JP4904495B2 - High-band atomic force microscope - Google Patents

Description

  The present invention relates to a high-band atomic force microscope apparatus.

  An atomic force microscope (AFM) is a cantilever that scans a probe attached to a fine lever called a cantilever along the surface of the sample and uses an atomic force acting between the sample and the probe. This is a device that measures the surface structure of a sample on a nanoscale by measuring the deflection of the sample and the distortion caused by the frictional force (see Non-Patent Document 1).

  To measure deflection and distortion, a laser beam is incident obliquely on the back of the cantilever, and the change in the reflection angle of the laser beam due to the displacement of the cantilever is detected as a relative change in the light intensity incident on the quadrant photodiode ( Optical lever method) and two methods of measuring the interference between the laser beam reflected from the end of the fiber and the laser beam reflected from the rear surface of the optical fiber (optical interference method). There is a detection method (see Non-Patent Document 1).

  Conventionally, the following method has been considered as a method for analyzing the surface shape of a sample. That is, in an open loop system in which the Z-axis fine movement piezo is not controlled, the output voltage y (t) from the quadrant photodiode at time t is converted as it is and recorded as a surface shape (open loop system). In the closed loop system that controls the Z-axis of the piezo so that the displacement of the cantilever is constant, the input voltage u (t) to the piezo at time t, that is, the drive voltage to the piezo is converted and recorded as a surface shape. This is a closed loop method.

  In the open loop method, the output is affected by the mechanical resonance of the plant consisting of the sample and the cantilever, and because no feedback is applied, the cantilever and sample can be used for surface shapes with large undulation changes on the sample surface. There is a problem that the surface is separated and measurement becomes impossible. Therefore, most AFMs employ a closed loop method. As with other precision positioning devices, the AFM bandwidth is limited by the Nyquist frequency determined by the sampling frequency and the resonant frequency of the plant.

  AFM is an invention developed from the scanning tunneling microscope (STM), which was the subject of the 1986 Nobel Prize in Physics, and as mentioned above, it is a product that cannot be realized without feedback control.

In recent years, advanced control as described below has been used as AFM control in addition to classical control such as proportional control or PI control conventionally used. For example, in Non-Patent Document 2, the _H∞ loop shaping control method is applied to AFM, and in Non-Patent Document 3, adaptive control theory is applied to AFM. In Non-Patent Document 4, a 2-degree-of-freedom _H∞ control system using feedforward control is applied to the AFM in contrast to the conventional method that is only feedback control, that is, a one-degree-of-freedom control system. Measurement error is suppressed and high-speed scanning of AFM is realized.

"First nanoprobe technology", Industrial Research Committee (2001) “Robust control approach to atomic force microscopy”, Conf. Decision Contr. , P. 3443-3444 (2003) “On automatic atomic force microscopes: An adaptive control approach”, Conf. Decision Contr. , P. 1574-1579 (2004) “Robust two-degree-of-freedom control of an atomic force microscope”, Asian Journal of Control, 6, 2, p. 156-163 (2004) “Motion control for advanced mechatronics”, IEEE / ASME Trans. Mechatronics, 1, 1, p. 56-67 (1996) “Introduction to Physical Chemistry”, Baifukan (1972) “Harmonic analysis based modeling-mode AFM”, Amer. Control Conf. , P. 232-236 (1999)

  However, these are attempts to improve the feedback characteristics by frequency shaping or adaptive control. Therefore, due to constraints inherent in the feedback control system such as the resonance characteristics of the plant, the sampling frequency, the integration integral of the Bode, etc., The band is inevitable.

  The present invention has been made to solve the above-described problems of the conventional advanced control used in the AFM. The present invention applies an estimation mechanism (see Non-Patent Document 5) using a disturbance observer, which has been used for motion control, to the AFM. Accordingly, it is an object of the present invention to provide a high-band AFM by making it possible to estimate the surface shape of an object measured by the AFM with high accuracy, relieving restrictions imposed on the feedback control system. .

