The Au capacitance plates are fabricated directly onto the glass substrate to form the capacitor with the low-resistivity silicon resonator, of which the resistivity U0126 cost is between 0.001 ��?cm and 0.004 ��?cm.Figure 1.Structure of the MEMS torsional resonant magnetometer.The operation principle is illustrated in Figure 2. If a DC current I is introduced into the excitation coil and a magnetic flux-density Bx in x-direction is presented, for one turn of the excitation coil with length Lc in y-direction, the Lorentz forces perpendicular to the silicon plane are:FL=I?Lc?Bx(1)The Lorentz Inhibitors,Modulators,Libraries forces are generated on both sides of the resonator with opposite directions. Therefore the torque caused by the Lorentz forces is of the same direction, which twists the torsional beams.Figure 2.

Operation principle of the MEMS torsional resonant magnetometer.If a sinusoidal current shown in (2) passes through the excitation coil instead of a DC current, the silicon Inhibitors,Modulators,Libraries resonator will vibrate around the torsional beams due to the alternating directions of the Lorentz force FL in (3):i=I0 sin 2�� ft(2)FL=i?Lc?Bx=I0LcBx sin 2�� ft(3)When the frequency f of the current Inhibitors,Modulators,Libraries is equal to the resonant frequency of the silicon resonator, the vibration amplitude will dramatically increase due to the resonance and the high quality factor of the structure. Then this vibration amplitude will be converted into the differential change of the two sensing capacitances as shown indicated in Figure 2. Here, a capacitance detection circuit could be used to measure the capacitance change that reflects the value of the magnetic flux-density [3].

For the Lorentz Force Magnetometer, the input is the magnetic flux-density Bx in x-direction and the output is the capacitance change ��C. The transfer function can be expressed as in (4):��C=SM S�� SC Bx=?M?B??��?M??(��C)?��?Bx(4)Here, SM, S and SC respectively stand for the transfer function from the magnetic flux-density Inhibitors,Modulators,Libraries B to the excitation torque M, from the excitation torque M to the torsional angle , and from the torsional angle to Anacetrapib the capacitance change ��C. When the structural parameters of the resonant magnetometer are determined, it can be proved that SM, S and SC are approximately constant under small deflection condition [6]. Therefore, the capacitance change ��C has a linear relationship with the magnetic flux-density Bx.

meantime The output signal of the capacitance detection circuit can accurately represent the magnetic flux-density Bx in x-direction when the torsional angle of the resonator is in an appropriate range. For instance, when the resonator surface area S is 3,000 ��m �� 2,000 ��m and the capacitance plate distance d0 is 15 ��m, the linearity of the sensor can be within 1.0% when the rotation angle does not exceed 6 �� 10?4 rad.3.?Fabrication ProcessThe fabrication process of the prototype is based on the anodic bonding of low-resistivity silicon and a Pyrex glass substrate.