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The growth of crystals, which can occur by natural or artificial processes. Crystal growth generally comes about by means of the following processes occurring in series: (1) diffusion of the atoms (or molecules, in the case of molecular crystals such as hydrocarbons or polymers) of the crystallizing substance through the surrounding environment (or solution) to the surface of the crystal, (2) diffusion of these atoms over the surface of the crystal to special sites on the surface, (3) incorporation of atoms into the crystal at these sites, and (4) diffusion of the heat of crystallization away from the crystal surface. The rate of crystal growth may be limited by any of these four steps. The initial formation of the centers from which crystal growth proceeds is known as nucleation.
During its growth into a fluid phase, a crystal often develops and maintains a definite polyhedral form which may reflect the characteristic symmetry of the microscopic pattern of atomic arrangement in the crystal. The bounding faces of this form are those which are perpendicular to the directions of slowest growth. How this comes about is illustrated in Fig. 1, in which it is seen that the faces b, normal to the faster-growing direction, disappear, and the faces a, normal to the slower-growing directions, become predominant. Growth forms, like that shown, are not necessarily equilibrium forms, but they are likely to be most regular when the departures from equilibrium are not large. See Crystal structure
The atomic binding sites on the surface of a crystal can be of several kinds. Thus an atom must be more weakly bound on a perfectly developed plane of atoms at the crystal surface (site A) than at a ledge formed by an incomplete plane one atom thick (site B). Atom A binds with only three neighboring atoms, whereas atom B binds to five neighbors. (An atom in the middle of the island monolayer has bonds with nine neighbors.) Therefore, the binding of atoms in an island monolayer on the crystal surface will be less per atom than it would be within a completed surface layer.
The potential energy of a crystal is most likely to be minimum in forms containing the fewest possible ledge sites. This means that, in a regime of regular crystal growth, dilute fluid, and moderate departure from equilibrium, the crystal faces of the growth form are likely to be densely packed and atomically smooth. There will be a critical size of monolayer, which will be a decreasing function of supersaturation, such that all monolayers smaller than the critical size tend to shrink out of existence, and those which are larger will grow to a complete layer. The critical monolayers form by a fluctuation process. Kinetic analyses indicate that the probability of critical fluctuations is so small that in finite systems perfect crystals will not grow, except at substantial departures from equilibrium. That, in ordinary experience, finite crystals do grow in a regular regime only at infinitesimal departures from equilibrium is explained by the screw dislocation theory. According to this theory, growth is sustained by indestructible surface ledges which result from the emergence of screw dislocations in the crystal face. See Crystal defects
When the departures from equilibrium (supersaturation or undercooling) are sufficiently large, the more regular growth shapes become unstable and cellular (grasslike) or dendritic (treelike) morphologies develop. Essentially, the development of protuberances on an initially regular crystal permits more efficient removal of latent heat or of impurities, but at the cost of higher interfacial area and the associated excess surface energy. When the supersaturation becomes so great that the energy associated with the increase in interfacial area is unimportant, protuberances proliferate and the crystal grows in a multibranched form that is even more complicated; its shape is characterized by fractal geometry. See Fractals
The advent of semiconductor-based technology generated a demand for large, high-quality single crystals, not only of semiconductors but also of associated electronic materials. With increasing sophistication of semiconductor devices, an added degree of freedom in materials properties was obtained by varying the composition of major components of the semiconductor crystal over very short distances. Thin, multilayered single-crystal structures, and even structures that vary in composition both normal and lateral to the growth direction, are often required.
Bulk single crystals are usually grown from a liquid phase. The liquid may have approximately the same composition as the solid; it may be a solution consisting primarily of one component of the crystal; or it may be a solution whose solvent constitutes at most a minor fraction of the crystal's composition. The most important bulk crystal growth technique is the crystal-pulling or Czochralski method, in which a rotating seed crystal is dipped into the melt (Fig. 2). Rotation reduces radial temperature gradients, and slow withdrawal of the rotating seed results in growth of a cylinder of single-crystal material. Crystal diameter and length depend upon the details of the temperature and pulling rate, and the dimensions of the melt container. Crystal quality depends very critically upon minimization of temperature gradients that enhance the formation of dislocations. Pulled silicon crystals 6 in. (15 cm) in diameter are important for the semiconductor industry. Ruby, sapphire, and group 13–15 compound semiconductor crystals are among the many crystals that are routinely grown by the Czochralski technique.
The evolution of methods for the growth of very thin but very high-quality epitaxial layers has resulted largely from the need for such layers of semiconductors and magnetic garnets. The technique most closely related to the methods used for bulk crystal growth is liquid-phase epitaxy. For a typical binary semiconductor, growth is done onto a substrate single-crystal wafer from a solution rich in the component with the lowest partial pressure. For a binary compound, the grown layers may differ only in impurity concentrations to modify their electrical characteristics. More often, multilayered structures with layers differing in major component composition but having the same crystal structure and lattice parameter are required. The simplest example of liquid-phase epitaxy with major composition changes in layers is the growth of layers of aluminum gallium arsenide (AlxGa1-xAs; 1 > x > 0) on a gallium arsenide (GaAs) substrate.
Growth by liquid-phase epitaxy is done in an apparatus in which the substrate wafer is sequentially brought into contact with solutions that are at the desired compositions and may be supersaturated or cooled to achieve growth. For crystalline solid solutions other than AlxGa1-xAs, very precise control over solution compositions is required to achieve a lattice match. Typically, structures grown by liquid-phase epitaxy have four to six layers ranging widely in composition and having thickness from 10-7 to 10-6 m.
The desirability of highly reproducible growth and even thinner epitaxial layers of 13–15 compounds on large wafer areas has led to the development of molecular-beam epitaxy and several forms of chemical-vapor deposition. Molecular-beam epitaxy is an ultrahigh-vacuum technique in which beams of atoms or molecules of the constituent elements of the crystal provided by heated effusion ovens, impinge upon a heated substrate crystal. It has been used for epitaxial layers as thin as 0.5 nanometer. Molecular-beam epitaxy has also been used for group 12–16 compounds and for silicon. See Artificially layered structures, Molecular beams, Semiconductor, Semiconductor heterostructures