In order to solve the above-mentioned problems, the invention of claim 1 is a high-band atomic force microscope apparatus for estimating the surface shape of the sample surface, and has a probe that interacts with the sample surface via the atomic force. And a cantilever that is deflected by an interatomic force and is distorted by a frictional force, a laser beam providing means that makes the first laser beam incident on the cantilever, and the cantilever is emitted by reflecting the first laser beam. By inputting the input voltage to the piezo, the distance between the sample surface and the probe so that the displacement of the cantilever is constant, and the light detection means for detecting the second laser light, the piezo on which the sample is placed, and the cantilever A controller that controls and detects the deflection and distortion of the cantilever from the relative change in the intensity of the second laser light as an output voltage, and estimates the surface shape of the sample surface from the output voltage, and the estimated surface shape And a data storage means for recording, the controller that inputs the input voltage and the output voltage, the surface shape of the resulting sample surface from the output voltage is regarded as a disturbance observer, and to estimate the surface shape of the sample surface Is a high-band atomic force microscope apparatus characterized by

The invention of claim 2 is a high-band atomic force microscope apparatus for estimating the surface shape of the sample surface, having a probe that interacts with the sample surface via the atomic force, and is deflected by the atomic force. A cantilever that is distorted by a frictional force, a laser beam providing means that makes the first laser beam incident on the cantilever, and a second laser beam that is emitted when the cantilever reflects the first laser beam. The distance between the sample surface and the probe is controlled by inputting an input voltage to the piezo so that the displacement of the cantilever is constant, and the second laser beam. A controller that detects the deflection and distortion of the cantilever as an output voltage from the relative change in intensity of the sample and estimates the surface shape of the sample surface from the output voltage, and a data storage means that records the estimated surface shape The provided, the controller, characterized in that a zero input voltage, the output voltage and the input, the surface shape of the sample surface obtained from the output voltage is regarded as disturbance observer estimates the surface shape of the sample surface by an open loop scheme And

The invention of claim 3 is a high-band atomic force microscope apparatus for estimating the surface shape of the sample surface, having a probe that interacts with the sample surface via the atomic force, and is bent by the atomic force. A cantilever that is distorted by a frictional force, a laser beam providing means that makes the first laser beam incident on the cantilever, and a second laser beam that is emitted when the cantilever reflects the first laser beam. The distance between the sample surface and the probe is controlled by inputting an input voltage to the piezo so that the displacement of the cantilever is constant, and the second laser beam. A controller that detects the deflection and distortion of the cantilever as an output voltage from the relative change in intensity of the sample and estimates the surface shape of the sample surface from the output voltage, and a data storage means that records the estimated surface shape The provided, the controller inputs the input voltage and the output voltage, the surface shape of the sample surface obtained from the output voltage is regarded as disturbance observer, sample by a closed loop system for an independent open-loop and feedback loop the disturbance observer The surface shape of the surface is estimated.

According to a fourth aspect of the present invention, in the high-band atomic force microscope apparatus according to any one of the first to third aspects, the light detection means is a quadrant photodiode.

According to a fifth aspect of the present invention, in the high-band atomic force microscope apparatus according to any one of the first to fourth aspects, the laser beam providing means is a visible light semiconductor laser.

  According to the present invention, in a closed loop system, a surface shape observer (STO) that is a disturbance observer for estimating the surface shape of an object measured by AFM is realized by an open loop independent of a feedback loop, and the AFM according to the present invention. This band does not affect the stability of the closed-loop system, so that it is possible to provide an AFM with a higher band than the feedback control system.

(Embodiment 1)
FIG. 1 shows a schematic diagram of an AFM 100 according to the present invention as an example. In FIG. 1, the AFM 100 employs an optical lever method, and scans a probe 102 attached to a cantilever 101 along a sample surface 103, and an atomic force acting between the sample surface 103 and the probe 102. By measuring the deflection of the cantilever 101 and the distortion due to the frictional force, the structure of the sample surface 103 is measured at the nanoscale.

  In the AFM 100 shown in FIG. 1, the laser beam 104 is incident on the back surface of the cantilever 101 obliquely by the laser beam providing unit 110. Then, the change in the reflection angle of the laser beam 104 due to the displacement caused by the deflection and distortion of the cantilever 101 is detected from the relative change in the intensity of the laser beam 106 incident on the quadrant photodiode 105. Finally, the AFM 100 can detect the deflection and distortion of the cantilever 101 from the relative change in the intensity of the laser beam 106 and measure the structure of the sample surface 103.

  Note that the mode shown here is merely an example, and the device for detecting the relative change in the intensity of the laser beam 106 is not limited to the quadrant photodiode, and is a light detection capable of detecting the relative change in the intensity of the laser beam. Any means may be used. Further, as the laser beam providing means 110, for example, a visible light semiconductor laser can be used.

