Abstract:
A fiber-facet AFM probe enabling high-resolution, high sensitivity measurement of a sample surface is presented. AFM probes in accordance with the present invention include an optically resonant cavity that is defined by two mirrors, at least one of which is a photonic-crystal mirror. One of the mirrors is movable and is mechanically coupled with an AFM tip such that a force imparted on the tip by an interaction with the sample surface induces a change in the cavity length of the optically resonant cavity and, therefore, its reflectivity.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    moon This case claims the benefit of U.S. Provisional Patent Application U.S. 61/724,271, which was filed on Nov. 8, 2012 (Attorney Docket: 512-419/PROV), and which is incorporated herein by reference. 
         [0002]    If there are any contradictions or inconsistencies in language between this application and one or more of the cases that have been incorporated by reference that might affect the interpretation of the claims in this case, the claims in this case should be interpreted to be consistent with the language in this case. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
       [0003]    This invention was made with Government support under Contract No. PHY-0830228 awarded by the National Science Foundation. The Government has certain rights in the invention. 
     
    
     FIELD OF THE INVENTION 
       [0004]    The present invention relates to imaging systems in general, and, more particularly, to atomic force microscopy. 
       BACKGROUND OF THE INVENTION 
       [0005]    Atomic-force microscopy (AFM) is a technique for imaging a surface of a surface at the sub-nanometer (nm) scale. It has become commonly used for surface characterization, as well as mapping of certain material-specific surface properties, for materials such as polymers, ceramics, composites, glass, and biological tissue. 
         [0006]    An AFM probe typically includes a very sharp tip that is mounted at the end of a cantilever. To image a surface, the tip is moved along the surface and its interaction with the surface is recorded. When the tip is in proximity with the surface, forces between the tip and the sample lead to a deflection of the cantilever, which can be measured with very high accuracy. By scanning the probe tip in two dimensions, a complete map of the surface structure and/or other physical properties of the surface can be developed. 
         [0007]    Tapping-mode AFM (TM-AFM) is a particular type of AFM wherein the probe tip is brought into intermittent-contact with the surface so that it intermittently touches or “taps” the surface. TM-AFM is particularly attractive for measuring soft materials, since the tip is less likely to be “stuck” in the material. In addition, lateral forces on the tip, such as drag (which can reduce measurement accuracy), are virtually eliminated. 
         [0008]    In TM-AFM, an actuator drives the cantilever such that it oscillates at its fundamental resonance frequency while the probe tip is scanned over the sample surface. The separation between the probe tip and the sample surface is adjusted via a feedback control loop to maintain constant oscillation amplitude at the probe tip. As the tip intermittently touches the sample during a scan, the tip experiences a contact force that induces dynamic effects on the mechanical behavior of the probe, such as oscillation amplitude changes, phase changes, and the development of harmonic components. These effects occur at frequencies much higher than the fundamental frequency of the probe and contain information about the physical properties of the surface over which the probe tip is scanned. Unfortunately, conventional AFM probes lack the capability to measure the higher signal frequency components with sufficient fidelity. 
         [0009]    To overcome the drawbacks of conventional AFM probes, AFM probes having higher bandwidth capability were developed to enable direct measurement (typically via optical means) of the higher frequency components of the tip-sample interactions while preserving conventional operation in tapping mode. Examples of high-bandwidth AFM probes are disclosed in U.S. Pat. No. 8,082,593, which is incorporated herein by reference. 
         [0010]    A typical high-bandwidth AFM probe has a cantilever body that extends from a reference structure to a first end, from which a sensor cantilevers to a second end that includes the probe tip. The sensor is characterized by higher resonance frequency than the cantilever portion; therefore, the sensor can respond to the dynamic effects that arise from tip-surface interactions. The mechanical behavior of the sensor versus that of the cantilever body is monitored, providing a signal that can be processed to yield more information about the properties of the surface than can be obtained with simpler cantilever-type probes. 
         [0011]    Unfortunately, prior-art AFM probes and resulting systems have several drawbacks. First, they are typically relatively large. As a result, they are not well suited to many biological-imaging applications, such as in-vivo imaging. 
