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Asymmetric X‐ray Bragg reflexion and shallow strain distribution in silicon single crystals
Author(s) -
Fukuhara A.,
Takano Y.
Publication year - 1977
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889877013508
Subject(s) - asymmetry , collimated light , diffractometer , crystal (programming language) , optics , materials science , bragg's law , silicon , single crystal , resolution (logic) , wafer , crystallography , geometry , molecular physics , physics , chemistry , crystal structure , laser , diffraction , programming language , mathematics , quantum mechanics , artificial intelligence , computer science , metallurgy , nanotechnology
Criteria are given for making use of an asymmetric Bragg reflection of X‐rays to analyse a shallow strain distribution near a crystal surface. The shallowness and the resolution of the strain impose opposing conditions on the asymmetry: extreme asymmetry favours the observation of shallow layers but symmetric reflection gives better resolution of the strain. As an example of a compromise, the 422 reflection of Cu K α 1 X‐rays was selected for the strain determination in a (100) Si wafer prepared so as to contain phosphorus diffusion. The rocking curve recorded with a triple‐crystal diffractometer (angular spread of the collimated X‐rays 0.1′′) showed fine agreement with the theoretical curve computed from a strain distribution: its surface value is −4.3 × 10 −4 and the depth at which the value is one‐tenth of the original is 1 μm. The distribution profile was assumed to be proportional to that of the phosphorus concentration, which was measured separately; the latter surface value was 1.4 × 10 20 atoms cm −3 . The proportionality coefficient estimated here, 3.0 7 × 10 −24 , was 1.7 9 times the coefficient for uniform doping; this multiplication factor can be explained in terms of elastic stiffness coefficients. Thus it was confirmed that X‐ray rocking curves are effective tools for strain determination even at such depth and magnitude of strain and that proportionality still holds between strain and phosphorus distributions with a coefficient depending on crystal orientation.