Epitaxial misfit

The study of ultra-thin Fe thin films on Cu(OOl) substrate has attracted a lot of interest in the past. This is due to the abundance of interesting phenomena associated with this system. Due to the small epitaxial misfit a good layer by layer growth is expected stabilizing the film in a structure related to the fee phase of bulk Fe which is otherwise unstable at low temperatures It also become a test system for magnetic measurements. 

Using X-ray spectrometry, De la Fuente et al. (1999) measured the thermal dependence of the a and c lattice parameters in a Er32/Lu 10)40 superlattice. Again, strong single-ion CEF contributions, originating from the Er/Lu interfaces, were observed in the volume and tetragonal distortions. Their analysis reveals also important contributions caused by epitaxial misfit. 

Another example of epitaxy is tin growdi on the (100) surfaces of InSb or CdTe a = 6.49 A) [14]. At room temperature, elemental tin is metallic and adopts a bet crystal structure ( white tin ) with a lattice constant of 5.83 A. However, upon deposition on either of the two above-mentioned surfaces, tin is transfonned into the diamond structure ( grey tin ) with a = 6.49 A and essentially no misfit at the interface. Furtliennore, since grey tin is a semiconductor, then a novel heterojunction material can be fabricated. It is evident that epitaxial growth can be exploited to synthesize materials with novel physical and chemical properties. 

Extended defects range from well characterized dislocations to grain boundaries, interfaces, stacking faults, etch pits, D-defects, misfit dislocations (common in epitaxial growth), blisters induced by H or He implantation etc. Microscopic studies of such defects are very difficult, and crystal growers use years of experience and trial-and-error teclmiques to avoid or control them. Some extended defects can change in unpredictable ways upon heat treatments. Others become gettering centres for transition metals, a phenomenon which can be desirable or not, but is always difficult to control. Extended defects are sometimes cleverly used. For example, the smart-cut process relies on the controlled implantation of H followed by heat treatments to create blisters. This allows a thin layer of clean material to be lifted from a bulk wafer [261. 

When a mismatch is inevitable, as in the combination Gej-Sii j. — Si, it is found that up to a value of jc = 0.4, there is a small mismatch which leads to a strained silicide lattice (known as commensurate epitaxy) and at higher values of jc there are misfit dislocations (incommensurate epitaxy) at the interface (see p. 35). From tlrese and other results, it can be concluded that up to about 10% difference in the lattice parameters can be accommodated by commensurately strained thin films. 

The structural form of brookite (TiO ) is expected to be bounded by 210 and 111, both being F faces by PBC analysis, but the actual growth form observed is platy Habitus bounded by largely developed 100, which is an S face. The misfit ratio between the PBC on the (0110) face of quartz and that on (100) ofbrookite is the smallest among any misfit ratios between the two crystal species. From this, it was found that the platy Habitus ofbrookite arose because quartz adsorbed in an epitaxial relation on 100 ofbrookite, thus diminishing thegrowthratekof(lOO) [30]. 

The corresponding relation between the host and guest crystals when evaluating the misfit ratio may be a one-to-one lattice relation in the same direction (a X b to a xb axes), or in different axial directions (aX b axes versus aX <110> axes), or on the basis of one unit cell versus a few unit cell sizes (see Fig. 7.13). Royer s misfit ratio is generally a two-dimensional correspondence, but Hartman [13] extended this relation to the misfit ratio in PBCs (see Section 4.2), which is a one-dimensional correspondence. Royer s epitaxial relations correspond to a relation between the F faces of the host and guest crystals containing more than two PBCs, and an epitaxial relation is not allowed between S faces or K faces. In Hartman s analysis, rela-... 

The freedom of the dangling bonds on the crystal surface increases with increasing temperature. As a result, there is a critical temperature below which an epitaxial relation cannot be realized. This temperature is called the epitaxial temperature, and it depends on interface orientation. If the misfit ratio is small, the epitaxial temperature is low if the misfit ratio is large, the epitaxial temperature is high, and an epitaxial relation will not be achieved unless the temperature is higher than the epitaxial temperature. 

Coaxial intergrowth is a paragenetic relation that describes crystals of two different species growing with a common axis the misfit ratios between the two crystals in the direction of the common axis are small, without exception. The formation of coaxial intergrowth can be understood to be one crystal conjunct to the other in an epitaxial relation, where both continue to grow. If a liquid of eutectic A-B component is solidified from one side (unidirectional solidification), crystals of the two phases A and B precipitate in dotted, columnar or lamellar (with common axis) form, and show unique textures for unidirectional solidification. This is a well known phenomenon in metallurgy. 

The main issue involving GaN substrates for nitride epitaxy concerns obtaining optoelectronic devices without mismatch dislocations. The critical conditions for misfit-dislocation creation include lattice mismatch between the layer and the substrate, layer thickness, growth conditions and substrate quality. 

The literature in this field is almost unduly preoccupied with lattice mismatch, so it seems appropriate to make a comment before proceeding. In this Datareview, I use the Matthew s convention [1] to compute the misfit. This convention gives a misfit which is simply related to the number of dislocations the film needs to accommodate the misfit. In practice, coherent epitaxy is never achieved for misfits larger than about 2%, so computation of a misfit may not be terribly meaningful. Lattice misfits to the nitride semiconductors for the materials discussed in this paper are given in TABLE 1. 

The terms incommensurate and semi-commensurate are analogous to incoherent and semi-coherent for interfaces - in grain boundaries, heterophase interfaces and epitaxial layers (cf. also Nabarro - with which layered misfit structures have much in common. In extreme cases noncommensurability may arise by mutual rotation (to varying degrees) of component layers with identical component lattices... 

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