JP2013145120A - Tapping mode afm including multiple cantilever for afm and scan method of the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide: a cantilever that can control impact energy in a collision and reduce damage to a sample to solve the problem in which in a tapping mode of an atomic force microscope the cantilever comes into contact with the measurement sample even in a very short time and damages a surface of the sample; and a scan device using the cantilever.SOLUTION: A multiple cantilever is a many-body vibration system formed by connecting one cantilever 8A with other two cantilevers 8B and 8C. An AFM device is fabricated so as to scan a surface of the sample while tapping the cantilever 8B and apply an excitation to the cantilever 8C. Since a certain amount of energy flows from the cantilever 8C to the cantilever 8B, when an input amount of energy by excitation and an attenuation of energy by collision in tapping are controlled to be equal to the energy transfer amount, a steady vibration is expected to occur thereby controlling the collision speed of the cantilever 8B and reducing the impact energy.

Description

The present invention provides a multi-body vibration system that achieves constant energy transfer per cycle between small oscillators by appropriately designing a mechanism in which two small oscillators are connected in parallel to a large oscillator. By applying damping to the small oscillator of this system and external excitation to the other small oscillator, it is possible to obtain a steady state condition for the vibration of the system. The present invention relates to a cantilever and a scanning system using the cantilever that can control impact energy at the time of collision in tapping mode AFM and improve the resolution of the position in the vertical direction by replacing with a resonant circuit system.

In addition, the present invention is designed by appropriately designing a mechanism in which two small vibrators are connected in parallel to a large vibrator, so that the vibration of a cantilever that performs tapping in the tapping mode AFM is coupled with the vibration of another cantilever. It is possible to evaluate the vibration of the cantilever that performs tapping in the tapping mode AFM by replacing the vibrator used for the evaluation in this mechanism with a resonance circuit system, from the vibration of the resonance circuit combined therewith. It relates to the technology that makes possible.

Today, Atomic Force Microscope (AFM) has a high resolution and can be used in any atmosphere (in air, in liquid, or in vacuum). It has become one of the useful tools. In particular, the tapping mode in which the surface of the sample is scanned while vibrating the cantilever can capture a slight change in the height and force on the surface, and thus has become the mainstream scanning method in AFM as a sensitive method.

In the tapping mode in AFM, scanning is performed while the cantilever is vibrated and the tip of the cantilever collides with the sample surface. At this time, the amplitude or frequency of the cantilever changes due to the unevenness of the sample surface. In the AFM system, the sample stage or the excitation center of the cantilever is moved up and down through a feedback mechanism so as to make these changes in the cantilever zero, and control is performed so as to keep the distance between the sample and the cantilever constant. Since the amount of movement corresponds to the unevenness of the sample surface, precise profile measurement is possible. In order to detect the vibration state of the cantilever, an optical lever method is used in which the tip of the cantilever is irradiated with a laser and the positional change of the reflected light is evaluated.

In this tapping mode, although the contact time between the measurement sample and the cantilever is extremely short, the sharp probe tip collides with the sample surface, so damage to the sample surface cannot be ignored. Therefore, in the case of a biological sample or a sample in which a substance is weakly adsorbed on the surface, there is a problem that a sufficiently sharp image cannot be obtained. Therefore, various researches aimed at controlling the impact force during tapping have been advanced (Non-Patent Document 1), but the conventional research is mainly based on empirical design by experiments and simulations. No analytical proposal has been made on the design method. There is also an attempt to suppress damage at the time of collision by feeding back the amplitude of the cantilever (Patent Document 1 and Patent Document 2). However, because of dynamic control, in the case of high-speed operation, the sample position control is performed. There were problems such as interference with feedback.

In general, many of the conventional AFMs are based on active feedback control. Therefore, when observing a flat sample with little unevenness, the oscillation of the system due to a strong feedback signal cannot be avoided, and the image resolution There was a problem such as not being able to get.

Further, in the tapping mode, since the measurement sample and the cantilever collide with each other, the vibration of the cantilever has a large non-linearity. Therefore, the vibration analysis of the cantilever using the differential equation cannot be performed. In addition, it is difficult to maintain a steady vibration state because a slight change in the collision position tends to show behavior such as fractional periodic motion and chaos. Therefore, from the viewpoint of vibration, there are not many examples of making cantilevers, and changes in amplitude and frequency due to changes in the distance between the sample and the cantilever are also observed from linear approximation solutions of nonlinear differential equations and observations in simulations and experiments. However, it has only been explained (Non-Patent Document 2).

Furthermore, in a normal AFM system, the cantilever is vibrated by vibration energy input from an actuator such as a piezo element and the tip of the cantilever collides with the sample to attenuate the energy, but the energy flow in the cantilever is designed. There are not many examples. For this reason, there has not been much discussion on a method for producing a cantilever that realizes steady motion, and even in the vibration analysis of a cantilever that has been reported so far, no analysis that considers collision has been performed (Non-Patent Document 1). ).

On the other hand, in the AFM, since the optical lever method is used for detecting the position of the cantilever at the time of initial setting, it is necessary to squeeze the laser at the tip of the cantilever. It was difficult to be a simple measurement method.

