JP5672200B2 - Dielectric property measurement method using atomic force microscope - Google Patents

Description

  The present invention relates to a dielectric property measurement method for measuring a dielectric property such as a dielectric constant of a substance using an atomic force microscope, and in particular, a measurement suitable for measuring a dielectric relaxation property locally on a sample, that is, in a minute region. Regarding the method.

  One of the conventional methods for analyzing the dynamic characteristics of materials is the measurement of dielectric relaxation characteristics by dielectric relaxation spectroscopy. In the generally known dielectric relaxation spectroscopy method, a pair of counter electrodes are inserted into a small liquid cell, the frequency characteristics of the electrical impedance between the electrodes are measured using an impedance analyzer, and the impedance frequency is measured. Dielectric relaxation characteristics are calculated from the characteristics. With such a method, it is possible to determine the overall dielectric relaxation characteristics of the bulk liquid, but it is not possible to measure the dielectric relaxation characteristics of, for example, molecules present on the electrode surface or the electric double layer.

  By the way, in recent years, elucidation of biological function expression mechanisms of biomolecules such as proteins and DNA has been actively promoted in various places for the purpose of investigating the causes of various diseases and diseases and developing pharmaceuticals. For that purpose, it is first necessary to grasp the structure of the biomolecule, and various measurement methods for grasping the structure have been developed. In the field of Atomic Force Microscope (AFM) as well, due to the recent rapid progress in technology, molecules of biomolecules such as proteins and DNA not only in ultra-high vacuum atmosphere but also in liquid and physiological environments It is now possible to perform structural analysis on a scale.

  In order to analyze the biological function expression mechanism of a biomolecule, it is indispensable to measure not only the structure of the biomolecule but also various physical properties of the biomolecule. For example, it is important to know the local dielectric relaxation characteristics of biomolecules in examining the activity of biomolecules, but conventional atomic force microscopes cannot meet such requirements. Therefore, the dielectric relaxation spectroscopy method as described above is used, that is, the dielectric relaxation characteristics must be obtained by measuring the impedance of the entire solution after dissolving the sample to be measured in the liquid. .

  In contrast, the inventors of the present application have recently been conducting research to measure local dielectric relaxation characteristics on a sample using an atomic force microscope capable of structural measurement and physical property evaluation on a nanometer scale. . This is a technique for evaluating local dielectric characteristics of the sample surface based on electrostatic force acting on a cantilever generally used in an atomic force microscope. Specifically, in Non-Patent Documents 1 and 2, for example, a probe of a vibration component induced in a cantilever when an AC voltage is applied between the conductive cantilever in the liquid and the conductive substrate opposed thereto— As a result of examining the inter-sample distance dependency, when the frequency of the AC voltage is high, the action of the interfacial tension between the cantilever surface and the liquid is weakened, and the vibration due to the electrostatic force becomes dominant, and the electrostatic force is detected. It is clarified that the distance between the needle and the sample is dependent.

  The above phenomenon will be described with reference to FIG. FIG. 8 is an electrical equivalent circuit at the interface between the conductive surface of the cantilever and the analysis liquid, that is, the solid-liquid interface, when the cantilever is immersed in the analysis liquid. As shown in FIG. 8, the equivalent circuit at the solid-liquid interface is a series connection circuit of the interface solution element and the bulk solution element. The interface solution element is a parallel circuit of a series connection circuit of resistance due to charge transfer and Warburg impedance due to diffusion and an electric double layer capacitance. On the other hand, a bulk solution element is a parallel circuit of bulk solution resistance and bulk solution capacity. When the frequency of the alternating voltage applied between the cantilever and the sample is lower than the dielectric relaxation frequency of the electric double layer capacitance, a voltage is applied to the interface solution element, and interfacial tension is generated. On the other hand, when the frequency of the AC voltage is higher than the dielectric relaxation frequency of the electric double layer capacitance, the voltage component applied to the interface solution element can be almost ignored, and only the voltage component applied to the bulk solution element. Should be considered. Therefore, in such a frequency region, electrostatic force due to the voltage component applied to the bulk solution capacity, in other words, Maxwell stress dominates the cantilever displacement.

  However, according to the study of the present inventor, in the excitation method in which, for example, a sinusoidal AC voltage is applied between the cantilever and the sample and the cantilever is directly vibrated at the frequency of the AC voltage, the resonance of the cantilever The detection signal is significantly attenuated in a frequency region higher than the frequency. Therefore, it is difficult to extract information on frequency shift and displacement from such a signal. The resonance frequency of the cantilever depends on the size and material of the cantilever, but is generally about 100 to 200 kHz. Therefore, in the above excitation method, the dependency of the vibration component on the probe-sample distance cannot be examined in a frequency region higher than such a frequency, and the dielectric relaxation characteristics cannot be measured based on such information.

