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  Carbon nanotube excitation systemRelated Patent Categories: Measuring And Testing, Surface And Cutting Edge Testing, RoughnessThe Patent Description & Claims data below is from USPTO Patent Application 20060156798. Brief Patent Description - Full Patent Description - Patent Application Claims
CROSS-REFERENCE TO RELATED APPLICATION [0001] Under 35 U.S.C. .sctn.120, this application claims the benefit of commonly owned U.S. patent application Ser. No. 09/881,650 entitled SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Jun. 13, 2001, which is also hereby incorporated by reference. [0002] In addition, under 35 U.S.C. .sctn.120, this application claims the benefit of commonly owned U.S. patent application Ser. No. 09/499,101 entitled SYSTEM AND METHOD OF MULTI-DIMENSIONAL FORCE SENSING FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Feb. 4, 2000, which is also hereby incorporated by reference. [0003] Additionally, via U.S. patent application Ser. No. 09/499,101, and under 35 U.S.C. .sctn.119(e) and 120 and 37 C.F.R. .sctn.1.53(b), this application further claims the benefit of commonly owned U.S. Provisional Patent Application No. 60/118,756 entitled MULTI-DIMENSIONAL FORCE SENSING SYSTEM FOR ATOMIC FORCE MICROSCOPY, by Vladimir Mancevski, Davor Juricic, and Paul F. McClure, filed on Feb. 5, 1999, which is also hereby incorporated by reference. [0004] This application also incorporates by reference commonly owned U.S. patent application Ser. No. 09/404,880 entitled MULTI-DIMENSIONAL SENSING SYSTEM FOR ATOM FORCE MICROSCOPY, by Vladimir Mancevski, hereinafter referred to as "MANCEVSKI1." [0005] Furthermore, this application also incorporates by reference commonly owned issued U.S. Pat. No. 6,146,227 entitled METHOD FOR MANUFACTURING CARBON NANOTUBES AS FUNCTIONAL ELEMENTS OF MEMS DEVICES, by Vladimir Mancevski, hereinafter "MANCEVSKI2." TECHNICAL FIELD OF THE INVENTION [0006] The present invention relates generally to the field of force measurement using scanning probe microscopy (SPM) and, more particularly, to a force measurement system for determining the topography or composition of a local region of interest by means of scanning probe microscopy. BACKGROUND OF THE INVENTION Introduction of Terms used in this Disclosure [0007] In this invention we use Cartesian coordinate systems with perpendicular axes as the coordinate system of choice. Nevertheless, one may implement any other well-defined coordinate system including, for example, polar, cylindrical, or spherical coordinate system. The "global" coordinate system X Y Z 40 is fixed with the sample and the "local" coordinate system X.sub.tip Y.sub.tip Z.sub.tip 42 is fixed with the apex 45 of the tip 44 of the scanning probe 48. In general, the scanning probe tip apex 45 may have an arbitrary position and orientation with respect to the sample, therefore, the local coordinate system 42 also may have arbitrary position and orientation with respect to the global coordinate system 40, as shown in FIG. 1A. In a special case, the local 42 and global 40 coordinate systems may be aligned with respect to one another, as shown in FIG. 1B. [0008] The origin of the local coordinate system 42 is at the apex 45 of the tip 44. The Z.sub.tip axis 46 is oriented along the length of the tip 44 and is perpendicular to a region of the oscillator 48 surface near the place where the tip 44 is attached The X.sub.tip axis 50 is parallel to the long axis of the oscillator 48. The Y.sub.tip axis 52 is transverse with respect to the X.sub.tip axis 50 so as to form a right-handed Cartesian coordinate system. [0009] It is known that a dipole-dipole interaction occurs between pairs of atoms located in volumetric regions of the tip 44 and sample 54 when they are in proximity to each other. The associated force is called Van der Walls force. The resulting integrated effect encompasses all dipole-dipole interactions between pairs of atoms in sufficient proximity to generate a measurable interaction between the tip 44 and the sample 54. This resultant of the integrated dipole-dipole interaction is represented by a three-dimensional "tip-sample interaction force vector" 56 as shown in FIG. 2A. A single point can be used to approximate the volumetric region near the tip apex 45, and a flat surface can be used to approximate the region of the sample 54 in proximity to the tip 44, as shown in FIG. 2B. If the surface of the sample 54 is horizontal (i.e., in the XY plane) the tip-sample interaction force vector 56 will be vertical. However, if the surface of the sample 54 is vertical (e.g., in the XZ plane) the tip-sample interaction force vector 56 will be horizontal. For a general orientation of the surface of the sample 54, the tip-sample interaction force vector 56 will have three non-zero components, corresponding to the three axes XYZ of the global coordinate system 40. The tip-sample interaction force vector F 56 can be represented either by its components F.sub.x tip, F.sub.y tip, F.sub.z tip in the local coordinate