Chapter 6
Hydrogen on Si(001)

... A molecular system ... (passes) ... from one state of equilibrium to another ... by means of all possible intermediate paths, but the path most economical of energy will be the more often traveled.

6.1 Hydrogen diffusing on Si(001)

Hydrogen adsorbs on the surface of silicon by breaking the -bond of the silicon dimer (Wu and Carter 1991) and bonding to one of the dangling bonds thus created. The remaining half-filled dangling bond appears as a bright blob in the STM, while the hydrogen at the other end is relatively dark (Boland 1991b), due to the bonding energy gain. Hydrogen adsorbs randomly at coverages of less than 0.1ML (Boland 1992,1993), but after that it pairs up onto a single dimer (Widdra et al. 1995). This arrangement, with one hydrogen on each end of a silicon dimer, is the most stable phase for adsorption, as the silicon atoms are both four coordinate, with no dangling bonds. Widdra et al. found that this pairing occurs at adsorption temperatures between 150K and 600K, and that the amount of pairing was independent of temperature; they proposed a mobile precursor mechanism (similar to that proposed by Sinniah et al. (1989) for desorption) to explain this. In this mechanism, the incoming hydrogen atom is in an excited, band state with a finite lifetime, which will sample several different adsorption sites. If the lifetime allows it to sample, say, 10 sites, then for coverages below 0.1 ML, the hydrogen distribution will appear random, and above that it will be almost entirely paired. Confirming that the diffusion barrier is sufficiently high to prevent diffusion on adsorption over a good part of the temperature range used (150-600 K) would lend weight to this argument. These two experiments suggest that the diffusion barrier is sufficiently high to prevent diffusion upon adsorption; this is the only experimental evidence available on diffusion apart from the work connected with this thesis (Owen et al. 1996).

There have been many theoretical investigations of hydrogen diffusion on Si(001), though none of them have been conclusive. Wu and Carter have performed many cluster calculations using CI techniques and initially (Wu and Carter 1992) predicted diffusion barriers of 2.0 eV along the dimer rows and 2.7 eV across the dimer rows. However, they used a small cluster consisting of 9 silicon atoms terminated with 12 “pseudo-hydrogen atoms”, and did not allow the substrate to relax during diffusion, which suggests that their barrier will give a poor answer to the actual barrier. The CI method finds a very accurate answer, but the degree of relevance of the answer found to the physical system is rather small, due to the use of clusters. When they later performed different calculations (Wu, Ionova and Carter 1994) using empirical potentials (based on the Stillinger-Weber potential) which they had generated from SCF-LCAO calculations, and allowed the slab substrate to relax, they found a significantly lowered barrier of 1.5 eV for diffusion along the dimer row and a slightly lowered value of 2.5 eV for diffusion across dimer rows.

This lower barrier fits with calculations by Vittadini, Selloni and Casarin (1993) who found a barrier of 1.3 eV, though I would argue that using empirical potentials to model a process where the bond breaking is vital, as Wu, Ionova and Carter did, will only get results by luck. Vittadini, Selloni and Casarin used LDA, and a repeated slab for their calculations, and allowed the top four layers of the slab to relax. They claim that the major difference between their calculations and those of Wu and Carter (1992) is the lack of surface relaxation in Wu and Carter. They attempt to estimate the magnitude of this effect by performing their diffusion calculations without allowing the substrate to relax, and conclude that the effect can be as large as 1 eV.

All of these sources of evidence indicate that the diffusion of hydrogen on Si(001) has an activation barrier of at least 1.3 eV, and that hydrogen is unlikely to hop across the dimer rows (as hopping across dimer rows is likely to occur in a similar temperature regime as desorption).

It is worth discussing briefly here the effect of the zero-point energy of hydrogen on diffusion barriers. If we assume that the dominant mode which is contributing to this is the Si-H bond stretch, which has a value of about 2100 cm^-1, then the zero-point energy (using the standard form of h) is about 0.04 eV for each of the three directions. This might double at the mid-point (but is unlikely to increase any more), leading to a change of up to 0.04 eV. Such a value fits well with the expectation found from EELS data that the change in zero-point energy for hydrogen even for heavy structural modifications varies by less than 3 % (Stucki et al. 1983). Thus it will be a relatively minor change.

