November 5, 2019.
1.Scanning Probe Microscopy
The resolution of far-field imaging system is limited by the diffraction of light. The diffraction-limited resolution, firstly studied by Ernst Abbe  and Lord Rayleigh [2,3], can be quantitatively described by the shortest resolvable distance between two points, r, which is given by
where λ and NA are the wavelength of light and the numerical aperture of the imaging system, respectively. Even though the resolution can be improved by several approaches such as increasing the numerical aperture by using oil-immersion objectives or applying shorter wavelengths in electron or ultraviolet microscopy, the resolution of far-field imaging systems cannot be greater than half of the wavelength.
Scattered light from an object consists of high and low spatial frequencies. Only the latter can propagate to conventional microscopes whereas the first, contributing to the finer details of the image whose resolution is not limited by the diffraction, is confined at the surface of the object . In order to detect the non-propagating field, a probe with the nanometer-sized aperture is required to be brought to close to the surface within the subwavelength range (around 100 nm). This is the technique utilized in the scanning probe microscopy (SPM).
The integral part of SPM is the probe height control system retaining the constant gap distance between the probe and the surface. The function of the control system is based on the detection of the distance-dependent interaction from the surface to the probe. In the scanning tunneling microscopy (STM), the probe height control can be achieved by detecting the deviation of the current from the metallic probe, induced by the electron tunneling phenomenon. On the other hand, the probe height control system in the atomic force microscopy (AFM) is based on the effect of Van der Waals force and Pauli force . One of the most widely used technique for controlling the probe height is the shear force feedback system . Variations in the resonance frequency and phase of the oscillating probe caused by shear force from the surface is inspected by the control system for adjusting the probe height in order to keep the constant gap distance between the probe and the surface. As a result, the probe height data at various locations while the probe scans across the surface renders the topographical image of the surface. Additional optical image of the surface can also be collected if the probe is an optical fiber as utilized in the scanning near-field optical microscopy (SNOM).
2. Prototype of a Compact SPM System
2.1 Quartz Tuning Fork (QTF) Probe
Several techniques can be adopted for the probe height control. Changes in the amplitude of the probe’s oscillation can be detected by detecting the intensity of the reflected light from the probe  or the differential interferometry. However, more compactness of the probe height control system can be achieved by attaching the probe with a tuning fork [8,9]. This approach is also adopted in this research. The quartz tuning fork (QTF) is a crystal oscillator used in quartz watches for generating signals with precise frequency. A shear force sensing tungsten or optical fiber tip can be attached at one prong of the tuning fork. Such a system can be treated as a damped oscillating system and its characteristic can be described with the parameter called quality factor or Q-factor, defined as
where f0 and Δf are the resonance frequency and the full width at half maximum (FWHM) of QTF’s frequency response, respectively.
High Q-factor reveals high sensitivity of the probe in shear force detection, but slow response which slows down the probe’s scan speed. Generally, the resonant frequency of QTF is 32.768 kHz with the Q-factor of 6400 in vacuum and 7500 in air . However, QTF’s Q-factor drops down to 300 - 1000  when it is attached with the tip.
Fig. 1 (a) Quartz tuning fork utilized as an SPM probe and (b) QTF’s frequency response measuring system.
Fig. 2 (a) Python-based control program for the measurement of QTF’s frequency response and (b) display of the QTF’s frequency response curve from the control program with the values of QTF’s resonance frequency and Q-factor tip.
Figure 1(a) shows the QTF used as an SPM probe in this research. The oscillation of the probe is driven by signals from a driving circuit which is basically scaling down the signal from the function generator. The QTF is a piezoelectric transducer converting mechanical vibration of the probe into the electrical current which is passed to a current-to-voltage converting electronic circuit and the outcome voltage signal is measured by an oscilloscope, as shown in Figure 1(b). The measurement of QTF’s frequency response is controlled by a Python based program developed in this research. Figure 2 displays the control panel of the program on which the parameters of the measurement such as the range of frequency scan and data size can be customized. After the measurement, the frequency response curve is displayed with the values of QTF’s resonance frequency and Q-factor.
2.2 Probe Height Control System
Fig. 3 Probe height control system
Figure 3 displays an SPM probe height control system. The system keeps monitoring variations of the QTF probe oscillation caused by the distance-dependent shear force effect from the surface upon the QTF probe. Since electrical signals from the QTF probe are extremely weak (the piezoelectric current of the probe oscillation is in the order of picoampere) and hidden in noises, a lock-in amplifier (LIA) is an indispensable instrument of the system. The LIA separates noises from the signals of the oscillating QTF probe whose deviation from a set point of the control system is analyzed and results in the vertical translation of the probe in order to keep constant gap distance between the probe and the surface.
Figure 4 (a) displays a home-built low-cost compact LIA we have developed in this research. In Figure 4(b), the capability of our LIA is tested and compared with that of a commercial LIA (SR860 Lock-in Amplifier by Stanford Research Systems). Our LIA functions efficiently as can be seen in Figure 4(c) which shows the frequency response of the QTF probe measured from both LIAs.
Fig. 4 (a) LIA developed in this research, (b) testing the performance of the home-built LIA and (c) comparison of the measurement from the home-built LIA and commercial SR860 LIA.
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2. J. W. Strutt, “Investigations in optics, with special reference to the spectroscope”, Philosophical Magazine, 8.
3. J. W. Strutt, “Investigations in optics, with special reference to the spectroscope”, Philosophical Magazine, 9: 40–55.
4. E. Wolf and M. Nieto-Vesperinas, “Analyticity of the angular spectrum amplitude of scattered fields and some of its consequences”, Journal of the Optical Society of America A, 2(6):886.
5. B. Birdi, “Scanning Probe Microscopes: Applications in Science and Technology”, CRC Press.
6. R. Toledo-Crow, P. C. Yang, Y. Chen, and M. Vaez-Iravani, “Near-field differential scanning optical microscope with atomic force regulation”, Applied Physics Letters, 60(24).
7. E. Betzig, J.S. Weiner, and P.L Finn, “Combined shear force and near-field scanning optical microscopy”, Applied Physics Letters, 60(20):2484–2486.
8. K. Karrai and R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes”, Applied Physics Letters, 66(14):1842–1844.
9. K. Karrai and R. D. Grober, “Piezo-electric tuning fork tip-sample distance control for near field optical microscopes”, Ultramicroscopy, 61(1):197–205.
10. G. Ctistis, E. H. Frater, S. R. Huisman, J. P. Korterik, J. L. Herek, W. L. Vos, and P. W. H. Pinkse, “Controlling the quality factor of a tuning-fork resonance between 9 and 300 k for scanning-probe microscopy”, Journal of Physics D: Applied Physics, 44(37):375502.
Dr. Tipsuda Chaipiboonwong
Dept. of Physics, Fac. of Science and Technology, Thammasat University, Pathum Thani-12120, Thailand