51.9 Design Considerations Many commercially available sensors(pressure, acceleration, vibration,.etc )are fabricated from piezoresistive materials(see for example, Chapter 56 in this handbook. The most commonly used geometry for pressure sensors is the edge clamped diaphragm. Four resistors are usually deposited on the diaphragm and connected to form a Wheatstone bridge. The deposition technique varies depending upon the piezoresistive material: standard IC technology and micro-machining for Si type diaphragms; sputtering for thin film metal strain gauges; bonding for wire strain gauges, and screen printing for thick film resistors. Different types of diaphragms (sapphire, metallic, ceramic,-. etc. have been reported in the literature for hybrid sensors To design a highly accurate and sensitive sensor, it is necessary to analyze the stress-strain response of the iaphragm using plate theory and finite element techniques to take into account: (1)elastic anisotropy of the diaphragm, (2)large deflections of plate(elastic non linearities), and(3)maximum sensitivity directions of the piezoresistivity coefficient. Signal conditioning must be provided to compensate for temperature drifts of the gauge offset and sensitivity Defining Terms P Electric resistivity tensor d kr: Converse piezoelectric tensor Ilik: Piezoresistivity tensor Pum: Nonlinear resistivity tensor 8 wme: Nonlinear piezoelectric tensor Related Topic 1.1 Resistors References A Amin, Numerical computation of the piezoresistivity matrix elements for semiconducting perovskite fer- electrics,Phys. Rev. B, voL. 40, 11603, 1989 C Canali, D. Malavasi, B Morten, M. Prudenziati, and ATaroni, "Piezoresistive effect in thick-film resistors J. AppL. Phys., vol. 51, 3282, 1980. F. Carmona, R. Canet, and P. Delhaes,"Piezoresistivity in heterogeneous solids, J. Appl. Phys., vol 61, 2550, C. Herring and E. Vogt, Transport and deformation-potential theory for many valley semiconductors with nisotropic scattering, "Phys. Rev, vol. 101,944, 1956. R. J. Kennedy, W.G. Jenks, and L R. Testardi, "Piezoresistance measurements of YBa, Cu,O, showing large magnitude temporal anomalies between 100 and 300 K, Phys. Rev. B, vol 40, 11313, 1989 W. Keyes,The effects of elastic deformation on the electrical conductivity of semiconductors," Solid State Phys,voL11,149,1960 W. P. Mason and R. N. Thurston, Use of piezoresistive materials in the measurement of displacement, force, d torque, J. Acoust. Soc. Am., vol. 10, 1096, 1957. Y. Onuma and K. K. Kamimura,"Piezoresistive elements of polycrystalline semiconductor thin films, Sensors and Actuators, vol. 13, 71, 1988. K. Rajanna, S. Mohan, M. M. Nayak, and N. Gunasekaran,Thin film pressure transducer with manganese film as the strain gauge, "Sensor and Actuators, vol. A 24, 35, 1990 H A Sauer, S.S. Flaschen, and D. C. Hoestery, "Piezoresistance and piezocapacitance effect in barium strontium titanate ceramics, Am Ceram. Soc., vol 42, 363, 1959 C.S. Smith, Piezoresistance effect in germanium and silicon, Phys. Rev, voL 94, 42, 1953 e 2000 by CRC Press LLC© 2000 by CRC Press LLC 51.9 Design Considerations Many commercially available sensors (pressure, acceleration, vibration,… etc.) are fabricated from piezoresistive materials (see for example, Chapter 56 in this handbook.) The most commonly used geometry for pressure sensors is the edge clamped diaphragm. Four resistors are usually deposited on the diaphragm and connected to form a Wheatstone bridge. The deposition technique varies depending upon the piezoresistive material: standard IC technology and micro-machining for Si type diaphragms; sputtering for thin film metal strain gauges; bonding for wire strain gauges, and screen printing for thick film resistors. Different types of diaphragms (sapphire, metallic, ceramic,… etc.) have been reported in the literature for hybrid sensors. To design a highly accurate and sensitive sensor, it is necessary to analyze the stress–strain response of the diaphragm using plate theory and finite element techniques to take into account: (1) elastic anisotropy of the diaphragm, (2) large deflections of plate (elastic non linearities), and (3) maximum sensitivity directions of the piezoresistivity coefficient. Signal conditioning must be provided to compensate for temperature drifts of the gauge offset and sensitivity. Defining Terms ri j : Electric resistivity tensor dik l : Converse piezoelectric tensor Pijk l : Piezoresistivity tensor rij m : Nonlinear resistivity tensor dikln o : Nonlinear piezoelectric tensor Related Topic 1.1 Resistors References A. Amin, “Numerical computation of the piezoresistivity matrix elements for semiconducting perovskite fer￾roelectrics,” Phys. Rev. B, vol. 40, 11603, 1989. C. Canali, D. Malavasi, B. Morten, M. Prudenziati, and A.Taroni, “Piezoresistive effect in thick-film resistors,” J. Appl. Phys., vol. 51, 3282, 1980. F. Carmona, R. Canet, and P. Delhaes, “Piezoresistivity in heterogeneous solids,” J. Appl. Phys., vol. 61, 2550, 1987. C. Herring and E. Vogt, “Transport and deformation-potential theory for many valley semiconductors with anisotropic scattering,” Phys. Rev., vol. 101, 944, 1956. R. J. Kennedy, W. G. Jenks, and L. R. Testardi, “Piezoresistance measurements of YBa2Cu3O7-x showing large magnitude temporal anomalies between 100 and 300 K,” Phys. Rev. B, vol. 40, 11313, 1989. R. W. Keyes, “The effects of elastic deformation on the electrical conductivity of semiconductors,” Solid State Phys., vol. 11, 149, 1960. W. P. Mason and R. N. Thurston, “Use of piezoresistive materials in the measurement of displacement, force, and torque,” J. Acoust. Soc. Am., vol. 10, 1096, 1957. Y. Onuma and K. K. Kamimura, “Piezoresistive elements of polycrystalline semiconductor thin films,” Sensors and Actuators, vol. 13, 71, 1988. K. Rajanna, S. Mohan, M. M. Nayak, and N. Gunasekaran, “Thin film pressure transducer with manganese film as the strain gauge,” Sensor and Actuators, vol. A 24, 35, 1990. H. A. Sauer, S. S. Flaschen, and D. C. Hoestery, “Piezoresistance and piezocapacitance effect in barium strontium titanate ceramics,” J. Am. Ceram. Soc., vol. 42, 363, 1959. C. S. Smith, “Piezoresistance effect in germanium and silicon,” Phys. Rev., vol. 94, 42, 1953