Heterogeneous Nucleation and Growth

Homogeneous nucleation occurs in volume (3D), randomly, and spontaneously, without the presence of any preferential nucleation sites. Homogeneous nucleating systems are nevertheless uncommon. Most of the nucleation processes develop at nucleation sites, i. e., on preexisting surfaces contacting the liquid (or vapor), such as the surface of an impurity, a nucleating agent (a deliberately added nano/micro — crystal), crucible walls, etc. Suspended particles or minute bubbles also provide nucleation sites. The nucleation process is then designated by heterogeneous nucleation.

Let us consider the film deposition on a planar solid substrate. The growth species in the vapor phase impinge on the substrate surface, diffuse and aggregate to form a nucleus with a cap shape as illustrated in Fig. 14.33. Analogous to homogeneous nucleation, there is a decrease in the Gibbs free energy and an increase in surface or interface energy, given by:

AG = a3r3A^v + ar2Yvf + a2r2f — a2r2ysv (14.17)

where r is the average radius of the nucleus, A^V is the change of Gibbs free energy per unit volume. The yvf, yfs, ysv are the surface (or interface energy) of vapor-

Fig. 14 .33 Geometric constraints of heterogeneous nucleation. Image Credits: http://soft-matter. seas. harvard. edu/index. php/Contact_angle

nucleus, nucleus-substrate, and substrate-vapor interfaces (Fig. 14.34), respec­tively, being related according to the Young’s equation:

0 = Ysg — Ysl — Ylg cos 0 (14-18)

where 0 is the contact angle.

In heterogeneous nucleation, cap geometry (Fig. 14.34) allows some geometric constraints. After rearranging [18], one may obtain the critical radius and the critical energy barrier for heterogeneous nucleation:

16nY3f 2 — 3 cos 0 + cos 30

3^Gv)2 4

The first term of Eq. (14.20) is the value of the critical energy barrier for homogeneous nucleation (Eq. (14.15)), whereas the second term is a wetting factor.

But other factors, such as the interaction between the film and the substrate, may play a critical role on the film growth mechanism. Three different nucleation mechanisms may develop: island or Volmer-Wever growth; layer or Frank-van der Merwe growth and island-layer or Stranski-Krastonov growth (Fig. 14.35).

One may then summarize the film growth mechanism as follows:

— When the contact angle is 0°, the deposit wets the substrate completely, there is no energy barrier for the formation of a new phase and a layer growth mecha­nism is observed (Fig. 14.35). A first complete layer is formed, before the deposition of second layer starts. In the layer growth mechanism, the growth species are stronger bonded to the substrate than to each other. Epitaxial growth of single crystal films is one of the examples.

— When the contact angle is less than 180° (but larger than 0°), the energy barrier for heterogeneous nucleation is smaller than that for homogeneous nucleation, being the reason for the predominance of heterogeneous nucleation. An island growth mechanism frequently developed (Fig. 14.35). Here the growth species

are more strongly bonded to each other than to the substrate. In the initial steps small islands form, and the subsequent growth will occur by their coalescence to form a continuous film. Systems of metals deposited on insulator/alkali halides/ graphite/mica substrates exhibited this nucleation mechanism during the initial film formation.

— When a strong mismatch (see mismatch) is observed between the film and the substrate (for a contact angle less than 180°, but larger than 0°) an island-layer mechanism will occur (Fig. 14.35). The development of in situ stress in the film is the common reason for the island-layer growth mechanism.

— When the contact angle is 180° (i. e., the film does not wet on the substrate at all) the wetting factor becomes 1, the nucleation is homogeneous (i. e., the critical energy barrier for heterogeneous nucleation equals that of the homogeneous nucleation).

Updated: 4 сентября, 2015 — 4:19 пп