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Fundamentals of Electromigration

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Fundamentals of Electromigration-Aware Integrated Circuit Design

Abstract

This chapter investigates in detail the actual low-level migration processes. A solid grounding in the physics of electromigration (EM) and its specific effects on the interconnect will give us the knowledge to establish effective mitigation methods during the design of integrated circuits. We first explain the physical causes of EM (Sect. 2.1) and then present options to quantify the EM process (Sect. 2.2), which enable us to effectively characterize key aspects of the process and its effects. In Sect. 2.3, we introduce EM-influencing factors arising from the specific circuit technology, the environment, and the design. We then investigate detailed EM mechanisms with regard to circuit materials, frequencies, and mechanical stresses (Sect. 2.4). Since EM is closely related to thermal and stress migration that also occur in the conductors of electronic circuits, we examine their interdependencies (Sect. 2.5). Finally, Sect. 2.6 outlines the principles of a migration analysis through simulation. This honors the importance of finite element modeling (using the finite element method, FEM) in electromigration analysis and enables the reader to develop and apply similar modeling and simulation techniques.

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Notes

  1. 1.

    The crystal lattice of metals is built up of ordered metal ions with an “electron fog” in-between, consisting of shared free electrons. The terms metal atoms and metal ions are considered equivalent in this context.

  2. 2.

    The Boltzmann constant, which is named after Ludwig Boltzmann (1844–1906), is a physical constant relating the average kinetic energy of particles with the temperature.

  3. 3.

    Long-range order in a crystal means that atoms are organized in a periodic order across many atoms, such as in a periodic lattice.

  4. 4.

    The heat equation is a differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.

  5. 5.

    A duty factor is the fraction of one period in which a signal or system is active, i.e., it expresses the ratio of the positive pulse duration to the period. The duty factor is commonly scaled to the maximum of one. A duty cycle expresses the same notion; however, it is labeled as a percentage.

  6. 6.

    The skin effect is due to opposing eddy currents induced by the changing magnetic field resulting from the alternating current. This effect leads to a reduction in current from the outside to the inside of a metallic conductor as a function of the frequency and the electrical material constants of the conductor (permeability and conductivity).

  7. 7.

    Entropy is a measure of the “disorder” of a system. Hence, the more “ordered” or “organized” a system is, the lower its entropy. For example, building blocks that have been used to construct a wall are “highly organized” (i.e., they are arranged in a complex structure) and are thus in a low-entropy state. This state is achieved only by the input of energy. If this structure is left unattended, it will decay after a number of years, and the disorganized, high-entropy state will return (i.e., an unorganized heap of blocks).

  8. 8.

    Electron mobility is a measure of how quickly an electron can move through a material such as a metal or semiconductor, when pulled by an electric field.

  9. 9.

    The Korhonen model combines vacancy dynamics with stress development. It assumes that the recombination and generation of vacancies alter the concentration of the available lattice sites, which influences the hydrostatic stress distribution. Specifically, the loss of the available lattice sites increases the hydrostatic stress.

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  1. Electrical and Computer Engineering, Dresden University of Technology, Dresden, Saxony, Germany

    Jens Lienig & Matthias Thiele

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Lienig, J., Thiele, M. (2018). Fundamentals of Electromigration. In: Fundamentals of Electromigration-Aware Integrated Circuit Design. Springer, Cham. https://doi.org/10.1007/978-3-319-73558-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-73558-0_2

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