JP5077938B2 - Atomic force microscope - Google Patents

Description

  The present invention relates to an atomic force microscope apparatus.

  In the precision measurement field, there is a scanning probe microscope (SPM) as one of the measuring devices having the highest resolution. As a pioneer of SPM, Scanning Tunneling Microscope (STM) was developed in 1932 by Vinich et al. The STM controls the position so that the tunnel current flowing through the tip of the cantilever and the sample surface is constant, and measures the surface shape of the sample using the feedback signal.

  With the advent of STM, high-resolution measurements that are incomparable to conventional ones became possible, which was the reason for winning the Nobel Prize in Physics in Binig.

  However, since STM requires measurement of tunnel current, there is a problem that measurement with an insulator sample is impossible.

  An atomic force microscope (AFM) invented four years after the birth of SPM has solved this problem. The AFM measures various forces acting between the tip of the cantilever and the sample surface from the displacement of the tip of the cantilever. Since force always acts between two adjacent objects, there is no restriction on the sample in AFM in principle (Non-patent Document 1).

  The AFM is a high-performance instrument that performs high-precision measurement, and various efforts have been made recently.

  For example, a counter balance method and an active damping method (Non-Patent Documents 2 and 3) for quickly driving a z-direction driven piezo element, a method for feedforward compensation of shift mode or line-by-line information (Non-Patent Document 4), Control of the Q value of the cantilever has been reported (Non-Patent Document 5).

“Scanning Probe Microscope and Local Spectroscopy”, Kanamebo (2005) Rev. Sci. Instrum. , 76,053708 (2005) Proc. Natl. USA. Sci. USA, 98, 12468 (2001) “Robust Two-Degree-of-Freedom Control of an Atomic Force Microscope”, Asian Journal of Control, Vol. 6, no. 2, p. 156-163 (2004) Phys. Rev. Lett. 90,046808 (2003) “PLINCIPLE OF PHYSICAL CHEMISTRY”, Putman Books Limited (1982) “Research on Fabrication and Control of Nanoscale Servo Devices for Atomic Force Microscope”, Institute of Electrical Engineers of Japan, IIC-06-132, p. 1-6 (2006) “Robust Control Approach to Atomic Force Microscopy”, Conf. Decision Contr. , P. 3443-3444 (2003) “Introduction to Power Electronics”, Asakura Shoten (2001)

  However, most of the AFMs are classical such as PID control, and mounting by analog circuits is the mainstream. On the other hand, in most of the current industrial equipment, digital control is applied, resulting in a significant performance improvement. There is also no tapping mode AFM having a control system designed based on a model using digital control.

In order to solve the above-described problems, an atomic force microscope apparatus according to the present invention is an atomic force microscope apparatus that images a surface shape of a sample surface in a tapping mode, and is configured to interact with the sample surface via an atomic force. The tip of the cantilever that acts, bends due to the interatomic force, and is distorted due to the frictional force, the laser beam providing means that makes the first laser beam incident on the cantilever, and the cantilever reflects the first laser beam A light detecting means for detecting the emitted second laser light, a piezo on which the sample is placed, a control means for controlling the piezo so as to scan the sample while keeping the atomic force constant, and a second laser light. The deflection and distortion of the tip of the cantilever from the intensity of the output as the output voltage, demodulating the output voltage modulated by the atomic force, demodulated by the demodulation means The output voltage, the operation of the distal end of the cantilever by averaging the operation of the distal end of the attraction regions and the repulsive force region of the cantilever is converted to linearize, from the converted output voltage, the surface topography observer An estimation means for estimating the surface shape of the sample surface and a data storage means for recording the estimated surface shape are provided.

  According to the present invention, it is possible to provide a tapping mode AFM with improved observation accuracy.

Embodiments according to the present invention will be described below. Embodiment described here is an example to the last, and this invention does not receive any restriction | limiting by the following embodiment.
Among the units used in the description of the present embodiment, 1 μm is 1 × 10 ⁻⁶ m (meter), and 1 nm is 1 × 10 ⁻⁹ m.

