1. Introduction

Near-field scanning optical microscopes (NSOM) have been developed to get images of much better resolution than that of the conventional diffraction-limited optical microscopes [1,2]. The NSOM often employs a tapered optical fiber as a probe to obtain near-field optical signals as well as topographic images. The highest possible resolution of the NSOM is achieved when the probe-to-surface separation is kept constant in the near-field regime over the entire scanning process. Therefore, various distance regulation schemes have been proposed, including electron tunneling[1], frustrate total internal reflection, atomic force probing, and shear-force distance control[3,4]. To date, the shear-force detection technique is widely adopted for the probe-to-surface distance control because of its simplicity, in which a probe is vibrated parallel to a sample surface and its oscillating amplitude is measured [5–8].

A method to produce the probe oscillation and measure its amplitude is to utilize a tuning fork with one prong attached to the tapered optical fiber and the other mounted on a dithering piezoelectric transducer (PZT) plate. At resonance, the tuning fork generates an oscillating piezoelectric signal proportional to the probe oscillation amplitude [5]. As the probe approaches normally onto the sample surface, the oscillating piezoelectric signal decreases since the resonance frequency is shifted to a higher frequency [6,7,9]. The shifting effects indicate that the low frequency slope of the main resonance peak should be used as the shear-force control signal. The resonance characteristics of the tuning fork play an important role to determine the shear-force detection sensitivity for the probe-surface distance regulation. High shear-force detection sensitivity requires a large quality factor Q of the tuning fork since the derivative of the smallest detectable force is proportional to $\frac{1}{\sqrt{Q}}$ [8,10]. For a standard proportional-integral closed loop configuration, electrical reduction of resonance background noise without minimizing Q should also be provided to get better stability as well as fast response [11]. However, since the feedback signal does not go to zero when the tip is in contact with the surface, a calibration for the approach curve is not accurate and the distance regulation signal becomes unstable. This problem always occurs such the techniques based on quartz mode tuning forks including the tapping mode, because the resonance frequency is shifted as the tip approaches the sample. Up to now, there are only few approaches to avoid such problems [12,13]. In order to obtain certain resonance characteristics desired for high resolution, we should consider many subtle details, such as the mounting conditions and the mounting positions of the tuning fork on the dithering PZT, along with the shape of the dithering PZT.

In this letter, we investigate symmetric and asymmetric responses of the tuning fork to enhance the shear-force detection sensitivity of the probe-sample distance-control for the NSOM system. Particularly, we present substantial improvement of the shear-force detection sensitivity utilizing the asymmetric resonance of a tuning fork. We show that the asymmetric frequency response with a large quality factor Q of ≥ 2500 and a suppressed background feedback signal can be generated by controlling the conditions on an edge-clipped dithering PZT plate. The asymmetric system applied to the NSOM allows us to acquire nano-scale surface images with a shear-force vertical stability of less than 2nm. A simplified model based on a coupled harmonic oscillator system is also presented to describe the asymmetric behavior of the tuning fork.

2. Experiments

A schematic diagram of our NSOM is shown in Fig. 1. A commercially available metal-coated tapered fiber-probe with an opening aperture of 100nm is glued along the side of one prong of a tuning fork with a resonance frequency of 32,768 Hz. The piezoelectric signal from the tuning fork is detected by a 1MΩ load resistor with a high-impedance pre-amplifier (AD524) of 100× gain. This signal is fed into a lock-in amplifier (EG&G 7265) and a “fast X” output from the lock-in amplifier is employed as an error signal for the feedback loop to take advantage of its rapid phase-signal response. The distance control using the amplified signal is achieved by a proportion and integration (PI) feedback controller. The bandwidth of our system was about 30Hz, which was measured by an actuator (Jena TRITOR 100) oscillating the sample intentionally. The distance between the tip and sample was positioned by a piezoelectric tube which was calibrated using a Michelson interferometer.