  In the AFM 100 shown in FIG. 1, when the conventional open loop method is adopted, the AFM 100 converts the output voltage y (t) at the time t from the quadrant photodiode 105 as it is and converts the output of the sample surface 103. The surface shape d (t) is recorded in the data storage unit 109. In the AMF 100 shown in FIG. 1, when the conventional open loop method is adopted, a controller that controls the Z axis of the piezo 107 (axis perpendicular to the sample surface on the piezo) so that the displacement of the cantilever 101 is constant. The input voltage u (t) at 108 time t (drive voltage to the piezo 107) is converted and recorded in the data storage means 109 as the surface shape d (t) of the sample surface 103.

  The invention according to Embodiment 1 adopts a new open-loop method and a new closed-loop method that are improved by using a control that applies an estimation mechanism by a disturbance observer over the conventional open-loop method and the conventional closed-loop method. Provided is an AFM having a higher bandwidth than a feedback control system. This makes it possible to estimate the surface shape of the sample surface 103 with higher accuracy than in the prior art.

  Hereinafter, modeling of a control target in the AFM according to the first embodiment will be described in detail. Note that the parameter group used in the following modeling is merely an example, and the first embodiment is not limited by these parameter groups.

(Force curve)
FIG. 2 shows a function of the distance R between the probe 102 and the sample surface 103 and the force N acting on the probe 102 before and after bringing the probe 102 shown in FIG. 1 into contact with the sample surface 103. It is a graph called a force curve. A state 201 represents that the probe 102 jumps to and adsorbs to the sample surface 103 at a certain point when the probe 102 is brought close to the sample surface 103. Thereafter, the state changes from attractive force to repulsive force in state 202, and in state 203, the probe 102 jumps away from the sample surface 103 (see Non-Patent Document 1).

  3 and 4, the states 201 to 203 can be confirmed from another viewpoint as follows. Here, immediately before the short needle 102 contacts the sample surface 103, a mountain-shaped voltage as shown in FIG. 3 is input to the Z-axis of the fine movement piezo 107, and the cantilever 101 detected from the quadrant photodiode 105. The response voltage of the deflection (FIG. 4) was measured. In FIG. 4, a small jump 401 of a voltage near 4.5 [seconds] that occurs when the probe 102 approaches the sample surface 103 corresponds to the state 201, and 16 [ A large jump 403 in the vicinity of [second] corresponds to the state 203. In the region 402 where the output voltage is saturated at −0.15 [V] or more, the probe 102 is adsorbed to the sample surface 103 at this point in time as in the state 202, and the laser beam 106 is divided into four parts. This means that the light has gone out of the sensing range of the photodiode 105.

  As described above, the reason why the force acting between the probe 102 and the sample surface 103 is switched to the attractive force and the repulsive force can be explained using the Lennard-Jones potential (LJ potential). The LJ potential will be described in detail in the next section.

(LJ potential)
As described in Non-Patent Document 6, the force acting on the probe 102 from the sample surface 103 is expressed by a typical LJ potential of the following equation.

ε represents the strength of the force, and σ represents the size of the atom. As described in Non-Patent Document 6, n is assumed to be an integer of 9 or more and 15 or less, but it is generally n because the exponents of both terms form a simple ratio of 2: 1. = 12 is used. FIG. 5 is a graph obtained by normalizing the expression (1). An important characteristic of the LJ potential is a strong repulsive force where the distance R is small (the first term in Equation (1)) and a weak attractive force where R is large (the second term in Equation (1)). As will be described later with reference to FIG. 6, the LJ potential is the dynamics of a long spring 601 (weak attractive force) having a negative spring coefficient -k _2a and a short spring 602 (strong repulsive force) having a large positive spring coefficient k _2b. It can be expressed as a system.

Further, as described in Non-Patent Document 7, a piecewise linear model of the interaction force acting between the cantilever 101 and the sample surface 103 can be illustrated as shown in FIG. In FIG. 6, the acting force from the cantilever 101 is expressed as a dynamic system in which a spring having a positive spring coefficient k ₁ bonded to a wall 604 is connected to the probe 102 (mass m) of the cantilever 101. Has been. In FIG. 6, a frictional force generation source 605 having a coefficient b is connected to the probe 102, and the displacement of the cantilever 101 is, as will be described later,

It is represented by

5 and 6, r ₁ represents the distance at which attractive force works, and r ₂ represents the distance from the probe 102 of the cantilever 101 to the sample surface 103.