On the other hand, many attempts have been made to provide functions by using multiple vibrators. Bajaj et al. (Non-Patent Document 3) have reported that a characteristic characteristic of vibration appears by coupling a large number of vibrators. Patent Document 3 proposes a motion control method that performs phase control between vibrators by arranging a plurality of physical vibrators in a robot. However, in the report of Non-Patent Document 3, the design method for giving a specific function is not clarified. In the report of Patent Document 3, control is provided using feedback. It just describes the effect on the stabilization of

Kotake et al. Have clarified the phenomenon of energy transfer between collisional two-body vibrations coupled to one oscillator using a wave algorithm (Non-Patent Document 4, Non-Patent Document 5, Non-Patent Document 6). The collision position is at a balanced position or two points away from each other, and the position of one point where the AFM cantilever collides has not been mentioned. Moreover, their discussion was about the behavior in the energy conservation system, and not about the vibration in the system with excitation and damping. In addition, they have reported a method of collecting natural energy using energy transfer between many-body linear vibrations coupled to one oscillator (Non-patent Document 7 and Patent Document 4). This is a case where a random external force is input to the vibrator, and is a device for efficiently collecting energy, and does not describe the steady state of the collision vibrator. Their discussion was limited to linear vibration systems.

On the other hand, Patent Document 5 proposes the design of probes that do not interfere with each other by shifting the resonance frequency for a plurality of cantilevers connected to the same holding unit, but the interaction of the multi-body vibration system is removed in reverse. It is a contrivance, not a function addition by making the vibrator multi-body.

JP 2004-101202 A JP 2010-2409 JP 2006-289602 JP 2010-65545 A JP 2010-112888

AFM cantilever amplitude control using van der Pol type self-excited oscillation, Junichi Hayashi, Goku Hamada, Koji Kanno, Masaharu Kuroda, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 73, No. 732 (2007) 2225-2231 Cantilever collision vibration and control for tapping mode atomic force microscopy, Toshitoshi Numazu, Andrew J. Dick, Koji Kanno, Masaharu Kuroda, Balakumar Balachandran, Transactions of the Japan Society of Mechanical Engineers (C), 74, 742 (2008) 1409-1415 Global dynamics of an autoparametric system with multiple pendulums, Transaction of the ASME, Journal ofcomputational and nonlinear dynamics, Vol. 1 (2006) 35-46 Analysis of periodic perfect approximate periodic vibration appearing in internal resonant collisional vibration system coupled to one oscillator by wave algorithm, Soichiro Takada, Shigeo Kotake, Yasuyuki Suzuki, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 77, No. 773 (2011) 14-27 Periodic Graze phenomenon due to energy transfer due to internal resonance of a two-body collision vibration system coupled to one oscillator, Soichiro Takada, Shigeo Kotake, Yasuyuki Suzuki, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 77, No. 777 (2011) 1911-1925 Wave algorithm to manipulate energy transfer between two internal small resonators coupled to one oscillator, Shigeo Kotake, Hiroaki Hanai, Yasuyuki Suzuki, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 77, No. 781 (2011 ) 3337-3349 Spatial coherent wave energy concentration by the Grover algorithm, Hidenori Uchida, Shigeo Kotake, Yasuyuki Suzuki, Transactions of the Japan Society of Mechanical Engineers (B), 76, 761 (2010) 85-94

When the AFM is used in the tapping mode, the cantilever vibration is a nonlinear system accompanied by a collision, so that it is difficult to perform a precise analysis using a differential equation. In addition, due to the collision position change due to the unevenness of the sample surface when scanning, the collision vibration tends to show complex behavior such as fractional period motion and chaos, so in one oscillator system with excitation and attenuation, It has been difficult to obtain a stable steady solution, and no such proposal has been made so far.

In order to obtain a stable vibration state by an operation such as feedback in an unstable system, a high-speed and advanced control method is required. Because of the danger of oscillation of the system, it was difficult to obtain an image with high resolution.

On the other hand, when the AFM is used in the tapping mode, a probe having a sharp cantilever tip collides with the sample, so damage to the sample surface cannot be ignored. For this reason, it is necessary to minimize the impact caused by the collision with the sample. However, in the current technology related to the tapping mode AFM, most of the solutions are based on dynamic control, so the cantilever is vibrated and scanned at high speed. In the measurement of the AFM image, this cannot be controlled sufficiently, and it has been difficult to observe a sample such as a living organism having a soft tissue with high resolution. On the other hand, since a clear relational expression between the impact force (collision speed) and the amount of vibration that enables passive control has not been obtained, the impact force cannot be controlled passively.

In addition, since the optical lever method using a laser is used for position detection at the initial setting of the AFM, it is necessary to accurately squeeze the focused laser beam to the tip of the cantilever, and a sensor such as a quadrant photodiode that detects reflected laser light Because it was necessary to adjust the system appropriately, there were problems such as that work required experience and time and automation was difficult.

Most of the conventional AFM techniques are related to a single cantilever. For multi-cantilevers in which a large number of vibrators are combined, there is a technique to remove these interactions, but these interactions are actively performed. There was no technology to use. There was no attempt to control a single cantilever simulating the effect of interaction between multiple cantilevers.

