We present a unified expression for surface-enhanced Raman spectroscopy (SERS). The expression contains a product of three resonance denominators, representing the surface plasmon resonance, the metal−molecule charge-transfer resonance at the Fermi energy, and an allowed molecular resonance. This latter resonance is that from which intensity is borrowed for charge transfer, and when the molecular resonance is active it is responsible for surface-enhanced resonance Raman spectroscopy. We examine this expression in various limits, to explore the relative contribution or each resonance. First, we look at the situation in which only the surface plasmon resonance is active and examine the various contributions to the Raman signal, including the surface selection rules. Then we examine additional contributions from charge-transfer or molecular resonances. We show that the three resonances are not totally independent, since they are linked by a product of four matrix elements in the numerator. These linked matrix elements provide comprehensive selection rules for SERS. One involves a harmonic oscillator in the observed normal mode. This is the same mode which appears in the vibronic coupling operator linking one of the states of the allowed molecular resonance to the charge-transfer state. The charge-transfer transition moment is linked to the surface plasmon resonance by the requirement that the transition dipole moment be polarized along the direction of maximum amplitude of the field produced by the plasmon (i.e., perpendicular to the metal surface). We show that these selection rules govern the observed SERS spectral intensities and apply these to the observed spectra of several molecules. We also suggest a quantitative measure of the degree to which charge transfer contributes to the overall SERS enhancement.

In the late 1970s, signal intensity in Raman spectroscopy was found to be enormously enhanced, by a factor of 10 6 and more recently by as much as 10 14 , when an analyte was placed in the vicinity of a metal nanoparticle (particularly Ag). The underlying source of this huge increase in signal in surface-enhanced Raman scattering (SERS) spectroscopy has since been characterized by considerable controversy. Three possible contributions to the enhancement factor have been identified: (i) the surface plasmon resonance in the metal nanoparticle, (ii) a charge-transfer resonance involving transfer of electrons between the molecule and the conduction band of the metal, and (iii) resonances within the molecule itself. These three components are often treated as independently contributing to the overall effect, with the implication that by properly choosing the experimental parameters, one or more can be ignored. Although varying experimental conditions can influence the relative degree to which each resonance influences the total enhancement, higher enhancements can often be obtained by combining two or more resonances. Each resonance has a somewhat different effect on the appearance of the resulting Raman spectrum, and it is necessary to invoke one or more of these resonances to completely describe a particular experiment. However, it is impossible to completely describe all observations of the SERS phenomenon without consideration of all three of these contributions. Furthermore, the relative enhancements of individual spectral lines, and therefore the appearance of the spectrum, depend crucially on the exact extent to which each resonance makes a contribution.In this Account, by examining breakdowns in the Born-Oppenheimer approximation, we have used Herzberg-Teller coupling to derive a single expression for SERS, which includes contributions from all three resonances. Moreover, we show that these three types of resonances are intimately linked by Herzberg-Teller vibronic coupling terms and cannot be considered separately.We also examine the differences between SERS and normal Raman spectra. Because of the various resonant contributions, SERS spectra vary with excitation wavelength considerably more than normal Raman spectra. The relative contributions of totally symmetric and non-totally symmetric lines are also quite different; these differences are due to several effects. The orientation of the molecule with respect to the surface and the inclusion of the metal Fermi level in the list of contributors to the accessible states of the molecule-metal system have a strong influence on the observed changes in the Raman spectrum.

A comprehensive development of the charge-transfer theory of surface enhanced Raman scattering (SERS) is presented. We incorporate the Herzberg–Teller mixing of zero-order Born–Oppenheimer electronic states by means of vibronic interaction terms in the Hamiltonian. This is similar to the theory of Tang and Albrecht12 except that we include metal states as part of a molecule–metal system. When this is done we may no longer discard a term involving mixing of ground-state vibrations. The theory is comprehensive in that both molecule-to-metal and metal-to-molecule transfer is considered. Furthermore, both Franck–Condon and Herzberg–Teller contributions to the intensity are obtained. The former, however, contribute only to the intensity of totally symmetric vibrations, while the latter contribute to nontotally symmetric vibrations as well. Since overtones are observed in SERS only weakly if at all, the Herzberg–Teller terms are most consistent with experimental findings. The resulting formulas may be interpreted as a type of resonance Raman effect in which intensity for the charge transfer transitions is borrowed from an allowed molecular transition. We may also carry out the sum over metal states. This procedure predicts a logarithmic resonance at the Fermi level of the metal. We thus predict intensity vs voltage profiles such as I ∝ ‖ln(ωFI−ω+iΓ)‖2 which fits the experimental curves quite well.

Dielectrics represent a new frontier for surface-enhanced Raman scattering. They can serve as either a complement or an alternative to conventional, metal-based SERS, offering key advantages in terms of low invasiveness, reproducibility, versatility, and recyclability. In comparison to metals, dielectric systems and, in particular, semiconductors are characterized by a much greater variety of parameters and properties that can be tailored to achieve enhanced Raman scattering or related effects. Light-trapping and subwavelength-focusing capabilities, morphology-dependent resonances, control of band gap and stoichiometry, size-dependent plasmons and excitons, and charge transfer from semiconductors to molecules and vice versa are a few examples of the manifold opportunities associated with the use of semiconductors as SERS-active materials. This review provides a broad analysis of SERS with dielectrics, encompassing different optical phenomena at the basis of the Raman scattering enhancement and introducing future challenges for light harvesting, vibrational spectroscopy, imaging, and sensing.

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 SERS 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.