An accurate electromagnetic theory study of surface enhancement factors for Ag, Au, Cu, Li, Na, Al, Ga, In, Zn, and Cd

An accurate but simple method for determining electromagnetic fields near the surfaces of small metal spheroidal particles has been used to determine field and Raman enhancements for 10 metals in groups 1, 11, 12, and 13. This method corrects the simple small particle LaPlace electrostatic field for electrodynamic depolarization and damping effects to give a result which is equivalent to solving Maxwell's equations to order k³ (k = 2π/λ), and it also incorporates size-dependent plasmon broadening effects which arise from small particle surface scattering of the conduction electrons. With this method we have studied the dependence of both field and Raman enhancement factors on particle size and shape, and from this we have determined optimal sizes, shapes, excitation frequencies, and enhancement factors for each metal. Comparisons with experiment are given where possible. Our results for the noble metals are in accord with the observed frequency dependence of SERS for Ag, Au, and Cu, but the optimized peak enhancements are still well below (factor of 10¹-10²) experimental enhancement estimates. Enhancements for the alkalis are comparable to those for the noble metals, but with a flatter dependence on frequency in the visible region, and with different optimum particle sizes and shapes. Al and In are found to give large enhancements over a broad region of the spectrum (IR → UV) but Ga only gives large enhancements in the IR. The size and shape dependences of the enhancements for the group 13 metals show great variation with metal and with frequency. Cd is found to exhibit relatively small electromagnetic enhancements in the visible and near-UV regions, while Zn has windows of significant enhancement at 2.5 and 3.5 eV.