Abstract:
A scanning probe microscope includes (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, (d) an adder which adds the detected change to the constant while the interaction is fed back to a distance between the probe and the object, to thereby temporarily vary the constant, (e) a collector which collects signals relating to a displacement which signals are varied as the constant is varied, and calculates a relation among the signals, and (f) a third device which returns the temporarily varied constant back to the constant for scanning the object, calculates products of the relation with each of the signals in real-time, and sums the products, which products indicate a profile of a surface of the object.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    The invention relates to a scanning probe microscope and a method of processing signals in a scanning probe microscope.  
           [0003]    2. Description of the Related Art  
           [0004]    A scanning probe microscope is designed to have a probe having a sharpened tip end. The scanning probe microscope scans a surface of an object through the sharpened tip end to thereby detect interaction between the probe and the object. Then, the scanning probe microscope controls a distance between the probe and the object to be equal to a constant, based on the detected interaction, and keeps on transmitting control signals indicative of a distance between the probe and the object. Based on the control signals, a shape of the object&#39;s surface is visualized.  
           [0005]    A scanning probe microscope which is designed to detect a tunnel current as interaction between a probe and an object is called a scanning tunneling microscope (STM). A scanning probe microscope which is designed to detect a force exerted between a probe and an object is generally called an atomic force microscope (AFM).  
           [0006]    When electric or magnetic interaction between a probe and an object is to be detected by means of a scanning probe microscope, the scanning probe microscope is required to have a function to carrying out a feedback control to a distance between a probe and an object in order to uniformize dynamic interaction between a probe and an object. Under such a feedback control, the scanning probe microscope scans a surface of an object to thereby electrically or magnetically carry out detection.  
           [0007]    A scanning probe microscope includes an actuator to actuate a probe for controlling a distance between a probe and an object. The actuator is generally comprised of a piezoelectric device. An area to be scanned by a probe is, for instance, 10·m×10·m, and a displacement by which a probe has to be displaced in order to compensate for an inclination and/or irregularities of an object is in the range of 0 to about 5·m.  
           [0008]    In order to accomplish the above-mentioned scanning area and displacement, a typical piezoelectric device is generally designed to have either a cylindrical shape having a height in the range of about 5 to 9 cm and an outer diameter equal to or smaller than 1 cm, or a tripod-shape.  
           [0009]    A piezoelectric device generally has a fundamental frequency for resonance at about 5 kHz or smaller, due to a size or a complicated structure thereof. Accordingly, when a surface of an object is scanned, a range of a frequency in which a distance between a probe and an object can be controlled is limited to about 5 kHz or smaller. This means that a scanning speed is also limited As a result, it takes a long time, specifically 5 to 8 minutes per one image, to have a shape of a surface of an object with high reliability, based on control signals transmitted from a probe. If a scanning speed is increased in order to reduce a time necessary for forming an image, fidelity of an image to a shaped of a surface of an object is degraded, resulting in degradation of an image.  
           [0010]    That is, the above-mentioned feedback control cannot catch up with a scanning speed, resulting in that a probe makes collision with an object, and accordingly, a probe and/or an object are damaged. In addition, it would become quite difficult to detect an electric characteristic of an object by means of an electrically conductive probe with high reliability, because interaction between the probe and the object varies.  
           [0011]    A frequency band of a signal transmitted from a probe is generally different from a frequency band of a piezoelectric device. For instance, a frequency band of a current signal in a scanning tunneling microscope (STM) is broader by columns than a frequency band in which a piezoelectric device is operable.  
           [0012]    Japanese Patent No. 2713717 (Japanese Unexamined Patent Publication No. 1-206202) has suggested a method of forming an image of a shape of a surface of an object, based on the above-mentioned difference. Specifically, the suggested method has a step of calculating a linear sum of a signal transmitted from a probe and a signal to be transmitted to a piezoelectric device to thereby increase a scanning speed.  
           [0013]    A probe may be arranged at one end of a cantilever. When a signal derived from a displacement of the probe is to be detected, based on a principle of an optical lever, it would be possible, by selecting a probe, to make a frequency band of a signal transmitted from the probe broader than a frequency band in which a piezoelectric device controlling a distance between an object and the probe is operable.  
           [0014]    Japanese Unexamined Patent Publication No. 2-5339 has suggested a method of a controlling a distance between an object and a probe by means of two actuators. In the method, a displacement caused by an inclination of an object is compensated for by means of an inch warm. A probe is arranged on a tripod complex piezoelectric device to thereby compensate for a displacement of the probe caused by irregularities existing on a surface of an object.  
           [0015]    Japanese Unexamined Patent Publication No. 10-311841 has suggested a method of scanning a surface of an object. In the method, there are used a first actuator having a high operation speed and a second actuator having a low operation speed for making it possible to scan a surface having high irregularities.  
           [0016]    Japanese Unexamined Patent Publication No. 10-10140 has suggested a method of scanning a shape of a surface of an object. In the suggested method, different frequencies in a displacement of a probe caused when irregularities on a surface of an object are scanned by means of two or more piezoelectric devices are compensated for. Images of the irregularities are formed by control signals transmitted to the piezoelectric devices.  
           [0017]    Japanese Unexamined Patent Publication No. 11-201977 has suggested a method of using both a signal to be input into a feedback system and a signal in the feedback system. It is assumed that a feedback system receives a signal A, a signal P is produced by applying conversion allowed in the feedback system, to the signal A, and an output signal transmitted from a device to which the signal P is input is negatively fed back to the signal A. The method includes the step of synthesizing the signal A and the signal P.  
           [0018]    However, it is quite difficult or almost impossible to rapidly have an image reflecting a shape of a surface of an object even by the above-mentioned conventional methods or scanning probe microscopes some of which includes a plurality of actuators.  
           [0019]    In order to accomplish high-speed scanning, when a displacement of a probe, indicative of irregularities existing on a surface of an object, is restored to a constant through the use of a plurality of control signals and/or probe signals transmitted from a probe which control signals and probe signals are complementary with each other, it is necessary to have a relation among those signals with high accuracy and as readily as possible.  
           [0020]    In general, a displacement of a probe is detected by an optical signal detected under a principle of an optic lever. Hence, a displacement of a probe is dependent on many parameters such as a geometric structure of an optic lever, an amount of a light, an optic reflectance of a cantilever having an end on which a probe is arranged, and/or a photoelectric transfer ratio of a photodetector.  
           [0021]    Furthermore, an electric-mechanical conversion rate at which a piezoelectric device converts a control signal into a displacement is dependent on stability of a piezoelectric device, and hence, has to be frequently calibrated.  
           [0022]    Hence, when an image of a shape of a surface of an object is to be formed at a high speed through the use of a signal indicative of a displacement of a probe and a control signal transmitted from a probe, even if requisite coefficients can be obtained through calibration, it would not be practical to keep those coefficients equal to a constant, and it would be quite difficult to ensure reliability in target coefficients.  
           [0023]    In order to make it possible to more practically use a scanning probe microscope at a high speed, it would be important to measure a relation among signals relating to a displacement of a probe, under the same conditions as conditions in which a displacement is actually measured.  
