1.07 6 0.03 (Follstaedt 1993); Eaglesham et al. (1993) give g001/g111 in the range 1.11 6

0.03, g113/g111 ,1.12 and g110/g111 ,1.16 at ,800°C.

However, at the higher temperature of 1050°C (1323 K, which is above the 737 to 131 transition), Bermond et al. (1995) ®nd a smaller anisotropy (,4%), as one might expect,

but they also ®nd that the ordering has changed to g111 $ g110.g113.g001. A curious feature is that the (001) face does not have a true cusp in the equilibrium form, which con-

sists largely of {111} and {113} facets and rounded regions. This is probably due to the long range stress ®eld, and the associated strain energy, due to the (231) surface domains, which results in the spontaneous formation of steps discussed by Alerhand et al. (1990) and observed by using LEEM by Tromp & Reuter (1992, 1993). A reminder that impurities can be in¯uential in such measurements was shown by the (reversible) segregation of 0.3% carbon to create extra facets, which are not in the clean equilibrium form.

Many studies on facetting transitions on Si and Ge surfaces vicinal to (111), including the eVect of the 737 to 131 transition for Si, have been made using LEED, LEEM and STM by Bartelt, Williams and co-workers, as reviewed by Williams et al. (1993), Williams (1994) and Jeong & Williams (1999). All this work suggests that at the higher temperatures the free energy diVerences between the various faces {hkl} are quite small, due to a subtle balance of substantial energetic and entropic factors. Large amplitude motion of steps on Si(111) has been observed also by REM (Pimpinelli et al. 1993, Suzuki et al. 1995), the analysis of which also implies a sizable adatom population on the terraces to mediate the step movement.

The surface entropies involved in these transitions are unknown, but microscopy is beginning to visualize directly some con®gurations (and motion) involved on the timescale of 1s and upwards. Molecular dynamics studies, as illustrated here by ®gure 7.9, can be used to estimate the entropy associated with con®guration and motion on the pico-second time scale. Another point to note is that the latent heats of melting of Si and Ge are almost a factor of 2 higher than that of close-packed metals which melt at similar temperatures. The interrelation of these apparently isolated facts can be explored further via project 7.4; a link is the angular nature of sp3 bonding in semiconductors, and its (partial) disappearance in the liquid state.

7.3.2Growth on Si(001)

The classic substrate for semiconductor growth is Si(001), since this has the simplest structure, and is used for growth of most practical devices. Typically device growers use a surface which is tilted oV-axis by about 2±4°, to form a vicinal surface which contains a regular step array. The reason for this is to promote layer by layer growth, sometimes referred to as step-¯ow, and to suppress random nucleation on terraces; nucleation is typically not wanted, because it increases the possibility of incorporating defects (e.g. threading dislocations) which have bad electrical properties. Thus the fact that higher miscut angles favor double-height steps (Chadi 1987, Tong & Bennett 1991, de Miguel et al. 1991, Men 1994) is of major importance for growing compound semiconductors such as GaAs (on Si), since single steps produce anti-phase boundaries, across which Ga and As are misplaced.

246 7 Semiconductor surfaces and interfaces

Figure 7.11. STM images of Si/Si(100) showing diVusional anisotropy of adatoms, and the eVects of SA and SB steps, after 0.1 ML deposition at R50.15 ML/min, T5(a) 563 K,

(b) 593 K. The surface steps down from upper left to lower right. In (a) anisotropic islands can be seen on all terraces; the underlying dimer rows are orthogonal to these islands. In

(b) diVusion is more rapid, so denuded zones are observed only on (231) terraces (after Mo & Lagally 1991, reproduced with permission).

Moreover, materials grown on such a substrate typically have a sizable mis®t, which may be accommodated initially by strain, but eventually by missing dimer rows at the atomic level, or by dislocations. Most growers search for low mis®t systems, so that dislocation introduction is delayed beyond the so-called critical thickness (Matthews 1975, Matthews & Blakeslee 1974, 1975, 1976, People & Bean, 1985, 1986). The bonding changes during semiconductor growth are extremely complex, since any surface reconstruction has to be undone in order for growth to proceed; at low temperatures there is the possibility of creation of many, largely unwanted, metastable structures. On the other hand if growth of complex multilayer structures, such as multiple quantum wells (MQWs) with diVerent compositions, is conducted at too high temperatures then they will be degraded by surface segregation and interdiVusion. Device engineers are always treading a ®ne line in trying to grow crystals at the lowest practicable temperature ± reducing the `thermal budget'; many of the more technical methods described in section 2.5 have been introduced solely for this reason.

