Patent Publication Number: US-9891084-B2

Title: Graphene-based magnetic hall sensor for fluid flow analysis at nanoscale level

Description:
CROSS-REFERENCE TO A RELATED PATENT APPLICATION 
     This patent application is a divisional patent application of copending U.S. patent application Ser. No. 14/944,766, filed Nov. 18, 2015, which claims priority to U.S. Provisional Patent Application Ser. No. 62/241,594, filed Oct. 14, 2015, the disclosures of which are incorporated by reference herein in their entireties. 
    
    
     BACKGROUND 
     The exemplary embodiments of this invention relate generally to Hall-effect sensors and, more specifically, to graphene-based Hall-effect sensors and the use thereof for the characterization and analysis of fluid flow at micro-scale or nanoscale levels. 
     Velocimetry is the measurement of fluid velocity. Velocimetric techniques at microscale levels, such as Microscopic Particle Image Velocimetry (microPIV) and Microscopic Particle Tracking Velocimetry (microPTV), use optical (e.g., laser) detection and are, therefore, limited to microchannels etched in transparent materials, such as glass, polydimethylsiloxane (PDMS), and polymethyl methacrylate (PMMA). Both microPIV and microPTV techniques rely on the excitation of fluorescent microbeads using intense laser light pulses. Both techniques also have several limitations that prevent their application to fluid flow on a nanoscale level. 
     Magnetic nanoparticles can be used in various velocimetric techniques as markers for biological assays or tracers for fluid flow characterization. However, nanoparticles are generally on the order of about 1 nanometer (nm) to hundreds of nanometers in diameter. As such, their reduced size, weak magnetic field, large surface-to-volume ratio, and thermal disturbance (superparamagnetism) introduce challenges for achieving detectability in moving fluids. 
     The fabrication and integration of sensors and generators of magnetic fields into micro-/nanosystems designed to work with nanoparticles may be a complex and difficult task. Use of sensors and generators may also require advanced detection strategies to compensate for poor signal-to-noise ratio in the detection methods. Such detection strategies can be implemented within a CMOS-compatible process, but they can also be implemented in arbitrary substrate devices. 
     Previous attempts to detect small magnetic particles with Hall sensors employed Si—, InSb—, and graphene-based Hall devices and were able to detect the presence of magnetic microbeads composed of thousands of nanometer-sized iron oxide particles dispersed in a polymer matrix. However, the detection of moving nanoparticles was generally not possible, since the microbeads had to be positioned with highly complex apparatuses (atomic force microscopes (AFM), nanomanipulators, etc.) precisely on top of the sensors, since there was no integration of the sensors into micro-/nanofluidic channels. Furthermore, the sensor areas, which are typically about 1 square micrometer (μm 2 ) to about 6 μm 2 , made it difficult or even impossible to integrate such sensors into certain micro-/nanofluidic devices. Aside from the difficulties associated with integrating the sensors into micro-/nanofluidic devices, the detection of single nanoparticles that are a few nanometers in diameter has not been demonstrated. Moreover, methods to characterize flow properties of a fluid through micro-/nanofluidic channels based on the exploration of dispersed magnetic nanoparticles have not been successfully carried out. 
     Alternatively, an Al 2 O 3 -based Magnetic Tunnel Junction (MTJ) has been used as a sensor for the detection of magnetic microbeads. The integration of this sensor into a microfluidic channel allowed for the detection of moving microbeads as they rolled on top of the MTJ. It was not, however, demonstrated how this approach could be used to detect the presence of single nanometer-sized magnetic particles, nor how the dispersed particles could be used to better characterize the flow of the surrounding fluid. Additionally, the relatively large size (about 10 μm 2 ) of the sensor hinders its integration into certain micro-/nanofluidic devices. 
     Along the same lines, MgO-based MTJs have been able to detect 2.5 micro molar (μM) target DNA labeled with 16 nm iron oxide nanoparticles. In doing so, the DNA strands were able to bond on the sensor surface. Provided the coverage was above a certain threshold, a signal was then detected denoting the presence of magnetic labels (nanoparticles). With this approach, it was not possible to detect single nanoparticles nor use them to characterize the flow of carrying fluid. It was also not possible to detect moving magnetic particles, since they had to be attached to the sensor surface for detection. Finally, the setup required a large array (4×10 4  μm 2 ) of elliptical MTJ sensors, each one having a surface area of 85 μm 2 , which made it unsuitable for integration into certain micro-/nanofluidic devices. 
