Uncertainty models improve
system design
ne
of the most promising applications of micro-fabrication technology is
in the development of small, ultra-fast mechanical switches called radio-frequency
microelectromechanical (RF-MEMS) switches. These switches have applications
in radio and communication and, says Assistant Professor Matt
Allen, they even could replace transistors in some applications,
potentially reducing the power consumption in cell phones and other
portable electronic devices.
As is the case with many emerging technologies, researchers must overcome
a number of hurdles associated with the micro-switches—not least
of which is developing a switch that is durable enough for the applications.
Among those hurdles is switch
failure. Based on their tests, researchers at Sandia National Laboratories
have suggested that large forces can be developed in the switches if
they close too quickly. As a result, the switches fail prematurely.
In soon-to-be published research,
Allen and a group of Sandia researchers reveal that fabricators actually
can worsen the problem if they don’t pay careful attention to
uncertainty and variability in the switches. “The processes used
to create these switches lead to significant uncertainties in their
dimensions—as one might expect, considering that they are trying
to control the thickness of parts that measure only a few microns, or
less than a tenth of the diameter of a human hair,” says Allen.
Allen’s group of researchers
was charged with predicting the performance of these switches and improving
the design. They created a model for the dimensional uncertainty in
the switches and then used that model to predict the performance of
an ensemble of nominally identical switches. “One key was developing
a model that captured the dominant physics, yet could be evaluated quickly
so that the performance of hundreds of randomly selected switches could
be evaluated,” says Allen.
By reducing the computation
time of their models from hours to seconds, Allen and his colleagues
were able to predict switch performance and explore a number of alternative
designs.
The design of these micro-mechanical
switches is simple: a thin gold plate held above a set of electrical
contacts by four leaf springs. An electrostatic force pulls the plate
down to the contacts, closing the circuit. As the plate approaches the
contacts, that force becomes stronger and the plate accelerates.
Sandia researchers discovered
a strong correlation between switch life and the plate speed as it reaches
the electrical contacts. So, the solution seemed simple. Rather than
just turning on the voltage that closes the switch, they delivered a
voltage pulse that moved the switches just enough that they coasted
to an almost-closed position. “Then they would turn on a voltage
that was just sufficient to hold the switches there,” says Allen.
The idea works great, he says, if you’re only dealing with one
switch with known dimensions. But over hundreds of switches on an array,
these critical dimensions vary widely—as well as the distance
that the switch has to move. “It’s kind of like landing
an airplane and not knowing how far away the ground is,” says
Allen.
It turns out that because the voltage shape the designers originally
proposed caused only a small fraction of the switches to close softly,
the rest would experience even higher forces than they would have if
the voltage had not been shaped at all.
To correct that problem, Allen and his colleagues modeled not only the
nominal switch, but an ensemble of switches from the manufacturing process,
by using random variables for the switch dimensions and properties.
“So now, rather than having a switch with thickness t and height
above the contacts h, we have random values there,” says Allen.
He
and his colleagues reviewed several methods for analyzing this model
and settled on creating a model that approximated the physics of the
system in known ways, rather than approximating the effect of uncertainty.
Because the model was small enough, the group could apply very robust
statistical methods that could accurately deal with the complicated,
nonlinear system. Then, they ran a simulation of an entire batch of
random switches in a matter of minutes, enabling them to test changes—for
example, a different design for the switch, or a manufacturing process
revision—that might improve the switch design or performance.
“We were able to explore different designs and predict, quantitatively
how much they would improve the performance,” says Allen.
With Sandia researchers Jordan Massad, Richard Field and Christopher
Dyck, Allen is the lead author of a paper about the modeling work that
will appear in the Journal of Vibration and Acoustics.