           [0024]    One of methods for having an image of a shape of a surface of an object at a high speed may include the steps of compensating for a displacement of a probe by means of a plurality of actuators, and obtaining the image, based on control signals to be input into the actuators.  
           [0025]    However, the method in which two piezoelectric devices are used, suggested in Japanese Unexamined Patent Publication No. 10-10140, is accompanied with a problem that even though a signal is transmitted in division through a plurality of feedback routes, control signals overlapping each other in a low frequency band may be included in two feedback routes, resulting in unstable operation of a scanning probe microscope.  
           [0026]    In the method suggested in Japanese Unexamined Patent Publication No. 10-10140, a sum of control signals to be transmitted to two piezoelectric devices are merely calculated in order to form an image of a shape of a surface of an object. However, since electric-mechanical conversion rates of two piezoelectric devices are different from each other, it would be impossible to accurately form the image merely by summing control signals to each other. Specifically, it would be necessary for the method to include steps of dividing a feedback route into a plurality of routes, and restoring signals indicative of a displacement caused by irregularities existing on a surface of an object, through the use of control signals being transmitted through the divided feedback routes.  
           [0027]    A method of accomplishing high-speed scanning through the use of two actuators is suggested, for instance, in Review of Scientific Instruments, 64,692, 1993.  
           [0028]    As mentioned above, the conventional scanning probe microscopes and methods of forming an image of a shape of a surface of an object are accompanied with a problem that a feedback control to be carried out by a plurality of controllers and a signal processing for obtaining the image, both of which are required to be compatible with high-speed scanning, are not well established.  
           [0029]    A scanning capacity microscope detects a capacity between a surface of an object and an electrode located below the surface. However, such a capacity cannot be readily detected. In particular, when a surface of an object below which an electrode is formed has great irregularities and is composed of dielectric material, it would be necessary to control a distance between a probe and a surface of an object such that the distance is kept equal to a constant, in order to scan and detect a capacity per a unit area of an object. As a result, it would take much time to have an image relating to a capacity in comparison with a time necessary for obtaining an image of irregularities of a surface of an object.  
           [0030]    Hence, it is important to reduce a time necessary for carrying out a control on a distance between a probe and an object, in order to rapidly obtain an image in a scanning capacity microscope. If the time could be reduced, it would be possible to rapidly obtain not only an image of a capacity but also an image of irregularities of a surface of an object.  
         SUMMARY OF THE INVENTION  
         [0031]    In view of the above-mentioned problems in the prior art, it is an object of the present invention to provide a scanning probe microscope and a method of processing signals in a scanning probe microscope both of which are capable of reducing a time necessary for forming an image of a surface of an object with a resolution being kept high.  
           [0032]    In one aspect of the present invention, there is provided a method of processing a signal in a scanning probe microscope, including the steps of (a) causing a relative displacement between an object and a probe, (b) detecting a change in interaction caused between the probe and the object by the relative displacement, (c) feeding the detected change back to the relative displacement to keep the interaction equal to a constant, the method further including the steps of (d) adding the detected change to the constant while the interaction is fed back to a distance between the probe and the object, to thereby temporarily vary the constant, the step (d) being to be carried out before scanning the object, (e) collecting signals relating to a displacement which signals are varied as the constant is varied, and operating a relation among the signals, and (f) returning the temporarily varied constant back to the constant for scanning the object, calculating products of the relation with each of the signals in real-time, and summing the products, which products indicate a profile of a surface of the object.  
           [0033]    In another aspect of the present invention, there is provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, (d) an adder which adds the detected change to the constant while the interaction is fed back to a distance between the probe and the object, to thereby temporarily vary the constant, (e) a collector which collects signals relating to a displacement which signals are varied as the constant is varied, and calculates a relation among the signals, and (f) a third device which returns the temporarily varied constant back to the constant for scanning the object, calculates products of the relation with each of the signals in real-time, and sums the products, which products indicate a profile of a surface of the object.  
           [0034]    For instance, the detector may operate with the probe being kept in contact with the object. As an alternative, the detector may operate with the probe making periodical contact with the object.  
           [0035]    It is preferable that the detector, when the probe is driven at dynamical resonance or in the vicinity of dynamical resonance, detects a resonance characteristic of the dynamical resonance.  
           [0036]    For instance, the probe may be comprised of an electrically conductive probe, and further including a detector which detects an electric capacity existing between the electrically conductive probe and the object, the electrically conductive probe acting as an open end or a leakage end in an electric resonance system, the detector detecting a resonance characteristic caused by electric interaction between the probe and the object.  
           [0037]    As an alternative, the probe may be comprised of an electrically conductive probe, and further including a detector which detects an electric capacity existing between the electrically conductive probe and the object, the electrically conductive probe acting as an open end or a leakage end in an electric resonance system, the detector detecting a resonance characteristic caused by electric interaction between the probe and the object, with a voltage applied to the object, being varied.  
           [0038]    There is further provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, (d) a third device which varies the constant while the change is being fed back to the relative displacement and the object is not being scanned, (e) a calculator which calculates a change rate of a first signal relative to a second signal, the first signal being transmitted from the probe and varied as the constant is varied, the second signal being transmitted from the third device, and (f) a fourth device which synthesizes the first and second signals in real-time to thereby transmit a third signal indicative of a profile of a surface of the object, based on the change rate.  
           [0039]    It is preferable that the third device includes means for adding a signal varying with the lapse of time, to the constant.  
           [0040]    For instance, the calculator may be comprised of (e1) an analog-digital converter which converts analog signals relating to a displacement which signals are varied as the constant is varied, into digital signals when the object is not being scanned, (e2) an arithmetic unit which calculates a change rate among the thus analog-digital converted signals, (e3) a memory which stores the change rate, and (e4) means for transferring the change rate.  
           [0041]    For instance, the fourth device may be comprised of (f1) a receiver which receives a change rate of a first signal to a second signal, the first signal being a reference signal selected among signals relating to a displacement which signals are varied as the constant is varied, the second signal being a signal other than the reference signal among the signals, (f2) at least one multiplier which calculates a product of the change rate with real-time signals each relating to a displacement associated with the change rate, and (f3) an adder which calculates either a sum of the reference signal and an output transmitted from the multiplier or a sum of outputs transmitted from a plurality of the multipliers.  
           [0042]    It is preferable that the multiplier includes a digital-analog converter which multiplies digital and analog signals with each other.  
           [0043]    There is still further provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, (d) a third device which varies the constant while the change is being fed back to the relative displacement and the object is not being scanned, (e) a calculator which calculates change rates of a first signal relative to each of a plurality of second signals, the first signal being transmitted from the probe and varied as the constant is varied, the second signals being transmitted from the third device, and (f) a fourth device which returns the temporarily varied constant back to the constant for scanning the object, and synthesizes the first and second signals in real-time to thereby transmit a third signal indicative of a profile of a surface of the object.  
           [0044]    For instance, the second device may include (c1) a low-pass filter and a high-pass filter which are complementary with each other and which divide a signal indicative of the change, and (c2) an actuator driven in accordance with the signal.  
