates in SiC are very low at the temperature of deposition and thus the nuclei would not have enough time to readjust themselves to the correct position. Once a mismatch boundary has formed stacking faults will grow on the {111} faces with further growth of the film. A schematic illustration of this is given in Fig. 5.2. It is assumed the stacking fault nucleated at point O due to some inhomogeneity and grow wider as the layer thickened in the [001] direction. Since the
<110> directions are parallel to the Peierls valleys in crystals with sphalerite structure, and the Peierls energy is expected to be very high in SiC, the growth occurs such that the partials bounding the stacking fault lie along these directions. Measuring the width of the fault at the top of the foil, W1 enables one to determine the depth below the surface, h, at which the stacking fault nucleated,
2
1/ W h
Yun et al. (2006) explained that the stacking fault formation is a result of a large number of twins forming on {111} planes during the early stages of growth prior to the coalescence of nuclei. The atomic stacking errors may form on {111} planes of
each nuclei because of the low surface energy of the plane. The atomic errors lead to twin formation and stacking faults appear at twin boundaries.
5.3.4. Stacking Fault Energy in SiC
The stacking fault energy in SiC has been found to be very low and this is one of the main reasons for the large number of hexagonal polytypes that are found in SiC. For 3C-SiC the stacking fault energies have been theoretically calculated by Denteneer et al. (1987), Iwata et al. (2002), Käckell et al. (1998) and Lindefelt et al. (2003).
Denteneer et al. (1987) used an adaptation of the ANNNI (axial next-nearest-neigbour Ising) and found the stacking fault energy γesf for the extrinsic fault as -15 mJ.m-2 and for the intrinsic γisf = 12 mJ.m-2. This is interesting since the value for the extrinsic fault is negative which shows that the formation of the fault is energy efficient.
Denteneer explains that this is an indicator of the occurrence of polytypism in SiC.
Iwata et al. (2002) also found a negative stacking fault energy in 3C-SiC of -2.70 mJ.m-2 and -6.27 mJ.m-2 using two different methods which are the supercell and ANNNI method respectively. Käckell et al. (1998) using a scheme based on density-functional theory and the local-density approximation found values of -28 mJ.m-2 and -3.4 mJ.m-2 for extrinsic and intrinsic faults respectively.
Furthermore Denteneer et al. (1989), Karch et al. (1994) and Cheng et al. (1990) found values of 13.8 mJ.m-2, 11.1 mJ.m-2, -7.1 mJ.m-2 for intrinsic and -6.1 mJ.m-2, -15.4 mJ.m-2 and -32.3 mJ.m-2 for extrinsic faults respectively. The negative SF energy values for the extrinsic fault is suggested to be due to the fact that the stacking sequence of the extrinsic fault is close to the bulk stacking sequence of the more stable hexagonal polytypes of SiC.