Abstract:
An apparatus capable of tracking a sample surface level in a z direction and oscillating a cantilever at resonant frequency by using a frequency separation scheme in non-contact mode and method thereof. The inventive apparatus includes a sensing unit for sensing a sample surface; a frequency transforming unit for transforming the sensed signal; a frequency combining unit for combining signals; and an actuating unit for actuating the sensing unit.

Description:
FIELD OF THE INVENTION 
     The present invention relates to a non-contact scanning apparatus and a method for non-contact scanning; and more particularly, to a non-contact scanning apparatus capable of simultaneously tracking a sample surface and oscillating a sensor mounted at a distal end of an actuator in an atomic force microscope (AFM) and similar type of microscope using a single actuator through the use of a frequency response separation scheme in a non-contact mode. 
     DESCRIPTION OF RELATED ARTS 
     There are two types of scanning probe microscopy (SPM) for measuring sample surface characteristics. One is a contact mode wherein a tip contacts a sample surface and the other is a non-contact mode wherein a tip does not contact a sample surface. 
     As for the non-contact mode, a cantilever tip must be oscillated with a resonant frequency and mostly a piezoelectric (PZT) scanner is used to make a movement of the sample in x-y-z directions by using a voltage from piezoelectric material which has a broad frequency range. 
     Particularly, in case of controlling the gap between a tip and a sample according to an optical method, two actuators are necessary, one for oscillating a cantilever and the other for moving a cantilever in a vertical direction with respect to the surface of sample so as to keep a consistent space between the probe and the surface of sample. In case of not using an optical method, a tuning fork to which an optical fiber or a carbon nano tube is attached is used for measuring oscillation. Also, for the non-contact mode, a sensor-doped or fabricated cantilever can be used, or an additional actuator can be used to oscillate the cantilever. 
     Prior arts related to this field will be described in the following. 
     [Prior Art 1] 
     A method for measuring a displacement at a distal end of a cantilever using a laser diode (LD) and a photo diode (PD) is the most broadly known method in SPM field. Although it is difficult to align the LD and the PD, those LD and PD can be aligned easily with use of a well-developed method in this field. 
     However, if a displacement arises in a large extent at a fixed part of the cantilever, an oscillation range of the cantilever gets sufficiently small because of deflected optical alignment. Because of this problem, an actuator for oscillating the cantilever at a resonant frequency and an actuator for controlling a tip/sample gap in a vertical direction cannot be used together. A signal from the PD is signal-processed in a lock-in amplifier. The signal processing in a lock-in amplifier is disclosed in U.S. Pat. No. 5,955,660 entitled “Method of controlling probe microscope.” 
     [Prior Art 2] 
     Another method for measuring a tip/sample gap in non-contact mode employs a tuning-fork. An optical fiber for a near field scanning optical microscope (NSOM) or a carbon nano tube for an atomic force microscope (AFM) is attached to a tuning-fork. In these two methods, the tuning-fork measures variation of an amplitude of oscillation in a form of electrical or optical signals as the tip/sample gap varies. However, attachment of the optical fiber or carbon nano-tube onto the tuning-fork is very difficult, and sensitivity varies with every attachment. 
     Also, an additional actuator for controlling a cantilever in a Z direction is necessary because the tuning-fork is solely used for sensing the tip/sample gap. A XYZ Scanner is usually used as the additional actuator, which is disclosed in an article by Masami Kageshima and et al., “Non-contact atomic force microscopy in liquid environment with quartz tuning fork and carbon nanotube probe”, Applied Surface Science, 7695, 2002, pp 1–5, and U.S. Pat. No. 6,094,971 entitled “Scanning-probe microscope including non-optical means for detecting normal tip-sample interactions.” 
     [Prior Art 3] 
     To solve the problem of difficulty in optical alignment of SPM, a cantilever with a sensor is broadly used, wherein the cantilever on which a Piezo-resistive material is doped or fabricated. This case is advantageous that a sensor mounted cantilever can be attached to the actuator moving in the Z direction. However, a sensor mounted cantilever in non-contact mode in as shown in the Prior art 1 should have one actuator for oscillating the cantilever with a resonant frequency and another actuator for driving the cantilever in the Z direction of a sample surface. If the difficulty of optimal alignment is negligible, this method can be used for measuring sample surface topography and characteristics. Although an optical method has a better sensitivity, resolution of the sample surface topography is low. However, there is not much difference in sensitivity when using a lock-in amplifier in non-contact mode, which is disclosed in an article by J. Thaysen et al., “Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement”, Sensor and Actuators 83, 2000, pp 47–53. 
