Tags: capacitor, CMOS, equations, impedance, quality factor, parameters, reactance, silicon

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Types of capacitors

Any layer can be used to form capacitor. However, dielectrics between layers are rather thick to reduce capacitance between layers. Hence, the capacitance is small (tens of aF/um2). Moreover, be aware of bottom plate capacitance that can be large and which limits capacitor performance.

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List of capacitors:

  • MIM (metal-insulator-metal or MOM – metal-oxide-metal)

    • parameters:

      • typical capacitance: 2 fF/um2

      • temperature coefficient TCC: 30-50 ppm/oC

        • is dominated by TC of the oxide’s dielectric constant itself

      • matching: good

    • additional mask required

      • oxides between metal layers are thick to create small capacitances between metals in order to isolate one metal path from another. Hence, additional mask is used to indicate that oxides between metal layers should be thinner. Consequently, MIM capacitors are useful.

    • used in RF circuits due to excellent RF characteristics

    • important in CMOS processes where only one poly layer is available (most digital processes)

    • extremely large bottom plate parasitic capacitance for metal2-metal1 capacitor. This parasitic capacitance may be even in the range of 80-100% of the targeted capacitance value.

    • vertical (stacked metal layers, e.g. metal2-metal3-metal4) structures, called sandwich structure, can be used to increase the capacitance from the single area

    • horizontal (e.g. metal2-metal2) structures can also be used

    • both horizontal and vertical structures can be implemented in one capacitor to use both lateral and vertical flux

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  • MOS transistor

    • gate capacitance serves as capacitor

    • typical capacitance: 1-10 fF/um2

    • transistor must be kept in strong inversion, otherwise the obtained capacitance is small, lossy, non-linear – see the picture here:

      http://images.slideplayer.com/13/4145276/slides/slide_22.jpg

      • NMOS in N-well is used to allow lower voltage operations

    • thin gate transistors (lower power supply) has higher capacitance per unit area than thick gate transistors (higher power supply)

    • thickness of gate oxide is very small thus high capacitance per unit area may be achieved. Moreover, the gate capacitance is produced with special care resulting with high quality oxide.

    • used as cap to ground or vdd. Sometimes used as floating cap, but only for small frequencies.

    • sometimes available in bipolar processes (emitter diffusion serves as source and drain)

    • to maximize quality factor Q, minimum length L should be used

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  • PIP (poly-poly capacitor or poly-insulator-poly)

    • parameters:

      • temperature coefficient TCC: ~20 ppm/oC

      • voltage coefficient VCC: ~10 ppm/V

      • matching: 0.1% (large area poly-poly capacitors)

    • used as floating capacitors

    • oxide between poly1 and poly2 may be almost as thin as the gate oxide

    • the bottom plate parasitic capacitance (between poly1 and substrate) may be very large (e.g. 20% of the desired capacitance value)

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Parameters

Capacitor parameters:

  • capacitance per unit area

  • temperature coefficient TCC

  • voltage coefficient VCC

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Capacitor equation

Q = C U

I = C dU/dt

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Capacitance

Capacitance equation:

capacitors - capacitance equation

The above equation does not take fringing into account. However, it is accurate as long as W and L dimensions are much larger than the distance between capacitor plates. In cases, where it is not satisfied, the fringing may be taken into account by a rough first-order correction where a value between H and 2H is added to each W and L. When choosing 2H, the capacitance equations changes to:

capacitors - capacitance equation more

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Reactance

capacitors - reactance equation

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Impedance

capacitors - impedance equation

-j indicates that voltage V across capacitor lags capacitor current by 90 degress.

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Quality factor

 capacitors - quality factor equation

where

  • ω – angular frequency

  • C – capacitance

  • XC – capacitive reactance

  • RC – series resistance of the capacitor

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Parasitic resistance of a capacitor can be represented by series or parallel resistor:

https://en.wikipedia.org/wiki/Capacitor#/media/File:Capacitor_equivalent_circuits.svg

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The quality factor Q of a capacitor is the ratio of its reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the capacitor, the closer it approaches the behavior of an ideal, lossless, capacitor.

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Resources:

  • Baker R. Jacob, CMOS Circuit Design, Layout, and Simulation, 3rd Edition, 2010, John Wiley & Sons

  • Lee T. H., The Design of CMOS Radio-Frequency Integrated Circuits, 2003