(Contact mode)
AFM measurement uses a non-contact mode in which the probe is not in contact with the sample surface, a contact mode in which the probe is in contact with the sample surface, and periodically contacts the sample surface by vibrating the probe. There is a tapping mode. In the first embodiment, modeling is performed using the most basic contact mode. In the case of an ideal contact mode, since the first term of the formula (1) is dominant, the acting force from the sample surface 103 can be regarded as only repulsive force. Therefore, since the length of the spring in contact with the sample surface 103 is a natural length, as shown in FIG. 7, the natural length of the spring 603 is _{La 0} , and the spring 701 in which the spring 601 and the spring 602 are combined is used. When the spring coefficient is k ₂ , the natural length is L _b0 , the length of the spring 603 at time t is L _a (t), and the length of the spring 701 at time t is L _b (t), the mass is m. The equation of motion of the probe 102 of the cantilever 101 is as shown in the following equation (2). In FIG.

Is the displacement distance by the operation in the Z-axis direction with respect to the piezo 107,

Represents the surface shape of the sample surface 103. F (t) indicates the force that the probe 102 receives from the spring 701, that is, the atomic force that the probe 102 receives from the sample surface 103.

The length L _b (t) of the spring 701 is

It is. However,

Is the displacement distance due to the operation of the piezo 107 in the Z-axis direction,

Represents the surface shape of the sample surface 103. L _a0 −L _a (t) is the displacement of the cantilever 101

Because

Substituting into Equations (2) and (4),

When equation (5) is transformed using Laplace transform

From equation (6), the plant transfer function is

Assuming that the surface shape of the sample surface 103 is the input end disturbance

It became clear that it can be considered. In the first embodiment, the displacement distance due to the operation of the piezo 107 in the Z-axis direction with respect to the input voltage u [V].

The ratio of [m] is 3.36 [nm / V], and the displacement of the cantilever 101

[M] is converted into an output voltage y [V] using the laser beam 106 and the four-division photodiode 105. The plant transfer function including the conversion coefficient and the amplifier gain is defined as follows by multiplying the constant gain g in the equation (6).

Based on the above, the plant transfer function of the AFM used in this paper is an identification experiment in which a voltage is input to the Z-axis of the fine piezo 107 and the response voltage of the deflection of the cantilever 101 detected from the quadrant photodiode 105 is measured. Formula (8) was used.

The Bode diagram of this identified plant is as shown in FIGS.

  Hereinafter, the design of the control system in the AFM according to the first embodiment will be described in detail.

(Controller design)
First, a controller for the identified model is designed. The controller 108 with a bandwidth of 300 Hz was designed taking into account the 3000 Hz resonance mode of the plant. The controller 108 estimates the surface shape of the sample surface 103 as described below.

  The sensitivity function S (s) and the complementary sensitivity function T (s) are obtained from C (s) and P (s) as follows.

The sensitivity function S (s) is shown in FIGS. 10 and 11, and the complementary sensitivity function T (s) is shown in FIGS. The complementary sensitivity function T (s) is a plant transfer function from the surface shape d of the sample surface 103 of the closed loop system to the input voltage u used for imaging.

(Design of surface shape observer (STO))
From the above-described modeling, it has become clear from Equation (6) that the surface shape 1401 of the sample surface 103 can be regarded as the input end disturbance d (t) at time t as shown in FIG. It is possible to introduce a new disturbance observer that estimates (t) by the disturbance observer theory (see Non-Patent Document 5). In the present invention, this special disturbance observer is named a surface shape observer (STO). Estimated surface shape of sample surface 103 from input voltage u and output voltage y

Can be obtained by the STO 1400 shown in FIG. STO1400 is plant transfer function (equation (8)), the inverse model of the nominal plant (equation (10)), and cut the low-pass filter off frequency omega _c (formula (11)) is used to estimate the surface shape. Specifically, as shown in FIG. 14, d (t) can be estimated by subtracting U (t) from the signal obtained by multiplying the output signal y (t) by Expression (10). Furthermore, in order to reduce the influence of the measurement noise expanded by Expression (10), an estimated value is obtained using Expression (11).

Note that the subscript n represents the nominalization of each parameter.

  As shown in FIG. 18, a method of obtaining an output 1802 using the STO 1400 in the estimation block 1800 of the open loop system is referred to as a new open loop method. However, in the estimation block 1800, the input voltage u is set to 0, the position where the probe 102 contacts the sample surface 103 and the cantilever 101 is bent is set as the origin of the output voltage y. In FIG. 18, r represents the coordinates of the location where the probe 102 is located on the sample surface 103.

  Here, the method of obtaining the output 1801 from the estimation block 1800 is referred to as the conventional open loop method, as in the prior art.

