Abstract:
A method of detecting the distribution of values of a physical property such as the dopant concentration of a semiconductor without being adversely affected by stray capacitance is offered. A scanning probe microscope capable of implementing this method is also offered. The method starts with applying an AC voltage of angular frequency ω between a probe and a sample from a fixed oscillator. The output from the oscillator is supplied to a piezoelectric device that drives the cantilever. The cantilever produces a deflection signal corresponding to forces corresponding to interactions between the probe and sample. A signal regarding the amplitude is extracted from the deflection signal. This signal is fed back to a means for controlling the distance between the probe and sample and supplied to a display device. As a result, an image of the surface topography of the sample is obtained. A harmonic component having a frequency higher than the triple or more of the angular frequency ω and contained in the cantilever deflection signal is extracted by a lock-in amplifier. As a result, information representing an image of differential capacitance (∂C/∂V) is obtained.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method of measuring values of a physical property, such as capacitance C or dielectric constant ∈, by detecting the electrostatic force acting between a probe and a sample. The invention also relates to apparatus, such as a scanning probe microscope (SPM), using this method. 
     2. Description of the Related Art 
     An atomic force microscope (AFM) is one kind of scanning probe microscope (SPM) and can image specimen surfaces at atomic-scale resolution. AFM provides a basis for various SPM techniques. Normal AFM can image surface topography. A procedure for imaging the distribution of values of a physical property near a sample surface, such as electric capacitance C or dielectric constant ∈, is scanning capacitance microscopy (SCM). Two methods have been proposed to measure capacitance C by AFM. In one method, a capacitance sensor is mounted close to the probe. In the other method, electrostatic force is detected and measured. 
     The prior art of this method using a capacitance sensor is described. Measurement of the electric capacitance C between a probe and a sample in a microscopic region was started by Matey et al. [J. R. Matey and J. Blanc,  J. Appl. Phys . 47, 1437 (1985)] using a capacitance sensor of an electrostatic video disk player developed by RCA for consumer applications [R. C. Palmer, E. J. Denlinger, and H. Kawamoto, RCA Rev. 43, 194 (1982)]. Matey et al. did not control the probe-sample separation. However, Williams et al. succeeded in measuring capacitance C in a microscopic region by a capacitance sensor while controlling the probe-sample separation using scanning tunneling microscopy (STM) [C. C. Williams, W. P. Hough, and S. A. Rishton,  Appl. Phys. Lett . 55, 203(1989)]. Furthermore, Barret et al. performed measurement of electric capacitance C on a silicon oxide film that is an insulator, using AFM [R. C. Barrett and C. F. Quate,  J. Appl. Phys . 70, 2725 (1991)]. In this way, products that are commercially available as SCM are based on an instrument where a capacitance sensor is mounted close to an AFM probe. 
     RCA&#39;s capacitance sensor is fitted with an oscillator oscillating at a fixed frequency. An LC resonator circuit is formed by the probe-sample capacitance C and the inductance L in the sensor. The resonant frequency of this LC resonator circuit varies. The amplitude of the output signal taken through the resonator circuit is detected using an amplitude detector. On the other hand, Cho et al. has proposed a capacitance sensor which uses a frequency variable oscillator whose oscillation frequency is varied by the probe-sample capacitance C and the inductance L in an externally attached sensor. The frequency of the output signal is detected by the use of a frequency detector [Y. Cho, A. Kirihara, and T. Saeki,  Rev. Sci. Instrum . 67, 2297 (1996)]. 
     With any capacitance sensor, the modulation method is used in practical operation to avoid the effects of stray capacitance. An AC electric field (alternating voltage) is applied between the probe and the sample. Amplitude or frequency modulated thereby is detected using a lock-in amplifier. Therefore, the actually obtained image is not an image of the distribution of electric capacitances C, but an image of the distribution of differential capacitances (∂C/∂V). In this method, the probe-sample separation is controlled by AFM technique. Detection of electric capacitance needs a special capacitance sensor and so the structure of the instrument is complex. 
     The prior art of the method by detecting electrostatic force is described. The prior art of the method using detection electrostatic force is described. Martin et al. proposed a method of detecting electric capacitance C on a sample surface using only AFM without employing a capacitance sensor [Y. Martin, D. W. Abraham, and H. K. Wickramasinghe,  Appl. Phys. Lett . 52, 1103 (1988)]. In this method, an AC electric field E of frequency f (angular frequency ω=2πf) is applied between a probe and a sample. The electrostatic force of the second harmonic component is detected. The principle of measurement is as follows. It is assumed that the probe-sample system is made up of flat metal plates parallel to each other. Let C be the capacitance. Let the direction vertical to the parallel plates be the Z-direction. When a voltage V is applied, an electrostatic force F given by Eq. (1) acts.              F   =       -     1   2              ∂   C       ∂   z            V   2               (   1   )                                
     If the voltage V applied between the probe and the sample is divided into a DC component V dc  and an AC component V ac , the voltage V is given by 
     
       
           V=V   dc   +V   ac  cos ω t   (2) 
       
