Journal of Crystal Growth, Vol.252, No.1-3, 92-101, 2003
A visco-plastic model of the deformation of InP during LEC growth taking into account dislocation annihilation
In order to determine which region is the major source of the dislocations which will be present in an LEC grown InP single crystal, a model of dislocation generation in InP has been designed and numerically solved in the actual growth parameters and geometry. The Haasen model of dislocation generation has been improved by projection of the mechanical stresses on the glide planes. This permits to take independently into account the interaction of dislocations situated in the same plane and in different planes (following works by Sumino). An important mechanism, acting principally at high temperatures, is the annihilation of dislocations by pairs. In the proposed model, the associated decrease of dislocation density is proportional to the square of the density of dislocations and of their velocity. The model has been solved numerically with the help of the finite element software MARC(R). It has been validated by comparison with deformation tests at high temperature and the annihilation mechanism permits to explain the fully plastic behaviour of InP above 1250 K. In a second step, this numerical model is interfaced with a global fully time-dependent modelling of heat transfer in the furnace. The model is adjusted by fitting the coefficient of dislocation annihilation in order to get the experimental number of dislocations in the first wafer of the reference crystal. The evolution of dislocation density with time, for a given location in the crystal, can therefore be predicted and is in good agreement, axially and radially, with experimental results. It is shown that dislocations situated in the centre of the crystal are generated close to the solid-liquid interface and that peripheral dislocations, which are the most detrimental, are generated at the surface of the encapsulant. (C) 2003 Elsevier Science B.V. All rights reserved.
Keywords:computer simulation;line defects;stresses;liquid encapsulated Czochralski method;phosphides