Nanoscale Mapping of Dielectric Function
A Study Using Scattering Scanning Near-Field Optical Microscopy
- Fig. 1: 2x2 µm2 images of the Si/SiO2 sample; a) AFM topography with nine marked regions; b)-c) s-SNOM images acquired on successive frequencies of the signal spectrum. In the s-SNOM images, the central Si region is marked with blue and the surrounding SiO2 region is marked with red. (Image from )
- Fig. 2: 3D representation of the a) topography image and b) of the dielectric function map. The height accounts for the real part of the dielectric function, while the color map represents the imaginary part of the dielectric function.
- Fig.3: Equation 1
- Fig.4: Equation 2
A recent method for the quantitative measurement of the dielectric function by using scattering Scanning Near-field Optical Microscopy is discussed. The nanoscale capabilities of the imaging technique hold significant potential for enabling novel applications in fields such as nano-electronics, nano-photonics, biology or medicine.
Scattering Scanning Near-field Optical Microscopy (s-SNOM)  is capable of probing optical properties of an investigated sample at nanoscale, regardless of the excitation beam’s wavelength . This is possible by using the tip of a sharp probe as a light scatterer. More precisely, s-SNOM requires the tip to be laterally illuminated by a laser beam which leads to the light being scattered by it in all directions. When the tip is brought in close proximity to the surface of a sample (a region known as “the near-field”), the medium represented by the sample will interact with the tip and the scattered light will suffer changes in terms of amplitude and phase. Thus, the amplitude and the phase of the scattered light will contain information connected to the optical properties of the sample’s surface. The dimension of the volume in which the interaction between the sample’s surface and the probe’s tip takes place depends on the dimension of the tip. Thus using tips with nanoscale radius of curvature in the apex leads to the acquisition of optical nanographs of corresponding resolution.
An s-SNOM system can be built as an upgrade to an Atomic Force Microscope (AFM), which leads to a configuration capable of simultaneous s-SNOM/AFM imaging. One of the key problems related to s-SNOM imaging is background light which affects the detection of the near-field scattered light. Two combined methods are typically used to filter out the background light: higher harmonic demodulation (HHD)  and pseudoheterodyne detection (PD) [3, 4]. HHD takes advantage of the nonlinear dependence of the near-field scattered light intensity on the tip-sample distance by oscillating the tip above the sample and demodulating the signal on a higher harmonic frequency. In this way, an important suppression of the background is obtained.
PD is an interferometric detection method in which the near-field scattered light interferes with a reference beam which is phase modulated by means of a vibrating mirror. As a result, two side-bands around each harmonic component of the HHD signal appear. It has been proven that the detection of the components located inside these side-bands is less affected by the background light .
To date, s-SNOM has been successfully employed for multiple applications such as nano-imaging, characterization of plasmonic structures, near-field spectroscopy, nano-chemical characterization, etc. Here we discuss a recent method  based on s-SNOM that allows the measurement of the dielectric function of a material with nanoscale spatial resolution in the visible domain. Different from other current techniques, our method  is based on a classical model (Oscillating Point Dipole Method - OPDM), which has the key advantage of using a reduced number of parameters. Probing the dielectric function at nanoscale holds massive potential for developing novel applications in various fields such as medicine, biology, nano-electronics, or materials science.
The method that we have recently proposed  for measuring the dielectric function is based on calculating a calibration factor between an experimental image and the OPDM-based simulated signal in the case of an investigated material of known dielectric function, under a particular s-SNOM scanning configuration. Once this calibration factor is known, it is further on used for determining the dielectric function of a second material present on the investigated sample, which is initially unknown. This can be achieved using the experimental s-SNOM image generated by the unknown material together with the calibration factor and running the OPDM backwards. Calculating the dielectric function of the second material allows for its exact identification via database matching.
Two s-SNOM images, acquired at two successive frequencies located inside the PD side-bands, are necessary for applying this method. The first image is acquired at two harmonics of the probe plus the frequency of the reference mirror and the second image at two harmonics of the probe plus two harmonics of the reference mirror. The method is very versatile in using the s-SNOM images: the experimental data can be constituted either from the entire image area, from selected image areas, or from different scanning lines depending on the application and on the shape of the different material regions of interest.
We present the results obtained on a sample consisting in a SiO2 layer (26.6 nm thick) deposited on a Si substrate. The sample contains periodic circular holes with a diameter of 500 nm that penetrate the SiO2 layer reaching the Si substrate. The grayscale image in figure 1a) represents the topography of the sample, on which nine regions containing both Si and SiO2 areas are delimited. The two s-SNOM images acquired on two successive frequencies are represented in figure 1b and 1c. For each of the nine regions, the areas for Si and SiO2 are delimited by using circular and ring-shape areas, respectively. The pixel-values obtained from these areas (together with the results obtained using the OPDM model) are used for calculating the calibration factor (using the available data for the known material) and for determining the dielectric function of the unknown material. To demonstrate the method, we run the experiment in two scenarios: in one scenario we consider the first material as known and the second material as the material of supposedly unknown dielectric function, and in other scenario we switch roles.
Using all the data obtained from the nine regions delimited in figure 1a, we obtained the following results (for wavelength 638 nm) :
ƐSiO2calculated =2.4± 0.1 + (-0.008 ± 0.01)j (fig. 3)
ƐSicalculated =14.1± 0.8 + (-0.19 ± 0.05)j (fig. 4)
The theoretical values of the dielectric function for the two materials at 638 nm are: εSiO2 = 2.379 and εSi = 14.996-0.144j .
The obtained results are very promising and many applications can be found. For example, a 3D map of the dielectric function can be built based on this method (fig.2). This can be done by scaling the s-SNOM images to the obtained dielectric function values. In this way, the distribution of the surface dielectric function is visually represented, enabling the facile identification of interest areas.
In biomedicine, the possibility to map the dielectric function with nanoscale resolution could be of great interest. For example, it is well known that the refractive index of cancer cells is relatively higher than that of normal cells, which is believed to be a good criterion for the quantitative diagnosis of cell malignancy . Therefore, a nanoscale dielectric function map of a representative area of a sample could be potentially exploited for pointing out malignant or premalignant cells.
The recent method  for mapping the dielectric function at nanoscale demonstrates high measurement precision and enforces the idea that a combined s-SNOM/AFM system can be regarded as a powerful tool for the simultaneous assessment of optical and topographic properties of an investigated sample. Such a tool has the potential to enable novel applications in critical fields such as medicine, biology, nano-electronics, or materials science.
The LANIR research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2012-2015) under grant agreement n°280804. The presented work was supported as well by the research grant PN-II-PT-PCCA-2011-3.2-1162. The work of D.E. Tranca was also partially supported supported by the Sectoral Operational Programme Human Resources Development (SOP HRD) financed from the European Social Fund and the Romanian Government under the contract number POSDRU/159/1.5/S/137390/.
Dr. Denis E. Tranca1
Dr. Stefan G. Stanciu1
Dr. Radu Hristu1
Dr. Catalin Stoichita1
Dr. Syed A. M. Tofail2
Prof. George A. Stanciu1
1Center for Microscopy, Microanalysis and Information Processing, University Politehnica of Bucharest, Bucharest, Romania
2Department of Physics and Energy, University of Limerick, Limerick, Ireland
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Prof. George A. Stanciu (corresponding author)
Center for Microscopy
Microanalysis and Information Processing
University Politehnica of Bucharest