Book chapter 5

Introduction to Surface and Thin Film Processes

John A. Venables

Cambridge University Press (2000)

Supplementary notes by John A. Venables

© Arizona Board of Regents for Arizona State University and John A. Venables

Chapter 5: Surface processes in epitaxial growth

Corrections, comments and updates

General comment: Of all the chapters, this chapter is closest to my research speciality, and is also closest in format to a review article. Thus readers who are expecting a self-contained description of 'all there is to know' about nucleation and growth processes, or alternatively about epitaxy, may feel somewhat frustrated. In a course, the chapter needs supplementing by some more introductory material, some more elementary problems, and some broader material on particular deposition methods, such as filling out chapter 2, section 5 with a more 'materials-oriented' book. All this is explicit in the text, and may be understood on the grounds that the book is as much a source-book as it is a text-book. In particular, to understand and explore further all the equations, reference to the original literature will typically be needed at some point.

5.1 Introduction: growth modes and nucleation barriers

In section 5.1.3 it may feel odd that I did not give the original references for the much-used "three growth modes". This was on purpose, as I feel these topics are best approached via more recent review articles, such as Bauer (1958) or our own Venables et al. (1984), both of which are quoted in the text. Much related historical work can be accessed via the review articles and book chapters quoted in section 5.1.1 on page 144.

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, primarily in the original (2000) printing, 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 γA < γB + γ*, where γ* 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 has been removed in the text of the 2006 printing; but the confusion was, and to a certain extent still 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, Uj. The first line of the second paragraph on page 151 starts with "A typical form of the Uj contains both growth and decay,...". In the detailed formulae that follow in the same paragraph, the expressions are actually for Uj-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 η(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: nx ~ Rp 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 nx. The full equation, with nx in ML units and R in (ML/s), is


where ν is a frequency factor, most obviously at low temperature the diffusion frequency νd 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 νa, 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) = Rτ(1-K0(X)/K0(Xk)), where the argument of the Bessel function X = r/√(Dτ), and Xk is as defined in the text following (5.12).

Note: in part d) which follows, the case r = rk results in equation (5.12a) for σk, and r = rx leads to equation (5.12b) for σx.

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Latest version 21 January 2013, ex 14 November 2007.