     Micrometer- and submicrometer-sized Hall sensors using graphene, InSb, and InAs/AlSb (2-dimensional electron gas) have also been characterized and optimized with regard to the detection of very small magnetic fields. The ability to detect a few magnetic nanoparticles with such devices has not been demonstrated. In fact, these attempts did not even anticipate the detection of a single nanoparticle. Furthermore, assumptions made to carry out such attempts were based on a perfect placement of nanoparticles on top of the sensor and did not provide a method to detect moving nanoparticles, nor to determine the flow properties of the carrying fluid. 
     Another attempt at single-nanoparticle detection employed giant magnetoresistance (GMR) spin valve sensors to detect a few tens to hundreds of 16 nm iron oxide nanoparticles. However, in such attempts it was not possible to detect a single nanoparticle of comparable size. The detection method required the nanoparticles to be bound to the sensor and, therefore, did not provide a way to characterize the flow of the surrounding fluid. 
     Submicrometric semiconductor-based Hall sensors have also been shown to perform single-nanoparticle detection in the case of 50-175 nm nanoparticles made of thousands of smaller (4 nm) FePt nanoparticles. The compound nanoparticle was positioned by an intricate operation that required the presence of a Si membrane, which ultimately limited the sensitivity of the device. The method was not suitable for detecting moving nanoparticles nor for characterizing the surrounding fluid via the magnetic tracers. The detection of a single nanoparticle of only a few nanometers (&lt;50 nm) with such devices was not demonstrated. 
     BRIEF SUMMARY 
     In one exemplary aspect, a method of detecting a particle comprises magnetizing a particle using an AC magnetic field; generating an AC voltage, from the magnetized particle, in a sensing device having a conductive substantially 2-dimensional lattice structure; superimposing a DC magnetic field on the generated AC voltage in the sensing device; and measuring an AC Hall voltage at the sensing device. 
     In another exemplary aspect, a method of determining a. flow velocity field comprises magnetizing a particle in a fluid flowing in a channel by applying an AC magnetic field to the particle; measuring a first AC Hall voltage at a first sensing device in the channel, the first sensing device comprising a first graphene element biased with a voltage; measuring a second AC Hall voltage at a second sensing device in the channel, the second sensing device comprising a second graphene element biased with a voltage; determining a time-shift between the first measured AC Hall voltage and the second measured AC Hall voltage; and determining a fluid flow velocity in the channel based on the determined time-shift and a spatial distance between the first sensing device and the second sensing device. 
     In another exemplary aspect, an apparatus comprises a first coil for providing a DC magnetic field; a second coil for providing, an AC magnetic field; and a conductive substantially 2-dimensional lattice structure proximate the first coil and the second coil and being biased with a voltage. The first coil, the second coil, and the conductive substantially 2-dimensional lattice structure are separated by dielectric layers. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The foregoing and other aspects of exemplary embodiments are made more evident in the following Detailed Description, when read in conjunction with the attached Drawing Figures, wherein: 
         FIGS. 1A and 1B  are schematic representations of side and top views, respectively, of one exemplary embodiment of a graphene-based Hall effect sensor; 
         FIGS. 2A and 2B  are schematic representations of side and top views, respectively, of a wafer defined by a substrate and a first dielectric layer, the wafer forming a portion of the sensor of.  FIGS. 1A and 1B ; 
         FIGS. 3A and 3B  are schematic representations of side and top views, respectively, of a photo-resist material deposited onto the wafer and patterned; 
         FIGS. 4A and 4B  are schematic representations of side and top views, respectively, of a metallic thin film forming a first on-chip coil on the wafer; 
         FIGS. 5A and 5B  are schematic representations of side and top views, respectively, of a second dielectric layer deposited onto the first on-chip coil; 
         FIGS. 6A and 6B  are schematic representations of side and top views, respectively, of a photo-resist material deposited onto the second dielectric layer, the photo-resist material being patterned; 
         FIGS. 7A and 7B  are schematic representations of side and top views, respectively, of a metallic thin film forming a second on-chip coil on the second dielectric layer; 
         FIGS. 8A and 8B  are schematic representations of side and top views, respectively, of a third dielectric layer deposited onto the second on-chip coil; 
         FIGS. 9A and 9B  are schematic representations of side and top views, respectively, of a graphene layer deposited on the third dielectric layer; 
