Chapter 8
Conclusion

Were I to await perfection, my book would never be finished

Over the course of the work, I have developed two key themes: for many of the calculations, the tight binding approximation has provided extremely accurate and useful predictions; and without collaboration and interaction with experiments much of the work would have been impossible. I shall expound these two, and point the way to the future in the remainder of this conclusion.

8.1 Tight Binding is Good Enough

The tight binding approximation described in Chapter 2 takes some liberties with the quantum mechanical framework of bonding in solids, though the approximations made are, in the main, justifiable. The form used in this thesis is the crudest possible (only the nearest atoms are allowed to bond to each other, and the basis functions are assumed to be orthogonal) but it has vindicated itself admirably. It has been extremely useful, and successful, throughout the thesis, and here I list the areas where it has been used:

1. Step energies and kinking behaviour. Good agreement with experiment has been found.
2. Long straight lines of bismuth. The structure has been identified, and a growth mode proposed, which agrees with available experimental observations.
3. A c(4x4) bismuth reconstruction. A structure has been proposed by careful comparison with many different experimental sources.
4. Hydrogen diffusion. The diffusion of a single atom on the clean surface has been reproduced in good agreement with experiment and DFT results. The diffusion mode on the saturated surface has been explained, the saturation of steps during growth confirmed, and the behaviour of a defect as a mirror described.
5. The dehydrogenation mechanism for an ad-dimer has been explored, and a barrier which seems reasonable found.
6. The formation of a square, along with its decomposition to form short dimer strings, have been shown. This is a key step in the growth of silicon from disilane.
7. The structure of anti-phase boundaries has been explored, and their behaviour as nucleation sites for silicon islands explained.

Through these simulations, the accuracy and transferability of the parameterisations developed herein have been proved. The approaches used for fitting should be extended to new areas where tight binding will be able to provide answers, particularly as interest in features on surfaces turns to larger length scales. The use of linear scaling tight binding has proved invaluable for exploring non-periodic features such as steps and defects.

There is a growing trend towards the meeting of tight binding and density functional theory. The use of so-called ab initio tight binding to obviate the need for fitting of parameters is extremely exciting, and will provide the ability to keep up with experiments much more easily, as simulations will not need to wait for months while the parameterisation is developed and validated.

The role which tight binding fills, in being a fast quantum mechanical method, will expand as simulations become larger and timescales longer. The links between length scales which are being emphasised in the MML will be strengthened as the energetics and barriers which tight binding has been shown to be able to predict will allow Monte Carlo methods, which use the barriers, to achieve simulations for timescales of up to seconds for microns of material.

8.2 Every theorist needs an experimentalist

When the Royal Oak pub (on the Woodstock Road) came up for sale a few years ago, several of us in the lab thought that the Department should bid for it. Over the last three years, many discussions have taken place there, often aided by beer and cider, and much of the most fruitful work in this thesis has stemmed from such conversations and the trust and respect built by them.

While this may seem a slightly frivolous idea, it is far from it. The level of interaction between James Owen and myself is, I am told, rare, and in our case has proved most fruitful, yielding two theses, at least seven papers and (most importantly) a deep understanding of the growth process of the Si(001) surface from disilane. This understanding has already provoked interest in two commercial growth centres (DRA, Malvern, and Hewlett-Packard, Palo Alto).

What this interaction actually produces covers several levels: on the day-to-day level, ideas can be examined from different perspectives; in the long term, a mutual trust and understanding of techniques result; and in specific investigations, discoveries which require both disciplines can be made (for instance the defect structure in Chapter 4 or the square in Chapter 7) and expectations overturned (for instance, the formation of monohydride dimers discussed in Chapter 7, where the structure formed is at least 1 eV less stable than the most stable structure, but has a formation pathway which makes it far more likely to be formed). Certainly this thesis would have been much poorer without the STM experiments going on in the Department, and I hope to continue the interaction in the future. Without experimental results to anchor the models, theoretical calculations can become meaningless; equivalently, without theoretical calculations to explain and interpret the experimental results, experiments can become meaningless.

8.3 Now we can do germanium

As electronics becomes more and more a part of our society, the demands and expectations made on circuits become higher. At present, all high frequency applications (above 2 GHz or so) require the use of transistors and circuits fabricated on GaAs (or other expensive III-V materials) , which increases the cost and difficulty of manufacture. One of the growth areas of research is SiGe alloys, and Ge structures on Si substrates, which offer the possibility of high frequency applications and tunable electronic properties (through different layered structures), all within the same growth technology as is used for silicon.

Figure 8.1: An STM image of “hut” clusters formed when more than about 6 layers of germanium are grown on silicon. The sides run along (100)-like directions (which are elastically soft), and the faces are all (501)-like. Image courtesy of Ilan Goldfarb

Now that the silicon growth process has been successfully investigated, germanium can take center stage. As well as the desirable properties which Ge has for manufacturers, there are problems in growth which are both scientifically intriguing and technologically frustrating. Firstly, germanium tends to segregate to the surface during growth, though this problem is being addressed through the use of surfactants such as bismuth and hydrogen as described in Chapter 5. Secondly, germanium is a larger atom than silicon, and this introduces strain into the system; the ways in which this strain is relieved are many and varied. At low concentrations, it is dissipated in defects, though at larger concentrations and thicknesses macroscopic effects appear: hut pits and clusters, ripples and slip planes. Hut clusters are possibly the most spectacular of these, and an example of them is shown in Figure 8.1.

The formation and growth of hut clusters, and the distribution of strain around their base, are fascinating problems, as is the peculiar propensity for them to have (501)-facets as their sides. I shall be investigating these questions using a linear-scaling density functional code, which is similar in many ways to the density matrix code used in this thesis. To model a hut cluster in LDA properly will the require the ability to simulate several thousand atoms, which should be achieved sometime in the next year and a half; this simulation will be the logical conclusion of many of the themes of this thesis.