Carbon incorporation during growth of epitaxial germanium(1-y)carbon(y) layers on germanium(001) substrates

The growth of Ge_1−yC_y layers on Ge(001) substrates by ultra-high vacuum ion beam sputter deposition was investigated in order to develop an understanding of the growth kinetics and the C incorporation probabilities in different lattice configurations as a function of growth conditions.; Epitaxial metastable Ge_1−yC_y alloy layers with y ≤ 0.035 were grown on Ge(001) from hyperthermal Ge and C atomic beams at deposition temperatures 250 ≤ T_s ≤ 550°C. I show that the use of hyperthermal beams allows me to controllably vary the concentration of C incorporated as Ge-C split interstitials. Ge_1−y C_y layers grown with incident Ge-atom energy distributions corresponding to ≤0.14 lattice d&barbelow;isplacement p&barbelow;er incident a&barbelow;tom (dpa) are in a state of in-plane tension and contain significant concentrations of C atoms incorporated in substitutional sites. Increasing the dpa to 0.24 yields layers in compression with C incorporated primarily as Ge-C split interstitials. Ab initio density functional calculations of the formation energies and strain coefficients associated with C atomic arrangements in Ge show that configurations containing multiple C atoms, referred to collectively as C nanoclusters, are energetically more favorable than substitutional C and Ge-C split interstitials and yield a nearly zero average strain. In contrast, substitutional C and Ge-C split interstitials produce large tensile and compressive strains, respectively. Using the calculated strain coefficients, measured layer strains obtained from high-resolution reciprocal lattice maps, and substitutional C concentrations determined by Raman spectroscopy, I calculate the fraction of C atoms incorporated in substitutional, Ge-C split interstitial, and nanocluster sites as a function of the total C concentration y and T_s. I find that at low y and T_s values, all C atoms are incorporated in single-C configurations: substitutional C and Ge-C split interstitials. Their relative concentrations are controlled by the dpa through the production of near-surface Ge self-interstitials which are trapped by substitutional C atoms to form Ge-C split interstitials. Increasing y and T_s, irrespective of the dpa, leads to an increase in the fraction of C nanoclusters, while the fractions of substitutional C and Ge-C split interstitials decrease, due to the higher C-C encounter probability at the growth surface.