There have been many studies of Si/Si(001) growth primarily using STM, in addition to spot pro®le analysis using LEED (Heun et al. 1991, Falta & Henzler 1992) and RHEED (Tong & Bennett 1991). Large area STM pictures such as ®gure 7.11 are very helpful (Mo & Lagally 1991, Liu & Lagally 1997); one can identify both SA and SB single height steps which have very diVerent roughness due to diVerent edge energies and the anisotropy of diVusion.

In one detailed study, the nucleation density N of 2D islands on the terraces was observed as a function of R and T, and an analysis similar to that of section 5.2 performed, but taking into account the diVusion anisotropy, and the anisotropy in binding

at the edges of the monolayer islands (Mo et al. 1991, 1992). The low temperature region of this N(R,T) data, with a slope of 0.165 eV, is consistent with a critical nucleus size i51, and a diVusion energy, in the `easy' direction parallel to the dimer rows, Ed5 0.67 6 0.08 eV. At higher temperatures, a transition to a higher critical nucleus size was observed, probably involving the breakup, and coarsening of, larger clusters into (stable) dimers, via dimer motion. In the initial papers it was not entirely clear what mechanism (e.g. adatom or ad-dimer motion) was actually being discussed; further work showed that adatoms typically move too fast to be observed directly by STM, but that for T,500 K, adatom motion is responsible for nucleation. Subsequently, many papers have been published on alternate diVusion mechanisms and their diVusion energies (Milman et al.1996, Borovsky et al.1997, Liu & Lagally 1997); some of these data are presented in table 7.3.

In addition to these observations of nucleation on the (001) terraces, the expected nucleus-free, or denuded, zones next to steps are seen in ®gure 7.11. In particular, the terraces to show denuded zones at lowest temperature have the (231) reconstruction, where the fast diVusion direction is towards the steps. A very elegant technique has shown the path of individual dimers can be tracked by an STM tip whose position is locked onto particular ad-dimers laterally (Swartzentruber 1996). This technique reveals preferred paths for the migrating dimers, and can also observe dimer rotation directly. The measurements, made as a function as both temperature and the ®eld produced by the tip, coupled with detailed quantum calculations, have shown that dimer rotation has an activation energy around 0.7 eV, and that dimer diVusion takes place at somewhat higher temperatures with an activation energy just less than 1 eV (Swartzentruber et al. 1996). The work of Borovsky et al. (1997, 1999) has extended these measurements to include dimer diVusion both along and across the troughs; one should note that all these measurements are made over limited ranges of temperature, where STM observations are sensitive to particular activation energies on experimentally accessible timescales.

Another piece of the jigsaw is provided by LEEM measurements of the ad-dimer concentration as a function of temperature. Patterned substrates were ®rst held between 1000,T,1300 K and then quenched so that the ad-dimers form islands (Tanaka et al. 1997, Tromp & Mankos 1998). The total area, and hence the number of dimers contained in the ML islands was measured. The data are shown in ®gure 7.12, from which the activation energy 0.35 6 0.05 eV was deduced for the formation of addimers from the reconstructed Si(001) surface. It is clear from this low value that almost all of the energy gained during deposition is due to condensation into addimers, and that relatively little is left to encourage the ad-dimers to incorporate into the growing (reconstructed) crystal. This makes it understandable that the critical nucleus size at normal growth temperatures has been found to be rather large, so that growth is typically quite close to 2D equilibrium, and the thermal population of dimers cannot be neglected (Theis & Tromp 1996). However, because of the large adsorption energies, equilibrium with the 3D vapor is far from being maintained. We can see that this general scheme is completely consistent with the range of energy values for Si and Ge binding and diVusion on Si(001) collected in table 7.3. Although there are gaps in