system 42 or by its components F.sub.X, F.sub.Y, F.sub.Z, in the global coordinate system 40. [0010] In one possible mathematical representation, the 3.times.1 vector functions .PHI..sub.i, for (i=1, 2, 3, . . . .infin.), of the spatial coordinates (e.g., X.sub.tip Y.sub.tip Z.sub.tip) represent mode shapes of the probe structure, and q.sub.i represent the corresponding generalized coordinates. In one instance of a classical modal analysis, the equations of motion of the probe are M.sub.jd.sup.2q.sub.j/dt.sup.2M.sub.j .omega..sup.2q.sub.j-.SIGMA..sub.i=1 to .infin.F.sub.ij'q.sub.i=F.sub.0j Where (j=1, 2, 3, . . . .infin.), M.sub.j is the modal mass, .omega..sub.j is the resonant frequency, and F.sub.oj is the static component of the generalized force corresponding to the tip-sample interaction force applied to the probe tip. The term--.SIGMA..sub.i=1 to .infin.F.sub.ij' q.sub.i can be interpreted as a negative spring force which alters the j.sup.th resonant frequency of the vibrating probe. The quantity F.sub.ij' can be represented in terms of the mode shapes by F.sub.ij'=[A].PHI..sub.i(tip).PHI..sub.j(tip). Where [A] is a 3.times.3 coefficient matrix arising from classical modal analysis and the symbol denotes an inner product of two vectors. [0011] The vector [A] .PHI..sub.i(tip), derived from classical modal analysis, is an example of a more general vector quantity that we call a "resultant surface force interaction." Our use of the term "resultant surface force interaction" is not limited to any particular physical origin of the tip-sample interaction force and may include, for example, both conservative and non-conservative tip-sample interaction forces. [0012] FIG. 3A shows typical orientations of three selected mode shape vectors, evaluated at spatial coordinates corresponding to the apex 45 of a probe tip 44. In this example, .PHI..sub.1 (tip) 58 represents the direction in which the tip apex 45 moves when the main bending mode is excited, .PHI..sub.2(tip) 60 represents the direction in which the tip apex 45 moves when the first torsional mode is excited and .PHI..sub.3(tip) 62 represents the direction in which the tip apex 45 moves when the second bending mode is excited. For a suitably chosen structural design of the probe 48 and tip apex 45 location, and for small-amplitude vibrations, .PHI..sub.3(tip) 62, .PHI..sub.2(tip) 60 and .PHI..sub.1 (tip) 58 are each substantially aligned with the unit vectors, i.sub.tip 64, j.sub.tip 66, and k.sub.tip 68, respectively, and the modal coordinates q.sub.3, q.sub.2, q.sub.1 can be approximated by tip 44 displacements along the in the X.sub.tip 50 Y.sub.tip 52 Z.sub.tip 46 axes respectively. In this example the resultants of the surface force interaction can be given a geometric interpretation as vectors aligned along the X.sub.tip 50 Y.sub.tip 52 Z.sub.tip 46 axes. [0013] The resultant surface force interaction vectors F'.sub.x tip 70, F'.sub.y tip 72 and F'.sub.z tip 74 can, in some cases, be modeled by the three virtual springs with variable spring constants k.sub.1 76, k.sub.2 78, and k.sub.3 80 that are functions of the tip-surface distance, as shown in FIG. 3B. The vector F' 82 shown in FIG. 3C is the sum of the three resultant surface force interaction vectors. As the force axis 84 and the distance axis 86 show in FIGS. 4A and 4B, the force-distance curve 88 shows that the resultant surface force is non-linear with respect to the tip-surface distance. Therefore, the modeled spring constants are also non-linear. However, for small amplitudes of vibration of the oscillator tip 44, the spring constants are linear with respect to the tip-surface distance. To maintain linear response, the oscillator 48 should vibrate with sufficiently small amplitude to keep the oscillator in a linear regime of operation, shown by area of measurement 90. Contrast that with area of measurement 92, used in tapping mode. Force axis 84 shows repulsive force 94 and attractive force 96. [0014] The term "oscillator," as used in conjunction with the present invention, represents a scanning probe 48 for which multiple resonant modes are intended to be used for force sensing. The term "cantilever" refers to a scanning probe 48 for which only the primary bending (i.e., "cantilever") mode is intended to be used for force sensing, even though, in general, the probe 48 structure would exhibit multiple resonant modal responses if excited at the appropriate driving frequencies. [0015] The term "force sensor" refers to the resonating oscillator 48 and its sensitivity to surface forces 82 associated with the tip-sample interactions. The purpose of the force sensor is to enable detection of the surface topology or composition by means of coupling the scanning probe tip 44 to the surface of the sample 54 via a tip-sample interaction force 82. In general, the interaction force 82 between the tip 44 and the sample 54 is a non-linear function of the tip-surface gap that includes the dipole-dipole interaction described above (which is conservative and hence describable by a potential), plus