Patent Publication Number: US-2003233870-A1

Title: Multidimensional sensing system for atomic force microscopy

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
     [0001] This application is a continuation of U.S. patent application Ser. No. 09/907,855, entitled MULTIDIMENSIONAL SENSING SYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, filed Jul. 18, 2001; claims the benefit thereof under 35 U.S.C. § 120; and hereby incorporates the cited application by reference.  
     [0002] Under 35 U.S.C. § 120, this application claims the benefit of commonly owned U.S. patent application Ser. No. 09/404,880 entitled MULTIDIMENSIONAL SENSING SYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, filed on Feb. 24, 1999, which is also hereby incorporated by reference.  
     [0003] Additionally, via U.S. patent application Ser. No. 09/404,880, and under 35 U.S.C. §§ 119(e) and 120 and 37 C.F.R. § 1.53(b), this application further claims the benefit of commonly owned U.S. Provisional Patent Application No. 60/101,963 entitled MULTIDIMENSIONAL SENSING SYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, filed on Sep. 26, 1998, which is also hereby incorporated by reference.  
     [0004] This application also incorporates by reference commonly owned U.S. patent application Ser. No. 09/881,650 entitled SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR SCANNING PROBE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Jun. 13, 2001.  
     [0005] Furthermore, this application also incorporates by reference commonly owned U.S. Pat. No. 6,146,227 entitled METHOD FOR MANUFACTURING CARBON NANOTUBES As FUNCTIONAL ELEMENTS OF MEMS DEVICES, by Vladimir Mancevski.  
     [0006] This application also incorporates by reference U.S. Pat. No. 5,367,373 entitled NONCONTACT POSITION MEASUREMENT SYSTEMS USING OPTICAL SENSORS to Ilene J. Busch-Vishniac, et al. and issued on Nov. 22, 1994, hereinafter “BUSH-VISHNIAC 1,” and U.S. Pat. No. 5,552,883 entitled NONCONTACT POSITION MEASUREMENT SYSTEMS USING OPTICAL SENSORS to Ilene J. Busch-Vishniac, et al. and issued Sep. 3, 1996, hereinafter “BUSH-VISHNIAC 2.” 
    
    
     
       TECHNICAL FIELD OF THE INVENTION  
       [0007] The present invention relates generally to the field of scanning probe microscopy tools and, more particularly, to a sensing system for a scanning probe microscopy tool that enables measurement of the absolute and relative position and orientation of an AFM probe and operation of the tool while the AFM probe is positioned and orientated so as to access vertical and reentrant features.  
       DESCRIPTION OF RELATED ART  
       [0008] A typical atomic force microscope (AFM)  100  operates as shown in FIG. 1. AFM  100  probes the surface of a sample  10  with a sharp tip  12 , which is a few microns long and less than 100 Angstroms in diameter. Tip  12  is located at the free end of a cantilever  14  that is typically 100 to 200 microns long. Forces between the tip  12  and the sample  10  surface cause the cantilever  12  to bend or deflect. A detector  16  measures the cantilever  12  deflection as the tip is scanned over sample, or as sample  10  is scanned under tip  12 . The measured cantilever deflections allow a computer  18  to generate a map  20  of surface topography.  
       [0009] Currently available AFMs detect the position of the cantilever with optical techniques. In the most common scheme, shown in FIG. 2, a laser beam  22  bounces off the top surface of the cantilever  24  onto a bi-cell or quadrant cell position detector  26 . As cantilever  24  bends, the position of the beam  25  on the bi-cell or quadrant cell detector  26  shifts. As beam  22  shifts, a current imbalance occurs indicating off center position. The feedback system that controls the vertical position of the tip,  27  typically operates in either constant height mode, constant force mode or one of several vibrating cantilever techniques. In constant-height mode, the spatial variation of the cantilever deflection can be used directly to generate the topographic data set because the height of the scanner is fixed as it scans. In constant-force mode, the feedback circuit moves the scanner  28  up and down in the z (i.e., vertical) direction, responding to the topography by keeping the cantilever  24  deflection constant. In this case, the image is generated from the motion of scanner  28 . When vibrating cantilever techniques are used, the feedback circuit  29  detects changes in vibration amplitude or phase as tip  12  comes near the sample  10  surface.  
       [0010] The bi-cell or quadrant cell position detectors  26  used to sense cantilever  24  position consist of two or four discrete elements on a single substrate. When a light beam  25  is centered on the cells, output currents from each element are equal, indicating centering or nulling. As the beam  25  moves, a current imbalance occurs indicating off-center position. Bi-cell and quadrant cell detectors  26  require use of a laser beam  22  with an intensity distribution that is constant both spatially uniform and temporally uniform. This is because a nonuniformly shaped or time varying intensity distribution would introduce unwanted bias errors in the output of bi-cell or quadrant cell detector  26 . Bi-cell and quadrant cell detectors  26  also require precise alignment and centering of the beam  25  on the bi-cell or quadrant cell detector.  
       [0011]FIG. 3 is a schematic of the noncontact position measurement system  200  previously disclosed in BUSH-VISHNIAC 1 and BUSH-VISHNIAC 2. This system combines optical and computational components to perform high-precision, six degree-of-freedom, (6-DOF) single-sided, noncontact position measurements. For in-plane measurements, reflective optical targets  30  are provided on a target object  32  whose position and orientation is to be sensed. For out-of-plane measurements, light beams  36  are directed toward the optical targets  30 , producing reflected beams  34 . Electrical signals are produced, indicating the points of intersection of the reflected beams and the position detectors  38 . The signals are transformed to provide measurements of translation along, and rotation around, three nonparallel axes which define the space in which the target object moves.  
