1 The Development of Crystal Growth Technology HANS

The industrial production of crystals started with A. Verneuil with his flamefusion growth method 1902. He can be regarded as the father of crystal growth technology as his principles of nucleation control and crystal-diameter control are adapted in most later growth methods from the melt, like Tammann, Stöber, Bridgman, Czochralski, Kyropoulos, Stockbarger, etc. The important crystal pulling from melts named after Czochralski was effectively developed by Teal, Little and Dash. The multi-disciplinary nature of technology of crystal and epilayer fabrication, the complex multi-parameter processes – where ten or more growth parameters have to be compromised and optimized, and also the scaling problem have impeded the scientific development of this important area. Only recently has the numerical simulation of Czochralski melts started to become useful for growth technologists, the deep understanding of the striation problem allowed the experimental conditions to grow striation-free crystals to be established, and the control of epitaxial growth modes permitted the preparation of atomically flat surfaces and interfaces of importance for the performance of opto-electronic and superconducting devices. Despite the scale of the multi-billion dollar crystal and epilayer fabrication and crystal-machining industry and the annual need worldwide of at least 400 engineers, there is so far no formation of specialists for crystal production, epitaxy technology, crystal machining and surface preparation. A special curriculum is required due to the multi-disciplinary character of crystal-growth technology (CGT) which does not fit into a single classical university discipline like chemical, mechanical, materials, or electrical engineering, or crystallography, thermodynamics, solid-state physics, and surface physics. The education scheme for CGT has to include all these disciplines and basic sciences to such an extent that the finished engineers and scientists are capable of interacting and collaborating with specialists from the various disciplines. It is up to the interested industries to request CGT engineers from the technical universities and engineering schools. Crystal Growth Technology, Edited by H. J. Scheel and T. Fukuda  2003 John Wiley & Sons, Ltd. ISBN: 0-471-49059-8 4 Crystal Growth Technology Crystal-growth technology and epitaxy technology had developed along with the technological development in the 20th century. On the other hand, the rapid advances in microelectronics, in communication technologies, in medical instrumentation, in energy and space technology were only possible after the remarkable progress in fabrication of large, rather perfect crystals and of large-diameter epitaxial layers (epilayers). Further progress in CGT and education of CGT engineers is required for significant contributions to the energy crisis. High-efficiency white light-emitting diodes for energy-saving illumination and photovoltaic/thermo-photovoltaic devices for transforming solar and other radiation energy into electric power with high yield depend on significant advances in crystal growth and epitaxy technology. Also, the dream of laserfusion energy and other novel technologies can only be realized after appropriate progress in the technology of crystal and epilayer fabrication. 1.1 HISTORICAL INTRODUCTION Fundamental aspects of crystal growth had been derived from early crystallization experiments in the 18th and the 19th century (Elwell and Scheel 1975, Scheel 1993). Theoretical understanding started with the development of thermodynamics in the late 19th century (Gibbs, Arrhenius, Van’t Hoff) and with the development of nucleation and crystal growth theories and the increasing understanding of the role of transport phenomena in the 20th century. The phenomena of undercooling and supersaturation and the heat of crystallization were already recognized in the 18th century by Fahrenheit and by Lowitz. The corresponding metastable region, the existence range of undercooled melts and solutions, was measured and defined in 1893/1897 by Ostwald and in 1906 by Miers, whereas the effect of friction on the width of this Ostwald–Miers region was described in 1911 and 1913 by Young. Although the impact of stirring on this metastable region is important in mass crystallization of salt, sugar and many chemicals, it is not yet theoretically understood. The rates of nucleation and crystallization in glasses were the foundation to nucleation theories. The crystal surface with steps and kinks of Kossel in 1927 allowed Stranski and Kaishew in 1934 to define the work of separation of crystal units as repeatable steps as the basis of the first crystal-growth theories. With the understanding of facet formation as a function of the entropy of fusion in 1958 by Jackson, and depending on the density of bonds in the crystal structure 1955 by Hartman and Perdok, the role of screw dislocations as continuous step sources in the formation of growth hillocks (Frank 1949), and with the generalized crystal growth theory of Burton, Cabrera and Frank 1951, many growth phenomena could be explained. In the growth of crystals from a fluid medium (melt, solution, gas phase) the heat and mass transport phenomena also play a significant role, as was observed early by Rouelle 1745 and Frankenheim 1835. The diffusion boundary layer Development of Crystal Growth Technology 5 defined by Noyes and Whitney 1897 was used in the growth-rate equation of Nernst 1904 and confirmed by interferometric measurements of concentration profiles around growing crystals by Berg 1938 and by others. Forced convection was recognized to be beneficial for diffusion-limited growth by Wulff 1886, Krüger and Finke 1910, and Johnsen 1915 for open systems with stirrers, whereas smooth stirring in sealed containers can be achieved with the accelerated crucible rotation technique ACRT of Scheel 1971/1972. The growth of inclusion-free crystals from the melt can be accomplished by observing the principles of “diffusional undercooling” of Ivantsov 1951 and “constitutional supercooling” of Tiller et al. 1953. Formation of inclusions, i.e. growth instability, can be prevented in growth from solutions by sufficient flow against or along the crystal facets: Carlson 1958 developed an empirical theory which was utilized by Scheel and Elwell 1972 to derive the maximum stable growth rate and optimized programming of supersaturation for obtaining large inclusion-free crystals. Microscopic and macroscopic inhomogeneities in doped crystals and in solid solutions are caused by segregation phenomena, which are related to mass and heat transfer. Based on the derivation of effective distribution coefficients for melt growth by Burton et al. (1953) and by van Erk (1982) for growth from solutions, the theoretical and experimental conditions for growth of striation-free crystals could be established (Rytz and Scheel 1982, Scheel and Sommerauer 1983, Scheel and Swendsen 2001). There have been remarkable developments with respect to size and perfection of crystals, with silicon, sapphire, alkali and earth alkali halides reaching diameters up to 0.5 m and weights of nearly 500 kg. These advances in Czochralski, Kyropoulos, heat-exchanger method, and Bridgman–Stockbarger growth were accompanied by numerical simulations which have become increasingly powerful to predict the optimized conditions. However, further advances in computer modelling and in the reliability of the used physico-chemical data are required in order to increase the efficiency and precision of computer simulations and to allow the prediction of the best crystal-growth technology including growth parameters for the growth of new large and relatively perfect crystals. 1.2 THE DEVELOPMENT OF CRYSTAL-GROWTH METHODS Industrial crystal production started with Verneuil 1902 who with the flame-fusion growth process named after him achieved for the first time control of nucleation and thus single crystals of ruby and sapphire with melting points above 2000 ◦C. By formation of the neck and the following enlargement of the crystal diameter, not only was the seed selection achieved in a crucible-free process, but also the structural perfection of the growing crystal could be controlled to some extent. Figure 1.1 shows the stages of Verneuil growth of high-melting oxides, and Figure 1.2 the relatively simple apparatus where powder is fed into the hydrogen–oxygen flame and enters the molten cap of first the cone and neck, and 6 Crystal Growth Technology