For the past five decades, computers have progressed on a predictable trajectory, doubling in speed roughly every two years in tune with Gordon Moore’s oft-cited observation-turned-prophecy. Although semiconductor scaling continues to yield performance gains, many perceive a tipping point is nigh, where the cost-benefit analysis of further miniaturization breaks down.

The latest researcher to weigh in on this tipping point, commonly referred to as the death of Moore’s law, is University of Michigan computer scientist Igor Markov. In a recent article in the journal Nature, Markov tackles the issue not just in terms of the physical limits of integrated-circuit scaling, but as a culmination of various limiting factors in the areas of manufacturing, energy, physical space, design and verification effort, and algorithms. With consideration of these limitations, as well as to emerging alternative technologies, Markov outlines “what is achievable in principle and in practice.”

“What are these limits, and are some of them negotiable?” he asks. “On which assumptions are they based? How can they be overcome?”

“Given the wealth of knowledge about limits to computation and complicated relations between such limits, it is important to measure both dominant and emerging technologies against them.”

Advanced techniques such as “structured placement,” shown here and developed by Markov’s group, are currently being used to wring out optimizations in chip layout. Different circuit modules on an integrated circuit are shown in different colors. Algorithms for placement optimize both the locations and the shapes of modules; some nearby modules can be blended when this reduces the length of the connecting wires.

Credit: Jin Hu, Myung-Chul Kim, Igor L. Markov (University of Michigan)

The Nature article addresses the more obvious physical limitations in materials and manufacturing as well as limits related to design and validation, power and heat, time and space, and information and computational complexity. Markov recounts how certain previous limits were circumvented, and compares loose and tight limits. An overview of emerging technologies includes the reminder that these can also indicate as yet unknown limits.

“When a specific limit is approached and obstructs progress, understanding the assumptions made is key to circumventing it,” remarks an NSF writeup of the research. “Chip scaling will continue for the next few years, but each step forward will meet serious obstacles, some too powerful to circumvent.”

“Understanding these important limits,” says Markov, “will help us to bet on the right new techniques and technologies.”