           [0045]    It is preferable that the scanning probe microscope further includes an amplifier which amplifies the signal, the actuator being driven in accordance with the thus amplified signal.  
           [0046]    For instance, the second device may include (c1) a first actuator driven in accordance with a first signal indicative of the change, (c2) a low-pass filter providing low frequency parts of the first signal, and (c3) a second actuator driven in accordance with a second signal transmitted from the low-pass filter.  
           [0047]    It is preferable that the second device further includes an amplifier for amplifying the first signal, the first actuator being driven in accordance with the thus amplified first signal.  
           [0048]    There is yet further provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, (d) a measurement device which measures a displacement caused by the second device and transmits a first signal indicative of the displacement, (e) a third device which varies the constant while the change is being fed back to the relative displacement and the object is not being scanned, (f) a calculator which calculates change rates of the first signal relative to each of second signals, the first signal being varied in accordance with a displacement caused by the third device, the second signals being independent of the measurement device, and (f) a fourth device which synthesizes the first and second signals in real-time to thereby transmit a third signal indicative of a profile of a surface of the object, based on the change rates.  
           [0049]    There is still yet further provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, and (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, the second device including (c1) a low-pass filter and a high-pass filter which are complementary with each other and which divide a signal indicative of the change, and (c2) an actuator driven in accordance with the signal.  
           [0050]    It is preferable that the scanning probe microscope further includes an amplifier which amplifies the signal, the actuator being driven in accordance with the thus amplified signal.  
           [0051]    There is further provided a scanning probe microscope including (a) a first device which causes a relative displacement between an object and a probe, (b) a detector which detects a change in interaction caused by the first device between the probe and the object, and (c) a second device which feeds the detected change back to the relative displacement to keep the interaction equal to a constant, the second device including (c1) a first actuator driven in accordance with a first signal indicative of the change, (c2) a low-pass filter providing low frequency parts of the first signal, and (c3) a second actuator driven in accordance with a second signal transmitted from the low-pass filter.  
           [0052]    It is preferable that the second device further includes an amplifier for amplifying the first signal, the first actuator being driven in accordance with the thus amplified first signal.  
           [0053]    The advantages obtained by the aforementioned present invention will be described hereinbelow.  
           [0054]    In accordance with the present invention, when a displacement indicative of irregularities existing on a surface of an object is to be restored by a plurality of signals such as a control signal indicative of a displacement used for compensating for a displacement of a probe caused by irregularities existing on a surface of an object, a probe signal transmitted from a probe, and an output signal indicative of a displacement caused by a controller, a relation among those signals is determined while a control for compensating for a displacement of a probe is in operation, prior to scanning a surface of an object. When a surface of an object is scanned, a displacement corresponding to irregularities existing on a surface of an object is synthesized from the thus determined relation and real-time signals. This ensures high-speed scanning.  
           [0055]    It is assumed that the above-mentioned control and probe signals include a signal indicative of a displacement of a probe, transmitted from the probe, and a control signal transmitted to an actuator, and a feedback control is in operation to a predetermined constant. In accordance with the present invention, a signal having a periodically varying waveform, such as a waveform in the form of teeth of a saw, a triangle waveform or a waveform in the form of a sine curve, is added to the constant before starting scanning a surface of an object. Then, a signal transmitted from a probe, indicative of variation in the constant, and the control signal are collected. Then, a relation among those signals is calculated and stored in a memory. When a surface of an object is actually scanned, a real-time signal transmitted from a probe and the control signal are synthesized to thereby form an image reflecting irregularities existing on a surface of an object, based on the stored relation among the above-mentioned signals. Herein, the signal transmitted from a probe and the control signal transmitted to an actuator are signals relating to a displacement and having different frequency bands from each other.  
           [0056]    When the above-mentioned signals relating to a displacement are control signals in a plurality of controllers, signals in frequency bands to which each of the signals belongs are added to the above-mentioned predetermined constant while all feedback systems are in operation, before starting scanning a surface of an object. Then, control signals which vary relative to the constant to which the above-mentioned signals have been added, and a detection signal transmitted from a probe are collected. Then, a relation among the signals is calculated, and is stored in a memory. When a surface of an object is actually scanned, a signal indicative of irregularities existing on a surface of an object is synthesized from the above-mentioned real-time signals relating to a displacement. Thus, an image is obtained in a scanning probe microscope.  
           [0057]    When the above-mentioned signals relating to a displacement include a signal indicative of a displacement caused by one of controllers, signals in frequency bands to which each of the above-mentioned signals belong are added to the predetermined constant while all feedback systems are in operation, before scanning a surface of an object. Then, a signal varying in accordance with a change in the constant, and a control signal transmitted from a controller having no measurement unit are collected. Then, a relation between the thus collected signals and the signals in frequency bands is calculated, and is stored in a memory. When a surface of an object is actually scanned, a signal indicative of irregularities existing on a surface of an object is synthesized from the above-mentioned signal indicative of a displacement caused by one of controllers, and the control signal transmitted from the controller having no measurement unit. Thus, an image is obtained in a scanning probe microscope.  
           [0058]    When a distance between a probe and an object is fed back to a displacement of a probe by means of a plurality of controllers in order to compensate for a signal transmitted from a probe, in order to ensure stability in each of feedback routes, it is necessary to avoid interference in the feedback routes.  
           [0059]    To this end, a signal transmitted from a probe is divided into two parts with respect to a frequency band by means of low-pass and high-pass filters which are complementary with each other. An amplifier is arranged for each of the parts. Herein, division of a signal means that a signal is divided into two parts without a loss with respect to a frequency band, and a sum of the thus divided parts would make the original signal.  
           [0060]    In one method of avoiding interference among the feedback routes, a signal transmitted from a probe is amplified, and the thus amplified signal is input into an actuator driven in a high frequency band. The actuator is driven with the control signal having passed through a low-pass filter in order to compensate for a low frequency part in a displacement caused by the actuator.  
           [0061]    A signal having a periodically varying waveform, such as a waveform in the form of teeth of a saw, a triangle waveform or a waveform in the form of a sine curve, is added to the constant while the feedback control is in operation, before starting scanning a surface of an object, in order to calibrate a relation among the signals relating to a displacement. Then, responses of the signals are collected.  
           [0062]    A device for varying the constant may be comprised of a waveform synthesizer for transmitting a signal having a periodically varying waveform, and an adder for adding the signal to the constant.  
           [0063]    The scanning probe microscope may receive a plurality of signals relating to a displacement which signals vary as the constant varies, and calculates a change rate of a first signal to a second signal. Herein the first signal is a reference signal selected among the signals relating to a displacement which signals are varied as the constant is varied, and the second signal is a signal other than the reference signal among the signals. The scanning probe microscope may include a memory to store both a band of a signal which can be described with the change rate, and the change rate therein.  