     
     When this voltage V is applied, the electrostatic force F is given by              F   =       -     1   4              ∂   C       ∂   z            (       2        V     d                 c     2       +     4        V     d                 c            V     a                 c         +     V     a                 c     2     +       V     a                 c     2        cos                 2                 ω                 t       )               (   3   )                                
     If the relation V dc =0 is introduced, we have              F   =       -     1   4              ∂   C       ∂   z            (       V     a                 c     2     +       V     a                 c     2        cos                 2                 ω                 t       )               (   4   )                                
     Since the value of V ac  is known, the (∂C/∂z) component can be detected by detecting the second harmonic ( 2 ω) component. That is, the values of the physical property, such as capacitance C or dielectric constant ∈, can be measured. 
     In this method, however, a modulation method is not used, unlike the method using a capacitance sensor. Therefore, the effects of stray capacitance cannot be neglected and the sensitivity is low. 
     SUMMARY OF THE INVENTION 
     The present invention is intended to solve the foregoing problems. 
     It is an object of the invention to provide a method of measuring values of a physical property, such as capacitance C or dielectric constant ∈, by detecting electrostatic force, for example, without using any special capacitance sensor. 
     It is another object of the invention to provide a scanning probe microscope for implementing this method. 
     A method of measuring values of a physical property in accordance with the present invention consists of applying an AC voltage oscillating at an angular frequency of ω between a probe and a sample to thereby induce a force oscillating at an angular frequency of n×ω (n≧3) and detecting the induced force. Thus, the values of the physical property, such as capacitance C or dielectric constant ∈, are measured. 
     In the conventional method using detection of an electrostatic force, a modulation method is not used as mentioned previously. Therefore, electric capacitance C is imaged instead of differential capacitance (∂C/∂V). Therefore, there are the effects of stray capacitances. In the present invention, to solve this problem, an AC voltage V of angular frequency of ω is applied between the probe and the sample. In this case, it is assumed that the probe-sample system consists of flat metal plates parallel to each other and has an electric capacitance of C. Let the z-axis vertical to the parallel plates. The component ∂C/∂z is not constant, but is modulated by the applied voltage V and so we consider that the component ∂C/∂z is modulated by the angular frequency ω as given by                  ∂     C        (     V   ,   z     )           ∂   z       =         ∂     C        (       V     d                 c       ,   z     )           ∂   z       +           ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z              V     a                 c          cos                 ω                 t               (   5   )                                
     Therefore, the electrostatic force is given by              F   =       -     1   4            (         ∂     C        (       V     d                 c       ,   z     )           ∂   z       +           ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z              V     a                 c          cos                 ω                 t       )          (       V     a                 c     2     +       V     a                 c     2        cos                 2                 ω                 t       )               (   6   )                                
     This can be varied to:                    F   =            -       1   4     [           ∂     C        (       V     d                 c       ,   z     )           ∂   z            V     a                 c     2       +           ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z              V     a                 c     3        cos                 ω                 t     +                                    ∂     C        (       V     d                 c       ,   z     )           ∂   z            V     a                 c     2        cos                 2                 ω                 t     +                            1   2              ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z                V     a                 c     3          (       cos                 3                 ω                 t     +     cos                 ω                 t       )         ]                 (   7   )                                
     Accordingly, there exists the third harmonic ( 3 ω) component given by              F   =       -     1   8            (           ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z              V     a                 c     3        cos                 3                 ω                 t     )               (   8   )                                
     Therefore, information corresponding to an image of differential capacitance (∂C/∂V) can be obtained by detecting the third harmonic ( 3 ω) component. 
     The measuring apparatus according to the present invention is designed to measure values of a physical property of a sample by placing a probe and the sample close to or in contact with each other and characterized in that the apparatus includes at least one oscillator for applying an AC voltage of angular frequency ω between the probe and sample, force detection means for detecting a force produced by interaction between the probe and sample, and harmonic component extraction means for extracting a harmonic component n×ω (n≧3) contained in the output from the force detection means. 
     Other objects and features of the invention will appear in the course of the description thereof, which follows. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a measuring apparatus according to one embodiment of the present invention; 
     FIG. 2 is a spectrum showing the positions of the first and second harmonic angular frequencies of free resonance of a cantilever  2  in the form of a short strip included in the apparatus shown in FIG. 1; 
     FIG. 3 is a graph showing variations in the capacitance of the apparatus shown in FIG. 1 in a case where the probe  1  is placed at ground potential and a voltage is applied to a sample  3  that is a p-type semiconductor; 
     FIG. 4 is a graph similar to FIG. 3, but in which the sample  3  is an n-type semiconductor; 
     FIG. 5 is a block diagram of a measuring apparatus according to a further embodiment of the invention; 
     FIG. 6 is a block diagram of a contact mode AFM according to a still other embodiment of the invention; 
     FIG. 7 is a spectrum showing the positions of the first and second harmonic angular frequencies of free resonance of the cantilever  2  in the form of a short strip included in the apparatus shown in FIG. 5; 
     FIG. 8 is a block diagram of a measuring apparatus according to a still further embodiment of the invention; 
     FIG. 9 is a block diagram of a measuring apparatus according to a yet other embodiment of the invention; 
     FIG. 10 is a block diagram of a measuring apparatus according to an additional embodiment of the invention; 
     FIG. 11 is a block diagram of a measuring apparatus according to a yet further embodiment of the invention; 
     FIGS.  12 ( a )- 12 ( d ) are views illustrating the operation of the apparatus shown in FIG. 11; 
     FIG. 13 is a flow chart illustrating the operation of a processing circuit  52  in the apparatus shown in FIG. 11; 
     FIG. 14 is a view illustrating the operation of the first scan of the apparatus shown in FIG. 11 in step S 2  illustrated in FIG. 13; 
     FIG. 15 is a view illustrating the operation of the second scan of the apparatus shown in FIG. 11 in step S 5  illustrated in FIG. 13; and 
     FIG. 16 is a block diagram of a measuring apparatus according to a still further embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 is a block diagram of a dynamic mode AFM embodying the concept of the present invention, the dynamic mode AFM being one kind of scanning probe microscope. This instrument includes a cantilever  2  having a probe  1 . Deflection of the cantilever  2  can be detected by a deflection sensor consisting of a laser diode  4 , a pair of photodiodes  5 , and a differential amplifier  6 . A signal having an angular frequency of ω 1  is applied from a fixed oscillator  8  to a piezoelectric device  7  that is a drive means. Thus, the cantilever  2  and fitted with the probe  1  can be excited into oscillation. 