     [Prior Art 4] 
     One step further of the cantilever with the sensor is a cantilever with a sensor and an actuator, each element being fabricated and incorporated with each other in one-step process. There are several advantages on the cantilever designed at its own resonant frequency, and another advantage is that the function of sensing and actuating is realized in single sensor/actuator cantilever. 
     However, when fabricating these cantilevers, a trade off between the design for high resonant frequency and the design for large actuating range exists. The general actuating range of the prior art was around 1 μm. Even though this level of actuating range can be used in a certain sample surface, the general sample surface needs actuating range of about 10 μm. 
     Therefore, in the prior art 4, an additional actuator for controlling a cantilever in a Z direction of a sample surface is necessary for a practical implementation, which is disclosed in an article by Shunji Watanabe and Toru Fujii, “Micro-fabricated piezoelectric cantilever for atomic force microscopy”, Rev, Sci. Instrum. 67(11), 1996, pp 3898–3903. 
     SUMMARY OF THE INVENTION 
     It is, therefore, an object of the present invention to provide an apparatus and method for tracking a sample surface level with a single actuator while not using an additional actuator for driving a cantilever in a Z direction and for oscillating a cantilever at its own resonant frequency in a non-contact mode by using a frequency response separation scheme. 
     In accordance with an aspect of the present invention, there is provided an apparatus for measuring in non-contact mode including a sensing unit for sensing through the amplitude variation of the sensor&#39;s resonant frequency keeping a distance from the sample which is moving in the X and Y directions; a frequency transforming unit for transforming the measured signal in the sensing unit to the first signal in the form of frequency; a frequency combining unit for combining the first signal and the second signal from the function generator, wherein the second signal is identical to the resonant signal and higher frequency compared to the first signal; and actuating unit for actuating the sensing unit responding to the first signal which is a low frequency compared to the second signal and providing the combined signal to sensing unit to actuate the sensing unit selectively in the second signal which is relatively high frequency compared to the first signal. 
     In accordance with another aspect of the present invention, there is also provided an apparatus for measuring by using a frequency response separation, including the steps of a) sensing through the amplitude variation of the sensor&#39;s resonant frequency keeping a distance from the sample which is moving in the X and Y directions; b) transforming the measured signal to the first signal in the form of frequency, wherein; c) combining the first signal and the second signal from the function generator, wherein the second signal is identical to the resonant signal and higher frequency compared to the first signal; d) transferring the combined signal by the feedback loop; and e) actuating the sensing unit responding to the first signal which is relatively low frequency compared to the second signal and executing the frequency response separation by providing the combined signal to sensing unit to actuate the sensing unit selectively in the second signal which is relatively high frequency compared to the first signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects and features of the present invention will become apparent from the following description of the preferred embodiments given in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram showing a microscope, wherein a self-sensing cantilever and an actuator are combined in accordance with the present invention; 
         FIG. 2  is a block diagram showing a combining of two different input signals applied to the actuator in accordance with the present invention; 
         FIG. 3  is a block diagram showing a mathematical modeling of a system including a sensor and an actuator to explain how to separate a combined signal in the system; 
         FIGS. 4A to 4C  are graphs showing mathematical analysis results with respect to a frequency response of an actuator and a sensor; 
         FIG. 5  is a graph showing a result of an experiment in frequency responses of an actuator; 
         FIG. 6  is a graph showing a result of an experiment in frequency responses of a sensor; 
         FIG. 7  is a graph showing an amplitude variation of the cantilever by a tip/sample gap and a gap setting for sensing a sample surface; 
