Key role of the wetting layer in revealing the hidden path of Ge/Si(001) Stranski-Krastanow growth onset

The commonly accepted Stranski-Krastanow model, according to which island formation occurs on top of a wetting layer (WL) of a certain thickness, predicts for the morphological evolution an increasing island aspect ratio with volume. We report on an apparent violation of this thermodynamic understanding of island growth with deposition. In order to investigate the actual onset of three-dimensional islanding and the critical WL thickness in the Ge/Si(001) system, a key issue is controlling the Ge deposition with extremely high resolution [0.025 monolayer (ML)]. Atomic force microscopy and photoluminescence measurements on samples covering the deposition range 1.75–6.1 ML, taken along a Ge deposition gradient on 4 in. Si substrates and at different growth temperatures $\left(T_{\text{g}}\right)$, surprisingly reveal that for $T_{\text{g}}>675°\text{C}$ steeper multifaceted domes apparently nucleate prior to shallow {105}-faceted pyramids, in a narrow commonly overlooked deposition range. The puzzling experimental findings are explained by a quantitative modeling of the total energy with deposition. We accurately matched ab initio calculations of layer and surface energies to finite-element method simulations of the elastic energy in islands, in order to compare the thermodynamic stability of different island shapes with respect to an increasing WL thickness. Close agreement between modeling and experiments is found, pointing out that the sizeable progressive lowering of the surface energy in the first few MLs of the WL reverts the common understanding of the SK growth onset. Strong similarities between islanding in SiGe and III/V systems are highlighted.

Figure 1

(Color online) Inclination-angle AFM images displaying the local surface slope with respect to the (001) surface. (a)–(d) Evolution of Ge islands for $T_{\text{g}}=700°\text{C}$. Domes $\left(D\right)$ appear prior to square based, large pyramids (SP). The insets in (a) and (c) show 3D AFM images of a typical dome and a pyramid. [(e) and (f)]: $T_{\text{g}}=625°\text{C}$. Up to ${\Theta }_{\text{Ge}}\approx 4.9\text{ML}$ only small, mp are observed; domes appear in addition for ${\Theta }_{\text{Ge}}>4.9\text{ML}$.

Figure 2

(Color online) $1.5\times 1.5\mu {\text{m}}^2$ AFM scans in derivative mode. Evolution of the island morphology for $T_{\text{g}}=700°\text{C}$. The Ge coverage ${\Theta }_{\text{Ge}}$ is indicated by the labels of panels (a)–(l).

Figure 3

(Color online) (a) and (b): Island density vs $T_{\text{Ge}}$ at $R_{\text{Ge}}=0.05\text{Å}/\text{s}$. At $T_{\text{g}}=700°\text{C}$ (a) domes form prior to pyramids. At $T_{\text{g}}=625°\text{C}$ (b) pre-pyramids (at $T_{\text{Ge}}\approx 2\text{ML}$) and metastable pyramids (at $T_{\text{Ge}}\approx 2.5\text{ML}$) are formed prior to domes (at $T_{\text{Ge}}\approx 4.9\text{ML}$). (c) NP-WL photoluminescence transition energy for $T_{\text{g}}=700°\text{C}$ (squares) and $625°\text{C}$ (circles). An abrupt blue shift of the WL signal occurs at the onset of dome formation originating from a transfer of $T_{\text{Ge}}\approx 0.93\text{ML}$ Ge from the WL to the islands.

Figure 4

(Color online) Three-dimensional plot of the PL spectra as a function of the Ge coverage for $T_{\text{g}}=700°\text{C}$.

Figure 5

(Color online) (a) and (b): calculated energy difference $\Delta \left(V\right)$ of pyramids and domes with respect to the flat WL. (a) At $N=3$ the pyramids (green, mp) are not stable except for very small volumes (inset). (b) At $N=4$ pyramids (SP) are more stable than the WL for any volume. At both thicknesses, instead, domes (red, $D$) display the usual nucleation behavior. (c) Critical island volumes vs WL thickness. Gray regions indicate areas where no islands can exist. For $N<3.8\text{mp}$ pyramids can only exist up to the maximum volume indicated by empty triangles. For $N\ge 3.8$ [$N_c\left(P\right)$ in the text], pyramids (SP curve) are more stable than the WL above a minimum (negligible) volume indicated by full triangles. Domes are stable for $N\ge 2.7$ [$N_c\left(D\right)$ in the text] and then only above the critical volume indicated by full circles.

Figure 6

(Color online) [(a), (c), and (d)]: AFM inclination images and (b) local height AFM image of Ge islands grown at $T_{\text{g}}=625°\text{C}$. At 2.1 ML (a) small prepyramids (base length: 20 nm) are observed, at 3.5 ML (c): pyramids (base length up to 50 nm). Annealing of the samples in (a) and (c) for 160 min at $700°\text{C}$ leads to flat film formation for $2.0<{\Theta }_{\text{Ge}}<3.2\text{ML}$ (b), and dome formation for ${\Theta }_{\text{Ge}}=3.2\text{ML}$ (d). [(e) and (f)]: AFM inclination images, at $T_{\text{g}}=700°\text{C}$ and $R_{\text{Ge}}=0.01\text{Å}/\text{s}$ domes $\left(D\right)$ are still formed prior to pyramids but already at ${\Theta }_{\text{Ge}}\approx 4.05\text{ML}$. Note the different length scales.

Figure 7

(Color online) Critical volumes vs WL thickness for different values of the dome surface energy (the number with the same color of the curve gives ${\gamma }_{dome}$ in $\text{meV}/{\text{Å}}^2$). The pyramid curve (green) is exactly the one reported in Fig. 5c. We recall that in the “mp” region the curve gives a maximum volume beyond which the WL becomes more stable than the metastable pyramids while in the “SP” one pyramids follow the usual nucleation theory and the curve indicates the volume above which pyramids become stable.

Figure 8

(Color online) As in Fig. 7, but keeping fixed ${\gamma }_{dome}=65\text{meV}/{\text{Å}}^2$, while considering three slightly different values of ${\gamma }_{pyr}$, given in $\text{meV}/{\text{Å}}^2$. Metastable pyramids (mp) are represented by empty triangles and stable pyramids (SP) by full triangles.