Analysis of strain in sub-grains with variable misorientation in GaN epilayers by digital processing of HRTEM images
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Analysis of strain in sub-grains with variable misorientation in GaN epilayers by digital processing of HRTEM images. S.Kret*, P.Ruterana, J. Chen, and G.Nouet ESCTM-CRISMAT UMR 6508 CNRS-ISMRA, 6 Boulevard du Maréchal Juin, 14050 CAEN Cedex, France. * Permanent address: Institute of Physics, Polish Academy of Sciences , Al. Lotników 32/46, 02-668 Warszawa , Poland ABSTRACT In epitaxial GaN layers on (0001) sapphire, the distance between edge dislocations in subgrain boundaries is variable. The strain state in such sub-grains is quantitatively measured by processing of HRTEM images. The dislocation core distribution maps and in plane Burgers vectors components are derived from experimental strain tensor by applying the continuum dislocation theorem. For image simulations the atomic models of edge dislocations are calculated using a modified Stillinger-Weber potential. It is shown that the strain field extracted from simulated images matches that from experimental ones. The corresponding dislocation density peaks are larger and more splitted than those from simulated images. INTRODUCTION The knowledge of local strain fields associated with defects is important for understanding and modelling the properties of semiconductor devices, as well as for optimizing the growth of heterostructures. This is particularly necessary in GaN based heterostructures where the density of defects is very high. The interference maxima of high resolution electron microscopy images give information about atomic positions in deformed crystals. Image processing and image simulations help to extract quantitative information. In the case of the strain field around a defect, one useful technique of image processing is the “geometric phase method” proposed by Hytch et al. [1]. This method is free from topological problems in crystals with defects. The dislocation core distribution measurement can be applied to determine the dislocation core type and Burgers vectors in automatic way[2] . In this work we determine the strain fields in subgrains present in GaN layers grown on (0001) sapphire. EXPERIMENTAL DETAILS The planar-view TEM samples of GaN epilayers on sapphire substrate were prepared in the conventional way by mechanical polishing followed by ion milling. HRTEM was carried out on a Topcon 002B microscope operating at 200KV, with a point resolution of 0.18nm. The HRTEM images were formed by using 01 1 0 diffracted beams, with a weak contribution of 11 20 ones. The images were recorded on photographic films and digitized by sampling of 0.15 Å/pixel with 8bits dynamic. Processing of experimental and simulated images was performed using routines written in ALI (Analytical Language for Images) of Optimas graphical environment [3]. In our procedure, the phase images Pgi ( z1 , z2 ) are calculated for 10 1 0 , 01 1 0 or 1 1 00 lattice periodicities.
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The local co-ordinate system is chosen for each dislocation : z1 and z 2 axes are respectively parallel and perpendicular to the Burgers vector and z 3 is perpendicular to image plane. The
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