**3.4 Texturing**

monolayer (*μc*) may be thought of as the 2D saturation vapor concentration,

*<sup>r</sup>* <sup>∗</sup> <sup>¼</sup> *<sup>β</sup> a RT Vmc* 

*<sup>Δ</sup>G*<sup>∗</sup> <sup>¼</sup> *πβ*<sup>2</sup> *a RT Vmc* 

Here, *a* is the monolayer thickness. Once supercritical nuclei form, the 2D gas continues to attach to their edges until coalescence occurs and the monolayer is complete. Meanwhile, the next monolayer is beginning to form, and the film continues to build up in this way, atomic layer by layer. In the special case of singlecrystal film deposition (epitaxy), the surface may contain many atomic terraces with straight edges as shown in **Figure 11**. The "kink" sites shown in **Figure 11** are also important surface features. Attachment of a 2D gas atom to a random site on the straight edge involves an increase in total edge energy, because it increases the length of the edge. Conversely, attachment to the kink site makes no change in the length of the edge; this is therefore an energetically preferred site, and edge growth can most easily occur by attachment-driven motion of these kink sites along the

It can be seen from the above that the surface energy depends not only on the facet direction discussed in Section 3.3.1 but also on the density of steps and kinks (Williams, 1994). The equilibrium densities of these two features increase with *T* because of their associated entropy (disorder), *S*. That is, when the *Ts* term for the Gibbs free energy, *G*, becomes larger; the internal energy term, *U*, also becomes larger to minimize *G*; and *U* here mostly consists of the potential energy of step and kink formation. This is the same *T*-driven tendency toward disorder that causes

During film deposition, if the surface diffusion rate is high enough and *ns* is low enough so that the 2D gas atoms are more likely to attach to an edge than to form a critical nucleus within an atomic terrace, then edge attachment becomes the dominant growth mode, that is, we have Λ > *L*, where Λ is the surface diffusion length and *L* is the distance between terraces. This is called the "continuous" growth mode, as opposed to the nucleated mode. The continuous mode of 2D growth is analogous to the type of 3D nucleation in which nucleation is more likely to occur at active surface sites than by spontaneous nucleation elsewhere on the surface. Active sites and step edges, especially kinked edges, break the nucleation barrier by providing

Two-dimensional nucleation is usually preferred to 3D because it leads to smooth growth. In nonepitaxial growth, large grain size (coarse nucleation) may be desired in addition to smoothness. Unlike in the 3D nucleation case, here large grain size and smoothness are not incompatible. That is, if adatom mobility on the substrate is sufficient, large 2D nuclei will form before the first monolayer coalesces, and then subsequent monolayers will grow epitaxially on those nuclei. But there is another problem. High adatom mobility requires a low surface diffusion activation energy, *Es*, in accordance with **Figure 8**, but *Es* tends to increase with the strength of the adsorption, *Ed* or *Ec*, as suggested in **Figure 7b**. At the same time, good

derive expressions for the critical nucleus as:

*21st Century Surface Science - a Handbook*

2D supersaturation ratio. By the same procedures as in the 3D case, we may then

). If *ns* is the actual concentration of the 2D gas, then (*ns=nv*) becomes the

*ln ns nv*

> *ln ns nv*

(14)

(15)

*nv* (mc*=*m<sup>2</sup>

and

edge.

vapor pressure to rise with *T*.

wetting at those sites.

**18**

The texturing described here refers to the crystal structure rather than the surface morphology, although they are often correlated. The degree of texturing is the degree to which the crystallites in a polycrystalline film are similarly oriented. In one limit, there is random orientation (no texturing), and in the other limit, there is the single crystal. A material in which the crystallites are nearly aligned in all three dimensions is called a "mosaic," and the limit of a perfect mosaic is a single crystal. The degree of texturing is best measured by X-ray techniques. Texturing can occur in one, two, or three dimensions. Epitaxy is the best way to achieve perfect threedimensional texturing. Epitaxy occurs when the bonds of the film crystal align with the bonds of the substrate surface, making the interfacial energy, *γi*, very low, zero in the case of homoepitaxy; this is when the film material is the same as the substrate material. In other cases, when there is no such arrangement to operate, the most common form of film texture is two-dimensional texture, in which the crystal plane is arranged relative to the rotation of two axes on the substrate plane. This means that the film has a preferred growth plane parallel to the substrate, but has a random orientation relative to the rotation of the axis (i.e., azimuth) perpendicular to the substrate plane. It is often desirable to deposit the film on a substrate that cannot be crystallographically aligned, such as an amorphous substrate (such as glass) or a substrate with crystal symmetry or lattice size very different from the film. In this case, it is very ideal to realize two-dimensional texture when the required film properties are also crystal anisotropy.