 

Fig. 1. Schematic diagram of the near field scanning optical microscope.

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Figure 2(a) displays a typical symmetric response of the piezoelectric signal amplitude, with a Q factor of ~1600 in our system. Raising the dithering voltage increases the off-resonance feedback signal, which limits the shear-force vertical sensitivity. In order to enhance the Q factor and locally suppress the feedback signal, as shown in Fig. 2(b), an asymmetric frequency resonance is proposed by attaching a fiber-probe along to one (upper) prong of the tuning fork and the other (lower) arm to the edge-clipped PZT plate. We found that the symmetric Lorentzian response curve can be readily broken by artificial perturbation, such as chipping off a piece of the corner of the PZT plate, and altering mounting conditions of the tuning fork on the dithering plate and the fiber probe on the prong. Practically, our interest is focused on the case where the asymmetric resonance peak has a better Q-factor in the lower frequency region with off-resonance amplitudes greatly suppressed. With such resonance curves, we have found that it is easier to obtain higher vertical and lateral resolutions, yielding naturally higher Q-factors. We have tried to create and amplify such additional resonances by using a specially shaped, such as a trapezoid, dithering PZT to induce altered modes with the excitation force, and also by controlling the amount of adhesive pasted onto the tuning fork. The shape of the resonance curve is also dependent on where the tuning fork is placed on the dithering PZT, how much adhesive is used, and what kinds of methods are used to mount the tuning fork onto the dithering PZT.

 

Fig. 2. The amplitude of the PZT signal measured as a function of driving frequency. (a) and (b) show symmetric and asymmetric responses with damping, respectively. The driving voltage is varied from 3mV to 15mV. A relatively high Q-factor (≥ 2500) is achieved in the case of (b) compared to (a), where the Q-factor is ~1600 and the background feedback signal is increased for higher dithering voltages.

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The breaking of the symmetric shape of the main resonance peak creates two or more resonance peaks of the tuning fork [14]. In fact, as shown in Fig. 3, many more supplemental peaks are observed when the voltage applied onto the dithering PZT plate is increased. The largest peak is located at 32,760 Hz near the original resonance frequency, whereas the other peaks are located at higher or lower frequencies. It is observed that a supplementary peak, largely damped, is located around 4.2 kHz away from the main peak, as shown in Fig. 3. Through a variety of experiments, such as breaking one of the prongs off, we find that the upper prong of tuning fork had a dominant effect on the main peak. As is expected, however, resonance characteristics are also strongly dependent upon the mounting position of the tuning fork on the dithering PZT plate. A large Q (≥ 2500) of the tuning fork and tip assembly with an almost completely suppressed off-resonance feedback signal can be obtained by gluing approximately two millimeters of the lower prong of the tuning fork to the edge-clipped dithering PZT plate. Here, Q is estimated to be two times of the half width at half maximum of the tuning fork resonance peak in the low frequency side of the peak since the slope of low frequency side is used for the tip-to-sample distance control. Note that the feedback signal at the low frequency side, specifically at around 32,735 Hz, remains below 2.5% of the amplitude of the resonance peak, even though the dithering voltage is increased. This strongly indicates that the asymmetric frequency dependence of the output signal can enhance the Q-factor and the detection sensitivity for the distance control process of shear-force modes. The asymmetric frequency dependence with a pinning down effect at the higher frequency side can also be used for the tapping mode NSOM system because for this case the resonance peak is slightly shifted to the lower side when the probe approaches to the sample surface [15].

 

Fig. 3. Resonance response profiles measured as a function of driving frequency. The driving voltage is varied from 5mV to 55mV. The main resonance peak is detected around 32 760 Hz while a second peak is also detected near 28 540 Hz, respectively. Additional supplementary modes are also apparent at higher frequencies than the main resonance frequency.