         [0012]    Second, their relatively large size and cantilever design leads to a reduction in measurement resolution. 
         [0013]    Third, prior-art AFM probes are typically too large and complex to use in array fashion. As a result, in order to image a two-dimensional region of a sample, an individual probe must be physically scanned over each object point in the region. Errors in the spatial positioning of the probe, as well as low-frequency signal components that arise from the scanning mechanism, can lead to a further degradation in measurement sensitivity. 
         [0014]    Finally, optically interrogated prior-art AFM probes normally require a light source having an extremely stable wavelength output, which increases AFM system cost and complexity. 
       SUMMARY OF THE INVENTION 
       [0015]    The present invention provides an ability to perform high-resolution AFM measurements in a confined space. Embodiments of the present invention are particularly well suited for use for in-vivo measurements of biological samples, wafer inspection, and arrayed measurement systems. 
         [0016]    Embodiments of the present invention include AFM probes that comprise a pair of mirrors that define an optically resonant cavity. One of the mirrors is a movable mirror that is mechanically coupled with an AFM tip; therefore, the cavity length of the optically resonant cavity is based on force imparted on the AFM tip. In addition, including a photonic crystal in at least one of the mirrors (thereby defining a photonic crystal mirror) increases the finesse of the optically resonant cavity, which provides the AFM probe with improved measurement sensitivity. Further, the inclusion of a photonic crystal mirror affords some embodiments of the present invention high sensitivity over a broad range of wavelengths. As a result, the need for extreme wavelength stability in the light signal used to interrogate the AFM probe is obviated. 
         [0017]    Embodiments of the present invention are suitable for attachment directly to a facet of an optical fiber. As a result, AFM probes in accordance with the present invention can have an extremely small form factor, thereby making them suitable for use for in-vivo measurements. The small form factor of these AFM probes can also be exploited to enable large, dense arrays of AFM probes that can rapidly scan a two-dimensional region of a surface with good spatial resolution. 
         [0018]    An illustrative embodiment of the present invention is a fiber-facet AFM probe for measuring a surface of a sample. The AFM probe comprises a first membrane mirror and second membrane mirror that includes a photonic crystal, where the mirrors collectively define an optically resonant cavity for a light signal having a first wavelength. The first mirror is affixed to a facet of an optical fiber. The second mirror is movable and includes an AFM tip suitable for interacting with the surface of a sample. As a result, the cavity length of the cavity is based on force imparted on the tip as it is scanned over a surface under measurement. 
         [0019]    In some embodiments, an AFM probe includes a first actuator for oscillating the AFM probe along the longitudinal axis of the optical fiber. In some embodiments, an AFM probe also includes a second actuator for scanning the AFM probe in a direction substantially orthogonal to the longitudinal axis. 
         [0020]    In some embodiments, multiple AFM probes are arranged in an array that enables rapid measurement of large surface areas. 
         [0021]    In some embodiments, only one of the first mirror and second mirror includes a photonic crystal. In some embodiments, at least one of the mirrors is not a membrane, but is disposed on the end of a mechanical element, such as a cantilever. In some embodiments, the first mirror is the facet of the optical fiber. 
         [0022]    An embodiment of the present invention comprises an atomic-force microscope probe comprising: a first mirror that is partially transmissive for a first light signal having a first wavelength; a second mirror that is partially transmissive for the first light signal, wherein the second mirror is movable, and wherein the first mirror and the second mirror collectively define an optically resonant cavity; and a tip that is mechanically coupled with the second mirror; wherein at least one of the first mirror and second mirror includes a first arrangement of features that collectively define a first photonic crystal that is operative for partially reflecting the first light signal. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIG. 1  depicts a schematic diagram of a fiber-facet AFM probe in accordance with an illustrative embodiment of the present invention. 
           [0024]      FIGS. 2A and 2B  depict schematic drawings of a bottom view and a side view, respectively, of a sensor in accordance with the illustrative embodiment of the present invention. 
           [0025]      FIG. 3  depicts operations of a method for fabricating an AFM probe in accordance with the illustrative embodiment of the present invention. 