           [0064]    As a synthesizer for synthesizing a signal indicative of irregularities existing on a surface of an object, in real-time, while the surface is being scanned and a feedback control is in operation, the scanning probe microscope may include means for receiving a change rate of a first signal to a second signal, the first signal being a reference signal selected among signals relating to a displacement which signals are varied as the constant is varied, the second signal being a signal other than the reference signal among the signals, calculating a product of said change rate with the change rate with real-time signals each relating to a displacement associated with the change rate, and calculating either a sum of the reference signal and an output transmitted from the multiplier or a sum of outputs transmitted from a plurality of the multipliers.  
           [0065]    In order to operate the above-mentioned synthesizer in real-time, the scanning probe microscope preferably includes a circuit which multiplies digital and analog signals with each other. Herein, the digital data includes the above-mentioned change rate, and the analog signal includes a real-time signal relating to the change rate. A result of the multiplication is output as a real-time analog signal. The scanning probe microscope may include an operational amplifier to carry out summing analog signals.  
           [0066]    Among the above-mentioned methods, the method in which a plurality of controllers is used is applicable to probes carrying out various operations. In a contact mode where a probe is kept in contact with a surface of an object, and in a tapping mode where a probe periodically makes contact with a surface of an object, the method is applicable also to a method including the steps of arranging a probe on a small-sized crystal oscillator, putting the oscillator in a dynamic resonance condition, and detecting a resonance parameter varying due to interaction between a probe and an object.  
           [0067]    When interaction between a probe and an object is to be controlled at a high speed, electric interaction between a probe and an object may be detected to do so.  
           [0068]    In a scanning capacity microscope where a probe is embedded in a micro-wave oscillator, and a distance between a probe and an object or a capacity in a piece of a surface of an object with a probe being kept in contact with an object is detected as a change in micro-wave oscillation, it would be possible to scan a surface of an object at a high speed through the use of a plurality of controllers.  
           [0069]    It would be also possible to scan a surface of an object at a high speed by detecting a change in micro-wave resonance with a voltage applied to a electrode located below the surface of an object, being varied, namely, by detecting dC/dV.  
           [0070]    The above and other objects and advantageous features of the present invention will be made apparent from the following description made with reference to the accompanying drawings, in which like reference characters designate the same or similar parts throughout the drawings. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0071]    [0071]FIG. 1 is a block diagram of a scanning probe microscope in accordance with the first embodiment of the present invention.  
         [0072]    [0072]FIG. 2 is a block diagram of a scanning probe microscope in accordance with the second embodiment of the present invention.  
         [0073]    [0073]FIG. 3A is a block diagram of a control block including low- and high-pass filters which are complementary with each other.  
         [0074]    [0074]FIG. 3B is a block diagram of a control block for transmitting two control signals.  
         [0075]    [0075]FIG. 4 is a block diagram of a scanning probe microscope in accordance with a variant of the second embodiment of the present invention.  
         [0076]    [0076]FIG. 5 is a block diagram of a scanning probe microscope in accordance with the third embodiment of the present invention.  
         [0077]    [0077]FIG. 6 is a circuit diagram of a scanning probe microscope in accordance with the fourth embodiment of the present invention.  
         [0078]    [0078]FIG. 7 is a block diagram of a scanning probe microscope in accordance with the fifth embodiment of the present invention.  
         [0079]    [0079]FIG. 8 is a block diagram of a scanning probe microscope in accordance with the sixth embodiment of the present invention.  
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0080]    Preferred embodiments in accordance with the present invention will be explained hereinbelow with reference to drawings.  
         [0081]    [First Embodiment] 
         [0082]    With reference to FIG. 1, a laser beam emitted from a laser source  101  is received in a probe  102  supported on a free end of a cantilever  103 . The laser beam is reflected at the probe  102  to and is detected in a divided photodetector  104 . The laser beam received in the divided photodetector  104  is output as a probe signal Vc through a circuit  105  for detecting a position of the probe  102 .  
         [0083]    The probe signal Vc is input into a first input port of an error amplifier  107 . On the other hand, a signal SP indicative of a predetermined constant is input into a second input port the error amplifier  107  through an adder  106 .  
         [0084]    A signal output from the error amplifier  107  is input into a low-pass filter  108 , and output from the low-pass filter  108  as a signal Vp, which is input into both a high-voltage amplifier  109  and an operation and memory unit  110 .  
         [0085]    The high-voltage amplifier  109  outputs a signal to a piezoelectric device  111 . The piezoelectric device  111  controls a distance between an object  112  and the probe  102  such that the probe signal Vc is equal to the signal SP. This feedback control keeps a distance between the object  112  and the probe  102  equal to a constant.  
         [0086]    The piezoelectric device  111  is in the form of a cylinder having a diameter of 12 mm, a height of 90 mm and a thickness of I mm. The piezoelectric device  111  has a dynamic resonance frequency of about 2 kHz. The low-pass filter  108  has a cut-off frequency in the range of 400 to 700 Hz both inclusive.  
         [0087]    As mentioned above, a distance between the probe  102  and the object  112  is feedback-controlled to the predetermined constant so as to ensure steady interaction between the probe  102  and the object  112 .  
         [0088]    Before starting scanning a surface of the object  112 , a controller  113  instructs a waveform synthesizer  114  to synthesize a variable signal and transmit the variable signal to the adder  106 . For instance, the waveform synthesizer  114  produces a signal having a waveform in the form of teeth of a saw and having a frequency which can pass through the low-pass filter  108 .  
         [0089]    The feedback control makes the probe signal Vc have the same waveform as the above-mentioned waveform in the form of teeth of a saw. Specifically, the piezoelectric device  111  is made to be extended or contracted to thereby cause a displacement in the probe  102 , deformation of the cantilever  103 , and then, a change in the probe signal Vc.  
         [0090]    Pairs of the probe signal Vc and the signal Vp are stored in the operation and memory unit  110 . The probe signal Vc is described with a polynomial of the signal Vp, and a range of the signal Vp described with the linear expression and a linear differential coefficient dVc/dVp are stored in the operation and memory unit  110 .  
         [0091]    The above-mentioned process is displayed on a display screen  116  equipped in the controller  113 .  
         [0092]    The feedback control is being carried out successively without a pause in a condition initially set.  
         [0093]    Then, scanning a surface of the object  112  starts. Before the scanning starts, the controller  113  stops the operation of the waveform synthesizer  114 , and instructs the waveform synthesizer  114  to supply a zero voltage to the adder  106 .  
         [0094]    Data stored in the operation and memory unit  110  can be read out therefrom. The read-out data is transmitted to an image signal synthesizer  115 .  
         [0095]    A scanning signal generator  117  equipped in the controller  113  transmits a scanning signal, which is amplified by a high-voltage amplifier  118  and then input into the piezoelectric device  111 .  
         [0096]    The probe  102  scans a surface of the object  112 .  
         [0097]    A frequency part in the probe signal Vc, which gradually varies as a surface of the object  112  is scanned, such as a frequency part derived from an inclination of the object  112  or a frequency part derived from small irregularities, passes through the error amplifier  107  and the low-pass filter  108 , and is output therefrom as the signal Vp. The signal Vp is input into the piezoelectric device  111  for compensating for the probe signal Vc.  
         [0098]    Accordingly, the probe signal Vc includes the rest of frequency parts, that is, a high frequency part such as a frequency part derived from steep irregularities existing on a surface of the object  112 .  
