Solid-phase epitaxial regrowth of fine-grain polycrystalline silicon
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I. INTRODUCTION A. Hardness anisotropy It is well known that the measured hardness of single crystal materials can vary with the orientation of the indenter relative to the material's crystallographic axes, particularly when the indenter is of low symmetry (as is the Knoop indenter). The form of the hardness anisotropy is characteristic of the material's active slip systems, the face indented and the shape of the indenter, and various models exist for its prediction. U4 Such models have been used to determine the active slip systems in crystals, and can be particularly useful for hard, brittle solids where microhardness testing is virtually the only means of inducing controllable plastic flow at low temperatures.5"7 Models of the types used in Refs. 1-5 relate the measured hardness at a particular orientation to the inverse of the resolved shear stress applied by each of the indenter facets to the active slip systems, with additional terms to allow for the constraints on flow directions imposed by the presence of the indenter. Any possible variation of workhardening rates with orientation are neglected. These "Effective Resolved Shear Stress" (ERSS) models assume a stress state equivalent to tension along the line of greatest slope in an indenter facet, compression normal to this direction, or some other simplified stress field. ERSS models predict the same variation of hardness with orientation for all materials with the same slip systems, regardless of bonding type, temperature, etc. In fact, considerable variations in hardness anisotropy are found even for materials which are apparently very similar, such as LiF and MgO1 (both ionic crystals of the same crystal structure, slipping on {110} ( l l o ) ) . Here, although the hard and soft directions on the two materials are the same (and are as predicted by the
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J. Mater. Res. 1 (1), Jan/Feb 1986
http://journals.cambridge.org
ERSS model), the variation in hardness is —10% for LiF and ~ 100% for MgO at room temperature. In a previous paper,8 it was shown that the polarity in hardness (i.e., difference in hardness between {hkl} and {hkl} faces) in GaAs on {111} faces can be explained in terms of the amount of slip occurring on diverging slip planes (with low workhardening rates) around the indentation and the different dislocation types active on these planes (see Sec. I C). The object of this paper is to examine whether the anisotropy of hardness is due to a similar effect, i.e., an orientation dependence of the amount of slip on slip planes with low workhardening rates. We present results that show considerable variations in the hardness anisotropy of germanium and gallium arsenide with temperature and doping. These variations are consistent with the known effects, in these materials, of temperature and doping on dislocation mobility,9'10 hardness and indentation dislocation rosette behavior11""13 (see below), and they are used to test the applicability of a proposed new model. B. Effects of doping on dislocation motion It has been known for some time that the
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