Umeda and 5 others, “FM-AFM observation in liquid using electrostatic force excitation”, Proceedings of the 57th Joint Conference on Applied Physics, March 2010, Japan Society of Applied Physics Umeda and 5 others, “Study on the dependence of electrostatic force on the measurement of local electric charge distribution at the solid-liquid interface-distance between samples”, Proceedings of the 71st JSAP Conference, September 2010 , Japan Society of Applied Physics Hiroshi Yokoyama and one other member, “Imaging High Frequency Dielectric Dispersion of Surfaces and Thin Films by Heterodyne Force-Detected Scanning Maxwell-Stress Micro Scopy (Imaging high frequency dielectric dispersion of surfaces and thin films by heterodyne force-detected scanning Maxwell-stress microscopy), Colloids and Surfaces A: Colloids and Surfaces A: Physicochemical and Engineering Aspects), Vol.93, 1994, p.359-373 W. Wittpahl and three others, “Quantitative high frequency-electric force microscope testing of monolithic microwave integrated circuits at 20 GHz (Quantitative high frequency-electric force microscope testing of monolithic microwave integrated circuits at 20 GHz), Microelectronics Reliability, Vol.39, 1999, p.951-956 F. Giessibl, "Advances in atomic force microscopy", Review of Modern Physics, Vol. 75, 2003, p. 949-983

  The present invention has been made to solve the above-described problems, and enables detection of vibration of a cantilever in a high frequency region exceeding the resonance frequency of the cantilever, and thereby AC electrostatic force acting between the probe and the sample. To provide a dielectric property measurement method capable of measuring dielectric characteristics such as local dielectric relaxation characteristics on a sample over a wide frequency range by measuring the probe-sample distance dependency of is there.

  As described above, there are mainly electrostatic force and interfacial tension effect in the force acting on the cantilever when alternatingly exciting the cantilever in the liquid, but in the region where the vibration frequency is high, the force acting on the cantilever is static electricity. Power becomes dominant. Since the electrostatic force is proportional to the square of the applied voltage, in an electrostatic force microscope (EFM) that detects electrostatic force, two AC voltages having different frequencies are applied between the probe and the sample. A method of exciting the probe with a frequency difference of AC voltage (Non-patent Document 3) or a method of applying an amplitude-modulated high-frequency voltage between the probe and the sample and exciting the probe at the frequency of the modulation signal (non-patent document 3) Patent document 4) is known.

  Although all of these conventional methods are excitations in the atmosphere and there is almost no influence of the interfacial tension effect as in liquids, the inventor of the present application has applied the electrostatic force to the applied voltage in such a case. Focusing on the fact that it is proportional to the square, the inventors have come up with the idea of using a high-frequency AC voltage that has been amplitude-modulated or an AC voltage of two different frequencies for exciting a cantilever in a liquid. Also, by applying experiments and simulation calculations, when applying a high-frequency AC voltage with amplitude modulation between the probe and the sample, the electrostatic force acting on the cantilever and the probe can be reduced if the carrier voltage frequency is increased to a certain extent. It was found that the relationship with the distance between samples has a strong carrier frequency dependency. The electrostatic force acting on the cantilever is affected by the dielectric properties of the electric double layer capacitance and the bulk solution capacitance formed on the sample surface and the cantilever surface. Therefore, by changing the carrier frequency of the amplitude-modulated AC voltage applied to the cantilever, it is possible to obtain information regarding the dielectric dispersion relationship.

The present invention has been made on the basis of the above-mentioned ideas and experiments obtained through experiments and the like, and the first aspect is that a probe provided at the tip of a cantilever is immersed in a liquid. Using a dynamic mode atomic force microscope that detects the interaction between the probe and the sample when the cantilever is vibrated at the resonance frequency close to the surface of the conductive sample. A measurement method for measuring the dielectric properties of
The cantilever between the conductor portion formed on at least one of the surface where the probe is located or the back surface thereof in the cantilever and the sample facing the conductor portion with a liquid interposed therebetween By applying an alternating voltage generated by amplitude-modulating a carrier wave having a frequency higher than the resonance frequency of the carrier wave with a modulation wave having a frequency lower than that, the cantilever is vibrated at a modulation frequency by electrostatic force,
Based on the vibration component, the carrier frequency dependency of the relationship between the electrostatic force acting between the probe and the sample and the distance between the probe and the sample is obtained, and information on the dielectric characteristics of the sample is obtained from the relationship between the frequency and the electrostatic force. It is characterized by obtaining.

Further, in the second aspect of the present invention, similarly to the first aspect, the probe provided at the tip of the cantilever is brought close to the surface of the conductive sample immersed in the liquid, and the cantilever has its resonance frequency. Using a dynamic mode atomic force microscope that detects the interaction between the probe and the sample when vibrated at a measuring method for measuring the dielectric properties of the sample,
The cantilever between the conductor portion formed on at least one of the surface where the probe is located or the back surface thereof in the cantilever and the sample facing the conductor portion with a liquid interposed therebetween By applying an excitation voltage generated by adding an alternating voltage having a first frequency higher than the resonance frequency of the first frequency and an alternating voltage having a second frequency higher or lower by a predetermined frequency than the first resonant frequency, Vibrate at a frequency that is the difference between the first frequency and the second frequency,
Based on the vibration component, the first frequency or the second frequency is maintained while the difference between the first frequency and the second frequency is kept constant with respect to the relationship between the electrostatic force acting between the probe and the sample and the distance between the probe and the sample. It is characterized by obtaining information on the dielectric characteristics of the sample from the relationship between the frequency and the electrostatic force.

