Page 274 - Microsensors, MEMS and Smart Devices - Gardner Varadhan and Awadelkarim

254 MICROSENSORS

Table 8.6 Some mechanical characteristics of three different microflexures
Parameter Hammock Folded Crab-leg
Bending deflection y Axial and bending Bending stress Bending stress
stress
Spring constant k y Nonlinear in y Constant and Constant and
independent of y independent of y
Axial deflection x Axial stress only Axial and bending Axial and bending
stress stress
Spring constant k x Stiff: 4E mA/l Quite stiff Stiff

Table 8.7 Some important mechanical parameters and material properties that define the dynamic
deflection of microflexures

Parameters/properties Nature
Point/distributed force, torque, stress, pressure Load applied/measurand
Width, breadth, thickness, length Size of structure
Young's modulus, yield strength, buckling strength, Material properties
Poisson's ratio, density, viscosity, friction
Spring constant, strain, mass, moment of inertia, natural Calculable parameters
frequency, damping coefficient
Lateral/vertical deflection, angular deflection, resonance, Response
bandwidth

Table 8.6 provides the characteristic properties of these flexures, in which their dynam-
ical response is much more complicated than that of a simple end mass and is often
determined using computational methods, for example, a finite-element or finite-difference
analysis.
When designing dynamic structures, we need to consider some additional parameters,
which are listed in Table 8.7.

8.4.4 Mechanical Microstmctures

The two most important questions that now need to be asked by the designer are as follows.
First, if these mechanical structures can be made on the micron scale and second, if they
still follow classical theory, for example, the linear theory of elasticity.
We know that microbeams, microbridges, and microdiaphragms can all be made in
silicon using the bulk- and surface-micromicromaching techniques, which were described
in Chapters 5 and 6. In fact, a number of worked examples of the process flow to fabricate
the following microstructures were given:
• A cantilever beam made of undoped silicon (WE 5.1)
• A thin cantilever beam (WE 5.4)

• A free-standing polysilicon beam (WE 6.1)
• An array of thin diaphragms/membranes (WE 5.3)
• A comb resonant structure (WE 6.7)