Jpn. J. Appl. Phys. Vol. 40 (2001) pp. 3646 3651 Part 1, No. 5B, May 2001 c 2001 The Japan Society of Applied Physics Estimation of Resolution and Contact Force of a Longitudinally Vibrating Touch Probe Sensor Using Lead Zirconate Titanate (PZT) Thin-Film Vibrator Takefumi KANDA, Takeshi MORITA 1, Minoru K. KUROSAWA 2 and Toshiro HIGUCHI The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan 1 The Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 2 Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan (Received November 23, 2000; accepted for publication January 17, 2001) In this paper, the evaluation of the sensitivity, resolution, and contact force of a touch probe sensor device for higher sensitivity and low contact force is reported. Our goal in designing our touch probe sensor was to realize high-resolution, low-contactforce, wide-scanning-area up to mm scale square, and quick-scanning surface profile measurement. The sensitivity and resolution of our touch probe sensor were 2.0 10 2 mv/nm and 2.4 nm, respectively. Although this resolution depends on the noise level, the noise level of the pre-amplifier circuit was much larger than that of the vibrator. By minimizing the noise of the circuit by using low-noise-type operational amplifiers, higher resolution up to 0.2 nm can be obtained. Although the contact force was estimated to be 25 µn under a 0.3 V p-p driving voltage, it will be 300 nn when using a low-noise circuit. KEYWORDS: touch probe sensor, surface profile measurement, PZT thin film, hydrothermal method, resolution, contact force, ultrasonic vibrator, piezoelectric transducer 1. Introduction Various types of longitudinally vibrating touch probe sensors for surface profile measuring tools or scanning probe microscopes (SPM) have been fabricated. 1 4) Although bending vibration is used for most SPMs including atomic force microscopes (AFM), the scanning speed is not very high and the measurement range is not large, 150 µm square at most. The longitudinally vibrating touch probe sensors can maintain a high mechanical Q value at high resolution and have high a resonance frequency. Thus these sensors can also be used in liquids, and can realize quick scanning. Our goal in designing our touch probe sensor was to realize high resolution, higher than 0.5 nm, low contact force, under 500 nn, a wide scanning area range, mm scale square, and quick scanning surface profile measurement. These features are the advantageous for measuring nano structures, for example, sub micron rule very large scale integration (VLSI) or micro electro mechanical systems (MEMS). In order to realize such measurement, the resolution of the sensor and evaluation of the contact force are important. We evaluate the piezoelectric constants and noise level to improve the sensitivity and resolution of the sensor. We also evaluate the contact force. 2. Principle and Structure of the Sensor The schematic view of the surface profile measurement setup using our probe sensor is shown in Fig. 1. The probe sensor consists of a longitudinally vibrating oscillator. When the tip end of the horn is in contact with a workpiece, the resonance frequency of the oscillator is shifted. In order to sense the contact, the frequency shift or the decrease of the vibration amplitude have to be detected. In order to obtain a much higher sensitivity, we fabricated a flat-type sensor as shown in Figs. 2 and 3. The sensor consists of a quarter wavelength longitudinal vibrating part and an exponential horn, which magnifies the amplitude at the contact Surface Profile Image Scanning Data Servo System Contact Signal Workpiece XYZ Stage Generator Driving Signal Probe Scanning Fig. 1. Schematic view of the surface profile measurement using the touch probe sensor. point. The length of the oscillator is 9.8 mm and the resonance frequency is about 300 khz. The vibration was excited and also detected using a lead zirconate titanate (PZT) thin film, which was deposited by a hydrothermal method. 5 7) By using a flat configuration, and due to the fact that the oscillator is miniaturized, the proportion of PZT to the Ti base increases. Therefore, the sensitivity of the sensor is improved. The Ti substrate thickness of this micro flat-type sensor and PZT film thickness on each side were 100 µm and 10 µm, respectively. The pick-up voltage was magnified by the pre-amplifier circuit. The pre-amplifier circuit is also shown in Fig. 3. When the driving voltage was 3 V p-p, the resonance frequency, vibrational amplitude and pickup voltage at the resonance frequency, and mechanical Q value were 304.4 khz, 126 nm o-p, E-mail address: kanda@intellect.pe.u-tokyo.ac.jp 3646
Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 5B T. KANDA et al. 3647 Cross Section Driving Source Au Electrode PZT Thin Film: 10 m Pickup Voltage (Reference Electrode) Pickup Ti Base: 100 m Free Vibration Tapping Damped condition Drive 9.8mm 1.0 mm Au Electrode Pickup (Ti Base) Supporting Part Contact Point V Amplifier circuit d - + - + - + V ~ Pickup Displacement Fig. 4. Relationship between δd and δv : δv is detection voltage variance against the gap variance δd. Fig. 2. Structure of the longitudinally vibrating touch probe sensor using PZT thin film. Fig. 3. Photograph of the touch probe sensor and pre-amplifier circuit. 3.4 mv rms and 705. 3. Evaluation of Sensitivity and Resolution To evaluate the sensitivity and the resolution of our sensor, we measured the relationship between pickup voltage and tip-workpiece distance. The pickup voltage was measured when the workpiece was brought close to the vibrator tip. Figure 4 shows the schematic view of the change of the pickup voltage when the workpiece was brought close to the vibrator tip. In Fig. 4, from the left side of the graph, each area corresponds to (A) free vibration, (B) tapping, cyclic contact, vibration, and (C) damped regions. From the change of the pickup voltage in region (B), the sensitivity P, which can be defined as the tangent of the region (B), is defined by δv/δd as shown in Fig. 4. The vertical resolution R s can be estimated from the sensitivity P and noise level V min as, R s = V min /P. (1) The gain of the amplifier circuit was 9.5. The sensitivity of our touch probe sensor and the noise level of the pre-amplifier circuit, were 2.0 10 2 mv/nm and 0.45 mv rms, and the resolution was 2.4 nm. 4) The aim is to obtain a resolution of 0.5 nm. Thus we have to realize a much higher resolution. From eq. (1), in order to significantly increase the resolution, the sensitivity P has to be much larger or the noise level V min has to be much smaller. 4. Piezoelectric Constant In order to evaluate the sensitivity, we use the equivalent circuit for the sensor. Figure 5 shows the equivalent circuit of the probe sensor when the sensor vibrates freely. 3, 4) Lumped element circuit components of L m,1/c m, R m, A 1 and A 2 are the equivalent mass, equivalent elasticity modules, equivalent viscosity coefficient, and force factors, respectively, in the driving piezo element and those in the pickup piezo element. C d1 and C d2 indicate the capacitance in the driving element and that in the pickup element due to the PZT film s ferroelectricity. The sensitivity of this sensor can be described as 4) P = C d2 A 1 ( 1 + A 2 1 ω r R m C d2 ) 2. (2) In eq. (2), ω r denotes the resonance angular frequency. By using the piezoelectric constant e 31, the force factor can be described as 4) A 1 = 2be 31. (3)
3648 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 5B T. KANDA et al. In eq. (3), b denotes the width of the oscillator. From eqs. (2) and (3), the relationship between the sensitivity P and piezoelectric constant e 31 can be obtained. Figure 6 shows the relationship between P and e 31 from the calculation. This result shows that the sensitivity P is proportional to the piezoelectric constant e 31 when the piezoelectric constant e 31 is smaller than 6 C/m 2. The piezoelectric constant e 31 can be estimated by measuring the vibration amplitude at the longitudinal vibrator. 7) The piezoelectric constant e 31 can be expressed as, 7) e 31 = t 1Y s + 2t 2 c11 E S 2. (4) 2t 2 E 3 In eq. (4), t 1, t 2, Y s, c11 E, E 3, and S 2 denote the thickness of the titanium substrate and PZT film, the Young s modulus of the titanium substrate, the elastic stiffness of the PZT film, the electric field, and the strain, respectively. From the calculation based on the experimental data, the piezoelectric coefficient of e 31 of the longitudinal transducer was estimated to be 0.2 C/m 2. 7) This values is one tenth of the constant of bulk materials, 3.1 C/m 2 calculated from the constants in ref. 8. These results indicate that the sensitivity P can be ten times larger, and thus the resolution R s can be smaller than the value that we obtained experimentally. When the piezoelectric con- V in Sensitivity P [mv/nm] C d1 Fig. 5. Fig. 6. e 31. 1 0.8 0.6 0.4 0.2 L m C m R m 1:A 1 A 2 :1 C d2 Equivalent circuit of the touch probe sensor vibrating freely. Vout 0 0 2 4 6 8 10 12 Piezoelectric constant e 31 [C/m 2 ] Relationship between the sensitivity P and piezoelectric constant stant e 31 is as large as that of bulk PZT, the value of the resolution is smaller than 0.3 nm, which is superior to the desired value, 0.5 nm. 5. Noise Level 5.1 Noise sources In order to improve the sensitivity, the decrease of the noise level is important as shown in eq. (1). From the measurement, the noise level of the sensor was 0.45 mv rms. The noise of the sensor has many sources. For example, thermal noise in the pre-amplifier circuit, the cable between the pre-amplifier circuit and the voltage meater, thermal excitation in the vibrator, Johnson noise in the PZT film, 1/f noise, vibration of the stage, influence of temperature and numerous other sourses can be considered. In this paper, noise in the vibrator and the pre-amplifier circuit is estimated. 