  In the dielectric property measurement method according to the present invention, an excitation voltage is applied between the conductive substrate on which the conductive sample is placed and the conductive portion, so that the conductive portion is placed between the sample and the conductive portion. An excitation voltage can be applied.

  Further, in the dielectric characteristic measuring method according to the present invention, it vibrates in response to application of an excitation voltage that is an amplitude-modulated carrier voltage, or vibrates in response to application of an excitation voltage in which two alternating voltages having different frequencies are added. The displacement of the cantilever to be detected can be detected, and the probe-sample distance dependency of the electrostatic force can be obtained from the amplitude and / or phase of the displacement. In this case, the method for detecting the displacement of the cantilever is not particularly limited. For example, the back surface of the cantilever is irradiated with laser light, and the reflected light is detected by a photodetector in which the light receiving surface is divided into a plurality of positions to determine the position of the reaching light. What is necessary is just to use the optical lever system to be determined.

  In the dielectric characteristic measurement method according to the first aspect of the present invention, an excitation voltage generated by amplitude-modulating a carrier wave having a frequency higher than the resonance frequency of the cantilever with a modulation wave having a frequency lower than that is used as a cantilever (probe). Apply between sample. When the frequency of the applied voltage, that is, the frequency of the carrier wave is changed, if the frequency becomes higher than the dielectric relaxation frequency of the electric double layer at the interface, the partial pressure ratio of the bulk solution element becomes larger than the partial pressure ratio of the interface solution element. The force due to the interfacial tension effect decreases. On the other hand, since the electrostatic force acting on the cantilever is proportional to the square of the voltage, the electrostatic force of the frequency component of the modulated wave is generated, and the vibration of the cantilever is induced. Thereby, the electrostatic force becomes dominant as compared with the force due to the interfacial tension effect. The frequency of the carrier wave can be set independently of the frequency of the modulation wave (that is, the resonance frequency of the cantilever), and the electrostatic force acting on the cantilever is proportional to the square of the applied voltage. Even when the frequency is considerably higher than that, vibration amplitude sufficient for vibration detection can be obtained.

  On the other hand, in the dielectric characteristic measuring method according to the second aspect of the present invention, an AC voltage having a first frequency higher than the resonant frequency of the cantilever and an AC voltage having a second frequency higher or lower by a predetermined frequency than the first frequency are added. The excitation voltage generated in this way is applied between the cantilever (probe) and the sample. In this case, an electrostatic force having a frequency component corresponding to the difference between the first frequency and the second frequency is generated, and cantilever vibration is induced. For example, when the first frequency and the second frequency are changed while keeping the frequency difference constant, if these frequencies become higher than the dielectric relaxation frequency of the electric double layer at the interface, the bulk solution element is compared with the partial pressure ratio of the interface solution element. The force due to the interfacial tension effect decreases, and the force acting on the cantilever is dominated by electrostatic force. The first and second frequencies can be set regardless of the resonance frequency of the cantilever, and the electrostatic force acting on the cantilever is proportional to the square of the applied voltage. Therefore, the second mode is the same as the first mode. Even when the first and second frequencies are considerably higher than the resonance frequency of the cantilever, a vibration amplitude sufficient for vibration detection can be obtained.

  As will be described in detail later, according to the experiments by the present inventors, when the distance between the probe and the sample is changed with the cantilever excited as described above, the electrostatic force acting on the cantilever changes. Further, the relationship between the electrostatic force and the probe-sample distance depends on the carrier frequency (or the first frequency or the second frequency). That is, the relationship between the electrostatic force and the probe-sample distance indicates frequency dispersion. Therefore, dielectric characteristics such as dielectric relaxation characteristics can be obtained based on this frequency dependence.

  According to the above dielectric property measurement method according to the present invention, the influence of the interfacial tension is suppressed in the high frequency region, and the electrostatic force acting between the sample and the probe is detected even in the liquid. Thus, the dielectric properties of the sample can be obtained. However, according to the study by the present inventor, when the probe is brought close to the vicinity of the sample surface, the bulk solution capacity increases, so that the capacitance in the Helmholtz layer in the electric double layer is relatively small. Therefore, the latter becomes dominant on the impedance. Since the electrostatic force induced in the probe by the AC voltage application depends on the bulk solution capacity, the impedance of the Helmholtz layer increases relatively, so that most of the applied AC voltage component is applied to the Helmholtz layer. In other words, it was found that the electrostatic force is no longer induced at the tip of the probe, and the locality of the detected electrostatic force is reduced. Therefore, if you want to measure the local electrostatic force on the sample with higher sensitivity, the frequency modulation that detects the amount of self-excited oscillation frequency shift by the action of the electrostatic force acting on the cantilever. (FM) A detection method may be combined.

