Piezoresistive+sensing

Piezoresistive+sensing - Piezoresistive sensing SEN2MET...

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Piezoresistive sensing SEN2MET
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Piezoresistive sensing •Piezoresistivity in Si discovered by C. S. Smith in 1954 •Is today one of the most important sensing schemes in micro systems •The metal strain gauge discovered earlier resembles the metal strain gauge utilized in mechanical transducers •Much larger effect in silicon than metal F l D l 2r Gauge factor Piezoresistive coefficient Poisson ratio Strain
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Resistivity tensor -1 In metals the conductivity/resistivity is isotropic For single crystal materials e.g. Si the conductivity/resistivity are generally anisotropic First rank tensor Second rank tensor Oversimplified definition: Nth rank tensor has 3 N components Resistivity tensor Conductivity tensor
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Resistivity tensor -2 Lars Onsager’s reciprocity theorem from 1931: Given a thermodynamic phenomenological equation between a flux and field: Then the coefficients of the phenomenological equations are symmetrical As a consequence both the conductivity tensor and the resistivity tensor is symmetrical ! Educated at NTH(NTNU) Nobel Price in Chemistry in 1968
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Resistivity tensor -3 For Si with cubic symmetry and no stress present we have: The resistivity tensor is isotropic for cubic symmetry and no stress present Stress free tensor
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Piezoresistive coefficient tensor -1 The stress tensor in a crystalline material causes a change of the resistivity tensor Stress free contribution Change due to stress introduced Piezoresistive coefficient tensor. Rank?
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Piezoresistive coefficient tensor -2 Introduce relative change of resistivity: Fourth rank tensor Second rank tensor
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For Si there are only 3 independent coefficients of the piezoresistive tensor. This due to the cubic symmetry of the Si lattice
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Piezoresistive+sensing - Piezoresistive sensing SEN2MET...

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