# Principles of Surface-Enhanced Raman Spectroscopy

## and related plasmonic effects

**By**

- Eric Le Ru
- Pablo Etchegoin

SERS was discovered in the 1970s and has since grown enormously in breadth, depth, and understanding. One of the major characteristics of SERS is its interdisciplinary nature: it lies at the boundary between physics, chemistry, colloid science, plasmonics, nanotechnology, and biology. By their very nature, it is impossible to find a textbook that will summarize the principles needed for SERS of these rather dissimilar and disconnected topics. Although a basic understanding of these topics is necessary for research projects in SERS with all its many aspects and applications, they are seldom touched upon as a coherent unit during most undergraduate studies in physics or chemistry. This book intends to fill this existing gap in the literature. It provides an overview of the underlying principles of SERS, from the fundamental understanding of the effect to its potential applications. It is aimed primarily at newcomers to the field, graduate students, researchers or scientists, attracted by the many applications of SERS and plasmonics or its basic science. The emphasis is on concepts and background material for SERS, such as Raman spectroscopy, the physics of plasmons, or colloid science, all of them introduced within the context of SERS, and from where the more specialized literature can be followed.

**Audience**

Graduate students, researchers and scientists working in physics, chemistry, chemical physics, physical chemistry, analytical chemistry and biology who require a general reference in the field of Surface-Enhanced Raman Spectroscopy

