Fig. 1. (Colour online) Theoretical calculations of h_c for Ge_1–ySn_y films grown on Si substrate via a relaxed Ge-VS using the People Bean (P–B) model and the Matthew Blakeslee (M–B) model^[13]. Experimental data collected from this work as well as previous research are included^[14−16].

Fig. 2. (Colour online) (a) HR-XRD ω–2θ coupled scans for Ge_1–ySn_y epilayers grown with different growth times on Si (001) via Ge-VS. Symmetric and asymmetric RSMs for Ge_1–ySn_y grown with different growth times on Si (001) via Ge-VS of (b) 79 nm thick Ge_0.884Sn_0.116 grown for 8 min, (c) 95 nm thick Ge_0.884Sn_0.116 grown for 10 min, (d) 128 nm thick Ge_0.882Sn_0.118 grown for 15 min, and (e) 150 nm thick Ge_0.878Sn_0.122 grown for 20 min. The Sn concentration for each of these samples was measured from RSMs and using the modified Vegard’s law. The thicknesses of these epilayers are measured using either thickness fringes appeared in their HR-XRD ω–2θ coupled scans or X-TEM images, as shown in the example in Fig. 3(a).

Fig. 3. (Colour online) (a) X-TEM image of 150 nm thick Ge_0.878Sn_0.122 grown on Ge-VS. The high resolution lattice resolved X-TEM micrographs of Ge_0.878Sn_0.122/Ge-VS interface as well as surface of Ge_0.878Sn_0.122 epilayer are presented. (b) Relationship between thickness, Sn concentration and total growth rate of Ge_1–ySn_y epilayers. (c) AFM scan of 95 nm thick Ge_0.884Sn_0.116. (d) AFM scan of 128 nm thick Ge_0.882Sn_0.118. (e) AFM scan of 150 nm thick Ge_0.878Sn_0.122. (f) Surface roughness (RMS) of Ge_1–ySn_y epilayers with different thicknesses. Surface roughness increased with the increase in thickness (growth time), particularly after the critical thickness of ~95 nm.

Fig. 4. (Colour online) (a) Average growth rate (nm/min) at the given thickness (nm) of the Ge_1–ySn_y and its corresponding growth time (min). As the thickness of the Ge_1–ySn_y increases, the growth rate decreases. (b) Actual data points collected experimentally for average growth rate (nm/min).

Fig. 5. (Colour online) The effect of strain relaxation in Ge_1–ySn_y epilayers on their growth rate. The growth rate at given strain relaxation state was estimated using the fitted line to the actual data points given in Fig. 4. In-plane and out-of-plane strain were calculated by Eqs. (1) and (2).