The invention according to claim 1 is a multi-cantilever which is a multi-body vibration system made by connecting another two cantilevers 8B and 8C to one cantilever 8A, and scans the sample surface while tapping the cantilever 8B. By designing the AFM apparatus to apply vibration to the cantilever 8C, a solution is provided for the above problem. At this time, each cantilever is appropriately designed according to the wave algorithm shown below, so that the vibration of the connected cantilevers 8B and 8C is discretely mechanically separated from the vibration of the cantilever 8A, thereby creating a controllable two-body problem. It will be returned. In addition, since constant energy flows from the cantilever 8C to the cantilever 8B, when the energy input amount due to the excitation and the energy attenuation amount due to the collision at the time of tapping are controlled to be equal to this energy transfer amount, It is expected that vibration will occur. In the following, the shape of the multi-cantilever that enables the above-described conditions and the features that appear in the system in which this is realized will be mentioned. We will also refer to the method of generating the same vibration in a single cantilever as in this multibody collision vibration system.

In general, a cantilever has a plurality of eigenmodes, but the primary mode is likely to stand as a fundamental vibration. In addition, when the displacement is very small, the non-linearity of the cantilever is not so great, so that most of the vibration can be approximated as a linear oscillator. Thus, the behavior of the cantilever can be approximately expressed by a linear vibration system generally composed of a mass-spring. When a cantilever of length l, moment of inertia of section I, Young's modulus E, weight m _b of cantilever and mass m ′ added to the tip is regarded as a spring-mass system, the relationship between each parameter is as follows: It is expressed in (Mechanical Vibration, Basic Knowledge of Dynamic Problem Solving, Hideki Sato, Saichi Okabe, Yoshio Iwata)

The multi-cantilever according to claim 1 is expressed by a three-body collision vibration model in a linear vibration system by replacing the cantilever with a mass-spring system. It can be created using the wave algorithm that appears.

Now, as shown in FIG. 1, a large vibrator 1 connected to a fixed wall and two small vibrators 3 and 5 connected to the large vibrator 1 are arranged on a wall 7 into which one of the small vibrators is taken in and out. Consider a three-body collision vibration model in which a complete elastic collision occurs every fixed time period Δt. In this model, the mass m ₁ and the spring constant k _{1 of} the colliding small oscillator (hereinafter referred to as the colliding small oscillator 3), the mass m ₂ and the spring constant of the small oscillator that does not collide (hereinafter referred to as the non-collision small oscillator 5). When k ₂ and the mass M and the spring constant K of the large vibrator 1 are set as follows, energy is alternately transferred between the two small vibrators, and an almost periodic vibration is generated. The wave algorithm that realizes this energy transfer is a kind of quantum algorithm, and is known to be equivalent to the Grover algorithm known as an algorithm for localizing the probability amplitude. (Non-Patent Document 4, Optimal Database Search: Wave and
Catalysis, Apoorva Patel, http://arxiv.org/abs/quant-ph/0401154) In the following, this algorithm is also referred to as the Grover algorithm.

Here, p is a natural number. In the following, each physical quantity is expressed in a non-dimensional manner by setting the representative time T _r = (k ₁ / m ₁ ) ^1/2 , the representative length as a unit length, and the representative mass as m ₁ . Each dimensionless physical quantity symbol is distinguished by adding a superscript. The mass and spring constant of the large oscillator 1, the small collision oscillator 3, and the non-collision small oscillator 5
Thus, the natural frequency Ω of the large oscillator 1 Ω = (2p + 1) (k ₁ / m ₁ ) ^1/2 / 4, and the natural frequency of the collision small oscillator 3 and the non-collision small oscillator 5 are equal. , Ω _r = (k ₁ / m ₁ ) ^1/2 . Γ in the above formula represents a mass ratio and a spring constant ratio. The natural frequency of the entire system is the natural frequency of the double spring model of the large oscillator 1 and the center of gravity of the entire small oscillator.
Is represented by

According to Non-Patent Document 4, the vibration of the two small oscillators connected under the condition of Δt ^* (ω ₊ −ω ₋ ) = 2nπ is discretely separated from the vibration of the large oscillator 1 to establish the Grover algorithm. . Equation 1 was thus determined.

On the other hand, in this dynamic system, the displacement and velocity of the dimensionless large oscillator 1 at the n-th collision are X ^* [n] and V ^* [n], and the dimensionless collision small oscillator 3 is made. X ^* ₁ [n], v ^* ₁ [n], the displacement and speed of the non-colliding non-collision small oscillator 5 are x ^* ₂ [n], v ^* ₂ [n], no Assuming that the dimensioned collision time period Δt ^* = 2π, these physical quantities are expressed by the following recurrence formula. Note that the discretized displacement of the collision small oscillator 3 represents a collision position, and x ^* ₁ [0] of the collision small oscillator 3 represents an initial position. In other words, in order for the wave algorithm to be established, it is necessary to start the initial position of the small collision oscillator 3 from the collision position of the same oscillator. However, in a system with excitation and attenuation, it converges to these values under arbitrary initial conditions. You don't have to worry too much about it.

Under the absolute coordinate system, which is now a coordinate system fixed to the wall, a constant speed dv ₂ is set for each time period in the collision attenuation to the collision small oscillator 3 (attenuation by the restitution coefficient a) and the speed of the non-collision small oscillator 5. Assuming excitation to be added. Since the energy transfer amount for each time period is obtained analytically by the Grover algorithm, a steady collision state can be obtained by applying collision attenuation and excitation so as to cancel this transfer amount. The conditional expressions are shown below.

The above formula is meant that a collision speed of the collision small vibrator 3 in the absolute coordinate system are determined from the pressure Furyou dv ^* _2, which is dimensionless and the coefficient of restitution, the collision speed control by pressure Furyou dv ^* ₂ It becomes possible. On the other hand, from this conditional expression and the recurrence expression of the speed at the n-th collision
The following equation is obtained. This means that the velocity at the time of collision of the two small vibrators in the absolute coordinate system is always constant.