     The output signal from the deflection sensor includes an oscillatory component synchronized with the angular frequency ω 1  of the fixed oscillator  8 . The amplitude of this oscillatory component corresponds to the force produced by the interaction between the probe  1  and the sample  3 . This amplitude can be detected by converting it into a voltage, using a lock-in amplifier  9  to which a signal of the angular frequency ω 1  is supplied as a reference signal. When the probe  1  comes sufficiently close to the sample  3 , the probe receives the aforementioned force and the amplitude decreases. This amplitude can be maintained constant by adjusting the Z position of the sample by feeding the output from the lock-in amplifier  9  back to an XYZ drive mechanism  13  via a feedback circuit  10 , the drive mechanism  13  using a piezoelectric device that is driven via a high cutoff filter  11  and a high-voltage amplifier  12 . 
     The scanning probe microscope shown in this FIG. 1 is an atomic force microscope (AFM). The cantilever  2  has the probe  1  at its front end and is oscillated toward and away from the sample  3  at the angular frequency ω 1  of the fixed oscillator  8  by the drive means achieved by the piezoelectric device  7 . Light from the laser diode  4  is shot at the rear surface of the cantilever  2 . The reflected light is received by the photodiodes  5  that are light-receiving devices. The outputs from the photodiodes  5  are supplied to the differential amplifier  6 , which in turn produces a signal indicative of periodic deflection of the cantilever  2 . This signal is fed to the lock-in amplifier  9 . 
     The Z position of the sample (i.e., the position taken in the up-and-down direction (Z-direction) as viewed in FIG. 1) that varies according to the topography of the top surface of the sample  3  is adjusted by the XYZ drive mechanism  13  while scanning the probe across the surface of the sample  3  within the XY-plane that is a virtual plane vertical to the plane of FIG. 1. A straight virtual line connecting the probe  1  and sample  3  extends along the Z-direction. The output from the lock-in amplifier  9  corresponds to the force owing to the interaction between the probe  1  and the sample  3 . The output from the feedback circuit  10  is such that a voltage corresponding to this force assumes a predetermined value. The drive mechanism  13  moves the sample in the Z-direction according to the output from the feedback circuit  10 . A control voltage that is supplied from the feedback circuit  10  for driving the probe in the Z-direction is supplied to a display device. As a result, a topographic image  14  of the surface can be displayed. 
     An AC voltage of angular frequency ω from the fixed oscillator  15  is applied between the probe  1  and the sample  3  (i.e., between the sample  3  and ground) . A reference signal Vref is produced by tripling the angular frequency ω using a multiplier  16 . The third harmonic ( 3 ω) component of the electrostatic force is detected in synchronism with the reference signal Vref. Consequently, an image  18  of differential capacitance (∂C/∂V) is obtained. In particular, the lock-in amplifier  17  extracts the component synchronized with the reference signal Vref from the deflection output from the differential amplifier  6  and supplies the extracted component to the display device, thus producing the differential capacitance image  18 . The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of angular frequency  3 ω. 
     FIG. 2 is a spectrum illustrating angular frequencies used in the embodiment illustrated in FIG.  1 . As can be seen from FIG. 2, the mechanical resonator portion including the probe  1  and cantilever  2  has a resonant frequency at which the amplitude is boosted greatly by a resonance phenomenon. In the dynamic mode, the frequency of the fixed oscillator  8  is set to the first harmonic angular frequency (ω 1 ) (also known as the fundamental angular frequency) of free resonance of the cantilever  2 . The oscillations of the cantilever  2  induced by electrostatic force are amplified greatly by a resonance phenomenon by setting the angular frequency ω in such a way that  3 ω is coincident with the second harmonic angular frequency ω 2  of free resonance of the cantilever  2 . In consequence, values of a physical property can be measured with high sensitivity. 
     As an example, it is assumed that the cantilever  2  assumes the form of a short strip, the first harmonic angular frequency ω 1  of free resonance is 30 kHz, and the second harmonic angular frequency ω 2  is 189 kHz. In this case, an image of differential capacitance (ωC/ωV) is derived by setting the angular frequency ω to 63 kHz, detecting variations in the amplitude and the phase of the cantilever oscillation by using the lock-in amplifier  17 , and supplying the output signal from the amplifier  17  to the display device. The reference signal of 189 kHz phase-synchronized to the angular frequency ω is supplied to the lock-in amplifier  17 . 
     FIG. 3 is a graph showing variations in the capacitance of the embodiment illustrated in FIGS. 1 and 2 in a case where the probe  1  is placed at ground potential and voltage V is applied from the fixed oscillator  15  to the sample  3  that is a p-type semiconductor of Si. The bold line  41  indicates a case where the sample  3  is heavily doped. The thin line  42  indicates a case where the sample is lightly doped. The capacitance C increases when the voltage V applied to the sample  3  swings to the positive voltage side and decreases when the voltage V swings to the negative voltage side. That is, the sign of differential capacitance (∂C/∂V) is positive. The dopant concentration can be known from the magnitude of the absolute value of |∂C/∂V|. 
     FIG. 4 is a graph showing variations in the capacitance of the embodiment illustrated in FIG. 1 in a case where the probe  1  is placed at ground potential and voltage V is applied from the fixed oscillator  15  to the sample  3  that is an n-type semiconductor of Si. The bold line  43  indicates a case where the sample  3  is heavily doped. The thin line  44  indicates a case where the sample is lightly doped. The capacitance C decreases when the voltage V applied to the sample  3  swings to the positive voltage side and increases when the voltage V swings to the negative voltage side. That is, the sign of differential capacitance (∂C/∂V) is negative. The dopant concentration can be known from the magnitude of the absolute value of |∂C/∂V|. 
     In FIGS. 3 and 4, when signal  45  of the angular frequency ω is applied from the fixed oscillator  15  between the probe  1  and the sample  3  as mentioned previously, the phase characteristics of the amplitudes of the waveforms  46 ,  47 ,  48 , and  49  that are third harmonic ( 3 ω) components of the lock-in amplifier  17  are detected. The dopant concentration of the sample  3  that is dependent on the amplitudes can be detected. 
     The sample  3  is a Si semiconductor as mentioned previously. SiO 2  is formed on the surface. Images  14  and  18  are displayed by the display device that is achieved by a liqud-crystal display or CRT. The display device may be hereinafter indicated by these reference numerals  14  and  18 . Reference numerals  25  and  36  may also be used later for the same purpose. 
     FIG. 5 is a block diagram of another dynamic mode AFM to which the present invention is applied. It is to be noted that those components which correspond to their respective counterparts of the embodiment of FIG. 1 are indicated by the same reference numerals as in FIG.  1 . Deflection of the cantilever  2  fitted with the probe  1  can be detected by the deflection sensor consisting of laser diode  4 , photodiodes  5 , and differential amplifier  6 . The output signal from the differential amplifier  6  indicates the deflection of the cantilever  2 , and is amplified or attenuated in amplitude by an amplitude control circuit  19 . The piezoelectric device  7  is again driven by a phase shift circuit  20 . Thus, a self-oscillating loop, in a sense, can be formed. Oscillation at the first harmonic angular frequency ω 1  of free resonance of the cantilever  2  is sustained. The first harmonic angular frequency ω 1  varies according to the force owing to the interaction between the probe  1  and the sample  3 . Variations in the frequency can be detected by converting the frequency in to a voltage using a frequency detection circuit  57 . When the probe  1  comes sufficiently close to the sample  3 , an attractive force reduces the angular frequency ω 1 , while a repulsive force increases it. The output from the frequency detection circuit  57  is fed back to the XYZ drive mechanism  13  via the feedback circuit  10 . The drive mechanism  13  uses the piezoelectric device that is driven through the high cutoff filter  11  and high-voltage amplifier  12 . Consequently, the Z position of the sample can be so adjusted that the output from the frequency detection circuit  57  is kept at a predetermined value. 
