1. Introduction

Scanning Probe Microscopy (SPM) has been vital to high resolution imaging of surfaces, and molecules on surfaces. Provided the tip is sufficiently sharp, atomic or molecular resolution can be achieved in topographic images. Some mechanical, magnetic and electronic properties can be mapped, but the chemical composition beneath the probe cannot in general be measured. Such a chemical analysis on the atomic scale would be of immense benefit to the analysis of samples from life science, nanotechnology and semiconductor applications.

Scanning Near-field Optical Microscopy (SNOM) [1] represents a way of chemical analysis via Raman or fluorescence spectroscopy, so fluorescently tagged biomolecules can be imaged with a resolution far smaller than the ~ 200 nm achieved with diffraction-limited confocal microscopy. Using apertured drawn optical fibres, a resolution of 30–100 nm is achievable. However, due to the low cross-section of Raman scattering and the low level of useable optical power density emitted from the apertured probe, it is only suitable for fluorescence mapping [2,3].

More recently, ‘apertureless’ SNOM [4,5] has generated great interest. Here, light is focused onto the apex of a gold- or silver-coated probe, and the scattered light is collected. As well as the improvement of optical resolution, the intensity of scattered light is greatly enhanced. Although molecular resolution (1 nm) has been achieved in interferometric apertureless SNOM [6] and light emission from the Scanning Tunnelling Microscope [7], the optimum published resolution in apertureless SNOM for Raman [8] and fluorescence imaging [9] is limited to around 10 nm by the size of the probe. Commercially available gold-coated Atomic Force Microscopy (AFM) probes can have a radius of around 30 nm, which is about the same as the minimum achievable radius of etched gold wires used in shear-force SNOM.

In order to achieve atomic resolution in optical imaging, smaller radius probes are required. Although atomic resolution can be achieved in topographic imaging, it is often realized by a controlled tip crash into a surface, whereby a single atom is attached to a large (10 – 50 nm radius) tip. However, this will not produce atomic resolution in the optical image. For true 1 nm radius tips, wires must first be etched down to ~ 30 nm, then sharpened by field emission in a very low pressure of neon [7]. Equivalently, a small colloid could be attached to the end of a non-metallic probe to achieve this radius of curvature. We chose to perform optical simulations of these small radius metal probes, as we need to know exactly what resolution could be expected. We also need to know whether there will be enough enhancement of the ‘near field’ signal (i.e. the light scattered from under the tip apex), for the signal not to be dominated by light scattered from the considerably larger diffraction-limited ‘far field’ laser spot around the tip.

2. Results

The method of electromagnetic finite element simulation is described in detail elsewhere [10,11], employing optical properties which have not been adjusted for size. It is widely believed when a particle decreases in size to the range below 10 nm, its optical properties change. The effect of surface scattering [12] – which is included in the finite element simulations – is increasingly important for small clusters, and clearly the optical spectrum of scattering does vary with size. However, it would be inappropriate to claim that the intrinsic dielectric or optical properties also vary. Indeed, SPM studies of the optical properties of very small metal spheres (< 1 nm diameter) confirm that their intrinsic optical properties do not change [13].

In this paper, we consider isolated tips without a substrate, whose presence close to the tip increases the enhancement factor [11]. Our first simulation is pictured in Figure 1; a 1 nm radius gold tip surrounded by air, illuminated with light incident at 45 degrees to the tip axis.

 

Fig. 1. Finite element simulation of the enhancement of the electric field amplitude around a gold tip of radius 1nm. The surrounding medium is air, and the tip is illuminated with p-polarized light of wavelength 886 nm at 45 degrees.

