![]() 13 With both signs for f RT0 − f TF (Fig. The plots are mirror-symmetric about the zero the frequency change | f RT0 − f TF|, caused by adding/subtracting to the prong, decreased the Q factor irrespective of sign ( f RT0 − f TF > 0 for extracting, and <0 for appending) Rychen described similar results adding mass to one prong. The Q factor, measured by sweeping the frequency of excitation signal, increased as f RT0 − f TF approached zero. ![]() Figure 3 shows the plots of their Q factors versus f RT0 − f TF in air (a) and in UHV (b). ![]() We measured the resonance properties of 24 retuned fork sensors each with a tip and with different f RT0. The sample was a Si(111)–7 × 7 surface cleaned by flashing in the UHV. We employed a home-made nc-AFM combined with a scanning tunneling microscope operated in 1.5 × 10 −10 Torr using the retuned fork sensor with the W tip. The sensitivity of the prong displacement of 0.6 nA/nm with a floor noise density of about 80 fm/▴Hz was evaluated by thermal vibration spectrum analysis. An operational amplifier (AD744, Analog Devices, Norwood, MA, USA) with a gain of 30 × 10 6 V/A was installed as the preamplifier, located near the force sensor in an ultrahigh vacuum (UHV) chamber for the nc-AFM. 10 This circuit generates the anti-phase sinusoidal signals with the same amplitude, one of which excites the oscillation of the tuning fork the other is used to cancel the leaked signal by adding the signal to the input of the amplifier through a capacitor adjustable to the stray capacitor. Thus, an electric circuit with a pulse transformer was used to measure the oscillation signal to reduce the leakage signal as well as to excite the anti-phase mode. Because of stray capacitance across the two sets of electrodes, the sinusoidal signal leaks at the output of the amplifier. In this study, we used one set for excitation by applying a sinusoidal signal and the other set for detection of the displacement signal of the tuning fork by connecting it to an operational amplifier. Meanwhile, commercial tuning forks are designed to excite the anti-phase mode by configuring the two sets of electrodes on the two prongs. However, a dither piezoelectric plate, frequently used for mechanical excitation, more easily excites the in-phase oscillation of the two prongs. To use the high Q factor of the tuning fork, the two prongs should be excited in the anti-phase mode. 9 To date, the high Q factor of a tuning fork has not been well exploited in nc-AFM. 8 In contrast, the two-prong force sensors with a tip imaged only step structures of Si(111) 6 and highly ordered pyrolytic graphite. 6 To overcome this problem, Giessibl developed the qPlus sensor by fixing one prong, so that it would not oscillate, and observed atom-resolved images of Si(111)–7 × 7 using the oscillation of the other prong. However, when an AFM tip is attached to one prong, the oscillations of two prongs become unbalanced through the detuning of the resonance frequencies of the prongs, resulting in a lower Q factor. This is because the anti-phase mode cancels the distortional oscillation amplitude at the join, leading to low energy dissipation at the join. ![]() 7 The Q factor of the tuning fork in its resonant state, the anti-phase oscillation mode of the two prongs, is greater than that in the in-phase oscillation mode and that for the one-prong sensor. One of the force sensors is a two-prong type, 6 and the other is a single-prong type, called the qPlus sensor. The tuning fork comprises two prongs joined at their ends the resonance frequencies ( f TF) of the two prongs are precisely tuned to the same frequency (typically, f TF = 32 768 Hz). Up to now, two types of force sensors, based on quartz tuning forks as the oscillator with high Q factor, have been frequently used in nc-AFM.
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