         [0099]    The image signal synthesizer  115  receives the linear differential coefficient dVc/dVp from the operation and memory unit  110 , and calculates a product of the linear differential coefficient and the signal Vp. The image signal synthesizer  115  gives an alarm in dependence on a range of the signal Vp.  
         [0100]    An output signal transmitted from the image signal synthesizer  115  is not but a signal scaled by the probe signal Vc and indicative of irregularities existing on a surface of the object  112 . This output signal is displayed as an image on the display screen  116  in synchronization with a scanning signal.  
         [0101]    [0101]FIG. 1 illustrates the scanning probe microscope which is in contact mode where the probe  102  is kept in contact with the object  112 .  
         [0102]    In contact mode, the probe signal Vc is indicative of a displacement of the cantilever  103 , that is, a degree of bent of the cantilever  103 .  
         [0103]    As an alternative, the probe signal Vc may be designed to indicate an amplitude of oscillation of the cantilever  103  which amplitude can be obtained when the cantilever  103  is positioned in the vicinity of resonance condition which can put others in a resonance condition, and hence, the probe  102  periodically makes contact with a surface of the object  112 .  
         [0104]    As an alternative, the probe signal Vc may indicate a phase of a compulsive force of the oscillation.  
         [0105]    As an alternative, if the probe  102  is fixed to a crystal oscillator located in the vicinity of resonance condition, the probe signal Vc may indicate an impedance of the oscillator.  
         [0106]    [Second Embodiment] 
         [0107]    [0107]FIG. 2 is a block diagram of a scanning probe microscope in accordance with the second embodiment of the present invention.  
         [0108]    The scanning probe microscope in accordance with the second embodiment is designed to include two actuators for carrying out high-speed scanning.  
         [0109]    The scanning probe microscope in accordance with the second embodiment includes the entire structure of the scanning probe microscope in accordance with the first embodiment, illustrated in FIG. 1, and additionally includes a control block  200  which transmits two control signals, a second piezoelectric device  203 , a power amplifier  202  which drives the second piezoelectric device  203 , and an operation and memory unit  204  which monitors the probe signal Vc transmitted from the probe  102 , a control signal Vp transmitted to the piezoelectric device  111  from the control block  200 , and a control signal Vph transmitted to the second piezoelectric device  203  from the control block  200 .  
         [0110]    The piezoelectric device Ill has a resonance frequency of about 2 kHz.  
         [0111]    The second piezoelectric device  203  has a multi-layered structure at a size of 3×4×5 mm, and has a resonance frequency of about 70 kHz.  
         [0112]    The control block  200  may be comprised of a pair of filters complementary with each other. An example of the control block  200  is illustrated in FIG. 3A.  
         [0113]    As illustrated in FIG. 3A, the control block  200  may be comprised of a low-pass filter  108  and a high-pass filter  201  complementary with the low-pass filter  108 .  
         [0114]    The probe signal Vc transmitted from the probe  102  passes through the error amplifier  107 , and then, is divided into a low-frequency signal Vp to be transmitted to the piezoelectric device  111  and a high-frequency signal Vph to be transmitted tot he second piezoelectric device  203 .  
         [0115]    The high-pass filter  201  is comprised of a capacitor a which receives the probe signal Vc from the error amplifier  107 , a resistor R 1  which is grounded at one end and electrically connected to a node between the capacitor C 2  and an amplifier  201   a , and an amplifier  201   a  which is electrically connected at an input port to both the capacitor C 1  and the resistor R 1 .  
         [0116]    The low-pass filter  108  is comprised of a resistor R 2  which receives the probe signal Vc from the error amplifier  107 , a capacitor C 2  which is grounded at one end and electrically connected to a node between the resistor R 2  and an amplifier  108   a , and an amplifier  108   a  which is electrically connected at an input port to both the capacitor C 2  and the resistor R 2 .  
         [0117]    In the high-pass filter  201 , the capacitor C 1  and the resistor R 1  cooperates with each other to thereby constitute a filter. In the low-pass filter  108 , the resistor R 2  and the capacitor C 2  cooperates with each other to thereby constitute a filter The resistors R 1 , R 2  and the capacitors a, C 2  are selected such that the following equation is established.  
           R 1× C 1= R 2× C 2=• 
         [0118]    Herein, “•” indicates a period of time obtained by multiplying a time defined as an inverse number of a resonance frequency of the piezoelectric device  111 , by 3 or 4.  
         [0119]    [0119]FIG. 3B illustrates another example of the control block  200 .  
         [0120]    The control block  200  is comprised of the low-pass filter  108  and an amplifier  205  which receives the probe signal Vc from the error amplifier  107 , and transmits an output signal to both the high-voltage amplifier  202  and the resistor R 2 .  
         [0121]    The probe signal Vc transmitted from the probe  102  passes through the error amplifier  107 , and then, is input as a control signal Vph into the high-voltage amplifier  202  which drives the second piezoelectric device  203 .  
         [0122]    A low frequency part in the control signal Vph is separated in the low-pass filter  108 , and is input into the piezoelectric device  111  as a control signal Vp.  
         [0123]    A displacement of the piezoelectric device  111  caused by the control signal Vp compensates for a displacement in a low frequency band among a displacement of the second piezoelectric device  203 . Though not illustrated, the control signal Vph is filtered in the high-pass filter  201  so that the control signal Vph has a resonance frequency equal to or smaller than a resonance frequency of the second piezoelectric device  203 , and then, is input into the high-voltage amplifier  202 .  
         [0124]    A relation among a plurality of signals relating to a displacement is determined under a feedback control as follows.  
         [0125]    The probe  102  and a surface of the object  112  interact with each other. When a distance between the probe  102  and the object  112  is feed-back controlled such that the probe signal Vc transmitted from the probe  102  is steady at a predetermined constant, the controller  113  instructs the waveform synthesizer  114  to synthesize a variable signal and transmit the thus synthesized variable signal to the adder  106 , prior to scanning a surface of the object  112 . For instance, the waveform synthesizer  114  produces a signal having a waveform in the form of teeth of a saw and having a frequency which can pass through the low-pass filter  108 .  
         [0126]    The feedback control makes the probe signal Vc have the same waveform as the above-mentioned waveform in the form of teeth of a saw. Specifically, the piezoelectric device  111  is made to be extended or contracted to thereby cause a displacement in the probe  102 , deformation of the cantilever  103 , and then, a change in the probe signal Vc.  
         [0127]    Pairs of the probe signal Vc and the signal Vp are stored in the operation and memory unit  204 . The probe signal Vc is described with a polynomial of the signal Vp, and a range of the signal Vp described with the linear expression and a linear differential coefficient dVc/dVp are stored in the operation and memory unit  204 .  
         [0128]    The above-mentioned process is displayed on the display screen  116  equipped in the controller  113 .  
         [0129]    Then, the controller  113  instructs the waveform synthesizer  114  to generate a voltage having a high frequency which cannot pass through the low-pass filter  108 . In response, the waveform synthesizer  114  generates a voltage having a sine-curve waveform.  