         FIGS. 10A and 10B  are schematic representations of side and top views, respectively, of a photo-resist material deposited onto the graphene layer, the photo-resist material being patterned; 
         FIGS. 11A and 11B  are schematic representations of side and top views, respectively, of the graphene layer after an etch process; 
         FIGS. 12A and 12B  are schematic representations of side and top views, respectively, of a photo-resist material deposited onto the graphene and the third dielectric layer, the photo-resist material being patterned; 
         FIGS. 13A and 13B  are schematic representations of side and top views, respectively, of a set of contacts formed adjacent the graphene; 
         FIG. 14  is a schematic representation of a side view of a photo-resist material deposited over the graphene and the set of contacts, the photo-resist material being patterned; 
         FIG. 15  is a schematic representation of a top view of an overlay of a first on-chip coil, a second on-chip coil, and a graphene layer of the graphene-based Hall effect sensor and showing various voltages; 
         FIG. 16  is a schematic representation of one exemplary principle of operation of the graphene-based Hall effect sensor; 
         FIGS. 17A-17C  are computer simulation results of the operation of sensors employing , various graphene layer geometries; 
         FIG. 18A  is a schematic representation of one exemplary determination of 2-dimensional flow -fields using multiple sensors; 
         FIG. 18B  is a graphical representation of sequential Hall voltage signals determined over time shifts; 
         FIG. 19  is a schematic representation of one exemplary illustration of a determination of a velocity field; 
         FIG. 20  is a block diagram of various electronic devices and apparatuses that may be suitable for use in providing a fluid flow analysis; and 
         FIG. 21  is a logic flow diagram that illustrates the operation of one exemplary method, and a result of execution of computer program instructions embodied on a computer readable memory, in accordance with an exemplary embodiment of providing a fluid flow analysis. 
     
    
    
     DETAILED DESCRIPTION 
     The exemplary embodiments described herein are directed to the detection and characterization of one or more magnetic nanoparticles, of about one to hundreds of nanometers in diameter, that operate as magnetic tracers, while dispersed in a carrying fluid that flows through a micro-/nanochannel. The exemplary embodiments are not limited to the detection and characterization of nanoparticles, however, as microparticles (particles that are-about one micrometer or larger in diameter) may also be detected. The apparatuses and methods used with the exemplary embodiments described herein allow for the characterization of the carrying fluid itself through information extracted from the magnetic tracers. 
     In embodiments of detecting and characterizing the magnetic nanoparticles, a conductive substantially 2-dimensional lattice structure (e.g., a graphene layer or sheet) of micro-/nanoscopic dimensions is integrated into a micro-/nanochannel and is biased with a voltage in order to promote the flow of a current. A nearby magnetic nanoparticle, flowing inside the micro-/nanochannel in a carrying fluid, is excited by an external magnetic field and creates a magnetic field at the graphene sheet. Due to the Hall effect, a detectable transversal Hall voltage is generated at the graphene sheet. The Hall voltage signal conveys information about the nearby magnetic nanoparticle and the flow properties of the carrying fluid. This allows for the detection of single nanoparticles with diameters from about 1 nanometer to hundreds of nanometers (as well as larger microparticles) while dispersed in a flowing fluid and for the use of this information to determine the fluid flow speed in micro-and nanochannels. Thus, the apparatuses and methods described herein facilitate techniques and processes associated with magnetic nanoparticle velocimetry. 
     Referring to  FIGS. 1A and 1B , a graphene-based magnetic Hall effect sensor is designated generally by the reference number  100  and is hereinafter referred to as “sensor  100 .” Sensor  100  comprises a first on-chip coil  105  disposed on a first dielectric layer  110  and covered by a second dielectric layer  115 , a second on-chip coil  120  disposed on the second dielectric layer  115  and covered by a third dielectric layer  125 , a conductive substantially 2-dimensional lattice structure  130  disposed on the third dielectric layer  125 , a first set of contacts  135  disposed on the third dielectric layer  125  and adjacent to the substantially 2-dimensional lattice structure  130 , a first set of vias  145  formed through the third dielectric layer  125  and the second dielectric layer  115  to the first on-chip coil  105 , and a second set of vias  140  formed through the third dielectric layer  125  to the second on-chip coil  120 . The first dielectric layer  110  may be disposed on a solid or flexible substrate  150 . The first on-chip coil  105  produces a direct current (DC) magnetic field. The second on-chip coil  120  produces an alternating current (AC) magnetic field. 