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According to the experiments, the special shape of the PZT plate provides many more subsidiary modes of vibration. We can observe many peaks not only around the region of resonance (~32768 Hz) but also along a larger inclusive span (10000 ~ 50000Hz). In particular, through repeated experiments, we have found that two peaks were observed to be relatively larger than other peaks, suggesting a simplified approximation of the shear force detection system as a 2 degree-of-freedom coupled oscillator with harmonic excitations.

3. Theoretical modeling

In order to understand the asymmetric resonance behavior of the tuning fork, therefore, we introduce a coupled two-degree-of-freedom harmonic oscillator system, i.e.,

Here, the effective mass, the damping coefficients, and the stiffness matrices with a coupling constant K can be written as $M=\left(\begin{array}{cc}{m}_1& 0\\ 0& m_2\end{array}\right),C=\left(\begin{array}{cc}{m}_1{\Gamma }_1& 0\\ 0& m_2{\Gamma }_2\end{array}\right),K=\left(\begin{array}{cc}{k}_1+K& -K\\ -K& k_2+K\end{array}\right)$.

Assuming a harmonic driving force, F(t) and x(t) can be written as F(t) = F₀ exp(iωt) and x(t) = X(iω) exp(iωt), respectively, where F₀ is a constant written vector and X(iω) is a complex vector depending on the driving frequency ω. Then, the solution of Eq. (1) is given by [16]

with a superposed response function defined as X_S(iω) ≡ X ₁(iω) + X ₂(iω). The magnitude of the frequency response, which is actually the superposed electrical signal from the quartz tuning fork, can be written by

Two resonance peaks are obtained when taking similar but slightly different mass and stiffness values for the two terms X ₁ and X ₂. If one of the peaks is substantially suppressed by damping, a rapid drop of amplitude is observed in either higher or lower frequency regions of the larger main peak, depending on the different values of the coupling constant K, and peak positions mostly depending on k ₁/m ₁ and k ₂/m ₂ as shown in Fig. 4(a), (b). Figure 4(b) shows simulations of resonance curves based on our model, with the parameters of m ₁ =1.000×10^-4 , m ₂ = 1.015×10^-4 , Γ₁ = 5, Γ₂ =10 , k ₁ = 107200, k ₂ =106300, and K = 100. The external forces are varied from 3F to 15F, where the force is given by $F=\left(\begin{array}{c}1\\ 10\end{array}\right)\exp \left(\mathit{i\omega t}\right)$.

The overall shape as well as the suppressed signal in the low frequency side of the experimentally observed asymmetric resonance profiles is well reproduced in the simulation. The resonance curve with a pinning down frequency response at the higher frequency side is also simulated for the tapping mode systems as shown in Fig. 4(a), where the parameters are the same as for the shear-force system except for the coupling constant set at K = 400. For the simulations, only two peaks are utilized in order to obtain the asymmetric resonance features with a suppressed off-resonance signal. As mentioned above, however, it should be emphasized that the actual system is much more complicated having many different resonance peaks [14]. These peaks come from different vibration modes of the tuning fork. One possibility is the existence of a vibration mode along the perpendicular direction of the typical vibration mode, owing to the fact that the dithering PZT is vibrating not only along the direction normal to its surface but also along the orthogonal direction. Since the tuning fork is a beam instead of a simple spring mass system and its beam vibrations have many harmonic modes and nonlinearities, in addition, multiple modes can be produced. Any such vibration mode which has a large damping term and a high F/m factor may contribute to a drop on one side of the main peak. According to our model, it is found that the asymmetric resonance curve with a drop at the lower frequency side is mainly due to a coupled vibration of the shear-force mode tuning fork. The coupling constant K may be determined by the mounting methods of the tuning fork.

 

Fig. 4. Asymmetric resonance response curves simulated by a coupled two-degree-of-freedom harmonic oscillator system. Simulations of a suppressed signal in the high frequency side with K=400 for tapping mode systems(a) and in the low frequency side with K=100 for shear-force mode systems(b).

