Patent Publication Number: US-10782240-B2

Title: Test mass compensation of mass measurement drift in a microcantilever resonator

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) AND PRIORITY DATE 
     This application is a continuation of U.S. patent application Ser. No. 14/477,287, entitled “TEST MASS COMPENSATION OF MASS MEASUREMENT DRIFT IN A MICROCANTILEVER RESONATOR”, filed Sep. 4, 2014, now U.S. Pat. No. 9,671,350, issued Jun. 6, 2017, which is entitled to the benefit of and/or the right of priority to U.S. Provisional Application No. 61/873,772, entitled “TEST MASS COMPENSATION OF MASS MEASUREMENT DRIFT IN A MICROCANTILEVER RESONATOR”, filed Sep. 4, 2013, which are hereby incorporated by reference in their entireties for all purposes. 
    
    
     TECHNICAL FIELD 
     The invention relates to resonance-based measurement of very small masses using a microcantilever, and in particular the measurement of very small particles accumulated at a substrate on the microcantilever. 
     BACKGROUND 
     Microcantilevers containing a microchannel can enable precise resonance-based measurement of very small masses entrained in a fluid flowing through the microchannel. Burg et al. describe one such system based on the principle that “the resonance frequency of a suspended microfluidic channel . . . is highly sensitive to the presence of molecules or particles whose mass density differs from that of the [fluid].” (Burg, Thomas P.; Godin, Michel; Knudsen, Scott M.; Shen, Wenjiang; Carlson, Greg; Foster, John S.; Babcock, Ken; Manalis, Scott R. “Weighing of biomolecules, single cells and single nanoparticles in fluid,” Nature, 446, 1066-1069 (Apr. 26, 2007)). 
       FIG. 1A  shows a schematic representation  100   a  of a microcantilever  110  with a microchannel  120  according to the prior art. A thin (e.g., with thickness O[μm]) silicon microcantilever  110  extends outward from an essentially rigid base  130  into a cavity  190 . As illustrated by the arrows indicating the direction of flow, a U-shaped microchannel  120  (e.g., with thickness and depth O[μm]) etched in the silicon transports a fluid outward from the rigid base  130  and into the body of the microcantilever  110  before returning the fluid to the rigid base  130 . The free end  140  of the microcantilever  110  readily flexes in and out of the plane of  FIG. 1A . Using an electrostatic drive electrode (not shown) driven by a gain controlled oscillator circuit, it is possible to excite the microcantilever  110  within a vacuum cavity to determine its characteristic resonance frequency. 
       FIG. 1B  shows an isometric view  100   b  of a microcantilever  110  as schematically represented in  FIG. 1 a   .  FIG. 1B  is provided to illustrate how a microcantilever  110  may be configured to extend outward from a rigid base  130  into a cavity  190 . 
       FIG. 1C  shows a first technique  100   c  for measuring small masses using a microcantilever  110  with a microchannel  120  according to the prior art. In this approach, the resonance frequency of the microcantilever  110  is monitored continuously as fluid flowing through the microchannel  120  conveys discrete sample particles  150   a - c  toward and away from the tip  140  of the microcantilever  110 . Provided that the concentration of the particles  150   a - c  within the fluid is relatively sparse (i.e. it is relatively unlikely that two particles will simultaneously flow along the length of microchannel  120  within the microcantilever  110 ), the resonance frequency will vary according to the following equation: 
                   f   =       1     2   ⁢   π       ⁢       k       m   _     +     α   ⁢           ⁢   m                     Equation   ⁢           ⁢     (   1   )                 
where k is the spring constant of the microcantilever  110 ,  m  is the effective mass of the microcantilever  110  and any fluid therein, m is the mass of an individual sample particle  150   a - c , and α is a geometric constant reflecting the current location of the sample particle  150   a - c . When an individual particle  150   a - c  is near the tip  140  of the microcantilever  110 , α≈1. When an individual particle  150   a - c  is near the rigid base  130  of the microcantilever  110  (or when no particles are within the length of the microchannel  120  within the microcantilever  110 ), α≈0. Thus, by observing the peak-to-trough differences in the resonance frequency as it varies over time, it is possible to determine the mass of an individual sample particle  150   a - c  as it flows past the tip  140  of the microcantilever  110 .
 