       [0012] The system comprises two sections, out-of-plane and in-plane. Each section has its own assembly of light sources, reflectors, and sensors. The arbitrarily selected reference plane serves as a reference for motion measurement. This reference plane contains the x and y axes of the three-axis set (x, y and z) which defines the space in which the sensed object moves. The position and/or the motion of the target object are derived from kinematic transformations based on information supplied by the components illustrated in FIG. 3. Position measurements of multiple light beams irradiating a single two-dimensional lateral-effect detector which can be made simultaneously through time, frequency, or wavelength multiplexing. The main advantage of multiplexing is that the number of detectors required in the existing system can be reduced, and the signal processing circuitry can be simultaneously simplified. The resulting system will be more compact, and alignment difficulties will be largely eliminated. Further, the effect of environmental variations is minimized as the number of detectors is reduced.  
       [0013] It is desirable to use a detector  26  that is capable of monitoring the position of a light beam  25  on its surface without the need for precise alignment and centering. Conventional AFM sensing systems  100  provide only the vertical, z, coordinate (or, in one known instance, the horizontal, x, and vertical, z, coordinates), of the cantilever with respect to an absolute reference frame, while relying on the output of a scanning stage for the x and y (or, just the Y) coordinate and providing no information at all about angular orientation of cantilever  24 .  
       [0014] It would be desirable to measure all six degrees of freedom without reliance on the output of a scanning stage to determine any of these measured coordinates.  
       [0015] All references cited herein are incorporated by reference to the maximum extent allowable by law. To the extent a reference may not be fully incorporated herein, it is incorporated by reference for background purposes, and indicative of the knowledge of one of ordinary skill in the art.  
       BRIEF SUMMARY OF THE INVENTION  
       [0016] The problems and needs outlined above are addressed by the present invention. The present invention provides a multidimensional sensing system for atomic force microscopy (AFM) that substantially eliminates or reduces disadvantages and problems associated with previously developed systems and methods used for AFM.  
       [0017] More specifically, the present invention provides a six degree of freedom atomic force microscope (6-DOF AFM). This 6-DOF AFM includes an AFM cantilever coupled to an AFM tip wherein the AFM tip deflects the cantilever in response to topographical changes on a sample. The AFM cantilever is illuminated by a light beam generated by a light source. This light beam is either collimated or focused. The light is reflected by the top surface of the AFM cantilever towards a detector placed in the path of the reflected light beam. The detector produces an output containing data representing the position and orientation of the AFM cantilever as three translations and three orientations. This output is processed by a data acquisition system to produce a representation of the topographical changes of the sample.  
       [0018] The present invention provides an important technical advantage in that the present invention eliminates the need for precise alignment and centering of the laser beam. A continuous PSD is capable of monitoring the position of a light beam on its surface without the need for precise alignment and centering, as is required when bi-cell or quadrant cell position detectors are used.  
       [0019] The present invention provides another important technical advantage in that the present invention eliminates the need to maintain spatial and temporal uniformity of the laser beam. Use of continuous PSDs eliminates the need to maintain spatial and temporal uniformity of the laser beam, as is required when bi-cell or quadrant cell position detectors are used. This is because continuous position-sensitive detectors (PSDs), unlike bi-cell and quadrant cell detectors, are inherently insensitive to spatial and temporal variations in the laser beam intensity distribution.  
       [0020] The present invention provides yet another important technical advantage in that the present invention eliminates the need for the laser beam spot to illuminate both halves or all four quadrants of the PSD aperture. Use of continuous PSDs, which do not have halves or quadrants, eliminates the need for the laser beam spot to illuminate both halves or all four quadrants of the detector aperture. This feature enables use of a smaller laser beam spot which, in turn, enables operation over larger ranges, since the smaller spot can traverse larger regions of the PSD surface without part of its intensity distribution falling outside the PSD aperture.  
       [0021] The present invention enables sensing of the position and orientation of an AFM cantilever and direct measurement of cantilever position and orientation coordinates in up to six degrees of freedom. Cantilever position and orientation measurements are provided relative to a reference frame that may be fixed with respect to the structure of the AFM or another relative reference frame.  
       [0022] A technical advantage provided by the present invention is the ability to sense the position and orientation of an object in multidimensional space.  
       [0023] Yet another technical advantage provided by one embodiment of the present invention is the ability to repair a workpiece or remove a defect from a workpiece such as a photolithography mask used in semiconductor manufacture.  
       [0024] Another key advantage of the present invention is the ability to examine re-entrant features with an AFM tip. Because a sensing system of the present invention monitors the AFM cantilever as it twists and while it operates in twisted orientation, the sensing system can accommodate large probe angles that can enable the AFM tip to access re-entrant features. Alternatively, the tip itself may be tilted with respect to the cantilever. This eliminates the need to access re-entrant features with boot-shaped tips that are very fragile, expensive, and blunt at the end of the boot.  
       [0025] The present invention is ideal for a variety of uses, including material characterization, chemical-mechanical planarization monitoring, precision surface profiling and critical dimension metrology.  
       [0026] Yet another feature of the present invention is to completely decouple position sensing of an AFM from the mechanical actuator which positions the AFM tip, enabling the present invention to measure at even better resolutions than the ability to position the mechanical actuator itself. Furthermore the present invention may do so while the actuator is in motion. Nonlinearities of the mechanical actuator have no effect on the accuracy of the system. This enables real-time, on-the-fly recording of the AFM cantilever tip position. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0027] For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings in which like reference numerals indicate like features and wherein:  
     [0028]FIG. 1 illustrates a typical AFM;  
     [0029]FIG. 2 depicts how an AFM detects position;  
     [0030]FIG. 3 is a schematic of a previously disclosed noncontact measurement system;  
     [0031]FIG. 4 illustrates one embodiment of a 6-DOF AFM of the present invention;  
     [0032]FIG. 5 presents a second embodiment of a 6-DOF AFM of the present invention.  
     [0033]FIG. 6 provides a representation of two laser beams focused on a cantilever surface;  
     [0034]FIG. 7 shows an alternative embodiment of the present invention that utilizes the cantilever edge as a reflective mark.  