From the recurrence formula of the displacement at the n-th collision, the position X ^* + x ^* ₁ of the collision small oscillator 3 at the time of collision in the absolute coordinate system can also be obtained analytically.
Is used, the position of the collision small oscillator 3 at the time of collision is
And always constant. This means that the position of the collision small oscillator 3 at the time of collision in the absolute coordinate system is always constant.

Also, the closer the collision position (initial position of the collision vibrator 3) is to the balance position of the vibrator, the smaller the mechanical energy of the collision vibrator in discrete mechanics. It is considered that the closer the position is to the fishing position, the smaller the amplitude of the vibrator is.

As described above, the multi-body collision vibration system including the three mechanical vibration systems described in claim 1 has a steady solution in which the collision position and collision speed of the collision small oscillator 3 in the absolute coordinate system are always constant. You can see that it exists. Similarly, the positions and velocities of the non-collision small vibrator 5 and the large vibrator 1 also become steady vibrations.

According to the second aspect of the present invention, the sample is scanned with the cantilever 8B of the multi-cantilever according to the first aspect, the amplitude change at that time is detected by the cantilever 8B or the cantilever 8C, and the three-dimensional of the actuator is set so that the amplitude becomes constant. Since the position (height) position is feedback controlled, the relationship between the position and speed at the time of collision of the cantilevers 8B and 8C (discrete time) is obtained as in (Equation 5) (Equation 3). The relationship between the amplitudes of the cantilevers 8B and 8C is also obtained, whereby the amplitude of the cantilever 8B is known from the amplitude of the cantilever 8C. Therefore, the change in the amplitude of the cantilever 8B can be detected by the change in the amplitude of the cantilever 8C. The relational expression between the amplitude of the two cantilevers obtained from (Equation 5) and (Equation 3) and the amplitude change amount due to the collision position change is shown below. When the mass ratio γ <1 and the collision time at the time of steady collision is t ^* = 2nπ, the displacement of the two small vibrators is almost maximized at time t ^* ≈ (2n + 1) π, 2nπ. both the amplitude a ₁ of the child _3, both the amplitude a ₂ of the non-collision-small vibrator 5 is respectively approximately expressed as follows.

Assuming that the amplitudes of the two small vibrators immediately after the collision position changes from x ₁ ^* → x ₁ ^* + dx ₁ ^* are A ₁ ′ and A ₂ ′, respectively, the difference in amplitude variation between the two vibrators is as follows: It is expressed in

From these equations, the ratio of the amplitude change amount of the two small vibrators is as follows.
As can be seen from this equation, it is analytically determined that the amplitude change amount of the non-collision small vibrator 5 is 1 / γ times the amplitude change amount of the collision small vibrator 3. By designing the cantilever so that γ takes a smaller value (γ <1), the amplitude change amount of the cantilever 8C becomes larger than the amplitude change amount of the cantilever 8B. At this time, it is considered that the accuracy in the depth direction is further improved by detecting the amplitude change due to the change in the collision position by the cantilever 8C, and provides a solution to the above problem.

In the invention according to claim 3, since the relational expression between the amount of vibration (velocity amount of vibration) of the cantilever 8C and the collision speed at the time of steady collision of the cantilever 8B is obtained by (Equation 3), By controlling the amount of vibration, the collision speed of the cantilever 8B can be determined arbitrarily, and the impact force on the sample can be mitigated, thus providing a solution to the above problem.
Among the multi-cantilevers according to claim 1 of the present invention, the cantilever 8B that collides with the sample and the cantilever 8C that performs vibration have a degree of freedom corresponding to the mass ratio γ. A cantilever suitable for detecting the cantilever 8C can be manufactured.

In the invention according to claim 4, by performing the scanning and detection shown in claim 2 in the multi-cantilever shown in claim 1, the control amount of the position in the three-dimensional direction (height) of the actuator can be reduced. Corresponds to the height, which measures the shape of the sample surface

According to a fifth aspect of the present invention, the multi-body collision vibration system including the three mechanical vibration systems described in the first aspect is based on the similarity between a mechanical vibrator and an electric vibrator (electric / mechanical vibration as an electronic circuit element). Child and its applications, Kenzo Nagai, Tadashi Konno, Corona (1974)), some of which can be replaced by electric vibrators, and other vibrators function as electrical resonance circuits, piezoelectric elements, etc. A similar function can be imparted to a single cantilever by substituting this actuator.

In general, an actuator joined to a mechanical vibrator is expressed by a combination of a capacitance component C, an inductance component L, and a resistance component R by an equivalent circuit. For example, a piezoelectric element connected to an AFM cantilever has a capacitance C ₀ (capacitor 12A) of the piezoelectric element itself, an equivalent capacitance C ₁ of a mechanical vibrator formed by coupling the piezoelectric element and the cantilever, and an equivalent inductance L ₁ . This is expressed by a series circuit including a capacitor 12B and a resonant parallel circuit of the coil 11B (FIG. 3). The natural frequency of the resonance circuit of C ₁ and L ₁ is equal to the mechanical natural frequency of the collision small oscillator formed by coupling the piezoelectric element and the cantilever, and ω ₁ = (L ₁ C ₁ ) ^−1/2. It is expressed.

