Chapter 5: Surface processes in epitaxial growth

Corrections, comments and updates

5.1 Introduction: growth modes and nucleation barriers

I had in mind that supervisors might not thank me for increasing their bill for copying and interlibrary loan, and students might also find that having got the papers they couldn't understand them. However, for completeness these references are given here for those who want to follow them up. They are Volmer & Weber (1926), Stranski & Krastanov (1938) and Frank & van der Merwe (1949). The first two of these papers are in German; the spelling of Dr K varies, since there is no unique transliteration of the cyrillic alphabet.

My own view is that quoting such papers just to show erudition is rather annoying, especially if one hasn't actually read them, which remains as a suspicion in the mind on reading some papers...

In this same section a point of confusion has been noted by some students about the relation between a) the statement on page 146 starting "When we deposit material A on B, we get layer growth if g_A < g_B + g*, where g* is the interface energy, and vice versa for island growth", and b) the illustrations of figure 5.3(a) and (b) on page 147. This confusion is sufficiently messy for me to wish to hide it on a separate page.

New references for section 5.1

5.2 Atomistic models and rate equations

In section 5.2.2 on pages 150-151, there is a description of capture processes in terms of net rates, U_j. The first line of the second paragraph on page 151 starts with "A typical form of the U_j contains both growth and decay,...". In the detailed formulae that follow in the same paragraph, the expressions are actually for U_j-1. Thanks to French research student Nicolas Moreau for uncovering this problem.

In section 5.2.4 on page 154, a pre-exponential is referred to as h(Z,i), and this quantity is illustrated for certain cases in figure 5.6 on page 155. Perhaps because the text is rather compressed, there may be some confusion as to how this quantity should be used, though it is explicit in the review paper of Venables et al. (1984, equation 2.15, page 411). This compression is a consequence of the section not being a review paper; you may need the relevant information from reviews and original papers in order to do full justice to problems 5.1 and 5.2 on pages 181-2.

If you go back to page 153, you will see the statement: n_x ~ R^p multiplied by an Arrhenius (exponential) term. However, this equation is not fully written out, and the term in R doesn't have the same dimensions as n_x. The full equation, with n_x in ML units and R in (ML/s), is

n_x=h(Z,i).(R/n)^p. exp(E/kT),

where n is a frequency factor, most obviously at low temperature the diffusion frequency n_d given in chapter 1, equation 1.16 on page 16. However, one can see on that same page that at higher temperatures, when re-evaporation is involved in the equations, the pre-exponential may well contain n_a, in addition or instead, as might be deduced from table 5.1 on page 154.

My conclusion is given at the end of section 5.2.4 on page 155, namely that it is relatively straightforward to check the energies E and power laws p in table 5.1, but that keeping track of the pre-exponential terms requires patience and cross checks with the original literature. Even that statement really underestimates the level of "scientific noise" in the system; there are many papers which I haven't quoted in the book, simply because I didn't want to carry on an ongoing, and possibly contentious, discussion of work in progress, minor differences of interpretation, etc. Although resolution of such issues is important in principle, it can rapidly send all but the most committed either to sleep or off to the nearest available bar.

In section 5.2.5 on page 156, figure 5.7(b) has the dotted and full lines reversed- the dotted lines correspond to the rate equation and the full lines to the KMC simulations.

New references for section 5.2

5.3 Metal nucleation and growth on insulating substrates

New references for section 5.3

5.4 Metal deposition studied by UHV microscopies

New references for section 5.4

5.5 Steps, ripening and interdiffusion

New references for section 5.5

Problems and projects for chapter 5

In problem 5.2 on page 182, part c) is incorrectly stated. It should read:

By considering the boundary condition at the edge of the cluster, show that the concentration n₁(r) = Rt (1-K₀(X)/K₀(X_k)), where the argument of the Bessel function X = r/Ö( Dt), and X_k is as defined in the text following (5.12).

Note: in part d) which follows, the case r = r_k results in equation (5.12a) for s_k, and r = r_x leads to equation (5.12b) for s_x.