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/um^{2}). Moreover, be aware of bottom plate capacitance that can be large and which limits capacitor performance.
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List of capacitors:

MIM (metalinsulatormetal or MOM – metaloxidemetal)

parameters:

typical capacitance: 2 fF/um^{2}

temperature coefficient TCC: 3050 ppm/^{o}C

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 metal2metal1 capacitor. This parasitic capacitance may be even in the range of 80100% of the targeted capacitance value.

vertical (stacked metal layers, e.g. metal2metal3metal4) structures, called sandwich structure, can be used to increase the capacitance from the single area

horizontal (e.g. metal2metal2) 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: 110 fF/um^{2}

transistor must be kept in strong inversion, otherwise the obtained capacitance is small, lossy, nonlinear – see the picture here:
http://images.slideplayer.com/13/4145276/slides/slide_22.jpg

NMOS in Nwell 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 (polypoly capacitor or polyinsulatorpoly)

parameters:

temperature coefficient TCC: ~20 ppm/^{o}C

voltage coefficient VCC: ~10 ppm/V

matching: 0.1% (large area polypoly 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:
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 firstorder correction where a value between H and 2H is added to each W and L. When choosing 2H, the capacitance equations changes to:
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Reactance
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Impedance
j indicates that voltage V across capacitor lags capacitor current by 90 degress.
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Quality factor
where

ω – angular frequency

C – capacitance

X_{C} – capacitive reactance

R_{C} – 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 RadioFrequency Integrated Circuits, 2003