Hardbound, 688 Pages

Published: November 2008

Imprint: Elsevier

ISBN: 978-0-444-52779-0

## Contents

- Preface Notations, units and other conventions 1 A quick overview of SERS 1.1 What is SERS? - Basic principles 1.2 SERS probes and SERS substrates 1.2.1 SERS substrates 1.2.2 SERS probes 1.2.3 Example 1.3 Other important aspects of SERS 1.3.1 SERS enhancements 1.3.2 Sample preparation and metal/probe interaction 1.3.3 Main characteristics of the SERS signals 1.3.4 Related techniques 1.3.5 Related areas 1.4 Applications of SERS 1.4.1 Raman with improved sensitivity 1.4.2 SERS vs. fluorescence spectroscopy 1.4.3 Applications specific to SERS 1.5 The current status of SERS 1.5.1 Brief history of SERS 1.5.2 Where is SERS now? 1.5.3 Current âhot topicsâ 1.6 Overview of the book content 1.6.1 General outline of the book 1.6.2 General âspiritâ of the book 1.6.3 Different reading plans 2 Raman spectroscopy and related techniques 2.1 A brief introduction 2.1.1 The discovery of the Raman effect 2.1.2 Some applications of Raman spectroscopy 2.1.3 Raman spectroscopy instrumentation 2.2 Optical spectroscopy of molecules 2.2.1 The energy levels of molecules 2.2.2 Spectroscopic units and conversions 2.2.3 Optical absorption 2.2.4 Emission and luminescence 2.2.5 Scattering processes 2.2.6 The concept of cross-section 2.2.7 The Raman cross-sections 2.2.8 Examples of Raman cross-sections 2.2.9 Mechanical analogs 2.3 Absorption and fluorescence spectroscopy 2.3.1 Optical absorption and UV/Vis spectroscopy 2.3.2 Fluorescence spectroscopy 2.3.3 Photo-bleaching 2.4 Phenomenological approach to Raman 2.4.1 Dipolar emission in vacuum 2.4.2 The concepts of polarizability and induced dipole 2.4.3 The linear optical polarizability 2.4.4 The Raman polarizability 2.4.5 The local field correction 2.4.6 Polarizabilities and scattering cross-sections 2.4.7 Final Remarks on the phenomenological description 2.5 Vibrations and the Raman tensor 2.5.1 General considerations 2.5.2 A primer on vibrational analysis 2.5.3 The Raman tensor 2.5.4 Link to the Raman polarizability 2.5.5 Limitations of the classical approach 2.5.6 A brief overview of related Raman scattering processes 2.6 Quantum approach to Raman scattering 2.6.1 Justification of the classical approach 2.6.2 The quantization of vibrations 2.6.3 The full expressions for the Raman cross-section 2.6.4 The anti-Stokes to Stokes ratio 2.7 Advanced aspects of vibrations in molecules 2.7.1 More on vibrational analysis 2.7.2 More on symmetries and Raman selection rules 2.7.3 Modeling of molecular structure and vibrations 2.8 Summary 3 Introduction to plasmons and plasmonics 3.1 Plasmonics and SERS 3.2 The optical properties of noble metals 3.2.1 The Drude model of the optical response 3.2.2 The optical properties of real metals 3.2.3 Non-local optical properties 3.2.4 What makes the metal-light interaction so special? 3.3 What are plasmons? 3.3.1 The plasmon confusion 3.3.2 Definition and history 3.3.3 The relation between plasmons and the dielectric function 3.3.4 Electromagnetic modes in infinite systems 3.3.5 Electromagnetic modes of a system of material bodies 3.3.6 Classification of electromagnetic modes 3.3.7 Other properties of electromagnetic modes 3.3.8 Summary and discussion 3.4 Surface plasmon-polaritons for planes 3.4.1 Electromagnetic modes for a planar dielectric/metal interface 3.4.2 Properties of the SPP modes at planar metal/dielectric interfaces 3.4.3 Coupling of PSPP modes with light 3.4.4 PSPP resonances at planar interfaces 3.4.5 Local field enhancements and SPPs at planar interfaces 3.4.6 SPP modes on planar interfaces: a brief summary 3.5 Localized surface plasmon-polaritons 3.5.1 Introduction to localized SPPs 3.5.2 LSP on planar structures 3.5.3 LSP modes of a metallic sphere 3.5.4 LSP modes of nano-particles 3.5.5 LSP Resonances 3.5.6 Local field enhancements and LSP 3.5.7 Interaction of SPPs - gap SPPs 3.6 Brief survey of plasmonics applications 3.6.1 Applications of surface plasmon resonances 3.6.2 SPP propagation and SPP optics 3.6.3 Local field enhancements 4 SERS enhancement factors 4.1 Definition of the SERS enhancement factors 4.1.1 General considerations 4.1.2 The analytical point of view 4.1.3 The SERS substrate enhancement factor - Experimental approach 4.1.4 The SERS cross-section and single molecule EF 4.1.5 The SERS substrate enhancement factor - Formal definition 4.1.6 Discussion and merits of the various definitions 4.2 Experimental measurement of SERS EFs 4.2.1 The importance of the non-SERS cross-section 4.2.2 Example of AEF measurements 4.2.3 Link between SSEF definition and experiments 4.3 Overview of the main EM effects in SERS 4.3.1 Analysis of the EM-problem of SERS 4.3.2 Local field enhancement 4.3.3 Radiation enhancement 4.3.4 Other EM