  Normally, the bandwidth of the entire closed loop system is limited by the Nyquist frequency. However, in the first embodiment, as shown in FIG. 19, in the estimation block 1900, the STO 1400 is realized as an open-loop disturbance observer independently of the feedback loop 1901. Therefore, the entire estimation block 1900 is a closed-loop system, but the estimation by the STO 1400 is not included in the closed-loop system created by the feedback loop 1901. Therefore, there is an advantage that the bandwidth of the entire closed-loop system can be further increased. A method of obtaining the output 1902 from this new closed loop system is called a new closed loop method. Here, as an example, the band of the new closed loop system is 2000, but the present invention is not limited to the value of the band of the new closed loop system. The frequency response of the new closed-loop disturbance observer is

It becomes. The Bode diagram of Q (s) is shown in FIGS.

  In FIG. 19, the method of obtaining the output 1903 from the estimation block 1900 is referred to as a conventional closed loop method, as in the prior art.

  Hereinafter, the performance of the control system in the AFM according to the first embodiment will be verified by simulation.

  FIG. 18 is a block diagram of the STO in the open loop system, and FIG. 19 is a block diagram of the STO in the closed loop system. In the open loop system, no signal is input to the Z-axis piezo, and in the closed loop system, the position where the probe touches and the cantilever bends slightly is the origin of y (t), so the target value in each system is 0. And In the conventional method, the output voltage y (t) is measured as the surface shape of the sample in the open loop system and the input voltage u (t) is measured in the open loop system. However, since the surface shape and the input voltage u (t) have opposite signs, -u (t) is recorded as the output voltage of the conventional closed loop method at the time of measurement.

  FIG. 20 is a diagram illustrating a result of simulating an output voltage when the AFM according to the first embodiment employs an open loop method and scans a rectangular wave sample surface. The conventional open loop method of FIG. 20 shows the result of simulating the output 1801 according to the block diagram of FIG. The new open loop method of FIG. 20 shows the result of simulating the output 1802 according to the block diagram of FIG.

  FIG. 21 is a diagram illustrating a result of simulating an output voltage when the AFM according to the first embodiment employs an open loop method and scans a sine wave sample surface. The conventional open loop method of FIG. 21 shows the result of simulating the output 1801 according to the block diagram of FIG. The new open loop method of FIG. 21 shows the result of simulating the output 1802 according to the block diagram of FIG.

  FIG. 22 is a diagram illustrating a result of simulating an output voltage when the AFM according to the first embodiment employs a closed-loop method and scans a rectangular wave sample surface. The conventional closed loop system of FIG. 22 shows the result of simulating the output 1903 according to the block diagram of FIG. The new closed loop method of FIG. 22 shows the result of simulating the output 1902 according to the block diagram of FIG.

  FIG. 23 is a diagram illustrating a result of simulating an output voltage when the AFM according to the first embodiment employs a closed loop method and scans a sine wave sample surface. The conventional closed loop system of FIG. 23 shows the result of simulating the output 1903 according to the block diagram of FIG. The new closed loop method of FIG. 22 shows the result of simulating the output 1902 according to the block diagram of FIG.

  FIG. 24 is a diagram illustrating a result of simulating an output voltage when the AFM according to the first embodiment scans a rectangular wave sample surface with the distance R constant. The new open loop method of FIG. 24 shows the result of simulating the output 1802 according to the block diagram of FIG. The new closed loop method of FIG. 24 shows the result of simulating the output 1902 according to the block diagram of FIG.

  FIG. 25 is a diagram illustrating a simulation result of an output voltage when the AFM according to the first embodiment scans the sample surface of a sine wave with the distance R being constant. The new open loop method of FIG. 25 shows the result of simulating the output 1802 according to the block diagram of FIG. The new closed loop method of FIG. 25 shows the result of simulating the output 1902 according to the block diagram of FIG.

  Note that the displacement distance due to the operation of the piezo in the Z-axis direction in the simulation whose simulation results are shown in FIGS. 24 and 25 is 3.36 [nm / V].

  The frequency response of the conventional open loop system is shown in FIGS. 8 and 9 which are Bode diagrams of the plant from y (s) / d (s) = P (s). When the step-shaped surface shape is given as the disturbance signal d, the resonance mode of the plant is excited, and therefore, as shown in FIG. The performance is inferior.

