Islands, Mounds and Atoms
Crystal growth far from thermodynamic equilibrium is nothing but homoepitaxy - thin film growth on a crystalline substrate of the same material. Because of the absence of misfit effects, homoepitaxy is an ideal playground to study growth kinetics in its p
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Was die Sch¨ onheit f¨ ur T¨ aler gehalten hat, waren in Wirklichkeit Berge.1 Elfriede Jelinek, Der Tod und das M¨adchen
While the growth of islands discussed in the last chapter could be considered as an essentially two-dimensional problem, the morphology of a multilayer film is determined not only by the transport of atoms within an atomic layer (intralayer transport), but in addition by the transport of atoms between different atomic layers (interlayer transport). In the same way as the evolution of island shapes with temperature can be understood in terms of the activation of atomic processes along the step edge, the sequence of multilayer growth regimes that unfold as a function of temperature is governed by the activation of atomic processes which enable the exchange of atoms between different atomic layers.
4.1 The Temperature Dependence of Multilayer Growth In this introductory section an overview over the temperature dependence of multilayer growth morphologies in Pt(111) homoepitaxy will be given. Before presenting the experimental examples, it may be useful to schematically distinguish four idealized growth modes (Fig. 4.1). • Step flow growth: Even the most careful preparation of a low Miller index single crystal surface leaves a certain number of atomic steps on the surface. Steps originate from the mosaic spread of the single crystal (i. e. the presence of low angle grain boundaries) or from limitations in the perfection of crystal orientation prior to and during the processes of crystal cutting and polishing. For metal and semiconductor surfaces the average step spacing l may be as large as 5000 ˚ A and the spread of step spacings around their average value may allow even terraces of several μm width to be present on the surface. Nevertheless, at high temperature the adatom diffusion coefficient D and the size i∗ of the critical nucleus will be large. According to (2.18), this implies that the island number density N is small, and hence the average island separation 1
“What Beauty took for valleys were in fact mountains.”
T. Michely et al., Islands, Mounds and Atoms © Springer-Verlag Berlin Heidelberg 2004
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4. Pattern Formation in Multilayer Growth
Fig. 4.1. Schematic representation of idealized growth regimes in homoepitaxy. (a) At sufficiently high temperature (large adatom diffusion coefficient) or small step spacing step flow takes place. At lower temperatures, adatom islands nucleate on the terraces, giving rise to either (b) layer–by–layer growth (perfect interlayer transport) or (c) mound formation (no interlayer transport). (d) At very low temperatures adatoms are immobile and a random, self-affine morphology without a characteristic length-scale forms
lD = N −1/2
(4.1)
may well exceed the terrace width l, l lD . Consequently, all adatoms are captured by preexisting steps and no nucleation takes place. As shown in the one dimensional sketch of Fig. 4.1a, under these conditions no new steps are created on the surface during growth and the steps move laterally with an average speed imposed by
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