     The conductive substantially 2-dimensional lattice structure  130  may be any suitable single-layer or multi-layer organic or inorganic layered material such as graphene, MoS 2 , WSe 2 , black phosphorous, regular arrays or random networks/thin films made of quasi-one dimensional lattice structures such as organic and inorganic nanotubes/nanowires (e.g. carbon nanotubes, Si nanowires, etc.), combinations of any of the foregoing materials, or the like. However, the substantially 2-dimensional lattice structure  130  is hereinafter referred to as “graphene  130 .” 
     Referring now to  FIGS. 2A through 14 , examples of the main process steps by which the sensor  100  can be fabricated are shown and described. 
     As shown in  FIGS. 2A and 2B , the substrate  150  can be an insulating, planarized substrate coated by the first dielectric layer  110  to form a wafer  155 . The substrate  150  may comprise, for example, one or more of glass, quartz, SiC, a silicon nitride such as Si 3 N 4 , plastic, and the like. Suitable dielectric materials for the first dielectric layer  110  include, but are not limited to, SiO 2 , Al 2 O 3 , HfO, combinations of the foregoing, and the like. Such dielectric materials may be deposited via standard processes such as atomic layer deposition, thermal evaporation, or chemical vapor deposition (CVD). 
     As shown in  FIGS. 3A and 3B , the wafer  155  may be coated with a positive photo-resist material (e.g., PMMA) for production of a mask  160 , followed by patterning using an e-beam or photolithography technique to expose portions of the photo-resist, and a develop step to remove exposed areas  165 . Generally, the mask  160  can be a soft mask, like optical or electron-beam lithography resist (e.g. PMMA, hydrogen silsesquioxane (HSQ), or polysilicon-based material (such as MICROPOSIT S1818 from available suppliers)) or a hard mask, likean oxide, nitride, or metal deposited by a compatible deposition method. 
     As shown in  FIGS. 4A and 4B , a metallic thin film may be deposited in the removed portions of the exposed areas  165  and onto the first dielectric layer  110  by means of a standard metal deposition process. This metallic thin film will form the first on-chip coil  105  for producing the DC magnetic field. Suitable metals for the metallic thin film to form the first on-chip coil  105  include, but are not limited to, W, Ti, Pd, Au, Cr, and the like. The mask  160  can be removed using any suitable lift off technique. 
     As shown in  FIGS. 5A and 5B , the first on-chip coil  105  may be coated with the second dielectric layer  115  such that the metallic thin film defining the first on-chip coil  105  is completely covered. The second dielectric layer  115  may then be planarized. Suitable dielectrics for the second dielectric layer  115  include, but are not limited to, SiO 2 , Al 2 O 3 , HfO, combinations of the foregoing, and the like, which may be deposited via standard processes such as atomic layer deposition, thermal evaporation, or CVD. 
     As shown in  FIGS. 6A and 6B , the second dielectric layer  115  may be coated with a positive photo-resist (e.g., PMMA) to produce a second mask  170 , followed by patterning using an e-beam or photolithography technique to expose portions of the photo-resist, and a develop step to remove exposed areas  175 . Generally, the second mask  170  can be a soft mask, like optical or electron-beam lithography resist (e.g., PMMA, HSQ, or S1818) or a hard mask, like an oxide, nitride, or metal deposited by a compatible deposition method. 
     As shown in  FIGS. 7A and 7B , a metallic thin film may be deposited in the removed portions of the exposed areas  175  and onto the second dielectric layer  115  by means of a standard metal deposition process. This metallic thin film forms the second on-chip coil  120  for producing the AC magnetic field. The second on-chip coil  120  may be a thin linear element, as shown in  FIG. 7B . Suitable metals for the metallic thin film to form the second on-chip coil  120  include, but are not limited to, W, Ti, Pd, Au, Cr; and the like. The second mask  170  can be removed using any suitable lift off technique. 
     As shown in  FIGS. 8A and 8B , the second on-chip coil  120  may be coated with the third dielectric layer  125  such that the metallic thin film defining the second on-chip coil  120  is completely covered. The third dielectric layer  125  may then be planarized. Suitable dielectrics for the third dielectric layer  125  include, but are not limited to, SiO 2 , Al 2 O 3 , HfO, combinations of the foregoing, and the like, which may be deposited via standard processes such as atomic layer deposition, thermal evaporation, or CVD. 