  That is, in the dielectric property measurement method using the atomic force microscope according to the present invention, an excitation voltage is applied between the conductor portion of the cantilever and the sample, and the cantilever is further self-oscillated at its resonance frequency. The frequency shift of the resonance frequency due to the electrostatic force acting on the cantilever is detected, and the probe-sample distance dependency of the electrostatic force acting between the probe and the sample is obtained from the vibration component with respect to the excitation voltage in the frequency shift. You may do it. In order to cause the cantilever to self-oscillate at its resonance frequency, an existing method such as a photothermal excitation method may be used. As a method for detecting the frequency shift, an existing method such as a frequency detection method using a phase locked loop circuit (PLL) may be used.

  In the dielectric property measurement method combined with the above-described FM detection method, even when the modulation frequency (or the difference frequency between the two frequencies) in the excitation voltage does not match the resonance frequency of the cantilever, the detection signal is captured as modulation of the resonance frequency. Therefore, a high sensitivity gain can be obtained. In the direct detection method described above, vibration is induced by the electrostatic force acting on the cantilever, and the magnitude of the vibration amplitude is determined by the electrostatic force at the vibration center position of the cantilever, whereas when the FM detection method is used. The cantilever is mechanically vibrated, and a resonance frequency shift is induced by the electrostatic force acting on the cantilever, and the magnitude of the resonance frequency shift is that when the cantilever is closest to the sample surface in the cantilever vibration period. It is almost determined by the electrostatic force at the position (see Non-Patent Document 5). As the cantilever approaches the sample surface, the electrostatic force acting on the tip of the probe becomes significantly larger than the electrostatic force acting on the cantilever and the entire probe. Therefore, in the FM detection method, the tip of the probe is compared with the direct detection method described above. Thus, the electrostatic force acting on the sample can be selectively detected, and the dielectric properties of the sample can be measured more locally.

  According to the dielectric property measurement method using an atomic force microscope according to the present invention, it is difficult to measure dielectric properties such as local dielectric relaxation properties of a sample immersed in a liquid. It becomes possible. In particular, since this dielectric property measurement method uses an atomic force microscope capable of nanometer-scale structure measurement, high-resolution structural observation of the sample surface and two-dimensional dielectric property measurement are performed in parallel. be able to.

The schematic block diagram of the cantilever excitation part of the atomic force microscope which is one Example for implementing the dielectric property measuring method which concerns on this invention. The schematic block diagram of the principal part of the atomic force microscope of a present Example. FIG. 2 is a diagram showing a result of actual measurement of a relationship between a normalized AC electrostatic force acting between a probe and a sample and a probe-sample distance when the carrier frequency is changed in the configuration of FIG. (B) is an actual measurement example of a sample placed in 1-heptanol in pure water. The figure which shows the frequency dependence of the normalization alternating current electrostatic force based on the result of FIG.3 (b). The block diagram of the principal part of the atomic force microscope which is another Example for enforcing the dielectric property measuring method which concerns on this invention. FIG. 6 is a diagram showing an actual measurement example of the relationship between the probe-sample distance and the amplitude of the frequency shift vibration measured using the atomic force microscope shown in FIG. 5. The schematic block diagram of the cantilever excitation part of the atomic force microscope which is another Example for enforcing the dielectric property measuring method which concerns on this invention. The equivalent circuit schematic of the interface vicinity of the electroconductive surface of the cantilever in the state immersed in the liquid, and the liquid.

  Hereinafter, an embodiment of a dielectric property measuring method according to the present invention will be described with reference to the accompanying drawings. FIG. 2 is a schematic configuration diagram of a main part of an embodiment of an atomic force microscope used in this dielectric property measuring method, and FIG. 1 is a schematic configuration diagram of a cantilever excitation unit in the atomic force microscope.

  As shown in FIG. 2, the sample 3 to be observed is held on a sample holder 2 mounted on a scanner 1 having a substantially cylindrical shape. The sample holder 2 is made of a conductor such as metal, and the sample 3 itself has conductivity. The scanner 1 includes an XY scanner that scans the sample 3 in two X- and Y-axis directions orthogonal to each other, and a Z-scanner that finely moves the sample 3 in the Z-axis direction orthogonal to the X-axis and Y-axis. The drive source is a piezoelectric element that is displaced by a voltage applied from the vertical position control unit 32. A cantilever 5 having a probe 6 at the tip is disposed above the sample 3, and the cantilever 5 is fixed to the pedestal 4 via a cantilever holder 7. In order to perform in-liquid measurement, a part of the pedestal 4 is a glass transparent body 4a having a flat bottom surface. The gap between the sample holder 2 and the pedestal 4 is filled with the analysis liquid 8, and the sample 3 is immersed in the analysis liquid 8. The upper surface of the analysis liquid 8 is completely in close contact with the lower surface of the pedestal 4 (transparent body 4a), and the fluctuation of the liquid surface of the analysis liquid 8 occurs even when the probe 6 scans the surface of the sample 3. Absent.

