Cryst. Res. Technol. 42, No. 3, 300 – 311 (2007) / DOI 10.1002/crat.200610817 © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetry K. Böttcher* 1 and K. A. Cliffe 2 1 Institute for Crystal Growth (in the Forschungsverbund Berlin e.V.), Max-Born-Str. 2, 12489 Berlin, Germany 2 School of Mathematical Sciences, Nottingham University, University Park, Nottingham NG7 2RD, United Kingdom Received 28 September 2006, accepted 20 October 2006 Published online 10 February 2007 Key words thermoelastic stresses, hexagonal crystal symmetry, off-axis orientation, Fourier Finite Element Method. PACS 02.60.Cb, 02.70.Dh, 46.25.Hf A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle φ of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction The evaluation of thermoelastic stresses is a very important topic in several branches of single crystal growth. In many cases the crystal growth process is a solidification from melt or solution or gas phase which occurs in most cases at rather high temperatures. In order to drive the crystal growth process, a definite temperature gradient normal to the growth interface needs to be established. Additionally, certain temperature gradients arise in any coordinate directions due to heater arrangements in typical crystal growth furnaces. In the end the crystal experiences a temperature field with gradients. Many crystal growth techniques are applied in axisymmetric furnaces and the temperature field is tried to be configured as axisymmetric as possible, too. In that case the temperature field will have gradients at least in axial and radial direction. Axisymmetric displacement and stress fields arise in isotropic solids under those conditions. Among solids, which are anisiotropic with respect to elasticity, only crystals with hexagonal lattice symmetry will develop axisymmetric displacement and stress fields, too, provided the c-axis of the crystal system is parallel to the z-axis of the cylindrical coordinate system. Several semiconductor single crystals of currently high scientific and economic interest as gallium nitride (GaN) and silicon carbide (SiC) belong to the hexagonal system. GaN and SiC have a very high figure of merit for high temperature, high power and high frequency applications [1]. Both materials do not melt under reasonable conditions and are preferentially grown only from vapour phase. For GaN a variety of techniques is utilized, among others the hydride vapor phase epitaxy and a sublimation technique [2]. The main growth technology for SiC bulk single crystals is the modified Lely method [3] where the mechanisms of sublimation ____________________ * Corresponding author: e-mail: boettcher@ikz-berlin.de