Isotopic effects on the dielectric response of Si around the E1 gap

The effect of isotopic composition on the dielectric function of silicon from 3.1 to 3.7 eV has been investigated using spectroscopic ellipsometric data obtained on Si-28, natural Si (Si-nat, M-nat = 28.09 amu), and Si-30 crystals. At low temperatures, the energies of the E-0' and E-1 interband transitions, which occur in the energy range under study, become mass dependent through the dependence of the electron-phonon interaction and the lattice parameter on the average isotopic mass. We determine the mass dependence of critical point energies and other optical parameters as accurately as possible by analyzing the ellipsometric data in reciprocal (Fourier-inverse) rather than direct (frequency) space. The obtained dependence of the critical point energy versus isotope mass [Delta E-1/Delta M= +1.9(4) meV/amu] is in reasonable agreement with estimated values obtained from the temperature dependence of E-1 in natural silicon.