Phonon broadening of bound exciton luminescence in silicon

We report accurate measurements of the broadening of the phonon replica luminescence lines of excitons bound to P, B, Ga, As, and Bi impurities in silicon and formulate a theory of the lineshapes. The broadenings were obtained experimentally from a comparison of the phonon replica lineshapes with the no-phonon lineshape. We explain these broadenings by a new mechanism in which the spread in recombination wave vectors of the localized electron and hole leads to a spread in energy of the photons emitted since the energy of the momentum-conserving phonon is wave vector dependent. We give an expression for the donor luminescence lineshape in terms of the impurity state wave functions and the phonon dispersion. It is not necessary to invoke phonon lifetime broadening to explain our data. We find that the broadening of the TA and TO bound exciton phonon replica lines is considerably smaller than the phonon lifetime broadenings previously invoked to explain the free exciton lineshapes in silicon. We feel that the 'broadening' which has been observed for the free exciton lineshapes can be accounted for by the splitting of the free exciton ground state and the associated nonparabolicity of the free exciton bands.