7.3 Stresses and strains in semiconductor ®lm growth	249

Table 7.3. Calculated and experimental surface and diVusion energies of Si and Ge adatoms on Si(001) substrates (eV). Adatom diVusion is either parallel (//) or perpendicular (') to the dimer rows, and dimer diVusion has also been measured in the troughs (t) between the dimer rows

Adatom/	g100	Adatom	Dimer	Dimer	Dimer
substrate	eV/131	diVusion	rotation	diVusion	formation
Si/Si(001)	1.3960.1a,f	0.6760.08b (//)	0.7060.08c	0.9460.09d (//)	0.3560.05e
		,1.0b (')		1.0960.05g (//)
				1.2760.08g (t)
				1.22±1.26h (t)
				1.3660.06g (')
Ge/Si(001)		0.62f (//)
		0.9560.1f (')

References: (a) Northrup (1993); (b) Mo et al. (1991, 1992); (c) Swartzentruber et al. (1996);

(d) Swartzentruber (1996); (e) Tromp & Mankos (1998); (f) Milman et al. (1994, 1996); (g) Borovsky et al. (1997, 1999); (h) Lee et al. (1999). References (a), (f) and (h) are calculations; other entries are experimental observations.

is negative, for the same reasons as there can be unstable facet orientations via equation (1.11).

From my own research perspective, that of trying to understand atomic processes at surfaces and determining the energies involved, nucleation and growth on these surfaces is intrinsically rather complicated. In principle, the dimer reconstruction has to be broken and reformed as each layer is grown, so there can be nucleation barriers at many stages of growth. At normal growth temperatures (400±650°C), dimerization is not the rate-limiting step. However, in a complex system, experiments which cover a large range of the temperature or deposition rate variables must take into account the possibility that diVerent atomic mechanisms may well become important under diVerent conditions. Semiconductor surfaces have this feature in common with molecular biology: the problem of rugged energy landscapes, including multiple energy minima and reaction pathways. If this is true for the simplest semiconductor system, it may color how we think about the more complex processes which are discussed later.

7.3.3Strained layer epitaxy: Ge/Si(001) and Si/Ge(001)

Ge and Si have the same structure, diVering only in the lattice parameter by 4.2%, with the Ge slightly less strongly bound as seen in tables 1.1 and 7.1. Thus, the surface energy of Ge is expected to be lower than that of Si, and deposition of Ge will ®rst occur in the form of layers. However, growth beyond the ®rst few ML will build up substantial strain due to the mismatch, and after a certain thickness, the Ge prefers to grow as islands in which (if the islands are large enough) the strain has been

2507 Semiconductor surfaces and interfaces

relieved by mis®t dislocations. The route to this state is quite complicated, but can be understood qualitatively by reference to ®gure 5.3(a). The equilibrium Ge layer thickness has been measured, after annealing, to be 3ML (Copel et al. 1989). But it is possible to grow much thicker coherent layers kinetically, or by using a surfactant; the ®rst islands to form are also coherent with the underlying layers, not dislocated (Eaglesham & Cerullo 1990, Krishnamurthy et al. 1991, Williams et al. 1991).

The growth of this system, and the inverse Si/Ge(001), and the growth of SiGe alloys for practical devices are suYciently important topics to warrant reprint collections, review articles and book chapters of their own (Stoneham & Jain 1995, Whall & Parker 1998, Hull & Stach 1999). For practical strained layer devices, there is a strong interest in suppressing island formation, which is practicable when alloys with low enough

Ge content are used, or when alternating Si and Ge layers are thin enough. In the ®rst few MLs 23n reconstructions, with n,8±12, are observed when monitoring the

growth of Ge/Si by RHEED (Köhler et al. 1992). STM has shown that these structures consist of rows of dimer vacancies (Chen et al. 1994) which both relieve and respond to surface stresses.

