Crystal growth process

J. C. Brice, Crystal Growth Processes, John Wiley Sons, Inc., New York, 1986. 

An example of an analysis done on polysilicon and single-crystal Czochralski silicon (CZ) is shown in Table 1. As can be seen, polysilicon, which was used to grow the crystal, is dirtier than the CZ silicon. This is expected, since segregation coefficients limit the incorporation of each element into the crystal boule during the crystal growth process. All values shown in the table are from bulk analysis. Table 2 shows NAA data obtained in an experiment where surface analysis was accom-... 

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. 

Here r is the distance between the centers of two atoms in dimensionless units r = R/a, where R is the actual distance and a defines the effective range of the potential. Uq sets the energy scale of the pair-interaction. A number of crystal growth processes have been investigated by this type of potential, for example [28-31]. An alternative way of calculating solid-liquid interface structures on an atomic level is via classical density-functional methods [32,33]. 

Chapters 15 through 17 are devoted to mathematical modeling of particular systems, namely colloidal suspensions, fluids in contact with semi-permeable membranes, and electrical double layers. Finally, Chapter 18 summarizes recent studies on crystal growth process. 

We have seen that the deposition of crystals from the vapor is much too slow to model by MD techniques. Most laboratory equipment for producing thin films involves relatively slow crystal growth processes, and is not suitable for direct simulation. Information on the stability and properties of thin films can be obtained by similar modeling techniques, however. We describe below some of our results that provide necessary data to find the equilibrium configuration of thin films at low temperatures. 

The process of substituting elements for the silicon is called doping, while the elements are referred to as dopants. The amount of dopant that is required in practical devices is very small, ranging from about 100 dopant atoms per million silicon atoms downward to 1 per billion. Dopants are usualty added to the silicon after the crystal growth process, when an integrated circuit is being formed on the surface of the wafer. 

Secondary nucleation is essentially a crystal growth process. Secondary nucleation occurs by the deposition of a stem of the polymer molecule on a preexisting crystal-face as shown in Figure 15. The overall rate of this process is given by the following expression [58],... 

In the early days of silicon device manufacturing the need for surfaces with a low defect density led to the development of CP solutions. Defect etchants were developed at the same time in order to study the crystal quality for different crystal growth processes. The improvement of the growth methods and the introduction of chemo-mechanical polishing methods led to defect-free single crystals with optically flat surfaces of superior electronic properties. This reduced the interest in CP and defect delineation. 

As a result of the crystal growth process Si wafers usually show striations, a variation in the bulk Si resistivity in a concentric ring pattern with a spacing in the order of millimeters. This variation of the bulk Si resistivity modulates the current density and thereby the porosity, which results in an interface roughness [Lel6]. Mesopore formation due to breakdown at the pore tips is very sensitive to striations and can be used for their delineation. 

The exponents i and s in equations 15.13 and 15.14, referred to as the order of integration and overall crystal growth process, should not be confused with their more conventional use in chemical kinetics where they always refer to the power to which a concentration should be raised to give a factor proportional to the rate of an elementary reaction. As Mullin(3) points out, in crystallisation work, the exponent has no fundamental significance and cannot give any indication of the elemental species involved in the growth process. If i = 1 and s = 1, c, may be eliminated from equation 15.13 to give ... 

The use of tailor made additives holds great promise in the area of crystal growth and morphology control. The routine selection and use of these type of additives will require a fundamental understanding of the mechanism which the additives work on a molecular basis. At the same time, the effect of solvent molecules on the crystal growth process is another related and important problem. In both instances, the relationship between internal aystal structure, aystal growth rate, solvent and impurities are needed to predict the habit of a crystal and thus allow seleaion of the proper conditions and components required to obtain a desired habit... 

Several high-temperature methods leading to fluoridated apatites can be found in the literature they involve solid-gas reaction, pyrolysis or crystal growth processes. 

Although the chemical properties of benzene-1,2,3-tricarboxylic acid (BTCA) were first studied over 100 years ago, the crystal stmcture of BTCA was not reported until a recent powder XRD study [117]. In contrast, the crystal stmctures of several solvate phases of BTCA were determined previously, including a dihydrate stmcture and solvate stmctures containing different alcohols and other solvent molecules. The preparation of a pure (nonsolvate) crystalline phase of BTCA by crystal growth fi om solution is difficult due to the competitive formation of solvate phases. In such cases of materials that cannot be prepared as a pure (nonsolvate) phase by conventional crystal growth processes, a possible route to obtain the pure phase is to carry out desolvation of a solvate phase at elevated... 

Natural crystal growth occurs under non-controlled conditions, which may vary greatly during the crystal growth processes. In such a case, growth may... 

There can be any number of types of sites on a surface. For example, in the simulation of a crystal growth process we might specify that a surface consists of step sites and terrace sites. The number of sites of each type may be characteristic of the crystal surface, for example, the mis-cut orientation of a crystal face. We denote each surface site type as a phase these phases reside in a particular surface (2D) domain. Surface species occupy the surface sites (i.e., populate the surface phases), which is the next step down the hierarchy. 

Because the adatoms diffuse relatively rapidly along the surface and the ledges to the kinks, many more atoms reach the kinks by these routes than by direct impingement from the vapor. Note the close similarity between this crystal growth process on a vicinal surface and the climb of dislocations depicted in Fig. 11.2. 

Molecular recognition of crystal interfaces makes possible the control of crystal growth processes in that suitably designed auxiliary molecules aci as promoters or inhibitors of crystal nucleation inducing, for instance, the resolution of enantiomers or Ihe crystallization of desired polymorphs and crystal habits. 

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