6.2 STM results and phenomenological modelling

While it seems a little unusual to be describing the experimental work in detail in a thesis which is primarily theoretical, the modelling does interact with the experiment, and the results are so elegant that they deserve repetition. Images obtained at up to 500 K show small white dots (which are the result of hydrogen adsorption, and are the dangling bond at the unhydrogenated end of the dimer) which do not move over periods of up to 15 minutes (a pair of images 15 minutes apart are shown in Figure 6.1). The means that the maximum hopping rate of the hydrogen is once every fifteen minutes.

Figure 6.1: STM images taken at 500 K, with imaging conditions of -1.3V, 0.08 nA. The images are 14 nm wide, and separated by 15 minutes. The grey lines are the Si dimer rows, while the bright white dots are the result of hydrogen adsorption. Note that there is no change between the two pictures. Images courtesy of James Owen.

Once the sample is warmed to about 600 K, the hydrogen starts to move between pictures. Figure 6.2 shows two pictures taken at 600 K, separated by 10 seconds. The dots are moving, and appear to be slightly fuzzy, when compared to the previous, lower temperature pictures. This change in appearance will be discussed below. This temperature gives two limits on the hopping rate: the minimum hopping rate is once every ten seconds, and the maximum is the scan rate of the tip, which is once every 1/50th of a second.

Figure 6.2: STM images taken at 600 K, with imaging conditions of -1.0V, 0.08 nA. The images are 20 nm wide, and separated by 10 seconds. While the two dots on both pictures cannot be categorically identified as the same, they probably are, in which case both have moved considerably. Note also the slightly fuzzy appearance, as discussed in the text. Images courtesy of James Owen.

If the sample is warmed further, the hydrogen starts to move on the timescale of the tip scan. An example of the behaviour at 640 K is shown in Figure 6.3. The STM tip scans down the image in a series of 512 line scans. On reasonably high resolution, each dimer will be broken down into between 3 and 5 lines - i.e., the STM tip samples each dimer 3-5 times. Once the hydrogen is hopping once every 1/50th of a second, it can move off any given dimer onto another in the time that the tip makes a single line scan. This means that on any given dimer, out of the 4 linescans in which it is sampled by the tip, it may be occupied, unoccupied, occupied and finally unoccupied, or any other combination; more to the point, it will appear on several dimers in this fashion, elongating its normal appearance. This will lead to the smudged appearance which has been circled in Fig. 6.3, and gives a minimum hopping rate, as we know that it is hopping faster than the tip can scan.

Figure 6.3: STM image taken at 640 K, with imaging conditions of -1.0V, 0.08 nA. The image is 30 nm wide. The fuzzy dots in Fig. 6.2 have now elongated into long white smudges; two of these have been outlined. Each STM scan line takes th of a second. Image courtesy of James Owen.

The imaging of a moving hydrogen atom by a scanning tip is an interesting problem; a phenomenological model was created to study this. As explained above, each dimer is scanned about four times in the course of the STM scanning down the selected area. In the model, the hydrogen started at a random site, and was given a certain probability of hopping each time the tip scanned (e.g. every 1/50th of a second). The length of available dimer row (e.g. 10 dimers, which represents the relatively high defect density on the surface, and an assumption that the hydrogen cannot hop over a defect which is justified later in this chapter) was fixed, and a given number of smudges for those initial conditions generated. A set of 10 smudges is given below for 10 dimers, with 4 line scans per dimer and a hopping probability of 0.2 per line scan; a 1 represents conjunction of the STM tip and the H, while a 0 represents no such conjunction. Each result is broken up into units of four, each representing a dimer.

Figure 6.4: An Arrhenius plot of the hopping rate against inverse temperature for the motion of single hydrogen atoms on the Si(001) surface. There are three different types of data point: minima, measured hopping rate and maxima, which are discussed more fully in the text. The solid line is fitted to a pre-exponential rate of 1013 s-1, and gives a hopping barrier of 1.68 eV. The dashed line is fitted to a pre-exponential rate of 1014 s-1, which gives a hopping barrier of 1.80 eV. Picture courtesy of James Owen.

6.3 Atomistic modelling of single atom diffusion

This problem has been approached from two directions: that of LDA and GGA, and that of tight binding. The former have been used for this problem essentially to validate the tight binding calculations, and for comparison with experiment; once the tight binding parameters have been validated, larger systems than can be tackled with LDA may be addressed, such as steps and defects. These will be described in Sections 6.4 and 6.5.

