Abstract:
A fast translation stage for a scanning probe microscope is provided. The stage includes at least one axis of translation driven at the natural resonant frequency of the translation stage such that distortion associated with rapid changes in scan direction is avoided. In one embodiment, the stage includes a sample plate or support that is driven, preferably by one or more piezoelectric actuator elements, so that the plate translates along the fast scan frequency at its resonant frequency.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application claims the benefit of U.S. Provisional Application Serial No. 60/435,518, filed Dec. 20, 2002. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0002]    This invention relates to scanning probe microscopy, such as for example, atomic force microscopy or near-field optical microscopy, and more particularly to a fast translation stage for scanning probe imaging that avoids imaging distortion associated with rapid changes of scan direction.  
           [0003]    It is highly desirable to increase the speed with which scanning probe microscopes can image, particularly in fluid, in order to permit visualization of processes that occur on timescales comparable to or faster than the imaging rate of conventional scanning probe microscopes. Present commercially-available scanning probe microscopes are limited by natural mechanical resonances so that several seconds or more are required to acquire an image. It would be highly desirable to be able to increase these imaging rates by an order of magnitude or more. In such a case, ten or many tens of images per second could be acquired, giving rise to near-video rate data acquisition.  
           [0004]    One of the limiting resonances is associated with the force sensing cantilever itself. The resonant frequency, f 0 , of a cantilever of effective bending force constant K in Newtons per meter (N/m) and mass m in kilograms (Kg) is given by  
         f   0     =       1     2      π                K   m       .                             
 
           [0005]    Because it is desirable to keep the force constant, K, small for imaging soft materials, the route to increasing the resonant frequency lies in making smaller cantilevers so as to reduce their mass m.  
           [0006]    Viani et al, “Fast imaging and fast force spectroscopy of single biopolymers with a new atomic force microscope designed for small cantilevers,”  Rev. Sci. Instrum.  70: 4300-4303 (1999), and Hansma et al, U.S. Pat. No. 5,825,020, describe microscopes in which the length of the cantilever is reduced to only a few times the optical wavelength, so that, using special focusing optics as taught in the &#39;020 patent, cantilevers with resonant frequencies of greater than 100 kHz (in water) and with spring constants as small as 0.06 (N/m) can be used. Ando et al, “A high-speed atomic force microscope for studying biological macromolecules,”  Proc. Natl. Acad. Sci. (USA)  98: 12468-12472 (2001), take a similar approach and have reported imaging at greater than 10 frames per second with cantilevers having resonant frequencies of about 500 kHz (in water) and with spring constants of 0.15 to 0.28 N/m.  
           [0007]    In practice, another severe limit on scanning speed is dictated by the sample (or probe) scanning stage. In order to fully exploit a cantilever with a 500 kHz resonant frequency, each line scan, sampling typically 100 or more points, would have to be completed in (5 kHz) −1  seconds or 20 microseconds (μs) if a height data point is to be acquired on each cycle of cantilever oscillation.  
           [0008]    Current practice in scanning probe microscopy includes scanning the probe in a raster pattern over the sample as shown in FIG. 1A. Alternately, the sample may be scanned in a raster pattern under a fixed probe. Considering just the fast scan axis (taken to be the X axis here) and referring to FIG. 1A, a time-varying voltage, V(t)  1 , is applied to electrodes  2 ,  3  on a piezoelectrically driven scanning element  4  so as to cause the element to bend and scan a probe  5  over the surface of a sample  6 . The desired motion is a linear sweep of the probe over the surface so that the displacement X(t) varies with time as shown in FIG. 1B.  
           [0009]    Because the displacement of a piezoelectric material is not linear with changes of applied voltage, it is usual to apply a non-linear ramp, such as that shown as V(t) in FIG. 1C so that the resultant displacement, X(t), is a linear function of time. See, Eilings, V. B. and J. A. Gurley, U.S. Pat. No. 5,051,646, and Lindsay, S. M. and I. W. Shepherd, “Linear Scanning Circuit for a Piezeoelectrically Controlled Fabry-Perot Etalon,”  Rev. Sci. Instrum.  48: 1228-1229 (1977). This approach results in a rapid change of direction at the turning points  7  of the scan where the derivative of the applied voltage changes sign as shown at  8 .  
           [0010]    Because the velocity of the probe is proportional to the time derivative of the applied voltage,  
                V        (   t   )              t       ,                         
 