         [0130]    The feedback control makes the probe signal Vc have the same waveform as the above-mentioned since-curve waveform. Specifically, the second piezoelectric device  203  is made to be extended or contracted to thereby cause a displacement in the probe  102 , deformation of the cantilever  103 , and then, a change in the probe signal Vc.  
         [0131]    Pairs of the probe signal Vc transmitted from the probe  102  and the signal Vph transmitted from the high-pass filter  201  are stored in the operation and memory unit  204 . The probe signal Vc is described with a polynomial of the signal Vph, and a range of the signal Vph described with the linear expression and a linear differential coefficient dVc/dVph are stored in the operation and memory unit  204 .  
         [0132]    The feedback control is being carried out successively without a pause at the initially set constant.  
         [0133]    Then, the controller  113  stops the operation of the waveform synthesizer  114 , and instructs the waveform synthesizer  114  to supply a zero voltage to the adder  106 .  
         [0134]    Data dependent on the signals Vp and Vph, stored in the operation and memory unit  204  can be read out therefrom. The read-out data is transmitted to the image signal synthesizer  115 .  
         [0135]    Then, the controller  113  instructs the scanning signal generator  117  to transmit a scanning signal, which is amplified by the high-voltage amplifier  118 , and then, input into the piezoelectric device  111 .  
         [0136]    Then, the probe  102  starts scanning a surface of the object  112 .  
         [0137]    A frequency part in the probe signal Vc, which gradually varies as a surface of the object  112  is scanned, such as a frequency part derived from an inclination of the object  112  or a frequency part derived from small irregularities, passes through the error amplifier  107  and the low-pass filter  108 , and is output therefrom as the signal Vp. The signal Vp is input into the piezoelectric device  111  for compensating for the probe signal Vc.  
         [0138]    The rest of frequency parts in the probe signal Vc, that is, a high frequency part such as a frequency part derived from steep irregularities existing on a surface of the object  112 , is input into the error amplifier  107  and output therefrom as the control signal Vph. The control signal Vph is input into the second piezoelectric device  203  for controlling the second piezoelectric device  203 , and compensates for a high frequency part of the probe signal Vc.  
         [0139]    The image signal synthesizer  115  receives the linear differential coefficients dVc/dVp and dVc/dVph from the operation and memory unit  204 , and calculates a product of the linear differential coefficients and the real-time signals Vp and Vph. The image signal synthesizer  115  gives an alarm if the signal Vp or Vph is in a band which is necessary to be compensated for with high-order paragraphs.  
         [0140]    An output signal transmitted from the image signal synthesizer  115  is not but a signal scaled by the probe signal Vc and indicative of irregularities existing on a surface of the object  112 . This output signal is displayed as an image on the display screen  116  in synchronization with the scanning signal.  
         [0141]    [0141]FIG. 4 illustrates a variant of the scanning probe microscope in accordance with the second embodiment, illustrated in FIG. 2.  
         [0142]    The scanning probe microscope illustrated in FIG. 4 is designed to include a digital signal processor (DSP).  
         [0143]    With reference to FIG. 4, the digital signal processor  205  is comprised of a first digital-analog (D-A) converter  206 , a second digital-analog converter  207 , a first analog-digital (A-D) converter  208 , a second analog-digital converter  209 , and a third analog-digital converter  210 .  
         [0144]    The digital signal processor  205  is controlled by the controller  113 .  
         [0145]    The first digital-analog converter  206  transmits a signal which is to be added to the predetermined constant through the adder  106 , before scanning a surface of the object  112 . By adding the signal, the constant is varied.  
         [0146]    The second digital-analog converter  207  transmits a scanning signal by which a surface of the object  112  is scanned.  
         [0147]    At the stage before scanning a surface of the object  112  does not start, the first to third analog-digital converters  208 ,  209  and  210  receives the signal Vp transmitted from the low-pass filter  108  and varied in accordance with a signal transmitted from the first digital-analog converter  206 , the probe signal Vc transmitted from the probe  102 , and the control signal Vph, and converts these analog signals into digital data.  
         [0148]    At the stage while a surface of the object  112  is being scanned, the first to third analog-digital converters  208 ,  209  and  210  receives the signals Vp, Vc and Vph which are all varied as the object  112  is scanned, and converts the analog signals Vp, Vc and Vph into digital signals.  
         [0149]    The thus analog-digital converted signals Vp, Vc and Vph are input into the digital signal processor  205 .  
         [0150]    At the stage when the feedback control is in operation and before scanning a surface of the object  112  does not start, the digital signal processor  205  receives the digital data or the analog-digital converted signals Vp, Vc and Vph, calculates a change rate of the probe signal Vc to the signal Vp or Vph, further calculates bands of the signals Vp and Vph which bands can be described with the associated change rate, and stores the thus calculated change rates and bands therein.  
         [0151]    At the stage while a surface of the object  112  is being scanned, the digital signal processor  205  receives the digital data or the analog-digital converted signals Vp, Vc and Vph which are all varied as the object  112  is scanned, and then, judges whether bands of the signals Vp, Vc and Vph are described with the stored change rates.  
         [0152]    If the bands are not described with the stored change rates, the digital signal processor  205  gives an alarm. If the bands are described with the stored change rates, the digital signal processor  205  multiplies the differential coefficients dVp/dVc and dVph/dVc by each other. Herein, the differential coefficients dVp/dVc and dVph/dVc are associated with the digital data derived from the signal Vp and Vh, respectively. Then, the digital signal processor  205  scales the products to the probe signal Vc, adds the products to each other, and transmits the sum to the controller  113 .  
         [0153]    The data transmitted to the controller  113  is displayed on the display screen  116 .  
         [0154]    The scanning probe microscope illustrated in FIG. 4 is designed to include the digital signal processor  205  as well as the controller  113 . However, it should be noted that the digital signal processor  205  may be omitted, in which case, the controller  113  is designed to include the first and digital-analog converters  206  and  207 , and the first to third analog-digital converters  208 ,  209  and  210  so as to have the functions of the digital signal processor  205 .  
         [0155]    In the above-mentioned second embodiment, the control signals Vp and Vph are scaled to the probe signal Vc. However, it should be noted that the control signals Vp and Vph may be scaled to any one the signals Vp, Vph and Vc. As an alternative, when a mechanical-electric conversion coefficient of the piezoelectric device  111  is used, it would be possible to display an image having actual dimensions, on the display screen  116 .  
         [0156]    In the above-mentioned second embodiment, low-frequency signals are first added to each other in order to determine a relation between the control signals Vp and Vc both transmitted to the piezoelectric device  111 , and then, high-frequency signals are added to each other in order to determine a relation between the control signals Vph and Vc both transmitted to the second piezoelectric device  203 . Namely, the relation among the signals relating to a displacement is determined one by one.  
         [0157]    As an alternative, the relation between the control signals may be determined as follows.  
         [0158]    While the feedback control is in operation and a surface of the object  112  is not scanned, a signal in a low frequency band to which the control signal Vp belongs and a signal in a high-frequency band to which the control signal Vph are synthesized to each other in the waveform synthesizer  114 . The thus synthesized signal is added to the predetermined constant. Then, the control signals Vp and Vph are concurrently detected for determining the relation.  