     [0035]FIG. 8 illustrates a standard semiconductor calibration grating used as an AFM sample;  
     [0036]FIG. 9 presents a CD AFM inspection tool provided by the present invention;  
     [0037]FIG. 10 provides a top view of the CD AFM inspection tool provided by the present invention;  
     [0038]FIG. 11 provides a perspective view of the CD AFM inspection tool provided by the present invention;  
     [0039]FIG. 12 presents an actuation mechanism coupled to a cantilever in a AFM of the present invention;  
     [0040]FIG. 13 illustrates an AFM cantilever with a fiducial surface;  
     [0041]FIG. 14 illustrates the method of computation of cantilever absolute position and orientation in one embodiment of the present invention;  
     [0042]FIG. 15 illustrates the sensor actuator concept of operation of a CD AFM of the present invention;  
     [0043]FIG. 16 illustrates a sensing system of the present invention that can access re-entrant features;  
     [0044]FIGS. 17 and 18 illustrate the results of AFM imaging with different x and y step issues;  
     [0045]FIG. 19 illustrates the ability of the present invention to measure absolute linear and angular measurements that are tied to a reference frame;  
     [0046]FIG. 20 illustrates the use of large beams to perform absolute scans over the diameter of the laser beam;  
     [0047]FIGS. 21 and 22 illustrate cosine errors due to bending and tilt;  
     [0048]FIGS. 23 and 24 illustrate adaptation of the present invention designed for mask repair;  
     [0049]FIG. 25 illustrates cantilever position and orientation relative to an absolute reference frame fixed with respect to the structure of the AFM;  
     [0050]FIG. 26 shows how various embodiments of sensing system of the present invention are capable of simultaneous multi-dimensional sensing;  
     [0051]FIG. 27 illustrates a method of scanning contact holes or vias with the system of the present invention; and  
     [0052]FIG. 28 illustrates a procedure for automated tip changing and self alignment. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
     [0053] Preferred embodiments of the present invention are illustrated in the figures, like numerals being used to refer to like and corresponding parts of the various drawings.  
     [0054] The present invention provides Six Degree-of-Freedom (6-DOF) Atomic Force Microscope (AFM) tools for use in microelectronics manufacturing that overcome limitations inherent in the sensing and control system architectures of existing lower degree-of-freedom AFMs. However, the present invention need not be limited to use in microelectronics manufacturing. This 6-DOF sensing system is capable of measuring all six absolute degrees of freedom of a body in space, such as a deflecting AFM cantilever.  
     [0055] The present invention is ideal for a variety of uses, including material characterization, chemical-mechanical planarization monitoring, precision surface profiling and critical dimension metrology. The sensing system of the present invention may be completely decoupled from the actuator, enabling it to measure at even better resolutions than the actuator itself, and do so while the actuator is in motion. The present invention is capable of simultaneous multi-dimensional sensing, as opposed to one-dimensional or several-step multi-dimensional sensing currently performed with existing AFMs. The simple, robust design of the present invention is readily adaptable to multi-cantilever operation.  
     [0056] The sensing system of the present invention may be completely decoupled from the mechanical actuator (stages, PZTs, etc.). Therefore, the cantilever displacements x, y, and z and the cantilever pitch, tilt and yaw angles ψ, φ and θ, are determined independently of actuator motion. Nonlinearities of the PZT or the stage will have no effect on the accuracy of the system. This enables real-time, on-the-fly recording of the AFM cantilever tip position at randomly selected x and y positions.  
     [0057] The present invention uses continuous position-sensitive detectors (PSDs) in lieu of bi-cell or quadrant cell position detectors, with adaptations of a noncontact position measurement system and other component technology innovations that enable sensing of the position and orientation of an AFM cantilever relative to an absolute reference frame.  
     [0058] A first embodiment of the present invention utilizes only the out-of-plane section of the existing 6-DOF sensing system concept. Height z and orientation in pitch and tilt of the AFM cantilever are determined simultaneously for each given x and y coordinate of the sample.  
     [0059] A second embodiment utilizes the entire existing 6-DOF sensing system concept, including both the out-of-plane and in-plane sections. Position in x, y and z and orientation in pitch, tilt, and yaw of the AFM cantilever are determined simultaneously for each unknown x and y displacement of the sample.  
     [0060] The first embodiment of the present invention utilizes only the out-of-plane section of the 6-DOF sensing system and therefore can only monitor out-of-plane positions and orientations for a given x and y. As shown in FIG. 4, two-dimensional PSD sensor  40 , laser diodes  42 , and the AFM cantilever  44  are fixed to a ground reference  41 , whereas sample  45  is moved under AFM tip  46  in x and y directions with a PZT actuator and a coarse motion stage  48 . This configuration relies on already existing external sensors (interferometric, capacitive, etc.) to direct the PZT actuator in the x and y directions. The collimated light beams  50  from laser diodes  42  are pointed toward top surface  52  of AFM cantilever  44  where they bounce off as light beams  54  intercepted by PSD  40 . Light beams  50  do not have to be parallel to each other. Care must be taken to assure that light spot  55  from light beams  50  fits on cantilever  44 .  
     [0061] The principle of operation of this embodiment of the present invention is as follows. First, the PZT actuator moves the sample  45  under the AFM tip  46  to a precise x and y location. AFM tip  46  will force the AFM cantilever  44  to deflect as it encounters topographic changes on sample  45 . These minute deflections will cause light beams  50  to alter their paths to produce light beams  54 . These changes are detected by two-dimensional PSD  40 . Information about the displacement of the light spots on the surface of the PSD  40  is then used to determine the out-of-plane position z and the pitch and tilt orientations of the cantilever  44 .  
     [0062] This AFM configuration can fully and simultaneously determine the vertical position and out-of-plane orientation of AFM cantilever  44 . Information about the vertical deflection in z is readily available, either to be displayed as a topography map (in constant height operation) or to provide a predetermined feedback signal to the PZT that will rapidly lift the AFM tip back to its original deflection, keeping a constant force to the cantilever  44  (constant force operation). This first embodiment is suitable for fast-scan multi-dimensional measurements, and also for multi-cantilever operation.  
