Transport of Deposited Atoms throughout Strain-Mediated Self-Assembly

Using enriched isotopes, we developed a method to elucidate the long-standing issue of Ge transport governing the strain-driven self-assembly. Here ${}^{76}\mathrm{Ge}$ was employed to form the 2D metastable layer on a Si(001) surface, while the 3D transition and growth were completed by additional evaporation of ${}^{70}\mathrm{Ge}$. This isotope tracing combined with the analysis of the Ge-Ge LO phonon enables the tracking of the origin of Ge atoms and their flow towards the growing islands. This atomic transport was quantified based on the quasiharmonic approximation of Ge-Ge vibrations and described using a rate equation model.

Figure 1

(a) Schematic illustration in the abrupt configuration of the two-isotope growth of a $\mathrm{Ge}/\mathrm{Si}(001)$ island. (b) Ge-Ge modes of ${}^{70}\mathrm{Ge}$ and ${}^{76}\mathrm{Ge}$ sources used in this study. (c) Raman spectra of Si(001) bare substrate (Si), 4.4 ML of ${}^{76}\mathrm{Ge}$ deposited on Si(001) (2D), and a ${}^{76}\mathrm{Ge}$ 3D island grown by depositing 1 ML of ${}^{76}\mathrm{Ge}$ on the 2D layer (3D).

Figure 2

(a) Ge-Ge LO phonon of $\mathrm{Ge}/\mathrm{Si}(001)$ islands grown by deposition of 0.6 ML on the 2D layer using the enriched sources ${}^{76}\mathrm{Ge}$ (all ${}^{76}\mathrm{Ge}$) and ${}^{70}\mathrm{Ge}$ (all ${}^{70}\mathrm{Ge}$), and the two-isotope approach (${}^{70}\mathrm{Ge}/{}^{76}\mathrm{Ge}$). (b) Ge-Ge Raman peak of ${}^{70}\mathrm{Ge}/{}^{76}\mathrm{Ge}$ islands recorded at different amounts of ${}^{70}\mathrm{Ge}$ deposited on the planar 4.4 ML-thick ${}^{76}\mathrm{Ge}$ layer. The asymmetric broadening of Ge-Ge modes can be associated with an inhomogeneous distribution of ${}^{70}\mathrm{Ge}$ and ${}^{76}\mathrm{Ge}$ within the islands.

Figure 3

The evolution as a function of $\theta$ of Ge-Ge (top panel) and Si-Ge (bottom panel) wave numbers for the three varieties of the grown islands investigated in this study. Each data point represents the average over several measurements.

Figure 4

The evolution of $y$ as a function of the amount of Ge deposited on the 2D layer (squares). Lines show the fits using the equations described in the text. The vertical dashed line denotes the end of the nucleation stage.