  In order to detect the displacement of the cantilever 5 in the Z-axis direction, an optical displacement detector 10 including a laser light source 11, mirrors 12 and 13, and a photodetector 14 is provided above the pedestal 4. In the optical displacement detection unit 10, the laser light emitted from the laser light source 11 is reflected substantially vertically by the mirror 12, and is irradiated to the vicinity of the rear end of the cantilever 5 through the transparent body 4 a of the pedestal unit 4. The cantilever 5 is made of silicon, silicon nitride, or the like, and a metal thin film 5a such as gold (Au) or aluminum (Al) is formed on the front surface (the surface facing the sample 3) and the back surface by vapor deposition or the like. As a result, the back surface of the cantilever 5 is a mirror surface, and the laser light irradiated from above is reflected with high efficiency and passes through the transparent body 4a again to the upper side of the pedestal portion 4. Then, the reflected light from the cantilever 5 is introduced into the photodetector 14 via the mirror 13. The photodetector 14 has a light receiving surface divided into a plurality (usually two) in the displacement direction (Z axis direction) of the cantilever 5, or has a light receiving surface divided into four in the Z axis direction and the Y axis direction. . When the cantilever 5 is displaced up and down, the ratio of the amount of light incident on the plurality of light receiving surfaces changes. Therefore, the amount of displacement of the cantilever 5 in the Z-axis direction is calculated by calculating the detection signal corresponding to the plurality of received light amounts. can do. The detection signal from the photodetector 14 is amplified and input to the amplitude / phase detection unit 30, and information regarding the amplitude / phase of displacement of the cantilever 5 obtained there is provided to the data processing unit 31.

The conductive sample holder 2 is connected to the excitation voltage generation unit 21 via a DC component blocking capacitor 25, and one end of the conductive sample holder 2 is electrically connected to the metal thin film 5a on the front surface and back surface of the cantilever 5. The other end of 20 is connected to the ground potential (GND) of the microscope. The excitation voltage generator 21 includes a carrier wave generator 22, a modulated wave generator 23, and an amplitude modulator 24. The carrier wave generator 22 generates a sine wave voltage having a frequency f ₀ within a predetermined frequency range higher than the resonance frequency of the cantilever 5. Meanwhile, the modulation wave generator 23 is for generating a sine wave voltage of frequency f _m is desired to excite the cantilever 5 at a lower frequency than the carrier wave. The amplitude modulation unit 24 modulates the amplitude of the carrier wave according to the modulation wave waveform. Accordingly, the output of the amplitude modulation section 24, i.e. the excitation voltage applied to the sample holder 2 thereof envelope frequency at f ₀ are matched to the modulated waveform. Thereby, an excitation voltage is applied between the metal thin film 5a on the front surface of the cantilever 5 and the conductive sample 3 facing each other with the analysis liquid 8 interposed therebetween. The capacitor 25 is for cutting off a large DC voltage generated when the excitation voltage generated by the excitation voltage generator 21 is switched.

  Further, the excitation voltage generation unit 21, the vertical position control unit 32, and the horizontal position control unit 33 are controlled by the main control unit 34, in order to set conditions, parameters, and the like necessary for measurement in the main control unit 34. An operation unit 35 and a display unit 36 for displaying measurement results are also connected.

探針−試料間に、直流電圧Ｖ_DCと振幅変調信号（搬送波の角周波数ω₀、変調波の角周波数ω_m）とを印加する場合、印加電圧Ｖ_modは次の(2)式で表される。

したがって、探針−試料間に電圧Ｖ_modを印加したときの探針−試料間の静電気力Ｆ^AM _esfは次の(3)式となる。

(3)式に示すように、静電気力Ｆ^AM _esfは、直流成分を始めとする様々な周波数の成分を含むが、その１つとして変調波の角周波数ω_mの成分が存在することが分かる。即ち、静電気力Ｆ^AM _esfによってカンチレバー５は変調波の角周波数ω_mの成分を以て振動するから、例えばロックインアンプなどによりこの特定の周波数成分を検出することにより、角周波数ω_m成分のみの静電気力を抽出することが可能である。 Here, the electrostatic force acting on the cantilever 5 when the excitation voltage is applied between the metal thin film 5a on the front surface of the cantilever 5 and the sample 3 (hereinafter referred to as "probe-to-sample") will be described.
Now, when a certain voltage V is applied between the probe and the sample, the electrostatic force F _esf between the probe and the sample is _expressed by the following equation (1). Here, C _ts is the capacitance between the probe and the sample, and z is the distance between the probe and the sample.

When a DC voltage _VDC and an amplitude-modulated signal (carrier angular frequency ω ₀ , modulated wave angular frequency ω _m ) are applied between the probe and the sample, the applied voltage V _mod is expressed by the following equation (2). Is done.

Therefore, the electrostatic force F ^AM _esf between the probe and the sample when the voltage V _mod is applied between the probe and the sample is _expressed by the following equation (3).