       FIG. 1D  shows a second technique  100   d  for measuring small masses using a microcantilever  110  with a microchannel  120  according to the prior art. In this approach, an agent  160  that will bind the sample particles is immobilized against the interior walls of the microchannel prior to testing. Fluid containing sample particles is then flowed through the microchannel  120  and a single layer of sample particles adheres to the binding agent  160 . A subsequent resonance measurement allows the mass of the layer of sample particles to be determined from Equation 1. However, in this approach,  m  includes the mass of the binding agent  160 , and a value of α≈0.25 reflects the approximately uniform distribution of the sample particle layer along the length of the microcantilever  110 . 
     The above two approaches do provide high measurement sensitivity, resolving masses as small as 300×10 −18  g. However, both approaches are only applicable to sample particles that can be conveyed by the fluid flowing through the microchannel. The above two approaches are thus not well suited, for example, to measurement of biological particles that must be grown on a mechanical substrate that is too large or too fragile to be conveyed through the microchannel. 
     SUMMARY 
     Embodiments of the present disclosure describe methods, systems, and apparatus for determining the mass of small particles using a microcantilever with an associated substrate. According to some embodiments, small particles may accumulate or are grown or reproduce on a substrate on a microcantilever. In order to determine the change in mass of the accumulated small particles, the microcantilever is excited and a resonance frequency is measured at a first and a second time, the resonance frequency of the microcantilever being a function of the mass of the accumulated biological particles. According to some embodiments, in order to correct for drift in the resonance behavior of the microcantilever over time, a test mass is introduced that may be actuated between two positions either off board or onboard the microcantilever. In such embodiments, two resonance frequencies are measured at the second time. Once with the test mass at a first position and once with the test mass at the second position. By taking two measurements of the resonance frequency of the microcantilever at the second time (with the test mass in two different positions) the drift in resonance behavior of the microcantilever caused by the additional mass of the biological particles may be accounted for. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present embodiments are illustrated by way of example and are not intended to be limited by the figures of the accompanying drawings. In the drawings: 
         FIG. 1A  shows a schematic representation of a microcantilever with a microchannel according to the prior art; 
         FIG. 1B  shows an isometric view of a microcantilever according to the prior art; 
         FIG. 1C  shows a first technique for measuring small masses using a microcantilever with a microchannel according to the prior art; 
         FIG. 1D  shows a second technique for measuring small masses using a microcantilever with a microchannel according to the prior art; 
         FIG. 2  shows a schematic representation of an example microcantilever incorporating a substrate according to some embodiments of the present disclosure; 
         FIG. 3  shows a first example technique for measuring small masses using a microcantilever and a microchannel based test mass, according to some embodiments of the present disclosure; and 
         FIG. 4  shows a second example technique for measuring small masses using a microcantilever and a sliding test mass, according to some embodiments of the present disclosure; and 
         FIG. 5  shows a third example technique for measuring small masses using a microcantilever and a linearly actuated test mass according to some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     From the foregoing, it will be appreciated that specific embodiments of the invention have been described herein for purposes of illustration, but that various modifications may be made without deviating from the scope of the invention. Accordingly, the invention is not limited except as by the appended claims. 
     The present teachings provide for methods and mechanisms for measuring small masses attached to a substrate within a microcantilever. Specifically, the teachings allows for measurement of particles accumulated, grown, or reproduced at a substrate that cannot be flowed through a microchannel within a microcantilever. While the present disclosure describes various embodiments in the context of grown or reproduced small biological particles, it shall be understood that this is done for illustrative purposes, and that the present teachings may be applied to the measurement of changes in mass of any types of small particles where those changes occur in situ, for example in the area of nanotechnology. 
