Crystal growth from vapor

The basic criteria to consider in crystal growth from vapor, solution, and melt phases are therefore whether the phase is condensed or dilute, and whether the phase involves a solute-solvent interaction or not. 

For crystal growth from the vapor phase, one better chooses the transition probability appropriate to the physical situation. The adsorption occurs ballistically with its rate dependent only on the chemical potential difference Aj.1, while the desorption rate contains all the information of local conformation on the surface [35,48]. As long as the system is close to equilibrium, the specific choice of the transition probability is not of crucial importance. 

In Fig. 12.4 the velocity of crystal growth from the vapor is plotted as a function of the excess vapor pressure (P — Peq). When the surface acts as an ideal sink for incoming vapor atoms, the plot indicates that the velocity of growth should vary linearly with (P - Peq). When the sink efficiency is lower, the curve of v vs. (P - Peq) falls below the ideal curve. Use the results of Exercise 12.1 to demonstrate that the velocity of growth for the model employed there can be expressed in the form... 

One aspect of crystal growth from the vapor is the diffusive transport of adatoms to ledges (see Exercise 12.1). A suggestion is that the motion of ledges can be ignored in the analysis of crystal growth if... 

Crystal growth from the vapor phase has been treated in Chapter 12. An expression for the net atom flux, Jv, gained at a macroscopically flat crystal surface during growth from the vapor has been obtained in Exercise 12.2 in the form of Eq. 12.27. To treat surfaces possessing nonuniform curvature, this relationship can be generalized in the form... 

The preceding treatment is, undoubtedly, an oversimplification. For example, many diatomic molecules dissociate upon adsorption (e.g., H2, SiH, GeH). Each atom from the dissociated molecule then occupies its own distinct surface site and this naturally changes the rate law expression. When these types of details are accounted for, the Langmuir-Hinshelwood mechanism has been very successful at explaining the growth rates of a number of thin-film chemical vapor deposition (CVD) processes. However, more important, our treatment served to illustrate how crystal growth from the vapor phase can be related to macroscopic observables namely, the partial pressures of the reacting species. 

Pearson, E., T. Takai, T. Halicioglu and W.A. Tiller 1984, Computer modeling of Si and SiC surfaces and surface processes relevant to crystal growth from the vapor. J. Cryst. Growth, 70(1-2) pp. 33 0... 

On solid metals the situation for ion deposition or dissolution in electrode reactions is much more complicated. The models for crystal growth from the vapor phase or atomic evaporation have to be applied, being modified by ion discharge or ion formation in passing the electrical double layer at the interface. Figure 2.31 represents the main positions of atoms on the surface of a low index face of a metal with one monoatomic step. It is assumed that the edge of the step is not smooth and contains several kink sites. 

In most cases, the activator impurity must be incorporated during crystal growth. An appropriate amount of impurity element is dissolved in the molten Ge and, as crystal growth proceeds, enters the crystal at a concentration that depends on the magnitude of the distribution coefficient. For volatile impurities, eg, Zn, Cd, and Hg, special precautions must be taken to maintain a constant impurity concentration in the melt. Growth occurs either in a sealed tube to prevent escape of the impurity vapor or in a flow system in which loss caused by vaporization from the melt is replenished from an upstream reservoir. 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

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