Measurement of small elastic strains in silicon using electron channeling patterns
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A silicon single-crystal slab 0.15 mm in thickness was bent to produce small, nonuniform surface strains of the order of 0.2%. The electron channeling patterns were observed in a JSM 840 SEM (scanning electron microscope) at an accelerating voltage close to 25 kV. Proper choice of the triangles formed by intersecting channeling lines of zero-order and of higher-order Laue zones allows one to measure the changes in their dimensions caused by imposed strain. It was estimated that the lower limit of detectable elastic strain is close to 0.1 %. The possibilities of using this method for estimation of the average elastic strains in thin epitaxial layers are discussed.
I. INTRODUCTION The application of a divergent beam of radiation for accurately measuring a crystal lattice parameter or its changes under the influence of various treatments dates back to the work of Kossel.' Lonsdale2 estimated the accuracy of lattice parameter determination as being close to 5 X 10~ 6 nm when intersections of Kossel lines were used. Later on, an analogous method was applied by H0ier3 to the intersections of Kikuchi lines. Here the accuracy of the (electron wavelength)/(lattice parameter) ratio determination was estimated to be close to 0.1 %. A similar method has been used by Olsen4 to measure lattice parameters in low symmetry crystals. Convergent-beam electron diffraction has also been used recently for the measurement of small changes in lattice parameter at interfaces by Ecob et al.5 and by Kaufman et al.6 There have also been several attempts to use electron channeling patterns (ECP's) for the measurements of small elastic strains. Schulson7 used electron channeling lines from silicon crystals to measure the accelerating voltage in a scanning electron microscope (SEM). His estimate of the accuracy of high-voltage measurements was 1.5%. Booker etal.s described essentially the same experiment with a bent silicon slab, as is reported in this article, but were unable to detect changes in the ECP, except some broadening of the lines. Later, Davidson9 did use the changes in width of the channeling bands to measure the elastic strains and detected strains as low as 0.8% in an aluminum alloy. In his review10 of the ECP technique in studying material deformation, he pointed out that the accuracy attainable with x rays in determination of small elastic strains is impossible to obtain with the ECP technique. However, some changes a)
b)
Present address: Institute of Materials Science, Warsaw University of Technology. N a r b u t t a 85, 02-524 Warsaw, Poland. M C N E M T , Pulaskiego 6 / 1 0 , 26-600 R a d o m , Poland.
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J. Mater. Res. 3 (4), Jul/Aug 1988
http://journals.cambridge.org
in channeling band widths are detectable if the change of interplanar spacings is large (close to 1%). Analysis of higher-order Laue zone lines (HOLZ) in channeling patterns given by Vicario et al.'' and recently by Madden and Hren, 12 indicated that the positions of these lines are more sensitive to changes in the lattice parameter. With this technique
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