4.4 Adsorbate diffusion

• Prutton, Chapter 5
• Surfaces , Gary Attard and Colin Barnes, Oxford Science Publications (1998)
• Zangwill, Chapter 14
• Although directed at researchers in the field, there are a number of very well-written articles on diffusion (and growth) processes in The Chemical Physics of Solid Surfaces, Vol. 8 , edt. D. A. King and D. P. Woodruff (Elsevier, 1997). For background reading, see in particular Chapter 1, Venables; Chapter 4, Tsong; Chapter 7, Liu and Lagally.
• Some excellent sites that feature STM movies of diffusion processes are:
  • Eric Ganz's STM group at the University of Minnesota (The movie to the left is from this site).
  • B.S. Swartzentruber's STM group at Sandia National Labs, New Mexico
  • ..and just to show you that atoms and molecules do diffuse on surfaces other than silicon!, try clicking here .

Fig. 4.12 is a simple illustration of an adsorbed atom on a surface (as viewed from the side). The atom, at position A, resides within a minimum of the surface lattice potential. Given enough energy, through thermal fluctuations, the atom will surmount the diffusion barrier , E_diff and hop to a neighbouring site. Fig. 4.12 illustrates that the diffusion barrier arises from the energetically unstable configuration the atom must adopt when moving from site to site. In the simplistic diagram shown in Fig. 4.12, at position B the atom forms only one bond with the surface. Note that at any particular site E_diff will scale directly with the number of bonds the adsorbed atom forms with its neighbours.

The diffusion barrier varies dramatically from surface to surface and depends on which direction the atom tries to hop. The rate of hopping across the surface, n_diff, is given by an Arrhenius law:

where n_0(diff) is related to the vibrational (attempt) frequency of the adsorbate in the potential well.

In Fig. 4.13 the atom shaded in green is diffusing to the right. Sketch the lattice potential the atom will "feel" as it diffuses across the step.

For a single atom undergoing a 2D random walk across a surface and not interacting with any other adsorbed atoms we can define the diffusion constant, D (usually expressed in units of cm²s^-1) as:

where N is the number of jumps in unit time and a is the distance an atom hops (of the order of or equal to the surface lattice constant). As, n_diff=N, we can write the diffusion constant as follows:

where D₀ is called the diffusion prefactor. (There is an entropic contribution to D₀ but for the systems we'll discuss it is negligibly small). Measurements of the diffusion constant as a function of temperature thus allow one to calculate the diffusion barrier.

NB It is very important to realise that the diffusion barrier for an isolated atom will differ drastically from that of an atom in a cluster or at a step edge.Why?!

Brian Swartzentruber at Sandia National Labs in New Mexico has recently pioneered an exciting extension to STM which enables the motion of a diffusing atom to be tracked in real time. You can read about the technique at his group's web site . This site also contains a number of fascinating STM movies showing Si atoms diffusing on the Si(100)(2x1) surface. (Diffusion and growth on Si(100) surfaces is a suggested article topic).