  The frequency response of the conventional closed loop system is a complementary sensitivity function of the system shown in FIGS. 10 and 11 from u (s) / d (s) = T (s). For this reason, in the conventional closed loop system, the band is limited to 300 Hz, resulting in a delay of about 3 ms as shown in FIG. This means that it cannot follow the rapid change in the surface shape of the sample surface 103, and the image measured by the AFM becomes unclear. Regardless of whether the STO frequency response is open loop or closed loop

As shown in FIG. 15 and FIG. Since the observer is designed with a bandwidth of 2000 Hz, as shown in FIG. 22, the new closed loop method is delayed by about 0.5 ms from the target value, which is a result that is far superior to the conventional closed loop method. It is. From the above, it can be concluded that both the new open loop method and the new closed loop method have advantages over the conventional type.

One problem here is the difference between the new open-loop method and the new closed-loop method. One of the criteria for judging this difference is the distance R between the sample surface 103 and the probe 102. As shown in FIG. 5, the slope of the repulsive portion of the LJ potential is not a linear slope. This point is not considered in the modeling process according to the first embodiment. However, in practice, depending on the distance R, the slope of the repulsive part of the LJ potential, that is, the value of k ₂ in the equation (7) changes depending on the distance R. Therefore, the feature of the model according to the first embodiment appears when the sample surface 103 is scanned while keeping the distance R as constant as possible. The distance R is represented by the length of the spring _{k 2 L} b (t). Deviation from the initial value of R

Then, from equation (4),

It becomes.

  FIG. 24 illustrates an AFM according to the first embodiment.

Is a diagram showing the result of simulating the output voltage when scanning the sample surface 103 of a rectangular wave.

  FIG. 25 illustrates an AFM according to the first embodiment.

Is a diagram showing the result of simulating the output voltage when scanning the surface of a sine wave sample with a constant value.

  As shown in FIG. 25, the new closed-loop system is better than the new open-loop system.

From the fact that is small, it can be seen that there is an advantage.

  Hereinafter, experimental results obtained by actually using the AFM of Embodiment 1 will be described.

(Signal input to the piezo Z axis)
Here, a pseudo disturbance signal d (t) is applied by applying a signal to the Z-axis of the piezo 107 while the probe 102 is in contact with the sample surface 103 and fixed at one point on the sample surface 103 without scanning. In other words, the result of measuring the output voltage using the AFM according to the first embodiment after creating the surface shape of the sample surface 103 will be described.

  FIG. 26 is a diagram illustrating an output voltage when the AFM according to the first embodiment employs an open loop method and scans a rectangular wave sample surface. The conventional open loop method of FIG. 26 shows the result of measuring the output 1801 in the block diagram of FIG. 26 shows the result of measuring the output 1802 in the block diagram of FIG.

  FIG. 27 is a diagram illustrating an output voltage when the AFM according to the first embodiment employs an open loop method and scans a sine wave sample surface. The conventional open loop method of FIG. 27 shows the result of measuring the output 1801 in the block diagram of FIG. The new open loop method of FIG. 27 shows the result of measuring the output 1802 in the block diagram of FIG.

  FIG. 28 is a diagram illustrating an output voltage when the AFM according to the first embodiment employs a closed loop method and scans a rectangular wave sample surface. The conventional closed loop system of FIG. 28 shows the result of measuring the output 1903 in the block diagram of FIG. The new closed loop system of FIG. 28 shows the result of measuring the output 1902 in the block diagram of FIG.

  FIG. 29 is a diagram illustrating an output voltage when the AFM according to the first embodiment employs a closed loop method and scans a sine wave sample surface. The conventional closed loop method of FIG. 29 shows the result of measuring the output 1903 in the block diagram of FIG. The new closed loop method of FIG. 29 shows the result of measuring the output 1902 in the block diagram of FIG.

  Similar to the simulation results shown in FIG. 20 and FIG. 22, from the results shown in FIG. 26 and FIG. 28, even when the AFM according to the first embodiment is actually operated, It can be concluded that both the new closed-loop method have advantages over the conventional type. However, unlike the simulation results shown in FIG. 21, from the results shown in FIG. 27, when the AFM according to the first embodiment is actually operated using the open loop method, A phenomenon that does not partially follow the surface shape of the sine wave sample surface occurs. This represents a drawback of the open loop method that cannot follow the surface shape of the large sample surface.

  FIG. 30 illustrates an AFM according to the first embodiment.

Is a diagram showing an output voltage when the sample surface 103 of a rectangular wave is scanned with a constant value. The new open loop method of FIG. 30 shows the result of measuring the output 1802 in the block diagram of FIG. The new closed loop method of FIG. 30 shows the result of measuring the output 1902 in the block diagram of FIG.

  FIG. 31 is a diagram illustrating an AFM according to the first embodiment.