     [0063] A second embodiment utilizes 6-DOF sensing system, including both out-of-plane and in-plane sections. FIG. 5 represents a second embodiment of the present invention. Two-dimensional PSD  60 , wide beam light emitting diode (LED) laser  62  and sample  64  are fixed to ground reference  61 . Laser diodes  66  and the AFM cantilever  68  are fixed to the PZT tube  70 . PZT tube  70  scans AFM tip  72  above sample  64  in the x and y directions and, if necessary, adjusts its vertical displacement, z. The laser diodes  66  are fixed to the bottom of PZT tube  70  so that laser diodes  66  can move together with cantilever  68  in the X-Y plane parallel to sample  64  to keep the collimated light beams  74  on the surface of the cantilever  68  at all times. Care must be taken that light spots  76  from light beams  74  fit on cantilever  68 . Care must also be taken that laser diodes  66  do not twist while moving with PZT tube  70 . This maintains a constant slope for light beam  74 . In the alternative, a larger cantilever area with the size of the scan may accommodate light spots  76  by keeping them within cantilever  68  surface  78  during the scan. Collimated light beams  74  from laser diodes  66  are pointed towards top surface  78  of AFM cantilever  68  where collimated light beams  74  are reflected off surface  78  and are intercepted by PSD  60  as light beams  80 . This part of sensing system  400  is responsible for determining the out-of-plane position and orientation.  
     [0064] For the in-plane part of the sensing system  400 , cantilever  68  is equipped with two reflective marks  82  on a nonreflective background, as also shown in FIG. 6. Collimated light  88  from the wide beam LED  62  illuminates reflective marks  82  on cantilever  68 , where the light beam reflections  86  created by reflective marks  82  bounce toward PSD  60  (or multiple PSDs). Care must be taken that wide beam  88  covers reflective marks  82  at all times during scanning of cantilever  68 . Because the AFM scanning ranges are typically 10-100 μm, this task can be readily accomplished.  
     [0065] Referring to FIG. 5 again, PZT tube  70  first moves AFM tip  72  above sample  64  to an unknown x and y location. As AFM tip  72  encounters topographic changes, AFM cantilever  68  will be deflected. These minute deflections will cause light beams  80  and  86  to alter their paths and move light spots  87  on two-dimensional PSD  60  to new two-dimensional locations. These changes are then detected by two dimensional PSD  60 , and used to determine the out-of-plane position z and the pitch and tilt orientations of the cantilever. The X-Y motion and deflection of AFM cantilever  68  also cause a deflection of the light beams  86  created by the reflective marks  82 . Two-dimensional PSD  60  will then detect the displacement of the light spots on the surface of PSD  60 , and use that information to determine the in-plane positions x and y and the yaw orientation of the cantilever. Therefore all three positions and all three orientations can be determined simultaneously.  
     [0066] The significance of this embodiment is that the full position and orientation of AFM cantilever  68  can be determined directly and simultaneously from information provided by the PSD  60  without prior knowledge of how the cantilever arrived in its final position. This means that this second embodiment of the 6-DOF AFM of the present invention is insensitive to any system imperfections, such as the PZT nonlinearities and nonorthogonality between the sample and the PZT axis. This enables real-time, in-flight recording of the AFM cantilever tip  72  at randomly selected x and y positions. Complete decoupling of the actuator from the sensing system means that the 6-DOF AFM can measure at even better resolutions than the actuator itself, and do so while the actuator is in motion.  
     [0067] The basic modes of operation of the 6-DOF AFM of the present invention can be contact, non-contact, and attractive-repulsive. In contact mode with constant-height operation, AFM tip  72  will scan above sample  64  surface while the position and orientation of cantilever tip are determined.  
     [0068] In contact mode with constant-force operation, information about the vertical deflection z of cantilever is used to drive the laser beam to its original position, keeping the cantilever force constant. The limits where the constant-height mode must switch to a constant-force mode due to large topography changes have yet to be determined. The laser beam(s) that monitor the AFM cantilever can be moved, in constant-force mode, closer to the center of the PSD where the AFM can again be operated in constant-height mode.  
     [0069] Typically, a vibrating AFM cantilever has a resonant frequency above 100 KHz, whereas the PSD, due to its response time limitations, can only monitor up to 50 KHz signals. If a longer AFM cantilever with lower resonant frequency is used, then the non-contact vibrating tip mode is applicable. The improved tip control made possible by the 6-DOF system will enable a low frequency non-contact mode to be implemented, in which the tip functions as both a contact and non-contact AFM (called here an “attractive-repulsive mode”).  
     [0070] The ability to determine the orientation of cantilever  68  provides the unique capability to detect lateral forces while scanning in either the x or y directions. This is particularly important for material characterization studies. It also provides the capability to precisely detect the exact vertical deflection vs. the x and y location, whereas many AFMs have an error component in x and y due to the cantilever&#39;s deflection in z. This problem has appeared, for example, when imaging adhesion forces on proteins with an AFM.  
     [0071] Cantilever  68  selected for the present invention must have size, shape, and other physical properties consistent with cantilevers used in the AFM industry. The present invention also requires that AFM cantilever  68  serve as a reflective surface. Rectangularly shaped cantilevers, 35 μm wide and 350 μm long, are used in one embodiment of the present invention. The reflective sides are coated with aluminum, making them highly reflective. However, the present invention need not be limited by this shape, size and coating for the cantilever.  
     [0072] In the first embodiment of the 6-DOF AFM of the present invention, as shown in FIG. 4, two separate laser beams  50  were focused on surface  52  of cantilever  44 , either on top of each other, or next to each other along the length of cantilever  44 . For the second embodiment, FIG. 5 also provides a representation of two laser beams  74  focused on cantilever surface  78 .  
