Quantitative determination of defocus, thickness and composition from high-resolution transmission electron microscopy lattice images

A quantitative method for the direct determination of defocusΔf, local thickness t and local compositionx from high-resolution transmission electron microscopy lattice images of wedge-shaped crystal samples is proposed. The method relies on the analytically derived relation between the first-order linear and nonlinear image Fourier coefficientsJ1 andJ2 onδf,t andx. By plotting J1 VSJ2 for varying t, ellipses with defocus- and composition-specific geometry are obtained. By reconstructing the appropriate ellipse for image regions of homogeneous composition, Δf and t can be determined independently. At interfaces, local compositionsx can be determined within the full range 0 ≤ x ≤ 1 by utilizing systematic variations of the ellipse's geometry with varyingx.

[1]  Andreas Thust,et al.  Quantitative high-speed matching of high-resolution electron microscopy images , 1992 .

[2]  Peter Schwander,et al.  An approach to quantitative high-resolution transmission electron microscopy of crystalline materials , 1995 .

[3]  H. Bethe Theorie der Beugung von Elektronen an Kristallen , 1928 .

[4]  Geoffrey H. Campbell,et al.  Determination of thickness and defocus by quantitative comparison of experimental and simulated high-resolution images , 1993 .

[5]  Pierre Stadelmann,et al.  EMS-A software package for electron diffraction analysis and HREM image simulation in materials science , 1987 .

[6]  Wolfgang Jäger,et al.  Compositional and structural characterization of SixGe1−x alloys and heterostructures by high-resolution transmission electron microscopy , 1993 .

[7]  W. Jäger,et al.  Compositional and structural characterization of strained Si/SixGe1−x multilayers and interfaces by high-resolution transmission electron microscopy , 1993 .

[8]  Kazuo Ishizuka,et al.  Contrast transfer of crystal images in TEM , 1980 .

[9]  Kim,et al.  Mapping projected potential, interfacial roughness, and composition in general crystalline solids by quantitative transmission electron microscopy. , 1993, Physical review letters.

[10]  John C. H. Spence,et al.  Experimental High-Resolution Electron Microscopy , 1980 .

[11]  A. Fukuhara Many-Ray Approximation in the Dynamical Theory of Electron Diffraction , 1966 .

[12]  P. Fisher The Evaluation of n-Beam Dynamic Electron Diffraction Intensities by Matrix Method , 1968 .

[13]  D. Dyck,et al.  An analytical approach for the fast calculation of dynamical scattering in HRTEM , 1995 .