Intrinsic Optical Absorption in Germanium-Silicon Alloys

TLDR

The study aims to explain the composition‑dependent phonon equivalent temperature by computing lattice vibrational modes using simplified models. The authors modeled lattice vibrational modes of Ge–Si alloys, emphasizing mass differences and short‑range order to capture phonon behavior. Measurements show that the intrinsic absorption of Ge–Si alloys is dominated by phonon‑assisted indirect transitions, with phonon temperatures ranging from ~270 K in pure Ge to ~550 K in pure Si, an abrupt change in band‑gap slope at ~15 % Si due to a conduction‑band structure switch, and a rapid shift of the [000] conduction band minimum relative to [111] as Si content increases.

Abstract

The intrinsic optical absorption spectrum for the germanium-silicon alloy system has been measured as a function of temperature and composition. Over the entire composition range the absorption near the threshold ($K<100$ ${\mathrm{cm}}^{\ensuremath{-}1}$) exhibits a temperature dependence which is characteristic of phonon-assisted indirect electronic transitions. There appears to be no temperature-independent component of the absorption attributable to disorder-assisted transitions. When the phonon contribution to the absorption is explicitly taken into account, as in a Macfarlane-Roberts type analysis, the experimental data yield an equivalent phonon temperature which varies from 270\ifmmode\pm\else\textpm\fi{}20\ifmmode^\circ\else\textdegree\fi{}K for pure Ge to 550\ifmmode\pm\else\textpm\fi{}50\ifmmode^\circ\else\textdegree\fi{}K for pure Si, with most of the variation occurring in the middle of the composition range. The composition dependence of the derived energy gap shows an abrupt change in slope at about 15 atomic percent Si. This is due to a switch from a Ge-like ([111]) to a Si-like ([100]) conduction band structure. The onset of direct electronic transitions (${10}^{2} {\mathrm{cm}}^{\ensuremath{-}1}<K<{10}^{4} {\mathrm{cm}}^{\ensuremath{-}1}$) was observed as a function of composition in the Ge-rich alloys. The data show that the [000] conduction band minimum moves more rapidly than the [111] minima as Si is added to Ge. In an attempt to account for the observed variation of the phonon equivalent temperature with composition, certain lattice vibrational modes were computed on the basis of a number of simplified models. The one which gives the most realistic results emphasizes the presence of atoms of different masses and some short-range order in the alloy lattice.