           [0026]      FIGS. 4A-H  depict substrate  400  at different stages of the fabrication of probe  102 . 
       
    
    
     DETAILED DESCRIPTION 
       [0027]      FIG. 1  depicts a schematic diagram of a fiber-facet AFM probe in accordance with an illustrative embodiment of the present invention. Probe  100  comprises sensor  102 , optical fiber  104 , vertical actuator  106 , and lateral actuator  108 . 
         [0028]    Sensor  102  is a Fabry-Perot cavity-based displacement sensor having a cavity length that is based on force arising from interactions between the sensor and surface  122 . Sensor  102  includes a photonic crystal suitable for enhancing the finesse of the Fabry-Perot cavity for the wavelength of light signal  116 . Sensor  102  is described in detail below and with respect to  FIG. 2 . 
         [0029]    Optical fiber  104  is a conventional single-mode optical fiber having longitudinal axis  110 , core  112  and facet  114 . Optical fiber  104  has a diameter of approximately 125 microns. The use of a single-mode fiber for optical fiber  104  is preferable, since this mitigates measurement-sensitivity degradation from modal noise; however, optical fiber  104  can also be a multimode fiber without departing from the scope of the present invention. 
         [0030]    Vertical actuator  106  is a conventional actuator operative for oscillating sensor  102  in the z-direction when AFM probe  100  is operated in tapping mode. Vertical actuator  106  is a conventional actuator, such as a piezoelectric actuator, which is mechanically coupled with sensor  102  and optical fiber  104 . 
         [0031]    Lateral actuator  108  is a conventional actuator operative for scanning sensor  102  along surface  122  of sample  120  (i.e., along a direction substantially orthogonal to longitudinal axis  110 ). In other words, lateral actuator  108  enables motion of sensor  102  in the x-y plane. Lateral actuator  108  is a conventional actuator, such as a piezoelectric actuator, which is mechanically coupled with sensor  102  and optical fiber  104 . 
         [0032]    Sensor  102  is affixed to optical fiber  104  at facet  114  in conventional fashion, using optically transparent epoxy, silicate solution, and the like. 
         [0033]      FIGS. 2A and 2B  depict schematic drawings of a bottom view and a side view, respectively, of a sensor in accordance with the illustrative embodiment of the present invention.  FIG. 2B  depicts a sectional view of sensor  102  through line a-a of  FIG. 2A . Sensor  102  comprises optically resonant cavity  202 , frame  208 , and tip  210 . It should be noted that sensor  102  is depicted in an idealized form. In practice, a typical sensor will have structure that deviates from this idealized form, as discussed below and with respect to  FIG. 4G . 
         [0034]    Optically resonant cavity  202  (hereinafter referred to as cavity  202 ) is a high-finesse cavity that comprises mirrors  204  and  206 , which are separated by cavity length L. When cavity  202  is in its unexcited state (i.e., its quiescent state), cavity length L is equal to quiescent cavity length L 0 . One skilled in the art will recognize that the instantaneous reflectivity of cavity  202  is strongly dependent upon the instantaneous cavity length L. 
         [0035]    Mirror  204  is a photonic-crystal mirror that comprises a portion of a membrane of single-crystal silicon having a thickness of approximately 500 nanometers (nm). Mirror  204  has a square shape of approximately 70 microns per side and defines x-y plane  218 . The size of mirror  204  is selected to accommodate the diameter of light signal  116 , as well as allow for space around the membrane sufficient for the inclusion of tethers  212 . 
         [0036]    Mirror  204  includes a two-dimensional array of features  214 , which are sized and arranged to collectively define photonic crystal  216 , such that photonic crystal  216  is partially transmissive for light signal  116 . Photonic crystal  216  is designed to support guided resonances that interfere with light signal  116  to create broadband reflections. As a result, the use of a photonic crystal mirror, such as mirror  204 , affords some embodiments of the present invention high sensitivity over a broad range of wavelengths, thereby providing more tolerance for wavelength variation in light signal  116  than can be tolerated by prior-art optically interrogated AFM probes. 