     [0073] A cantilever  68  with two reflective marks  82  is shown in the second embodiment of FIG. 5. Reflective marks  82  provide a means to use the cantilever itself for measuring in-plane motion instead of relying on the sample stage. One reflective mark allows the detection of in-plane cantilever displacements (x and y) as shown in FIG. 6. Two reflective marks allow the detection of the in-plane rotation (cantilever&#39;s yaw angle θ). Reflective marks  82  each have a diameter smaller then the width of cantilever  68  and are placed close to the free end of the cantilever, side by side along its length, as shown in FIG. 6. Cantilever edge  90  itself can be used in lieu of a reflective mark to define a reflective region  92 . This alternative embodiment for detecting in-plane motion shown in FIG. 7.  
     [0074] The single reflection from cantilever surface  78  depicted by the rectangular region  92  shown in FIG. 7 enables the detection of both in-plane cantilever displacements x and y. This may also be achieved by having two reflective strips along the length of the cantilever  68  separated by a non-reflective strip. Fabrication of such reflective strips is less complicated and less expensive then fabrication of two reflective dots within the cantilever. In addition, because such reflective strips are larger in size, the reflective strips produce more intense reflected light then the reflective marks. Increasing intensity reflected from the cantilever improves the signal-to-noise ratio of detection electronics. In the reflective strip design, the focused light beam (used for the out-of-plane measurement) will also use one of the reflective strips as the reflective surface needed to monitor the cantilever&#39;s out-of-plane displacement.  
     [0075] The 6-DOF AFM sensing system of the present invention required changing the beam shapes. In the first embodiment of the present invention, the diameter of narrow-beam laser  50  had to be less than the cantilever width. Therefore, a focused laser beam having a diameter less than the width of the cantilever at its focal distance may be used. A focused laser beam can function similarly to a narrow collimated beam for purposes of determining the out-of-plane components. The transformation equations used to compute the absolute position and orientation of the cantilever based on PSD outputs may need to be modified to take account of beam shape effects when focused beams are used instead of collimated beams.  
     [0076] One embodiment of the present invention specifically uses lasers specified as having 18 μm beam diameter at 100 μm focal distance. The 100 μm focal length provides adequate space for positioning the laser mounts, stage, PSD mounts and other components. Optics may be modified to change the focal length of a laser. Modifying these focal lengths allows the laser casings to be positioned next to each other and focused at the same spot on the cantilever.  
     [0077] Excessive beam diameter cause unwanted reflections from the edges of the cantilever. With a smaller laser beam, the quality of the laser light is improved and the signal to noise ratio significantly increased. In addition, a better focused laser beam provides a reflected beam with higher light intensity. This higher light intensity improves the signal to noise ratio of the system. Unwanted effects of the cantilever edges on the quality of the reflected laser beam provide that smoother edges, or reflective strips that do not extend out to the edges of the cantilever, will provide a higher quality reflected beam.  
     [0078] In the in-plane AFM implementation, shown as FIG. 5, the diameter of the wide beam laser  88  must be large enough to allow the reflective marks  82  to displace within the beam for at least 100 μm, which corresponds to the range required for of a typical AFM scan. Otherwise, the reflective mark  82  or strip would fall outside the region illuminated by beam  88 . If reflective mark or strip  82  is 35 by 35 μm, the wide beam should be approximately 100 μm to allow for 30 μm scans while keeping the reflective regions within the aperture of the collimated beam. One specific embodiment of the present invention uses a pseudo-collimated wide-beam laser light that is commercially available. This laser light has a diameter of 100 microns and depth of focus of 2 mm. The pseudo-collimated light was produced by using a focused light beam with a large depth of focus.  
     [0079] Continuous-position PSDs are robust with respect to the laser beam&#39;s shape, intensity variation over the beam profile, temporal intensity variation, and the position of the laser beam with respect to the physical center of the PSD when compared to split PSDs. Surface-mounted, tetra-lateral, two-dimensional (5×5 mm) PSDs may be used in embodiments of the present invention.  
     [0080] The required surface area of the PSD depends on the diameter and divergence of the beam reflected from the reflective region on cantilever. This is because the incident light spot must fit within the PSD aperture. When using focused rather than collimated light beams, the distance between the PSD and the cantilever also plays a role. At some focal distances, the laser beam may be larger than the cantilever, resulting in the reflection from the cantilever edges producing a reflected light beam with a very irregular, non-continuous shape.  
     [0081] At certain distances from the cantilever, most but not all of the light intensity distribution of the reflected laser beams may fall within the PSD apertures. Using larger PSDs enables the present invention to capture the entire intensity distribution. However, based on the physics of these devices, a larger PSD area would result in decreased device resolution. Achieving high resolution is an important objective. The split PSDs typically used in conventional AFMs cannot detect anything from this type of reflected laser light. The fact that the present invention is able to obtain a degraded, but still meaningful measurement demonstrates that the present invention is robust in relation to intensity variations over the beam profile.  
     [0082] A major challenge overcome by the present invention in the use of multiple lasers with an AFM cantilever is the difficulty of aligning the reflected laser beams with the PSDs. Split PSDs used with most AFMs cannot overcome this difficulty because multiple laser beams would have to be aligned with the centers of the split PSDs so as to allow the laser beam to illuminate all four quadrants, while maintaining uniform beam shape and intensity. Continuous position PSDs do not have this disadvantage because they can accommodate a laser beam with arbitrary shape and non-uniform intensity. In addition, a continuous position PSD can also be positioned away from the centroid of the incident beam, as long as this does not cause the beam to fall outside the PSD aperture.  
     [0083] Embodiments of the present invention may use both AC and DC modulated lasers. The constant (DC) laser beam intensity produced a more stable signal in relation to drift and noise, but it also increased the sensitivity of the PSD signal to variations in environmental lighting conditions and to the quality of the laser. The AC scheme approach should shift the electronic signals to frequency bands where the noise floor is lower, thereby further improving signal-to-noise-ratio and, with it, overall system resolution.  
     [0084] Phase lock loop amplifiers are ordinarily used when superior signal recovery capability is required. However, embodiments of the present invention may use a 6-DOF AFM without using phase lock loop amplifiers. If phase lock loop amplifiers are used, several phase lock loop amplifiers are needed to process the signals from two PSDs. Embodiments of the present invention demonstrate the ability to achieve nm-scale resolution without using phase lock loop amplifiers. A more refined resolution and repeatability may be achieved with the use of phase lock loop amplifiers in the circuit.  