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4. Results and conclusions

Figure 5(a) shows the topographic image of the blue-ray optical disc obtained by using the asymmetric response of the tuning fork while Fig. 5(b) and (c) show the cross-section points measured along the black lines. The cross section lines are low-pass filtered to remove high frequency noise. As shown in the inset of Fig. 5(b), it is also found that the shear-force vertical stability is less than 2 nm while scanning the surface along the black line.

 

Fig. 5. (a) Topographic NSOM images of a blue-ray optical disc obtained by utilizing an asymmetric response and (b),(c) show the cross-section view having a vertical stability of less than 2 nm.

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The low frequency slope of the main resonance peak is used as the shear-force control signal since the resonance frequency is shifted to a higher frequency as the tip approaches normally onto the sample surface. The asymmetric response with a drop in the low frequency region is more sensitive than that of the high frequency region. Applying this asymmetric system to our NSOM, high resolution images are obtained for a blue-ray optical disc having a sequence of nano-scale pits. The commercialized AFM images of the poly-carbonate high-density optical disc reveal that the track pitch, the pit width, and the depth of the pit are measured to be ~ 320nm , ~100nm, and ~ 70nm , respectively[17].

Figure 6(a) shows the topographic images of the blue-ray optical disc and its cross-section view was obtained as shown in Fig. 6(b) using a symmetric frequency response of the tuning fork. The measured vertical stability of the symmetric case was about 10nm which was inferior to the asymmetric case(~2nm).

 

Fig. 6. (a) Topographic NSOM images of blue-ray optical disc obtained by utilizing a symmetric response and (b) the cross-sectional view having a vertical stability of about 10nm.

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The fiber probe has an outer diameter larger than 500 nm, which is much larger than the pit size, not having have a super tip which is verified by tunneling electron microscope(TEM) images. Therefore, the probe should not be able to trace the sample surface to the bottom of the pits, indicating that the measured data(~20nm) do not display the actual topographical depth of the pits but in fact show a variation of the distance regulation signal due to the inconstant density distribution of the surface. The regions of the pits have a relatively lower density than its surroundings, giving a non-uniform density distribution

On the other hand, patterns of larger scale compared to the blue-ray disc sample were traced from peak to valley as shown in Fig. 7(a), where the probe was able to follow the actual topographical surface of the patterns. Because the width of pattern was large enough for the probe to trace the bottom of a valley, it was observed that the depth of the mask pattern was about 100 nm while that of a blue-ray disc was below 20nm as shown in Fig. 5. The optical image of the chromium pattern on a quartz glass plate was also obtained by the asymmetric response of a tuning fork as shown in Fig. 7(b) simultaneously. The scanning area was 5×5μm ². The optical probe was able to emit a laser light of 650nm and diffracting lights from the mask sample was gathered by the objective lens. The optical signal consistent with the topogrpahic image was obtained using a photo-detector (see Fig. 1). Therefore, this method has the potential of sensing the density fluctuations of the samples with almost no height variations and obtaining an optical image through the opening aperture of the probe simultaneously.

 

Fig. 7. Topographic image(a) and optical image(b) of chromium mask pattern respectively and the cross-section view(c) along white dotted line.

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In conclusion, we have investigated symmetric and asymmetric responses of the tuning fork to enhance the shear-force detection sensitivity of the probe-sample distance-control for our NSOM system. Particularly, we have demonstrated that the asymmetric frequency response of Q ≥ 2500 , with the suppressed background feedback signal, can be reproduced by controlling the mounting conditions on an edge-clipped dithering PZT plate. The asymmetric system applied to the NSOM allows us to acquire nano-scale surface images with a shear-force vertical stability of less than 2nm which was enhanced 5 times as much as for the conventional case. A simplified model based on a coupled harmonic oscillator system is also presented to theoretically describe the asymmetric behavior of the tuning fork. We believe that it will be particularly useful in imaging biological samples having density fluctuations and/or refractive index variations of comparably high lateral and vertical resolution.