PORTLAND, Ore. — Sensor manufacturers have continued to improve the sensitivity of their designs through engineering innovations derived from trial-and-error experimentation. Electrical engineers have been guided by "black art" principles, which sensor-gurus claim in abundance. Unfortunately, no overarching framework has been available that incorporates these principles into a methodology for new sensor designs.

Now EEs at Purdue University (West Lafayette, Ind.) claim to have invented that missing framework, providing a new method of modeling sensor designs that is already solving long-standing puzzles.

"Other groups have come up with a whole array of conflicting principles regarding how to make better sensors," said Ashraf Alam, an EE and professor of electrical and computer engineering at Purdue. "But we have unified those principles in a systematic way, so that now there is a consistent framework regarding how to make sensors better." He performed the research with his student, an EE doctoral candidate, Pradeep Nair.

To test their sensor design principles, the researchers addressed the issue of which nanoscale sensor designs are optimal for sensor applications where target molecules stick to the sensing element. EEs have long known that when sensing individual molecules—from smoke detectors to biological and chemical sensors—the smaller the sensing element, the better. The reason smaller is better, however, has been only anecdotally related to how diffusion of the target molecule limits the speed at which a sensor can act.

Alam and Nair, however, now claim to have provided a theoretical solution to this puzzle that they subsequently verified by experiment. First, the researchers compared a traditional flat planar sensor element with a cylindrical single-nanotube sensor element. The results showed that the smaller cylindrical sensor was at least 100 times more sensitive—more than could be accounted for by conventional smaller-is-better theories.

"We were surprised to see that the cylindrical sensor is orders of magnitude more sensitive than planar sensors," said Alam.

The reason why was even more surprising. EEs have often speculated that nanoscale sensors were better because the sensing element was closer in size to the molecules being detected—that the so-called "swamping effect" of a large planar sensor could be mitigated by making the sensing element smaller. But the Purdue EEs said that is not the reason.

The reason that nanoscale cylindrical sensors are better than flat planar sensors, they said, is that the target molecules can diffuse onto the surface of the planar sensor only from the "front" side, whereas the cylindrical nanotube has no "front," thus canceling out the slowing effect of diffusion.

"What happens when you have a small cylindrical sensor like a nanotube or nanowire is that the molecules you are trying to sense can come from any direction—which per unit area makes it more likely to sense a molecule than a traditional planar sensor," said Alam.

Because cylindrical nanoscale sensors were known to be more sensitive, but were hard to make, some sensor designers have resorted to nanocomposite (also called nanonet) sensing elements that utilize multiple cylindrical nanotubes or nanowires grown in a bushy jumble-of-nanowires that resembles the opening move in the game of "pick-up sticks."

"Several manufacturers are using these pick-up-stick-like sensors—some claiming they are even better than single cylindrical sensors," said Alam. "But we found that while these sensors were better than planar sensors, they were not as good as the single nanowire sensor."

To prove their case mathematically, the researchers modeled both sensors. However, the jumble-of-nanowires was impossible to model accurately with traditional techniques, so the researchers invented a Cantor transformation to simplify the process.

The Cantor set, invented by mathematician Georg Cantor, averages results by iteratively removing the middle one-third of a data set—that is, after the middle third is removed, then the middle third of the two remaining thirds is removed, and the process repeats until you get down to individual observations.

By transforming their modeling data into a Cantor set, performing the simulation, then transforming the results back, they were able to simplify the simulation enough for it to be run on the nanoHub—an Internet-based parallel processor that is part of Purdue's Network for Computational Nanotechnology.

"We showed that the Cantor set has the same fractal dimension as the pick-up-stick sensors, so that any problem you want to solve about that sensor might as well as solved on the Cantor set, and the results will be the same," said Alam.

The EEs also investigated nanodot sensors because their spherical shape would appear to enable even more sensitivity than a cylindrical sensor, since molecules can collide and become attached to a sphere from even more directions than a cylinder. However, Alam and Nair's model showed that there was no great advantage to spherical nanodot sensors over cylindrical nanowires or nanotubes.

"We found that both the cylindrical and spherical sensors have comparable sensitivity—there is not as much difference as you would think," said Alam.

Currently, the researchers are using their model to discover a sensor architecture that can detect DNA sequences electronically, so that genome sequencing can be more easily automated.

"Today, genome sequencing depends on chemical detection of molecules, which is slow and cumbersome," said Alam. "What we are trying to do is invent a sensor that can electrically detect molecules types, for faster and more efficient genome sequencing."

This research was funded by the National Science Foundation and the National Institute of Health, as well as by Purdue's Network for Computational Nanotechnology and its Birck Nanotechnology Center.