Vibrations of interstitial Li+ions in silicon: II. Frequencies of localized modes

The dynamical equations describing local modes of interstitial Li + in silicon are derived, using the force constants derived in the previous paper. They lead to a relationship between the isotopic mass of the interstitial and the frequency of the local mode, which is solved numerically. Local modes occur only if the interstitial mass is below a critical value. The deviation of the local mode frequency from the top of the silicon vibration spectrum is proportional to the square of the deviation of the mass from the critical value, for small deviations. The critical mass is calculated from the model to be 12 A.U. Experimental data on boron-doped, lithium-compensated silicon suggest 8 A.U.