Faults, stacking

Stacking faults are another form of surface defects. They occur from mistakes during crystal growth, often from growing too fast where the ad atoms have not had a chance to reach equilibrium at the surface. They can also be caused by stresses or by vacancy 

Grain boundaries of a polished and etched steel nail at x60. Note the elongated grains that result from the drawing process. (Photograph courtesy of Dr. Michael Banish, University of Alabama in Huntsville. Personal communication.) 

Tilt boundaries. Formation of a low-angle tilt boundary through a series of dislocations. 

Similar research has been done on planes perpendicnlar to the [0001] basal plane. Micropipe-free material has been grown, however, new defects appear as reported by the authors [60]. 

Furthermore, the stacking order has been identified as that of the 3C-SiC polytype and, according to the stndy by Stahlbnsh, an explanation to the recombinative behavior of the stacking fanlt is that the 3C-SiC, having a lower bandgap than 4F1-SiC, acts as a qnantnm well, thereby enhancing the recombination [63]. It is a very serious materials issue that must be solved prior to the realization of commercial bipolar devices. 

Work is ongoing to reduce defects in SiC material. One of the more interesting concepts is the reduction of defects through epitaxial growth on porous SiC substrates [64]. This approach has clearly demonstrated a reduction in intrinsic defects, as evidenced by photoluminescence measurements. It is too early to tell whether this technique can provide a path forward for the bipolar devices but it will clearly find its applicability in several areas where SiC will have a market. 

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Figure B3.3.13. Intersecting stacking faults in a fee crystal at the impact plane induced by collision with a momentum mirror for a square cross section of side 100 unit cells. The shock wave has advanced half way to the rear ( 250 planes). Atom shading indicates potential energy. Thanks are due to B Holian for tliis figure.

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

Alternatively, the effects of valency may be felt through the decrease in stacking fault energy (SFE) of fee alloys having increasing electron to atom ratio (14). 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

Pure metallic cobalt has a soHd-state transition from cph (lower temperatures) to fee (higher temperatures) at approximately 417°C. However, when certain elements such as Ni, Mn, or Ti are added, the fee phase is stabilized. On the other hand, adding Cr, Mo, Si, or W stabilizes the cph phase. Upon fcc-phase stabilization, the energy of crystallographic stacking faults, ie, single-unit cph inclusions that impede mechanical sHp within the fee matrix, is high. 

Stacking faults thereby providing barriers to sHp. If carbides are allowed to precipitate to the point of becoming continuous along the grain boundaries, they often initiate fracture (see Fracture mechanics). A thorough discussion of the mechanical properties of cobalt alloys is given in References 29 and 30 (see also Refractories). 

Figure 6.13, Brightfield electron micrographs of dislocations and stacking faults in NijAl as a function of peak pressure, (a) 14 GPa and (b) 23.5 GPa.

The key here was the theory. The pioneers familiarity with both the kinematic and the dynamic theory of diffraction and with the real structure of real crystals (the subject-matter of Lai s review cited in Section 4.2.4) enabled them to work out, by degrees, how to get good contrast for dislocations of various kinds and, later, other defects such as stacking-faults. Several other physicists who have since become well known, such as A. Kelly and J. Menter, were also involved Hirsch goes to considerable pains in his 1986 paper to attribute credit to all those who played a major part. 

T. Sinno, R. A. Brown, W. Van Ammon, E. Dornberger. Point defect dynamics and the oxidation-induced stacking-fault ring in Czochralski-grown silicon crystals. J Electrochem Soc 145 302, 1998. 

Using the constructed potentials the y-surface for the (111) plane was calculated. (For more details see Girshick and Vitek 1995). T e lowest energy minimum on this surface corresponds to the ideal Llo structure. However, there are three different metastable stacking fault type defects on (111) the antiphase boundary (APB), the complex stacking fault (CSF) and the superlattice intrinsic stacking fault (SISF). The displacements... 

The core structure of the 1/2 [112] dislocation is shown in Fig. 4. This core is spread into two adjacent (111) plames amd the superlattice extrinsic stacking fault (SESF) is formed within the core. Such faults have, indeed, been observed earlier by electron microscopy (Hug, et al. 1986) and the recent HREM observation by Inkson amd Humphreys (1995) can be interpreted as the dissociation shown in Fig. 4. This fault represents a microtwin, two atomic layers wide, amd it may serve as a nucleus for twinning. Application of the corresponding external shear stress, indeed, led at high enough stresses to the growth of the twin in the [111] direction. 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

Rosengaard and Skriver [5] have demonstrated, that in all 3d, 4d, and 5d transition metals, the intrinsic stacking fault energy, 7, can be accurately estimated from the relation,... 

Figure 1 Intrinsic stacking fault energy for chemically disordered solid solution Al-X (where X=Cu or Mg) as a function of composition.

As we show in Fig. 2 this relation holds as well for the two Al-based alloys studied here. This finding has consequences on the nature of the inter-atomic interactions. From a fee point of view, the hep structure has a stacking fault every second layer. The fact that relation (1) holds means that these stacking faults weakly interact, and therefore the range of the inter-atomic interactions should not go beyond the second neighbor shell whereas conventional central potentials require at least three atomic shells to differentiate the fee and hep stacking sequences. 

Figure 2 Comparison between intrinsic stacking fault energy (solid line) with two times the energy difference between the hep and the fee structure (dashed line) for Al-Cu (left panel) and Al-Mg (right panel) solid solution as a function of alloy composition.

Figure 3 Compositional dependence of the stacking fault energy calculated from the rigid-band model (solid line) compared with the more accurate results from the LKKR-CPA calculation (dashed line) for the Al-Cu alloy system.

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