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We plot the enhancement of the amplitude of the incident electric field (E), and find a maximum in E for an incident wavelength of 886 nm, though the spatial distribution does not change noticeably with wavelength. The lateral resolution (fwhm) of E in Figure 1 is approximately the diameter of the tip (2 nm). The scattered light intensity can be approximated by E⁴, and has a much tighter spot of diameter 0.2 nm, which can be taken as the lateral resolution (fwhm) of imaging. This E⁴ dependence of the scattered light intensity can be explained as follows. The enhancement of the intensity of the incident light is E²; the square of the enhancement of the amplitude, E. The enhancement of the intensity of the radiated field is also E² – the processes of excitation and radiation are identical, with the tip acting like an antenna. The overall enhancement of the scattered light intensity is E²(λ_inc).E²(λ_rad), where λ_inc and λ_rad are the incident and radiated wavelengths respectively. This expression reduces to E⁴ when λ_inc=λ_rad. The vertical decay of E occurs over 0.5 nm, whereas E⁴ decays over only 0.15nm. These lateral and vertical resolutions can be considered as atomic resolution : inorganic lattices have an inter-atomic spacing of typically 0.2 – 0.4 nm, though C-C bonds are 0.15 nm long and C-H bonds are only 0.1 nm in length. To achieve this 0.1 nm optical resolution, the tip radius should thus be scaled to around 0.5 nm. Advances in AFM using frequency modulation (FM) detection have improved the topographic imaging resolution to 0.077 nm [14], which should also be achievable in the optical image.

In Figure 2 we plot the spectral dependence of the enhancement of the amplitude of the incident electric field (E) of a gold tip, for a range of tip radii from 1 to 40 nm. The first effect observed from this set of curves is that the spectral peak is unexpectedly and significantly redshifted from 516 nm to 886 nm as the radius decreases from 40 nm to 1 nm. The plasmon modes in the tip apex and vicinity are red-shifted with increasing radius, yet conversely the peak in Figure 2 is blue-shifted with increasing radius. No results have been published for scattering from small (~1 nm) gold spheres, but a peak in the absorption spectrum for small gold spheres is slightly red-shifted as cluster size decreases [15]. Also, the height of the absorption peak reduces with decreasing cluster size. This means that the peak no longer occurs close to the surface plasmon wavelength to be dominated at long wavelengths by Rayleigh scattering, which varies as 1/λ⁴.

 

Fig. 2. Spectral dependence of the enhancement of the electric field (E) at the tip apex, for gold tips of various radii. The surrounding medium is air, and the tip is illuminated with p-polarized light at 45 degrees. Values of the enhancement of the intensity of scattered light, E⁴, are also plotted on the right of the graph.

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The second effect to observe in Figure 2 is that the highest value of E occurs for the smallest radius tip, which again was unexpected. The overall enhancement of optical scattering, E⁴ ~ 10⁷ – 10⁸, in the wide range of 750–1000 nm, is larger than any published enhancement (the highest reported being 6×10⁶ [16]). When a gold substrate is brought into close proximity to the 1 nm radius gold tip apex – at 1 nm separation – the spectrum has a very similar shape, but with an increase of E at the peak to 151.

We performed simulations of 1 nm radius tips of several different materials, in Figure 3. Gold is the most widely used material for apertureless SNOM, mainly for its resistance to oxidation, but silver is also used. The spectra for gold, silver and copper are all very similar, which is not entirely surprising as they belong in the same group in the periodic table. They have very similar values for the real part of dielectric function, ε_real in range 700 – 1200 nm : the peak corresponds to ε^real=-32 for copper, -35 for gold, -35 for silver. The spectrum of aluminium is very distinct from the others, due to its different dielectric function, but the peak also corresponds to a similar ε^real=-29. This peak relating to ε^real=-30 to -35 is not observed for larger tips. For example, for 20 nm radius gold tip, the peak at 533 nm corresponds to ε^real=-6.

 

Fig. 3. Spectral dependence of the enhancement of the electric field (E) at the tip apex, for 1 nm radius tips of various metals in air, illuminated with p-polarized light at 45 degrees. The curve for copper has a maximum in E of 136, at 886 nm. Values of the enhancement of the intensity of scattered light, E⁴, are also plotted on the right of the graph.