           [0011]    the momentum change, or impulse applied to the scanning element is proportional to the second derivative  
                        2        V          (   t   )                t   2         .                         
 
           [0012]    This quantity is infinite at the turning points  7  and  8 , though in practice it is limited by the time response of the driving electronics. The result is that a sharp impulse is given to the scanning element at the turning points, and this causes the scanning element to ring at its resonant frequency, f 0   SCANNER .  
           [0013]    The ringing continues for approximately Q/f 0   SCANNER  seconds, where Q is the mechanical Q factor of the scanning element. Because a rapid response is desired from the scanning element, and critical damping is not easy to implement, scanning elements generally have a Q&gt;1. Thus, given a typical scanning element with a resonant frequency of a few kHz and a Q of 5, the ringing motion,  9  in FIG. 1D may continue for 5 or more milliseconds. If, in turn, this distortion is not to affect more than 10% of a scan, the fast scan time is limited to 50 milliseconds or more, which is several hundred times slower than needed to realize the potential speed offered by small (optical wavelength-sized) cantilevers.  
           [0014]    One solution to this problem has been proposed by Ando et al, supra, using a balanced pair of scanning elements moving in opposite directions, one scanning the sample stage, and the other scanning a dummy mass. The scanning elements are driven so that the total momentum of the system is always approximately zero. This, however, greatly increases the mass and complexity of the scanning stage and also increases the possibility of spurious resonances in the scanning element.  
           [0015]    Accordingly, a need still exists in the art to provide a fast-scanning stage that is free from artifacts associated with any turn-around in scan direction. There is a further need for a scanning stage that can complete fast line scans at a rate of several kHz, and which is free from turn around artifacts. There is a further need in the art for a scanning stage having scan amplitudes on the order of approximately one micron with small (i.e., less than about one hundred volts) voltages applied to the scanning elements.  
         SUMMARY OF THE INVENTION  
         [0016]    These needs are met by embodiments of the present invention in which a fast translation stage for a scanning probe microscope, such as for example an atomic force microscope, is provided. The stage includes at least one axis of translation driven at the natural resonant frequency of the translation stage such that distortion associated with rapid changes in scan direction is avoided. The stage includes a sample plate or support that is driven, preferably by one or more piezoelectric elements, so that the plate translates along the fast scan frequency at its resonant frequency. This avoids distortion and artifacts at points where the scanning element undergoes a rapid change in scan direction such as at turn-around points. The acquired data is subsequently linearized, for example, using a digital computer.  
           [0017]    In accordance with one aspect of the invention, a fast scanning stage for a scanning probe microscope is provided. The microscope includes a probe and the fast scanning stage includes a sample stage having at least one axis of translation and means for causing displacement of the stage relative to the probe. Thus, a sample secured to the stage will also be displaced relative to the probe. A preferred means for causing displacement of the stage comprises at least one actuator element supporting the stage and a sine waveform generator for actuating the at least one actuator element. In a preferred form, the stage includes four actuator elements supporting the stage.  
           [0018]    The stage is displaced by being driven at the frequency of resonant vibration corresponding to translation of the sample with respect to the probe. Preferably, the stage has a square or rectangular configuration and each corner of the stage is supported by one of the actuator elements. Preferably, the actuator elements comprise a PZT bimorph material. The stage is preferably comprised of an electrically insulating material such as, for example, ceramics, heat resistant polymers, and anodized aluminum.  
           [0019]    The present invention also includes a method of operating a fast-axis scanning stage for a scanning probe microscope including a probe comprising providing a sample stage having a sample thereon and causing displacement of the sample on the stage relative to the probe. In a preferred form, driving the stage at its resonant frequency causes the displacement. The resonant frequency of the stage is preferably about 1/100 th  that of the resonant frequency of the probe.  