     As shown in  FIGS. 9A and 9B , graphene may be disposed onto the planarized top surface of the third dielectric layer  125  to provide the graphene  130  as a layer. One suitable method of depositing the graphene includes, but is not limited to, deposition of the graphene on a copper foil using CVD to synthesize the layer, followed by dissolving the copper such that the graphene floats on water, and subsequently transferring the floating graphene onto the planarized top surface of the third dielectric layer  125 . 
     As shown in  FIGS. 10A and 10B , the graphene  130  may then be coated with a negative photoresist (e.g, PMMA) to produce a third mask  180  followed by patterning using an e-beam or photolithography technique to expose portions of the negative photo-resist, and a develop step to remove non-exposed areas of the third mask  180 . Generally, the third mask  180  can be a soft mask, like optical or electron-beam lithography resist (e.g., PMMA, HSQ, or S1818) or a hard mask, like an oxide, nitride, or metal deposited by a compatible deposition method. 
     As shown in  FIGS. 11A and 11B , the exposed portions of the graphene  130  (which were under the removed non-exposed. areas of the third mask  180 ) may be etched by a suitable technique (e.g., oxygen reactive ion etching (RIE)). This may leave the graphene  130  in a cross-type pattern on the third dielectric layer  125 . 
     As shown in  FIGS. 12A and 12B , the graphene  130  and the top surface of the third dielectric layer  125  may be coated with a positive photo-resist (e.g., PMMA) to produce a fourth mask  190  followed by patterning using an e-beam or photolithography technique to expose portions of the positive photo-resist, and a develop step to remove exposed areas  195  of the fourth mask  190 . Generally, the fourth mask  190  can be a soft mask, like optical or electron-beam lithography resist (e.g., PMMA, HSQ, or S1818) or a hard mask, like an oxide, nitride, or metal deposited by a compatible deposition method. 
     As shown in  FIGS. 13A and 13B , a metallic thin film may be deposited in the removed exposed areas  195  and onto the third dielectric layer  125  adjacent to the graphene  130  by means of a standard metal deposition process. This third metal film deposited in the removed exposed areas  195  forms the first set of contacts  135 . Suitable metals for the third metal film to form the first set of contacts  135  include, but are not limited to, W, Ti, Pd, Au, Cr, and the like. 
     As shown in  FIG. 14 , the top surface of the third dielectric layer  125 , the graphene  130 , and the first set of contacts  135  may be coated with a positive photo-resist (e.g., PMMA) to produce a fifth mask  210  followed by patterning using an e-beam or photolithography technique to expose portions of the positive photo-resist, and a develop step to remove exposed areas  215  of the fifth mask  210 . Generally, the fifth mask  210  can be a soft mask, like optical or electron-beam lithography resist (e.g., PMMA, HSQ, or S1818) or a hard mask, like an oxide, nitride, or metal deposited by a compatible deposition method. 
     Open areas under the exposed areas  215  of the fifth mask  210  can be sequentially etched using any suitable etching method (such as RIE) to open areas of the third dielectric layer  125  down to the second on-chip coil  120  and to open areas of the third dielectric layer  125  and the second dielectric layer  115  down to the first on-chip coil  105 . 
     Referring back to  FIGS. 1A and 1B , the opened areas down to the second on-chip coil  120  and down to the first on-chip coil  105  may be followed with deposition of a metallic thin film into the opened areas by means of a standard metal deposition process. This deposition of metal forms the first set of vias  145  through the third dielectric layer  125  and the second dielectric layer  115  to the first on-chip coil  105  and the second set of vias  140  through the third dielectric layer  125  to the second on-chip coil  120 . 
     Referring now to  FIG. 15 , the overlay of the different metal layers (forming the first on-chip coil  105  and the second on-chip coil  120 ) and the graphene  130  is schematically shown. Source voltage (V source ) is shown across opposing ends of the graphene  130 . Other measured voltages are also indicated. For example, a measured voltage across the graphene  130  in the direction of flow when the sensor  100  is located in a fluid is indicated at V detect  . The AC and DC voltages are also indicated as V AC  and V DC  across the first set of vias  140  and the second set of vias  145 , respectively. 