But the growth process of most interest is the evolution of the islands, in competition with further growth of layers, and the instabilities which result at relatively high Ge content, or in the limit using pure Ge and Si layers. Here a large literature has been created, studying island densities and size distributions. Bimodal size distributions, some of them quite narrow can be created, which themselves may be of interest as quantum dot structures. As seen in TEM pictures, taken ex situ after UHV preparation, the smaller Ge islands are strongly strained as shown in ®gure 7.13(a). The strong black±white contrast is due to the bending of the substrate (Si) lattice caused by the Ge island, and indicates a radial strain, which also has a component normal to the substrate. This strain is relieved somewhat in the dislocated islands, which rapidly grow much larger. An individual dislocated island, observed in UHV SEM and UHV STEM is shown in ®gure 7.13(b) and (c). The higher secondary electron contrast from the ridges shows up the facetting in (b); moiré patterns in (c) indicate the presence of mis®t dislocations between the island and the substrate.

The facets have been subsequently characterized principally by AFM and STM, and various shape transitions identi®ed, both with and without surfactants (Horn-von Hogen et al. 1993, Floro et al. 1997, 1998), and by in situ TEM (Ross et al. 1998). At deposition temperatures above 500°C, where surface diVusion is rapid, the size to which these coherent islands grow is markedly dependent on the presence of other sinks within the diVusion distance. Dislocated islands can be nucleated, preferentially from the larger coherent islands, or at impurity particles; once nucleated these islands form the strongest sinks, they grow rapidly and the supersaturation in the (u.3 ML) Ge layer reduces. At a temperature of 500°C, diVusion distances are of order 5 mm, whereas below 400°C this ®gure drops below 0.5 mm. Assuming that the dimer energetics are similar on Ge to that on Si(001), then all these rearrangements on the surface are occurring via a substantial sea of migrating ad-dimers.

Similar eVects are seen when Ge ®lms, grown at room temperature to thicknesses above 3 ML are annealed at comparable temperatures, although the detailed

7.3 Stresses and strains in semiconductor ®lm growth		251
(a)		(b)

(c)

Figure 7.13. Island formation in vicinal Ge/Si(001). Ex situ bright ®eld TEM image, showing

(a) coherent islands. The strong black±white contrast parallel to the re¯ection g5220 indicates a radial dilatational strain ®eld; (b) UHV SEM and (c) UHV STEM images of a single dislocated island, showing (b) facets and (c) moiré fringes indicative of mis®t dislocations (from Krishnamurthy et al. 1991, reproduced with permisison).

mechanisms and diVusion coeYcients will be diVerent. Initially, there are no large (. 10 nm radius) islands, but as annealing proceeds the bigger islands grow rapidly, while the size distribution of the smaller islands (,10 nm radius) stays constant. This evidence suggests that the material for the rapid growth of the dislocated islands occurs primarily from the supersaturated layer rather than from the coherent islands, and in particular, that their strain ®elds are eVective in keeping out migrating adatoms and/or dimers (Krishnamurthy et al. 1991, Drucker 1993, TersoV et al. 1996).

Since Ge is less strongly bound than Si, growth of SiGe alloys leads to Ge segregation at the surface. This eVect has been studied by several authors (Godbey & Ancona 1992, 1993, Li et al. 1995), and simple kinetic models have been developed to explain these results in terms of a segregation energy, Es or Eseg. Segregation proceeds by an atomistic mechanism which is con®ned to essentially the surface layer, as diVusion within the bulk is quite negligible at typical growth temperatures; but within a twolayer model, segregation is almost complete for thin Si layers on Ge at T$ 500°C. From the surface composition, as measured by AES on thin Si/Ge/Si layers (Li et al. 1995)

2527 Semiconductor surfaces and interfaces

or XPS work on SiGe alloys (Godbey & Ancona 1992, 1993), energies in the range 0.24±0.28 eV have been determined. If interchanges are allowed between three layers

(where Es is the sum of the layer segregation energies) the same values are obtained (Godbey & Ancona 1997, 1998). Calculation has retrieved Es ,0.25 eV, both at the Si(001) surface, and interestingly also at the `surface' around an internal vacancy

(Boguslawski & Bernholc 1999).