As shown in equation (3), the electrostatic force F ^AM _esf includes components of various frequencies including a direct current component, and one of them is a component of the angular frequency ω _m of the modulated wave. . That is, the cantilever 5 vibrates with the component of the angular frequency ω _m of the modulated wave due to the electrostatic force F ^AM _esf . For example, by detecting this specific frequency component with a lock-in amplifier or the like, the static electricity of only the angular frequency ω _m component is detected. It is possible to extract the force.

As described above, when an excitation voltage is applied between the metal thin film 5a and the sample 3 in the analysis liquid 8, the electrostatic force acting on the cantilever 5 includes the ω _m component, but is actually applied to the metal thin film 5a. The angular frequency of the applied voltage is in the vicinity of ω ₀ . Since this angular frequency ω ₀ is higher than the dielectric relaxation frequency of the electric double layer capacitance in the equivalent circuit shown in FIG. 8, the voltage component applied to the interface solution element can be ignored, and is related to the modulation angular frequency ω _m . The electrostatic force due to the voltage component applied to the bulk solution element is dominant. In the dielectric property measuring method according to the present invention, the cantilever 5 is excited in the frequency range of the carrier wave in which the electrostatic force due to the voltage component applied to the bulk solution element becomes dominant.

By using the atomic force microscope having the configuration shown in FIG. 2, using the platinum plate as the sample 3, fixing the modulation wave frequency f _m to 2 kHz and changing the carrier frequency f ₀ in a range equal to or higher than the resonance frequency of the cantilever 5. The dependence of the electrostatic force acting between the probe and the sample on the distance between the probe and the sample was evaluated by actual measurement. Specifically, the measurement position (XY position) on the sample 3 is fixed by the horizontal position control unit 33, and the scanner 1 is driven by the vertical position control unit 32 so that the probe-sample distance is gradually increased. Change in steps. Then, optical displacement detection of the amplitude and phase of the displacement of the cantilever 5 at each probe-sample distance is performed while scanning the probe-sample distance within a predetermined range with the carrier frequency fixed to a certain one. Detected by the unit 10 and the amplitude / phase detector 30. Then, the data processor 31 calculates the electrostatic force based on the detection signal. By repeating this every time the carrier frequency is changed, the relationship between the electrostatic force using the carrier frequency as a parameter and the probe-sample distance as shown in FIG. 3 is obtained. Of course, the displacement of the cantilever 5 may be detected while gradually changing the carrier frequency with the probe-sample distance fixed. FIG. 3 (a) shows the actual measurement results in pure water (20 ° C.), and FIG. 3 (b) shows the actual measurement results in 1-heptanol (3 ° C.).

Looking at the result of FIG. 3A, in the frequency range of 0.1 MHz to 1.0 MHz, there is a clear difference in the probe-sample distance dependency depending on the carrier frequency f ₀ , whereas frequency dispersion is seen. It can be seen that there is almost no difference in the probe-sample distance dependency in the frequency range beyond that. A frequency dispersion in the frequency range of 0.1 MHz to 1.0 MHz indicates that the dominant factor for vibration has shifted from the bulk solution resistance in the bulk solution element to the bulk solution volume. On the other hand, the fact that no frequency dispersion is observed in a frequency range exceeding 1.0 MHz means that a phenomenon such as dielectric relaxation does not occur in the bulk solution element and the electric double layer capacitance in this frequency range. A thick dotted line in the figure is a theoretical curve obtained by calculating the electrostatic force acting on the probe and the cantilever in consideration of the partial pressure effect of the electric double layer. The relationship obtained by actual measurement shows a very good agreement with the theoretical curve, and it is clear that this actual measurement is in conformity with the theory.

  On the other hand, in the result of FIG. 3B, there is almost no difference in the probe-sample distance dependency in the frequency range of 0.1 MHz to 10 MHz, whereas in the frequency range of 30 MHz or more, the distance between the probe and the sample. It can be seen that there is a clear difference in distance dependence and frequency dispersion is observed. Since the dielectric relaxation frequency of 1-heptanol at 0 ° C. is about 42.5 MHz, the frequency dispersion in the frequency range of 30 MHz or higher is caused by the dielectric relaxation phenomenon of 1-heptanol, and the bulk solution is higher in the frequency region than the dielectric relaxation frequency. Even when the capacitance is reduced and the probe is close, it can be assumed that the AC voltage component applied to the Helmholtz capacitance is reduced and a large electrostatic force acts on the tip of the probe.

  FIG. 4 is a plot of the normalized AC electrostatic force in the vicinity of the sample in the experimental results of FIG. As can be seen from FIG. 4, the change in electrostatic force is reliably captured in the frequency range of 10 MHz or higher. This electrostatic force is an electrostatic force that acts between the tip of the probe 6 and a specific position on the sample 3 facing it, and reflects the local dielectric characteristics of the specific position on the sample 3. Therefore, the dielectric relaxation phenomenon in the frequency region of several tens of MHz or more can be obtained by measuring the relationship between the electrostatic force when the carrier frequency is changed and the distance between the probe and the sample with an atomic force microscope as described above. It can be confirmed that it can be clearly understood.

