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    The confinement effect in thin(and small width) metal tracks?

    "The electrical resistivity of metallic conductors is increased
    compared to the bulk resistivity if the diameter of the
    wire is in the range of or smaller than the mean free path of
    the electrons ~about 40 nm for copper at room temperature!."
    from: DOI: 10.1103/PhysRevB.66.075414

    My questions:

    1. Do EDAs include/recognize the confinement effect in thin(and small) metal tracks during resistance calculation/extraction?

    2. If yes, can confinement-effect-included resistance be represented as a sheet resistance which is included in the technology file? because so far what I know/consider/keep in mind during layout making is only the sheet resistance, capacitance, and design rules.

    3. What is the smallest metal tracks in advance node, let's say in 7 nm node?


    Quantum confinement:
    https://en.wikipedia.org/wiki/Potent...um_confinement
    https://en.wikipedia.org/wiki/Quantu...semiconductors
    https://www.researchgate.net/post/Wh...inement_effect

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  2. #2
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    Re: The confinement effect in thin(and small width) metal tracks?

    There are several effects affecting resistivity of narrow width (and small height) wires - surface scattering, grain size and structure, cladding (liner) layer (having much higher resistivity versus core), etc.
    PDKs (Process Design Kits) take into account all of these effects, by measuring wire (and via) resistivity for different widths, contexts (line width / spacing / density / upper and lower metal layers, etc.), temperatures, etc. - and creating multi-dimensional tables, that are used by parasitic extraction tools.
    Metal resistivity is defined either as volume resistivity or sheet resistvity, depending on process and on foundry.

    According to public data, metal pitch in 7nm process is about 40nm:

    https://en.wikipedia.org/wiki/7_nanometer


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    Re: The confinement effect in thin(and small width) metal tracks?

    @timof
    Thank you.
    Your answer really connect the dots.

    Is there any information about the height in that tech node?
    Or at least the ratio, whether height>width or the opposite.



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  4. #4
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    Re: The confinement effect in thin(and small width) metal tracks?

    Quote Originally Posted by melkord View Post
    @timof
    Thank you.
    Your answer really connect the dots.

    Is there any information about the height in that tech node?
    Or at least the ratio, whether height>width or the opposite.
    I would say, that the height is larger than the width in lower metal layers in N7 - judging by SEM/TEM images people publish in their papers.
    But the metal height is a top secret information, guarded by the foundries, this info (along with many other important pieces of information about MEOL/BEOL stack) is encrypted in the tech files / PDK that fabless companies receive from the foundries.


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