       FIG. 2  shows a schematic representation of a microcantilever  210  incorporating a substrate  270  according to some embodiments of the present disclosure. Similar to microcantilever  110  described in  FIGS. 1A-1D , microcantilever  210  may comprise a thin (e.g., with thickness O[μm]) body having a free end  240  and a rigid end connected to a rigid base  230  and extending outward into a cavity  290 . Formed at least partially on or within microcantilever  210 , a microchannel  220  (e.g. with width and depth O[μm]) may be configured to transport fluid (e.g. water) along the body of the microcantilever from the rigid based  230  to the free end  240  and back to the rigid base  230 . In some embodiments, the microchannel  220  may be configured to transport sample particles and/or food to substrate  270  in order to seed and/or support growth and reproduction of particles accumulating at the substrate  270 . According to some embodiments, the microchannel  220  may be configured to transport waste produced by the particles away from the substrate  270 . 
     According to some embodiments, microcantilever  210  with microchannel  220  may be fabricated by creating buried channels in silicon-on-insulator wafers and then dry etching the wafer to form the microchannel within the microcantilever. A person having skill in the art will recognize that other materials and fabrication processes may be suitable to use while remaining within the scope of the present teachings. As a non-limiting example for illustrative purposes, a microcantilever  210  may be approximately 200 μm long (i.e., from rigid base  230  to free end  240 ) 50 μm wide and 10 μm thick with a microchannel  220  of approximately 10 μm wide and 3 μm deep, according to some embodiments. A person having skill in the art will recognize that different dimensions may be suitable depending on a number of factors, including the size of the sample particles to be measured. 
     Using a means for exciting microcantilever  210 , for example via an electrostatic drive electrode (not shown) driven by a gain controlled oscillator circuit (not shown), microcantilever  210 , may be caused to vibrate within cavity  290 . The resulting vibrations of microcantilever  210  may then be measured and a resonance frequency determined using a light source and optical sensor, for example a laser pointed substantially at the free end  240  of the microcantilever  210 , wherein the reflected light from the laser is picked up by a position sensitive photo detector. 
     The cavity  290 , within which the microcantilever  210  is located, may be filed with gas (e.g. air) or fluid (e.g. water), however, due to the damping effect of the surrounding material within cavity  290 , a microcantilever resonator within a gas (e.g. air) filed cavity will have a higher quality factor (i.e. exhibit less energy loss due to damping) than fluid (e.g. water) filed cavity (assuming equal dimensions of the microcantilever in each instance). A higher quality factor may result in reduced phase noise leading to more accurate determinations of the resonance frequency due to the higher stability of the measured frequency. According to some embodiments, in order to maximize the quality factor of a given microcantilever resonator, microcantilever  210  may be surrounded by a vacuum enclosed by cavity  290 . 
     The substrate  270  may provide mechanical support to the sample particles (not shown) that are to be measured. In other words, substrate  270  may be configured to support the accumulation, growth and/or reproduction of the particles to be measured. Generally, the substrate  270  may be formed within or upon the microcantilever  210  using micromechanical etching and deposition techniques (e.g. bulk micromachining and surface micromachining) well known in the art. For example, according to some embodiments, the substrate  270  may comprise a lattice, mesh, or set of linear notches within a chamber located along the etched microchannel  220 . As described earlier, according to some embodiments, a fluid (e.g. water) may flow through the microchannel  220 , conveying food to and removing waste from the biological particles (e.g. bacteria) growing or reproducing on the substrate  270 . An example substrate  270  is schematically shown in  FIG. 2  located substantially near the free end  240  of microcantilever  210 , however it shall be understood that this is a non-limiting example. Substrate  270  may include one or more individual substrates of varying geometry located anywhere along (on or within) the body of microcantilever  210 , wherein the configuration is accounted for in the geometric parameter α, as referenced below in Equation 4. 
     To measure changes in the mass of the biological particles on the substrate  270 , resonance measurements can be made at two different points in time. However, as noted above, simply determining two resonance frequencies according to Equation 1 at widely separated times, namely 
                     f   1     =       1     2   ⁢   π       ⁢         k   1         m   _     +     α   ⁢           ⁢     m   1                       Equation   ⁢           ⁢     (   2   )                   f   2     =       1     2   ⁢   π       ⁢         k   2         m   _     +     α   ⁢           ⁢     m   2                       Equation   ⁢           ⁢     (   3   )                 
in some cases may not suffice because it is possible for the resonance behavior of the microcantilever  210  to drift over time. That is, m 1  may be determined using Equation 2 as described for Equation 1, but m 2  may in some cases not be reliably calculated because it is possible that k 2 ≠k 1 .
 