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To optically image biological molecules, aqueous or buffer environments should be used. To model this, we performed simulations on the same variety of 1 nm radius tips but with water as the surrounding medium. Figure 4 shows spectra for gold, silver, copper and aluminium tips in water, which are far more complex than those in air. However, the peaks correspond to ε_real=-54 for copper, -63 for gold, -67 for silver, and -54 for aluminium. Isolated spheres in water are predicted to shift to where ε_real (in water)=1.78 ε_real (in air), meaning that the peaks of Figure 3 are predicted to shift from ε_real ≈ -33 to around -60. This is not precisely observed, but a similar sized red shift to this prediction is seen in Figure 4. As a monolayer of water molecules is absorbed onto all surfaces, and a meniscus often bridges the tip apex to the surface, the true spectrum appropriate for imaging in air may be somewhere between that of the predictions in Figures 3 and 4.

 

Fig. 4. Spectral dependence of the enhancement of the electric field (E) at the tip apex, for 1 nm radius tips of various metals in water, illuminated with p-polarized light at 45 degrees. The curve for copper has a maximum in E of 208, at 1378 nm. Values of the enhancement of the intensity of scattered light, E⁴, are also plotted on the right of the graph.

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3. Discussion

Measurement of optical scattering from 1 nm tips in air can be performed by the use of near infra-red light in order to match the peak in Figure 3. Fluorescence cannot generally be excited by near infra-red light, apart from by 2-photon excitation with femtosecond pulses. Otherwise, fluorescence is best suited to aluminium tips, with λ_inc=400 – 500 nm and λ_rad=500 – 600 nm. For tip-enhanced Raman imaging and spectroscopy, λ_rad is also greater than λ_inc. For optimum Raman enhancement with a 1 nm gold tip in air, illumination should be with laser diodes in the range 750 – 850 nm, and detection in the range 800 – 1050 nm. This is approaching the wavelength limit for detection by silicon avalanche photodiodes and CCDbased spectrometers, but photon counting is still achievable with a good efficiency and low dark counts. In water by contrast, gold, silver and copper tips have their peaks well into the near infrared so detection could be performed with AlGaAs avalanche photodiodes, which have a good efficiency up to 1550 nm. Illumination could be performed with Neodymium lasers around 1064 nm, or a HeNe laser at 1152 nm.

For dilute concentrations of species across the surface, signals from the far field laser spot should be insignificant compared to the near field signal when the species is directly under the tip apex. However, for continuous films or high concentrations of species, signals from the far field diffraction-limited laser spot could outweigh the near field signal due to the considerably larger area of this laser spot with respect to the atomic size near field spot. For illumination at 45 degrees from the (vertical) tip axis with a wavelength of 785 nm, the far field spot area is calculated as 0.8 µm² for a numerical aperture (NA) of 0.55, whereas for illumination from beneath, the far field spot is 0.09 µm² with a NA of 1.4. Given that the near field spot of diameter 0.2 nm will have a size of 0.03 nm², this means that the far field to near field area ratio is 2.5 × 10⁷ for illumination from above and 3 × 10⁶ for illumination from beneath. However, given that the enhancement is greatly reduced for illumination from beneath, illumination from above is recommended at an angle between 45 and 60 degrees to the tip axis. Results in air (in Figure 3) show that this ratio can be overcome by the all of the tip materials, resulting in a near field signal which is larger than the total far field signal. In practice, this far field ‘background’ can be subtracted by taking a second image with the probe retreated far from the surface. For an aqueous environment, only the copper and aluminium tips give a near field signal which is predicted to be larger than far field signal, though both of these metals will of course oxidize.

4. Conclusion

We have performed finite element simulations of optical scattering from sharp SPM tips. For 1 nm radius tips, we predict both large optical enhancements and significantly red-shifted spectra. A number of metals are modelled as potential tip materials with large enhancements of the optical signal. Crucially, we also demonstrated that atomic resolution should be achievable with such 1 nm radius tips, in air and in water. This atomic scale chemical characterization of surfaces and molecules has massive potential in applications as diverse as materials science, nanotechnology and biomedicine.