6.3.1 DFT calculations

The hydrogen diffusion was modelled using LDA to obtain coordinates and charge densities, and both LDA and post hoc GGA to obtain the energies, using the standard unit cell. The hydrogen atom which was to diffuse was placed on one end of a dimer in one row, and to prevent the system from having an unfilled band, a hydrogen atom was also placed on the other side of the other dimer row. This hydrogen atom played no part in the diffusion (except to obviate the need for a subspace rotation at every step to correctly half-fill one band). The only constraint applied to the system was to force the hydrogen atom to remain in a plane of constant y (in Figure 6.5(b), the y axis runs vertically up the page), which was moved along the dimer row at each point in the calculation. The energies from both LDA and GGA calculations are shown in Figure 6.5(a).

Figure 6.5: (a) The energy for a hydrogen atom diffusing on the Si(001) surface, calculated using LDA and post-hoc gradient corrections (GGA). The barriers are 1.55 eV from GGA and 1.39 eV from LDA. (b) The process indicated schematically. The letters A,B and C refer to Fig. 6.7, and letter D is for reference in the discussion of the tight binding results.

The mid-point ((ii) in Fig. 6.5(b)) is highly unstable, as shown by the sharp peak in the graph. This is not unreasonable, as the hydrogen is bonded to two silicon atoms at this point, which is not an energetically favourable state for a 1s¹ atom to be in. The distances between the hydrogen and the two silicon atoms are shown in the next section, in Fig. 6.7; these show that once the hydrogen is past the mid-point it bonds strongly to the atom towards which it has been diffusing, and less strongly to the atom on which it started. The energies obtained (1.55 eV from GGA and 1.39 eV from LDA) are a little smaller than the experimental number (1.68 eV), but bring home the point that gradient corrections can be important in obtaining the correct value of barrier heights, for the GGA result agrees to within experimental error. The barrier is increased to 1.6 eV with the addition of spin to the calculation, which brings the calculated value well within experimental errors. Another point worth raising here is that of attempt frequencies: the experimental number of 1.68 eV was found from hopping rates and assuming an attempt frequency of 10¹³ s^-1, while another frequency which fits perfectly well (10¹⁴ s^-1) gives a barrier of 1.80 eV. It is certainly accepted that LDA cannot predict attempt frequencies accurately (Smith and Jónsson (1996) state that a factor of 5 is too sensitive for LDA to correctly model; see Blöchl, van de Walle and Pantelides (1990)), and so it has been decided that the prefactor relevant for comparing LDA/GGA hopping rates should be taken as 10¹³ s^-1. This fits well with values from the literature found using, for example, experimental vibrational mode studies. This is the first ab initio study of this system to predict a barrier which agrees with the experimental value.

6.3.2 TB calculations

To calculate the energy of a hydrogen atom diffusing on the Si(001) surface using tight binding is a difficult task. Particularly, the bonding at the saddle point will be highly non-equilibrium and therefore test the fitting of the parameterisation enormously. The fitting employed in the parameterisation developed during this work has been described in Chapter 3; here I will describe the application to a problem of diffusion.

Figure 6.6: The TB energy for a hydrogen atom diffusing on the Si(001) surface. The barrier is 1.96 eV (see text for a discussion of a correction to be applied to this). The process is illustrated schematically in Fig. 6.5(b).

The standard unit cell was used for this calculation. The only constraint applied to the system was the same as for the LDA modelling, i.e. constraining the hydrogen to lie in planes of constant y. The hydrogen was only allowed to bond to two silicon atoms - the one it starts on and the one it ends on. The other atom to which it could bond is the second layer atom to which the two dimers are bonded (marked as ‘D’ in Fig. 6.5(b)). Tests showed that if this atom was allowed to bond to the hydrogen, the bond energy was almost zero, but the repulsive energy was high; this was clearly unphysical and solved by removing the interaction. Examining surfaces of constant charge density from the LDA calculations showed that there was almost no charge between these two atoms, indicating that any interaction is negligible and that the above approximation is good. The start and end points are not exactly symmetrical, as the cell is p(2x2), but the energy difference is small.

Figure 6.7: The distance from the two Si atoms which bond to the hydrogen, as calculated by tight binding and LDA, as the hydrogen moves. All distances in Ångström. The letters refer to the atoms shown schematically in Fig. 6.5(b).

