† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant No. 11434017) and the National Basic Research Program of China (Grant No. 2013CB632704).
In 2013, a breakthrough experiment pushed the Raman mapping of molecules via the tip-enhanced Raman scattering (TERS) technique to a sub-nanometer spatial resolution, going into the single-molecule level. This surprising result was well explained by accounting for the critical role of elastic molecule Rayleigh scattering within a plasmonic nanogap in enhancing both the localization and the intensity level of the Raman scattering signal. In this paper, we theoretically explore the influence of various geometric factors of the TERS system on the spatial resolution of Raman mapping, such as the tip curvature radius, tip conical angle, tip–substrate distance, and tip–molecule vertical distance. This investigation can help to find out the most critical geometric factor influencing the spatial resolution of TERS and march along in the right direction for further improving the performance of the TERS system.
Raman spectroscopy offers a powerful means to observe vibrational, rotational, and other low-frequency modes in molecules, and thus has become a popular and useful technology for molecular identification. As the cross section of Raman scattering is extremely low under usual conditions of laser excitation, many methods have been explored to advance the power of Raman spectroscopy to the fundamental single-molecule limit. Among them, surface-enhanced Raman scattering (SERS)[1] is an important spectroscopic tool with which the Raman signals from molecules adsorbed on the surface of noble metal (Au, Ag, etc.) nanoparticles and nanostructures can be significantly enhanced. Many schemes have been investigated to build high-performance SERS substrates, including nanoparticles with sharp corners and tips[2–8] and Ag nanoparticle dimers[9,10] or aggregates[11,12] that involve nanogaps.
An important goal of Raman spectroscopic science and technology is to probe the Raman signal with ultrahigh spectroscopic sensitivity down to the single-molecule detection level[11,12] and ultrahigh spatial resolution down to the single-molecule size scale. This would allow people to identify, monitor, and manipulate single molecules in both temporal and spatial domains. When Raman spectroscopy works together with various mature scanning probe microscopy technologies under the scheme of tip-enhanced Raman spectroscopy (TERS),[13–21] the spatial resolution of Raman probing and monitoring can be greatly upgraded and essentially reach the single-molecule level.[19,21] The metal tip in either atomic force microscopy (AFM) or scanning tunneling microscopy (STM) can induce a highly concentrated electric field focus spot far below the diffraction-limit scale (about half of the laser wavelength, usually several hundred nanometers) with greatly enhanced field intensity in the vicinity of the tip apex due to the surface plasmon resonance (SPR) effect. It is generally believed that the spatial resolution of TERS is nearly the same as the focus spot size of the metallic AFM or STM tip, which strongly depends on many factors, such as the molecule–tip vertical distance, the curvature radius of the tip, the excitation wavelength, and the substrate composition, but at best is on the order of 10 nm. However, in 2013, a seminal experimental work[19] pushed the TERS into the sub-nm spatial resolution regime, which allows for probing and mapping the chemical infrastructure of molecules, and stimulated intensive investigations and discussions on the inner new physical origin.[22,23]
Recently, we have proposed a brand-new physical picture and a systematic theoretical formalism to understand single-molecule Raman mapping via TERS.[24] In this theory, the elastic Rayleigh scattering always accompanies the inelastic Raman scattering when the incident light shines on molecules, and the Rayleigh scattering can play a much more pronounced role than it is generally assumed in the conventional Raman physics. In fact, the role of Rayleigh scattering is completely omitted in the classical Raman scattering theory. By introducing the near-field interaction of the molecule with the plasmonic nanogap formed between the metallic tip and the substrate of the TERS system, the local field and its interaction with the inelastic scattering of the molecule (Stokes and anti-Stokes light radiated by the vibrational molecule) are strongly modified by the multiple elastic scattering not only from the nanostructure (Mie scattering) but also from the molecule itself (Rayleigh scattering). Applying our theory to the TERS system, we have succeeded in clarifying the surprising experimental discovery of sub-nanometer resolution in TERS. Although there are many works[13–21] about how the geometry factors of TERS influence the spatial resolution in the framework of the traditional SERS theory, our new theory would reveal some different results. Furthermore, it would yield useful suggestions for improving the resolution because the near-field interaction strongly depends on many geometry factors, such as the molecule–tip vertical distance and the curvature radius of the tip. Therefore, in this paper we proceed to investigate in detail how the TERS scanning resolution is influenced by various geometric factors of TERS considering the molecule Rayleigh scattering. This systematical investigation would help to uncover the critical factor determining the spatial resolution of TERS and point to the right direction to improve the resolution.