Is a diagram showing an output voltage when a sample surface of a sine wave is scanned with a constant value. The new open loop method of FIG. 31 shows the result of measuring the output 1802 in the block diagram of FIG. The new closed loop method of FIG. 31 shows the result of measuring the output 1902 in the block diagram of FIG.

  As shown in FIGS. 30 and 31, since the output voltage is small, the superiority of the new closed loop system can be confirmed.

(Observation of n-Si)
FIG. 32 is a diagram illustrating an image obtained by scanning the n-Si substrate using the conventional open loop method in the AFM according to the first embodiment. FIG. 33 is a diagram illustrating an image obtained by scanning the n-Si substrate using the new open loop method in the AFM according to the first embodiment. FIG. 34 is a diagram illustrating an image obtained by scanning the n-Si substrate using the conventional closed loop method in the AFM according to the first embodiment. FIG. 35 is a diagram illustrating an image obtained by scanning the n-Si substrate using the new closed-loop method in the AFM according to the first embodiment.

  32 to 35 show images obtained by using the n-Si substrate having a roughness of about several nm on the surface as a sample to be scanned in the AFM according to the first embodiment. The image has a range of 100 nm × 100 nm. As shown in FIGS. 32 and 33, the AFM that employs the open loop method cannot follow the surface shape of the sample surface, and it is impossible to appropriately image the scanning target. However, the AFM employing the closed loop method can follow the surface shape of the sample surface, and can appropriately image the scanning target. Furthermore, as shown in FIG. 35, the AFM that employs the new closed loop method according to the first embodiment is based on images imaged by the AFM that employs the open loop method shown in FIGS. 32 and 33. However, the object to be scanned can be clearly imaged. Thereby, it can be said that the new closed loop method according to the first embodiment is superior to the conventional method in imaging the sample surface by actual AFM.

(Embodiment 2)
Hereinafter, the design of the atomic force observer (AFO) in the AFM of the second embodiment will be described in detail.

  In the formula (3), the atomic force that the cantilever 101 receives from the sample surface 103 is defined. AFO is a method for estimating the atomic force F (t) from the output voltage y based on the same concept as the STO described above. By substituting equation (a) into equation (2) and performing Laplace transform on both sides, the following equation is obtained.

A disturbance observer is designed using this equation. As with STO, the AFO is composed of an inverse model of the nominal plant P _n2 (s) and a low-pass filter having a cutoff frequency ω _c2 . A block diagram of the AFO is shown in FIG.

It is a figure which shows the outline of the atomic force microscope apparatus (AFM) which concerns on this invention. It is a figure which shows a force curve. It is a figure which shows an input voltage. It is a figure which shows an output voltage. It is a figure which shows a Lennard-Jones potential (LJ potential). It is a figure which shows the interaction force which acts between a probe and a sample surface. It is a figure which shows the interaction force which acts between the probe based on contact mode and a sample surface. It is a figure which shows a Bode diagram. It is a figure which shows a Bode diagram. It is a figure which shows a sensitivity function. It is a figure which shows a sensitivity function. It is a figure which shows a complementary sensitivity function. It is a figure which shows a complementary sensitivity function. It is a block diagram of a surface shape observer (STO). It is a figure which shows the frequency response of Q (s) in STO. It is a figure which shows the frequency response of Q (s) in STO. It is a block diagram of an atomic force observer (AFO). It is a block diagram by the open loop system of STO. It is a block diagram by the closed loop system of STO. In the AFM according to the first embodiment, it is a diagram illustrating a result of simulating an output voltage when an open loop method is employed and a sample surface of a rectangular wave is scanned. In the AFM according to the first embodiment, it is a diagram illustrating a result of simulating an output voltage when an open loop method is employed and a sine wave sample surface is scanned. FIG. In the AFM according to the first embodiment, it is a diagram illustrating a result of simulating an output voltage when a closed-loop method is employed and a sample surface of a rectangular wave is scanned. In the AFM according to the first embodiment, it is a diagram illustrating a result of simulating an output voltage when a closed-loop method is employed and a sine wave sample surface is scanned. FIG. In the AFM according to the first embodiment, it is a diagram showing the result of simulating the output voltage when scanning the sample surface of the rectangular wave. In the AFM according to the first embodiment, it is a diagram showing the result of simulating the output voltage when scanning the sample surface of a sine wave. In the AFM according to the first embodiment, it is a diagram illustrating an output voltage when an open loop method is employed and a sample surface of a rectangular wave is scanned. In the AFM according to the first embodiment, it is a diagram illustrating an output voltage when an open loop method is employed and a sample surface of a sine wave is scanned. In the AFM according to the first embodiment, the closed loop method is employed and the output voltage when the sample surface of the rectangular wave is scanned is shown. In the AFM according to the first embodiment, it is a diagram illustrating an output voltage when a closed-loop method is employed and a sample surface of a sine wave is scanned. In the AFM according to the first embodiment, it is a diagram illustrating an output voltage when a sample surface of a rectangular wave is scanned. FIG. 6 is a diagram illustrating an output voltage when a sine wave sample surface is scanned in the AFM according to the first embodiment. FIG. 4 is a diagram illustrating an image obtained by scanning an n-Si substrate using a conventional open loop method in the AFM according to the first embodiment. FIG. 3 is a diagram showing an image obtained by scanning the n-Si substrate using the new open loop method in the AFM according to the first embodiment. FIG. 6 is a diagram illustrating an image obtained by scanning an n-Si substrate using the conventional closed loop method in the AFM according to the first embodiment. FIG. 4 is a diagram illustrating an image obtained by scanning the n-Si substrate using the new closed loop method in the AFM according to the first embodiment.