effects 4.3.5 The common |E|4-approximation to SERS enhancements 4.4 Modified spontaneous emission 4.4.1 Introduction 4.4.2 The link between spontaneous emission and dipolar emission 4.4.3 Modification of dipole emission: definitions of enhancement factors 4.4.4 Spontaneous Emission and self-reaction 4.4.5 The Poynting vector approach 4.4.6 Spontaneous emission and the optical reciprocity theorem 4.5 Formal derivation of SERS EM enhancements 4.5.1 Definitions, notations, and assumptions 4.5.2 The SERS EM enhancement: general case 4.5.3 SERS EM enhancements in the back-scattering configuration 4.6 Surface-enhanced fluorescence 4.6.1 Similarities and differences between SEF and SERS 4.6.2 Modified (enhanced) absorption 4.6.3 Modified fluorescence quantum yield 4.6.4 Fluorescence quenching and enhancement 4.7 Other EM effects in SERS 4.7.1 Fluorescence quenching in SERS 4.7.2 Photo-bleaching under SERS conditions 4.7.3 Non-radiative effects in SERS 4.8 The chemical enhancement 4.8.1 Introduction 4.8.2 The charge-transfer mechanism 4.8.3 Electromagnetic contribution to the chemical enhancement 4.8.4 The chemical vs. electromagnetic enhancement debate 4.9 Summary 5 Calculations of EM enhancements 5.1 Definitions and approximations 5.1.1 The EM problem 5.1.2 Far field and local/near field 5.1.3 Some key EM indicators 5.1.4 The electrostatic approximation (ESA) 5.1.5 Other approximations 5.2 Analytical tools and solutions 5.2.1 Plane surfaces 5.2.2 The perfect sphere 5.2.3 Ellipsoids 5.2.4 Other approaches 5.3 Numerical tools 5.3.1 A brief overview of the EM numerical tools 5.3.2 The discrete dipole approximation 5.3.3 Direct numerical solutions 5.3.4 Other approaches 6 EM enhancements and plasmon resonances 6.1 Quenching and enhancement at planar surfaces 6.1.1 The image dipole approximation for the self-reaction field 6.1.2 Enhancement and quenching at plane metal surfaces 6.2 The metallic sphere 6.2.1 Metallic sphere in the ES approximation 6.2.2 Localized surface plasmon resonances and far field properties 6.2.3 Local field effects 6.2.4 Distance dependence 6.2.5 Non-radiative effects - SEF cross-sections 6.3 Shape effects on EM enhancements 6.3.1 Shape effects on localized surface plasmon resonances 6.3.2 Shape effects on local fields 6.3.3 Summary of shape effects 6.4 Gap effects - junctions between particles 6.4.1 Coupled localized surface plasmon resonances and SERS 6.4.2 EF distribution and hot-spot localization 6.5 Additional effects 6.5.1 Nano-particles on a supporting substrate 6.5.2 Surface roughness 6.6 Factors affecting the EM enhancements: summary 7 Metallic colloids and other SERS substrates 7.1 Metallic colloids for SERS 7.1.1 Silver vs. gold 7.1.2 Citrate-reduced colloids 7.1.3 Other types of colloids 7.1.4 Remarks on colloid fabrication methods 7.1.5 Dry colloids and other â2D planarâ SERS substrates 7.2 Characterization of SERS substrates 7.2.1 Microscopy 7.2.2 Extinction or UV/Vis spectroscopy of SERS substrates 7.2.3 Dynamic Light Scattering (DLS) 7.3 Colloid stability 7.3.1 Introduction 7.3.2 The van der Waals interaction between metallic particles 7.3.3 The screened Coulomb potential 7.3.4 The DLVO interaction potential 7.3.5 Colloid aggregation within the DLVO theory 7.4 SERS with metallic colloids 7.4.1 Molecular (analyte) adsorption and SERS activity 7.4.2 Colloid aggregation for SERS 7.4.3 Focus on the âchloride-activationâ of SERS signals 7.4.4 SERS from âdriedâ colloidal solutions 7.4.5 SERS signal fluctuations 8 Recent developments 8.1 Single molecule SERS 8.1.1 Introduction 8.1.2 Early evidence for single molecule detection 8.1.3 Langmuir-Blodgett monolayers 8.1.4 Bi-analyte techniques 8.1.5 Single molecule SERS enhancement factors 8.1.6 Single-molecule SERS: discussion and outlook 8.2 Tip-enhanced Raman spectroscopy (TERS) 8.2.1 Introduction to TERS 8.2.2 TERS with an atomic force microscope (AFM) 8.2.3 TERS with a scanning tunneling microscope (STM) 8.2.4 Theoretical calculations on tips 8.2.5 Discussion and outlook 8.3 New substrates from nanotechnology 8.3.1 Chemical synthesis of metallic nano-particles 8.3.2 Self-organization 8.3.3 Nano-lithography 8.3.4 Adaptable/Tunable SERS substrates 8.3.5 Microfluidics and SERS 8.4 Optical forces 8.4.1 A simple theory of optical forces 8.4.2 Radiation pressure in colloidal fluids 8.4.3 Optical trapping of metallic particles 8.4.4 Optical forces on molecules 8.5 Applications of SERS 8.5.1 Analyte engineering and surface functionalization 8.5.2 Substrate reproducibility and SERS commercialization 8.6 Epilogue? A Raman DFT calculations A.1 A brief introduction to DFT A.1.1 Computing aspects of DFT A.1.2 Principles of DFT A.1.3 Important parameters A.2 Applications of DFT to Raman A.2.1 Principle A.2.2 Geometry optimization using DFT A.2.3 