Page 45 - An Introduction to Microelectromechanical Systems Engineering

24 Materials for MEMS

material “remembers” its original shape after being strained and deformed. The dis-
covery was first made in a gold-cadmium alloy in 1951 but was quickly extended to
a broad range of other alloys, including titanium-nickel, copper-aluminum-nickel,
iron-nickel and iron-platinum alloys. A basic understanding of the underlying physi-
cal principles was established in the 1970s, but extensive research remains ongoing
in an effort to develop a thorough theoretical foundation. Nonetheless, the potential
applications for shape-memory alloys abound. It has been estimated that upwards of
15,000 patents have been applied for on this topic. Titanium-nickel alloys have been
the most widely used of shape-memory alloys because of their relative simple com-
position and robustness.
An important factor that determines the practical utility of the alloy is its transi-
tion temperature. Below this temperature, it has a low yield strength; in other words,
it is readily deformed into new permanent shapes. The deformation can be 20 times
larger than the elastic deformation. When heated above its transition temperature,
the material completely recovers its original (high-temperature) shape through com-
plex changes in its crystal structure. The process generates very large forces, making
shape-memory alloys ideal for actuation purposes. By contrast, piezoelectric and
electrostatic actuators exert only a fraction of the force available from a shape-
memory alloy, but they act much more quickly.
Bulk titanium-nickel alloys in the form of wires and rods are commercially avail-
able under the name Nitinol™ [16]. Its transition temperature can be tailored
between –100° and 100°C, typically by controlling stoichiometry and impurity con-
centration. Recently, thin titanium-nickel films with thicknesses up to 50 µm were
successfully demonstrated with properties similar to those of Nitinol. Titanium-
nickel is a good electrical conductor, with a resistivity of 80 µΩ•cm, but a relatively
poor thermal conductor, with a conductivity about one tenth that of silicon. Its yield
strength is only 100 MPa below its transition temperature but rapidly increases to
560 MPa once heated above it. The Young’s modulus shows a similar dependence
on temperature; at low temperatures, it is 28 GPa, increasing to 75 GPa above the
transition temperature.

Important Material Properties and Physical Effects

The interaction of physical parameters with each other—most notably electricity
with mechanical stress, temperature and thermal gradients, magnetic fields, and
incident light—yields a multitude of phenomena of great interest to MEMS. We will
briefly review in this section three commonly used effects: piezoresistivity, piezoelec-
tricity, and thermoelectricity.

Piezoresistivity
Piezoresistivity is a widely used physical effect and has its name derived from the
Greek word piezein meaning to apply pressure. Discovered first by Lord Kelvin in
1856, it is the phenomenon by which an electrical resistance changes in response to
mechanical stress. The first application of the piezoresistive effect was metal strain
gauges to measure strain, from which other parameters such as force, weight, and
pressure were inferred (see Figure 2.4). Most the resistance change in metals is due to