7.1         Sub-pN shear-force feed back system in air and liquid

This section presents the paper currently in preparation. The authors are :

-         Philippe Giaccari, Omar Sqalli and Hans G. Limberger : Institute of Applied Optics, Swiss Federal Institute of Technology

Scanning near-field optical microscopy requires a performant sensor to measure the tip-to-sample distance. In this letter, we report on a novel shear force detection scheme for scanning near-field optical microscopy applications. It is based on an all fiber low-coherence interferometer. This setup makes possible the measurements of the tip oscillation amplitude of less than 50 pm both in air and aqueous environment with a precision of 160 fm. Hz^-1, thus demonstrating the ability to perform topographic measurements both in air and in liquids with a resolution better than 1 nm in the height direction. Stable feedback in air and fluids is obtained with tip-sample interaction forces below 1 pN.

Scanning near-field optical microscopy (SNOM) has drawn considerable research interest in recent years since it allows the measurement of both the topography and the optical contrast of a sample with sub-wavelength resolution [7-1]. The instrument works by scanning a sub-wavelength size probe very close to the sample surface. The probe consists of a glass tip that can be covered with an opaque metal layer, with a clear aperture of sub-wavelength dimension at the tip apex [7-2]. A large majority of today's probe-sample distance control mechanisms works by detecting the damping of the oscillating tip by lateral forces (the so called "shear force") close to the surface [7-3]. Scanning-near-field optical microscopes require consequently performant sensors to measure nanometric oscillations of SNOM tips. Different methods have been proposed in the last ten years, such as a compact near-field optical module based on an external cavity laser interferometer [7-4] or the tuning fork [7-5,7-6] that allows measuring tip oscillation amplitudes of a few picometers in air. However, working in aqueous environment is more critical since a huge damping of the tip vibrations occurs upon immersion of several microns into liquid [7-7]. For investigations in aqueous environment, a new type of liquid cell was proposed, in order to limit the immersion depth of the SNOM probe [7-8]. Measurements in aqueous environment with the tuning fork system are possible only upon complete immersion of the tuning fork into liquid [7-9] with a typical vibrating tip amplitude of about 1 nm.

In this letter, a novel force detection scheme for scanning near-field optical microscopy applications is presented, theoretically described and experimentally tested. It is based on an all fiber low-coherence interferometer to measure extremely small SNOM tips oscillation amplitudes, both in air and aqueous environments.

The novel force detection scheme for scanning near-field optical microscopy applications is based on an all fiber low-coherence interferometer. The experimental set-up is presented in Fig. 7-1. A super luminescent laser diode (SLD) beam coupled into a single mode fiber (port 1) is used to illuminate a Michelson interferometer based on a 50/50% fiber coupler. At the end of the second interferometer arm (port 2), the measurement fiber, 4% of the light is reflected at the glass-air interface. 96% of the light is transmitted and partially reflected on the SNOM tip. The distance d between the SNOM tip and the end interface of the control fiber is typically 2 microns. Therefore, the tip interface and the fiber end face form a Fabry-Perot interferometer. A large part of the light reflected in this structure is coupled back into the optical fiber and is detected with a balanced detection system consisting of to photodiodes mounted at the other arms (port 3 and 4) of the Michelson interferometer. Monitoring the intensity of the interference fringes allows measuring the tip vibration amplitude. The balanced detection scheme improves the S/N ratio by reducing the source noise. The SLD source (SLD 56-MP SUPERLUM, 0.5 mW) spectrum has a full width at half maximum Dl of 44 nm centered at lo=1319nm, leading to a coherence length of the source of about 20 microns. The low coherence of the SLD source has ths advantage to eliminate spurious interference signals resulting from other reflections in the set-up (e.g., the coupler), thus leading to an increase of the signal-to-noise ratio of 30 dB. The SNOM-tip is mechanically excited by a piezoelectric element P2 located at x=0. The excitation is being supplied by a digital Lock-In Amplifier (SRS, RF Lock-In Amplifier, Model SR844). The measured optical interference signal is amplified by the Lock-in Amplifier and finally sent to a PC for storage and display.

Fig. 7-1. Schematic drawing of the experimental set-up of the shear-force system based on low coherence interferometry. R1 (=4%) and R2 (=96%) are the reflection coefficients at the end of the control fiber and the SNOM tip, C a 50/50 optical coupler, D1 and D2 two detectors, p₂ a dithering piezo.

In order to calculate and characterize the SNOM fiber tip oscillations, we consider the vibration model of a beam clamped at one end and free at other [7-10]. The tip is described as a homogenous quartz cylinder, since the 100 microns long conical part of the tip is insignificant in comparison to several millimeters long cylindrical fiber. We thus consider a uniform radius R of 62.5 mm along the entire SNOM fiber length. The mass per unit length of the quartz is 8.6 mg/m, E the Young modulus is 72 GPa. For a given harmonic excitation frequency and a given fiber length, the vibrations amplitude at a distance from the clamped end is calculated by resolving the Euler fourth order differential equation [7-10]. Fig. 7-2 shows (a) the measured and (b) the calculated oscillations amplitudes at the middle of a 9.2 mm long quartz fiber that has a diameter of 125 mm. We observe six resonances with different amplitudes that correspond to the vibration modes. The precision of the vibration amplitude measurement is 160 fm/Hz^-1/2. The calculated resonance positions and relative amplitudes are similar to the experimental measurements.

