Lattice isotope effects on optical transitions in silicon

We report the changes with lattice isotope of the energies of the zero-phonon lines (ZPLs) and some of the local vibrational modes (LVMs) of commonly encountered radiation-damage centers in silicon. On changing from Si-nat to Si-30, ZPLs of the different centers shift by +0.8 to +1.8 meV. The carbon-oxygen "C" center is taken as the primary example. For this center, the measured changes in the frequencies of the LVMs in the electronic ground state of the center agree closely with the results of density functional theory (DFT). We suggest that the LVM frequencies in the excited state can be obtained from DFT calculations of the positive charge state. The effect on the ZPL is broken into three parts. The dependence of the ZPL on the isotopically induced change in the LVMs and in the lattice volume is shown to be small compared to the effects of the electron-phonon coupling to the continuum of lattice modes. This dominant effect can be found, in principle, from the temperature dependence of the energy of the ZPL, but data can only be measured over too small a temperature range. We suggest that an estimate of the isotope effects can be derived by rescaling the appropriate data for the indirect energy gap. This simple empirical approach reproduces the measured isotope shifts of the ZPLs of the "C" and "P" centers within similar to10%, of the "I" and "T" centers within similar to30%, and within a factor of 2 for the "G" center.