Melt techniques, crystal growth

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

Redistillation does not gready reduce the impurity level of volatile materials such as magnesium. Volatile alkali metals can be separated from calcium by passing the vapors over refractory oxides such as Ti02, Zr02, or Ci 03 to form the nonvolatile Na and I O (14). Purification techniques include reactive distillation (15), growth of crystals from the melt (16), and combined crystal growth and distillation techniques (17). 

Overview of Unit Operations. To maximize the electron or hole (carrier) mobility and thus device speed, ICs are built in single-crystal substrates. Methods of bulk crystal growth are therefore needed. The most common of these methods are the Czochralski and float-zone techniques. The Czochralski technique is a crystal-pulling or melt-growth method, whereas the float-zone technique involves localized melting of a sintered bar of the material, followed by cooling and, thus, crystallization. 

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. 

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