Predicted Raman spectra of Si[111] nanowires

We present calculated Raman spectra for freestanding Si[111] nanowires with diameters from d≈10.3em0exnm up to 50.3em0exnm. In the first step, we calculate eigenmodes with a Stillinger-Weber-type model. After this, a bond polarizability model is used to calculate Raman spectra out of the eigenmodes obtained in the first step. In addition to the usual silicon peak at 5190.3em0excm^-1, we find for all wires a Raman signal originating in a low-frequency breathing mode with a $1∕d$ frequency dependence. We also give an analytic derivative that generalizes this result to arbitrary nanowires. Our findings can therefore be used for a new and simple way to determine the diameter of nanowires.