The energy for the diffusion reaction is shown in Figure 6.6, and the bond lengths between the hydrogen and the two atoms to which it bonds are shown, along with the equivalent LDA lengths, in Figure 6.7. This latter figure displays the biggest problem which tight binding has: when the hydrogen is just within bonding range of the second dimer, instead of a slight attractive interaction (as seen in LDA) there is a slight repulsive one (shown by the knee in the TB curve, and caused by the same effect as that alluded to above for the second layer Si atom - a high repulsive term where there is a low electron density). This is due to the fact that TB cannot take into account screening - the physical interactions represented by the TB repulsive term are very small, but this is not reflected in the relatively large repulsive interaction. The error induced by the repulsion has been estimated as 0.2 eV; this was found by taking the unit cell at the mid-point, and comparing the energy for the cell both as it is and after re-relaxing without the interaction between the hydrogen and the second atom (C). This makes the overall barrier 1.76 eV (with an error of up to ± 0.15 eV), which is much more in line with experiment. This correction will be applied throughout the thesis where hydrogen diffusion processes are modelled. More importantly, however, it should be noted that this anomalous repulsive interaction will be reasonably independent of whatever diffusion process is being modelled, and that energy differences between processes will reflect reality extremely accurately. This will be important in the remaining sections of this chapter. It is extremely encouraging that, with the correction applied, TB predicts a barrier in good agreement with experimental and LDA results.

6.4 Diffusion on the saturated surface

It has been shown above that the diffusion of single hydrogen atoms on a clean silicon (001) surface can be understood both by experiment and theory; however, the growing surface is likely to be saturated with hydrogen, and it is necessary to understand diffusion in this situation as well. As mentioned in the introduction to this chapter, it is energetically favourable for two hydrogen atoms to adsorb on the same dimer on the silicon surface, and once there is more than about 0.2 ML of hydrogen, this occurs. Once the coverage reaches 0.8 ML or above, most of the surface will be covered with paired hydrogens, and it becomes helpful to think of the clean dimers as the minority species. While these dimers do not migrate as such, the effect of two hydrogens moving in one direction will be to produce a vacancy moving in the other. It is particularly easy to image these vacancies in STM in empty states, as the ^* orbital stands out; it is a beautiful image of an anti-bonding orbital, which has a node in its middle. An example of the hydrogen saturated surface is shown in Figure 6.8.

Figure 6.8: STM images showing paired hydrogen diffusion. The dark background is silicon dimers saturated with hydrogen. Clean dimers appear as a bright feature, with a node down the middle. The two clean dimers circled in (a) appear to have moved at least one dimer closer together in (b) - an effect caused by diffusion of paired hydrogen. Images courtesy of James Owen.

The saturated surface does not start to show any signs of movement until 600 K, at which point changes occur on the timescale of minutes, and changes between sequential images are not visible until 650 K (as compared to the clean surface with single hydrogens where changes between sequential images were visible at 600 K). Once movement occurs, it occurs in pairs. That is, the ^* orbitals appear to move, which is actually caused by pairs of hydrogen moving. The tight binding parameterisation described in Chapter 3 and validated above in Section 6.3.2 has been used to investigate the cause of the barrier for paired diffusion being higher than for single atom diffusion, and the mechanism underlying paired diffusion.

The standard unit cell was used, with five of the dimers saturated with hydrogen, and one dimer clean. There are two obvious ways for the pairs of hydrogen to move: in a concerted motion, with both moving simultaneously; and for one to diffuse, creating two single hydrogens briefly, and for the second then to follow (or, equivalently, for the first to return). Both of these possibilities were modelled, applying different constraints. For the concerted motion, both atoms were forced to remain in the same plane of constant y, which was moved along the dimer row at each point in the calculation. In Figure 6.9(b), the y axis lies vertically up the page. For the separate motion, the first of the diffusing atoms was constrained to lie in a plane of constant y, while the second was left free; once the first atom had moved to the new dimer, the same process was applied to the second atom. As was true for single hydrogen diffusion, the second layer atoms labelled ‘D’ were not allowed to bond to the hydrogen. The results are shown in Figures 6.9 and 6.10 for the separate and concerted motions respectively.

Figure 6.9: (a) The energy for a pair of hydrogen atoms diffusing on the Si(001) surface separately, calculated using TB. The barriers are 2.18 eV from the end to the middle, and 1.89 eV from the middle to the end. (b) The process indicated schematically. (i) corresponds to 0.0 Å; (ii) to the minimum at 1.92 Å; and (iii) to the end point at 3.84 Å.

Figure 6.10: The energy for a pair of hydrogen atoms diffusing on the Si(001) surface in a concerted manner, calculated using TB. The barrier is 3.6 eV.