additional contributions from other conservative forces (e.g. electrostatic and magnetic forces) and non-conservative forces (e.g., meniscus forces and other forces due to surface contamination). However, whatever its origin in terms of atomic interactions, molecular interactions or other surface physics phenomena, the tip-sample interaction force vector 56 can still be represented by a vector composed of three generally non-zero components, corresponding to the three axes XYZ of the global coordinate system 40. Alternatively, the tip-sample interaction force 82 can be represented by a vector 56 composed of three generally non-zero components, corresponding to the three axes X.sub.tip Y.sub.tip Z.sub.tip of the local coordinate system 42. Equal and opposite tip-sample interaction forces 82 act on the tip 44 and sample 54, respectively, consistent with Newton's law of action and reaction. [0016] "Force sensing" occurs when the surface force interaction alters the effective elastic restoring force associated with one or more resonant modes of the primary probe 48 structure so as to shift the respective natural frequencies of its resonant modes. The shifts in natural frequency can be sensed, for example, by monitoring either the amplitudes or phases of the respective modal oscillations. [0017] When using the term "at" in the claims herein to describe a positional relationship between two objects, the term "at" is intended to be interpreted as meaning: (i) contacting the surface 54 or (ii) located near to but not contacting the surface 54. For example, when a SPM tip 44 is "at" a sample surface 54 during a scan, the tip 44 may be contacting the surface 54 (as in contact or tapping mode testing), or the tip 44 may be located near to the surface 54 but without contacting the surface 54 (as in non-contact testing). As another example, when a distal end of a nanotube is "at" a surface 54 of a semiconductor integrated circuit, the distal end of the nanotube may be contacting or tapping the surface 54, or the distal end of the nanotube may be located near the surface 54 without contacting the surface 54. BACKGROUND OF THE RELATED ART [0018] A scanning probe typically consists of a primary probe structure 48, (which may be either an oscillator or a cantilever) and a high aspect-ratio, sharply-pointed tip 44 extending from its end. The tip 44 is generally much less massive than the primary probe structure 48. The function of the primary probe structure is to provide one resonant mode (in the case of a cantilever) or more than one resonant mode (in the case of an oscillator), which are utilized for force sensing. Typically, the primary probe structure 48 is about 100 microns long by 30 microns wide by 2 microns thick. The function of the tip 44 is to rigidly couple the primary probe structure 48 to a relatively small volumetric region (the tip apex 45) which can be positioned so as to interact with a relatively small region of the sample 54 in proximity to the tip apex 45. Typically, the tip 44 is an inverted cone or a pyramid with its apex 45 pointing towards the sample surface 54. Ideally, the apex 45 of the tip 44 would be a single atom that couples with the sample surface 54 via the tip-sample force interaction. In reality, the apex 45 of the tip 44 typically has a radius of about 10 nanometers, and the cone-shaped or pyramid-shaped tip 44 is typically a few microns long. [0019] In conventional scanning probe microscopy (SPM), the force sensor is only sensitive to the resultant of the surface force interaction F'.sub.z tip 74, in the Z.sub.tip 46, direction, as illustrated in FIGS. 5A and 5B. The other two components of the surface force interaction vector, F'.sub.X tip 70 in X.sub.tip 50 direction and F'.sub.Y tip 72 in the Y.sub.tip 52 direction, are not detected in conventional scanning probe microscopy. The XYZ and X.sub.tip Y.sub.tip Z.sub.tip coordinate systems are shown in FIGS. 5A and 5B as being aligned for ease of illustration. For conventional non-contact mode scanning, a SPM cantilever 48 is excited in its first bending mode with small amplitude, thereby causing the tip 44 to move within the attractive region of the surface force interaction profile. This region 90 is illustrated in FIG. 4A. In the conventional "tapping" mode, the amplitude of the cantilever 48 vibration is larger and the tip 44 dips in and out of both the attractive 96 and repulsive 94 regions of the surface force interaction region 92, as shown in FIG. 4B. A change in the tip-surface distance during the scanning process shifts the cantilever 48 resonance. A feedback loop uses the resonance shift to maintain either the amplitude or phase of the oscillation at a predetermined value. The output from the resulting scan is used to represent the topography or composition of the surface. Scanning of the probe in an XY raster plane while recording the response of the force sensor in Z direction can be used to construct a three-dimensional profile of the surface 54. Continue reading... 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