On the other hand, the capacitance C ₀ (capacitor 12A) of the piezoelectric element attached to the cantilever is connected in series with the coil 11A having the inductance component L ₀ , and the natural frequency of the series resonance circuit composed of the coil 11A (L ₀ ) -capacitor 12A (C ₀ ). Is designed to be equal to the natural frequency Ω of the large vibrator 1 in this multi-body collision vibration system (Ω = (L ₀ C ₀ ) ^−1/2 ), so that the large vibrator 1 is connected to the coil 11A. It can be replaced with a resonant circuit comprising an inductance L ₀ and a capacitance C ₀ (capacitor 12A) of the piezoelectric element.

Further, the non-collision small vibrator 5 is a parallel resonance circuit including a coil 11C having an inductance L ₂ having a resonance frequency equal to ω ₁ and a capacitor 12C having a capacitance C _{2 according} to an equivalence rule of a mechanical vibrator and an electric vibrator. (Ω ₂ = (L ₂ C ₂ ) ^−1/2 ). However, the following relational expression corresponding to the mass ratio γ of the collision small oscillator 3 and the non-collision small oscillator 5 needs to be established between L ₂ and L ₁ and C ₂ and C ₁ .

By connecting the parallel resonance circuit of the coil 11A (L ₀ ) and the coil 11C-capacitor 12C in series to the piezoelectric element connected to the cantilever, the three-body collision vibration model of FIG. Since this is an equivalent circuit (FIG. 4), the single cantilever coupled with the resonance circuit according to claim 5 has the same function as the multi-cantilever according to claim 1.

According to the sixth aspect of the present invention, in the coupling system of the cantilever and the resonance circuit designed as described above, energy is exchanged between the resonance circuit composed of the coil 11C and the capacitor 12C and the cantilever. By obtaining the relational expression with the voltage applied to the resonance circuit composed of the coil 11C and the capacitor 12C, the vibration state of the cantilever colliding with the sample can be detected by the voltage applied to the coil 11C and the capacitor 12C connected to the piezoelectric element. In this method, since the mechanical vibration of the actuator needs to be closely coupled with the cantilever, it is necessary to devise such as forming an actuator such as a piezoelectric element on the surface of the cantilever.

According to the seventh aspect of the present invention, in the multi-body collision vibration system comprising the three mechanical vibration systems described in the first aspect, the position and speed of each vibrator are stationary vibrations, and the values are expressed analytically. Therefore, even in a single cantilever, the cantilever collision is achieved by feeding back the system to maintain a steady state that is realized when a constant vibration is applied to other small vibrators in the three-body collision vibration model. Speed control and higher resolution in the height direction can be realized. An actuator such as a piezoelectric element is attached to the base of one cantilever, the base position of the cantilever is set to the position where the large vibrator 1 should be taken, and the speed of the base of one cantilever is set to the speed that the big vibrator 1 should take. Apply a voltage to the actuator so that When the collision position of one cantilever coincides with the collision position of the cantilever in the multi-body collision vibration system shown in claim 1, steady vibration occurs.

On the other hand, when the collision position of one cantilever is away from the collision position of the cantilever in the multi-body collision vibration system shown in claim 1, the amplitude of one cantilever increases and The amplitude of one cantilever is reduced. As a result, the impact force at the time of the cantilever collision can be controlled by scanning the sample while controlling the base position of the cantilever so that the amplitude of one cantilever becomes a constant steady state. An AFM apparatus having a horizontal resolution is possible, and a control method according to claim 3 is realized.

According to the third aspect of the present invention, an analytical steady solution is obtained in the collision vibration of the cantilever according to the first and second aspects, and the collision speed changes in proportion to the excitation force. By doing so, the collision speed to the sample can be changed. By reducing the cantilever collision speed, it can be as close to Graze collision as possible, minimizing damage to the sample, and soft surfaces such as biological samples and weakly adsorbed samples attached to the substrate. It becomes possible to observe with high resolution.

According to the second aspect of the present invention, the amplitude of the cantilever 8B can be detected by the amplitude of the cantilever 8C, and the amplitude change of the cantilever 8B due to the unevenness of the sample surface can be expanded by the amplitude change of the cantilever 8C by the system design. Further, by using the present invention, the steady vibration of the cantilever can be designed analytically, and the change in the sample height can be regarded as a continuous change in the amplitude of the cantilever. In the conventional AFM technology, the sample height is regarded as a change in the amplitude and frequency of the cantilever. However, the change in these amounts when a distant sample is brought close is discontinuous, and the cantilever that started to vibrate As the position of て い remains uncertain as much as its amplitude, this technique can be expected to improve the resolution in the depth direction, making it easier to change the height of the atomic order, which was difficult to observe in the past. May be obtained.

In the sixth aspect of the present invention, by using the mechanical-electrical coupling in the fifth aspect, the change in the collision position of the cantilever corresponding to the change in the sample height is applied to the parallel resonance circuit including the external coil 11C and the capacitor 12C. Since it can be detected by the generated voltage, the conventional technique such as the optical lever method for detecting the cantilever and the trouble of adjusting the optical axis required for it can be eliminated, and the inspection apparatus using a large number of AFM probes can be automated. .

According to claim 7 of the present invention, even a single cantilever is claimed by performing vibration using the relationship between the collision speed and the amount of vibration obtained from the analytical steady solution appearing in the multi-cantilever in claim 1. The steady vibration similar to that of the multi-cantilever in No. 1 can be obtained, and by controlling this feedback, it is possible to control the collision speed of the cantilever and increase the resolution in the height direction. High-resolution AFM observation is possible.

