Modeling Semiconductor Crystal Growth Under Electromagnetic Fields
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Growth of semiconductor single crystals under electric and magnetic fields is of interest to increase and better control of crystal growth rate, to suppress and control the adverse effect of natural convection and to obtain better mixing in the growth melt (liquid solution) for better crystal uniformity, which all are favorable conditions for a prolonged growth of high quality crystals. To this end, in parallel to well-designed experiments, modeling is essential to shed light on various aspects of these growth processes and also to better understand the transport phenomena involved. In this article the models developed over the years, mostly based on Professor Gerard Maugin’s well-known contributions to “electromagnetic interactions”, are briefly presented for “solution growth” conducted under electric and magnetic fields. Basic and constitutive equations of a binary electromagnetic continuum mixture are specialized for two important solution growth techniques—Liquid Phase Electroepitaxy (LPEE) and Travelling Heater Method (THM). As an application, an LPEE growth of GaAs bulk crystals under a strong static magnetic field is considered. Experimental results, that have shown that the growth rate under an applied static magnetic field is also proportional to the applied magnetic field and increases with the field intensity level, are predicted from these models. The contribution of a third-order material constant in LPEE is also predicted from these models. The prediction of increasing growth rate in THM growth under rotating magnetic fields from modeling was verified by experiments.
The financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canada Research Chairs (CRC) Program is gratefully acknowledged.
- 1.Eringen, A.C., Maugin, G.A.: Electrodynamics of Continua, vol. I and II. Springer, New York (1989)Google Scholar
- 2.Bowen, R.M.: Theory of mixtures. In: Eringen, A.C. (ed.) Continuum Physics, vol. 3, pp. 1–127. Academic Press, New YorkGoogle Scholar
- 10.Baumgartl, J., Muller, G.: Calculation of the effects of magnetic field damping on fluid flow: comparison of magnetohydrodynamic models of different complexity. In: Proceedings of the VIIIth Enropean Symposium on Materials and Fluid Sciences in Microgravity, Noordwijk, The Netherlands, pp. 161–164 (1992)Google Scholar
- 12.Salk, M., Lexow, B., Benz, K.W., et al.: CdTe crystal growth in the soviet facility ZONA 4. Microgravity Sci. Technol. 6, 88 (1993)Google Scholar
- 13.Hurle, D.T.J. (ed.): Handbook of Crystal Growth 2: Bulk crystal growth, Part B: Growth Mechanisms and Dynamics, North-Holland (1994)Google Scholar
- 14.Oshima, M., Taniguchi, N., Kobayashi, T.: Numerical investigation of 3-dimensional melt convection with the magnetic Czochralski method. J. Crystal Growth 137, 48–53 (1994)Google Scholar
- 23.Qin, Z., Dost, S.: A model for liquid phase electroepitaxial growth of ternary alloy semiconductors. Int. J. Electromagnet. Mech. 7(2), 129–142 (1996)Google Scholar
- 29.Dost, S.: Numerical simulation of liquid phase electroepitaxial growth of GaInAs under magnetic field. ARI-the Bull. ITU 51, 235–246 (1999)Google Scholar
- 31.Dost, S., Sheibani, H.: In Mechanics of Electromagnetic Materials and Structures in Studies in Appl. Electr. Mech., (Eds. J.S. Yang, G.A. Maugin), 19, pp. 17–29. IOS Press, Amsterdam (2000)Google Scholar
- 38.Liu, Y.C., Sheibani, H., Sakai, S., Okano, Y., Dost, S.: In: Kleijn, C.R., Kawano, S. (eds.) Computational Technologies for Fluid/Thermal/Structural/Chemical Systems with Industrial Applications. ASME Proceedings, New York, PVP-vol. 448-1, pp. 65–72 (2002). ISBN: 0-7918-4659-8Google Scholar
- 45.Liu, Y.C., Dost, S., Sheibani, H.: A three dimensional numerical simulation for the transport structures in liquid phase electroepitaxy under applied magnetic field. Int. J. Transp. Phenom. 6, 51–62 (2004)Google Scholar
- 59.Minakuchi, H., Okano, Y., Dost, S.: A three dimensional numerical study of marangoni convection in a floating full zone. In: Dost, S. (ed.) Crystal Growth of Semiconductor from the Liquid Phase. IJMPT 22(1/2/3), 151–171 (2005)Google Scholar