Piezoresistive coefficient

In bulk material, the resistivity is independent of crystal orientation because silicon is cubic. However, if the carriers are constrained to travel in a very thin sheet, eg, in an inversion layer, the mobility, and thus the resistivity, become anisotropic (18). Mobility is also sensitive to both hydrostatic pressure and uniaxial tension and compression, which gives rise to a substantial piezoresistive effect. Because of crystal symmetry, however, there is no piezoelectric effect. The resistivity gradually decreases as hydrostatic pressure is increased, and then abrupdy drops several orders of magnitude at ca 11 GPa (160,000 psi), where a phase transformation occurs and silicon becomes a metal (35). The longitudinal piezoresistive coefficient varies with the direction of stress, the impurity concentration, and the temperature. At about 25°C, given stress in a (100) direction and resistivities of a few hundredths of an O-cm, the coefficient values are 500—600 m2/N (50—60 cm2/dyn). 

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. 

Sensitivity Middle A R — l/2RA(mu 7144= Piezoresistive coefficient Low 7r44= One sixth of single-crystal silicon High High Low... 

The sensitivity of a piezoresistive pressure sensor depends on the piezoresistive coefficient. Silicon crystal face selection and gage layout on the crystal face are important because of the anisotropy of the piezoresistive effect. Silicon (100) and (110) are often used with P-type diffused resistors to achieve a desired sensitivity. The next consideration is the thermal stress effect originating from the silicon crystal face. Fig. 7.3.5 shows the stress-distribution maps for silicon (100) and silicon (110) by the finite element method (FEM). 

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. 

The automotive applications of semiconductor pressure sensors utilizing the large piezoresistive coefficient of silicon have been greatly expanded, owing to the following three advantages. 

Since the relationship between the change of the gauge relative resistance and the measured pressure is given by Eq. (4.53), then the slope of the calibrating diagram represents the piezoresistive coefficient K. 

Semiconductors. Semiconductor strain gauges are also available. These operate on the same piezoresistive effect that applies to metal strain gauges. This effect incorporates the change in electrical resistivity of a material due to an applied stress. The piezoresistive coefficients of germanium and silicon can be extremely high, with gauge factors up to 175 as compared to 2-5 for metallic wires. 

Comparisons of published results suggest that capacitive sensing is as good or better than alternative techniques, including tunnelling, piezoresistive, and piezoelectric interfaces [2], Other attractive features of capacitive interfaces include compatibility with many sensor fabrication processes, low temperature coefficient, and low power dissipation. 

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