5.2 Noise in the vibrator The noise in the vibrator is caused by electrical and mechanical sources. The mechanical noise is caused by thermal excitation in the vibrator. The electrical noise sources in the vibrator are Johnson noise, and 1/f noise in the PZT film. When the frequency is over 100 khz, Johnson noise is much larger than 1/f noise. The amplitude at the tip of the vibrator caused by the thermal excitation, A nm, can be described as, 9) 4Qk B TB A nm =. (5) 2π f o k e In eq. (5), Q, k B, T, B, f o, and k e denote the mechanical Q factor, Boltzmann constant, temperature, bandwidth, frequency, and equivalent elastic constant, respectively. The Johnson noise, e j, can be described as, 10) e j = 4k B TZB. (6) In eq. (6), Z denotes the input impedance to the piezoelectric film. From eq. (6), the amplitude at the tip of the vibrator caused by Johnson noise, A nj, can be described A nj = e j /P. (7) The total noise can be given by the square root of the sum of each noise value squared. To estimate the influence of noise, we compare the vibration amplitude at the tip of the vibrator caused by the noise. The vibration amplitude at the tip caused by the thermal excitation, and that caused by Johnson noise are calculated. To estimate the dependence on the dimensions of the vibrator, we estimated the amplitude of a bending vibrator sensor caused by each noise as shown in Fig. 7. Electrodes are positioned on each side, one is for driving, and the other is for pickup. The length, width, and thickness of the Ti substrate and those of the PZT film are l, b, t 1, and t 2, respectively. PZT thin film layers are present on both surfaces of the Ti substrate. The ratio between l, b, and t 1 is 40 : 10 : 1. The thickness of the PZT film, t 2, was constant at 10 µm, since the thickness of the film was kept constant at about 10 µm when the PZT thin film was deposited using the hydrothermal method. Figure 8 shows the results of the calculation. The length l is changed from 0.4 mm to 4 cm. The influence of the thermal
Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 5B T. KANDA et al. 3649 excitation is much larger than that of Johnson noise. The sensor that we fabricated is 4 mm long. From Fig. 8, when the length is 4 mm, the influence of Johnson noise is much larger than that of the thermal excitation on the order of 10 2. When all noise sources except for those in the vibrator are ideal, the resolution is determined based on the noise level of the vibrator, particularly Johnson noise. In the sensor that x z y l b PZT Film (Thickness: t 2 ) Ti Substrate (Thickness: t 1 ) Fig. 7. 10-9 Vibrator for evaluating the noise level. we fabricated, the ideal resolution was 5.8 10 11 m, namely 58 pm. We compare the influence of the noise of the sensor between the longitudinal vibrator and the bending vibrator. For the comparison, we used the vibrator shown in Fig. 7. The vibrational amplitude at the tip of the vibrator caused by the thermal excitation, and that caused by Johnson noise were also calculated in the bending vibrator. Figure 9 shows the results of the calculation. As shown in the case of the longitudinal vibrator, the influence of Johnson noise is much more than that of the thermal excitation. It is on the order of 10 when the length is 4 mm for the vibrator that we fabricated. The values of the noise of the bending vibrator are larger than those of the longitudinal vibrator. Figure 10 shows the comparison of the amplitude at the tip of the vibrator caused by each noise between both vibrators. As shown in Fig. 10, the influence of the noise in the longitudinal vibrator is smaller than that in the bending vibrator on the order of 10 3. These results indicate that the sensor using the longitudinal vibrator can have higher resolution than that using the bending vibrator when those sensors have the same sensitivity. In addition, the sensitivity of the longitudinally vibrating sensor is higher than that of the bending vibrating Vibration noise [m] 10-10 10-11 10-12 4 mm 0.0001 0.001 0.01 0.1 10-13 Johnson noise Thermal excitation Length [m] Fig. 8. Comparison between the thermal excitation and Johnson noise of the longitudinal vibrator. 10-6 Vibration noise [m] 10-6 10-7 10-8 10-9 10-10 10-11 10-12 Bending Longitudinal 4 mm 0.0001 0.001 0.01 0.1 Length [m] Fig. 10. Comparison of the vibration noise level between the longitudinally vibrator and bending vibrator. Vibration noise [m] 10-7 10-8 10-9 Thermal excitation Johnson noise Displacement Trace of the tip Surface Am2 Am1 4 mm 0.0001 0.001 0.01 0.1 10-10 Length [m] Fig. 9. Comparison between the thermal excitation and Johnson noise of the bending vibrator. Fig. 11. Time Workpiece Schematic view of the surface under the tapping mode.