         [0037]    In the illustrative embodiment, features  214  are through-holes having a diameter of approximately 800 nm. Features  214  are arranged in a square array having a feature pitch of approximately 950 nm. One skilled in the art will recognize that the size, spacing, and depth of features  214  are based on the wavelength of light signal  116 , as well as the desired reflectivity and finesse of optical cavity  202 . As a result, one skilled in the art will recognize that the features of photonic crystal  216  can have any suitable dimensions and arrangement. 
         [0038]    Mirror  206  is a continuous membrane of single-crystal silicon having a thickness of approximately 500 nm. Mirror  204  has a diameter larger than the diameter of light signal  116 , but smaller than the diameter of optical fiber  104 . A non-limiting exemplary value for the diameter of mirror  206  is within the range of approximately 80 microns to approximately 110 microns. In some embodiments, mirror  206  includes a photonic crystal that is analogous to photonic crystal  216 . In some embodiments, each of mirrors  204  and  206  includes a photonic crystal, but the features of the two photonic crystals do not have the same dimensions. 
         [0039]    Tethers  212  suspend mirror  204  from frame  208  such that mirrors  204  and  206  are separated by quiescent cavity length, L 0 , which is approximately 1.5 microns, and typically within the range of approximately 1 micron to approximately 2 microns. Tethers  212  are designed such that they readily bend in a direction out of the x-y plane, but resist bending within the x-y plane. As a result, tethers  212  substantially enable mirror  204  to move along the z-direction but inhibit its motion within the x-y plane. 
         [0040]    In some embodiments, tethers  212  and mirror  204  are collectively characterized by a mechanical resonance frequency that is higher than the oscillation frequency imparted on the probe by vertical actuator  106 . This enables probe  100  to measure frequency components associated with tip-surface interactions that occur at frequencies higher than the oscillation frequency. As a result, in some embodiments, probe  100  is a high-bandwidth AFM probe. For the purposes of this Specification, including the appended claims, the term “high-bandwidth AFM probe” is defined as a probe that is designed for TM-AFM operation at a drive frequency, wherein the probe is operative for measuring frequency components associated with tip-surface interactions that occur at frequencies higher than the drive frequency. Examples of high-bandwidth AMF probes are found in U.S. Pat. Nos. 8,082,593, 7,302,833, 7,404,314, and 7,089,787, and U.S. Patent application Ser. No. 13/829,626, filed Mar. 14, 2013 (Attorney Docket: 146-035US1), each of which is incorporated herein by reference. 
         [0041]    For clarity, each of tethers  212  is depicted as a simple beam; however, a typical tether  212  has a more complex design, such as a serpentine spring, a folded-beam spring, and the like. It will be clear to one skilled in the art, after reading this Specification, how to specify, make, and use tethers  212 . 
         [0042]    It should be noted that the thickness of mirrors  204  and  206 , the materials they comprise (and their refractive indices), quiescent cavity length L 0 , and the design of photonic crystal  216  are based on the wavelength of light signal  116  and the desired sensitivity of AFM probe  100 . 
         [0043]    Tip  210  is a column of suitable structural material having a height sufficient to enable it to scan surface  122  and a diameter that is typically is on the order of one period of photonic crystal  216 . 
         [0044]    In typical TM-AFM operation, AFM probe  100  is scanned over surface  122  while vertical actuator  106  oscillates sensor  102  along the z-direction, as shown. The separation distance between the probe and surface  122  is controlled such that tip  210  intermittently interacts with the surface as the probe is scanned in the x-y plane. As tip  210  taps surface  122 , a tip-surface interaction force is imparted onto the tip. This force causes dynamic changes in cavity length L, thereby changing the reflectivity of optically resonant cavity  202 . These dynamic changes give rise to high-frequency signal components in light signal  118 , where these signal components are characteristic of the physical properties of surface  122 . 
         [0045]      FIG. 3  depicts operations of a method for fabricating an AFM probe in accordance with the illustrative embodiment of the present invention. 
         [0046]      FIGS. 4A-H  depict substrate  400  at different stages of the fabrication of probe  102 . 