         [0159]    When a surface of the object  112  is scanned, it would be possible to synthesize a signal indicative of irregularities existing on a surface of the object  112  which signal is scaled to the control signal Vp or Vph, based on the relation.  
         [0160]    [Third Embodiment] 
         [0161]    [0161]FIG. 5 illustrates a scanning probe microscope in accordance with the third embodiment.  
         [0162]    The scanning probe microscope in accordance with the third embodiment has a measurement unit for measuring a displacement caused by a plurality of controllers. Specifically, the measurement unit measures a displacement of a movable end of an actuator on which the object  112  is mounted.  
         [0163]    With reference to FIG. 5, the scanning probe microscope includes a displacement measurement unit  301  for measuring a displacement of the object  112  relative to a base  120 . The displacement measurement unit  301  transmits a signal “z” indicative of the displacement to the operation and memory unit  204 . That is, the signal “z” is substituted for the control signal Vp transmitted to the piezoelectric device  111  in the second embodiment.  
         [0164]    The probe  102  and a surface of the object  112  interact with each other. When a distance between the probe  102  and the object  112  is feed-back controlled such that the interaction between the probe  102  and the object  112  is steady, the controller  113  instructs the waveform synthesizer  114  to synthesize a variable signal and transmit the thus synthesized variable signal to the adder  106 , prior to scanning a surface of the object  112 . For instance, the waveform synthesizer  114  produces a signal having a waveform in the form of teeth of a saw and having a frequency which can pass through the low-pass filter  108 .  
         [0165]    The feedback control makes the probe signal Vc have the same waveform as the above-mentioned waveform in the form of teeth of a saw. Specifically, the piezoelectric device  111  is made to be extended or contracted to thereby cause a displacement in the probe  102 , deformation of the cantilever  103 , and then, a change in the probe signal Vc.  
         [0166]    Pairs of the probe signal Vc and the signal “z” transmitted from the displacement measurement unit  301  are stored in the operation and memory unit  204 . The probe signal Vc is described with a polynomial of the signal “z”, and a range of the signal “z” described with the linear expression and a linear differential coefficient dz/dVc are stored in the operation and memory unit  204 .  
         [0167]    The above-mentioned process is displayed on the display screen  116  equipped in the controller  113 .  
         [0168]    Then, the controller  113  instructs the waveform synthesizer  114  to generate a signal having a frequency which is in a range of the high-pass filter  201 . In response, the waveform synthesizer  114  generates a signal having a sine-curve waveform.  
         [0169]    The feedback control makes the probe signal Vc have the same waveform as the above-mentioned since-curve waveform. Specifically, the second piezoelectric device  203  is made to be extended or contracted to thereby cause a displacement in the probe  102 , deformation of the cantilever  103 , and then, a change in the probe signal Vc.  
         [0170]    Pairs of the probe signal Vc transmitted from the probe  102  and the signal Vph transmitted from the high-pass filter  201  are stored in the operation and memory unit  204 . The probe signal Vc is described with a polynomial of the signal Vph, and a range of the signal Vph described with the linear expression and a linear differential coefficient dVc/dVph are stored in the operation and memory unit  204 .  
         [0171]    The operation and memory unit  204  further calculates a differential coefficient dz/dVph from the differential coefficients dz/dVc and dVc/dVph, and stores the thus calculated differential coefficient dz/dVph therein. In scanning a surface of the object  112 , the operation and memory unit  204  adds the real-time signal “z” transmitted from the displacement measurement unit  301 , to a product of the real-time control signal Vph and the differential coefficient dz/dVph to thereby have a signal indicative of irregularities existing on a surface of the object  112  which signal is scaled to the signal “z” transmitted from the displacement measurement unit  301 .  
         [0172]    In the third embodiment, low-frequency signals are first added to each other in order to determine a relation between the probe signal Vc and the signal “z”, and then, high-frequency signals are added to each other in order to determine a relation between the control signal Vc and the control signal Vph transmitted to the second piezoelectric device  203  driven in a high frequency band. Namely, the relation among the signals relating to a displacement is determined one by one.  
         [0173]    As an alternative, the relation between the signals may be determined as follows.  
         [0174]    While the feedback control is in operation and a surface of the object  112  is not scanned, a signal in a low frequency band to which the signal “z” belongs and a signal in a high-frequency band to which the control signal Vph are synthesized to each other in the waveform synthesizer  114 . The thus synthesized signal is added to the predetermined constant. Then, the signals “z” and Vph are concurrently detected for determining the relation.  
         [0175]    When a surface of the object  112  is scanned, it would be possible to synthesize a signal indicative of irregularities existing on a surface of the object  112  which signal is scaled to the signal “z” or Vph, based on the relation.  
         [0176]    [Fourth Embodiment] 
         [0177]    [0177]FIG. 6 illustrates a scanning probe microscope in accordance with the fourth embodiment.  
         [0178]    In the fourth embodiment, the image synthesizer  115  is comprised of a digital-analog converter (DAC) having a function of carrying out multiplication. In accordance with the fourth embodiment, it is possible to synthesize a signal indicative of irregularities existing on a surface of the object  112 , in real-time, based on a plurality of real-time signals relating to a displacement.  
         [0179]    With reference to FIG. 6, real-time analog signals A 1  and A 2  relating to a displacement are input into first and second digital-analog converters  401  and  403 , respectively. The first and second digital-analog converters  401  and  403  receives digital input signals D 1  and D 2 , respectively, and weighs currents having amplitudes which are in proportion to amplitudes of the analog signals A 1  and A 2 , with the digital input signals D 1  and D 2 . The thus weighed currents are converted into analog voltage signals A 3  and A 4  in operational amplifiers  402  and  404 . The analog voltage signals A 3  and A 4  indicate the products having been calculated in the first and second digital-analog converters  401  and  403 .  
         [0180]    In the above-mentioned first embodiment, the analog signal A 1  corresponds to the probe signal Vc transmitted from the probe  102 , and the analog signal A 2  corresponds to the control signal Vp transmitted to the piezoelectric device  111 . The digital input signal Dl corresponds to a digital signal having a weight of one (1), and the digital input signal D 2  corresponds to a digital signal indicative of the differential coefficient dVc/dVp read out of the operation and memory unit  110 .  
         [0181]    In the above-mentioned second embodiment, the analog signal Al corresponds to the control signal Vp transmitted to the piezoelectric device  111 , and the analog signal A 2  corresponds to the control signal Vph transmitted to the second piezoelectric device  203 . The digital input signal D 1  corresponds to a digital signal indicative of the differential coefficient dVc/dVp, and the digital input signal D 2  corresponds to a digital signal indicative of the differential coefficient dVc/dVph.  
         [0182]    In the above-mentioned third embodiment, the analog signal A 1  corresponds to the signal “z” transmitted from the displacement measurement unit  301 , indicating extension or contraction of the piezoelectric device  111 .  
         [0183]    In all of the first to third embodiments, the analog signals A 3  and A 4  are added in the same weight by an operational amplifier  405 . That is, resistors R 1 , R 2  and R 3  are equal to one another (R 1 =R 2 =R 3 ), and have a resistance of about 10 k•.  