Lateral segregation can also occur, since Si diVuses preferentially to compressed regions and Ge to expanded regions. This is one factor in producing a `rippled' surface, and in subsequent non-linearities and growth instabilities in Ge±Si alloys. When dots and/or ripples interact there are elastic eVects, and this can in¯uence nucleation and subsequent growth. As such issues are potentially important for device materials, a full (but rather complex) literature has been created, and various regimes have been studied over several years (Cullis et al. 1992, Jesson et al. 1996, Deng & Krishnamurthy 1998, Chaparro et al. 1999). These types of eVect, plus the perceived potential for fabricating self-assembled quantum dots, have sparked a great deal of related theoretical activity, and continued discussion of the relative role of thermodynamic and kinetic argument in understanding the structures formed (TersoV & LeGoues 1994, Shchukin et al. 1995, Daruka & Barabási 1997, Medeiros-Ribeiro et al. 1998). Such discussions often go through complicated gyrations before they get resolved, but this one should get clari®ed before too long if we all keep at it!

We are now able to begin compiling tables of experimental and theoretical energies for Si and Ge growth systems, as in table 7.3, which one believes will eventually make the various observations comprehensible within a reasonably uni®ed picture. But we always need to bear in mind that what actually happens in a given experiment or growth procedure may be a subtle combination of thermodynamic and kinetic eVects, in which the competing eVects of strain, adatom/dimer mobility and binding, surface and lateral segregation, facetting and coarsening play important parts. The subtleties of the transitions and the many competing structures, should make one rather wary of supposed clear-cut proofs of particular mechanisms; this is an area where metastabilty is very important, and where there are many routes to the supposedly ®nal structures.

7.3.4Growth of compound semiconductors

The properties of compound semiconductors such as GaAs, or more recently group III nitrides, grown by MBE and other techniques, are suYciently important to have whole books devoted to the topic (Tsao 1993, Gil 1998). Often there is interest in growing such epitaxial layers on Si or GaAs substrates, in order to incorporate III±V, II±VI or IV±VI features with mature Si and GaAs-based device technology. Like Si and Ge, GaAs(001) surfaces also exhibit such higher order vacancy line structures, such as the 234 and 6 34 and various centered arrangements (Pashley et al. 1988, Chadi 1989, Biegelsen et al. 1990). Questions of layer growth versus nucleation on terraces have been addressed, as well as alloy segregation and pattern formation at steps (Arthur 1994, Gossard 1994, Joyce et al. 1994). The atomic (diVusion±reaction±incorporation) mechanisms are com-

7.3 Stresses and strains in semiconductor ®lm growth	253

plicated, but calculations have developed to the point where the energies associated with some of the processes can be studied in some detail (Madhukar & Ghaisas 1988, Krishnamurthy et al. 1994, Kley et al. 1997).

Given the complexity of III±V chemistry, it is remarkable that the resulting microstructures of GaAs are rather similar to the elemental deposits described in the previous section. The main lesson to draw is that, in the presence of an As (i.e. group V) overpressure, the rate-limiting processes on the surface are typically associated with the incorporation of Ga (i.e. the group III cation). There are, of course, many subtle eVects, particularly in relation to the incorporation of dopants. In general, II±VI and IV±VI compounds are prepared from compound sources, and then stoichiometry is less of an issue. However, in these cases, dopant incorporation presents particular challenges, as described by Han et al. (1999) and Springholz et al. (1999).

Several groups have monitored the growth of GaAs in situ using RHEED oscillations and a variety of light scattering techniques, such as ellipsometry or re¯ectance diVerential spectrometry. Of particular interest in the present context are those studies which correlate surface and step structures observed by a microscopic technique, typically STM or AFM, with the real time monitoring technique, such as RHEED or an optical technique. Nucleation of 2D islands and subsequent (rough) growth has been observed on wide terraces, for all the materials discussed in this section including GaAs, and the measured roughness correlated with the diVraction intensity (Johnson et al. 1993, 1994, Sudijono et al. 1993).

