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This module covers the diffused resistor and sheet resistance.

Sometimes, in a circuit design, we will need a resistor. This is usually made either with poly or with a diffusion . If we took our n-tank or similar n-type diffusion, we could make a long narrow strip of it, anduse it as a resistor. As long as we keep the substrate at ground, and any voltages on the resistor greater than ground,the n-p junction will be reverse biased and the resistor will be isolated from the substrate. Now we all know

R ρ L A L n q μ t W

A diffused resistor

The only trouble is, what is n for a diffused resistor? A quick look at the chart showing carrier concentration as a function of depth after a diffusion shows that when we do a diffusion, n is not a constant, but varies as we go down into the wafer. We will have to do some kind ofintegral, assuming lots of parallel, thin resistors, each with a different carrier concentration! This is not very satisfactory.

In fact, it is so unsatisfactory that IC engineers have come up with a better description resistance thanone involving n and μ . Note that we could write as

R 1 n q μ t L W
We define the first fraction (which contains the carrierconcentration, thickness etc.) as the sheet resistance R s of the diffusion. While this can be more-or-less predicted, it is usually also a post-fabrication measured value.
R s 1 n q μ t
R s has units of "ohms/square", and you are probably tempted to ask "per square what?". Well it can be any square atall, cm,μm, km, since all we really need to know is R s and the length to width ratio of the resistor structure to find the resistance of a resistor. We do not needto know what units are used to measure the length and the width, so long as they are the same for both. For instance if theresistor in has a sheet resistivity of 50Ω/square, then by blocking the resistor off into squares W x W in dimension, we see that the resistor is 7 squares long ( ) and so its resistance is given as:
R 50 Ω square 7 squares 350 Ω

Counting the squares

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Source:  OpenStax, Introduction to physical electronics. OpenStax CNX. Sep 17, 2007 Download for free at http://cnx.org/content/col10114/1.4
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