(Embodiment)
(Measurement by tapping mode AFM)
The measurement method in AFM is roughly classified into two called contact mode and dynamic force mode. Both differ in the detection method of atomic force, but the other is the same.

  A sample is mounted on the scanner and is operated in three directions xyz along the shape of the sample surface. The driving force is a piezo element, and has nanoscale driving resolution.

  The xy direction is controlled only by feedforward. On the other hand, the z direction is closed.

In the contact mode described above, the shape of the sample surface is measured in a state where the sample surface is in contact with the tip of the cantilever or the tip of the cantilever and the sample surface are dragged.
In the contact mode, it is known that the sample surface is always in contact with the tip of the cantilever, and the contact force is larger than that in the dynamic force mode, so that the sample surface is damaged. For this reason, the contact mode is not suitable for measurement of a plastic sample typified by a biological sample.

  The dynamic force mode, which is another measurement method, will be described.

  The dynamic force mode uses the fact that the amplitude, frequency, and phase of the tip of the cantilever change due to deflection due to atomic force and distortion due to frictional force when approaching the sample surface while the tip of the cantilever oscillates. Then, the shape of the sample surface is measured from these changes.

  In the dynamic force mode, a method in which the tip of the cantilever measures the change in amplitude while hitting the sample surface periodically is called a tapping mode. Further, in the dynamic force mode, a method of measuring a change in frequency at the tip of the cantilever while the sample surface and the tip of the cantilever are in non-contact is called a non-contact mode. In order to clearly distinguish the difference in control method, the tapping mode AFM may be referred to as AM-AFM, and the non-contact mode AFM may be referred to as FM-AFM.

  In the present embodiment, an invention related to a tapping mode AFM is disclosed. In the tapping mode AFM, the contact force between the tip of the cantilever and the sample surface is small, and it can be observed by imaging the shape of the sample surface with high measurement accuracy.

  FIG. 1 is a diagram showing a tapping mode AFM measurement method. First, the cantilever tip 104 is oscillated to periodically contact the sample surface 120 with the cantilever tip 104. Here, an oscillation piezo element 101 provided at the rear end of the cantilever 103 is compensated by a DDS (direct digital synthesizer) 102 to compensate for vibration attenuation due to internal friction. Drive at several hundred kHz). In the tapping mode AFM, the laser beam providing means 107 irradiates the tip 104 of the cantilever with an LD (laser beam) 105. The tapping mode AFM measures the displacement of the cantilever tip 104 by receiving light reflected from the tip 104 of the cantilever with a PD (photodiode) 106.

  Here, for example, a quadrant photodiode may be used as the photodiode which is a light detection means of the laser beam. Further, a visible light semiconductor laser may be used as the laser light providing means.

  The signal measured by the PD 106 is AM-modulated by an atomic force described later. First, a signal measured by the PD 106 passes through a BPF (band pass filter) 108. Next, in order to demodulate the signal measured by the PD 106, the signal measured by the PD 106 is converted into an effective value by the RMS-DC 109. In this embodiment, this effective value is regarded as an atomic force.

  In order to perform scanning while keeping the obtained atomic force constant, the controller 110 drives the z-direction drive piezo element (z-scanner) 111 on the base of the sample by feedback control. The control input at this time is given so as to cancel the interatomic force received from the surface shape. The surface shape is obtained by taking it out and imaging it, and the surface shape data is stored in the data storage means 116.

  Here, the scanning circuit 113 included in the controller 110 controls the xy-scanner 112 that scans the xy plane horizontal to the piezoelectric element surface 115 on which the sample is placed. The compensator 114 included in the controller 110 controls the z-scanner 111 that performs scanning in the z direction perpendicular to the piezoelectric element surface 115 on which the sample is placed.

(Control target modeling)
In AFM, it has been described that the amplitude and the like change depending on the atomic force, but here, the atomic force and the mechanical handling of the atomic force will be described.

(What is interatomic force)
Hereinafter, the atomic force acting between the tip of the cantilever and the sample surface will be described.

  In general, there is an interaction between two nonpolar atoms that can be approximated by a Leonard-Jones type potential as represented by the following formula (1).