         [0047]    Method  300  begins with optional operation  301 , wherein substrate  400  is provided. Substrate  400  is a conventional silicon-on-insulator (SOI) substrate comprising handle substrate  402 , buried oxide layer  404 , and active layer  406 . Handle substrate  402  is a conventional single-crystal silicon substrate, buried oxide layer  404  is a conventional silicon dioxide layer having a thickness of approximately 1 micron, and active layer  406  is a layer of single-crystal silicon having a thickness of approximately 2.5 microns. It will be clear to one skilled in the art, after reading this Specification, how to specify, make, and use probes formed from substrates comprising different materials and/or different layer thicknesses. 
         [0048]    At operation  302 , features  214  and tethers  212  are defined in active layer  406 . Features  214  and tethers  212  are defined in active layer  406  via a suitable mask layer and a deep reactive-ion etch (DRIE) process. The DRIE process is timed so that features  214  extend only through the thickness of stratum  408 , which has a thickness of approximately 500 nm. As a result, the depth of features  214  is approximately 500 nm. In some embodiments, a directional etch other than DRIE is used to define features  214  and tethers  212 . 
         [0049]      FIG. 4A  depicts a schematic drawing of a cross-sectional side view of a portion of substrate  400  after the definition of mirror  204 , features  214 , and tethers  212  in stratum  408 . For clarity, tethers  212  are not shown in  FIG. 4A . 
         [0050]    At operation  303 , handling frame  414  and connecting tabs  416  are defined outside the region of sensor  102  via an appropriate mask and DRIE. Handling frame  414  and connecting tabs  416  are formed by etching completely through active layer  406  to buried oxide  404 . 
         [0051]      FIG. 4B  depicts a schematic drawing of a top view of a portion of substrate  400  after the definition of mirror  204 , features  214 , and tethers  212  in stratum  408 . 
         [0052]    At operation  304 , thermal oxide  420  is grown on all exposed silicon surfaces. 
         [0053]    At operation  305 , thermal oxide  420  is removed from the bottom surface  422  of each of features  214 , as well as from regions  418  (as shown in  FIG. 4B ), which exposes the surface of silicon in stratum  410 . 
         [0054]    At operation  306 , mirror  204  is partially released from substrate  400  in release etch  424 . Release etch  424  is a substantially isotropic RIE etch, which attacks the exposed single-crystal silicon in stratum  410  through features  214 . Since the etch attacks the silicon in a substantially isotropic manner, etch front  426  proceeds laterally at approximately the same rate as it proceeds vertically. As a result, the silicon material is removed from underneath the structural material of mirror  204  and tethers  212 . 
         [0055]      FIG. 4C  depicts a schematic drawing of a sectional view of a portion of substrate  400  after the exposure of the bottom surfaces of features  214  and during release etch  424 . 
         [0056]    Release etch  424  is a timed to remove most, but not all, of active layer material from stratum  410 . As a result, release etch  424  leaves pedestal  428  that provides support for the center of mirror  204  during subsequent operations. In some embodiments, all active layer material is removed from stratum  410  during release each  424 . 
         [0057]      FIG. 4D  depicts a schematic drawing of a sectional view of a portion of substrate  400  after release etch  224 . 
         [0058]    At operation  307 , all exposed silicon is again thermally oxidized. This oxidation accomplishes two results. First, it provides protection for the structural components of sensor  102  during subsequent processing. Second, it converts the remaining silicon in pedestal  428  into silicon dioxide. 
         [0059]    In some embodiments, sensor  102  comprises two photonic-crystal mirrors. In these embodiments, a second directional etch is performed through features  214 , using these features as a mask to pattern a matching arrangement of features into the silicon in stratum  412 . This matching set of features collectively defines a second photonic crystal in mirror  206 . In some embodiments, this matching arrangement of features extends completely through stratum  412 . In some embodiments, it extends only partially through the thickness of stratum  412 . 
         [0060]    It should be noted that the second photonic crystal can be formed in mirror  206  at any of several points in method  300 —for example, after either of operations  306  and  307 . 
