Page 258 - Mechanics of Microelectromechanical Systems

4. Microtransduction: actuation and sensing 245
microcantilever, two situations are possible, in terms of the direction of the
external magnetic field. When the field is parallel to the polarization
direction, as indicated in Fig. 4.53 (a), the piezomagnetic layer will stretch
and the bimorph will bow downward. When the external magnetic field is
perpendicular to the polarization direction, as shown in Fig. 4.53 (b), the
piezomagnetic material will contract and will bow the bimorph upward. The
material properties that define the coupled magnetic-mechanical behavior of
a piezomagnetic material are generally determined experimentally, and the
strain of Eq. (4.144) can be found as a function of the applied magnetic field.
An example of piezomagnetic bimorph will be solved next.

Example 4.16
Find the tip bending moment produced by an amorphous negative
piezomagnetic bimorph when the external magnetic field acts as shown in
Fig. 4.53 (b). Assume that the polysilicon substrate is individually heated by
The induced strain has a value of for a field of H =
1000 Oe. The thicknesses of the two layers are and and
the common width is The elastic properties are: and
and the coefficient of linear thermal expansion is
for the polysilicon.

Solution:
The deformation of this bimorph is the one sketched in Fig. 4.53 (a)
because the piezomagnetic material is negative and has the opposite reaction
compared to a positive material under identical external magnetic influence.
The interface strain equation is in this case:

By coupling this equation with the curvature radius Eq. (4.134) – where
– and the moment equilibrium Eq. (4.132), the equation of the tip
bending moment becomes:

and its numerical value is

8.5 Shape Memory Alloy (SMA) Bimorph

An SMA bimorph is formed of a layer of shape memory alloy (sputter-)
deposited over a substrate layer. The following scenario can be envisioned
for actuation: the bimorph is heated from a temperature to a temperature