Crystal growth is a vital and fundamental part of materials science and engineering, since crystals of suitable size and perfection are required for fundamental data acquisition and for practical devices such as integrated circuits.

The word “crystal” comes from the Greek and means “congealed by cold.” The term was originally applied to ice crystals and to crystalline quartz found in such locations as the Alps and thought, at one time, to be some permanently frozen form of water. As a crystallization process, crystal growth extends throughout recorded history—the crystallization of salt from sea water may have preceded pottery-making as the oldest method for controlled phase transformation of materials.

The crystallization of salts such as sodium carbonate was known to the Egyptians, and the process of purification by recrystallization from aqueous solution was described by Greek and Roman writers before the Christian era. The “father” of crystal growth, however, is generally considered to be the English scientist, Robert Boyle, who in 1672 described experiments relating the form of crystals to impurities and changes in growth rate. Boyle believed in the healing powers of crystals, part of the mysticism which has had a strong revival in recent times. We understand that crystals are particularly valued for enhancing the ability of the third eye to perceive auras, but are unable to offer warranted samples.

Recognition as the “founder” of the theory of crystal growth is normally given to the American J. Willard Gibbs, who in 1878 published a seminal work on phase transformations, including a theory of the energy to generate a crystal nucleus and of the equilibrium form of crystals.

The growth of single crystals with precisely controlled properties is one of the most demanding goals of modern materials processing, and its realization depends on the application of fundamentals from solid-state physics, chemistry, thermodynamics, and transport phenomena. Bulk semiconductor substrates and many high-power solid-state laser host materials are typically produced by solidification from the melt. The quality of the crystals produced this way hinges on process conditions which are predominantly determined by the transport of heat, mass, and momentum in the melt and crystal. Accurate modeling of melt crystal growth promises to enhance our understanding of existing systems and improve the design and control of future processes, thereby accelerating the development of advanced materials and devices.

Theoretical modeling is often the only way to probe the complex interactions which characterize melt crystal growth, especially the effects of process changes on internal features of growth that cannot be directly measured on-line, such as the shape of the melt/crystal interface or temperature gradients within the growing crystal. In this way, computer simulation can serve as a design tool for developing control strategies and process innovations. Further, modeling serves as a test-bed for theoretical experiments which extend our knowledge of how fundamental physical phenomena govern the process.

This report attempts to provide a glimpse of how analysis and modeling have impacted the understanding of Czochralski (CZ) crystal growth. The reader is referred to several excellent reviews for more in-depth information regarding melt crystal growth modeling.

From a commercial viewpoint, gallium arsenide (GaAs) is currently the leading member of the III-V compound family. Oriented substrates, cut and polished from single-crystal boules, form the materials foundation for a rapidly maturing technology of high speed and high frequency electronic devices and circuits. The initial thrust of GaAs applications was in high powered lasers and light-emitting diodes (LEDs) fabricated on n-type (Si-doped) GaAs wafers grown by the horizontal Bridgman technique. One of the important benefits of using GaAs is the high electron mobility compared to Si. This property has driven the development of low noise and power field-effect transistors (FETs) for microwave applications. The semi-insulating substrate requirement (>107 Ω-cm) was initially met by chromium doping. Currently, the interest is focused on MMIC (microwave monolithic integrated circuits), MIMIC (millimeter microwave ICs), analog ICs for lightwave transmitters and receivers, and digital ICs. The digital circuits have been realized with ion-implanted FETs, selectively doped heterostructure transistors (SDHTs), and heterostructure bipolar transistors (HBTs). Presently, most of the semi-insulating (SI) material processed by the industry is nominally undoped, and grown by the liquid encapsulated Czochralski (LEC) technique. The SI behavior is attained via a delicate balance of deep EL2 donors and carbon acceptors, avoiding chromium in order to eliminate the anomalous out-diffusion and type-conversion associated with this dopant.

GaAs wafers up to 4 inches in diameter, with electrical properties homogenized by whole ingot annealing, are currently available from U.S. domestic and overseas suppliers. However, the overall quality is compromised by the large dislocation densities, varying 104 – 105/cm2.

Single-crystal fibers represent perhaps one of the most underexplored areas of material science. Despite some early interest and excitement 30 years ago, the lack of immediate applications led to a decline in research activity, and until recently, little was known about their growth behavior and properties. During the past few years single-crystal fiber research has been revived and preliminary results have stimulated considerable interest in the scientific community.

At present, the most extensive and broadly based single-crystal fiber program is at Stanford University, where the focus has been on studying fibers for optical applications. This program emerged from a desire to combine the light-guiding properties of fiber geometries with the unique physical properties of crystalline materials, as was done during the last decade for glass fiber applications. Such materials could lead to a range of novel devices with higher efficiencies than possible in bulk crystals. But single-crystal fiber growth technology may have an even broader applicability. While single-crystal fibers of semiconductor, superconductor, and high strength materials could play an important role in future device applications, an important current use for the single-crystal fiber growth technology is in preparing single crystals of a wide variety of materials for property evaluation. Fiber crystals may have much higher crystalline perfection than bulk crystals of the same composition, making them useful for studying the intrinsic properties of a material and for improving device performance. Other areas of interest which have been identified include metastable phase formation and the growth of oriented ferroic domain and multiphase structures.

The discovery of high temperature superconductivity (HTSC) in oxide compounds has confronted materials scientists with many challenging problems. These include the preparation of ceramic samples with critical current density of about 106 A/cm2 at 77 K and sufficient mechanical strength for large-scale electrotechnical and magnetic applications and the preparation of epitaxial thin films of high structural perfection for electronic devices.

The main interest in the growth of single crystals is for the study of physical phenomena, which will help achieve a theoretical understanding of HTSC. Theorists still do not agree on the fundamental mechanisms of HTSC, and there is a need for good data on relatively defect-free materials in order to test the many models. In addition, the study of the role of defects like twins, grain boundaries, and dislocations in single crystals is important for understanding such parameters as the critical current density. The study of HTSC with single crystals is also expected to be helpful for finding optimum materials for the various applications and hopefully achieving higher values of the superconducting transition temperature Tc than the current maximum of about 125 K. It seems unlikely at present that single crystals will be used in commercial devices, but this possibility cannot be ruled out as crystal size and quality improve.