  In the above embodiment, an excitation voltage generated by amplitude-modulating a carrier wave with a modulated wave is applied from the excitation voltage generation unit 21 between the metal thin film 5a and the sample 3 (actually the sample holder 2). The cantilever 5 was vibrated with the frequency of the modulated wave, but an excitation voltage obtained by adding alternating voltages of two different frequencies was applied, and the difference between the frequencies, that is, depending on the beat component of the two frequencies. The cantilever 5 may be vibrated.

FIG. 7 is a configuration diagram of another embodiment in which the configuration of the excitation voltage generator is changed in the embodiment shown in FIG. In the excitation voltage generation unit 210, the first wave generation unit 220 generates a sine wave voltage having a predetermined angular frequency ω ₀ that is higher than the resonance frequency of the cantilever 5, and the second wave generation unit 230 generates an angular frequency ω ₀ . A sinusoidal voltage having an angular frequency ω ₀ + ω _m (or ω ₀ −ω _m ) that is higher (or lower) by the angular frequency ω _m that the cantilever 5 is to be excited is generated. The adding unit 240 adds the two frequency sine wave voltages and outputs the result.

したがって、探針−試料間に電圧Ｖ_modを印加したときの探針−試料間の静電気力Ｆ^beat _esfは次の(5)式となる。

Now, the probe - between samples, the DC voltage V _DC, the first alternating voltage is the angular frequency omega _0, and the case of applying the second AC voltage is the angular frequency ω ₀ + ω _m, the applied voltage V _mod is the following It is expressed by equation (4).

Therefore, the electrostatic force F ^beat _esf between the probe and the sample when the voltage V _mod is applied between the probe and the sample is _expressed by the following equation (5).

Similar to Equation (3), the electrostatic force F ^beat _esf shown in Equation (5) includes components of various frequencies including a direct current component, one of which is the angular frequency of the first alternating voltage and the second. 2 It can be seen that there is a component of the difference ω _{m from} the angular frequency of the AC voltage. That is, since the cantilever 5 vibrates with a component of the angular frequency difference ω _{m due to} the electrostatic force F ^beat _esf , the electrostatic force of only the angular frequency ω _m component is detected by detecting this specific frequency component with a lock-in amplifier, for example. It is possible to extract. Therefore, even when such a cantilever excitation method is used, the relationship between the electrostatic force and the probe-sample distance when the difference frequency between the two frequencies is changed is measured by an atomic force microscope. It is possible to grasp the dielectric relaxation phenomenon in the frequency range above 10 MHz.

  By the way, according to the study of the present inventor, when the probe 6 is very close to the vicinity of the sample 3, the capacitance of the Helmholtz layer in the electric double layer becomes dominant, and the bulk solution capacity is reduced. It was found that the locality of the electrostatic force is poor compared to the dominant case. Therefore, in order to improve the locality of the electrostatic force, the excitation voltage that is the above-described amplitude-modulated AC voltage (or an AC voltage obtained by adding two-frequency AC voltages) is applied between the cantilever 5 and the sample 3. The method may be combined with a known FM detection method.

  FIG. 5 is a configuration diagram of a main part of an embodiment of an atomic force microscope for carrying out a dielectric property measurement method when the FM detection method is used in combination. Constituent elements which are the same as or correspond to those of the embodiment shown in FIG.

  The atomic force microscope according to this embodiment includes a photothermal excitation drive unit 41, an excitation laser light source 42 driven by the drive unit 41, and a mirror 43 in order to cause the cantilever 5 to self-oscillate near its resonance frequency. . An optical filter 44 that blocks light having the wavelength of the excitation laser is disposed in front of the photodetector 14. Further, a detection signal from the photodetector 14 is input to an FM detection unit 40 configured by, for example, a PLL, and the FM detection unit 40 changes the resonance frequency of the cantilever 5 that changes due to electrostatic force acting between the probe and the sample. The shift amount of is detected. The amplitude and phase of the frequency shift vibration of the modulation frequency (or difference between the two frequencies) component in this shift amount are detected by the amplitude phase detector 30 and the detection result is input to the data processor 31. The cantilever 5 is excited by an excitation signal output from the FM detector 40 and shifted by a fixed phase at the same frequency as the displacement signal of the cantilever 5. In the embodiment shown in FIG. 5, the excitation signal is converted into the drive current signal of the excitation laser light source 42 in the photothermal excitation drive unit 41, and the vibration of the cantilever 5 is induced by modulating its power.

