This topic is currently not treated at the WIAS.Before further processing for application in opto-electronic devices, single crystal GaAs wafer must be heat treated. However, arsenic-rich GaAs with a composition corresponding to the congruent melting point, exhibits unwanted arsenic precipitations during the heat treatment.
The technological problem appears because the wafer passes through a critical temperature range during heating from room temperature to the operating temperature of the heat treatment. In that range there exist are stable equilibrium between the solid and the liquid arsenic-rich phase. After crossing the line of retrograde solubility, the liquid phase is no more stable. In this regime, that starts at the line of retrograde solubility and ends below the congruent melting point, the heat treatment is carried out.
In the critical range, GaAs without precipitations exists in a supersaturated state, where homogeneous and heterogeneous nucleation of a liquid phase is possible. If the randomly arising nuclei exceed a critical size the growth of liquid precipitates sets in. If the liquid precipitates are not completely dissolved during the heat treatment, or if new nuclei appear during subsequent cooling, the liquid precipitates freeze to solid arsenic-rich precipitates in the wafer during further cooling. While heterogeneous nucleation takes place in the very neighborhood of dislocation rings, homogeneous nucleation becomes possible in its dislocation-free interior.
The nucleation models that are developed in the research group Thermodynamic Modeling and Analysis of Phase Transitions concern the following questions: (i) Does nucleation occur during the heating phase? (ii) Does the precipitates completely dissolve during the holding time? (iii) Does new nucleation occur during the subsequent cooling? Furthermore the growth process in supersaturated GaAs within the heat treated range is mathematically analyzed with different evolution models.
In addition to surface tension and the entropy of mixing of clusters of precipitates, the nucleation models include deviatoric mechanical stresses in the solid vicinity of the liquid precipitates. Moreover the models accounts for the mixing character of the single phases. The deviatoric stresses are due to a liquid-solid misfit situation, which is induced by different densities of the involved phases.
There are evolution models for a single precipitate in setting of sharp interface models . These models serve to clarify whether the two limiting cases diffusion controlled and interface controlled growth, respectively are met during heating, holding and cooling. In addition the evolution of many precipitates is studied in the setting of a so-called mean-field model.
Articles in Refereed Journals
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.
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.