         [0184]    As a result, an analog signal A 4  transmitted from the operational amplifier  405  indicates a voltage linear to irregularities existing on a surface of the object  112 , in the first to third embodiments.  
         [0185]    In the fourth embodiment, the scanning probe microscope further includes a digital-analog converter  406  receiving a digital signal D 3  and having a function of carrying out multiplication, and an operational amplifier  407  which transmits an analog signal A 6 .  
         [0186]    When the control signals Vp (or “z”) and Vph are concurrently detected to determine a relation between those two signals, as mentioned in the above-mentioned second and third embodiments, the scanning probe microscope may include any one of the digital-analog converter  406  and the operational amplifier  407 . Of course, the scanning probe microscope may include both the digital-analog converter  406  and the operational amplifier  407 .  
         [0187]    That is, if the real-time signal Vp (or “z”) as the analog signal A 1  is input into the first digital-analog converter  401 , the differential coefficient dVph/dVp (or dVph/dz) as the digital signal D 1  is input also to the first digital-analog converter  401 , the control signal Vph as the analog signal A 2  is input into the second digital-analog converter  403 , and the digital signal D 2  is designed to be digital data equivalent to one (1), the analog signal A 6  would be a real-time signal indicative of irregularities existing on a surface of the object  112 .  
         [0188]    [Fifth Embodiment] 
         [0189]    [0189]FIG. 7 illustrates a scanning probe microscope in accordance with the fifth embodiment.  
         [0190]    The scanning probe microscope in accordance with the fifth embodiment is designed to include a third piezoelectric device  501  on which the cantilever  103  is fixed at a proximal end of the cantilever  103 . The probe  102  is fixed on the cantilever  103  at a distal end of the cantilever  103 .  
         [0191]    The third piezoelectric device  501  oscillates the cantilever  103  at the proximal end at a frequency close to a resonance frequency of the probe  102 . Hence, an amplitude of the distal end of the cantilever  103 , that is, a displacement of the probe  102  varies in dependence on interaction between the probe  102  and a surface of the object The third piezoelectric device  501  receives a voltage signal having a sine-curve waveform, from a signal transmitter  502 , and accordingly, oscillates the cantilever  103  at the proximal end of the cantilever  103  at a frequency in the vicinity of a resonance frequency of the probe  102 .  
         [0192]    In the fifth embodiment, the resonance frequency is about 300 kHz. The signal transmitter  502  transmits the voltage signal to the third piezoelectric device  501 , and at the same time, transmits data about a phase of the voltage signal to a lock-in amplifier  503 .  
         [0193]    A laser beam emitted from a laser source  101  is directed to the probe  102 , and is reflected at the probe  102 . The reflected laser beam is detected in a divided photodetector  104 , and then, is input into a circuit  105  for detecting a position of the probe  102 . The circuit  105  transmits a voltage signal having a sine-curve waveform and indicative of a displacement of the probe  102 .  
         [0194]    The lock-in amplifier  503  detects a phase of the voltage signal transmitted from the circuit  105 , and transmits an amplitude signal Vamp indicative of a displacement of the probe  102  in a sine curve.  
         [0195]    A predetermined constant SP together with the amplitude signal Vamp is input into the error amplifier  107 . The error amplifier  107  transmits a signal Vp to both the high-voltage amplifier  109  and the operation and memory unit  204  through the low-pass filter  108 .  
         [0196]    The high-voltage amplifier  109  transmits a signal to the piezoelectric device  111 . In accordance with the signal transmitted from the high-voltage amplifier  109 , a distance between the object  112  and the probe  102  is controlled such that the predetermined constant SP is coincident with the amplitude signal Vamp. This feedback control keeps the distance equal to a constant.  
         [0197]    The piezoelectric device  111  has the same size as the size of the piezoelectric device  111  in the first embodiment. The resonance frequency and a cut-off frequency of the low-pass filter  108  are identical with those in the first embodiment.  
         [0198]    [Sixth Embodiment] 
         [0199]    [0199]FIG. 8 illustrates a scanning capacity microscope in accordance with the sixth embodiment.  
         [0200]    The scanning capacity microscope in accordance with the sixth embodiment includes the entire structure of the scanning probe microscope in accordance with the second embodiment, and additionally includes a sensor  601  which senses an electric capacity, a plurality of electrodes  602  arranged below the object  112 , and a circuit  603  which applies a bias to the electrodes  602 .  
         [0201]    In scanning a surface of the object  112 , a signal Vcap transmitted from the sensor  601 , indicative of an electric capacity sensed by the sensor  601 , is collected to thereby form an image of irregularities existing on a surface of the object  112 .  
         [0202]    A relation among the signals Vc, Vp and Vph is determined, prior to scanning of a surface of the object  112 , by means of the controller  113 , the waveform synthesizer  114 , the adder  106  and the operation and memory unit  204  in the same way as the second embodiment.  
         [0203]    In scanning a surface of the object  112  before measurement starts, the real-time signals Vp and Vph are input into the image synthesizer  115 . The image synthesizer  115  reads data such as differential coefficients out of the operation and memory unit  204 , and calculates a product of the signals Vp and Vph and the thus read-out data. Then, the operation and memory unit  204  transmits a signal indicative of irregularities existing on a surface of the object  112 .  
         [0204]    The probe  102  in the sixth embodiment is composed of electrically conductive material. For instance, the probe  102  is composed of silicon nitride coated with iron and/or chromium.  
         [0205]    The circuit  603  applies a voltage difference across the probe  102  and the electrodes  602 . When a surface of the object  112  is scanned, a capacity formed between the object  112  and the probe  102  is detected by the sensor  601 . The capacity is dependent on the voltage difference.  
         [0206]    The signal indicative of irregularities existing on a surface of the object  112  and the signal Vcap transmitted from the sensor  601  and indicative of the detected capacity are received in the controller  113 , and displayed on the display screen  116  equipped in the controller  113 .  
         [0207]    The scanning capacity microscope in accordance with the sixth embodiment is in a contact mode where the probe  102  is kept in contact with a surface of the object  112 . However, it should be noted that the scanning capacity microscope in accordance with the sixth embodiment can be applied to a mode where a compulsive force acts on the probe  102 , and hence, a displacement of the probe  102  is close to a resonance, as having been explained in the above-mentioned fifth embodiment.  
         [0208]    As an alternative, an image of irregularities existing on a surface of the object can be scaled in actual dimensions by means of the displacement measurement unit  301  shown in the third embodiment, illustrated in FIG. 5.  
         [0209]    While the present invention has been described in connection with certain preferred embodiments, it is to be understood that the subject matter encompassed by way of the present invention is not to be limited to those specific embodiments. On the contrary, it is intended for the subject matter of the invention to include all alternatives, modifications and equivalents as can be included within the spirit and scope of the following claims.  
         [0210]    The entire disclosure of Japanese Patent Application No. 2000-112478 filed on Apr. 13, 2000 including specification, claims, drawings and summary is incorporated herein by reference in its entirety.