Theory of Surface-Enhanced Raman Scattering in Semiconductors

We develop an analytical expression for the lowest order nonzero contribution to the surface-enhanced Raman spectrum from a system composed of a molecule adsorbed on a semiconductor nanoparticle. We consider a combined molecule-semiconductor system and include Herzberg-Teller vibronic coupling of the zero-order Born-Oppenheimer states. This follows a previous derivation for metallic SERS, but instead of a Fermi level, the semiconductor system involves a band gap and we find that the SERS enhancement is maximized at either the conduction or valence band edge. The resulting expression may be regarded as an extension of the Albrecht A-, B-, and C-terms and show that the SERS enhancement is caused by several resonances in the combined system, namely, surface plasmon, exciton, charge-transfer, and molecular resonances. These resonances are coupled by terms in the numerator, which provide strict selection rules that enable us to test the theory and predict the relative intensities of the Raman lines. Furthermore, by considering interactions of the various contributions to the SEAS enhancement, we are able to develop ways to optimize the enhancement factor by tailoring the semiconductor nanostructure thereby adjusting the location of the various contributing resonances.