     [0085] A piezoelectric transducer (PZT) stage is capable of moving either the sample or the AFM cantilever in the x, y and z directions. Typical PZT stages are available from Piezosystem Jena, with 80 μm range in x and y, and 9 μm in z.  
     [0086] The function of the data acquisition system (DAQ) is to acquire the signals from the PSD signal processing circuits. These signals are digitally filtered to parse the acquired data into frequency components, average the signals, normalize the signals, display and store the experimental data, and provide analog output to drive the PZT stage in all three axes.  
     [0087] A package such as National Instruments&#39; LabView software and data acquisition hardware may be used in the DAQ. The measurements may be taken on-demand or during continuous sampling. The results may be processed by passing the PSD output signal through a Fourier transform and discarding all frequency components except the residual DC signal. Each data point represents a sample average of this DC signal, acquired at a sampling rate of 10 KHz per channel. This number of samples is empirically based on minimizing the observed standard deviation. However, the present invention need not be limited by this method of sampling.  
     [0088] A calibration grating may be used as an AFM sample. A standard semiconductor calibration grating with pyramidal ridges, 1.8 μm high and 3 μm apart, with their faces aligned at 70° with respect one another is shown in FIG. 8.  
     [0089] The simple, robust design of a 6-DOF AFM will make it readily adaptable to multi-cantilever operation. Because the continuous PSD is better for alignment and centering, it is more suitable for monitoring the position of many light beams, where each is from a different cantilever. A single continuous PSD can be used to monitor more than one light beam from more than one than one cantilever. In a multi-probe application the sample will be displaced by a piezoelectrically actuated stage in the same x and y step under each AFM cantilever tip. A separate sensing system will be used to instantaneously determine the z position, or the z position plus the orientation, of each individual cantilever. This information about position and orientation can be used to independently control the height and orientation of each cantilever.  
     [0090] The embodiments previously described are not the only possible AFM architectures that can be implemented with the multidimensional sensing system. Different embodiments of the invention include different positions and orientations of the lasers and the PSDs with respect to each other, and with respect to the AFM cantilever. Another embodiment involves the number of the lasers and PSDs. Using multiplexing schemes, one could reduce the number of PSDs so that one PSD monitors more then one laser light. Another embodiment utilizes beam-splitters that enable a single laser beam to illuminate different sensed bodies, of which one or more are AFM cantilevers (two AFM cantilevers or an AFM cantilever and a reference body). Still another variation uses a single reflected laser beam that illuminates more then one PSD. This approach is effective in reducing the number of lasers.  
     [0091] Another embodiment uses mirrors to manipulate the laser beam to reach an AFM cantilever when direct pointing from a laser is hard, or to divert the light beam path to improve the sensing.  
     [0092] An additional embodiment of an AFM sensor-actuator uses only one or more fiducial surfaces to detect all six degrees-of-freedom of a body in space, including an AFM cantilever. This embodiment departs from the previously described approach where the out-of-plane sensing and the in-plane sensing are done separately with different types of laser beam light (narrow beam collimated, wide beam collimated, focused). The combination of reflective surface and fiducial surface is replaced by a fiducial surface. Although this AFM sensor-actuator configuration can be used for a variety of applications suitable for AFMs, such as roughness measurement, inspection of chemical-mechanical-planarization (CMP) wafer processes, the present invention is well suited for critical dimension atomic force microscopy (CD AFM). As CD AFM inspection involves sudden topography changes and vertical or re-entrant sidewalls, CD AFM inspection is the most challenging application for an AFM based tool.  
     [0093]FIG. 9 presents a side view of this CD AFM architecture configuration. The architecture consists of two collimated laser beams and four PSDs. FIG. 9 shows the side view and therefore only one laser  110  and the corresponding pair of PSDs (PSD 1  112  and PSD 3  114 ). A second laser and a second pair of PSDs are behind the first laser-PSD set. FIG. 10 provides a top view of the entire sensing system. FIG. 11 shows the perspective view of the sensing system but does not show the secondary PSDs (PSD 3  114  and PSD 4  116 ) as shown in FIG. 10 that detect the laser beams  122  and  124  reflected off the primary PSDs (PSD 1  112  and PSD 2  118 ). Lasers  110  and  111  and PSDs  112 ,  114 ,  116  and  118  are all fixed to absolute reference frame  126  and the cantilever  120  is attached to an actuation mechanism  130  shown in FIG. 12. FIG. 13 presents a cantilever suitable for this embodiment. Use of one fiducial and three PSDs allows detection of five absolute degrees-of-freedom (the sixth one, yaw about the z axis, is not determined using only one fiducial). However, use of four PSDs provides sensing redundancy. Use of a second fiducial requires four PSDs and will allow determination of the yaw, but also adds an extra necessary complexity in constructing a sensing system. For AFM applications, yaw of standard AFM cantilever is not important, and therefore the presented embodiment does not include this but may be incorporated.  
     [0094] The principle of operation is as follows. A collimated laser beam from laser  110  is pointed toward an AFM cantilever  120  with fiducial surface  121 . Fiducial surface  121  reflects a primary reflected beam  111  towards a PSD  112 . With the help of beam-splitters one can split the reflected laser beam towards PSD 1  112  and PSD 3  114 . The principle is the same for a second laser  132  and PSDs 2  118  and 4  116 . In the presented architecture the primary PSDs  112  and  118  function as a mirror that reflects the primary reflected laser beam  111  towards the secondary PSDs  114  and  116 . Available off-the-shelf PSDs reflect enough light to achieve the second laser beam bounce. Additional coatings can further improve the quality of the secondary reflected light  122  and  124 . In any case, the electronic processing for the primary and secondary PSDs must account for the different laser beam intensity of the primary and secondary laser beam. The use of secondary reflected laser beam replaces the need for an extra laser. Without the secondary reflected laser beam one would need four lasers. A pair of primary and secondary PSDs in principle enables the detection of the directionality of the laser beam, which is not possible with a single PSD.  
