Lattice isotope effects on the widths of optical transitions in silicon

Using measured isotope shifts for the 607 cm^-1 local vibrational mode, LVM, of substitutional carbon, C_s, we demonstrate that isotope disorder contributes ∼0.5 cm^-1 to the width of that LVM in natural silicon. The width of the LVM of C_s also depends on its energy relative to the density of two-phonon states, and increases along the sequence ¹³C in natural silicon, ¹²C in natural silicon and ¹²C in ³⁰Si. Other LVMs show larger isotope effects, and so discrete structure rather than line broadening. In the case of zero-phonon lines, we take the 3942 cm^-1 line as a potentially favourable example. We estimate that the isotope disorder contributes only 0.09 cm^-1 to the linewidth in a natural silicon sample, a contribution that is negligible compared to typical strain-broadening effects, but would be a lower limit to the linewidth in high-purity natural silicon.