  Here, ε represents the strength of the force, σ represents the size of the atom, and R represents the distance between the atoms. FIG. 2 illustrates Equation (1). FIG. 2 shows that an attractive force due to van der Waals force works at a long distance, and a strong repulsive force explained by Pauli's exclusion principle works at a short distance (Non-Patent Document 6).

  As explained above, repulsive force is dominant in the short distance and attractive force in the long distance. Since the contact mode is a contact state, most of the interatomic force is considered to be repulsive. On the other hand, in the tapping mode, the atomic force that affects the tip of the cantilever is an attractive force and a repulsive force.

(Mechanical model)
FIG. 3 shows a dynamic model in consideration of all dynamics of the cantilever oscillation piezoelectric element, cantilever, atomic force, sample, and z-direction driven piezoelectric element. FIG. 4 is a block diagram in consideration of all dynamics of the cantilever oscillation piezoelectric element, cantilever, atomic force, sample, and z-direction driven piezoelectric element.

  3 and 4, the attractive force is represented by a negative spring coefficient and a viscous friction coefficient.

3 and 4, m _pν [kg] is the mass of the oscillating piezoelectric element, m _c [kg] is the mass of the tip of the cantilever, and m _s [kg] is the mass of the sample. m _pz [kg] is the mass of the z-direction driven piezo element.

3 and 4, k _pν [N / m] is the spring coefficient of the spring 301, and k _c [N / m] is the spring coefficient of the spring 302. 3 and 4, k _a [N / m] is the spring coefficient of the spring 303, k _r [N / m] is the spring coefficient of the spring 304, and k _s [N / m] is , K _pz [N / m] is the spring coefficient of the spring 306.

3 and 4, b _pν [N × s / m] is a viscous friction coefficient of the frictional force generation source 311, and b _c [N × s / m] is a viscous friction of the frictional force generation source 312. It is a coefficient. 3 and 4, b _a [N × s / m] is a viscous friction coefficient of the frictional force generation source 313, and b _r [N × s / m] is a viscous friction of the frictional force generation source 314. It is a coefficient. 3 and 4, b _s [N × s / m] is a viscous friction coefficient of the frictional force generation source 315, and b _pz [N × s / m] is a viscous friction of the frictional force generation source 316. It is a coefficient.

3 and 4, x _pν [m] is the displacement of the oscillating piezo element, and x _c is the displacement of the tip of the cantilever. 3 and 4, x _s [m] is the displacement of the sample, and x _pz [m] is the displacement of the z-direction drive piezo element.

  Further, in FIG. 1 and func. 2 is a saturation function.

  The model shown in FIGS. 3 and 4 has a high degree and is difficult to analyze. Therefore, in consideration of the high rigidity of the oscillating piezo element, the z-direction drive piezo element, and the sample, these are regarded as rigid bodies for simplification. A model simplified in this way is shown in FIGS.

5 and 6, m _c [kg] is the mass of the tip of the cantilever.

5 and 6, k _c [N / m] is a spring coefficient of the spring 502. 5 and 6, k _a [N / m] is the spring coefficient of the spring 503, and k _r [N / m] is the spring coefficient of the spring 504.

5 and 6, b _c [N × s / m] is a viscous friction coefficient of the frictional force generation source 512. 5 and 6, b _a [N × s / m] is a viscous friction coefficient of the frictional force generation source 513, and b _r [N × s / m] is a viscous friction of the frictional force generation source 514. It is a coefficient.

5 and 6, x _pν [m] is the position of the oscillating piezo element, and x _c [m] is the displacement of the tip of the cantilever probe. 5 and 6, x _pz [m] is the position of the z-direction drive piezo element. 5 and 6, x ₀ [m] is the initial position of the tip of the cantilever probe, L _a [m] is the natural length position of the spring 503, and L _r [m] is It is the position of the natural length of the spring 504, and d [m] is the height of the sample.

  Also, in FIG. 1 and func. 2 is a saturation function.

  4 and 6, func. 1 and func. A saturation function represented by 2 outputs a value for an arbitrary input value, and represents that the range in which the repulsive force and attractive force constituting the interatomic force reach is limited.