As the best means for carrying out the present invention, the measurement method in the mechanical vibration system using the multi-cantilever in claim 1 and the mechanical-electrical coupling system of the cantilever and the electric circuit in claim 5 are used below. The measurement method and a measurement method applying this technique to the single cantilever in claim 7 will be described as an example.

First, an example in which the measurement method in a mechanical vibration system using a multican lever according to claim 1 is applied will be described. The multi-cantilever determines each dimension shown in FIG. 4 by using the following equation in which simple vibration corresponds to primary vibration of the cantilever. Here, p is a natural number, and the height, length, and width of the cantilevers 8A, 8B, and 8C are h ₀ , l ₀ , b ₀ , h ₁ , l ₁ , b ₁ , h ₂ , l ₂ , b _{2, respectively.} (FIG. 2).

Each dimension is determined so that the above conditional expressions are satisfied and m ₁ ″ and m ₂ ′ obtained from the conditional expressions of Expressions 11 and 12 are appropriate values.
Here, m ₁ ′ and m ₂ ′ are masses added to the tips of cantilevers 8B and 8C corresponding to the small collision oscillator 3 and the small collision small oscillator 5, respectively. The multi-cantilever shown in claim 1 can be obtained by designing to satisfy the above conditions.

A magnetic material such as cobalt is deposited on the tip of the cantilever C of the multi-cantilever so as to apply a driving force by applying an external magnetic field. In addition, a piezoelectric element is attached to the root of the cantilever 8C, a metal coil is deposited on the tip of the cantilever 8C to give an eddy current due to a high-frequency magnetic field, and the pressure of photons is utilized by techniques such as optical tweezers. It is possible to devise such as

Next, a sample is fixed on a piezo stage having XYZ axes. Like the conventional AFM apparatus, this piezo stage has a function of moving a sample with atomic resolution, and is controlled by a D / A converter connected to a PC using an external piezo drive circuit. Next, the multi-cantilever is attached to the automatic XYZ stage. The automatic stage with the multi-cantilever attached and the piezo stage with the sample attached should be connected using a low thermal expansion material such as Invar alloy that is not significantly affected by external temperature changes. A micro coil is placed near the multi-cantilever, and a high frequency magnetic field is applied from the outside using a high frequency bipolar power source. An arbitrary waveform can be applied to the high-frequency bipolar power source by a D / A converter or a programmable frequency generator connected to the PC. By applying a magnetic field from this coil, the cantilever 8C can be vibrated. When the cantilever 8C is vibrated, the cantilever 8B coupled thereto also starts to vibrate.

Further, a laser is focused on the tip of the collision cantilever, and the amplitude of the cantilever 8B is measured by the voltage difference from the four-divided photodiode at the position where the reflected light is separated. At this time, the laser is not necessarily applied only to the cantilever 8B, and the amplitude amount of the cantilever 8B can be evaluated by applying the laser to the cantilever 8C by the relational expression of steady vibration. When the amplitude of the cantilever 8C is used for the evaluation of the amplitude of the cantilever 8B, in order to reduce the influence of the vibration, the vibration frequency is a burst wave, and a measure such as evaluating the change in the amplitude when the vibration is stopped is added. . By designing the cantilever 8C to be larger (wider) than the cantilever 8B, it becomes easier to align the optical axis of the laser.

Next, the automatic XYZ stage is moved to bring the multi-cantilever closer to the sample. At that time, the Z-axis of the piezo stage on the sample side is extended to the cantilever side as much as possible to keep the distance between the sample and the cantilever close. When it is detected that the cantilever 8B is in contact with the sample surface, the Z-axis of the piezo is By shortening, the distance between the sample and the cantilever is increased to prevent damage to the cantilever itself or the probe at the tip of the cantilever. When the cantilever 8B comes into contact with the sample, the vibration energy flows from the excited cantilever 8C into the cantilever 8B according to the wave algorithm, so that the amplitude increases rapidly. This signal is detected, the approach of the multi-cantilever to the sample tip is stopped, and the piezo is contracted in the Z-axis direction.

By providing the base cantilever 8A with a damping characteristic, the system shifts to steady vibration, and the cantilever can be scanned in the tapping mode. The sample is scanned by scanning the piezo stage with the sample fixed in the horizontal direction of the sample surface.

In this steady vibration state, the amplitude of the cantilever 8B is proportional to the amplitude of the cantilever 8C and is a function of the distance between the cantilever balance position and the sample surface. Thus, the change in the sample height can be evaluated. However, since the amplitude of the cantilever is also a function of the excitation force, the excitation must be constant in this case. If feedback in the height direction is applied to the sample stage so that the amplitude of the cantilever 8B and cantilever 8C is constant, the same usage as a normal AFM can be performed. However, in the method according to the present invention, since there is a continuous relationship between the sample height and the amplitude, an improvement in accuracy in the height direction can be expected. Furthermore, for changes in the sample height within a certain range, the information on the sample height appears as the amplitude of the cantilever, so it is expected that profile measurement can be performed without the need for a feedback mechanism. However, it is necessary to make the design to suppress the influence of the excitation system as much as possible. When this is realized, it is possible to evaluate the profile change of the sample without using feedback, so that it is expected that higher-speed scanning will be realized.

