The fundamental limit defines the minimum amount of energy needed to perform the most basic computing operation: binary logic switching that changes a 0 to a 1 or vice-versa. This limit provides the foundation for determining a set of higher-level boundaries on materials, devices, circuits and systems that will define future opportunities for miniaturization advances possible through traditional microelectronics -- and its further extension to nanoelectronics.

"Future opportunities for gigascale integration (chips containing up to a billion devices) and even terascale integration (chips containing trillions of devices) will be governed by a hierarchy of physical limits," said James D. Meindl, professor of electrical and computer engineering and director of the Microelectronics Research Center at the Georgia Institute of Technology. "We now know the fundamental limit on microelectronics and where we are relative to it."

Meindl explained the limits and their implications February 16 in a seminar on nanotechnology held at the 167th annual meeting of the American Association for the Advancement of Science (AAAS) in San Francisco.

Meindl and collaborator Jeffrey A. Davis reported in the October issue of IEEE Journal of Solid State Circuits that the fundamental limit depends on just a single variable: the absolute temperature. Based on this fundamental limit, however, engineers can derive a hierarchy of limits that are much less absolute because they depend on assumptions about the operation of devices, circuits and systems.

The researchers studied the fundamental limit from two different perspectives: the minimum energy required to produce a binary transition that can be distinguished, and the minimum energy necessary for sending the resulting signal along a communications channel. The result was the same in both cases.

The fundamental limit, expressed as E(min) = (ln2)kT, was first reported 50 years ago by electrical engineer John von Neumann, who never provided an explanation for its derivation. (In this equation, T represents absolute temperature, k is Boltzmann's constant, and ln2 is the natural log of 2).

Though this fundamental limit provides the theoretical stopping point for electrical and computer engineers, Meindl says no future device will ever operate close to it. That's because device designers will first bump into the higher-level limits -- and economic realities.

For example, electronic signals can move through interconnects no faster than the speed of light. And quantum mechanical theory introduces uncertainties that would make devices smaller than a certain size impractical. Beyond that is a more important issue -- devices operating at the fundamental limit would be wrong as often as they are right.

"The probability of making an error while operating at this fundamental limit of energy transfer in a binary transition is one-half," Meindl noted. "In other words, if you are operating just above the limit, you'll be right most of the time, but if you are operating just below it, you'd be wrong most of the time."

What does this mean for electronic and computer engineers?

"We can expect another 10 to 15 years of the exponential pace of the past 40 years in reducing cost per function, improving productivity and improving performance," Meindl said. "There will be lots of problems to solve and inventions that will be needed, just as they have over the past four decades."

He expects the world's use of silicon will follow the pattern set by its use of steel. During the second half of the 19th century, steel use increased exponentially as the world built its industrial infrastructure. Growth in steel demand fell after that, but it remains the backbone of world economies, though other materials increasingly challenge it.

"In the middle of the 21st century, we are going to be using more silicon than we are now, by far," he predicted. "There will be other materials that will come in to replace it, like plastics and aluminum came in to push steel out of certain applications. But we don't know yet what will replace silicon."

Though the limits provide a final barrier to innovation, Meindl believes economic realities will bring about the real end to advances in microelectronics.

"What has enabled the computer revolution so far is that the cost per function has continued to decrease," he said. "It is likely that after a certain point, we will not be able to continue to increase productivity. We may no longer be able to see investment pay off in reduced cost per function."

Beyond that point, designers will depend on nanotechnology for continuing advances in miniaturization.

"What happens next is what nanotechnology research is trying to answer," he said. "Work that is going on in nanotechnology today is trying to create a discontinuity and jump to a brand new science and technology base. Fundamental physical limits encourage the hypothesis that silicon technology provides a singular opportunity for exploration of nanoelectronics."

Related Links
Beyond a Profound and Pervasive Impact
Microelectronics Research Center at GIT
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