For completeness, we first briefly summarize the major physics in the new Raman theory. In the form of dipole approximation, the Stokes (or anti-Stokes) light radiated by the vibration molecule could be expressed as the radiation from the induced dipole
![](cpb_25_9_095203/cpb160380ieqn1.gif)
In contrast, in our theory,[24] when considering the molecule self-interaction in the nanogap, the local electric field is expressed as
![](cpb_25_9_095203/cpb160380ieqn2.gif)
Figure
First, we consider the influence of the conical angle to the local field. We use the 3D-FDTD method to simulate the local field of the nanostructure, where the tip is set as R = 25 nm, d = 2 nm, and θ varies from 0° to 50°. Our calculation demonstrates that the shape and profile of the local field, in particular the hot spot size, is not sensitive to the conical angle. This means that the local field is mainly determined by the geometry of the local nanostructure (such as the curvature radius of the tip apex and the tip–substrate distance). Figure
Then we consider the influence of the geometry of the local nanostructure like the radius of the tip apex. Figure
After acknowledgement of the connection between the super hot spot and the super resolution of TERS in our theory, some tentative designs could be proposed to improve the resolution. An easy attempt is changing the height of the molecule. Figure
From the above comprehensive analyses, the super resolution of TERS directly originates from the special characteristics of the super hot spot. Moreover, a larger gradient in the nanostructure and the nearby local field would benefit the scanning resolution. Following this conception, some suggestions could be made to improve the performance of TERS. One is to manufacture a sharp tip. Although the head radius of the tip fabricated by the electrochemistry method is limited to tens of nanometers, one can still try to do some tip apex modification to improve the gradient, such as adsorbing a small molecule or cluster on the tip apex. Another useful suggestion is to decrease the relative distance between the molecule and the tip, which could construct a nanogap mode more concentrated at the larger gradient nanostructures. A simple method is reducing the height of the tip relative to the molecule or raising the molecule vertical position relative to the tip apex. Figure
We have considered the influence of various geometry factors to the scanning resolution of TERS when considering the molecule self-interaction effect that originates from the multiple Rayleigh scattering of molecule upon the local field. According to the analysis of the movement of the “upper hot spot”, we have illustrated some recipes for designing the tip–molecule nanostructure to have a better performance for TERS. With the new theory, we have gained some deeper understanding of TERS, which is helpful for the further development of this technology.
It is well known that Rayleigh scattering is much stronger than Raman scattering for molecules. However, the old wisdom is that these two processes are mutually independent, or in other words, Rayleigh scattering has no contribution to Raman scattering. Although this is right for Raman experiments involving molecules in air and other usual homogeneous media, at the nanoscale where many SERS and TERS experiments are involved, Rayleigh scattering can play a critical role in shaping Raman scattering. These two physical processes are strongly intercorrelated via the nanoscale environment, e.g., a plasmonic nanogap, surrounding the molecule. Because of this strong correlation, many geometric factors can strongly and sensitively influence the performance of the TERS system used for Raman mapping against molecules. From these observations, one can find the most critical factor that determines the scanning resolution of TERS. More importantly, these analyses allow one to march along the right direction toward an even better spatial resolution of Raman mapping, e.g., against a small molecule like O2, CO2, and so on.
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