Phenomenological local field enhancement factor distributions around electromagnetic hot spots

We propose a general phenomenological description of the enhancement factor distribution for surface-enhanced Raman scattering (SERS) and other related phenomena exploiting large local field enhancements at hot spots. This description extends naturally the particular case of a single (fixed) hot spot, and it is expected to be "universal" for many classes of common SERS substrates containing a collection of electromagnetic hot spots with varying geometrical parameters. We further justify it from calculations with generalized Mie theory. The description studied here provides a useful starting point for a qualitative (and semiquantitative) understanding of experimental data and, in particular, the analysis of the statistics of single-molecule SERS events.