Nukleation und Evolution unerwünschter Ausscheidungen bei der Wärmebehandlung von Einkristallen

W. Dreyer, F. Duderstadt, On the modelling of semi-insulating GaAs including surface tension and bulk stresses, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences, 464 (2008), pp. 2693-2720.
Abstract
Necessary heat treatment of single crystal semi-insulating Gallium Arsenide (GaAs), which is deployed in micro- and opto- electronic devices, generate undesirable liquid precipitates in the solid phase. The appearance of precipitates is influenced by surface tension at the liquid/solid interface and deviatoric stresses in the solid.
The central quantity for the description of the various aspects of phase transitions is the chemical potential, which can be additively decomposed into a chemical and a mechanical part. In particular the calculation of the mechanical part of the chemical potential is of crucial importance. We determine the chemical potential in the framework of the St. Venant--Kirchhoff law which gives an appropriate stress/strain relation for many solids in the small strain regime. We establish criteria, which allow the correct replacement of the St. Venant--Kirchhoff law by the simpler Hooke law.
The main objectives of this study are: (i) We develop a thermo-mechanical model that describes diffusion and interface motion, which both are strongly influenced by surface tension effects and deviatoric stresses. (ii) We give an overview and outlook on problems that can be posed and solved within the framework of the model. (iii) We calculate non-standard phase diagrams, i.e. those that take into account surface tension and non-deviatoric stresses, for GaAs above 786°C, and we compare the results with classical phase diagrams without these phenomena.

W. Dreyer, F. Duderstadt, M. Naldzhieva, Thermodynamics and kinetic theory of nucleation and the evolution of liquid precipitates in gallium arsenide wafer, Journal of Crystal Growth, 303 (2007), pp. 18-22.

W. Dreyer, F. Duderstadt, On the Becker/Döring theory of nucleation of liquid droplets in solids, Journal of Statistical Physics, 123 (2006), pp. 55--87.

F. Duderstadt, Keimbildung bei Fest-Flüssig-Phasenübergängen von Galliumarsenid, 21. Workshop ``Composite-Forschung in der Mechanik'', December 1 - 3, 2008, Institut für Technische Mechanik, Universität Karlsruhe (TH), Bad Herrenalb, December 2, 2008.

F. Duderstadt, On the growth of the water droplets in wet air, Third Workshop ``Micro-Macro Modelling and Simulation of Liquid-Vapour Flows'', January 24 - 25, 2008, Centre National de la Recherche Scientifique, Strasbourg, France, January 23, 2008.

F. Duderstadt, Ein Becker-Döring-Modell zur Entstehung von Ausscheidungen in GaAs, 7. Kinetikseminar der DGKK, February 14 - 15, 2006, Max-Planck-Institut für Mikrostrukturphysik, Halle, February 14, 2006.

F. Duderstadt, Diffusion in der festen GaAs-Umgebung eines flüssigen As-Prezipitats --- Modellierung unter Berücksichtigung des inhomogenen mechanischen Spannungsfeldes, DGKK Arbeitskreis Angewandte Simulation in der Kristallzüchtung, November 2 - 4, 2005, Deutsche Gesellschaft für Kristallwachstum und Kristallzüchtung e.V., Heigenbrücken, November 3, 2005.