     The output from the differential amplifier  6  is fed to the frequency detection circuit  57  consisting of a phase-locked loop circuit. The Z position of the sample (i.e., the position taken in the up-and-down direction (Z-direction) as viewed in FIG. 1) that varies according to the topography of the top surface of the sample  3  is adjusted by the XYZ drive mechanism  13  while scanning the probe across the surface of the sample  3  in the X- and Y-directions within a virtual plane vertical to the plane of FIG. 1. A straight virtual line connecting the probe  1  and sample  3  extends along the Z-direction. The output from the frequency detection circuit  57  corresponds to the force owing to the interaction between the probe  1  and the sample  3 . The output from the feedback circuit  10  is such that a voltage corresponding to this force assumes a predetermined value. The drive mechanism  13  adjusts the Z position of the sample according to the output from the feedback circuit  10 . A control voltage that is supplied from the feedback circuit  10  for driving the probe in the Z-direction is supplied to the display device. As a result, a topographic image  14  of the surface is displayed. 
     An AC voltage of angular frequency ω from the fixed oscillator  15  is applied between the probe  1  and the sample  3 . A reference signal Vref is produced by tripling the angular frequency ω using the multiplier  16 . The third harmonic ( 3 ω) component of the electrostatic force synchronized with the reference signal Vref is detected using the lock-in amplifier  17 . Consequently, an image  18  of differential capacitance (∂C/∂V) is obtained. In particular, the lock-in amplifier  17  extracts the output component synchronized with the reference signal Vref either from the output from the differential amplifier  6  or from the output from the frequency detection circuit  57  and supplies the extracted component to the display device, thus producing the differential capacitance image  18 . The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of the angular frequency  3 ω. 
     The signal supplied to the lock-in amplifier  17  to extract the component of the angular frequency  3 ω can be switched between the output from the differential amplifier  6  and the output from the frequency detection circuit  57 . When the switch  58  is connected to the side of the differential amplifier  6 , the same configuration as the embodiment of FIG. 1 is obtained. Therefore, oscillations of the cantilever due to electrostatic force are amplified greatly by a resonance phenomenon by setting the angular frequency ω in such a way that  3 ω is coincident with the angular frequency of the second harmonic component ω 2  of free resonance in the same way as in FIG.  1 . Consequently, measurement of values of a physical property at high sensitivity is performed. 
     Since the output from the frequency detection circuit  57  corresponds to the force owing to the interaction between the probe  1  and the sample  3 , an image  18  of differential capacitance (∂C/∂V) can also be obtained by connecting the switch  58  to the side of the frequency detection circuit  57  and detecting the third harmonic ( 3 ω) component contained in the output from the frequency detection circuit  57 , using the lock-in amplifier  17 . At this time, the Z position of the sample is so controlled that the output from the frequency detection circuit  57  assumes a preset value by feeding the output from the frequency detection circuit  57  back to the XYZ drive mechanism  13  using the piezoelectric device driven through the high cutoff filter  11  and high voltage amplifier  12  using the feedback circuit  10 . Since the response band of this control of distance is about 1 kHz, it is necessary to set the angular frequency ω to above about 1 kHz in order to prevent crosstalk and to obtain a correct image  14  of the surface topography. The frequency detection response band of the frequency detection circuit  57  is usually about 10 kHz. It is necessary to set the angular frequency ω such that  3 ω is about below 10 kHz. 
     In this atomic force microscope, the output signal from the differential amplifier  6  that is a signal indicative of the deflection of the cantilever  2  is delayed in phase by 90° with respect to the signal that controllably drives the piezoelectric device  7 . The output signal from the differential amplifier  6  is amplified or attenuated in amplitude by the amplitude control circuit  19  and supplied to the phase shift circuit  20  as mentioned previously. The phase is delayed by 90° and inverted in this phase shift circuit  20 . As a result, the signal from the phase shift circuit  20  is positively fed back to the piezoelectric device  7 . Therefore, the mechanical oscillation of the cantilever  2  continues. The frequency detection circuit  57  produces a voltage corresponding to the output frequency of the differential amplifier  6 . 
     FIG. 6 is a block diagram of a contact mode AFM embodying the concept of the invention. Those components which correspond to their respective counterparts of FIG. 1 are denoted by the same reference numerals as in FIG.  1 . In the present embodiment, the piezoelectric device  7  shown in FIG. 1 is omitted. The base end of the cantilever  2  is fixedly mounted to a stationary position. In this embodiment, the probe  1  is kept in contact with the surface of the specimen  3 . Deflection of the cantilever  2  fitted with the probe  1  can be detected by a deflection sensor consisting of laser diode  4 , photodiodes  5 , and differential amplifier  6 . While the probe  1  is scanned on the sample  3 , deflection of the cantilever  2  is detected by this deflection sensor. The output from this deflection sensor is fed back to the XYZ drive mechanism  13  driven through the high cutoff filter  11  and high voltage amplifier  12  using the feedback circuit  10 . The deflection can be maintained constant by adjusting the Z position of the sample. A topographic image  14  of the surface can be displayed by scanning the probe in the X- and Y-directions by the XYZ drive piezoelectric device  13 , simultaneously adjusting the Z position of the sample  3  according to the topography of the sample, and supplying a Z-drive control voltage to the display device from the feedback circuit  10 . 
     An AC voltage of angular frequency ω from the fixed oscillator  15  is applied between the probe  1  and the sample  3 . A reference signal Vref is produced by tripling the angular frequency o using the multiplier  16 . The third harmonic ( 3 ω) component of the electrostatic force synchronized with the reference signal Vref is detected using the lock-in amplifier  17 . Consequently, an image  18  of differential capacitance (∂C/∂V) is obtained. In particular, the lock-in amplifier  17  extracts the component synchronized with the reference signal Vref from the deflection output from the differential amplifier  6  and supplies the extracted component to the display device, thus producing the differential capacitance image  18 . The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of the angular frequency  3 ω. 
     FIG. 7 is a spectrum illustrating angular frequencies used in the embodiment illustrated in FIG.  6 . As can be seen from this FIG. 7, when the probe  1  is in contact with the surface of the sample  3 , the mechanical resonator portion including the probe  1  and cantilever  2  has a contact resonant angular frequency ωc determined by the interaction between the probe  1  and the sample  3 . Therefore, oscillations of the cantilever  2  due to electrostatic force are greatly amplified by a resonance phenomenon by setting the angular frequency ω of the fixed oscillator  15  in such a way that  3 ω is coincident with the contact resonant angular frequency ωc. Hence, the values of a physical property can be measured with high sensitivity. 
