This paper presents an in-depth study of Surface Enhanced Raman Scattering (SERS) enhancement factors (EFs) and cross-sections, including several issues often overlooked. In particular, various possible rigorous definitions of the SERS EFs are introduced and discussed in the context of SERS applications, such as analytical chemistry and single molecule SERS. These definitions highlight the importance of a careful characterization of the non-SERS cross-sections of the probes under consideration. This aspect is illustrated by experimental results for the non-SERS cross-sections of representative SERS probes along with average SERS EFs for the same probes. In addition, the accurate experimental determination of single molecule enhancement factors is tackled with two recently developed techniques, namely: bi-analyte SERS (BiASERS) and temperaturedependent SERS vibrational pumping. We demonstrate that SERS EFs as low as 10 7 , as opposed to the figure of 10 14 often claimed in the literature, are sufficient for the observation of single molecule SERS signals, with maximum single molecule EFs typically on the order of ∼10 10 .

Single-molecule surface-enhanced Raman scattering (SERS) detection of nonresonant molecules is demonstrated experimentally using the bianalyte SERS method. To this end, bianalyte SERS is performed at 633 nm excitation using the nonresonant molecule 1,2-di-(4-pyridyl)-ethylene (BPE) in combination with a benzotriazole derivative as a partner. The results are then extended to the even more challenging case of a small nonresonant molecule, adenine, using an isotopically substituted adenine as bianalyte SERS partners. In addition, SERS cross sections of single-molecule events are quantified, thus providing estimates of the enhancement factors needed to see them. It turns out that an enhancement factor on the order of approximately 5 x 10(9) was sufficient for single-molecule detection of BPE, while maximum enhancement factors of approximately 5 x 10(10) were observed in extreme cases. In the case of adenine, single-molecule detection was only possible in the rare cases with enhancement factors of approximately 10(11). This study constitutes a quantitative fundamental test into the lowest detection limits (in terms of differential cross sections) for single-molecule SERS.

The mathematical background, based on a variation of the principal component analysis (PCA) method, is developed for the understanding of fluctuating multiple analyte single-molecule (SM) surface enhanced Raman scattering (SERS) signals; with emphasis on the bianalyte SERS technique developed recently. The method and its significance are presented to provide a systematic framework with which several aspects of the statistics of SM-SERS signals can be analyzed in general. We also apply the method to a concrete example of bianalyte statistics in silver colloidal solutions and discuss related topics around experimental issues and the interpretation of single-molecule SERS data.