Fig. 7-2. Measured (a) and calculated (b) vibration amplitudes at the middle (x=4.6mm) of a 9.2 mm long SNOM tip.vibration amplitudes at the middle (x=4.6mm) of a 9.2 mm long SNOM tip.

Fig. 7-3. Calculated vibration amplitudes of a 9.2 mm long SNOM tip as a function of the position x on the tip and the oscillation amplitude.

Fig. 7-3 illustrates the tip oscillations amplitudes calculated at a position x on the tip and as a function of the oscillation frequency. We observe six resonances with different amplitudes that correspond to the vibration modes. The theoretical calculations allow correctly estimating the oscillations at the end of the tip by measuring the oscillation amplitude in another part of the fiber tip, for a given eigenmode. The above described set-up makes possible to detect a minimal vibration amplitude of the SNOM tip of about 5 pm for a lock-in time constant of 1 ms, and of 1 pm for a time constant of 30 ms. Near-field optical microcopy measurements are consequently performed with typical oscillation amplitudes of 50-100 pm at the tip extremity, and a signal to noise ratio always superior to 10.

The vibration modes of the tip are experimentally investigated in aqueous solution. Fig. 7-4 illustrates the vibration amplitude measurements of 6.2 mm long quartz SNOM tip in air and in water, for different immersion depths of the tip in water. The vibrations measurements have been carried out at the middle of the fiber tip for the third eigenfrequency. First, a damping of the vibrations amplitude as well as a shift of the resonance frequency to lower values is observed when the immersion depth increases. The resonance position is shifted from 46.8 kHz to 44.5 kHz for a 2 mm immersion depth. Second, the Q factor decreases from 100 to 80 but remains always sufficiently high and makes possible performing SNOM measurements in water, even for immersion depth of 2 mm. The same behavior is observed for the other resonances showing that the vibration modes are preserved in water.

Fig. 7-4. Damping of the L=6.2 mm long tip oscillations, as a function of the oscillation frequency, for several tip immersion depths in water. The measurement is performed at x=3.1 mm, at the middle of the oscillating SNOM tip.

Fig. 7-5. Two topographic images of a 21 nm deep chromium on glass grating with a period of 372 nm performed with the same tip on the same sample in air then in water.

The previously described interferometric system is mounted in the SNOM set-up. A z-piezo vertically moves the tip, whereas an x-y piezo horizontally moves the sample. Fig. 7-5 shows two topographic slices of chromium on glass grating with a period of 372 nm performed with the same tip, in air and in water. The tip vibration amplitude at the tip extremity of 50 pm during the scan in both cases, with a signal-to-noise ratio was of about 50. The similarity of the images proves the reliability of the technique to perform accurate measurements both in air and aqueous environment with a height precision better than 1 nm. Moreover, the topographical contrast is nearly the same in air and in water. The lateral resolution is given by the probe shape.

To gain a better qualitative and quantitative understanding of the interaction force between the tip and the sample, a simple model called the effective mass harmonic model and described in reference [7-5,7-8] is used. Again, the SNOM fiber tip is considered as an uniform cylinder with a static spring constant k_spring. The tip-sample interaction shear-force Fint is obtained by measuring the free U_l and attenuated U_int vibration amplitude, at a specific resonance frequency with a precise Q quality factor: . The SNOM tip described in Fig. 7-3 has a length L of 9.2 mm, a spring constant k_spring=3EI/L³ of 3 N/m (fundamental eigenfrequency), where I=pR⁴/4 is the inertia mement of the tip, a working free oscillation amplitude U_l at 2 kHz of about 50 pm, a Q factor of about 80. By choosing U_int equal to 0.9_*U_l, the measured shear force F_int is about 0.2 pN. Note that an increase of the probe length leads to a decrease of the probe static spring constant, and therefore to the detection of a smaller shear force for the same vibration amplitude. Higher eigenfrequencies are usually characterized by a higher Q factor, that allows measuring smaller forces, but also a higher spring constant of the tip, since the nodes reduce the effective oscillating length of the tip.

In conclusion, a new low coherent system has been implemented in force detection schemes for scanning near-field optical microscopy applications. It allows characterizing the SNOM-tip oscillation modes and amplitudes on the one hand, and, on the other hand, performing topographical measurements with a high precision both in dry and aqueous environments using the shear-force technique. The SNOM tip vibration amplitudes are typically 50-100 pm at the tip extremity during the scan. Topography measurements with a precision better than 1 nm in the z direction were performed without any control of the ambient temperature and humidity.