  4 and 6, s represents a Laplace operator (time differentiation operator), and 1 / s represents time integration.

  The simplified model shown in FIGS. 5 and 6 is similar to the model proposed in Non-Patent Document 5. From FIG. 5, the following equations (2) to (5) are obtained when an equation of motion is established for the cantilever.

Here, f (t) is an interatomic force, and f (t) is the sum of attractive force f _a (t) and repulsive force f _r (t) as shown in the following equation (3). is there.

In Expression (3), f _a (t) and f _r (t) are expressed as Expression (4) and Expression (5) below, respectively.

Here, x _a (t) and x _r (t) are expressed by the following equations (6) and (7).

  6 is obtained by drawing a block diagram from the above equations (2) to (7). Here, the saturation function func. 1 and func. 2 is represented by the following formulas (8) and (9).

  As shown in the saturation functions of the equations (8) and (9), the tapping mode AFM includes a non-linear element. In the contact mode AFM, most of the operating range is a repulsive region with strong linearity, whereas in the tapping mode AFM, both non-linear attractive and repulsive regions are included in the operating range. For this reason, the vibration response in the tapping mode AFM becomes complicated, and it is said that it is difficult to strictly analyze the vibration response in the tapping mode AFM (Non-Patent Document 1).

(Approximate analysis by state space averaging method)
As described above, in the tapping mode AFM, the controlled object has nonlinearity. Therefore, in this embodiment, the control target in the tapping mode AFM is linearized by averaging and handling the operation in the attractive force region and the repulsive force region of the control target. Accordingly, a surface shape observer (STO) that can be applied on condition that the input / output relationship of the control target has linearity can be applied to the control of the tapping mode AFM.

  In this embodiment, a state space averaging method (Non-Patent Document 9) is used to linearize the control target of the tapping mode AFM.

  The state space averaging method is a basic technique in the field of power electronics, and is an approximate analysis method used when exact analysis is difficult because discontinuous operation is repeated by switching. When the frequency at which the state is switched is sufficiently higher than the natural frequency of the system, it can be analyzed using the state space averaging method. Since the resonance frequency of the tapping mode cantilever is about 180 [kHz] and the natural frequency of the system is sufficiently higher than the resonance frequency of the tapping mode cantilever, the state space averaging method can be applied.

  In the state space averaging method, the state space of each state is weighted by the duty ratio D, and the averaged state space is treated as a state space as a whole, and the state is expressed by a relational expression such as the following equation (10). Average the space.

  In equation (10), the system with subscript 1 indicates state 1, the system with subscript 2 indicates state 2, and normally, state 1 ≠ state 2.

Here, as shown in FIG. 7, state 1 is the case where the tip of the cantilever is in the repulsive force region, and state 2 is the case where it is in the attractive region. Further, the vibration displacement at the tip of the cantilever is approximated as x _pν (t) = 2V _{m sin} ω _c t. Then, in state 1, x _pν = V _m , and in state 2, x _pν = −V _m . ω _c is the natural angular frequency of the cantilever tip.

Here, it is assumed that the natural frequency 1 / T [Hz] of the cantilever is unchanged.
The times of state 1 and state 2 are T ₁ [seconds] and T ₂ [seconds], respectively. Here, if the duty ratio D is used, T ₁ = DT and T ₂ = (1−D) T can be expressed. In this embodiment, analysis is performed using these T ₁ and T ₂ .

(State 1 state space)
The state space of state 1 is obtained from the following equations (11) and (12). In Expression (11), e ₁ is a summation of constant terms including the initial position x ₀ of the tip of the cantilever, the natural length position L _a of the spring 503, and the natural length position L _r of the spring 504. In the equations (11) to (15) and (17), the state variable is

And the control input is

It is. Here, u _pz is a control input to the Z-direction driving piezo elements, an x _pz = g × u _pz, is g = 311.8 [nm / V] .

(State space of state 2)
Similarly to the case of the state 1, the state space of the state 2 can be obtained from the following equations (13) and (14).

