Page 275 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

MECHANICAL SENSORS 255

Table 8.8 Some mechanical properties of bulk materials used to make micromechanical sensors
Material Property Si (SC) Si (poly) SiO 2 Si 3N 4 SiC Diamond Al PMMA
Young's modulus (GPa) 190 a 160 73 385 440 1035 70 -
Yield strength (GPa) 6.9 6 8.4 14 10 53 0.05 0.11
Poisson's ratio 0.23 0.23 0.20 0.27 - - 0.35 -
Fracture toughness 0.74 — — 4-5 3 30 30 0.9-1
2
(MN/m )
Knoop hardness 0.8 0.8 3.5 7.0
2
9
(10 kg/m )
"For [111] Miller index (168 GPa for [110], 130 GPa for [100]). Shear modulus 58 GPa for [111], 62 GPa for
[110], and 79 GPa for [100]
Clearly, the microstructures can then be fabricated from single-crystal silicon, polycrys-
talline silicon, and also from metals and other types of material. The processes shown also
demonstrate that the residual strain is negligible because the cantilevers and diaphragms
shown are neither curling nor buckling when free from any external load.
Table 8.8 summarises the mechanical properties of some of the materials that have
been used to make micromechanical structures and are important in their practical design
and usage. Other important physical properties of these materials, such as density, thermal
conductivity, and heat capacity, may be found in the Appendices F (metals), G (semicon-
ductors), and H (ceramics and polymers).
As stated in Table 8.8, the question that must be asked is whether a material behaves
on the micron scale in the same way as it does on the macro scale? The answer to this
important question is 'yes' for pure single-crystal silicon. In this case, there are very few
defects and so structures on the micron scale have the same fundamental properties as on
the large scale. In fact, the same rule also applies for polycrystalline materials provided
the average grain size is much smaller than the smallest dimension of the microstructure.
As the typical grain size in low-pressure chemical vapour deposition (LPCVD) polysilicon
is 50 to 80 nm, the material will behave elastically down to about the micron level. The
same rule can be applied to other polycrystalline materials, such as metals.
Accordingly, we can apply classical geometric scaling rules to structures down to a
few microns in size without a breakdown in the laws. For example, a reduction in the
size of a cantilever structure will increase its resonant frequency by a factor K but reduce
3
its mass by K , deflection by K, spring constant by K, and so on.
Finally, we must consider the types of transducer for a microstructure that convert its
deflection into an electrical quantity. There are a number of different ways in which the
movement could be detected such as

• Capacitive (electrostatic) pickup

• Resistive (conductive) pickup
• Inductive (amperometric) pickup

The two most commonly used forms of transduction are capacitive and resistive.
Figure 8.25 shows a microflexure in which its end is capacitively coupled to a stationary
sense electrode.