         FIG. 8  is a graph showing a result of measuring a sample surface of about 10 μm square lattice in non-contact mode; 
         FIG. 9  is a block diagram showing combinations to which a frequency separation scheme can be applied in accordance with the present invention; and 
         FIG. 10  is a flowchart showing a method of measuring a sample surface by using a frequency separation scheme in accordance with the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a diagram of an electronic microscope combined with a self-sensing cantilever and an actuator in accordance with the present invention. 
     Referring to  FIG. 1 , the electronic microscope includes an X-Y scanner  11  for scanning a sample surface in the direction of X and Y on a base unit  10 . A sample  12  is located on the base unit to be measured by the X-Y scanner  11 . 
     A cantilever  15  has a self-sensing unit over the sample  12  and a tip  14  mounted at a distal end of the cantilever  15  for sensing a sample surface. The cantilever  15  is supported by an actuator  16  which drives the cantilever  15  in a Z direction. The actuator  16  is supported by a fixed member  17 . 
     The variation of a gap between the tip  14  and the sample  12  is compared to a resonant frequency, f R  is a resonant frequency of the cantilever  15 , and then a lock-in amplifier  18  calculates an actual distance between the tip  14  and the sample  12  and outputs a low frequency f L  signal responding to the calculated distance between the tip  14  and the sample  12 . 
     A function generator  19  outputs a resonant frequency f R  for oscillating the cantilever. Herein, the outputted resonant frequency f R  is greater than the above low frequency f L , for example, f L =1 kHz, f R =37 KHz. A frequency combining unit  20  modulates the resonant frequency f R  and the low frequency signal f L  to drive the actuator  16  in the Z direction. 
     Subsequent operation procedure will be explained in detail below. 
     The frequency combining unit  20  outputs a combined signal f R +f L , which is, in turn applied to the actuator  16 . Herein, the signal f R +f L  is a combined signal of the resonant frequency f R  outputted from the function generator  19  for oscillating the cantilever  15  and the low frequency signal f L  which is a surface profile of sample. The combined signal f R +f L  drives the actuator  16  with a voltage signal and driving force makes the movement of the cantilever  15  in the Z direction and oscillates the cantilever  15  with the resonant frequency f R  simultaneously. 
     A magnitude of an oscillation signal, i.e., an amplitude of the signal varies with the gap between the tip  14  of cantilever  15  and the sample  12 . Therefore, the variation of these amplitudes is measured by a self-sensing unit  13  which is attached to the cantilever  15  and then these variable amplitudes are calculated into a surface profile of the sample  12  in the lock-in amplifier  18 . 
     The above measured signal is passed to a feedback loop which starts with measuring the sample surface profile in the lock-in amplifier  18  with use of the measured signal, which is in turn, used as a low frequency signal f L  for driving the actuator  16  by being coupled to the actuator  16 , and subsequently being coupled to the frequency combining unit  20 . 
       FIG. 2  is a block diagram showing a method for combining two different signals, which are a resonant frequency signal of the cantilever and a low frequency voltage signal responding to a surface profile of the sample  18 . 
     In  FIG. 2 , the highest value and the lowest value of a voltage signal does not exceed the maximum voltage. Although a voltage of the resonant frequency is small, it is high enough to oscillate the cantilever  15 . 
       FIG. 3  is a block diagram showing a frequency separation scheme based on a difference in frequency responses, particularly showing how a combined voltage signal from a frequency combining unit  20  is separated in a unit including the actuator  16  and the sensing unit  13 . 
     In  FIG. 3 , the actuator  16  and the sensing unit  13  can be modeled in the structure of mass, i.e., M and m, spring, i.e., K v  and K c , and damper, i.e., b v  and b c . 
     The actuator  16  and the sensing unit  13  have a different frequency band sensitively responding to the combined signal. 
     The resonant frequency of the cantilever  15  is even higher than that of the actuator  16  and the actuator  16  functions same as a low pass filter. The actuator movement for a high frequency band is very small and the response to a low frequency voltage signal becomes about 1:1. In this manner, signals are separated by their frequency responses. 
     The frequency response of the actuator  16  responding to a high frequency band of these separated signals is very small and negligible because the cantilever  15  has a sufficiently big response to a high frequency signal. 
     Eq. 1 and Eq. 2 are dynamic equations which express the block diagram shown in FIG.  3 .
 
