One-Dimensional to Three-Dimensional Ripple-to-Dome Transition for SiGe on Vicinal Si (1 1 10)

SiGe heteroepitaxy on vicinal Si (1 1 10) is studied as a model system for one-dimensional (1D) to three-dimensional growth mode transitions. By in situ scanning tunneling microscopy it is shown that the 1D-3D transition proceeds smoothly from perfectly facetted 1D nanoripples to coarsened superripples, tadpoles, asymmetric domes, and barns without involving coalescence or agglomeration. By extension of the studies to a wide range of SiGe compositions, a 1D-3D growth phase diagram is obtained. Total energy calculations reveal that the observed critical transition volumes are fully consistent with thermodynamic driven strain relaxation.

Figure 1

STM images of Ge deposited on Si (1 1 10) before (a) and after (b) the 1D-3D ripple-to-dome transition at 4.5 and 5.5 ML coverage, respectively. The surface orientation map (SOM) inset and the high-resolution STM image in (c) reveals complete $\{105\}$ facetation. The successive stages of the ripple-to-dome transition are indicated by the labels from “1” to “4” and corresponding high-resolution STM images are shown in Fig. 2.

Figure 2

High-resolution STM images showing the evolution of from ripples, to tadpoles, domes, and barns with increasing island volume: (a) Coarsened superripple with (001) facet termination, (b) tadpole with $V$-shaped tail and $\{105\}$ faceted head, (c) transitional island between tadpoles and domes, (d) fully developed dome with $\{113\}$ and $\{15323\}$ facts, (e) transitional barn with densely stepped edges, and (f) fully developed barn with steep $\{101\}$, $\{20423\}$, and $\{111\}$ facets. Image size: $100\times 100{\mathrm{nm}}^2$. Different facets are indicated by the symbols and colors in the models shown in (g) to (j). The insets show the surface orientation maps of the STM images.

Figure 3

SiGe layers on Si (1 1 10) after postgrowth annealing for $x_{\mathrm{Ge}}=0.25$ (a),(b) and $x_{\mathrm{Ge}}=1$ (c),(d) at coverages below and above the ripple-to-dome transition. Note the different scale of the images. (e) Equilibrium phase diagram for the 1D-3D transition derived from the annealing experiments, representing the stability regions for the different phases. (f) Comparison of the experimental average base width of tadpoles (triangles) and domes (black) with the critical base widths $b_c$ (diamonds) derived from total energy calculations. The dotted lines indicate the theoretical variation of $b_c$ obtained when the less known facet, edge, and step energies are varied.

Figure 4

Calculated relative total energies $\Delta E=E_{\mathrm{isl}}-E_{\mathrm{WL}}$ of the tadpoles and domes as a function of base width $b$ for $x_{\mathrm{Ge}}=0.25$, 0.5, and 1.0 as indicated. The corresponding geometries were constructed based on the STM images of Fig. 2 and a perfectly $\{105\}$ facetted wetting layer was assumed. The arrows indicate the critical base widths $b_c$ where the dome energy becomes lower than that of the tadpoles.