Emergence point

From this expression we observe that R > / hc- The terrace connecting two spirals, one left-handed and the other right-handed, will grow indefinitely if the diameter of the critical 2D nucleus, 2Rc, is less than the distance between the emerging points of the two spirals (Frank, 1949). The minimum measured separation between coupled spirals is about 50 nm, so that R < 25 nm (see Section 5.1). Asymmetric hollow cores can be clearly seen in Fig. 5.13 and are in fact composed of two single hollow cores of the same sign separated by about 2/ hc, as can be inferred from the figure. 

OD point inhomogeneities, such as atomic disorder, vacancies, interstitials, emergence points of edge and screw dislocations,... 

A perfect crystal face should be completely free of any surface defects. In view of its further application for crystal growth studies, however, a face not intersected by screw dislocations can be considered conditionally as perfect. All other defects have either little or no effect on the growth behavior of the face. To meet this situation, the term quasi-ideal or quasi-perfect" has been introduced for the description of faces free of screw dislocations [5.14]. A quasi-perfect face is characterized by extended atomically smooth terraces separated by monatomic steps and absence of emergence points of screw dislocations. A smooth quasi-perfect face without steps can be described as an intact quasi-perfect face". 

Figure 5.4 Pyramids of growth on an Ag(lOO) face obtained by applying a short overvoltage pulse on an initially flat crystal face in the standard system Ag(100)/AgNO3 [5.7]. The pyramids mark the emergence points of the screw dislocations. The quadratic symmetry of the pyramids corresponds to the (100) nature of the face. Face areay4(ioo) = 2 x 10" cm. ...

Frank [5.50] was the first to recognize the major role of screw dislocations in the process of the growth of real crystals. Due to the helicoidal structure of this crystal imperfection, a step originates from the point where the screw dislocation line intersects the surface of the crystal face (Fig. 5.26b). This step is constrained to terminate at the dislocation emergence point and winds up into a spiral during the growth process (Fig 5.27). 

Figure 5.27 Successive stages of formation of a growth spiral around the emergence point of a screw dislocation on a singular crystal face.

A more complex situation is obtained if the emergence points of two or more screw dislocations on a crystal face are located at distances comparable to the size of the 2D nucleus. This case has been discussed by different authors [5.61-5.63, 5.68-5.72]. When a crystal face is intersected by two screw dislocations of opposite sign, they produce only one step at equilibrium which connects both emergence points of the dislocations (Fig. 5.31). 

Figure 5.31 Successive stages of step loop formation by pairs of screw dislocations with opposite sign 15.71, 5.72]. (a) Dislocation emergence points situated along a line parallel to the step edges djisl = 2icrit (b) dislocation emergence points situated along a line at an angle of 45° with respect to the step edges djisl = Vi Lcrit.

Figure 5.33 Growth spirals produced by groups of screw dislocations with same sign [5.61], (a) Pair of screw dislocations at a distance djisl < 2npa[

As already discussed above, the application of a cathodic overpotential step to a crystal face growing at steady state conditions leads to the formation of new growth pyramids at the emergence points of screw dislocations. The slope of these new pyramids is determined by the new final overpotential, rn, and is steeper than that of the pyramids growing at the initial overpotential, rji, before application of the potential step. If the new pyramids grow at rjf independently, i.e., without interaction or overlapping effects, they cover a part, Sex(0. of the crystal face surface given by [5.83]... 

For assessment of the dislocation density the etch pit density (epd) is measured according to DIN 50454-1 for LEC crystals and by a full-wafer mapping for VGF material using automated equipment. To reveal the emerging points of dislocations, the as-cut wafers are chemically polished in a H2S04-based solution to remove the damage and etched in a KOH melt at 400 °C. Typical examples of etched wafers are represented in Fig. 9.16. 

The present chapter treats the subject of etching of crystals from the viewpoint of electrochemical processes. The fundamental mechanisms of dissolution and selective etching are first outiined in Secs. 2 through 7. The morphoiogy of etch pits and the reliability of etch figures in locating the emergence points of dislocations are then briefly discussed in Secs. 

Figure 4. Schematic representation of the free energy change involved during the formation of two-dimensional circular dissolution nuclei on (I) a perfect surface, and (II) at the emergence points of a dislocation.

In Sec. 2 the overall surface dissolution was considered. Except in the case of surface diffusion, we assumed that a dissolving surface is free from defects. Since real crystals usually contain dislocations and other defects, it Is necessary to know their effect on dissolution rates and the mechanism of formation of etch pits at their emergence points. 

If a crystal can be deformed plastically, the appearance of slip bands and indentation rosettes (Fig. 24) on a surface Implies that the etch figures locate the emergence points of dislocations. Comparison of etch... 

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