(Averaged state space)
The state space averaged based on the equation (10) is obtained as the equation (22) from the following equations (15) to (21).

Here, since A ⁻¹ is regular, the state variable x can be replaced with a new state variable X represented by the following equation (19).

In the equation (19), A ⁻¹ e is a constant term, so the equations (15) and (16) are converted into the following equations (20) and (21).

When the output y passes through the BPF (band pass filter) 108 shown in FIG. 1, the influence of the constant term −CA ⁻¹ e in the equation (21) is eliminated, and the direct current due to the constant term is obtained in the RMS-DC 109. Not affected by minutes.

  From A, B, and C obtained as described above, the averaged state space is obtained as in the following Expression (22).

From equation (22), it can be seen that the averaged displacement of the cantilever tip x _c (t) behaves linearly. The envelope of the effective value of x _c (t) is extracted by a low-pass filter. Since the behavior of x _c (t) is linearized, by applying a surface shape observer (STO) to the tapping mode AFM, frequency response characteristics and transfer functions by STO can be obtained, and further state quantities can be estimated. It becomes possible.

(Identification of control target)
In the averaged state space, in the tapping mode AFM, the behavior of the displacement x _c (t) of the tip of the cantilever with respect to the input u has linearity, and therefore the control target is identified by the frequency response.

9 and 10 show the frequency characteristics of the plant P (s) obtained by the servo analyzer. 9 and 10 also show the frequency characteristics of the nominal plant P _n (s) fitted to the plant P (s).

In the analysis of the frequency characteristics shown in FIGS. 9 and 10, the control target is a secondary system, but a higher order response is manifested in the frequency response shown in FIGS. Therefore, in this embodiment, in order to improve the accuracy of the surface shape observer used in the control, the nominal plant P _n (s) is a sixth order system represented by the following equation (23).

In the formula (23), b ₀ , b ₁ , b ₂ , a ₀ , a ₁ , a ₂ , a ₃ , a ₄ , and a ₅ are determined as follows. That is, b ₀ = 1.700 × 10 ²⁵ , b ₁ = 1.856 × 10 ²¹ , and b ₂ = 3.516 × 10 ¹⁸ . Also, a ₀ = 6.141 × 10 ²³ , a ₁ = 2.473 × 10 ²⁰ , a ₂ = 1.303 × 10 ¹⁷ , a ₃ = 3.108 × 10 ¹³ , a ₄ = 9.008 × 10 ⁸ and a ₅ = 6.98 × 10 ⁴ .

(Comparison between conventional method and surface shape observer)
Non-Patent Document 7 shows that, in the contact mode AFM, the surface shape observer (STO) is effective during fast scanning measurement. In the present embodiment, the surface shape observer is applied to the tapping mode AFM.

  Hereinafter, the STO will be described with reference to the block diagram shown in FIG. STO is an open loop and is independent of the feedback system. Further, it can be seen from FIG. 8 that the control structure of the STO is equal to the disturbance observer.

  As shown in FIG. 8, the STO includes an AFM control unit and a DSP.

  In FIG. 8, a BPF (band pass filter) 108 is inserted to extract frequencies near the natural frequency at the tip of the cantilever. Here, the high-pass cutoff frequency is 10 [kHz], and the low-pass cutoff frequency is set to 200 [kHz]. The RMS-DC 109 is a low-pass filter used for calculation, and its cutoff frequency is set to 10 [kHz]. As shown in FIG. 8, the signal output from the RMS-DC 109 passes through the AD converter 822 and is input to the DSP.

  The feedback compensator 114 shown in FIG. 8 is a phase lag compensator. The signal from the compensator 114 passes through the DA converter 821 and is input to the z-direction drive piezo element 111. Since the STO is an open loop and does not contribute to the stability of the feedback system, the introduction of the STO does not limit the design of the feedback compensator. In the present embodiment, as an example, a JSPM-5200 compensator, which is an AFM manufactured by JEOL Ltd., is used, but the present invention is not limited to this. Further, in the present embodiment, as an example, the following equation (24) in which the gain and the cutoff frequency are tuned according to the product manual of JSPM-5200 is used for the feedback compensator. Not limited.

