Ambient phase

If one is interested in the configuration of a singular surface or a vicinal surface close to the singular orientation, the surface is better characterized by the local height hj. The description assumes that there should be no vacancy in the crystal, no floating-solid atoms in the ambient phase, nor... 

For the case of a thin film on the electrode (see Figure 2.61) the total reflection coefficients of the S- and P-components from the ambient phase/ film and film/electrode interfaces, rp and rs, are given by ... 

Crystals formed under small driving force conditions (see Section 3.2) in a dilute ambient phase, such as the vapor phase or solution phase, will generally exhibit polyhedral forms, irrespective of their size. Even crystals of micrometer size, such as clay minerals, show polyhedral forms. However, there are crystals that show elongated needle forms that resemble whiskers, coils, hollow tubes, and even ice cream cones (see Figs. 2.2 (a), (b)) others exhibit tree-like polycrystalline aggregates of dendrites (see Fig. 2.2 (c)). 

Here, /x, /xjs>, and are, respectively, the chemical potentials of the supersaturated vapor (or the ambient phase such as the solution phase), the saturated phase, and the solid phase. From this, a generalized driving force maybe expressed as... 

As can be seen from the expression for the driving force in terms of the chemical potential differences, which are related to the differences in temperature and concentration, the two transporting processes, heat transfer and mass transfer, are coupled in crystal growth. The degree of contribution from the respective transport process is determined by the degree of condensation of the environmental (ambient) phase. To grow crystals in a diluted ambient phase, a condensation process is required, and so mass transfer plays an essential role. The contribution of heat generated by crystallization in this case is small compared with that of the mass transfer. However, for crystallization in a condensed phase, such as a melt phase, heat transfer plays the essential role, and the contribution from the mass transfer will be very small, because the difference in concentration (density) between the solid and liquid phases is very small, smaller, say, than 1 or 2%. It is therefore necessary to classify the types of ambient phases and to be familiar with their respective characteristics from this standpoint. 

In contrast to solid state crystallization, crystallization from vapor, solution, and melt phases, which correspond to ambient phases having random structures, may be further classified into condensed and dilute phases. Vapor and solution phases are dilute phases, in which the condensation process of mass transfer plays an essential role in crystal growth. In the condensed melt phase, however, heat transfer plays the essential role. In addition to heat and mass transfer, an additional factor, solute-solvent interaction, should be taken into account. 

Crystallizing particles arriving at the surface will diffuse onto the surface (surface diffusion). As this occurs, some may return to the ambient phase, while some will be caught at kinks or steps (see Section 3.6) on the surface and will be incorporated into the crystal. When these particles are incorporated into the crystal, the solvent component will be dissociated. This process is called desolvation. In solution growth, this process will determine the growth rate. At certain points in these processes, it is necessary to overcome the energy barriers required to climb the respective steps (Fig. 3.5). 

In this section we have explained the relation between a bulk ambient phase and a bulk crystal (where the crystal is assumed to have an ideal, regular structure). Since the 1930s, theoretical and experimental investigations have indicated that a real crystal contains defects of lattice order, and that these defects have a significant effect on the physical properties of the crystal. This understanding has led to the present day semiconductor industry. 

Figure 3.15 is a schematic diagram of R versus the A/ir/kT relation expected in one crystallographic direction in an imaginary ambient phase. 

Figure 3.16. The different positions of A/jLjkT and A/ii/kT depending on the ambient phases, (a) Vapor phase (b) solution phase (c) melt phase.

Figure 3.17. Relation between interface and lines of equal concentration in the ambient phase when morphological instability occurs.

The structural and equilibrium forms of crystals are predicted assuming that the crystal is perfect and that the ambient phase is isotropic. Growth forms, however, describe real crystals containing lattice defects growing in a real ambient phase. We should therefore consider the following factors, which may affect the growth forms. 

The factors inducing anisotropy into the ambient phase flows in solution, such as laminar or turbulent flow, convection induced by temperature difference, concentration difference, or difference in surface tension. 

The values of XJh are different for different ambient phases and growth conditions. The ratio is of the order 10 for crystals grown from the vapor phase. 

Since the edge free energies, y, are different for the vapor and solution phases, and particularly for solute-solvent interaction energies, the same crystal species will exhibit different Tracht and Habitus in different ambient phases and different solvents. If impurities are present in the system, this affects y and the advancing rates of steps. There are two opposite cases in impurity effects, and, depending on the interface state, some will promote growth, whereas others will suppress growth. 

The most commonly encountered distribution of dislocations in crystals grown from solution or vapor phase (dilute ambient phases) by natural nucleation and without seed may be observed as dislocation bundles starting from the center of a crystal and running nearly perpendicular to the habit faces. In addition to these dislocations, smaller dislocation bundles originating from inclusions may be observed. See Figs. 6.1(e) and 6.5 for examples. 

---