     To address this difficulty, according to some embodiments, a test mass may be introduced that may be actuated between two positions a and b. The mass of the test mass is known with a high degree of accuracy. According to some embodiments, position b may be onboard the microcantilever, so that the test mass moves with the microcantilever as it flexes, and is known with a high degree of accuracy. Position a may either be onboard or offboard the microcantilever; if onboard the microcantilever, position a may also be known with a high degree of accuracy. 
     A resonance measurement may be made at a first time, generally as described for Equation 1, to determine the mass of the biological particles at the first time. More specifically, m 1  is determined from the following equation: 
     
       
         
           
             
               
                 
                   
                     f 
                     1 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           k 
                           1 
                         
                         
                           
                             m 
                             _ 
                           
                           + 
                           
                             
                               α 
                               s 
                             
                             ⁢ 
                             
                               m 
                               1 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     Here,  m  is the effective mass of the microcantilever, the substrate, and any fluid therein; and α s  is a geometric parameter reflecting the distribution of the biological particles along the length of the microcantilever (i.e. the location and lengthwise extent of the substrate). 
     A pair of resonance measurements may be made at second time—one with the test mass at position a and one with test mass at position b. As indicated by the following equations: 
     
       
         
           
             
               
                 
                   
                     f 
                     2 
                     a 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           k 
                           2 
                         
                         
                           
                             m 
                             _ 
                           
                           + 
                           
                             
                               α 
                               s 
                             
                             ⁢ 
                             
                               m 
                               2 
                             
                           
                           + 
                           
                             
                               α 
                               t 
                               a 
                             
                             ⁢ 
                             
                               m 
                               t 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     f 
                     2 
                     b 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           k 
                           2 
                         
                         
                           
                             m 
                             _ 
                           
                           + 
                           
                             
                               α 
                               s 
                             
                             ⁢ 
                             
                               m 
                               2 
                             
                           
                           + 
                           
                             
                               α 
                               t 
                               b 
                             
                             ⁢ 
                             
                               m 
                               t 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     As noted above, the mass of the test mass and the locations of the two positions a (if onboard the microcantilever) and b are known with a high degree of accuracy. Thus m t , α t   a , and α t   b  are known and Equations 5 and 6 can be solved for the two unknowns k 2  and m 2 . Comparing m 2  and m 1  allows the change in the mass of the biological particles to be determined. 
     It should be noted that the test mass can also be used to perform an initial calibration of the microcantilever with an empty substrate. At a time before any biological particles have grown on the substrate, a pair of resonance measurements is made. 
     
       
         
           
             
               
                 
                   
                     f 
                     0 
                     a 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           k 
                           0 
                         
                         
                           
                             m 
                             _ 
                           
                           + 
                           
                             
                               α 
                               s 
                             
                             ⁢ 
                             
                               m 
                               0 
                             
                           
                           + 
                           
                             
                               α 
                               t 
                               a 
                             
                             ⁢ 
                             
                               m 
                               t 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     f 
                     0 
                     b 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         
                           k 
                           0 
                         
                         
                           