As can be seen, while the energy barrier for the concerted motion (Fig. 6.10) is less than twice the energy for a single hydrogen diffusing, it is still 3.6 eV, which is far too high for any diffusion to occur, even at 650K (even applying the correction mentioned above yields a barrier of 3.2 eV). The separate case (Fig. 6.9) is more interesting. The initial barrier of 2.18 eV (1.98 eV corrected) is higher than that found for the clean surface (1.96 eV or 1.76 eV corrected), but the barrier for the second hydrogen to diffuse is significantly lower than the initial barrier (1.89 eV or 1.69 eV corrected). The corrected barrier for the first atom to diffuse (1.98 eV) matches extremely well with the experimental value of 1.95 ± 0.2 eV (Owen, Bowler, Miki and Briggs 1997) and 1.69 eV for the second hydrogen means that the second diffusion event will occur extremely fast at 600 or 650 K. This makes the diffusion mechanism clear: the rate-limiting step is the breaking up of the paired hydrogen, which is then followed extremely quickly by the repairing, with a 50% probability of reforming without having moved. This means that at 600K, the second hydrogen is about 300 times more likely to diffuse than the first, and at 700K it is about 150 times more likely. So, at an experimental temperature at which the vacancies are observed to be hopping once every 10 seconds or so (i.e. once per image on average) the mean hopping time for the first atom will be 10 seconds, while for the second atom it will be 1/20th of a second. This leads to the appearance of concerted motion in STM.

This investigation is a clear case of where the experimental/theoretical interaction is so vital: without the experimental images of the vacancies moving, the question to address would have been unclear; without the theoretical modelling, however, the mechanism could not have been elucidated. This is one way in which the collaboration proceeded: experiment finds an interesting, but inexplicable, phenomenon, and theory is guided to the explanation.

6.5 Behaviour of hydrogen at steps and defects

As has already been discussed in Chapter 4, the bonding at steps and defects is different to that on the perfect surface. It is important to understand how this affects both diffusion and stability, as these will have a strong influence on growth if different.

6.5.1 Saturation of steps and relation to growth

The question of growth of silicon will be covered in more detail than it is here in Chapter 7; however, it is worth discussing the question of denuded zones and steps here. In solid-source MBE, large areas of clean terrace are seen both above and below B-type steps on the growing surface - there are no islands and very few atoms in these areas. The explanation for this is that the B-type step is a nucleation site for growth, and all atoms which are within a certain distance of the step bond there, resulting in step-flow growth and double steps, eventually. In the gas source growth experiments performed, however, (Owen et al. 1997a,b) none of these denuded zones were found below 700K, and islands nucleated close to the step edge. The only explanation available for this is that the rebonded edges of the step are being saturated with hydrogen, which is stopping growth.

To determine whether this is correct, two questions must be answered: is the step a good site for hydrogen to adsorb at, and how does it get onto the step edge ? The first question can be answered by finding the energies for adsorbing hydrogen at different step edges in different configurations; these are given in Table 6.1 from TB calculations, which used a unit cell fourteen dimers long and two dimer rows wide. The hydrogens at the top of the step are adsorbed on the dimer at the edge, while the hydrogens at the bottom are adsorbed on the three-coordinate second-layer atoms. See Fig. 4.8 for a diagram of the B-type step. The energies are given for pairs of hydrogen, as this is the configuration found on the growing surface.

The most obvious manner for a hydrogen to get onto a rebonded B-type step is by diffusion down from the terrace above; diffusion along the step will be blocked by any other hydrogen already present, and may well have a higher barrier due to a more stable start point (by analogy with the saturated surface diffusion). The diffusion from the top of the step onto the base has been modelled with TB, and the results are presented in Figure 6.11(a) below, along with a schematic diagram showing the process in Fig. 6.11(b). As with all processes modelled in this chapter, the atom labelled ‘D’ was not allowed to bond to the hydrogen.

Figure 6.11: (a) The energy for a hydrogen atom diffusing down a B-type step, from the upper terrace to one of the rebonded atoms below. The barrier is 1.57 eV. (b) The process indicated schematically. (i) is the start point and (ii) is the end point.

