Page 215 - An Introduction to Microelectromechanical Systems Engineering

194 MEM Structures and Systems in RF Applications

An optimal solution is to make the spring beams short, thick, and wide, but within
the constraint of the spring constant. The resistance can also be kept to a minimum
by the use of a highly conductive metal.
Design and fabrication so that the top plate moves as desired present a particular
challenge due to the effects of stress. Similar challenges are faced by other freestand-
ing micromachined structures, making this a subject worth exploring. The use of
straight beam springs, such as those shown in Figure 7.2(b), does not allow stress
relief. Compressive residual stress can cause the plate to flex upward or downward,
while tensile residual stress increases the voltage that must be applied to cause a
given amount of plate motion. Even if the plate material is deposited with a low
residual stress, differential thermal expansion between the freestanding structure
and the substrate results in stress that varies with temperature (e.g., many consumer
products are specified to operate over wide range from –20º to +40ºC). Differential
thermal expansion problems for this type of design can be avoided by choosing sub-
strate and structural materials with the same coefficient of thermal expansion, such
as single-crystal silicon and polycrystalline silicon. Because silicon is neither a good
insulator nor a good conductor, this approach is not adequate if the design requires
an insulating substrate and a highly conducting capacitor to minimize losses, as dis-
cussed earlier.
Several different designs have been made in attempts to reduce the effects of
stress and simultaneously achieve a high Q. The design shown in Figure 7.2(c) uses
LPCVD polysilicon springs and top plate, with the beam springs laid out in a T
shape in an attempt to relieve stress, but fabricated structures were still warped at
room temperature [8]. A thin layer of gold on top of the polysilicon lowers the resis-
tance, giving a Q of 20 at 1 GHz and a self-resonant frequency above 6 GHz for a
2-pF capacitor. The measured tuning range is 1.5:1 at 4V. In general, a single mate-
rial should be used if it is desired that a freestanding structure remain flat; the metal
on silicon used in this capacitor imparts an undesired curvature to the plate as the
temperature varies.
The design in Figure 7.2(d) uses sputtered aluminum for the top plate and
springs, with a sacrificial photoresist layer that is removed in an oxygen plasma [5].
The circularly oriented L shape of these springs allows the plate to rotate to give some
relief of both residual and temperature-induced stresses. Even with this design, how-
ever, plate warpage was sufficiently large that only capacitors smaller than 200 µm
on a side could be used, so several small capacitors are wired in parallel. Capacitors
with a nominal 2.1-pF value have a Q of 62 at 1 GHz and a tuning range of 1.16:1 at
5.5V. An aluminum ground plane under the bottom plate, traces, and bond pads
shields the silicon substrate, reducing eddy-current loss. As there is also capacitance
that does not vary with voltage between the traces and the ground, the maximum
possible tuning range with a higher voltage is less than 1.5:1. Unlike the polysilicon-
based capacitor described earlier, the use of low-temperature process steps allows
integration of such capacitors on wafers with previously fabricated circuitry.
The design in Figure 7.2(e) [7] uses electroplated gold for the plate and springs,
with a sacrificial PECVD oxide layer etched in hydrofluoric acid followed by super-
critical drying (see Chapter 3). In contrast to the other designs, the anchor is in the
center of the structure, which allows the outer edge of the plate to freely expand or
contract in order to relieve both residual and thermal stresses. A bond wire to the