                             m 
                             _ 
                           
                           + 
                           
                             
                               α 
                               s 
                             
                             ⁢ 
                             
                               m 
                               0 
                             
                           
                           + 
                           
                             
                               α 
                               t 
                               b 
                             
                             ⁢ 
                             
                               m 
                               t 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     Because m 0 ≡0, Equations 7 and 8 can be solved for k 0  and, more significantly,  m . The test mass can thus aid in characterizing the effective mass of the microcantilever, substrate, and any fluid therein. 
       FIG. 3  shows a first technique  300  for measuring small masses using a microcantilever  310  with a microchannel  320 , substrate  370 , and a microchannel-based test mass  350 , according to some embodiments of the present disclosure. According to some embodiments, the test mass  350  may be actuated fluidically in a manner similar to the movement of the sample particles along the microchannel  220  in  FIG. 2 . As shown in  FIG. 3 , a separate test mass microchannel  380  interior to the feed and waste microchannel  320  may allow the test mass  350  to be conveyed by a precise switchable flow between predetermined positions  350   a  and  350   b . As previously described position  350   b  may be on the microcantilever  310  (e.g. substantially near fee end  340 ) and position  350   a  may either be on the microcantilever  310  or offboard the microcantilever  310  and within the rigid base  330 . Note that in  FIG. 3 , position  350   a  is shown offboard the microcantilever  310 , and thus need not be known with great precision. Despite slight possible variations in position  350   a , in such a configuration, α t   u =0. 
       FIG. 4  shows a second technique  400  for measuring small masses using a microcantilever  410  with a microchannel  420 , a substrate  470 , and a sliding test mass  450 , according to some embodiments of the present disclosure. In some embodiments, pressure and suction may be used to actuate the test mass  450  to and from positions  450   a  and  450   b  within a test mass chamber  480  that extends outward from the rigid base  430  onto the microcantilever  410  towards the free end  440 . According to some embodiments, a lossy (e.g. thin) return line  482  may vent to atmosphere or a fluid reservoir (i.e. outside the vacuum cavity  490 ) and may allow gas (e.g. air) or fluid (e.g. water) to flow into the region of the test mass chamber  480  between the test mass  450  and the distal end of the test mass chamber  480 . Alternatively, according to some embodiments, the test mass chamber  480  may be evacuated and the test mass  450  magnetically actuated to either end of the chamber  480 . Note that in  FIG. 4 , as in  FIG. 3 , position  450   a  is shown as being offboard the microcantilever  410 , and therefore α t   a ≡0. 
       FIG. 5  shows a third technique  500  for measuring small masses using a microcantilever  510  with a microchannel  520 , substrate  570 , and a linearly actuated test mass  550 , according to some embodiments of the present disclosure. In such embodiments, an actuator  582  may slide an oblong test mass  550  from position  550   a  outward to position  550   b  along a path  580  that extends outward from rigid base  530  onto the microcantilever  510  towards the free end  540 . According to some embodiments, actuator  582  may be a micromechanical actuator such as an electrostatic linear stepper motor fabricated using micro-machining techniques well known in the art. (See e.g., Tas, N. R.; Sonnenberg, A. H.; Sander, A. F M; Elwenspoek, M. C., “Surface Micromachined Linear Electrostatic Stepper Motor”, Micro Electro Mechanical Systems, 1997. MEMS &#39;97, Proceedings, IEEE, Tenth Annual International Workshop, pp. 215-220, 26-30 Jan. 1997.) The test mass  550 , coupled to the shuttle of the actuator  582  (e.g., stepper motor), may slide along the path  582 . For example, path  582  may be a track, in a slot, or under a cover that ensures that the test mass  550  moves with the microcantilever  510  as it flexes. Note that in  FIG. 5 , as in  FIGS. 3 and 4 , the test mass  550  is entirely offboard the microcantilever  510  when in position  550   a , therefore α t   a =0. In a variation of the system illustrated in  FIG. 5 , an actuator  582  may be a rotary motor that moves the test mass  550  between positions  550   a  and  550   b  in an oscillatory fashion, wherein the pair of measurements described by Equations 5 and 6 are obtained in a periodic fashion. 
     Disclaimers 
     The above detailed description of embodiments of the disclosure is not intended to be exhaustive or to limit the teachings to the precise form disclosed above. While specific embodiments of, and examples for, the disclosure are described above for illustrative purposes, various equivalent modifications are possible within the scope of the disclosure, as those skilled in the relevant art will recognize. The scope of the invention is limited only by the claims. 
     Reference in this specification to “one embodiment”, “an embodiment”, or “some embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. The appearances of the phrase “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Moreover, various features are described which may be exhibited by some embodiments and not by others. Similarly, various requirements are described which may be requirements for some embodiments but not other embodiments. 
     The terms used in this specification generally have their ordinary meanings in the art, within the context of the disclosure, and in the specific context where each term is used. Certain terms that are used to describe the disclosure are discussed above in more detail, or elsewhere in the specification, to provide additional guidance to the practitioner regarding the description of the disclosure. For convenience, certain terms may be highlighted, for example using italics and/or quotation marks. The use of highlighting has no influence on the scope and meaning of a term; the scope and meaning of a term is the same, in the same context, whether or not it is highlighted. It will be appreciated that same thing can be said in more than one way. 
     Consequently, alternative language and synonyms may be used for any one or more of the terms discussed herein, nor is any special significance to be placed upon whether or not a term is elaborated or discussed herein. Synonyms for certain terms are provided. A recital of one or more synonyms does not exclude the use of other synonyms. The use of examples anywhere in this specification including examples of any terms discussed herein is illustrative only, and is not intended to further limit the scope and meaning of the disclosure or of any exemplified term. Likewise, the disclosure is not limited to various embodiments given in this specification. 
     While some aspects of the disclosure may be presented herein in some claim forms, the inventors contemplate the various aspects of the disclosure in any number of claim forms. For example, while only one aspect of the disclosure is recited as a means-plus-function claim under 35 U.S.C. § 112(f), other aspects can likewise be embodied as a means-plus-function claim, or in other forms. (Any claims intended to be treated under 35 U.S.C. § 112(f) will begin with the words “means for”.) Accordingly, the applicant reserves the right to add additional claims after filing the application to pursue such additional claim forms for other aspects of the disclosure.