Morphological classification and quantitative analysis of etch pits
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(a) Illustration of different types of etch pits for the example of etching with HCl (4 min at ). AFM investigation allows a clear identification of pointed ( and ) and flat-bottomed etch pits. Etch pits may either be eccentric or centric . (b) Etch pit with a kinked-wall created by etching with (10 min at ). (c) Classification of etch pit morphology for the examples shown in frames (a) and (b). (d) Schematic representation of an eccentric pointed etch pit in top view (upper) and a cross-sectional view along a plane perpendicular to the surface including the root point of the etch pit and the triangle centroid (lower). The etch pit is bound by an equilateral triangle with a side length and has three inner ledges with lengths . The length of the projection of a line connecting points and onto the surface plane is the eccentricity . The angle enclosed by the dislocation line and the surface normal can be calculated from the depth of the etch pit and its eccentricity .
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The angle between the dislocation line and the surface normal plotted against the flatness for eccentric (type-I) pointed etch pits as derived from a large number of etching experiments with HCl (upper graph) and conc. (lower graph). Dots represent results from an analysis of individual etch pits while the dashed lines serve as a guide for the eye indicating the unknown functional relationship. The flatness diverges for the inclination angle approaching 90° while it approaches a value of 28 for HCl and 22 for for the dislocation angle approaching 0°. For comparison, the respective flatness values of 50 for HCl and 26 for found for centric (type-II) etch pits are included in the graph.
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[(a)–(e)] Representative etching results for type-I [(a) to (c)] and type-II [(d) and (e)] kinked-wall etch pits resulting from etching with HCl and , respectively. (a) Transition of a pointed etch pit to a flat pit by etching with conc. (10 min at ). Parameters: , , , and , inner edges , , and are , , and , respectively, , the flatness of is typical for eccentric type-I etch pits. (b) Type-I etch pit with a flat bottom by etching with conc. (120 min at ). Parameters: , , , and , inner edges , , and are 736 nm, 773 nm, and 634 nm, respectively, , . The white dot is the geometric center . There is an unevenness at the bottom pointing to a localized defect that presumably has been the pinning center of the dislocation line. Due to its small height, the pot is hardly visible. (c) Type-I flat pit etched by conc. (20 min at ) with a clearly discernible pot. Parameters: , , , and , inner edges , , and are , , and , respectively, and . The flatness points to a very large eccentricity. (d) Transition state from a pointed etch pit to a flat pit by etching with HCl (4 min at 25°). Parameters: , , , and , inner edges , , and are each 645 nm, and . The centric appearance together with the typical flatness identify the etch pit as type-II. (e) Type-II flat pit by etching with HCl (2 min at ) with a laterally extended pot. Parameters: , , , and , inner edges , , and are each 250 nm, and . The small value for indicates that the defect creating the etch pit was close to the surface. (f) Schematic representation of an eccentric flat pit introducing the notation for the depth of the pot , the size of the upper part of the etch pit wall and the length of the inner ledges together with a redefinition of other relevant length parameters by analogy with Fig. 1(c).
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Schematic representation of the structure of straight wall [frames (a) to (e)] and kinked-wall [frames (f) to (o)] etch pits as they develop with etching time. The left column represents the initial situation before etching. The level of the original surface before etching is indicated by dashed horizontal lines in snapshots taken later during progressive etching (from left to right). The solid and dashed slanted lines indicate a present dislocation line and the position of a vanished dislocation line, respectively, while black dots and dashed circles indicate present and vanished localized defects. [(a)–(e)] Structure of an eccentric pointed etch pit caused by a dislocation breaking through the surface. [(f)–(j)] Structure of an eccentric flat pit caused by the combination of a dislocation and a localized defect. [(k)–(o)] Structure of a centric flat pit caused by a localized defect.
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