         [0061]    In some embodiments, release etch  424  completely removes active layer material from both strata  410  and  412 . In such embodiments, sensor  102  includes only one mirror within its structure. When attached to fiber  104 , facet  114  acts as the second mirror of the optically resonant cavity. 
         [0062]    At operation  308 , well  430  is formed in handle substrate  402 . Well  430  has a diameter that is slightly larger than that of optical fiber  104  so that well  430  can locate the fiber when sensor  102  is affixed to facet  114 . 
         [0063]      FIGS. 4E and 4F  depict schematic drawings of a top and sectional view of substrate  400  after the formation of well  230 . The sectional view shown in  FIG. 4F  is taken through line b-b of  FIG. 4E . 
         [0064]    At operation  309 , the exposed silicon dioxide on substrate  400  is removed in a vapor-phase hydrofluoric acid release. At the end of operation  309 , the single-crystal material of stratum  410  is substantially completely removed in region  432  of substrate  400 ; however, the single-crystal silicon in strata  408  and  412  in region  432  remains and forms the basis for the structural elements of sensor  202  (i.e., mirrors  204  and  206 , and tethers  212 ), as well as handling frame  414  and connecting tabs  416 . 
         [0065]    At operation  310 , tip  210  is provided at mirror  204  such that the tip and the mirror are mechanically coupled. 
         [0066]    Tip  210  is fabricated separately using a single-crystal substrate other than substrate  400 . To form tip  210 , a conventional crystallographic-dependent etch (e.g., potassium hydroxide (KOH), ethylene diamine pyrocatechol (EDP), hydrazine, etc.) is used to create a pyramidal projection (i.e., nascent tip  210 ). Typically, this projection has a height within the range of approximately 2.3 microns to approximately 10 microns, although the projection can have any practical height. If desired, after its formation, nascent tip  210  can be further sharpened by thermal oxidization followed by oxide removal, via ion-beam milling, etc. 
         [0067]    Once nascent tip  210  is fully formed on its native substrate, it is removed via ion-beam milling (or a similar process), transferred to mirror  204 , and bonded to the mirror using a conventional bonding or welding technology. 
         [0068]    In some embodiments, tip  210  is fabricated on substrate  400  at the beginning of the method  300 ; however, in such embodiments, the height of tip  210  must be carefully controlled to avoid hindering subsequent fabrication steps. 
         [0069]    In some embodiments, tip  210  is grown directly on mirror  204  via a suitable deposition method, such as beam-assisted deposition. 
         [0070]      FIG. 4G  depicts a schematic drawing of a sectional side view of sensor  102  after it has been completely fabricated and is still attached to handling frame  414  by connecting tabs  416 . 
         [0071]      FIG. 4H  depicts a scanning-electron microscope picture of a portion of a fully fabricated substrate  400  with tip  210  attached. 
         [0072]    As depicted in  FIG. 4G , each of mirrors  204  and  206  exhibit some surface features that are artifacts of the fabrication process used to form sensor  102 . Although this surface structure may reduce the finesse of optically resonant cavity or shift the ideal operational wavelength slightly, it does not significantly degrade measurement sensitivity of AFM probe  100 . In some embodiments, the design of sensor  102  compensates for such surface structure by choosing features sizes and mirror thicknesses that give rise to an acceptable finesse for cavity  202  (e.g., to achieve a reflectivity of greater than 90%). 
         [0073]    At operation  311 , sensor  102  is attached to facet  114 . In some embodiments, sensor  102  is attached by first disposing a layer of adhesive (e.g., UV-curable epoxy, silicate solution, etc.) on facet  114 . This layer of adhesive is then thinned by repeatedly contacting it with bare silicon or another suitable surface. Once the adhesive is suitably thin, optical fiber  104  is inserted into well  430  to align facet  114  with mirror  206 . The adhesive is then fully cured. 
         [0074]    At operation  312 , handling frame  414  is removed by breaking connecting tabs  416 , leaving the structure described above and with respect to  FIG. 1  (without actuators  106  and  108 ). 
         [0075]    It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.