Quantifying SERS enhancements
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Introduction 1–3
Surface-enhanced Raman scattering (SERS) has been around for almost 40 years.4–6 Yet, compared to other fields of research in an equivalent period of time, where progress is steady and the community discards wrong interpretations over time and moves on, a considerable amount of time has been spent arguing about the very basic aspects of SERS. This ranges from historical questions such as: “When was the effect originally discovered?”7–9 to more technical (but still basic) questions on the magnitude of the SERS enhancement factor,10 the role of the so-called chemical enhancement,11 the reality and interpretation of SERS vibrational pumping,12,13 or the conditions needed to ensure single-molecule (SM) detection.14–16 These controversies are perhaps a natural consequence of the multidisciplinary nature of the technique and the resulting diverse background of researchers studying it (chemistry, physics, biology, engineering). By far, the most important aspect of the SERS effect is the enhancement factor (EF) (i.e., by how much the Raman signal can be amplified). The SERS EF can be large enough to allow, in many cases, the observation of single molecules14,15— an interesting subfield of SERS in its own right. Yet, the magnitude of the SERS EF was, for a long time, part of the self-perpetuating controversies in the field, with quoted values that could differ by several orders of magnitude for similar experimental conditions. The myth of SERS EFs as large as
1014, which originates in the pioneering SM-SERS studies17,18 from an incorrect normalization of the SERS intensity with respect to a non-resonant Raman signal,10,16 has long been (and to some extent still is) an impediment to progress in the field. It has created innumerable problems for theorists who tried for a long time to justify it from electromagnetic (EM) calculations, and frustration for experimentalists whose estimates of the SERS EF fell short by factors on the order of ∼104–106 (estimates which are, in fact, correct). There is clearly no hope of being able to build a useful analytical tool with a technique that cannot agree on some of its fundamental physical characteristics by several orders of magnitude (up to ∼106). But these discrepancies, which resulted from a combination of different experimental practices and improper definitions of the EF, are well understood now. The state of the art of the technique at the moment is such that when all is taken into account, there should be no controversies on the magnitude and origin of the enhancement factor.
The origin of the SERS enhancement In its most basic and phenomenological form, the Raman effect can be understood as the emission from a Raman dipole p0 oscillating at the Raman-shifted frequency ωR and induced by the electric field E0 of the exciting laser at frequency ωL. Within a linear response approximation and using complex notations to account for the harmonic time dependence, we have
Eric C. Le Ru, School of Chemical and Physical Sciences, MacDiarmid Institute for Advanced Materials an
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