     As shown in  FIG. 16 , one exemplary operation principle for the detection of magnetic nanoparticles using the sensor  100  is shown. In order to improve detectability of a magnetic nanoparticle  250  using the sensor  100 , a small AC magnetic field of a few millitesla (mT) operating at a frequency of hundreds of Hertz (Hz) is used to induce an in-phase AC magnetization in the nanoparticle. The induced magnetization of the nanoparticle  250  generates an external AC field at the graphene  130  of the sensor  100 . By superimposing an external DC magnetic field on the external AC field, an AC Hall voltage measured across the graphene  130  will be greatly increased by the presence of the nanoparticle  250  as compared to an identical system without a magnetized nanoparticle  250  close to the sensor  100 . The AC Hall voltage can be measured using a lock-in amplifier operating at a frequency of the external field. Based on this measured AC Hall voltage, an AC contribution to the magnetic field can be deduced. 
     In the example embodiment shown, a nanoparticle 250 of γ-Fe 2 O 3  of about 20 nm in diameter is detected using a sheet of graphene  130  about 1 μm in width (L x ) and about 100 nm in length (L y ) and across which a biasing voltage of 100 mV is applied. The nanoparticle  250  has an energy density (K) of 12.5 kilojoules per cubic meter (kJ/m 3 ) and a magnetic field strength (M s ) of 380 kiloamperes per meter (kA/m). The graphene  130  has an electron mobility (μ) of 1.5 square meters per volt second (m 2 /(Vs)) and an assumed charge carrier density (n) in the graphene  130  used for simulations of 10 16 /m 2 . The AC magnetic field applied is about 5 mT at 250 Hz. Relaxation times with regard to the applied AC (T AC ) and DC magnetic fields (T m ) are 0.6 ms and 1 ms, respectively. The nanoparticle  250  is detectable at a distance of about 100 nm from the graphene  130 . Although particular physical values are attributed to the drawing, the operation principle described herein is not limited to those particular values. 
     As shown in  FIGS. 17A-17C , simulations of the operation of the sensor  100  exemplified in  FIG. 16 , but employing various graphene layer geometries, are shown generally at  300 ,  310 , and  320 . A sensor  100  having the multiple-cross geometry, as indicated at  310  and  320  in  FIGS. 17B and 17C , respectively, allows for independent measurements of the Hall voltage at different X positions across a fluid channel. The crosses also facilitate the electrical contact for the voltage measurements. In these simulations, the magnetic nanoparticle  250  was placed at the center of the graphene  130 . Measuring the Hall voltage anywhere else other than at the central cross (as well as, for example, anywhere across the sensor  100  as indicated in  FIG. 17A ) will give zero signal. This feature allows for spatial resolution along X regarding the detection of the nanoparticle  250 . The multi-cross geometry may have an arbitrary number (N) of crosses, not just 3 as depicted. For larger numbers of crosses, the detection resolution across the channel will accordingly improve. This detection scheme allows for detecting the presence of magnetic nanoparticles  250 , thereby enabling the use of the sensor  100  for biological immunoassays, where a detection antibody may be labeled with a magnetic nanoparticle  250  for determining the presence of an antigen. 
     As shown in  FIGS. 18A and 18B , a determination of 2-dimensional flow velocity fields is shown generally at  400 . By placing multiple sensors  100 , each comprising a graphene sheet  130 , at several positions along the channel (indicated at  410 ), a series of time-shifted Hall voltage signals can be measured when a magnetic nanoparticle  250  flows along the channel  410 . By cross-correlating these multiple Hall voltage signals using the equation:
 
 V   corr ( Δt )= ∫dt′V   1 ( t′ )· V   2 ( t′+Δt )   (Eq. 1)
 
where V corr  is the correlated voltage, V 1  is a first Hall voltage signal, V 2  is a second Hall voltage signal, and t is time, it is possible to determine the time-shift between the voltage signals which, together with the spatial distance between the graphene sheets, gives the average flow speed of the surrounding fluid in that region as indicated by:
 
 U=ΔY/Δt    (Eq. 2)
 
where U is speed, Y is distance along the channel, and t is time. The sequential Hall voltage signals (V 1 , V 2 ) are determined over time-shifts (Δt), as indicated graphically at  450  in  FIG. 18B . Thus, it is illustrated how the average flow speed of the fluid could be&#39;determined by employing two sensors  100  displaced a known distance (ΔY) along the channel  410  (which may be a nanochannel or a microchannel). This velocimetry technique may use an arbitrary number (M) of sensors  100 , not just two as depicted. Such array of M equally spaced sensors  100  may improve the signal-to-noise ratio of the cross-correlation calculation involved in the determination of the time-shifts (Δt).