  As shown in FIG. 8, the initial position r of the z-direction drive piezo element (z-scanner) 111 and the xy-scanner 112 is input to the compensator 114 as an initial condition.

  In the conventional method used in comparison with the present embodiment, in the DSP shown in FIG. 8, only the compensator according to the equation (24) is used as a controller for controlling the z-direction drive piezo element.

  In the present embodiment, the following expression (25) having a cutoff frequency of 1 [kHz] is used as the expression of the Q filter 815.

  In the conventional method, the control input u is a surface shape. In the conventional method, the transfer function from the surface shape d to the control input u is equal to the complementary sensitivity function T (s) of this system, and the complementary sensitivity function is expressed by the following equation (26).

  From the above equation (26), in principle, u which is the image information of the conventional method can be reflected even if the surface shape d is scanned at a high speed if the compensator C (s) is a high gain controller. . However, since C (s) constitutes a closed-loop pole, it tends to be unstable when it is unnecessarily high.

In the present embodiment, as is apparent from the open loop frequency characteristics of FIGS. 11 and 12, the gain margin g _m = 15.12 [dB] and the phase margin p _m = 73 [deg (degrees)].

  On the other hand, the surface shape estimated by STO

Is represented by the following equation (27).

  Further, the surface shape estimated from the surface shape d

The transfer function up to is expressed by the following equation (28).

Here, if the control object P (s) is expressed as P (s) = P _n (s) (1 + Δ (s)) using the nominal plant P _n (s) and the multiplicative model error Δ (s). Equation (28) can be transformed into Equation (29) below using Equation (26).

  From equation (29), it can be seen that when the modeling error Δ (s) is large, the effect converges at the speed of the pole of the feedback system. Further, when modeling with high accuracy, that is, when the modeling error Δ (s) is small, the surface shape estimated by STO

Is immediately converged to the true surface shape d according to the time constant of the high-speed Q filter. This is an advantage gained from the fact that STO is independent of the closed loop pole.

(simulation)
FIG. 15 shows the simulation result of the open loop characteristic in the simple model shown in FIG. From FIG. 15, it can be seen that when a sine wave is applied to x _pz corresponding to the control input, the displacement x _c of the tip of the cantilever is subjected to AM modulation. In FIG. 15, it can be confirmed that the RMS output y has the same frequency as the input x _pz . From this, it can be seen that the approximation that defines the transfer function as in Expression (28) is appropriate.

(Operation of tapping mode AFM)
In the tapping mode AFM according to the present embodiment, as shown in FIG. 8, as an example, the control unit of JSPM-5200 manufactured by JEOL Ltd. is configured with an external control DSP (digital signal processor). doing. In the present embodiment, a compensator designed for continuous time is discretized with sampling time T _s = 50 [μs] (1 μs = 10 ⁻⁶ seconds) and mounted on the control DSP.

FIG. 16 is a diagram showing data obtained by actually operating the tapping mode AFM according to the present embodiment. Actually, since it is difficult to fix the tip of the cantilever to the set point only by feedforward control, feedback is applied in this embodiment. FIG. 16 shows u, x _c , and y of the tapping mode AFM according to the present embodiment. By comparing FIG. 15 and FIG. 16, it can be confirmed that the result of the simulation model shown in FIG. 15 can well simulate the operation of the actual tapping mode AFM.

  13 and 14 show the frequency characteristics of the complementary sensitivity function T (s) of the AFM according to the present embodiment.

(Observation of grating elements by tapping mode AFM)
FIG. 17 shows a grating element observed by AFM. The shape of this grating element is a sawtooth groove, the height of the sawtooth groove is 100 [nm], and the interval is 400 [nm].

  FIG. 18 shows a surface shape obtained at a scanning speed of 9.77 [μm / s] by the tapping mode AFM using the conventional method. FIG. 19 shows the surface shape obtained at a scanning speed of 39.1 [μm / s] by the tapping mode AFM using the conventional method. FIG. 20 shows a surface shape obtained at a scanning speed of 195 [μm / s] by the tapping mode AFM using the conventional method.

