The theory of the phonon broadening of impurity spectral lines is discussed within the framework of a Kubo-type formulation of the adiabatic dielectric susceptibility and the subsequent calculation of this using double-time Green's functions. The interaction of the bound electron (or hole) with the lattice vibrations is assumed to be weak and is treated as a small perturbation of the independent systems of electron and vibrating lattice; the use of the adiabatic approximation is thereby avoided. The cases in which the bound carrier states are degenerate and nondegenerate are discussed separately. The results are compared with previous work in the field.

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.

The general theory of the phonon broadening of impurity spectral lines discussed in a n earlier paper is applied to shallow impurity levels in silicon.With the use of a modified hydrogenic model and a deformation potential description of the electron-phonon interaction, expressions are obtained for typical contributions to the half-widths. S o~u e numerical estimations are made for both acceptor and donor cases and are compared with experiment.

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