Page 223 - Electrical Properties of Materials

Gas sensors 205

which can be rearranged as
p is Poisson’s ratio.
Fractional resistance change dR/R dρ/ρ
= =1 + 2p + . (9.31)
Strain dL/L dL/L
The last term on the right-hand side is called the gauge factor,
dρ/ρ
G = . (9.32)
dL/L

For p-type silicon this factor can be between 100 and 200. Of course, for a
metal G ∼ 0 and, since the other two terms on the right-hand side of eqn (9.31)
are of the order of unity, the gauge factor gives a measure of the increased sens-
itivity of strain gauges since semiconductor strain gauges became generally
available.
Piezoresistive strain gauges convert mechanical strain into a change in
resistance. If a piezoresistor is incorporated into one arm of a Wheatstone
bridge, this change may in turn be converted into a voltage. Piezoresistors
therefore provide a simple method of readout in a variety of silicon-based
physical sensors in which the measurand is arranged to generate a mechan-
ical strain in a flexible element such as a beam or a diaphragm. Examples
include strain sensors, pressure sensors, and accelerometers fabricated by using
microelectromechanical systems technology (see Section 9.26).

9.20 Measurement of magnetic field by the Hall effect
We can rewrite the Hall-effect equation (1.20) in terms of the mobility and of
E l , the applied longitudinal electric field, as

E H = BE l μ. (9.33)

Hence, B may be obtained by measuring the transverse electric field, the sensit-
ivity of the measurement being proportional to mobility. One semiconductor is
quite outstanding in this respect, n-type indium antimonide. It has an electron
2
–1 –1
mobility of about 8 m V s , an order of magnitude greater than GaAs and
about fifty times greater than Si. In general, this is a simpler and more sensit-
ive method of measuring a magnetic field than a magnetic coil fluxmeter, and
the method is particularly useful for examining the variation of magnetic field
over short distances, because the semiconductor probe can be made exceed-
ingly small. The disadvantages are that the measurement is not absolute, and
that it is sensitive to changes in temperature.

9.21 Gas sensors
A quite sophisticated effect is that traces of particular oxidizing, reducing, or
other reactive gases will modify device performance, for example by changing
the conductivity of a semiconductor, such as doped tin oxide. This is a very
versatile ‘Varistor’, which can be doped to sense various gases. For example,
in its n-type form it has a lattice deficient in O. Oxygen is chemisorbed and re-
moves conduction band electrons by trapping them on the surface. A reducing