     FIG. 8 is a block diagram of a contact mode AFM according to a still other embodiment of the invention. It is to be noted that those components which correspond to their respective counterparts of the embodiments of FIGS. 1 and 5 are indicated by the same reference numerals as in FIGS. 1 and 5. The probe  1  is kept in contact with the surface of the specimen  3 . Deflection of the cantilever  2  fitted with the probe  1  can be detected by a deflection sensor consisting of laser diode  4 , photodiodes  5 , and differential amplifier  6 . When the probe  1  touches the sample  3 , deflection of the cantilever  2  is detected by this deflection sensor. The output from this deflection sensor is fed back to the XYZ drive mechanism  13  driven through the high cutoff filter  11  and high voltage amplifier  12  using the feedback circuit  10 . The deflection can be maintained constant by adjusting the Z position of the sample in such a way that the output from the differential amplifier  6  assumes a preset value. A topographic image  14  of the surface can be displayed by scanning the sample relative to the probe in the X- and Y-directions by the XYZ drive piezoelectric device  13 , simultaneously adjusting the Z position of the sample  3  according to the topography of the sample, and supplying a Z-drive control voltage obtained at this time from the feedback circuit  10  to the display device. 
     Because the contact resonance frequency is determined by the interaction between the probe  1  and the sample  3 , this frequency varies depending on the state of contact between the probe and sample, on the elastic constant of the sample surface, and on the undersurface structure. The output signal from the differential amplifier  6  indicates deflection of the cantilever  2 , and is amplified or attenuated in amplitude by the amplitude control circuit  19 . The piezoelectric device  7  is a gain driven by the phase shift circuit  20 . Thus, a self-oscillating loop, in a sense, can be formed. In this case, if the contact resonance frequency of the cantilever  2  varies, it can be maintained in oscillation at the contact resonance frequency at all times. Therefore, a voltage corresponding to variations in the contact resonance frequency of the cantilever  2  can be obtained by the frequency detection circuit  21  that is accomplished by a phase-locked loop, for example. At this time, the variations in this voltage are supplied to the display device and imaged as a contact resonant frequency image  25 . In this way, information about the elastic constant of the sample surface and the under surface structure can be derived. 
     When a voltage control switch  23  for a voltage variable oscillator  24  is switched to the side of a fixed-voltage DC power supply  22 , the oscillator  24  can be controlled by the fixed-voltage DC power supply  22  that produces a constant preset DC voltage. An AC voltage of the obtained constant angular frequency ω can be applied between the probe  1  and the sample  3 . The output from the voltage variable oscillator  24  is supplied to the multiplier  16 . A reference signal having a frequency that is the triple of the angular frequency ω is obtained. This reference signal is fed to the lock-in amplifier  17 . In consequence, the third harmonic ( 3 ω) component of electrostatic force synchronized to this reference signal can be detected. The resulting signal is supplied to the display device. In this way, an image  18  of differential capacitance (∂C/∂V) is obtained. The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of the angular frequency  3 ω. 
     When the voltage control switch  23  for the voltage controlled oscillator  24  is switched to the side of the frequency detection circuit  21 , the oscillation frequency of the voltage controlled oscillator  24  can be dynamically controlled corresponding to the variations in the contact resonance frequency detected by the frequency detection circuit  21 . An AC voltage of the obtained variable angular frequency ω of is applied between the probe  1  and sample  3 . Consequently, the third harmonic frequency ( 3 ω) of the angular frequency ω can be brought into coincidence with the contact resonance frequency of the cantilever  2 . The third harmonic ( 3 ω) component of electrostatic force can be obtained as the output from the lock-in amplifier  17 . In consequence, the stability of the measurement of the values of a physical property of the sample  3  can be enhanced. 
     In this atomic force microscope, the output signal from the differential amplifier  6  that is a signal indicative of the deflection of the cantilever  2  is delayed in phase by 90° with respect to the signal that controllably drives the piezoelectric device  7 . The output signal from the differential amplifier  6  is amplified or attenuated in amplitude by the amplitude control circuit  19  and supplied to the phase shift circuit  20  as mentioned previously. The phase is delayed by 90° and inverted in this phase shift circuit  20 . As a result, the signal from the phase shift circuit  20  is positively fed back to the piezoelectric device  7 . Therefore, the mechanical oscillation of the cantilever  2  continues. The frequency detection circuit  21  produces a voltage corresponding to the output frequency of an amplifier circuit  19 . 
     FIG. 9 is a block diagram showing a measuring apparatus according to a yet other embodiment of the invention. The present embodiment is similar to the embodiment of FIG. 1, and those components which correspond to their respective counterparts of FIG. 1 are indicated by the same reference numerals as in FIG.  1 . In the present invention, the interaction between the probe  1  and the sample  3  is maintained constant by maintaining constant the tunneling current flowing between the probe  1  and sample  3 . As a DC voltage is applied between the sample and probe, a tunneling current flows from the sample  3  to the cantilever  2  fitted with the probe  1 . This current is detected by a current-voltage converter circuit  30  and fed back to the XYZ drive mechanism  13  via feedback circuit  10 , high cutoff filter  11 , and high-voltage amplifier  12 . Thus, the Z position of the sample is controlled. As a result, the tunneling current can be maintained at a preset constant value. When the sample is scanned relative to the probe by the XYZ drive mechanism  13 , the Z position of the sample  3  is adjusted according to the topography of the sample  3 . The control voltage that is supplied from the feedback circuit  10  for driving the sample in the Z direction is fed to the display device. As a result, a topographic image  14  based on the tunneling current can be displayed. In this embodiment of FIG. 9, the piezoelectric device  7  used in the embodiment of FIG. 1 is omitted. The base end of the cantilever  2  is fixedly mounted to a stationary position. 
     In the present embodiment, an AC voltage of the angular frequency ω is applied between the probe  1  and sample  3  from the fixed oscillator  15  when the Z position of the sample  3  is controlled according to the tunneling current as mentioned previously. Interaction between the probe and sample which is induced by the AC voltage deflects the cantilever  2 . The output signal from the differential amplifier  6  that is a signal indicative of the deflection is supplied to the lock-in amplifier  17 , which is supplied with a reference signal obtained by tripling the angular frequency ω using the multiplier  16 . As a result, the third harmonic ( 3 ω) component of electrostatic force synchronized to the reference signal is detected. The resulting signal is supplied to the display device. Consequently, an image  18  of differential capacitance (∂C/∂V) is obtained. The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of the angular frequency  3 ω. 
     Furthermore, the angular frequency ω is so set that  3 ω is coincident with the first harmonic angular frequency (ω 1 ) of the free resonance (ω 1 = 3 ω). Oscillations of the cantilever due to electrostatic force are amplified greatly by a resonance phenomenon. Therefore, the values of a physical property can be measured with high sensitivity. 
     FIG. 10 is a block diagram of a measuring apparatus according a yet other embodiment of the invention. This embodiment provides an example of structure of dynamic mode AFM. This embodiment is similar to the embodiment of FIG. 1, and those components which correspond to their respective counterparts of FIG. 1 are indicated by the same reference numerals as in FIG.  1 . In the present embodiment, plural AC voltages having different angular frequency components ωA and ωB (where ωA&gt;ωB) are simultaneously applied between the probe  1  and sample  3 , inducing forces oscillating at angular frequencies |(m−n)×ωA±n×ωB|(m&gt;n), where n and m are natural numbers. These forces are detected. 
     Fixed oscillators  26  and  27  produce angular frequencies ωA and ωB, respectively. Signals of these angular frequencies ωA and ωB are denoted by V A  cos ωAt and V B  cos ωBt, respectively. These are added up by an adder  28 , resulting in signal V given by 
     
