Journal of Crystal Growth 291 (2006) 340–347 In-plane and out-of-plane lattice parameters of [1 1 n] epitaxial strained layers A. Navarro-Quezada, A.G. Rodrı´guez à , M.A. Vidal, H. Navarro-Contreras Instituto de Investigacio´n en Comunicacio´n O ´ ptica (IICO), Universidad Auto´noma de San Luis Potosı´, A ´ lvaro Obrego´n 64, San Luis Potosı´, S L P 78000, Me´xico Received 14 July 2005; received in revised form 15 March 2006; accepted 21 March 2006 Communicated by M.S. Goorsky Available online 11 May 2006 Abstract A procedure is proposed to determine the in-plane (a || ) and out-of-plane (a ? ) lattice parameters of ½11 n epitaxial cubic strained layers by high resolution X-ray diffraction (HRXRD) rocking curves (RC). The common approach followed to obtain the lattice parameters from asymmetrical diffraction RC of ½001 grown films, is extended to apply it to ½11 n grown layers. Epitaxial pseudomorphic Ge layers were grown on ½001, ½110, ½111, ½112, ½113 and ½114 GaAs substrates to analyze them by HRXRD. Reciprocal space maps (RSM) were also measured to obtain the lattice parameters of these samples. We observe an excellent agreement of the RC and RSM results, which demonstrates the validity of the suggested RC approach. r 2006 Elsevier B.V. All rights reserved. PACS: 61.10.Nz; 68.55.Jk; 81.15.Cd Keywords: A1. High resolution X-ray diffraction; A1. Lattice parameters; A1. Substrates; B1. GeAs 1. Introduction Heteroepitaxy is very important in the technology and science of semiconductors. Many electronic and optoelec- tronic devices have been developed with strained layer heterostructures. To estimate the degree of possible strain relaxation in these heterostructures it is important in particular to know the in-plane (a || ) and out-of-plane (a ? ) lattice parameters of strained layers. These can be precisely determined by high resolution X-ray diffraction (HRXRD), following procedures described elsewhere [1,2]. However, most of the attention has been paid to [0 0 1] grown layers and the equations found in the literature to obtain both a || and a ? from HRXRD rocking curves (RC) are readily applicable only to films grown on substrates with this orientation [1]. On the other hand, the usage of high index orientation substrates is more frequent in heteroepitaxy everyday, as an additional variable that modifies the properties of grown materials. For instance, the formation of InAs and In x Ga 1x As quantum dots is influenced by the orientation of the substrate and many experiments have been carried out on [1 1 7], [1 1 5], [1 1 4], [1 1 3] and [1 1 2] GaAs substrates [3,4]. On the other hand, [1 1 n] grown In- x Ga 1x As/GaAs 1y P y and GaAs 1y P y /GaAs quantum wells have exhibited photoluminescence dependence on growth direction [5,6]. Also, it has been reported the influence of growth direction on the zincblende to diamond transition of (GaAs) 1x (Ge 2 ) x and (GaAs) 1x (Si 2 ) x alloys grown on [1 1 0], [1 1 1], [1 1 2] and on [1 1 3] GaAs [7,8]. Thus, it is very important to follow a systematic procedure, to experimentally determine the lattice parameters of strained layers from HRXRD rocking curves, for other orientations besides [0 0 1]. In this work we present a study of strained Ge layers grown on GaAs. We chose these materials as a model heterostructure system with a lattice mismatch below 0.1%. We grew epitaxial strained Ge layers on [0 0 1], [1 1 0], [1 1 1], [1 1 2], [1 1 3] and [1 1 4] GaAs substrates. The ARTICLE IN PRESS www.elsevier.com/locate/jcrysgro 0022-0248/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2006.03.017 à Corresponding author. Tel.:+52 444 8250183; fax:+52 444 8250198. E-mail address: agabriel@cactus.iico.uaslp.mx (A.G. Rodrı´guez).