Melt crystal growth

Many review papers and several books (1-3) have focused on the science and technology of crystal growth. The purpose of this chapter is not to duplicate these works but to focus on the fundamental transport processes that occur in melt crystal growth systems, especially advances in understanding that have occurred during the last decade of vigorous research. The chapter also accentuates the features and research issues that are common to many of the techniques used today in laboratories and industrial production. 

The many technological innovations in melt crystal growth of semiconductor materials all build on the two basic concepts of confined and meniscus-defined crystal growth. Examples of these two systems are shown schematically in Figure 1. Typical semiconductor materials grown by these and other methods are listed in Table I. The discussion in this section focuses on some of the design variables for each of these methods that affect the quality of the product crystal. The remainder of the chapter addresses the relationship between these issues and the transport processes in crystal growth systems. 

Figure 1. Schematic diagrams of several commonly used systems for melt crystal growth of electronic materials (a) vertical Bridgman, (b) Czochralski, and (c) small-scale floating-zone systems.

Figure 3. Three spatial scales for modeling melt crystal growth, as exemplified by the vertical Bridgman system.

The governing equations and boundary conditions for modeling melt crystal growth are described for the CZ growth geometry shown in Figure 6. The equations of motion, continuity, and transport of heat and of a dilute solute are as follows ... 

Other mechanisms for flows in melt crystal growth arise from surface stresses along or the relative motion of the boundaries of the melt. The noslip boundary condition describes the relative motion of a rigid boundary dDhl... 

A major complication in the analysis of convection and segregation in melt crystal growth is the need for simultaneous calculation of the melt-crystal interface shape with the temperature, velocity, and pressure fields. For low growth rates, for which the assumption of local thermal equilibrium is valid, the shape of the solidification interface dDbI is given by the shape of the liquidus curve Tm(c) for the binary phase diagram ... 

Figure 2. Three spatial scales for modeling melt crystal growth, as exemplified by the vertical Bridgman process. From Theory of Transport Processes in Single Crystal Growth from the Melt, by R. A. Brown, AJChE Journal, Vol. 34, No. 6, pp. 881-911, 1988, [29]. Reproduced by permission of the American Institute of Chemical Engineers copyright 1988 AIChE.

In Chapter 6, precipitation from a solvent was discussed. This subject, which includes nucleation and crystal growth, has the same fundamentals as precipitation from the melt. Crystal growth mechanisms are summarized in Table 16.11. These mechanisms include diffusion. 

Chani VI, Boulon G, Zhao W, Yanagida T, Yoshikawa A (2010) Correlation between segregation of rare earth dopants in melt crystal growth and ceramic processing for optical applications. Jpn J Appl Phys 49 075601... 

Keywords. Ice, Surface Melting, Crystal Growth, Intermoleculm forces... 

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