           [0020]    Accordingly, it is a feature of the present invention to provide a fast-scanning stage that is free from artifacts associated with any turn-around in scan direction. It is a further feature of the invention to provide for a scanning stage that can complete fast line scans at a rate of several kHz, and which is free from turn around artifacts. It is still a further feature of the present invention to provide a scanning stage having scan amplitudes on the order of approximately one micron with small (less than about one hundred volts) voltages applied to the scanning elements. These and other features and advantages of the invention will become apparent from the following detailed description, the accompanying drawings, and the appended claims. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0021]    Reference will now be made by way of example to the accompanying drawings in which like elements are represented by like reference numerals and in which:  
         [0022]    [0022]FIG. 1A is a schematic illustration of a prior art scanning element and probe being scanned in a raster fashion over a substrate; FIG. 1B illustrates a plot of the desired fast-scan direction displacement, X(t) as a function of time (t); FIG. 1C illustrates a plot of the desired fast scan direction displacement. X(t), as a function of time using a voltage waveform chosen to achieve the displacement; and FIG. 1D illustrates a plot of the actual X displacement showing scanning element resonances at the turn around points in the scan.  
         [0023]    [0023]FIG. 2A is a schematic plan view of the fast scanning stage according to one embodiment of the present invention; and FIG. 2B is a schematic elevational view showing the scanning probe in place.  
         [0024]    [0024]FIG. 3A illustrates a plot of a sinusoidal drive waveform as applied to the scanning element at its resonant frequency; and FIG. 3B illustrates a plot of the displacement, X(t), when the scanning element is driven at resonance (the response is phase shifted by 90° with respect to the drive).  
         [0025]    [0025]FIG. 4A is a schematic drawing showing the displacement of the four bimorph elements as one embodiment of the scanning stage is driven; and FIG. 4B is a schematic drawing of a simple model for the dynamics of the stage.  
         [0026]    [0026]FIG. 5A is a schematic drawing showing a combination of one embodiment of the fast scan stage with PZT stacks to achieve X-Y raster scanning; and FIG. 5B is a schematic drawing showing one embodiment of the fast-scan stage combined with a conventional tube scanning element to obtain X-Y raster scanning. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0027]    One embodiment of the fast scanning stage is shown in FIG. 2. The sample to be scanned is affixed to a sample stage  21  that comprises a generally flat plate of an electrically insulating material such as, for example, a ceramic, a temperature resistant polymer, or anodized aluminum. The sample may be fixed in place with a thermally reversible or soluble adhesive. The stage  21  is affixed to fixed supports  23  using four piezoelectric bending elements (actuators)  22 , such as lead zirconate titanate (PZT) elements manufactured by Piezo Systems Inc. of Massachusetts under the designation T220.  
         [0028]    The assembly forms a parallelogram scanning element capable of uniform small translations in the direction that corresponds to the bending of the piezoelectric elements. The scanning elements are electrically connected in parallel and driven by a sinusoidal waveform generator  20  at the resonant frequency for translational displacements of the scanning stage. The elevational view in FIG. 2B shows the location of the scanning probe  24  with respect to the scanning stage  21 . A transducer  25  controls the height (Z-axis) of the probe  24  with respect to the sample stage  21 . At this point, for ease of understanding and clarity, just the fast scan axis is described. The addition of a second slow scan axis can be implemented as will be discussed below.  
         [0029]    One aspect of the present invention provides for the driving of scanning stage  21  at its resonant frequency with a sinusoidal drive waveform  31  as shown in FIG. 3A. If the time dependent driving force is described by F 0  sin(ωt), then the response at resonance is given by  
           X        (   t   )       ≈         Q                   F   0       K        sin                   (       ω                 t     +     π   2       )         ,                         
 
