Biomedical Engineering Reference
In-Depth Information
affects the band gap
2
, making it easier (or harder, depending on the material and strain)
for electrons to be raised into the conduction band. This results in a change in resistivity
of the semiconductor.
From the macroscopic point of view, the change in resistance is linearly related to the
applied strain, according to:
R
R
=
G
L
L
where
R
is the resistance,
L
is the length, and the constant,
G
, is the gauge factor of a
piezoresistor. By rearranging the above equation, an explicit expression for
G
is derived
as follows:
R
/
R
L
/
L
=
R
εR
G
=
where
ε
is the strain.
The resistance of a resistor is customarily measured along its longitudinal axis. Exter-
nally applied strain, however, may contain three primary vector components, one along
the longitudinal axis of a resistor and two arranged 90
◦
to the longitudinal axis and each
other, which results in two gauge factors. Longitudinal and transverse gauge factors are
different for any given piezoresistive material. For polycrystalline silicon, the transverse
gauge factor is generally smaller than the longitudinal one.
The piezoresistive effect of semiconductors has been used for sensor devices employing
all kinds of semiconductor materials, such as germanium, polycrystalline silicon, amor-
phous silicon, and single crystal silicon. Due to the magnitude of the piezoresistive effect
in silicon, this semiconductor has attracted much attention in the research and development
of sensor devices. Piezoresistors have also been successfully employed in the development
of various strain gauges and force sensors. Single-crystal and polycrystalline silicon are
used for manufacturing semiconductor strain gauges by selectively doping silicon [16 - 19].
2.7.1 Conductive Elastomers, Carbon, Felt, and Carbon Fibers
Conductive elastomers are insulating rubbers, either natural or silicone based, which are
made conductive by adding particles of conducting or semiconducting materials such
as silver or carbon. Most of these forms of conductive rubbers show little change in
bulk resistance as they are compressed. However, area of contact and hence inverse
contact resistance can be made to vary with applied force. An example of a sensor
using conductive elastomers described by Hillis [20] is shown in Figure 2.8. At a certain
threshold force, the conductive elastomer makes contact with the electrode. Additional
force increases the area of contact and thus reduces the contact resistance.
Larcombe [21] has described piezoresistive sensors constructed by sandwiching carbon
felt and carbon fibers between metal electrodes, as shown in Figure 2.9. As the load
increases, the carbon fibers are compacted together, making more electrical contacts and
reducing the felt resistance. At loads in excess of 5 kg, the area of contact between
2
A band gap or energy gap is an energy range in a solid where no electron states can exist. The band gap is
a major factor determining the electrical conductivity of a solid. Substances with large band gaps are generally
insulators and those with smaller band gaps are semiconductors.
