- 3 A Micromechanical Bulk Mode Block Resonator Is Actuated Using A Parallel Plate Electrostatic Actuator Shown In Blu 1 (156.34 KiB) Viewed 36 times
- 3 A Micromechanical Bulk Mode Block Resonator Is Actuated Using A Parallel Plate Electrostatic Actuator Shown In Blu 2 (90.3 KiB) Viewed 36 times
3. ) A micromechanical bulk mode block resonator is actuated using a parallel plate electrostatic actuator (shown in blue). To sense the vibrations of the resonator, a 6um wide, 5um deep n-type doped piezoresistor is formed at the center of the resonator. The doping level of the piezoresistors is precisely controlled to result in a resistivity of 10 12.cm in the doped region. The resistor is oriented along the 110 direction and for n-type silicon with resistivity of 10 S2.cm along 110 direction, ti and it coefficients are -30x10-11 Pal and -18x10-11 Pal respectively. The block resonator is 50um wide and 200um long and resonates in its width extensional mode with a frequency of 85MHz. During the width extensional resonance the width of the block periodically increases and decreases. In this resonance mode, the vibration amplitude of each part of the block is a sine function of its distance from the central plane of the block (vertical plane passing through the piezoresistor and the resonator support beams), i.e. A(x) = Amax Sin(tx/W), where A(x) is the vibration amplitude at a location x microns away from the central plane, Amax is the maximum vibration amplitude that occurs at the very edge of the block, and W is the width of the block. a) (15 points) Find similar equations for the stress an strain at different locations of the resonator as a function of x. (E = 170x10° Pa) (Hint: strain at each small element in the structure with length of dx, is the difference between the displacements at the beginning (xo) and end points (Xo+dx) of that element divided by the length of the element! That should remind you of the concept of derivative...) b) (10 points) Based on the derived equations in part a, and assuming that the block is vibrating with an amplitude of Inm (at the edge), what is the amplitude of the stress experienced by the piezoresistor? What is the resistance value at rest and resulting change in resistance due to stress? You can assume the stress at every point of the piezoresistor to be equal to the stress at the center of the block (x = 0).
c) (10 points) Assumin at the meander shaped doped-resistor that extends on top of the anchored pad has the same length as the piezoresistor on the resonator(200um) and the combination of the two resistors is biased with a 50V voltage source, what is the output AC voltage amplitude measured at the location where the two resistors join (Vout)? Vbias Vibration Direction (frequent expansion and compression) ил X Deformed shape of the resonator at resonance out GND GEDOTHEK d) (5 points) Knowing that the AC voltage amplitude required by the electrostatic actuator that results in a Inm vibration amplitude in the block edge is 0.1V, can this device work as an oscillator (resonator with self-sustained vibrations) by feeding the output signal back to its input? Why?