When observing a material that dislikes the impact force of a cantilever, such as a soft sample, it is possible to reduce the impact force when tapping the cantilever by reducing the excitation force using this method. In the case of a sample with a rough surface, if the excitation force is reduced beyond a certain level, the cantilever may exceed the Graze condition and may not collide with the sample. There must be. As described above, the tapping mode AFM using the multi-cantilever according to claim 1 of the present invention is possible.

Next, a measurement method using a mechanical-electrical coupling system between a cantilever and an electric circuit according to claim 5 will be described as an application example. Since the mechanical system is almost the same as the tapping mode AFM using the multi-cantilever described above, the following points will be mainly described.

First, a normal single cantilever is used as the cantilever. A piezoelectric element is formed on the surface of the cantilever, or the piezoelectric element is closely attached to the base of the cantilever so that the mechanical vibration of the piezoelectric element coincides with that of the cantilever. In addition, an electrode is attached to the piezoelectric element to enable excitation by an external power source. Next, a coil 11A and a resonance circuit (a coil 11C and a capacitor 12C connected in parallel) are connected in series with this piezoelectric element to form a closed circuit. Each electronic component is selected by using the equivalence of a mechanical vibrator and an electric vibrator so as to fit each cantilever in the multi-cantilever. At this time, the piezoelectric element attached to the cantilever also needs to be evaluated by an equivalent circuit, and the value of the equivalent element at the excitation frequency needs to be obtained by an impedance analyzer or the like.

Next, excitation by an external power source is performed by electromagnetic coupling between the coil 14 connected to the high frequency bipolar power source and the coil of the resonance circuit described above. Although the signal to the power supply may be a sine wave with limited amplitude, a signal that is controlled so as not to disturb the oscillation of the resonant circuit by a programmable high-frequency generator or an A / D converter connected to a PC Is better. The energy of vibration input to the resonance circuit is transmitted through the coupled coil to vibrate the cantilever.

The amplitude of the cantilever can be evaluated using an optical lever method in which a laser is applied to the tip as in the case of a conventional AFM, but can also be similarly evaluated by the voltage at the element end constituting the resonance circuit. In that case, since the coupling between the coil connected to the external power supply and the coil of the resonance circuit is affected, it is necessary to devise such as a burst wave for the excitation by the external power supply. In addition, the convenience of this system is omitted since it is almost the same as the tapping mode AFM using the multi-cantilever described above.

Finally, an example of applying this technique to a single cantilever according to claim 7 will be described. Since the mechanical system is almost the same as the tapping mode AFM using the multi-cantilever described above, the following points will be mainly described.

First, a normal single cantilever is used as the cantilever. The cantilever can be vibrated by attaching a piezoelectric element to the base of the cantilever. This piezoelectric element is connected to a high-frequency bipolar power source, and can be excited by an arbitrary waveform by a programmable high-frequency generator or an A / D converter connected to a PC. The input waveform is controlled so as to reproduce the position and speed of the large vibrator 1 in the multi-cantilever. Since the position and speed of the large vibrator 1 in the steady state are periodic functions, the waveform is calculated in advance. When calculating the position and velocity of the large vibrator in the steady state, the design is made so that the collision velocity and the collision position of the target cantilever match. By applying such an excitation force, it is possible to emulate the vibration caused by the multi-cantilever described above. Since the input waveform is not a simple sine wave, high-frequency bipolar power supplies, programmable high-frequency generators, and A / D converters require a high-speed response at an order of magnitude greater than the excitation frequency of the cantilever.

When the cantilever is brought close to the sample in the tapped state in this way, the amplitude of the cantilever shifts to steady vibration after the collision. After confirming this, the cantilever is scanned over the sample surface by moving the piezo stage of the sample horizontally. Since the change in the sample position due to scanning appears as a change in the amplitude of the cantilever, when the amplitude is increased, feedback is performed so that the sample is closer to the cantilever side, and when the amplitude is reduced, Conversely, control is performed so that the sample is kept away from the cantilever. In this method of emulation, although it is possible to move close to the above two methods by controlling to maintain steady vibration by feedback of the sample position, it does not have a vibration system that causes internal resonance with the cantilever. If the sample height deviates from the steady state, the cantilever vibration is expected to be a turbulent vibration such as chaos. In order not to cause such disturbance, high-speed feedback of the sample position is important so as to be within the planned steady vibration.

The above-described form enables the three methods in the claims proposed in the present invention.

The industrial applicability of the cantilever according to the present invention will be described below.
By using the techniques according to claims 1 to 4, it is possible to control the collision speed of the cantilever in the AFM tapping method by the amount of vibration, so that control close to Grazing and almost zero speed is performed. By applying, the impact force to the sample can be reduced. As a result, AFM observation is also effective for observation of the surface of a cell membrane in a biological material and observation of irregularities on the surface of a substance weakly attached to the substrate surface. At the same time, since the damage to the cantilever and the probe can be reduced, the life of the cantilever is prolonged, so that the cost and time required for the probe and replacement can be reduced.

By setting the mass ratio γ <1 in claims 1 and 2, the resolution in the height direction in the tapping mode AFM can be improved. As a result, it is important to design a strict size, and it becomes possible to measure a precise sample, and it becomes possible to manufacture a device with higher performance.

According to the fifth and sixth aspects, since the continuous change in the sample height can be evaluated by the amplitude of the cantilever that is not caused to collide and the voltage applied to the parallel resonance circuit, a minute change in the force on the sample surface can be sensitively measured. . Thereby, the measurement regarding the change in force at the tip of the cantilever can be observed more sensitively.

