Inverse-Computation Design of a SiC Bulk Crystal Growth System
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Inverse-Computation Design of a SiC Bulk Crystal Growth System Alexey V. Kulik a), Svetlana E. Demina a), Sergey K. Kochuguev a), Dmitry Kh. Ofengeim a), Sergey Yu. Karpov a), Andrey N. Vorob’ev a), Maxim V. Bogdanov a), Mark S. Ramm b), Alexander I. Zhmakin b), Anna A. Alonso c), Sergey G. Gurevich c), Yuri N. Makarov d) a) Soft-Impact Ltd., P.O.Box 33, 194156, St.Petersburg, Russia. b) A.F.Ioffe Physical-Technical Institute, Russian Academy of Sciences, St.Petersburg, Russia. c) High Frequency Current Institute, St.Petersburg, Russia. d) Semiconductor Technology Research Corporation, Richmond, VA, U.S.A.
ABSTRACT Inverse modeling was applied to the optimization of a crucible design for SiC sublimation growth. We found a crucible shape providing the optimal temperature distribution in terms of the powder source stability during long-term operation and of the convex crystal shape. Considerable improvement of temperature uniformity throughout the powder charge was achieved. The results obtained show selective sensitivity of the thermal field inside the crucible to modification of the crucible design. The inverse problem approach is easy-to-adapt to various optimization criteria and seems to be especially effective in the case of multi-factor optimization. INTRODUCTION Silicon carbide is one of the most promising semiconductors for fabrication of high power and high temperature electronic devices. Nowadays, production of SiC devices is restricted by lack of SiC wafers with low dislocation and micropipe densities. The wafers are commonly grown by sublimation technique being constantly improved by a proper equipment design and growth optimization. However, experimental trial-and-error approach based for the most part on the intuition and experience of growth engineers is normally time-consuming, expensive and ineffective in multi-factor optimization. Along with the experiment, modeling is found to be a powerful tool to improve the equipment and growth conditions [1,2,3]. Generally, direct simulation is used for optimization of the temperature distribution in the growth crucible. For this, coupled heat and mass transport is analyzed for various conditions and growth system geometries [4]. On the other hand, there is an alternative way of numerical optimization based on the inverse problem solution [5,6]. The inverse computations provide a system design and/or process parameters best of all fitting specified requirements for the temperature distribution and/or other factors of growth. We distinguish two subjects of optimization − (i) growth conditions that can be varied in time and (ii) growth system design. Normally, a grower controls many parameters to get the best quality of the grown SiC crystal: the gas pressure in the growth chamber, the heater power (if a resistively heated system is used), the position and power of inductor coil (if an inductively heated system is employed). The task-oriented manipulation of the operating conditions can be optimized by using, for instance, the optimal control theory [7,8]. In thi
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