       
           V=V   A  cos ω A   t+V   B  cos ω B   t   (9) 
       
     
     
       
         
           
             
               
                 
                   
                     
                       
                         F 
                         = 
                           
                          
                         
                           
                             - 
                             
                               1 
                               2 
                             
                           
                            
                           
                             
                               ∂ 
                               C 
                             
                             
                               ∂ 
                               z 
                             
                           
                            
                           
                             
                               ( 
                               
                                 
                                   
                                     V 
                                     A 
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ω 
                                     A 
                                   
                                    
                                   t 
                                 
                                 + 
                                 
                                   
                                     V 
                                     B 
                                   
                                    
                                   cos 
                                    
                                   
                                       
                                   
                                    
                                   
                                     ω 
                                     B 
                                   
                                    
                                   t 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             
                               1 
                               4 
                             
                           
                            
                           
                             
                               
                                 ∂ 
                                 C 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                             [ 
                             
                               
                                 V 
                                 A 
                                 2 
                               
                               + 
                               
                                 
                                   V 
                                   A 
                                   2 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ω 
                                   A 
                                 
                                  
                                 t 
                               
                               + 
                               
                                 V 
                                 B 
                                 2 
                               
                               + 
                               
                                 
                                   V 
                                   B 
                                   2 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ω 
                                   b 
                                 
                                  
                                 t 
                               
                               + 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             
                               V 
                               A 
                             
                              
                             
                               V 
                               B 
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   
                                     ω 
                                     A 
                                   
                                   + 
                                   
                                     ω 
                                     B 
                                   
                                 
                                 ) 
                               
                             
                              
                             t 
                           
                           + 
                           
                             
                               V 
                               A 
                             
                              
                             
                               V 
                               B 
                             
                              
                             