 
     Since the magnetic field of a nanoparticle  250  is very localized, by measuring the Hall voltage at different locations of the graphene  130 , the position of the nanoparticle  250  with X (wall-normal) and Y (streamwise) resolution can be determined, providing two-dimensional information on the presence of nanoparticles  250 . By allying this two-dimensional positional information with the cross-correlation of the time-shifted signals received from different positions along the channel  410 , a two-dimensional flow velocity field of the surrounding fluid can be obtained using only the magnetic character of the tracers. 
       FIG. 19  illustrates how a velocity field determination could be obtained using a matrix of N crosses by M sensors with resolution ΔX and ΔY in the wall-normal and streamwise directions of the channel  410 , respectively. An additional cross (shown at  500 , located external to the flow of magnetic particles  250  in the channel  410 ), could be included for providing a reference signal V ref  and further improving the reliability of the detection scheme. 
     Additionally, a determination of 3-dimensional flow velocity fields could also be made. For example, with a knowledge of the properties (size and material) of the magnetic nanoparticles  250 , a vertical position of a nanoparticle  250  can be inferred by exploring the reciprocal of the distance-cubed of the magnetic field at large distances. Since the Hall voltage depends on the strength of the magnetic field associated with the nanoparticle  250 , the Hall signal will be modulated by the vertical distance between the nanoparticle  250  and the graphene  130 , offering an additional source of information that could potentially enable 3-dimensional localization of nanoparticles  250 . By allying the 3-dimensional positional information pertaining to the nanoparticles  250  with the cross- correlation of time- shifted signals coming from an array of sensors  100  at different positions along the channel  410 , a 3-dimensional flow velocity field of the surrounding fluid may be obtained. 
     Referring now to  FIG. 20 , a simplified block diagram of various electronic devices and apparatuses that are suitable for use in practicing the exemplary embodiments described herein is shown. For example, a computer  2010  may be used to control one or more of the processes as described above. The computer  2010  includes a controller, such as a computer or a data processor (DP)  2014  and a computer-readable memory medium embodied as a memory (MEM)  2016  that stores a program of computer instructions (PROG)  2018 . 
     The PROG  2018  includes program instructions that, when executed by the associated DP  2014 , enable the various electronic devices and apparatuses to operate in accordance with exemplary embodiments. That is, various exemplary embodiments may be implemented at least in part by computer software executable by the DP  2014  of the computer  2010 , or by hardware, or by a combination of software and hardware (and firmware). 
     The computer  2010  may also include dedicated processors, for example a processor  2015  that controls the inducement of in-phase AC magnetization in the nanoparticle  250 , measures a generated AC contribution to the magnetic field at the sensor  100 , superimposes an external DC magnetic field on an external AC field, and/or measures an AC Hall voltage across a graphene portion of the-sensor  100 . 
     The computer readable MEM  2016  may be of any type suitable to the local technical environment and may be implemented using any suitable data storage technology, such as semiconductor based memory devices, flash memory, magnetic memory devices and systems, optical memory devices and systems, fixed memory, and removable memory. The DP  2014  may be of any type suitable to the local technical environment, and may include one or more of general purpose computers, special purpose computers, microprocessors, digital signal processors (DSPs), and processors based on a multicore processor architecture, as non-limiting examples. 
     The exemplary embodiments, as discussed herein and as particularly described with respect to exemplary methods, may be implemented in conjunction with a program storage device (e.g., at least one memory) readable by a machine, tangibly embodying a program of instructions (e.g., a program or computer program) executable by the machine for performing operations. The operations comprise utilizing the exemplary embodiments of the methods described herein. 
     Based on the foregoing, it should be apparent that various exemplary embodiments. provide methods for the detection and characterization of magnetic nanoparticles while dispersed in a carrying fluid flowing through a channel. 
       FIG. 21  is a logic flow diagram that illustrates the operation of one exemplary embodiment of a method  2100  for the detection and characterization of magnetic nanoparticles while dispersed in a carrying fluid flowing through a channel. In method  2100 , at  2110 , an in-phase AC magnetization is induced in a nanoparticle. At  2120 , an AC contribution to a magnetic field is received at a Hall-effect sensor. The received AC contribution is measured at  2130 , and an external DC magnetic field is superimposed on the AC contribution to the magnetic field at  2140 . At  2150 , an AC Hall voltage is measured across a graphene sheet of the Hall-effect sensor. At  2160 , the measured AC Hall voltage is used to determine one or more of a position of the nanoparticle and a velocity of the nanoparticle in a fluid. 
