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Process Variations and Probabilistic Integrated Circuit Design pp 11–67Cite as

Physical and Mathematical Fundamentals

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Abstract

This chapter provides a short overview on the basics of CMOS transistor modeling with respect to deep submicron requirements and mathematical approaches to analyze variations in the design process. Technical terms are going to be defined and explained; physical processes and mathematical theories will be illustrated.

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Notes

  1. 1.

    Whether the symbol y refers to the value or to the function should be evident from the context.

  2. 2.

    \(\frac{1} {{\sigma }^{2}} \sim {\Sigma }^{-1}\) and erf\(\left ( \frac{c} {\sqrt{2}}\right ) = \mathcal{P}\left (\frac{1} {2}, \frac{{c}^{2}} {2} \right ).\)

  3. 3.

    PCA can be applied in the same manner.

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Authors and Affiliations

  1. MunEDA GmbH, Stefan-George-Ring 29, 81929, Munich, Germany

    Bernd Lemaitre

  2. Design Automation Division EAS, Fraunhofer Institute for Integrated Circuits IIS, Zeunerstraße 38, 01069, Dresden, Germany

    Christoph Sohrmann, Lutz Muche & Joachim Haase

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  1. Bernd Lemaitre
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  3. Lutz Muche
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Correspondence to Bernd Lemaitre .

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  1. Integrierte Schaltungen, Institutsteil Entwurfsautomatisierung, Fraunhofer -Institut fur, Zeunerstr. 38, Dresden, 01069, Germany

    Manfred Dietrich

  2. Integrierte Schaltungen, Institutsteil Entwurfsautomatisierung, Fraunhofer -Institut fur, Zeunerstr. 38, Dresden, 01069, Germany

    Joachim Haase

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Lemaitre, B., Sohrmann, C., Muche, L., Haase, J. (2012). Physical and Mathematical Fundamentals. In: Dietrich, M., Haase, J. (eds) Process Variations and Probabilistic Integrated Circuit Design. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6621-6_2

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