Limitations of DFT calculations for Raman A.3 Practical implementation A.3.1 Brief overview of the input and output files A.3.2 Common units and definitions in Raman calculations from DFT A.3.3 Normal mode patterns and Raman tensors A.4 Examples of DFT for SERS A.4.1 Validation of cross sections of reference compounds A.4.2 Raman tensor and vibrational pattern visualizations A.4.3 Depolarization ratio breakdowns under SERS conditions B The bond-polarizability model B.1 Principle and implementation B.1.1 Principle B.1.2 Calculation of bond polarizabilities B.1.3 Practical implementation B.2 A simple example in detail B.2.1 Bond-Polarizability analysis B.2.2 Raman polarizabilities B.2.3 A brief comment on the symmetry C Maxwellâs equations in media C.1 Maxwellâs equations in vacuum C.1.1 The equations C.1.2 Maxwellâs equations for harmonic fields in vacuum C.1.3 Plane wave solutions in free space C.2 Maxwellâs equations in media C.2.1 Microscopic and macroscopic fields C.2.2 The electromagnetic response of the medium C.2.3 Electric polarization and magnetization C.2.4 Constitutive relations C.2.5 Boundary conditions between two media C.3 Other aspects relevant to SERS and plasmonics C.3.1 The microscopic field C.3.2 Plane waves in media C.3.3 Electromagnetic problems in SERS C.3.4 Link with the static approach D Lorentz model of the polarizability D.1 The Lorentz oscillator D.1.1 Principle D.1.2 Multiple transitions (multiple resonances) D.1.3 Example: linear optical polarizability of rhodamine 6G D.2 Link with macroscopic properties D.2.1 Dielectric function in a dilute medium D.2.2 Dielectric function in solids D.2.3 The metallic limit D.3 Summary E Dielectric function of gold and silver E.1 Model dielectric function for Ag E.1.1 Analytical expression E.1.2 Comparison to experimental results E.2 Model dielectric function for Au E.2.1 Analytical expression E.2.2 Comparison to experimental results E.3 Remarks on the model dielectric functions E.3.1 Limitations of the models E.3.2 Comparison between Ag and Au F Plane waves and planar interfaces F.1 The plane wave electromagnetic fields F.1.1 General expressions F.1.2 Propagating plane waves F.1.3 Evanescent plane waves F.1.4 Inhomogeneous plane waves F.2 Plane waves at a single planar interface F.2.1 Plane wave polarization at an interface F.2.2 General solution for plane waves at a planar interface F.2.3 Physical waves in a semi-infinite region F.2.4 The Fresnel coefficients F.2.5 Surface modes F.2.6 Incident wave modes F.3 Reflection/Refraction at an interface F.3.1 Incident, reflected, and transmitted waves F.3.2 Snellâs law F.3.3 TM or p-polarized waves F.3.4 TE or s-polarized waves F.3.5 Special cases F.4 Multilayer interfaces F.4.1 Principle F.4.2 p-polarized or TM waves F.4.3 s-polarized or TE waves F.4.4 Particular cases of interest F.4.5 Implementation in Matlab F.5 Dipole emission close to a planar interface F.5.1 Total decay rates F.5.2 Radiative decay rates G Ellipsoids in the electrostatic approximation G.1 General case G.1.1 Some definitions G.1.2 Ellipsoidal coordinates G.1.3 The electrostatic solution G.1.4 Some important EM indicators for ellipsoids G.1.5 Some aspects of the numerical implementation G.2 Oblate spheroid (pumpkin) G.2.1 Geometrical factors G.2.2 Surface averages G.2.3 Limit of large aspect ratio G.3 Prolate spheroid (rugby ball) G.3.1 Geometrical factors G.3.2 Surface averages G.3.3 Limit of large aspect ratio H Mie theory and its implementation H.1 Introduction H.1.1 Motivation H.1.2 Overview of this appendix H.2 The concepts of Mie theory H.2.1 The electromagnetic equations H.2.2 The vectorial wave equation in spherical coordinates H.2.3 Scattering by a sphere H.2.4 Optical resonances of the sphere H.2.5 Some aspects of the practical implementation of Mie theory H.3 Basic formulae of Mie theory H.3.1 Conventions H.3.2 Spherical coordinates: a brief reminder H.3.3 Definition and properties of the vector spherical harmonics H.3.4 Expressions for the susceptibilities H.3.5 More on optical resonances H.3.6 Absorption, scattering, and extinction for an incident beam H.3.7 Absorption and radiation for a localized source H.3.8 Far field radiation profile H.3.9 The local field at the surface H.4 Plane wave excitation of a sphere H.4.1 Expansion of a plane wave in vector spherical harmonics H.4.2 Extinction, scattering, and absorption for plane wave excitation H.4.3 Average local field at the surface H.4.4 Useful expansions for plane wave excitation H.5 Extensions of Mie theory H.5.1 Emitter close to a sphere H.5.2 Coated spheres H.5.3 Multiple spheres and generalized Mie theory (GMT) H.6 Implementation of Mie theory H.6.1 Common problems H.6.2 Other issues specific to Matlab H.6.3 Some aspects of our implementation References Index