Understanding Smart Sensors - Nomads.usp

The Nature of Semiconductor Sensor Output 517060ER+∆R R+²RR−∆RR-²R R−∆RR+²RR+∆REoOutput (in mVdc)50403020100010203040506070Column252° CColumn + 1253° CColumn − 404° C80 90 100110SpanOutputOffsetPressure differential (in kPa)(a)(b)Figure 3.1 (a) Wheatstone bridge and (b) output curve for piezoresistive pressure sensor.used and provides temperature compensation that is independent of the supplyvoltage.Different approaches to piezoresistive strain gauges range from traditionalbonded and unbonded to the newest integrated silicon pressure sensors. Pressureapplied to the diaphragm produces a change in the dimension of the diaphragm,an increase in the length of the gauge (l ), and a change in its resistance(R = rl /A, where R is the resistance of the gauge, r is the resistivity of the material,l is the length of the resistive element, and A is the cross-sectional area).The change in length per unit length is the strain. The sensitivity of a straingauge is indicated by the gauge factor (GF), which is defined by:KR R= ∆ /∆l / l(3.2)where K = p ⋅ e = the gauge factor, p is the piezocoefficient, and e is the modulusof elasticity for the material.K for metals is 2; for silicon, it is approximately 100 to 200, dependingon the doping level and the design [2]. In contrast to metals, the change inresistance is a secondary effect for silicon. The primary effect is the change inconductivity of the semiconductor material due to its dependence on mechanicalstress.The GF for a strain gauge is improved considerably (to about 150) byusing a silicon strain gauge. However, besides the conventional resistive Wheatstonebridge, silicon processing techniques and the miniature size of piezoresistiveelements in silicon enable the design of a unique piezoresistive sensor. This