Hybrid surface roughening modes during low-temperature heteroepitaxy: Growth of fully-strained metastable ${\mathrm{Ge}}_{1-x}{\mathrm{Sn}}_x$ alloys on $\mathrm{Ge}\left(001\right)2\times 1$

Fully-strained single-crystal metastable ${\mathrm{Ge}}_{1-x}{\mathrm{Sn}}_x$ alloys were grown on Ge(001) up to their critical epitaxial thickness values $t_{\mathrm{epi}}\mathrm{}\left(x\right)\mathrm{}$ in order to probe surface roughening pathways leading to heteroepitaxial breakdown during low-temperature molecular-beam epitaxy under large compressive strain. All films with $x>\mathrm{}0.09\mathrm{}$ have comparable roughnesses while films with $x<\mathrm{}0.09\mathrm{}$ are considerably rougher with larger lateral feature sizes. Roughening rates increase with increasing x for films with $x>\mathrm{}0.09\mathrm{}$ due to a new hybrid relaxation path which only becomes accessible under high strain as kinetic roughening provides surface oscillations on lateral length scales that allow bulk relaxation through strain-induced islanding at growth temperatures where it could not otherwise proceed.