DOCUMENTA MATHEMATICA, Vol. Extra Volume: Optimization Stories (2012), 401-415

Raúl Rojas

Gordon Moore and His Law: Numerical Methods to the Rescue

In this chapter we review the protracted history of «Moore's Law», that is, the expected doubling of the number of transistors in semiconductor chips every 18 months. Such an exponential increase has been possible due to steady improvements in optical imaging methods. The wavelength of light used for photolithography has been reduced every decade, but it is reaching tough limits. Mathematical methods capable of simulating optical systems and their interference properties play now a significant role in semiconductor design and have kept Moore's Law alive for at least the last ten years. As we show, advances in semiconductor integration and numerical optimization methods act synergistically.

2010 Mathematics Subject Classification: 00A69, 01A61

Keywords and Phrases: Fourier optics, photolithography, Moore's law, numerical simulation

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