 Mx   v   ″+b   v   x   v   ′+k   v   x   v   +b   v ( x   v   ′−x   c ′)+ k   c ( x   v   −x   c )= F   [Eq. 1]
 
 mx   c   ″+b   c ( x   c   ′−x   v ′)+ k   c ( x   c   −x   v )=0  [Eq. 2]
 
     M is a mass of the actuator  16 , m is a mass of the sensing unit  13 , x v  is a displacement of the actuator  16 , x v ′ is a first order derivative of x v  and a velocity of the actuator  16 , x v ″ is a second order derivative of x v  and an acceleration of the actuator  16 , x c  a displacement of the sensing unit  13 , x c ′ is a first order derivative of x c  and x c ′ is a velocity of the sensing unit  13 , x c ″ is a second derivative of x c  and a acceleration of the sensing unit  13 , k v  is a spring constant of the actuator  16 , k c  is a spring constant of the sensing unit  13 , b v  is a damper constant of the actuator  16 , b c  is a damper constant of the sensing unit  13 , and F is an applied force and a driving force which moves the actuator  16 . 
     Therefore, Eq. 1 shows specific forces arisen by the applied force. The summation of the forces of a left hand side is equal to the applied force of a right hand side. 
     Specific forces expressed in the Eqs. 1 and 2 are explained in details below. 
     Mx v ″ is a multiple of the mass of the actuator  16  and the acceleration of the actuator  16  by the applied force F and physically shows that the actuator  16  is moving with a predetermined acceleration by the applied force. b v x v ′ is a multiple of the damper constant b v  and the velocity of the actuator  16 . k v x v  is a multiple of the spring constant k v  of the actuator  16  and the displacement x v  of the actuator  16 . 
     Also, b v (x v ′−x c ′), the force with respect to the damper and k c (x v −x c ), the force with respect to the spring characteristics, both are taking account of a relative displacement of the actuator x v  against the displacement of the cantilever x c . 
     Eq. 2 shows the cantilever motion accompanying the motion of the actuator  16  in Eq. 1. 
     The value of the right hand side is “0” because no force is applied to the cantilever  15 . mx c ″ is a multiple of the mass m of the cantilever  15  and the acceleration x c ″ of the cantilever  15 , and physically shows that the cantilever is moving with a predetermined acceleration by the applied force “0”. 
     Also, b c (x c ′−x v ′) the force with respect to the damper and k c (x c −x v ), the force with respect to the spring characteristics, both are taking account of a relative displacement of the actuator x c  against the displacement of the cantilever x v . 
     Eqs. 3 to 5 show a ratio of the displacement by the applied force with the Laplace transform of Eqs. 1 and 2. 
     
       
         
           
             
               
                 
                   
                     