This roughness is thought to be caused by the Ehrlich±Schwoebel barrier, just as in the elemental case, though it is possible that selective adsorption at steps could also play an important role. In model computations, one can increase the strength of this barrier to the point that straight steps become wavy; for larger barriers, well developed mounds are seen. This is a fascinating example of pattern formation or self organization; in eVect, the surface rearranges itself so that it (just) creates conditions for step ¯ow, as illustrated in ®gure 7.14. There are also discussions in the literature of the role of adatom and ad-dimer concentrations in setting the chemical potential during growth (Northrup 1989, TersoV et al. 1997) which parallel those discussed in the previous section for the silicon and germanium systems, but may contain further complexities yet to be explored. These compound systems are of particular interest for quantum dot structures.

One set of studies of GaAs(001) growth, combining RHEED oscillations and more recently STM observations, has been pursued over several years (Shitara et al. 1992, Smilauer & Vvedensky 1993, Joyce et al. 1994, Itoh et al. 1998). These studies are very interesting in respect of the relationship between model calculations, simulations and the growth of real materials. The presumption is that the RHEED intensity, measured at a particular well-chosen glancing incident angle, is most aVected by the roughness of the surface, and thereby measures the step density. This is consistent with the ML oscillation period, and if true, would enable ®ner details of the waveform to be interpreted; however, this is not the key point. Most informative comparisons have been with studies on vicinal surfaces, in the relatively narrow temperature region where the transition from 2D island nucleation on the terraces to step ¯ow takes place. Interest

254 7 Semiconductor surfaces and interfaces

Figure 7.14. (a) STM image of a GaAs buVer layer; (b) after termination of growth at the fourth RHEED maximum. Scan range for (a) and (b) 2003 200 nm2; (c) and (d) Monte Carlo calculation after 50 layers deposition, original scale 2003 200 sites2. Vicinal surface with slope 50.1 in (c), showing wavy steps, and on-axis surface in (d), showing large mounds (adapted from Johnson et al. 1993, with permisison).

was focused on the amplitude and phase of the initial transient which establishes the ML oscillation period, and in the relaxation to the smoother surface after the ¯ux is switched oV.

A set of experiment±model comparisons is given in ®gure 7.15, showing essentially perfect agreement with a conceptually simple solid-on-solid model containing no more than three important energy parameters. The key ingredients are: (1) the initial transient relaxation is caused by 2D nucleation and initial growth which establishes surface roughness at the ML level. The oscillations persist if the surface regains its smoothness each ML, but die out if growth is spread over several MLs, i.e. reaching a steady-state distribution. (2) The relaxation at the end of deposition has two components. These

7.3 Stresses and strains in semiconductor ®lm growth	255

Figure 7.15. Experimental RHEED intensities during growth of GaAs(001) layers (miscut 2° towards [010], Shitara et al. 1992) in comparison with KMC simulations at a Ga ¯ux rate of

(a) 0.20 and (b) 0.47 ML/s (after Smilauer & Vvedensky 1993, reproduced with permission).

are a fast relaxation which is associated with processes taking place on the same level (island edge smoothing, loss of adatoms, some coarsening between islands) and a slow relaxation which requires mass transport between layers (long range diVusion including the ES barrier).

There have been several attempts to break down these processes into elemental steps, but they have not been without problems. From the description given here and from the discussion in chapter 5, it is clear that each process observed may well be composite. Moreover, we might well expect that any mechanisms deduced are only valid in a relatively narrow range of temperature and ¯ux, so that the model cannot be used uncritically in other situations. In particular, the observed transition from 2D nucleation to step ¯ow is remarkably sharp, which means that rather high activation energies would result from a direct comparison of the model with experiment. However, examination of the surface ex situ by STM shows that this transition does not imply that 2D nuclei are not produced at the higher temperatures, just that they are rapidly swept up by the steps. Models of the 2D nucleation process which take account of the need to reform the 234 structure as each layer is added give realism to the growth simulations, at the expense of several extra parameters (Itoh et al. 1998). But now we are beginning to see what speci®c features of the bonding are behind the growth of GaAs(001)! This is important and fascinating, but is rather a long way from the primary uses of RHEED oscillations, namely to count monolayers, and to provide a qualitative measure of surface and thin ®lm quality.

The mathematics of step ¯ow and mound formation is itself very interesting, both with and without impurities (Kandel & Weeks 1995, Siegert & Plischke 1996, Orme & Orr 1997). Models of multilayer growth inhabit a region where, although atomistic