4.1 Mechanical sensing principles (piezoresistive, capacitive, resonant)

Mechanical sensing principles form the backbone of MEMS/NEMS devices. Piezoresistive, capacitive, and resonant sensors convert physical phenomena into measurable electrical signals, enabling precise detection of force, pressure, acceleration, and more.

These sensing mechanisms exploit material properties and device geometries to achieve high sensitivity and resolution. Understanding their principles is crucial for designing and optimizing MEMS/NEMS sensors for various applications in modern technology.

Piezoresistive Sensing

Piezoresistive Effect and Strain Gauges

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• Piezoresistive effect occurs when the electrical resistance of a material changes due to applied mechanical stress or strain
• Piezoresistive materials (silicon, germanium, polysilicon) exhibit a change in resistivity when subjected to stress or strain
• Strain gauges are devices that utilize the piezoresistive effect to measure strain or deformation in a material
• Strain gauges consist of a piezoresistive material patterned onto a flexible substrate (polyimide, kapton) which is bonded to the surface of the object being measured

Wheatstone Bridge Configuration

• Wheatstone bridge is a circuit configuration used to measure small changes in resistance with high accuracy
• Consists of four resistors connected in a diamond-shaped bridge configuration with a voltage excitation source and a voltage measurement device
• Piezoresistive strain gauges are often used in a Wheatstone bridge configuration to maximize sensitivity and minimize temperature effects
• When the resistance of one or more strain gauges changes due to applied strain, the bridge becomes unbalanced, resulting in a measurable voltage output proportional to the strain

Piezoresistive Force Sensors

• Piezoresistive force sensors utilize the piezoresistive effect to measure applied force or pressure
• Typically consist of a diaphragm or membrane with piezoresistive strain gauges integrated onto its surface
• When force is applied to the diaphragm, it deforms, causing a change in resistance of the strain gauges
• The change in resistance is measured using a Wheatstone bridge circuit and can be calibrated to determine the applied force
• Piezoresistive force sensors are used in various applications (pressure measurement, tactile sensing in robotics, force feedback in haptic devices)

Capacitive Sensing

Capacitive Sensing Principles

• Capacitive sensing is a method of measuring changes in capacitance to detect physical parameters (displacement, pressure, acceleration)
• Capacitance is the ability of a system to store electrical charge, and it depends on the geometry and dielectric properties of the materials involved
• In capacitive sensing, a change in the physical parameter of interest causes a change in the capacitance of the sensor
• The change in capacitance is typically measured using electronic circuits (charge amplifiers, capacitance bridges) and converted into an electrical signal proportional to the measured parameter

Parallel Plate Capacitor Sensors

• Parallel plate capacitors are a common type of capacitive sensor used in MEMS devices
• Consist of two parallel conductive plates separated by a dielectric material (air, vacuum, or a solid dielectric)
• The capacitance of a parallel plate capacitor is given by $C = \frac{\varepsilon A}{d}$, where $\varepsilon$ is the permittivity of the dielectric, $A$ is the area of the plates, and $d$ is the distance between the plates
• In capacitive sensing applications, one of the plates is typically fixed, while the other is movable and responds to the physical parameter being measured
• Changes in the distance between the plates or the effective area of the plates result in a change in capacitance, which can be measured and correlated to the physical parameter

Capacitive Accelerometers and Pressure Sensors

• Capacitive accelerometers measure acceleration by detecting the displacement of a proof mass suspended between two fixed plates
• When acceleration is applied, the proof mass moves, changing the capacitance between the proof mass and the fixed plates
• The differential capacitance change is measured and used to determine the acceleration
• Capacitive pressure sensors use a similar principle, with a flexible diaphragm acting as one of the capacitor plates
• When pressure is applied, the diaphragm deflects, changing the capacitance between the diaphragm and a fixed reference plate
• The capacitance change is measured and correlated to the applied pressure
• Capacitive sensors offer high sensitivity, low power consumption, and good stability, making them suitable for various applications (inertial navigation, automotive systems, biomedical devices)

Resonant Sensing

Resonant Sensing Principles

• Resonant sensing is a technique that utilizes the resonant behavior of mechanical structures to measure physical parameters
• Resonant sensors consist of a mechanical resonator (beams, plates, or membranes) that vibrates at its natural frequency
• The natural frequency of a resonator depends on its geometry, material properties, and the physical parameter being measured
• When the physical parameter changes, it alters the resonant frequency of the sensor, which can be measured and correlated to the parameter of interest
• Resonant sensors offer high sensitivity, high resolution, and low drift, making them suitable for precision measurements

Quality Factor and Frequency Shift

• Quality factor (Q) is a measure of the sharpness of the resonance peak and the energy dissipation in a resonant system
• A high Q indicates low energy loss and a sharp resonance peak, which enables high-resolution measurements
• The Q factor is defined as $Q = \frac{f_0}{\Delta f}$, where $f_0$ is the resonant frequency and $\Delta f$ is the bandwidth of the resonance peak
• In resonant sensing, a change in the physical parameter causes a shift in the resonant frequency of the sensor
• The frequency shift $\Delta f$ is related to the change in the physical parameter and can be measured using electronic circuits (phase-locked loops, frequency counters)
• The sensitivity of a resonant sensor is determined by the magnitude of the frequency shift for a given change in the physical parameter

Cantilever Beam Resonators

• Cantilever beams are a common type of mechanical resonator used in resonant sensing applications
• A cantilever beam is a structure that is anchored at one end and free to vibrate at the other end
• The resonant frequency of a cantilever beam depends on its dimensions, material properties, and the effective mass of the beam
• Cantilever beam resonators can be used to measure various physical parameters (mass, force, temperature, magnetic fields) by monitoring changes in their resonant frequency
• Mass sensing is a common application of cantilever beam resonators, where the adsorption of particles or molecules onto the beam's surface changes its effective mass and resonant frequency
• Cantilever beam resonators can achieve extremely high sensitivity and resolution, enabling the detection of single molecules or nanoparticles