The diffusion was modelled using TB with a unit cell in which there were 5 dimers in the upper terrace, and the equivalent of 5 in the lower (as discussed in Chapter 4, this is the smallest unit cell for a rebonded step which has no clear interactions between steps), with the bottom layers of the cell terminated in hydrogen and frozen in bulk-like positions in the usual manner. The diffusing hydrogen was constrained in planes of constant y (lying along the dimer row in the upper terrace - the y axis runs vertically up the page in Fig. 6.11(b)), and only permitted to bond to the atoms it starts and finishes on - specifically not to atom D. The barrier found is 1.57 eV, which is reduced to 1.37 eV taking into account the correction. This is 0.4 eV lower than the barrier on the clean surface, and means that by the time the hydrogen is diffusing on the clean surface, it will diffuse extremely fast down the steps (3000 times as fast as on the clean surface at 600K). The plateau just to the right of the peak is an unusual feature, and is caused by the geometry of the system. Whereas for diffusion on the clean surface the mid-point is unstable, and the hydrogen is only bonded to one atom either side of the peak, the step geometry allows the hydrogen to remain bonded to both atoms by increasing its height at each point away from the step edge. Eventually, the distance to the top of the step becomes too high, and the drop starts. In the context of saturating the bottom of a step with hydrogen, it is worth noting that the barrier is equally low for the hydrogen to climb the step as to descend it. There are, however, other factors that will combine to maintain the saturation: the extra stability gained from pairs of hydrogens at the bottom; and the population of hydrogen on the upper terrace - if the site at the top of the step is occupied (as it may well be, given the amount of hydrogen on the surface), then the diffusion will not occur.

To sum up, the evidence for hydrogenated B-type steps during growth is as follows: a pair of hydrogens is 0.2 eV more stable at a rebonded B-type step than on a clean dimer; the barrier for diffusing down a step is 1.37 eV; hydrogenating a step does not stop enhancement in STM at low voltages (see Chapter 4); experimental images show a lack of denuded zones. Altogether, this offers a strong case for believing that the steps are hydrogenated, and this is what causes the edges to stop being a nucleus for dimer growth.

6.5.2 Hydrogen at defects: nano-mirrors

While the bonding of the 1DV has been discussed in Chapter 4, and shown to be such that it is less reactive that an equivalent dimer site, the bonding of the dimers either side of it has not been investigated. If they pin - or alternatively repel - hydrogen, then this will have an effect on the mobility of hydrogen and hence growth. As was the case for steps, the first test is to investigate stabilities for adsorbing hydrogen, and these are shown in Table 6.2. These energies come from TB calculations, with a unit cell consisting of two standard unit cells side-by-side, with one defect in the system.

Figure 6.12: (a) The energy for a hydrogen atom diffusing away from a 1DV, starting next to the defect and moving away. The barrier is 2.5 eV. (b) The process indicated schematically. (i) shows the start point and (ii) the midpoint.

This figure shows that the defect acts as both a sink for hydrogen atoms (for once they are adsorbed next to it, they require a large amount of energy to get off) and also a mirror (it is as hard to get on as to get off). As with the step, it is the bonding of the situation which is responsible for the barrier height. The dimer which the hydrogen starts on is next to a 1DV, and is pulled away from the normal position in the surface. This means that the distance between the dimer the hydrogen starts on and the one it is going towards is increased - as can be seen by comparing Figs. 6.6 and 6.12. This increased distance means that at the mid-point, the hydrogen atom has much longer bonds to both dimers, giving an increased barrier relative to diffusion on the clean surface. The barrier is remarkably symmetrical, which implies that the defect may well act as a mirror - any hydrogen adsorbed two dimers away from a defect will be far more likely to diffuse away from the defect than towards it, due to the increased barrier of 0.5 eV.

This resolves a question from experiment (Owen 1996, p.72 and Fig. 4.7); there were several observations of a smudge trapped between two defects, which then disappeared at high temperature (700 K). The only explanation given the above result is that the hydrogen atom hopped across dimer rows (an event seen experimentally at 700 K, though very rarely), rather than across the defect.

Conclusions The behaviour of hydrogen has been investigated, using tight binding and LDA. The diffusion on a clean surface has been modelled, and shows good agreement with experiment; the tight binding parameterisation has proved reliable. The mechanism for diffusion on the saturated surface has been found using experimental results to produce a path, and theoretical modelling to explain the behaviour along this path. The behaviour of hydrogen near steps and defects has been modelled, and an explanation provided for the lack of denuded zones in gas source growth. The rebonded B-type step proves to be a sink for hydrogen, while the 1DV will act as a mirror due to the high barrier for diffusion onto dimers adjacent to it.