         [0030]    where Q is the mechanical Q-factor of the stage and K is the spring constant for bending motion. Thus, the response of the scanning stage is also sinusoidal ( 32  in FIG. 3B) with no spurious resonance. This is because the derivative of the driving force is a smooth co-sinusoidal function with no impulse applied at the turning points of the raster scan.  
         [0031]    The motion of the scanning stage may be further described by considering the bending displacement of all four piezoelectric bending elements caused by a parallel electrical drive. This is shown schematically in FIG. 4A. The free resonance (undriven) corresponds to motion of the scanning stage  41  against all four of the bending elements or actuators  42 . However, when all four bending elements are driven this way, there is no interaction causing acceleration or retardation of one element by any of the others. Thus, the motion is equivalent to the self-resonance of any one bending element  42  attached to a fixed surface  44  at one end (FIG. 4B) and free to move at the other end  45 , but loaded with the mass  43  of the sample stage.  
         [0032]    In terms of the length L, width w, and thickness t of the illustrated bending element  42  (see FIG. 4B), the self-resonance is given by (Technical Publication TP-237 from Morgan Electro Ceramics)  
         f   r     =     0.162                   t     L   2                Y   11   E     ρ                               
 
         [0033]    where Y 11   E  is the bending Young&#39;s modulus applied in short circuit conditions and ρ is the material density. For an unloaded bending element (i.e., the sample stage mass m=0), the geometry of the bending element leads to  
               f   r     =     0.162              t   3       L   3                Y   11   E        w     M                   (   1   )                               
 
         [0034]    where M is the mass of the bending element.  
         [0035]    When the mass of the stage is added, M can be replaced by αm where m is the mass of the stage and α is a factor on the order of unity that reflects the difference between the mass distribution in this simple model and the real mass distribution. Cast in terms of a bending spring constant for the system,  
               f   r     =       0.162          K     α                 m                         where                   K     =         w                   t   3         L   3              Y   11   E     .                 (   2   )                               
 
         [0036]    For PZT 5B bimorph materials (Technical Publication TP-237 from Morgan Electro Ceramics), Y 11   E  is 6×10 10  N/m 2 .  
         [0037]    As an example of a practical implementation of the sample stage shown in FIGS. 2A and B, consider a stage  21  that includes four of the T220 piezoelectric elements  22  manufactured by Piezo Systems Inc. of Massachusetts. The dimensions for these elements are t=0.5 mm and w-1 mm. A convenient length for the free part of each element is 6 mm (though this dimension is easily shortened). A useful sample stage may be made from a 1 cm by 1 cm slab of 1 mm thick anodized aluminum. This sample stage has a mass of 0.26 gm.  
         [0038]    Calculating K to be equal to 4×10 4  N/m, taking α=1, and ignoring the mass of the bending element compared to the mass of the stage, Equation 2 predicts f r =2 kHz. A real stage manufactured with these materials is found to have a measured self-resonance for translational motion of 2.8 kHz, so that α is empirically determined to be 0.51. Thus, an empirical relation for the self-resonant frequency is  
               f   r     =       0.162          K     0.51                 m                         where                   K     =         w                   t   3         L   3            Y   11   E                 (   3   )                               
 
         [0039]    and m is the mass of the stage.  
         [0040]    The peak displacement amplitude at resonance is equal to Q times the displacement amplitude at low frequency. Because all four bending elements work together, Equation 2 for the free (unloaded) displacement can be used. This is, neglecting a small correction for non-linearity and the thickness of the metal vane incorporated into these bending elements (Technical Publication TP-237 from Morgan Electro Ceramics):  
               d   F     =       3   2          d   31            L   2       t   2          V             (   4   )                               
 
