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                       FIGURE 19.125  Schematic diagram illustrating the operation principle of a momentum-transfer based flow sensor.
                       FIGURE 19.126  Schematic diagram of the plastic deformation magnetic assembly (PDMA) process.
                       Flow Sensors Based on Momentum Transfer Principles
                       For sensors based on momentum transfer principles, a mechanical member is bent by the momentum
                       imparted by a moving fluid (Fig. 19.125). The amount of the bending is used to decipher the strength
                       of the fluid flow. The schematic diagram of an exemplary flow sensor is shown in the figure below. It
                       consists of a vertical shaft attached to the end of a cantilever beam (a). When an external  flow is
                       exerted, it will apply a distributed force onto the vertical shaft, hence causing the cantilever to bend.
                       The extent of the bending, as sensed by the embedded piezoresistor, is proportional to the average
                       flow rate.
                         The fabrication process is similar to the tactile sensor except for the attachment of the integrated
                       vertical shaft. A number of techniques for assembling three-dimensional microstructures using efficient
                       integrated processes have been developed in the past. For example, three-dimensional structures can be
                       realized using hinged microstructures and using solder joints or polymer joints. Recently, a process called
                       the plastic deformation magnetic assembly (PDMA) has been developed. In the following paragraph the
                       PDMA process is briefly discussed.
                         The PDMA technique is discussed using a simple surface micromachined cantilever as an example.
                       As shown in the diagram below (Figs. 19.126 and 19.127), a single-clamped cantilever made of a
                       ductile metal (e.g., gold or aluminum) is suspended from the substrate.  A piece of Permalloy, a
                       ferromagnetic alloy made by electrodeposition, is attached to the cantilever. When a magnetic field
                       is applied from underneath the wafer, the magnetic piece will be magnetized and will experience a
                       magnetic torque M. The torque lifts the cantilever beam away from the substrate. If the amount of
                       bending is significant, the ductile metal will be displaced permanently due to plastic deformation at
                       the hinge region.
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