2 Principles and Theory of Tip-enhanced Raman Spectroscopy
2.5 Diffraction Limit in Optical Measurements 28
Optical diffraction implies the limit that restricts the lateral resolution of optical
measurements.47 The origin of diffraction limit in optical microscopy can be understood through an overview of the interferences of Airy patterns.48 An Airy pattern presents the
distribution of a best focused spot of light made by a perfect lens with a circular apex. Mathematically, an Airy diffraction pattern has the following definition:
2 1 0 sin sin 2 vb vb J I I (2.23)I0 is the maximum intensity of the pattern at the Airy disc center, J1 is the Bessel function of the first kind of order one, v2 , b is the radius of the aperture and is the angle
of observation. The dark rings in Airy pattern are produced at zeros of the Bessel function. An illustration of an Airy pattern is presented in Figure 2.7a.
Figure 2.7 Illustration of the diffraction limit problem and its dependence on the relative positions of neighboring Airy patterns (a) shows the top and side view of Airy pattern (b) demonstrates the diffraction limit (x) to be the distance between
the center of the two Airy patterns when the first intensity minimum of each Airy pattern is aligned with the intensity maximum of the neighboring one (c) For center- to-center distances larger than x the neighboring objects will be completely
resolved.
The diffraction pattern created by illumination of a circular aperture shows a bright area in the middle which corresponds to maximum intensity and a series of concentric bright rings with decreasing intensity at farther distances from the center. As it is illustrated in
separated by a minimum distance equal to the radius of the central disk in the Airy pattern. This minimum distance is referred to as x in Figure 2.7b and also in the next paragraph. The minimum value of x, required for two neighboring objects to be
resolved, corresponds to a situation where the first minimum in Airy pattern of one of the objects is aligned with the maximum intensity in Airy pattern of the other object.
The diffraction-limited resolution theory was refined by Ernst Rayleigh49 in 1873 and refined by Lord Rayleigh50 in 1896. The theory was used to estimate the smallest distance between two objects to be distinguished as separate entities in an optical measurement. In Rayleigh criterion the lateral resolution (x) is estimated by the following equation:
sin
2
22
.
1
n
x
(2.24) This equation suggests that at each wavelength, x can be improved by changing the surrounding media into one with larger index of reflection (n) and by choosing a focusing lens with larger collection angle (The denominator in equation (2.24) is known as the numerical aperture (N.A.) of the objective lens which indicates the focusing properties of the lens. Microscope objectives with larger N.A. values focus light more tightly and efficiently. However, there is a limit for improving the diffraction limit in conventional microscopy and spectroscopy. Ideal experimental conditions lead to roughly 200-300 nm resolution in visible light region provided that a microscope objective with N.A.=1.4 (oilimmersion objective) is used. This limit is clearly not suitable for studying smaller features are of interest.
In the last century, surpassing the diffraction limit of light to acquire higher lateral resolution in microscopic and spectroscopic investigations has been the subject of many researches. In 1928 Synge suggested scanning the surface of the sample by an opaque metal screen with an aperture smaller than the wavelength of light which is illuminated from the back.51 If the aperture is located within the near-field of the sample, a few nanometers away from it, the resolution of the measurement is no longer limited by the diffraction limit. The size of the aperture will indeed determine the limits of resolution in
this case. This hypothesis built the basis for the realization of scanning near-field optical microscopy (SNOM) in 1984 due to the progresses in nanoscale motion control provided in scanning tunneling microscopy and atomic force microscopy.52,53
Aperture SNOM was the first generation of near-field optical microscopy. In aperture SNOM an optical fiber with sharpened end is used as light source to scan the near-field of the sample.54 The fiber is generally coated with a thin metal film, everywhere except at the apex of the tip.55,56 However, the low throughput of SNOM and specially fiber probe in combination with the low cross-section of the scattered Raman signal and the tedious fabrication and thin film coating procedure delayed the development of SNOM-Raman until 1994.57 Clearly, the coupling of an intense light source was not a proper solution to the low throughput problem since it would lead to local thermal effects that could damage the integrity and subsequent resolution of the tip. The dimension of the uncoated part of the apex determines the spatial resolution of aperture SNOM and since the fiber tips have flatted apex, the optical resolution of the method was limited to about60 nm.58,59
Nowadays, hollow aperture probes are made using commercial AFM tips through creating a hole at their apex by using advanced nanofabrication techniques such as focused ion beam (FIB). Alpha300 S AFM tips fabricated by WITecTM are an example of these tips where an aperture (100 nm) is created at the apex of a hollow pyramid.
Nevertheless this type of approach is marginal and is rarely used for Raman spectroscopy purposes.
It was later proposed that localized surface plasmon be employed through illuminating the metallic tip of scanning tunneling microscopes (STM). In such a case, the tip would act as a nanosource with light confined at its extremity. The idea was to enhance the Raman scattering and to surpass the diffraction limit within the confined electric field at the STM tip apex. This combination of SERS and near-field microscopy was first named apertureless Raman near-field60 and later, on the same principle, tip-enhanced Raman spectroscopy (TERS). First spectroscopic applications of apertureless SNOM was performed in 1999 in a two photon fluorescence study61 and in 2000 for tip-enhanced Raman spectroscopy.62-64 Nowadays, it is also common to use atomic force microscope (AFM) tips in conjunction with an AFM feedback mechanism. As opposed to STM based
TERS setups, AFM feedback does not require the use of conductive samples, a feature that makes TERS accessible for a larger variety of samples. Various TERS configurations will be discussed in detail in Chapter 3 of this thesis. The different SNOM methods that are mentioned above are however summarized in Figure 2.8:
Figure 2.8 Schematic of various SNOM configurations (a) Principle of SNOM using a small aperture on an opaque substrate (b) aperture SNOM with a coated optical fiber attached to a tuning fork. The tip is shown in excitation mode but can also be used for light collection purpose. (c) aperture SNOM provided through making hollow AFM probes (d) apertureless metallic tip, in close proximity of sample surface.