         [0041]    where d 31  is the piezoelectric strain coefficient relating transverse strain to the electric field, and V is the applied bias. At resonance, Equation 4 becomes  
               d   F   RES     =     Q                   3   2          d   31            L   2       t   2          V             (   5   )                               
 
         [0042]    where Q is the mechanical Q factor. For a commercial PZT 5B product, d 31 =−1.8×10 −10  m/V.  
         [0043]    Taking the dimensions used previously (L=6 mm, t=0.5 mm) and calculating, d F   RES ≈40 Q nm/V. The measured Q of a sample stage built with these dimensions was about 2, so that a peak deflection of about 80 nm/volt is expected. Interferometric determination of the actual deflection of the stage yielded a measured sensitivity of about 10 nm/V. This is less than estimated, but satisfactory, permitting a scan of 1 micron with an applied bias of 100V.  
         [0044]    The sample stage can be incorporated into an existing atomic force microscope (AFM) in a number of ways, one of which is shown in FIG. 5A. Here, the sample stage is modified by the addition of PZT stack bending elements  50  such as, for example, elements commercially available under the designation AD0203D04 from Tokin of Tokyo, Japan. These elements serve to translate the entire stage in a direction normal to the fast scan axis. To accomplish this, one stack of bending elements, e.g.,  50   a  is expanded as the other stack, e.g.,  50   b  is contracted. Because the scan in the Y direction is slower than that in the X-direction by a factor equal to the number of lines scanned per frame, these stacks may be driven in a conventional manner to achieve a displacement that is a linear function of time. The ends of the stack elements  50  are mounted to a rigid frame  51 . The sample (not shown) is placed on scanning stage  21  and raster scanned under the force sensing cantilever probe  53 . The probe is in turn, positioned by a Z-axis actuator  52  that can move the probe along a vertical axis as shown.  
         [0045]    In order to realize the full potential of the fast scan stage, small cantilevers and fast servo control mechanisms such as those described by Ando et al, supra, should be used. However, existing AFMs can operate with conventional cantilevers that resonate in water at as high as 50 kHz with a spring constant of a few N/m. Thus, acquiring 100 data points in the X-axis direction and sampling once each oscillation period, a fast scanning stage resonant frequency of 500 Hz is appropriate. With 100 lines per image, data can be acquired at 5 frames per second. While this is less than a standard video rate, it represents a significant increase in speed over existing instruments.  
         [0046]    In another embodiment, the fast scan axis of a conventional AFM (FIG. 5B) is simply turned off, and the fast scan stage is positioned under the probe. The probe is then moved only in the slow-scan (Y) and height (Z) directions by the existing scanner  54 , the X-axis motion being generated by the fast-scan stage  22 ,  23 . This embodiment represents one very simple method of obtaining significant speed enhancements using the fast scan sample stage of the present invention retrofitted onto a conventional (slow) AFM. Excellent results can be obtained by using a slow height servo response to control the overall position of the probe while collecting raw deflection (or amplitude) data to record local changes in topography at a fast rate.  
         [0047]    In order to realize the full potential of the fast scan stage of the present invention, it should be incorporated into an instrument that uses diffraction limited optics to detect the signal from a small probe such as the instrument described by Ando et al, supra.  
         [0048]    The resonant scanning stage has the disadvantage that, because the scan is non-linear, data acquired at equal intervals in time will not correspond to equal intervals in displacement. However, this problem is well known and is solved by the use of algorithms that process the data after acquisition. Lindsay and Jing, U.S. Pat. No. 5,805,448, the disclosure of which is hereby incorporated by reference, describe these methods and algorithms.  
         [0049]    While certain representative embodiments and details have been shown for purposes of illustrating the invention, it will be apparent to those skilled in the art that various changes in the methods and apparatus disclosed herein may be made without departing from the scope of the invention, which is defined in the appended claims.