                       
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     Eq. 3 shows the ratio of the displacement x v  of the actuator  16  by the applied force F, and Eq. 4 shows the ratio of the displacement x c  of the cantilever  15  by the applied force F. Eq. 5 shows the ratio of the displacement x c  of the cantilever  15  by the relative displacement (x c −x v ). 
       FIGS. 4A to 4C  are graphs showing a mathematical analysis of the frequency response of the actuator  16  and the self-sensing cantilever  15 . Eqs. 3 to 5 show different frequency responses in view of the mathematical modeling of  FIG. 3 , and the representations are shown in  FIGS. 4A to 4C . 
     Referring to  FIGS. 4A to 4C , a voltage is applied to the actuator  16 . The actuator  16  subsequently produces a force F which results a displacement of the actuator  16  and also oscillates the cantilever  15 . 
       FIG. 4A  shows that the displacement of the actuator  16  has a small response at a resonant frequency f R  of cantilever  15 , which is a high frequency and has a large response at a low frequency f L  which is about 10 2  Hz as described as ‘A’. 
       FIG. 4B  shows that the displacement of the cantilever  15  also has a peak value at the low frequency f L , which is about 10 2  Hz and a high frequency, which is about 10 5  Hz. 
     ‘B’ and ‘C’ in  FIG. 4B  show that there are two resonant frequencies. 
     Consequently, the relative displacement of the cantilever  15  by the actuator  16  has the highest frequency response at a high frequency signal, which is about 10 5  Hz. In actual operation, a self-sensing unit  13  can work only when a relative displacement in  FIG. 4C  arises, and thus, it senses such relative displacement shown in  FIG. 4C . 
     As shown in  FIG. 4C , the sensing unit  13  most highly responds to the resonant frequency. Using this characteristic, a voltage signal at the resonant frequency of the sensing unit  13  is added to a sample surface profile signal. 
       FIG. 5  is a graph showing a result of an experiment in frequency responses of the actuator  16 , which is a voice coil motor (VCM). 
       FIG. 6  is a graph showing a result of an experiment in frequency response of the sensing unit  13 . 
     In  FIG. 5 , the actuator  16  has a peak value between about 10 Hz and about 100 Hz, which is similar to the result ‘A’, i.e., profile frequency range as shown in  FIG. 4A . The result has a weak response in a range of frequency around 10 3  Hz˜10 5  Hz, i.e., Oscillation frequency range. 
       FIG. 6  shows that sensing unit  13  has the highest input to output ratio at the resonant frequency f R , which is about 37.425 Hz. 
     As shown in  FIGS. 5 and 6 , the VCM has a high response at a low frequency, but a low response at the resonant frequency of the cantilever, which is a high frequency. This shows that a mechanical system is functioning as a low pass filter. 
     The actuator  16  has several oscillation regions at a high frequency because of its several frequency modes, but basically those responses become smaller. The cantilever  15  has high sensitivity at the resonant frequency. This sensitive response helps the sensitive sensing of the tip-sample gap. 
       FIG. 7  is a graph showing an amplitude variation of the cantilever  15  due to the tip-sample gap measured in μm and a sensing gap setting for measuring a sample surface. The cantilever tip closes to the sample surface and a sensor voltage which is produced from cantilever amplitude information, is measured. 
     ‘E’ in  FIG. 7  shows that the amplitude of the cantilever  15  and a sensor voltage decrease when the cantilever tip  14  closes to the sample  12 . The decreasing sensor voltage abruptly changes in proportion to the tip-sample gap. As a result, a feedback control sets the point at which the value is suddenly changing and the tip-sample gap can stay near to the controlled point. In this manner, the tip-sample gap can be controlled within a range of regulating the point ‘P’. 
       FIG. 8  is a graph showing results of measuring a sample surface of about 10 μm square lattice in non-contact mode. The sample of the 10 μm square lattice with the feedback control from the  FIG. 7  was measured with 50 μm 2  and 15 μm 2  through the use of the non-contact scanning apparatus. 
     As shown in  FIG. 8 , the present invention allows a high resolution imaging of the sample  12  and the frequency response separation scheme improves the performance. 
       FIG. 9  is a block diagram showing possible combinations to which the frequency separation scheme can be applied in accordance with the present invention. 
       FIG. 9  shows exemplary actuators; they are a piezo actuator  91 , a Bimorph actuator  92  and a VCM  93 . 
     The piezo actuator  91  includes a fixed member  910  and an actuator which is attached to the fixed member  910  and driven in a Z direction. 
     The bimorph actuator  92  is driven in a Z direction through which a fixed member  920  is connected to one end of the bimorph actuator  92  including two metal having different electrical and thermal characteristics and being contacted to each other. 
     The VCM  93  includes a base  933 , a supporting member  930 , a connecting member  932  and an actuator  931 , and is driven in a Z direction. 
     The piezo actuator  91 , the bimorph actuator  92  and the VCM  93  have common characteristics of an actuating range exceeding height of the sample surface. Because of this characteristic, even though a response displacement is small in a high frequency range, these actuators reach the sample surface. 
     The cantilever has self-sensing units  941  and  951  which have either a tip  942  or a tip with an aperture  952 . AFM topography measurement is allowed for the tip  942  and NSOM is allowed for the tip with an aperture  952 . 
       FIG. 10  is a flowchart describing a method of non-contact surface measurement with use of the frequency separation scheme in accordance with the present invention. 
     In  FIG. 10 , at step  100 , keeping a uniform distance from the sample, sample surface topography is measured with the amplitude variation of the resonant frequency. 
     At step  101 , the measured signal is transformed into a first signal which is a frequency signal. The first signal is an analog signal which is transformed from the tip-sample gap of a second signal. 
     At step  102 , the first signal is combined with the second signal by a function generator. The second signal is the resonant frequency which is a higher frequency than the first signal. 
     At step  103 , the combined signal is transferred to the actuator through the feedback loop. At step  104 , the actuator is driven responding to the first signal of the combined signal, which is a low frequency compared to the second signal of the combined signal. At step  105 , the sensing unit is driven by the second signal which is relatively a high frequency compared to the first signal. The frequency separation is then executed. 
     Using the frequency separation scheme which can be applied to the AFM and the NSOM, one actuator can track the height of the sample surface and oscillate the cantilever with the resonant frequency. Therefore, the present invention can simplify the apparatus structure and minimize the number of actuators. According to this simplification of the structure and the actuator amplification, there are great advantages in aspects of the price and the structure. 
     Because of the simple structure, the present invention can be used not only in the AFM but also in the NSOM, which measures optical and topographical information, an alpha step, which measures a step height of the surfaces, and a gap control system between a pick-up head and a sample, which is necessary to record and play optical information in aperture-type tip high density data storage apparatus. 
     While the present invention has been described with respect to certain preferred embodiments, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.