3650 Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 5B T. KANDA et al. Electrical (Driving) Mechanical Surface Electrical (Detecting) F 1:A 1 A 2 :1 L m C m R m V in C d1 C d2 Vout Fig. 12. Equivalent circuit of the touch probe sensor under the tapping mode: F indicates the contact force. sensor. 4) Therefore, the sensor using a longitudinally vibrator has higher resolution than the sensor using a bending vibrator. 5.3 Noise in the pre-amplifier circuit The noise caused by the pre-amplifier circuit is also an important source of noise. The pre-amplifier circuit consists of a simple differential amplifier circuit as shown in Fig. 2. The noise source in the amplifier circuit is mainly thermal noise in the amplifier and impedance elements. In our experiments, the amplifier circuit consisted of an operational amplifier element, LF356. By the calculation for this circuit, the noise level is 0.45 mv. This noise level corresponds to the resolution of 2.1 nm. From the calculation in the section 5.2, the vibration amplitude at the tip of the sensor caused by noise in the vibrator is 58 pm. Although this resolution depends on the noise level, the noise level of the preamplifier circuit is much larger than that of the vibrator. From the measurement, the resolution was 2.4 nm. This experimental value means the noise in the measurement is mainly caused by the pre-amplifier circuit. By minimizing the noise at the circuit by using low-noise type operational amplifiers, for example, AD711, a higher resolution up to 0.2 nm can be obtained. 6. Contact Force To realize non destructive surface profile measurement, the contact force has to be extremely small. By using the tapping mode, namely the cyclic contact mode, the extent of damage to the surface can be decreased. Figure 11 shows the schematic view of the surface when the tip of the sensor has a contact in the tapping mode. The contact force depends on the ratio of the contact quantity A m2 against the amplitude A m1. In order to estimate the contact force in the tapping mode, we use the equivalent circuit. To estimate the contact force in the tapping mode using the equivalent circuit, it is required to describe the non linearity in the tapping mode in the circuit. Figure 12 shows the equivalent circuit of the sensor when the sensor is in the tapping mode. When the sensor vibrates is in tapping mode, the tip of the sensor repeats contact and noncontact conditions. When the sensor is in contact with the surface, the force acts on the surface. This condition can be described by the resistance and capacitance equivalent to the viscosity and elasticity, respectively, between the workpiece surface and the tip of the sensor. On the contrary, the noncontact condition means that the force does not act on the surface. This condition can be described as a short in the circuit. In the equivalent circuit, the change of these two conditions can be described by using the ideal diode. To evaluate the magnitude of the contact force, we can use the analog circuit simulation software. To estimate the largest magnitude of the contact force, we calculated the value under the condition A m1 = A m2. When the driving voltage was 0.3 V p-p and the vibration amplitude was 13 nm o-p, the contact force was estimated to be 25 µn. The ratio of A m2 to A m1 depends on the noise level. When the noise level is low, the contact ratio can be decreased. Therefore, when the low-noise circuit is used, the maximum contact force will be 300 nn. The desired contact force value is 500 nn. Thus the desired contact force value, 500 nn, can be realized by using a low-noise circuit. 7. Conclusions We have evaluated the sensitivity, resolution, and measurement force of a touch probe sensor device for high sensitivity and low contact force. The sensitivity and resolution of our touch probe sensor were 2.0 10 2 mv/nm and 2.4 nm, respectively. Although this resolution depends on the noise level, the noise level of the pre-amplifier circuit is much larger than that of the vibrator. By minimizing the noise in the electrical circuit by using low-noise-type operational amplifiers, a higher resolution up to 0.2 nm can be obtained. Although the contact force was estimated to be 25 µn under a 0.3 V p-p driving voltage, it will be improved to 300 nn by using a low noise electrical circuit. This result implies that a high-resolution and low-contact-force touch probe sensor for surface profile measurement can be realized by using a longitudinally vibrating probe. Acknowledgement This work was supported by a Grant-in-aid for general scientific research from the Ministry of Education, Science, Sports and Culture, by the Proposal-Based New Industry Creative Type Technology R&D Promotion Program from the New Energy and Industrial Technology Development Organization (NEDO) of Japan, and by the Grant-in-aid for Research Fellowship for Young Scientists of the Japan Society for the Promotion of Science. The authors would like to thank Mr. Yasui of the University
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