In claim 5 and claim 6, since an apparatus such as an optical lever method used for conventional cantilever detection is not required, the AFM apparatus can be miniaturized, and a microscope, vacuum apparatus, TEM And SEM can be easily added to the inside of the evaluation apparatus. In addition, since a large number of cantilevers can be arranged, this also contributes to the automation of the apparatus and the reduction of the inspection time even in the inspection apparatus for semiconductors and the like.

Furthermore, since there is no need to adjust the optical axis of the laser, which was necessary with conventional methods such as the optical lever method, observation becomes easier, and specially skilled techniques are no longer necessary, improving work efficiency. Expected. In addition, since measurement errors due to optical axis misalignment and the like are eliminated, continuous measurement is possible, which contributes to a reduction in industrial costs.

Furthermore, by using the technique of claim 7 of the present invention, even in an AFM using a single cantilever, the present technique can be applied by improving the simple apparatus, and no new apparatus development is required. . Further, by producing the cantilever shown in claim 1 of the present invention, the present technology can be applied by slightly improving the conventional tapping mode AFM.

Finally, in the present invention, since the change in the sample height appears as a change in the amplitude of the cantilever within a certain range, feedback is applied in the height direction of the sample for a flat sample with no severe surface irregularities. It is possible to measure the change in height. Since feedback is not required in the AFM system, noise such as signal transmission is difficult to enter, and therefore, even a sample with a small change in surface height may be able to be measured with high accuracy. In addition, since high-speed scanning that does not require feedback is possible, it is possible to observe changes in molecules such as living bodies in situ.

Three-body collision vibration model with two small oscillators coupled to a large oscillator Image of replacing the mass-spring system of the three-body collision vibration model with a cantilever Circuit diagram when the mass-spring system of the three-body collision vibration model is replaced with a coil and capacitor Equivalent circuit of piezoelectric element

1 Large oscillator 2 Large oscillator spring
3 Collision small oscillator 4 Collision small oscillator spring 5 Non-collision small oscillator
6 Spring of non-collision small oscillator 7 Wall 8A to be taken in and out every time period Cantilever equivalent to large oscillator
8B Cantilever equivalent to a collision small oscillator
8C Cantilever equivalent to non-collision small oscillator
9 Sample 10 Probe 11A Coil corresponding to mass of large vibrator 11B Coil corresponding to mass of collision small vibrator
11C Coil corresponding to mass of non-collision small vibrator
12A Capacitor corresponding to the spring of the large oscillator 12B Capacitor corresponding to the spring of the small collision oscillator 12C Capacitor corresponding to the spring of the non-collision small oscillator 13 Piezoelectric element-cantilever equivalent circuit 14 Power supply for supplying energy to the system

Claims (7)

A cantilever A, a cantilever B connected to the cantilever A, and a multi-cantilever for AMF composed of the cantilever C, wherein the cantilever B and the cantilever C have the same natural frequency, and the cantilever B and the cantilever C The product of the center of gravity of C, the difference between the two coupled natural frequencies created by the cantilever A and the collision period is an integral multiple of 2π, and the cantilever C is vibrated and used to collide with the sample surface. A multi-cantilever for AFM characterized by being used. The actuator equipped with the AFM multi-cantilever is a tapping mode AFM in which the sample surface is scanned in a two-dimensional (planar) direction, and the amplitude of the cantilever B or the cantilever C is maintained at a predetermined value during the scanning period. The tapping mode AFM is characterized in that the position of the actuator in the three-dimensional (height) direction is feedback-controlled. 3. The tapping mode AFM according to claim 2, wherein an impact force that the cantilever B collides with a sample surface is controlled by controlling an excitation force of the cantilever C. 4. The tapping mode AFM according to claim 2, wherein the shape of the sample surface is measured by scanning the position of the cantilever B in a three-dimensional (height) direction. 5. A piezoelectric element is attached to the cantilever, a coil A is connected in series to the piezoelectric element, and a coil C and a capacitor C connected in parallel to the coil A are connected in series.
The natural resonance frequency of the parallel resonance circuit of the capacitor B-coil B and the parallel resonance circuit of the capacitor C-coil C having the equivalent capacitance and equivalent inductance of the mechanical vibrator by attaching the piezoelectric element to the cantilever is the same, In addition, the capacitor B-the parallel resonance circuit of the coil B and the capacitor C-the parallel resonance circuit of the coil C connected in series and the capacitor A-the coil A having the equivalent capacitance of the piezoelectric element are connected in series. The difference between the two coupled natural frequencies with the resonant circuit and the collision period of the cantilever is an integer multiple of 2π,
A power supply circuit that vibrates the parallel resonant circuit (capacitor B-coil B), vibrates the cantilever, the cantilever contacts the sample surface in a tapping mode, and supplies power to the coil C from the outside by electromagnetic induction. A tapping mode AFM, comprising: 6. The tapping mode AFM according to claim 5, wherein the amplitude of the cantilever is estimated from a voltage between both terminals connected to the capacitor C.   A constant energy per cycle from the actuator to the cantilever B by operating an actuator connected to the base of a single cantilever so as to realize the movement of the position and speed of the cantilever B according to claim 1. A tapping mode AFM scanning method that uses a moving system to perform feedback control on the distance between the sample and the cantilever in the three-dimensional (height) direction so that the amplitude of the cantilever remains constant.