Ultramicroscopy 107 (2007) 1186–1193 The Peak Pairs algorithm for strain mapping from HRTEM images Pedro L. Galindo a,Ã ,S"awomir Kret b , Ana M. Sanchez c , Jean-Yves Laval d , Andre´s Ya´n˜ez a , Joaquı´n Pizarro a , Elisa Guerrero a , Teresa Ben c , Sergio I. Molina c a Departamento de Lenguajes y Sistemas Informa´ticos, CASEM, Universidad de Ca´diz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz, Spain b Institute of Physics, PAS, AL. Lotniko ´w 32/46, 02-668 Warszawa, Poland c Departamento de Ciencia de los Materiales e Ing. Metalu´rgica y Q. Inorga´nica, Facultad de Ciencias, Universidad de Ca´diz, Pol. Rio San Pedro s/n. 11510, Puerto Real, Cadiz, Spain d Laboratoire de Physique du Solide, UPR5 CNRS-ESPCI, Paris, France Received 6 July 2006; received in revised form 18 January 2007; accepted 31 January 2007 Abstract Strain mapping is defined as a numerical image-processing technique that measures the local shifts of image details around a crystal defect with respect to the ideal, defect-free, positions in the bulk. Algorithms to map elastic strains from high-resolution transmission electron microscopy (HRTEM) images may be classified into two categories: those based on the detection of peaks of intensity in real space and the Geometric Phase approach, calculated in Fourier space. In this paper, we discuss both categories and propose an alternative real space algorithm (Peak Pairs) based on the detection of pairs of intensity maxima in an affine transformed space dependent on the reference area. In spite of the fact that it is a real space approach, the Peak Pairs algorithm exhibits good behaviour at heavily distorted defect cores, e.g. interfaces and dislocations. Quantitative results are reported from experiments to determine local strain in different types of semiconductor heterostructures. r 2007 Elsevier B.V. All rights reserved. PACS: 68.37.d; 68.55.a Keywords: Strain mapping; High-resolution transmission electron microscopy (HRTEM); Data processing/image processing 1. Introduction Due to the increasing importance of the quantitative stress and strain measurements at atomic scale, a large amount of research has been carried out to speed up techniques over the last decade. The development of nanotechnology has been stimulated by the microelectro- nics industry, which has pursued the optimisation and miniaturisation of devices. Since the device properties depend on composition control in three dimensions, the structural characterisation by high-resolution transmission electron microscopy (HRTEM) constitutes a potential breakthrough to optimise heteroepitaxial systems, allowing quantitative measurements at subnanometric level. Recent advances in digital imaging and image-processing techniques, together with improved point-to-point resolution of microscopes have offered the possibility of locally determining the elastic strain of materials at subnanometric scale using HRTEM images. However, the reliability of strain mapping determination relies on the assumption of a constant spatial relationship between the intensity maxima in the HRTEM micrograph and the relative positions of the atomic columns in the specimen. Due to some known effects, such as thin foil relaxation, local crystal tilts and thickness and/or composition variation across the material, the reliability of these strain measurements is somewhat problematical [1,2]. A detailed analysis of the impact of such effects on the accuracy of lattice-distortion analysis in the case of the ARTICLE IN PRESS www.elsevier.com/locate/ultramic 0304-3991/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2007.01.019 Ã Corresponding author. Tel.: +34 956 016434; fax: +34 956 016437. E-mail address: pedro.galindo@uca.es (P.L. Galindo).