Enhanced Relaxation and Intermixing in Ge Islands Grown on Pit-Patterned Si(001) Substrates

We compare elastic relaxation and Si-Ge distribution in epitaxial islands grown on both pit-patterned and flat Si(001) substrates. Anomalous x-ray diffraction yields that nucleation in the pits provides a higher relaxation. Using an innovative, model-free fitting procedure based on self-consistent solutions of the elastic problem, we provide compositional and elastic-energy maps. Islands grown on flat substrates exhibit stronger composition gradients and do not show a monotonic decrease of elastic energy with height. Both phenomena are explained using both thermodynamic and kinetic arguments.

Figure 1

Logarithmic intensity distribution in the vicinity of the (400) Bragg reflection for Ge islands grown on the flat (a) and patterned (b) sample part. Corresponding AFM images ($1\mu {\mathrm{m}}^2$ in size) are shown as insets. (c) Ge content inside the islands as a function of lattice parameter for growth on the flat (full line) and on the patterned part (dashed line). (d) elastic energy as a function of lattice parameter as extracted from the x-ray data. All figures correspond to the same lattice-parameter scale.

Figure 2

Experimental data of the Ge-content as a function of lattice parameter together with FEM fitted data after proper separation of the Si substrate contribution (flat case).

Figure 3

Cross section map of the 3D-reconstructed Ge content profile for islands grown on flat (a), (b) and patterned (c), (d) samples. Sections are shown along the [100] (a), (c) and the [110] (b), (d) crystallographic directions. Panel (e) displays the average Ge content as a function of height. Panel (f) reports the elastic energy profile corresponding to the fitted Ge distribution on flat (filled box) and patterned (empty box) substrates. Plots made for the case of uniform concentration are analogously displayed for flat (filled triangles) and pit (empty triangles) case. The quantity $h/h_{\max }$ is a normalized height to allow the proper comparison between both island types at every height $h$.