     [0095] As cantilever  120  moves to a different position and orientation under the flood of collimated laser beam  110 , fiducial surface  121  reflects the laser beams to a new position on the surface of the four PSDs. For example, a cantilever twist (Ψ) around its axis as shown in FIG. 12 would create a laser beam trace on the surface of the PSD in a shape of an arch  134  shown in FIG. 11, and a z displacement would produce up-down trace  136 .  
     [0096] The output from the PSDs is the two-dimensional position of the laser spot  138  on the surface  140  of the PSD. An electrical current output from the PSDs is electronically and then digitally processed. The eight PSD outputs are part of a set of eight independent nonlinear equations with five unknowns. Simultaneous solution of the decoupled equations, or numerical solution of the coupled equations produces the absolute position and orientation of the AFM cantilever as illustrated in FIG. 14.  
     [0097]FIGS. 9, 12 and  15  show the functioning of the actuating system for a CD metrology application. The sample is attached to a coarse XY stage  141  that is used to position the sample  142  (semiconductor wafer with ICs) under the AFM tip  144 . AFM cantilever  120  is approached with the help of a z approach stage  146  that has as large a range (on the order of 100 mm) and as needed twisted in Ψ (with the help of the angular approach stage  148 ) as to allow tip  144  to reach undercut features. Angular approach stage  148  is mounted atop the XYZ PZT stage  146  that is used for scanning AFM tip  144  across sample  142 . A 3-D PZT driver that is used to drive (vibrate) the cantilever  120  is attached to the angular approach stage  148 . The cantilever is attached to the PZT driver module. This actuation system allows AFM tip  144  to be positioned with respect to a feature on sample  142 . Because the sensing system monitors AFM cantilever  120  as it twists, the sensing system can accommodate large twist angles that can enable tip  144  to access re-entrant features  150  as shown in FIG. 16. The only other way to currently access re-entrant features is with boot-shaped tips that are very fragile, expensive, and blunt at the end of the boot.  
     [0098] The present invention also allows operating the cantilever and the tip in the x, y, and z directions. This enables one to determine all components of a 3-D vector normal to the surface, the length of which is equal to the distance from tip  144  to the surface of sample  142  and the XYZ position of the corresponding point on the sample surface. The 3-D capability of the CD AFM of the present invention enables a new AFM scanning strategy where the raster step in y can be altered for faster AFM imaging and better inspection of profiles in y direction that might have been omitted if one did not have information about the y direction and scanned with constant y raster step as illustrated by the results presented in FIGS. 17 and 18. It is also possible to scan in the XY direction.  
     [0099] Since the PSDs of the sensor-actuator system always track the reflected laser beams from the cantilever  120 . The present invention enables measurement of absolute linear and angular measurements tied to a fixed reference frame. FIG. 19 illustrates this capability which is not possible with existing AFMs.  
     [0100] Tracking of cantilever  120  directly with the sensing system also enables XY measurements independent of the scanning stage. In existing AFMs the XY measurements are provided by an external sensor.  
     [0101] Use of large collimated beams and use of a fiducial surface enables absolute scans over the diameter of the laser beam, 1 to 5 mm as shown in FIG. 20. Existing AFMs do not even have an absolute reference frame and cannot scan more then 100 μm without saturating the sensing system.  
     [0102] Yet another advantage of the CD AFM of the present invention is the elimination of the cosine errors due to cantilever bending and tilt, vertical tip and sample alignment, and x and y orthogonality error. These errors occur when the sensing system measures coupling of the displacements. Since all coordinates are determined simultaneously, measurements are decoupled. FIGS. 21 and 22 illustrate cosine errors due bending and tilt.  
     [0103] Other configurations possible with the sensing system include special adaptations designed for mask repair, as shown in FIGS. 23 and 24.  
     [0104] A micro-machining tool or, in one embodiment, a mask repair tool is illustrated in FIGS. 23 and 24. In this embodiment, the AFM tip  202  may be used to either perform a quality assurance check on the profile of the mask structures  204  or remove a defect from the mask  206  or repair a defect on a mask structure  204  on mask  206 . In this embodiment, the AFM tip  202  is coupled to AFM cantilever  208  which is positioned by a mechanical stage  210 .  
     [0105] Mechanical stage  210  consists of at least one laser source  212  and a PZT actuator stage  214  coupled directly to AFM cantilever  208 .  
     [0106] Motion of AFM tip  202  through mechanical stage  210  cantilever is controlled by a computer control system  216 . This computer control system  216  will contain software to process data on workpiece or mask  206  to determine the location of defects  218  on mask  206  and coordinate the removal and/or repair of defects  218  from the workpiece.  
     [0107] Laser sources  212  contained within mechanical stage  210  provide collimated laser beams to measure out-of-plane and in-plane movements of AFM cantilever  208  as described in earlier embodiments.  
     [0108] A knowledge of the geometry of how AFM tip  202  is coupled to AFM cantilever  206  allows one to determine the position of AFM tip  202  from a knowledge of the position of AFM cantilever  206 .  
     [0109] The present invention may use laser sources  212  to provide a laser beam  218  which is reflected from a surface, wherein the surface may be the top surface of cantilever  206 , towards PSDs  220 . The system will utilize at least one PSD  220  to determine a variable describing the location and orientation of AFM cantilever  206 . The present invention may determine the x coordinate, y coordinate and z coordinate, as well as the pitch angle, yaw angle and tilt angle or any combination of these variables associated with the position and orientation of the AFM cantilever from the reflected beams onto continuous PSD  220  apertures. These PSDs may be continuous PSDs, however need not necessarily be continuous PSDs. PSD  220  provides an output signal to a signal processing system  222  which will then determine the location of AFM tip  202  from the outputs of PSDs  220 . This information is supplied to control system  216  to reposition the AFM tip  202  as needed or desired to execute a repair strategy. In one embodiment of the present invention, AFM tip  202  may be used to mechanically agitate or remove a defect from an object. In another embodiment, AFM tip  202  may be used to repair an object on the workpiece or mask  206 , as described in FIGS. 23 and 24. In a further embodiment, AFM tip  202  may be used to deposit a material to repair a structure on the workpiece or mask  206 .  
