Figure 1: Schematic illustration of the interaction between nucleation and growth stages. The adatom density n1 determines the critical cluster density ni; however, n1 is itself determined by the arrival flux or rate (F or R) in conjunction with the various loss processes, which have associated characteristic times (ta, tn and tc) as described in the text (after Venables 1987, 2000).
Figure 2: Algebraic solution to rate equations for Ea = 2.55, Eb = 0.7, and a range of Ed values between 0.8 and 1.2 eV: a) temperature dependence for F = 0.06 ML/min; b) flux dependence for T = 450oC. Pair-binding model for Ej up to j = 3, but with E3 = 2.2Eb, rather than 2Eb, which allows a range of i = 2 that would otherwise be absent (this range is longer the more E3 is above 2Eb). Extension to higher i-values might require higher values of Ea for comparable agreement at high temperature in panel a). Experimental nucleation densities for Ti/Si(001) are taken from McDaniels et al. (2001), and show agreement with Eb = 1.1 ± 0.1 eV. See text for discussion.
Figure 3: a) Model for nucleation at attractive random point defects (density nt), which can be occupied by adatoms (density n1t), clusters (density nxt) or can be empty; b) Algebraic solution to rate equations for trapping energy Et = 0.5, Ea = 1.16, Eb = 1.04, and a range of Ed values between 0.1 and 0.6 eV. Originally for experiments on Fe/CaF2(111) (Heim et al. 1996) recalculated for Venables (2000). See text for discussion.
Figure 4: Arrhenius representation of Pd island density Nx (cm-2) at 0.1 ML coverage on Ar-cleaved Mg(001): a) The solid line is the model for Ed = 0.2, Et = 1.5, Eb = 1.2 and Ea = 1.2 eV, plus curves for Ed = 0.3 (dashed) and 0.4 eV (dotted lines), and experimental data from Haas et al. (2000). The insert shows the model for i = 3 applicable at high temperatures, using the same notation as figure 3a; b) Sensitivity to the parameter Eb = 1.0 (dashed) and 1.2 (full lines), with Ea = 1.2 eV important at high temperature, where the experimental data (triangles) indicate condensation to be incomplete (after Venables & Harding 2000). See text for discussion.
Figure 5: Predicted n1 and nx annealing curves as a function of (D1t)0.5, for annealing at 16.5 K with attachment barriers EB = 0, 5 and 10 meV, compared to KMC simulations. The capture numbers used are based on an interpolation scheme between attachment barrier and diffusion solutions, showing essential agreement with the KMC simulations. See text for discussion of how these curves apply to STM experiments on Cu/Cu(111). (Abstracted from Venables & Brune 2002).
Figure 6: Predicted annealing curves as a function of barrier height V0, at temperatures 17 < Ta < 23K. Plotted is the ratio (n1 +nx) after a 2 minute anneal, divided by the initial value ntot = (n1 +nx) after deposition. These curves use the time-dependent capture number expression as in figure 5. The curves for 19 and 21K are also compared with the KMC simulations. Additionally a curve for annealing at 22 K for 20 minutes is given. See text for discussion of how these curves apply to STM experiments on Cu/Cu(111). (Abstracted from Venables & Brune 2002).
Figure 7: Size distributions of Ge/Si(001) islands grown at 450 and 600oC to coverages indicated. For each temperature, the left-hand peak corresponds to huts, while the right-hand peak corresponds to domes. At 600 and 650oC (not shown), large alloyed hut peaks exist between the two outer peaks; these large hut peaks are not present at 550 (not shown) and 450oC. Note also that the dome peak shifts to larger sizes at higher growth temperatures. The existence of large, alloyed huts and the shift of the dome peak to larger sizes is indicative of Si interdiffusion. Formation of a lower misfit alloy allows clusters to attain larger sizes prior to shape transitions of dislocation introduction. (after Chaparro et al. 2000a).
Figure 8: Summary of shape evolution of Ge clusters grown at F = 1.4 ML/min. onto Si(001) at 600oC. The vertical position of the horizontal bars represents the contact angle of the dominant facet with the (001) substrate. The horizontal extent of the bar represents the size range over which that morphology exists. The top half of the figure shows the evolution of the <110> cross section and the bottom half the <100> cross section. (after Chaparro et al. 2000a).