Piezoresistive principle

This is necessary both for process control as well as the reliabihty of the system. The integration of sensors into the microreactor or building a multisensor module for the four functions of state is easy for a microreactor made of sUicon. For the process pressure, the piezoresistive principle is used often. With diEFerential pressure measurements, the flow rate can be determined. Alternatively, calorimetric principles are used widely. These are easy to implement technically, but a calibration is needed for eatii new medium. The most robust sensors are the Coriolis mass flow sensors. In process engineering, they are very common, but in terms of micro process engineering, there is still a need for research. In Ref. [26], sensors of this type are described. Ref [25] is a good summary of other microflow sensors. For measurement of temperature, there are many equivalent principles but will not be discussed here. Substantially, it is more difficult to measure the concentration in the reactor. In addition to optical principles, the impedance spectroscopy is often used. See Ref [27-31] for more details. 

The principle of the resistance strain gauge 2 0 is that the electrical resistance of a conductor will change when it is stretched or compressed due to the consequent variation in its physical dimensions. There is an additional effect called the piezoresistance which is the relation between the resistivity p of the material and the mechanical strain. The resistance R of a conductor of area of cross-section A and length x is given by ... 

The principle of operation of transducers is based on the conservation of either linear (i.e., Coriolis effect) or angular momentum, making a transducer well suited for micromachined rate-sensing gyros. One or more linearly or rotationally vibrating probe masses are required, for which the input motion stimulus and the output signal can be accomplished by various physical effects (electrostatic, electromagnetic, piezoresistive, etc.). Usually the drive motion is resonant, so the detection motion can also be resonant or the two natural frequencies are separated by a certain frequency shift. Drive and detection motion can be excited by inplane motions or by a mixture of in-plane and out-of-plane motions. 

Before describing the signal evaluation principles, the general observed imperfections of the piezoresistive bridge, which must be taken care of in the evaluation circuit, will be discussed. 

The excitation can be realized by electrostatic, electromagnetic, or piezoelectric methods. The detection is carried out by capacitive, piezoelectric, or piezoresistive techniques. The principle of vibrating gyroscopes can be traced back to Foucault s pendulum in 1851. There are numerous design possibilities for the construction of vibrating gyroscopes [1-5, 9] Fig. 7.2.1 shows one principle. 

Fig. 7.2.6 Functional principle of a silicon micromachined tuning fork, the tines are excited by piezoelectric actuators, the Coriolis forces bend the suspensions and are detected by piezoresistive resistors in the suspension bars. Source Conti Temic, Produktlinie Sensorsysteme...

Tab. 7.3.1 provides a summary of the principles and features of the pressure sensors. The pressure sensors are broadly divided into three groups according to which principle they employ piezoresistive sensors, capacitive sensors, and piezoelectric sensors. 

Fig. 7.3.1 shows the principle of the piezoresistive sensor. Diffused resistors (gages) are formed on the thin-walled section called the diaphragm. An applied pressure is detected via the piezoresistive effect, which is the change in electrical resistance when a stress is applied to the diaphragm. The sensitivity is determined by the material, diameter, and thickness of the diaphragm. The thin-film piezoresistive sensor offers low sensitivity because the piezoresistive coefficient of thin-film silicon is less than one-third of that of single-crystal silicon. 

P-type silicon piezoresistive elements in high concentration of 1020 cm-3 are used to make a bridge configuration. The resistance of those elements increases with temperature (positive temperature characteristic). On the other hand, the piezoresistive coefficient 7r44 determines the sensibility decrease with temperature (negative temperature characteristic). The temperature-compensation circuit is made by making use of these characteristics. Fig. 7.3.8 shows the principle of the temperature-compensation circuit and the concept of temperature compensation. 

Figure 1 illustrates the operational principle of hydrogel-based sensors. Pressure sensor chips with a flexible thin silicon bending plate and with an integrated piezoresistive Wheatstone bridge inside this plate have been employed as... 

Functional principle of textile-based piezoresistive carbon filament yarn sensors for application in a wind turbine blade... 

The operating principle of a piezoresistive sensor yam made with conductive coating applied to an original core yam is represented in Fig. 17.6 with and I, respectively, the cross-section and the longitudinal length of the sensor yarn (Koncar et al., 2009). 

Figure 17.6 Operating principle of a piezoresistive strain sensor yam.

Strain is naturally present in pSi (Miu et al. 2011), and it could also be applied externally. In particular, there are many studies carried out in SiNW observing, for example, a piezoresistance several orders of magnitude greater than that of bulk Si (He and Yang 2006). On the theoretical side, computational studies through semiempirical (Shiri et al. 2008 Stanojevic et al. 2010) and first-principle methods (Leu et al. 2008 Hong et al. 2008) have been performed. Axial strain can be... 

Other mechanical sensors rely on the piezoresistive effect, which represents the variation of resistance of a given material when subjected to strain (Fraden, 2010). The change in resistance results from the mechanical deformation of the material and is the physical principle underlying the operation of many force and pressure sensors. 

Microcantilever, which owes its existence to atomic force microscopy, is based on the principle that binding the analyte to a biological recognition layer on the microcantilever induces surface stress, resulting in nanomechanical motion that can be measured optically or by a piezoresistive readout system (Rackus et al., 2015). 

---