                               cos 
                                
                               
                                 ( 
                                 
                                   
                                     ω 
                                     A 
                                   
                                   - 
                                   
                                     ω 
                                     B 
                                   
                                 
                                 ) 
                               
                             
                              
                             t 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     Since the above relations hold, in a case where ∂C/∂z can be regarded as constant with respect to z, when a voltage of a single angular frequency ω is applied, a frequency component of (ωA+ωB) or (ωA−ωB) may be detected by the lock-in amplifier  17  instead of measuring the second harmonic. Since V A  and V B  are known, ∂C/∂z can be detected. 
     Furthermore, in a case where ∂C/∂z is not constant but is modulated by the applied voltage V, we have                        ∂     C        (     V   ,   z     )           ∂   z       =                ∂     C        (       V     d                 c       ,   z     )           ∂   z       +                                ∂   2          C        (       V     d                 c       ,   z     )             ∂   V          ∂   z              (         V   A        cos                   ω   A        t     +       V   B        cos                   ω   B        t       )                     (   11   )                                
     Therefore, in a case where a voltage of a single angular frequency ω is applied, any one of four frequencies |ωA+(ωA+ωB)|, |ωB+(ωA+ωB)|, |ωA+(ωA−ωB)|, and |ωB−(ωA−ωB)| (i.e.,  2 ωA±ωB and |ωA± 2 ωB|) is detected by the lock-in amplifier  17  instead of a measurement where the third harmonic is detected. 
     In FIG. 10, deflection of the cantilever  2  fitted with the probe  1  can be detected by a deflection sensor consisting of a laser diode  4 , a pair of photodiodes  5 , and a differential amplifier  6 . A signal from a fixed oscillator  8  is applied to a piezoelectric device  7  to excite the cantilever  2  into oscillation, the cantilever  2  being fitted with the probe  1 . 
     The amplitude of the oscillatory component synchronized to the angular frequency ω 1  of the fixed oscillator  8  can be converted into a voltage and detected using the lock-in amplifier  9 . The angular frequency of the fixed oscillator  8  is set to the first harmonic angular frequency ω 1  of free resonance of the cantilever  2 . When the probe  1  comes sufficiently close to the sample  3 , the amplitude decreases. This amplitude can be maintained constant by adjusting the Z position of the sample by feeding the output from the lock-in amplifier  9  back to an XYZ drive mechanism  13  using a piezoelectric device that is driven via high cutoff filter  11  and high-voltage amplifier  12  using the feedback circuit  10 . 
     An AC voltage that is obtained as the output from the adder  28  is applied between the probe  1  and the sample  3  as described above. The amplitude and phase of the signal component having the same frequency as a reference signal having a frequency equal to a desired one of the  2 ωA±ωB and |ωA± 2 ωB | obtained by the frequency converter  29  are detected using the lock-in amplifier  17  and supplied to the display device. Consequently, an image  18  of differential capacitance (∂C/∂V) is obtained. The combination of the frequency converter  29  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes a desired one of angular frequency components  2 ωA±ωB and |ωA± 2 ωB|. 
     The oscillations of the cantilever  2  induced by electrostatic force are amplified greatly by a resonance phenomenon by setting ωA and ωB in such a way that  2 ωA−ωB is coincident with the second harmonic angular frequency (ω 2 ) of free resonance. In consequence, the values of a physical property can be measured with high sensitivity. As an example, it is assumed that the cantilever  2  assumes the form of a short strip, the first harmonic angular frequency ω 1  of free resonance is 30 kHz, and the second harmonic angular frequency ω 2  is 189 kHz. Let ωA and ωB be equal to 5.189 MHz and 10.189 MHz, respectively. Then,  2 ωA−ωB is 189 kHz. The values of a physical property, such as electric capacitance C or dielectric constant e, for high-frequency signals in the megahertz range can be detected by detection of a signal in a lower-frequency range. 
     The oscillations of the cantilever  2  induced by electrostatic force are amplified greatly by a resonance phenomenon by setting ωA and ωB in such a way that  2 ωA−ωB is coincident with the second harmonic angular frequency (ω 2 ) of free resonance. In consequence, the values of a physical property can be measured with high sensitivity. As an example, it is assumed that the cantilever  2  assumes the form of a short strip, the first harmonic angular frequency ω 1  of free resonance is 30 kHz, and the second harmonic angular frequency ω 2  is 189 kHz. Let ωA and ωB be equal to 5.189 MHz and 10.189 MHz, respectively. Then,  2 ωA−ωB is 189 kHz. The values of a physical property, such as electric capacitance C or dielectric constant e, for high-frequency signals in the megahertz range can be detected by detection of a signal in a lower-frequency range. 
     FIG. 11 is a block diagram of a measuring apparatus according to a further embodiment of the invention. This embodiment is similar to the embodiment illustrated in FIG.  1 . Those components which correspond to their respective counterparts of FIG. 1 are denoted by the same reference numerals as in FIG.  1 . It is to be noted that this embodiment has a processing circuit  52  realized by a microcomputer. The outputs from the feedback circuit  10  and lock-in amplifier  17  are fed to this processing circuit  52 . The processing circuit  52  controls the operation of the high-voltage amplifier  12  via a selector switch  54 . This switch  54  switches the signal supplied to the high-voltage amplifier  12  between the output from the high cutoff filter  11  and the output from the processing circuit  52 . A memory  53  is connected with the processing circuit  52 . Another switch  59  is interposed between the fixed oscillator  8  and piezoelectric device  7 . A further switch  60  is inserted between the fixed oscillator  15  and the sample  3 . These switches  54 ,  59 , and  60  are turned on and off under control of the processing circuit  52 . 
     FIGS.  12 ( a )- 12 ( d ) are views illustrating the operation of the embodiment illustrated in FIG. 11. A case similar to the embodiment of FIG. 1 is now considered. That is, the probe  1  is scanned while maintaining constant the interaction between the probe  1  and the sample  3 . Thus, the surface topography is measured. At the same time, information about the values of a physical property, such as an image of differential capacitance (∂C/∂V), is obtained. As shown in FIG.  12 ( a ), sample  3  has portions A 1  and B 1  which differ in the value of a physical property on its surface. The probe  1  is scanned on the sample  3  as indicated by the arrow  61 . The topography of the sample surface is measured. At the same time, the value of a physical property is measured. As a result, a normal image of the surface topography, as shown in FIG.  12 ( b ), is derived. In some cases, an inaccurate image containing information about the distribution of the values of a physical property, as shown in FIG.  12 ( c ), may be obtained. That is, as the surface topography varies, as shown in FIG.  12 ( c ), signals  55  and  56  independent of the distribution of the correct values of a physical property of the sample surface may be obtained as a distribution of the physical property values. 
     In the present embodiment, the surface topography of the sample is first measured. Information about the obtained topography is recorded. Then, the probe is again scanned along a trajectory at a predetermined distance from the sample surface according to the recorded information about the surface topography. The value of a physical property is also measured. In this way, information about the physical property values is obtained without being affected by the surface topography. The procedure is next described. 
     FIG. 13 is a flowchart illustrating the operation of the processing circuit  52  in the embodiment shown in FIG.  11 . The switch  54  shown in FIG. 11 has been previously switched to the output side of the high cutoff filter  11 . Control proceeds from step S 1  to S 2 , where the switch  59  is first turned ON and the switch  60  is turned OFF as shown in FIG.  14 . The cantilever  2  is oscillated at the angular resonant frequency ω 1  by the fixed oscillator  8 . The surface topography of the sample  3  is measured. In step S 3 , data about the surface topography obtained from the feedback circuit  10  is stored in the memory  53 . 
     Then, in step S 4 , a predetermined distance L 1  is added to or subtracted from the data about the surface topography. In step S 5 , the switch  54  of FIG. 11 is switched to the output side of the processing circuit  52 . As shown in FIG. 15, the switch  59  is turned OFF and the switch  60  is turned ON. Under this condition, a second scan is made to measure the values of a physical property. At this time, the high-voltage amplifier  12  is controlled according to the results of the calculation performed in step S 4 . Consequently, the probe  1  is moved along the surface topography of the sample. Therefore, the distance between the sample and the probe is maintained constant at all times. Under this condition, the values of a physical property are measured. In the embodiment of FIG. 11, signals  55  and  56  independent of the distribution of values of a physical property are not contained as shown in FIG.  12 ( d ). Thus, correct information about the distribution of only values of a physical property is obtained. 
     FIG. 16 is a block diagram showing the structure of a measuring apparatus according to a yet additional embodiment of the invention. The present embodiment is similar to the embodiment already described in connection with FIG. 1, and those components which correspond to their respective counterparts of FIG. 1 are indicated by the same reference numerals as in FIG.  1 . The present embodiment is characterized in that electrostatic force acting between the probe  1  and the sample  3  is canceled to thereby obtain information about the work functions of the probe  1  and sample  3 . An AC voltage Vp of angular frequency ωp produced by the fixed oscillator  31  is added to the output voltage Vdc from an inverting amplifier  35  by the adder  32  and applied to the sample  1 . Where the probe  1  and sample  3  differ in material, there is a voltage Vcpd that is a work function difference. The electrostatic force is given by                    F   =                -     1   2              ∂   C       ∂   z            V   2       =         -     1   2              ∂   C       ∂   z              (       V     c                 p                 d       +     V     d                 c       +       V   p        cos                   ω   p        t       )     2       =                              -     1   2                ∂   C       ∂   z       [         (       V     c                 p                 d       +     V     d                 c         )     2     +                                2        (       V     c                 p                 d       +     V     d                 c         )          V   p        cos                   ω   p        t     +       V   p   2          cos   2          ω   p        t       ]                 (   12   )                                
     The components of the angular frequency ωp are detected by the lock-in amplifier  33 . The voltage V dc  that satisfies the relation 
     