In this configuration, the modulation wave frequency f _m (or 2-frequency omega _0, the difference frequency omega _m of ω ₀ + ω _m) be itself is not consistent with the resonance frequency of the cantilever 5 is detected as a FM modulated component of the resonant frequency Will be. FIG. 6 is a diagram in which the relationship between the amplitude of the frequency shift vibration of the modulated wave frequency component in the resonance frequency shift of the cantilever 5 and the probe-sample distance is measured in the configuration shown in FIG. The figure also shows a theoretical curve calculated in consideration of the partial pressure effect due to Helmholtz layer capacitance (= 0.1 F / m ² ). As can be seen from FIG. 6, the actual measurement agrees well with the theoretical curve, and even when FM detection is used together as described above, the dependence of the electrostatic force acting between the probe and the sample on the distance between the probe and the sample can be obtained. I can confirm that. Therefore, even if this method is used, the dielectric property of the sample can be measured as in the direct detection method in which the FM detection method is not used in combination.

  The present invention can be widely used not only for frequency modulation detection type AFM but also for dynamic mode AFM such as amplitude detection method and phase detection method.

  Moreover, the said Example is only an example of this invention, and it is clear that even if it changes suitably, amends, and is added in the range of the meaning of this invention, it is included by the claim of this application.

DESCRIPTION OF SYMBOLS 1 ... Scanner 2 ... Sample holder 3 ... Sample 4 ... Base part 4a ... Transparent body 5 ... Cantilever 5a ... Metal thin film 6 ... Probe 7 ... Cantilever holder 8 ... Analytical liquid 10 ... Optical displacement detector 11 ... Laser light source 12 , 13, mirror 14, photodetector 20, lead unit 21, 210, excitation voltage generation unit 22, carrier wave generation unit 23, modulation wave generation unit 24, amplitude modulation unit 25, capacitor 220, first wave generation unit 230, first. 2-wave generator 240 ... adder 30 ... amplitude phase detector 31 ... data processor 32 ... vertical position controller 33 ... horizontal position controller 34 ... main controller 35 ... operation unit 36 ... display unit 40 ... FM detector 41 ... photothermal excitation drive unit 42 ... excitation laser light source 43 ... mirror 44 ... optical filter

Claims (5)

The probe provided at the tip of the cantilever is brought close to the surface of the conductive sample immersed in the liquid, and the mutual action acting between the probe and the sample when the cantilever is vibrated at its resonance frequency. Using a dynamic mode atomic force microscope to detect the action, a measurement method for measuring the dielectric properties of the sample,
The cantilever between the conductor portion formed on at least one of the surface where the probe is located or the back surface thereof in the cantilever and the sample facing the conductor portion with a liquid interposed therebetween By applying an alternating voltage generated by amplitude-modulating a carrier wave having a frequency higher than the resonance frequency of the carrier wave with a modulation wave having a frequency lower than that, the cantilever is vibrated at a modulation frequency by electrostatic force,
Based on the vibration component, the carrier frequency dependency of the relationship between the electrostatic force acting between the probe and the sample and the distance between the probe and the sample is obtained, and information on the dielectric characteristics of the sample is obtained from the relationship between the frequency and the electrostatic force. A dielectric property measuring method characterized by: The probe provided at the tip of the cantilever is brought close to the surface of the conductive sample immersed in the liquid, and the mutual action acting between the probe and the sample when the cantilever is vibrated at its resonance frequency. Using a dynamic mode atomic force microscope to detect the action, a measurement method for measuring the dielectric properties of the sample,
The cantilever between the conductor portion formed on at least one of the surface where the probe is located or the back surface thereof in the cantilever and the sample facing the conductor portion with a liquid interposed therebetween By applying an excitation voltage generated by adding an alternating voltage having a first frequency higher than the resonance frequency of the first frequency and an alternating voltage having a second frequency higher or lower by a predetermined frequency than the first resonant frequency, Vibrate at a frequency that is the difference between the first frequency and the second frequency,
Based on the vibration component, the first frequency or the second frequency is maintained while the difference between the first frequency and the second frequency is kept constant with respect to the relationship between the electrostatic force acting between the probe and the sample and the distance between the probe and the sample. A dielectric property measurement method characterized by obtaining dependence on a sample and obtaining information on the dielectric property of a sample from the relationship between the frequency and electrostatic force. A dielectric property measuring method using the atomic force microscope according to claim 1,
Detecting the displacement of a cantilever that oscillates in response to the application of an excitation voltage that is an amplitude-modulated carrier wave voltage, and determining the probe-sample distance dependence of electrostatic force from the amplitude and / or phase of the displacement. Dielectric property measurement method. A dielectric property measurement method using the atomic force microscope according to claim 2,
The displacement of the cantilever that vibrates in response to the application of the excitation voltage in which the alternating voltage of the first frequency and the alternating voltage of the second frequency are added, and the electrostatic force probe-sample from the amplitude and / or phase of the displacement A method for measuring a dielectric property, characterized by determining distance dependency. A dielectric property measuring method using the atomic force microscope according to claim 1 or 2,
An excitation voltage is applied between the conductor part of the cantilever and the sample, the self-oscillation of the cantilever is further performed at the resonance frequency, and a frequency shift of the resonance frequency due to the electrostatic force acting on the cantilever is detected. A dielectric characteristic measuring method, characterized in that the dependence of the electrostatic force acting between the probe and the sample on the distance between the probe and the sample is obtained from the vibration component with respect to the excitation voltage in the shift.

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