Line Broadening of an Impurity Spectrum in Silicon

Adapting an idea proposed by Fermi to explain the shifts of the high-series lines in the alkali spectra under perturbation by foreign gases, the present paper develops a theory of the broadening of impurity levels in semiconductors. In its principal assumptions it follows the work of Lax and Burstein, but it is simpler and leads perhaps to somewhat better agreement with their own experimental data. While in the problem of the alkalis a large valence orbit is disturbed by the random motion of foreign gas molecules, the same effects result in the present instance from collisions between a hole and the phonons. In detail, the broadening arises from two mechanisms: the scattering of the bound hole by the acoustic motion of the crystal atoms and the fluctuation in polarization energy of the atoms lying between the approximately hydrogen-like orbits of the hole. The former effect is dominant and accounts reasonably well for the experimental results. The calculation is applied to boron-doped silicon and yields a total zero-point broadening of 1.6×{}10^-3 electron volts; this is to be compared with an experimental value of about 1×{}10^-3 ev and the result of 3×{}10^-3 ev obtained by Lax and Burstein. Some question remains about the temperature dependence of the effect.