Island shapes

Island-shaped surface portions of a p-type substrate 11 are doped so as to form photodiodes 12. Enclosure regions 13 surrounding but apart from the islands are also formed. Gate electrodes 15 are formed upon an insulating layer 14 so as to cover the portions in between the photodiodes and the enclosure reigons. 

Island-shaped individual detector elements are formed followed by insulating layer 30 and electrode 31. 

The Ge deposition was carried out at tenqieratures of 550 and 600 °C. The choice of such temperatures was guided by the fact that in this temperature range the islands in a single layer exhibit a dome shape, a point which is crucial for the study of the island shape transformation and will be discussed below. The Ge growth rate is about 1.5 monolayers (ML) per min. The Si deposition was carried out at 600 °C with a growth rate of about 2.5 nm per min. 

Coal pillar is an isolated body during exploitation. Since the presence of residual coal pillar, the stress field of coal pillar is different from that of other areas. Island-shaped or peninsula-shaped pillar may sustain the bearing pressure caused by multiple goaf directions. Not only the pillar itself is prone to burst, but also the upper pillar will pass concentrated stress to the lower pillar, which is consequently easier to suffer from rock burst. 

The rest of this chapter is organized as follows. We start with the mobility of metal surfaces, which we investigated by the KMC technique. This requires the rates of all possible processes as input, which we obtain by a combination of DFT and a semiempirical potential. The first application is to a Ag(l(X)) electrode, which is quite mobile even at room temperature. Interestingly, the mobility increases when the electrode potential is raised, which we explain by field-dipole interactions. Explicitly, we consider island shapes and dynamics, step fluctuations, and Ostwald ripening for this surface. In contrast to silver, a clean Au(lOO) surface is not mobile at ambient temperatures however, the adsorption of chloride ions enhances the mobility. We explain the underlying mechanism and present results for Ostwald ripening. 

In the following, we will present results on the surface self-mobility of metals obtained in our own group in cooperation with our partners from Ulm and Jlich [10, 11]. We have organized this part of the chapter as follows In Section 3.3, we briefly discuss the principles that underlie the KMC method, and the way the inputs for the simulation were obtained. In the next section we discuss the effect of an electric field on electrodes of silver (Section 3.4) this part contains two subsections on step fluctuations and the analysis of island shapes. In Section 3.5, we deal with Ostwald ripening in two systems the first is Ag in the presence of electric field and the second is Au in the presence of chloride atoms. 

Depending on the surface structure, the temperature, and the applied field, various island shapes can be observed. On fcc(lOO) and (111) surfaces, the equilibrium shape of islands show a quadratic or hexagonal profile for low temperatures and/or low fields, respectively. 

FIGURE 3.5 Ag island shapes on Ag(IOO), (a) at different temperatures in the absence of a field and (b) at different electric fields at 600 K. Reproduced with permission from Potting et al. [10], 2009, Elsevier. 

All in all, the simulations reviewed provide a consistent picture of the surface dynamics. With increasing field, the surface becomes more mobile, which entails larger step fluctuations and a decrease of the step stiffness. At the same time, the island shapes become more rounded and the coarsening faster. The same effects occur with increasing temperature. It has often been observed that in certain electrochemical experiments, the potential plays a similar role to that of the temperature in UHV. Thus, electrochemical desorption spectra obtained by a potential sweep bear a certain similarity to thermal desorption spectra in UHV. 

Fig. 8.35. Representative plots of free energy reduction per unit island volume versus island size for several combinations of relative surface energy density and island aspect ratio. The crossover points of the grafts identify conditions under which an island shape with larger aspect ratio becomes more favorable manned the smaller aspect configuration.

Fig. 8.36. Island shape transitions are represented in Figure 8.35 under the assumption that only abrupt transitions from one conical shape with relatively small aspect ratio ai to another with relatively large aspect ratio U2 are possible. This diagram suggests a more gradual transition from one conical shape to another, effected by having the steeper orientation 02 gradually expand on the lateral face of the island until the transition is completed.

The foregoing discussion is based on the assumption that the only possible island shapes are truncated solid cones with any of a discrete set of aspect ratios. The transitions from one to another aspect ratio implied by this simple picture are abrupt. A more realistic situation involving gradual transition might emerge if it is assumed that the islands take on shapes with surface orientation constrained by the slopes ai and 02, but that these orientations can coexist. For example, an intermediate shape might consist... 

The role of elastic interactions in influencing island shape transitions... 

Fig. 9.7. The figure shows a time sequence of surface profiles of h x, t) versus x for a strained film with a constant deposition flux onto a lattice-mismatched substrate. All the dimensions are in nanometers. The insets in (a)-(c) show the evolution of the third island from the right. To aid in the comparison of shapes at different times, the island shape from (a) has been included in (b). Similarly, the island shapes from (a) and (b) in (c). The slope of the largest island in each of the smaller insets is indicated.

Twesten, R. D. (1998), SiGe island shape transitions induced by elastic repulsion, Physical Review Letters 80, 4717-4720. 

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