Strain in a single ultrathin silicon layer on top of SiGe islands: Raman spectroscopy and simulations

By means of resonant Raman spectroscopy we investigated the strain on a single ultrathin crystalline silicon layer, locally induced by buried SiGe nanostructures. The spectrum of a 5-nm-thick silicon layer on top of SiGe islands shows a single highly strained feature attributed to the out-of-plane phonon. The direct comparison of the experimental results with finite-element methods through spectral simulation shows excellent agreement that clarifies the physical origin of the spectrum. An increase in the silicon layer thickness up to 40 nm results in a progressive reduction in the strain.

Figure 1

(a) Atomic force microscopy scan of SiGe islands overgrown with a 5-nm-thick Si layer. The shading is proportional to the local surface slope with respect to the (001) plane. The buried nanostructures are uniform dome-shaped islands, coexisting with a negligible number of barn and superdome-shaped islands. A statistical analysis of island base area and height is shown in (b) and (c), respectively.

Figure 2

(Color online) (a) Subtractive Raman spectra of a single ultrathin layer of silicon on top of SiGe nanostructures. The vertical solid line marks the unstrained value of $520.5{\text{cm}}^{-1}$. The region close to this value is corrupted by an artifact of the subtraction process. (b) Corresponding in-plane strain obtained by assuming that there is the same linear relationship between $\Delta \omega$ and $ϵ$ as in the case of a flat (001) surface. The validity of this assumption is discussed in the text. The two solid lines show the $1/t$ behavior from Ref. 18 and the $1/t^3$ predicted by an analytical model (Ref. 19).

Figure 3

(Color online) (a) Cross-sectional images of the map of the $\left({ϵ}_{xx}+{ϵ}_{yy}\right)/2$ component of the silicon strain for the four thicknesses from 5 to 40 nm. The black solid line marks the upper $d_p/2$ thick region. (b) Top view bidimensional map of the average strain in the upper $d_p/2$ thick region of the 5-nm-thick Si layer. The four quadrants report the four independent components of the strain tensor as calculated from the finite-element simulations. The lower edge is parallel to [100]. The island facets are superimposed for clarity. The side of the map is 110 nm wide. (c) Plot of $\left({ϵ}_{xx}+{ϵ}_{yy}\right)/2$ component of the strain in silicon as a function of depth along the island axis. The shaded zone is $d_p/2$ deep.

Figure 4

Intensity $I$ and relative Raman shift $\Delta \omega$ of the observable phonon as a function of the position of the dot. The colorbar is shown on the left. For the intensity $I$, black corresponds to 0 and white to 1. For the relative shift $\Delta \omega$, black corresponds to $-15{\text{cm}}^{-1}$ and white to $0{\text{cm}}^{-1}$. For clarity the components outside of the dot are set to 0 intensity.