     In one exemplary aspect, a method of detecting a particle comprises magnetizing a particle using an AC magnetic field; generating an AC voltage, from the magnetized particle, in a sensing device having a conductive substantially 2-dimensional lattice structure; superimposing a DC magnetic field on the generated AC voltage in the sensing device; and measuring an AC Hall voltage at the sensing device. 
     In the method, generating an AC voltage, from the magnetized particle, in a sensing device may comprise applying an AC voltage across an AC coil on the sensing device. Superimposing a DC magnetic field on the generated AC voltage in the sensing device may increase the AC Hall voltage for measuring at the sensing device as compared to a generated AC voltage in the sensing device without a DC magnetic field superimposed thereon. Superimposing a DC magnetic field on the generated AC voltage in the sensing device may comprise applying a DC voltage across a DC coil on the sensing device. The method may further comprise applying a source voltage across opposing ends of the conductive substantially 2-dimensional lattice structure. Generating an AC voltage in a sensing device having a conductive substantially 2-dimensional lattice structure from the magnetized particle may comprise generating an AC voltage in a graphene element biased with a voltage. 
     In another exemplary aspect, a method of determining a flow velocity field comprises magnetizing a particle in a fluid flowing in a channel by applying an AC magnetic field to the particle; measuring a first AC Hall voltage at a first sensing device in the channel, the first sensing device comprising a first graphene element biased with a voltage; measuring a second AC Hall voltage at a second sensing device in the channel, the second sensing device comprising a second graphene element biased with a voltage; determining a time-shift between the first measured AC Hall voltage and the second measured AC Hall voltage; and determining a fluid flow velocity in the channel based on the determined time-shift and a spatial distance between the first sensing device and the second sensing device. 
     Measuring a first AC Hall voltage at a first sensing device in the channel may comprise generating an AC voltage, from the magnetized particle, in a conductive substantially 2-dimensional lattice structure of the first sensing device, and superimposing a DC magnetic field on the generated AC voltage in the conductive substantially 2-dimensional lattice structure of the first sensing device. Determining a time-shift between the first measured AC Hall voltage and the second measured AC Hall voltage may comprise cross-correlating the first measured AC Hall voltage and the second measured AC Hall voltage using Equation (1) as described herein. An average flow speed of the fluid flowing in the channel may be indicated by Equation (2) as described herein. The method may further comprise providing a reference voltage to the first sensing device and the second sensing device external to the channel. 
     In another exemplary aspect, an apparatus comprises a first coil for providing a DC magnetic field; a second coil for providing an AC magnetic field; and a conductive substantially 2-dimensional lattice structure proximate the first coil and the second coil and being biased with a voltage. The first coil, the second coil, and the conductive substantially 2-dimensional lattice structure are separated by dielectric layers. 
     The apparatus may further comprise a first set of contacts disposed in contact with the conductive substantially 2-dimensional lattice structure. The apparatus may further comprise a first set of vias in contact with the first coil and a second set of vias in contact with the second coil. The conductive substantially 2-dimensional lattice structure may comprise graphene. The conductive substantially 2-dimensional lattice structure may comprise MoS 2 , WSe 2 , black phosphorous, carbon nanotubes, Si nanowire, or a combination of any of the foregoing materials. At least one of the dielectric layers may be disposed on a substrate of glass, quartz, SiC, silicon nitride, plastic, or a combination of any of the foregoing materials. At least one of the dielectric layers may comprise SiO 2 , Al 2 O 3 , HfO, or a combination of any of the foregoing materials. The second coil may be a thin linear element. 
     The foregoing description has provided by way of exemplary and non-limiting examples a full and informative description of the best method and apparatus presently contemplated by the inventors for carrying out various exemplary embodiments. However, various modifications and adaptations may become apparent to those skilled in the relevant arts in view of the foregoing description, when read in conjunction with the accompanying drawings and the appended claims. However, all such and similar modifications will still fall within the scope of the teachings of the exemplary embodiments. 
     Furthermore, some of the features of the preferred embodiments could be used to advantage without the corresponding use of other features. As such, the foregoing description should be considered as merely illustrative of the principles, and not in limitation thereof.