Concentration broadening of absorption lines from shallow donors in multivalley bulk semiconductors

Abstract

Concentration broadening of donor absorption lines is studied by numerical simulation at donor densities so low that overlap of the wave functions of electrons bound to different donors is completely negligible. At such densities broadening of donor absorption lines due to overlap is replaced by broadening due to resonant van der Waals interaction between donors, an effect which produces linewidths proportional to the first power of the donor concentration. It is argued that in three dimensions, but not in two, the van der Waals interaction completely delocalizes the excitation induced by the absorption of a photon by the donor system initially in its ground state. Detailed line-shape calculations are made for P donors in Si. For that donor species the concentration broadened $1\stackrel{\ensuremath{\rightarrow}}{s}{2p}_{\ifmmode\pm\else\textpm\fi{}}$ transition line is predicted to be 32% broader than the zero-density (lifetime-broadened) line at a P concentration of $1\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^{3}$ whereas the $1\stackrel{\ensuremath{\rightarrow}}{s}{2p}_{0}$ transition at the same P density is only 8% broader. Comparison is made with available data.