Researchers find way to design nonsticky MEMS

Researchers find way to design nonsticky MEMS

New mathematical tool can solve Casimir-force equations for any number of objects, with any conceivable shape

Researchers at the Massachusetts Institute of Technology have developed a powerful new mathematical tool for calculating the effects of Casimir forces, the complex quantum forces that affect objects when they are extremely close. The discovery, which has ramifications for basic physics, can change the way in which microelectromechanical systems (MEMS) are designed and improve their reliability.

Using the tool, one of the researchers discovered a way to arrange tiny objects so that Casimir forces, which are the ordinarily attractive, become repulsive. Thus engineers could design MEMS devices so that Casimir forces would prevent their moving parts from sticking together, rather than causing them to stick, which may substantially reduce failure rates. It could also help enable new, affordable MEMS devices for use in medical or scientific sensing and microfluidics.

Creating the tool was not a simple matter. In the 1960s, physicists developed a mathematical formula that, in principle, describes the effects of Casimir forces on any number of tiny objects, with any shape. But in the vast majority of cases, that formula remained impossibly hard to solve.

“People think that if you have a formula, then you can evaluate it. That’s not true at all,” says Steven Johnson, an associate professor of applied mathematics, who helped develop the new tools. “There was a formula that was written down by Einstein that describes gravity. They still don’t know what all the consequences of this formula are.” For decades, it was the same for the formula for Casimir force; physicists could solve it for only a small number of cases, such as that of two parallel plates.

More recently, researchers have found ways to solve the formula for other configurations. For instance, in 2006, MIT physics professors Robert Jaffe and Mehran Kardar and Thorsten Emig of the University of Köln in Germany showed how to calculate the forces acting between a plate and a cylinder; the next year, they demonstrated solutions for multiple spheres. But a general solution remained elusive.

In a paper published last month in Proceedings of the National Academy of Sciences , Johnson, physics Ph.D. students Alexander McCauley and Alejandro Rodriguez (the paper’s lead author), and Professor John Joannopoulos describe a way to solve Casimir-force equations for any number of objects, with any conceivable shape.

The breakthrough resulted from the researchers’ insight that the effects of Casimir forces on objects 100 nm apart can be modeled precisely using objects and distances 100,000 times larger in a conductive fluid. This simplified calculations, and the researchers proved the computations were mathematically equivalent. For objects with odd shapes, calculating electromagnetic-field strength in a conducting fluid is still fairly complicated, but it can be done using off-the-shelf engineering software.

In one geometry for achieving Casimir repulsion (a), an elongated metal particle is placed above a thin metal plate with a hole; the idealized version is the limit of an infinitesimal particle polarizable only in the z direction. At z = 0, vacuum-dipole field lines (b) are perpendicular to the plate by symmetry, and so dipole fluctuations are unaffected by the plate (shown here for ω = 0). The particle-plate interaction energy U(z) U(∞∞) is graphed in (c); energy is zero at z = 0 and as z goes to ∞, and attractive for z >> W, so there is Casimir repulsion (negative slope) close to the plate. The new tool for calculating Casimir forces for any geometries can affect design of MEMS devices such as that in (d). (Photo courtesy of Sandia National Laboratories)

Diego Dalvit, a Casimir forces specialist at the Los Alamos National Laboratory, notes that with the new technique, “in principle, you can tackle any geometry. And this is useful. Very useful.” Since Casimir forces can cause the moving parts of MEMS to stick together, Dalvit says, “One of the holy grails in Casimir physics is to find geometries where you can get repulsion,” which is what the new techniques allows. In a separate paper published in March, physicist Michael Levin of Harvard University’s Society of Fellows, together with the MIT researchers, described the first arrangement of materials that enable Casimir forces to cause repulsion in a vacuum (see figure ).

The tools by themselves cannot create geometries that cause repulsion. Physicists using the new technique must still rely on intuition when devising systems of tiny objects with useful properties, Dalvit notes. “Once you have an intuition of what geometries will cause repulsion, then the [technique] can tell you whether there is repulsion or not,” Dalvit says. For more information, call Alejandro Rodriguez at 617-253-4780 or e-mail alexrod7@mit.edu.

Richard Comerford