Surface energetics and structure of the Ge wetting layer on Si(100)

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of $\sim 3$ MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the $c(4\times 2)$ and $4\times 6$ DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of $\sim 3$ MLs, which is largely unaffected by the presence of dimer vacancy lines. The $4\times 6$ DVL reconstruction is found to be thermodynamically stable with respect to the $c(4\times 2)$ structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown.

Figure 1

(Color online) Schematic showing a two layer $4\times 6$ DVL Ge wetting layer on Si(100). Surface Ge atoms are darker than second layer Ge atoms to highlight underlying $c(4\times 2)$ tilted dimer structure, clearly visible at right, and second layer $\mathrm{Ge}-\mathrm{Ge}$ rebonding. Dimer bonds, and therefore dimer vacancy lines, run into and out of the page.

Figure 2

Schematic of two-component slab geometries employed in calculations of surface energies (a) and interface energies (b). In Ge on Si(100) wetting layer slabs, $\alpha$ layers are Ge and $\beta$ layers are Si substrate layers. ${\gamma }^{\text{top}}$ is then ${\gamma }^{\mathrm{WL}}$, and $I_{\alpha \text{−}\beta }$ is $I_{\mathrm{WL}\text{−}\text{substrate}}$, where ${\Gamma }^{\mathrm{WL}}$ is the sum of these excess energies.

Figure 3

${\Gamma }^{\mathrm{WL}}$ as a function of $n_{\mathrm{Ge}}$, the number of Ge atoms in a $4\times 2$ surface cell, for the $c(4\times 2)$ alternating tilted dimer and $4\times 6$ DVL reconstruction of a Ge on Si (100) wetting layer. The threshold values are ${\gamma }_{c(4\times 2)}^{\mathrm{Si}}=90.01\mathrm{meV}∕{\mathrm{\AA }}^2$, ${\Gamma }_{c(4\times 2)}^{\mathrm{Ge}}=67.12\mathrm{meV}∕{\mathrm{\AA }}^2$, and ${\Gamma }_{4\times 6}^{\mathrm{Ge}}=62.86\mathrm{meV}∕{\mathrm{\AA }}^2$.

Figure 4

Chemical potential of a Ge atom in the surface of a Ge on Si (100) wetting layer with thickness $l+1$. Dashed lines are the threshold values ${\mu }^{\mathrm{Ge}}\left({ϵ}_{\mathrm{Si}}^{\mathrm{XY}}\right)=-5.16\mathrm{eV}∕\text{atom}$ and ${\mu }^{\mathrm{Ge}}\left({ϵ}_{\mathrm{Ge}}^{\mathrm{XY}}\right)=-5.19\mathrm{eV}∕\text{atom}$, corresponding to the chemical potential of a bulk Ge atom biaxially strained to, respectively, the Si and Ge lattice constant.

Figure 5

Fraction of total local deformation appearing in layer $\alpha$ of a $c(4\times 2)$ reconstructed surface slab $D^{\alpha }$ and fraction of total energy relaxation realized with the addition of Ge layer $\alpha$ to a $c(4\times 2)$ reconstructed wetting layer slab $G^{\alpha }$.