  FIG. 21 shows a surface shape obtained by a tapping mode AFM using STO at a scanning speed of 9.77 [μm / s]. FIG. 22 shows a surface shape obtained at a scanning speed of 39.1 [μm / s] by tapping mode AFM using STO. FIG. 23 shows a surface shape obtained by a tapping mode AFM using STO at a scanning speed of 195 [μm / s].

  18 to 23, the scanning range by AFM is 2 [μm] × 2 [μm].

  In the observation of the surface shape shown in FIGS. 18 and 21, since the servo is sufficiently applied, the output (error signal) y is small. That is, in the observation of the surface shape shown in FIGS. 18 and 21, the control input u can suppress the disturbance d, the operation amount follows the surface shape, and the surface shape of the grating element can be accurately reproduced. ing. For this reason, as is apparent from the equation (27), the STO almost outputs the control input u, and the difference between the surface shape shown in FIG. 18 and the surface shape shown in FIG. There is almost no.

On the other hand, when the scanning speed of the AFM is increased, the surface shape observed by the AFM becomes unclear in the conventional method, as is clear from the comparison between FIGS. 20 and 23, and the height of the grating sample is low. Observed lower than when scanned. This is because in the conventional method, the influence of the pole of the closed loop system has come out. On the other hand, in the STO, as shown in FIG. 23, the observed surface shape is clear even when the scanning speed of the AFM is increased. That is, in STO, even if the scanning speed is increased, the surface shape can be observed with little deterioration.
As described above, according to the present embodiment, it is possible to provide a tapping mode AFM with improved observation accuracy.

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 the interaction force which acts on the element of AFM based on a tapping mode. It is a figure which shows a block diagram. It is a figure which shows the interaction force which acts on the element of AFM based on a tapping mode. It is a figure which shows a block diagram. It is a figure which shows the track | orbit of the front-end | tip of a cantilever. It is a figure which shows a block diagram. It is a figure which shows a frequency characteristic. It is a figure which shows a frequency characteristic. It is a figure which shows a frequency characteristic. It is a figure which shows a frequency characteristic. It is a figure which shows a frequency characteristic. It is a figure which shows a frequency characteristic. It is a figure which shows the result of the simulation of a time response. It is a figure which shows the result of observation of a time response. It is a figure which shows the shape of a grating element. It is a figure which shows the image of the sample measured by AFM. It is a figure which shows the image of the sample measured by AFM. It is a figure which shows the image of the sample measured by AFM. It is a figure which shows the image of the sample measured by AFM. It is a figure which shows the image of the sample measured by AFM. It is a figure which shows the image of the sample measured by AFM.

Explanation of symbols

101 Oscillation piezo element 102 DDS
103 Cantilever 104 Cantilever tip 105 LD
106 PD
107 Laser beam providing means 108 BPF
109 RMS-DC
110 controller 111 z-direction driving piezo element 112 xy-scanner 113 scanning circuit 114 compensator 115 piezo element surface 116 data storage means 120 sample surface

Claims (3)

An atomic force microscope apparatus that images a surface shape of a sample surface in a tapping mode,
The tip of the cantilever that interacts with the sample surface via an interatomic force, bends due to the interatomic force, and distorts due to 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;
Control means for controlling the piezo to scan the sample while keeping the atomic force constant;
Demodulation means for detecting the deflection and distortion of the tip of the cantilever from the intensity of the second laser light as an output voltage, and demodulating the output voltage modulated by the atomic force;
The output voltage demodulated by the demodulating means is converted so as to linearize the operation of the tip of the cantilever by averaging the operation of the attractive region and the repulsive region of the tip of the cantilever, and the converted output voltage From the estimation means for estimating the surface shape of the sample surface by a surface shape observer,
An atomic force microscope apparatus comprising data storage means for recording the estimated surface shape.   The atomic force microscope apparatus according to claim 1, wherein the light detection means is a quadrant photodiode.   The atomic force microscope apparatus according to claim 2, wherein the laser beam providing means is a visible light semiconductor laser.

Images