Explanation of symbols

100 AFM
101 Cantilever 102 Probe 103 Sample surface 104 Laser light 105 Quadrant photodiode 106 Laser light 107 Piezo 108 Controller 109 Data storage means

Claims (5)

A high-band atomic force microscope that estimates the surface shape of a sample surface,
A cantilever having a probe that interacts with the sample surface via an interatomic force, deflected by the interatomic force, and distorted by a frictional force;
A laser beam providing means for entering the first laser beam toward the cantilever;
A light detection means for detecting a second laser light emitted by the cantilever reflecting the first laser light;
Piezo on which the sample is placed;
As the displacement of the cantilever becomes constant, the distance between the probe and the sample surface is controlled by inputting an input voltage to the piezo, from said relative change in the intensity of the second laser beam A controller that detects the deflection and distortion of the cantilever as an output voltage, and estimates a surface shape of the sample surface from the output voltage;
Data storage means for recording the estimated surface shape ,
The controller receives the input voltage and the output voltage, and regards the surface shape of the sample surface obtained from the output voltage as a disturbance observer, and estimates the surface shape of the sample surface. Band atomic force microscope. A high-band atomic force microscope that estimates the surface shape of a sample surface,
A cantilever having a probe that interacts with the sample surface via an interatomic force, deflected by the interatomic force, and distorted by a frictional force;
A laser beam providing means for entering the first laser beam toward the cantilever;
A light detection means for detecting a second laser light emitted by the cantilever reflecting the first laser light;
Piezo on which the sample is placed;
The distance between the sample surface and the probe is controlled by inputting an input voltage to the piezo so that the displacement of the cantilever is constant, and the relative change in the intensity of the second laser light is A controller that detects the deflection and distortion of the cantilever as an output voltage, and estimates a surface shape of the sample surface from the output voltage;
Data storage means for recording the estimated surface shape,
The controller estimates the surface shape of the sample surface by an open loop method, assuming that the input voltage is zero, the output voltage is an input, the surface shape of the sample surface obtained from the output voltage is regarded as a disturbance observer A high-band atomic force microscope apparatus characterized by that . A high-band atomic force microscope that estimates the surface shape of a sample surface,
A cantilever having a probe that interacts with the sample surface via an interatomic force, deflected by the interatomic force, and distorted by a frictional force;
A laser beam providing means for entering the first laser beam toward the cantilever;
A light detection means for detecting a second laser light emitted by the cantilever reflecting the first laser light;
Piezo on which the sample is placed;
The distance between the sample surface and the probe is controlled by inputting an input voltage to the piezo so that the displacement of the cantilever is constant, and the relative change in the intensity of the second laser light is A controller that detects the deflection and distortion of the cantilever as an output voltage, and estimates a surface shape of the sample surface from the output voltage;
Data storage means for recording the estimated surface shape,
The controller receives the input voltage and the output voltage, regards the surface shape of the sample surface obtained from the output voltage as a disturbance observer, and makes the disturbance observer an open loop independent of a feedback loop. A high-band atomic force microscope apparatus characterized by estimating a surface shape of the sample surface by a method . 4. The high-band atomic force microscope apparatus according to claim 1, wherein the light detection means is a quadrant photodiode . The high-band atomic force microscope apparatus according to any one of claims 1 to 4, wherein the laser beam providing means is a visible light semiconductor laser .

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