Metal Strain Gauge
`
`Related terms:
`
`Semiconductor, Resistors, Gauge Factor, Piezoresistor, Semiconductor Strain
`Gauge, Strain Gauge, Metal Foil, Piezoresistive Sensor, Resistance Change
`
`Mechanical transducers: Cantilevers, acoustic wave
`sensors, and thermal sensors
`John X.J. Zhang, Kazunori Hoshino, in Molecular Sensors and Nanodevices
`(Second Edition), 2019
`Metal strain gauges
`Metal strain gauges are also commonly used. They are typically a winding pattern
`of etched metal wire on a flexible polyimide film. The copper-nickel alloy is among
`the commonly used materials. Unlike semiconductor strain gauges, metal strain
`gauges change their resistance due to geometry changes. Although metals also
`show some piezoresistive effects, they are usually very small compared to those of
`semiconductors. As shown in Fig. 6.21, when the wire experiences a tensile strain,
`it becomes longer and the cross-sectional area becomes smaller, both of which
`contribute to the increase in the resistance, and vice versa for a compressive strain.
`
`Fig. 6.21. Metal strain gauge.
`
`One typical configuration for the metal strain gauge is composing a half bridge
`using two gauges with one attached on the top side and the other on the back with
`both being near the base of the cantilever (see Fig. 6.15 for strain distribution in a
`
`Samsung Electronics Co. Ltd. et al v. Neodron Ltd
`Exhibit 2003
`IPR2020-00308
`
`

`

`cantilever). One experiences largest tensile strain, while the other experiences the
`largest compressive strain with the same magnitude. See Problems 6.11 and 6.12.
`
`Read full chapter
`URL: https://www.sciencedirect.com/science/article/pii/B9780128148624000065
`
`Introduction to MEMS Devices
`
`Minhang Bao, in Analysis and Design Principles of MEMS Devices, 2005
`§1.1.1 Piezoresistance Effect
`(1) Metal Strain Gauge
`The metal strain gauge was discovered long before the discovery of the
`piezoresistance effect in semiconductors and has still been widely used for
`mechanical transducers in industries. Due to the affinity between metal strain
`gauge sensors and piezoresistive sensors, the metal strain gauge is first briefly
`introduced in this section.
`Consider a metal filament with a circular cross section. If the radius of the cross
`section is r, the length of the filament is l and the resistivity of the material is ρ, the
`resistance of the filament is R=ρl/πr . If the filament is stretched by an external
`2
`force F, the stress in the filament is T=F/πr and the strain (the relative elongation)
`2
`in the filament is ε≡ Δl/l=T/E, where E is the Young's Modulus of the material. As
`metal is usually a polycrystalline material with a fine grain structure, its mechanical
`and electrical properties are isotropic. Thus, the relative change in resistance
`caused by the force is
`
`As well known in mechanics, the longitudinal stretch of a filament is always
`accompanied with it a lateral contraction, i.e. Δr/r = −v(Δl/l), where v is the Poisson
`ratio of the material. For most materials, vhas a value of about 0.3. Thus we have
`
`Usually, the relative change of resistivity, Δρ/ρ, is a function of stress/strain and is
`expressed as πT = πEε, where π is the piezoresistive coefficient of the material.
`Therefore, we have
`
`where G, the relative change in resistance per unit strain, is referred to as the
`gauge factor, or, G factor, of the filament.
`As π is negligible for metal materials, the gauge factor is just a little larger than
`unity, i.e., G ≈ 1 + 2v = 1.5
` 2.0. As the maximum strain of the gauge is in the
`order of 10 , the relative change of the resistance is also in the order of 10 .
`−3
`−3
`(2) Strain Gauge Sensors
`Strain gauges can be made of metal foil as well as metal wire. Fig. 1.1.1(a) and (b)
`schematically show a force sensor using four metal foil strain gauges as sensing
`elements. The strain gauges R
` R are glue-bonded onto the metal beam
`1
`4
`supported by a metal cylinder. The strain gauges are interconnected into a
`Wheatstone bridge as shown in Figure 1.1.1(c). As the output of the bridge, ΔV, is
`proportional to the force F, a force sensor is formed.
`
`Samsung Electronics Co. Ltd. et al v. Neodron Ltd
`Exhibit 2003
`IPR2020-00308
`
`∼
`∼
`ɛ
`ɛ
`ɛ
`