     [0110] Cantilever position and orientation measurements are provided relative to an absolute reference frame fixed with respect to the structure of the AFM as shown in FIG. 25. This is in contrast to conventional AFM sensing systems that provide only the vertical, z, coordinate (or, in one known instance, only the horizontal, x, and vertical, z, coordinates), of the cantilever with respect to an absolute reference frame. Conventional AFM sensing systems rely on the output of a scanning stage for the x and y (or, just the Y) coordinate and providing no information at all about the cantilever&#39;s angular orientation.  
     [0111] Various embodiments of the six-degree-of-freedom sensing system of the present invention are capable of simultaneous multi-dimensional sensing, as opposed to one-dimensional or several-step multi-dimensional sensing currently performed with existing AFMs as illustrated in FIG. 26.  
     [0112] The present invention provides a method of scanning contact holes and vias as shown in FIG. 27. Here cantilever  120  is tilted so as to allow access of tip  144  to one sector of the curved sidewall of hole or via  160 . Tip  144  is scanned in XY and rastered in z. Cantilever  144  is then tilted in the other direction so as to allow access of the tip to another sector of the curved sidewall. Tip  144  is again scanned in XY and rastered in z. The results of the scans are combined to provide contour lines  162  describing the surface of hole or via  160 .  
     [0113]FIG. 28 illustrates how the multidimensional sensing system adapted to an AFM can be used for automated tip changing. The multidimensional sensing system uses PSD outputs, x ′PSD and y ′PSD , to calibrate new cantilever orientation angles, ψ and φ, after a tip change. The XYZ stage then reapproaches the sample and resumes scanning.  
     [0114] Position in x, y and z and orientation in pitch, tilt, and yaw of the AFM cantilever are determined simultaneously for each unknown x and y displacement of the sample.  
     [0115] The present invention provides an important technical advantage in that the present invention eliminates the need for precise alignment and centering of the laser beam. A continuous PSD is capable of monitoring the position of a light beam on its surface without the need for precise alignment and centering, as is required when bi-cell or quadrant cell position detectors are used.  
     [0116] The present invention provides another important technical advantage in that the present invention eliminates the need to maintain spatial and temporal uniformity of the laser beam. Use of continuous PSDs eliminates the need to maintain spatial and temporal uniformity of the laser beam, as is required when bi-cell or quadrant cell position detectors are used. This is because continuous position-sensitive detectors (PSDs), unlike Bi-cell and quadrant cell detectors, are inherently insensitive to spatial and temporal variations in the laser beam intensity distribution.  
     [0117] The present invention provides yet another important technical advantage in that the present invention eliminates the need for the laser beam spot to illuminate both halves or all four quadrants of the PSD aperture. Use of continuous PSDs eliminates the need for the laser beam spot to illuminate both halves or all four quadrants of the PSD aperture. This feature enables use of a smaller laser beam spot which, in turn, enables operation over larger ranges, since the smaller spot can traverse larger regions of the PSD surface without part of its intensity distribution falling outside the PSD aperture.  
     [0118] Also, use of continuous PSDs instead of bi-cell or quadrant cell position detectors eliminates the need to maintain spatial and temporal uniformity of the laser beam. This is because continuous position-sensitive detectors (PSDs), unlike bi-cell and quadrant cell detectors, are inherently insensitive to spatial and temporal variations in the laser beam intensity distribution. Using continuous PSDs also means the laser beam spot is not required to illuminate both halves or all four quadrants of the PSD aperture. This feature enables use of a smaller laser beam spot which, in turn, enables operation over larger ranges, since the smaller spot can traverse larger regions of the PSD surface without part of its intensity distribution falling outside the PSD aperture.  
     [0119] The present invention enables sensing of the position and orientation of an AFM cantilever. Present invention allows direct measurement of cantilever position and orientation coordinates in all six degrees of freedom without reliance on the output of a scanning stage to determine any of these measured coordinates. Cantilever position and orientation measurements are provided relative to an absolute reference frame fixed with respect to the structure of the AFM.  
     [0120] A technical advantage provided by the present invention is the ability to sense the position and orientation of an object in multidimensional space.  
     [0121] Yet another technical advantage provided by one embodiment of the present invention is the ability to repair a workpiece or remove a defect from a workpiece such as a photolithography mask used in semiconductor manufacture.  
     [0122] Another key advantage of the present invention is the ability to examine re-entrant features with an AFM tip. Because a sensing system of the present invention monitors AFM cantilever as it twists, the sensing system can accommodate large twist angles that can enable the AFM tip to access re-entrant features. This eliminates the need to access re-entrant features with boot-shaped tips that are very fragile, expensive, and blunt at the end of the boot.  
     [0123] The present invention is ideal for a variety of uses, including material characterization, chemical-mechanical planarization monitoring, precision surface profiling and critical dimension metrology.  
     [0124] Yet another feature of the present invention is to completely decouple position sensing of an AFM from the mechanical actuator which positions the AFM tip, enabling the present invention to measure at even better resolutions than the ability to position the mechanical actuator itself. Furthermore the present invention may do so while the actuator is in motion. Nonlinearities of the mechanical actuator have no effect on the accuracy of the system. This enables real-time, on-the-fly recording of the AFM cantilever tip position at randomly selected positions.  
     [0125] Although the present invention has been described in detail herein with reference to the illustrative embodiments, it should be understood that the description is by way of example only and is not to be construed in a limiting sense. It is to be further understood, therefore, that numerous changes in the details of the embodiments of this invention and additional embodiments of this invention will be apparent to, and may be made by, persons of ordinary skill in the art having reference to this description. It is contemplated that all such changes and additional embodiments are within the spirit and true scope of this invention as claimed below.