       
           V   cpd   +V   dc =0  (13) 
       
     
     can be adjusted using the feedback circuit  34  and inverting amplifier  35 . At this time, we have 
     
       
           V   dc   =−V   cpd   (14) 
       
     
     The difference in work function between the probe  1  and sample  3  is canceled out. The voltage required for this cancellation is imaged. Consequently, a surface potential image  36  can be obtained. 
     An AC voltage of the angular frequency ω from the fixed oscillator  15  is applied between the probe  1  and sample  3  through the adder  32 . A reference signal is produced by multiplying the angular frequency ω using the multiplier  16 . The third harmonic ( 3 ω) component of electrostatic force synchronized to the reference signal is detected using the lock-in amplifier  17 . Thus, an image  18  of differential capacitance (∂C/∂V) is obtained. The combination of the multiplier  16  and lock-in amplifier  17  used in the present embodiment can be replaced by a bandpass filter that passes the component of the angular frequency  3 ω. 
     The oscillations of the cantilever  2  induced by electrostatic force are amplified greatly by a resonance phenomenon by setting the angular frequency ω in such a way that  3 ω is coincident with the second harmonic angular frequency ω 2  of free resonance of the cantilever  2  (ω 2 = 3 ω) , in the same way as in the embodiment illustrated in FIG.  1 . In consequence, the values of a physical property can be measured with high sensitivity. 
     It is to be understood that the present invention is not limited to the above embodiments but can be modified variously. For example, where the instrument is so designed that the factor of multiplication of the multiplier can be switched also to 2, the mode of operation can be switched to a mode in which measurements of the values of physical properties based on the second harmonic as proposed heretofore can be carried out. 
     In the above embodiments, the sample is driven in making scans. The probe may be moved relative to the sample. In summary, one of the probe and sample may be moved relative to the other. 
     Furthermore, in the above embodiments, the Z position of the sample is varied by the drive mechanism  13  to thereby adjust the distance between the sample and probe. Instead, the Z position of the probe may be varied.