Crystal thickness and extinction distance determination using energy filtered CBED pattern intensity measurement and dynamical diffraction theory fitting

A new method for measuring thickness and extinction distance of single crys tals based on computed adjustment of measured and calculated CBED pattern i ntensity profiles is presented and discussed. The experimental beam intensi ty distribution is measured from an energy filtered CBED pattern recorded o n a CCD camera, The calculated profile is based on dynamical diffraction th eory, and with the two-beam approximation the analytical expression contain s only two free parameters: specimen thickness t and extinction distance xi (g). Parameter refinement through minimization of the difference between e xperimental and calculated intensity profiles is carried out using Origin ( TM) 5.0 software from Microcal, The iterative procedure always converges to a unique solution in a few seconds, yielding an accurate value for both th ickness and extinction distance, The method is extensively tested on silico n using the(004) Bragg reflection. On specimens in the usual TEM thickness range, the method gives result similar to the conventional (P.M. Kelly et a i., Phys. Stat. Sol. A31 (1975) 771; S.M. Alien, Philos. Mag. A 43 (1981) 3 25) graphical methods, both based on the measurement of fringe spacing. Mor eover, it is shown that the calculation matches perfectly both the position s of the minimums and maximums as well as the amplitude of maximums. For an y single intensity profile, specimen thickness and extinction distance can be determined with a precision of about 0.2%. A statistical comparison of o ur method with the Kelly and Alien techniques, based on more than 50 experi ments, shows an improvement in measured extinction distance dispersion. Usi ng 197 keV electrons, and liquid-nitrogen cryo-holder. the new technique yi elds an experimental value of 161 +/- 3 nm for the extinction distance for silicon with the (004) Bragg reflection. The equivalent tabulated value at 0 K is about 156 nm. Using the Kelly and Alien methods, the extinction dist ance is found to be 162 +/- 6 nm. The improvement in precision is a direct consequence of matching the intensity profile envelope, which contains info rmation on the extinction distance. Also the accuracy of thickness determin ation is improved and is around 0.5 to 1% for common specimen thickness. Th e minimum measurable sample thickness is shown to be two to three times thi nner than with the Kelly and Alien methods (0.3 xi (g) as opposed to 0.8 xi (g)). With no independent calculation of the extinction distance needed, t he method is also applicable on unknown crystals. The method is fast, simpl e and can be easily automated. (C) 2001 Elsevier Science B,V. All rights re served.