# MOS Capacitance and Performance

I was learning about the advantages and challenges in scaling down MOS transistors. I came across this statement in Wikipedia :

The main device dimensions are the transistor length, width, and the oxide thickness, each (used to) scale with a factor of 0.7 per node. This way, the transistor channel resistance does not change with scaling, while gate capacitance is cut by a factor of 0.7. Hence, the RC delay of the transistor scales with a factor of 0.7.

Reduction in RC delay means improvement in switching speed.

But as per my understanding, capacitance per unit area is given by the relation C = eps/Tox, where eps is the epsilon and Tox is the oxide thickness. So when Tox is reduced, C increases, which in turn should increase the delay. But what wikipedia says is opposite.

So my question is, how scaling down the transistor reduces the capacitance?

Any good reference or link also will be appreciated.

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The general formula for calculating capacitance is:

$C=\dfrac{\epsilon \times A }{D}$

Where A is the area of the capacitor's plates, and D is the distance between each plate. In terms used for designing a transistor, we would make the following substitutions:

$C = \dfrac{\epsilon \times W \times L}{t_{ox}}$

Where W and L are the Width and Length of the transistor, and tox is the oxide thickness (distance between capacitor plates). If we were to scale all three by a factor of n, then we would see the following:

$C_{new} = \dfrac{\epsilon \times 0.7W \times 0.7L}{0.7t_{ox}} = 0.7\dfrac{\epsilon \times W \times L}{t_{ox}}$

$C_{new}=0.7 \times C_{old}$

This scaling doesn't end up changing the channel resistance, because both the width and the length are scaled. Examining the MOSFET drain current expression, we can see that the current (and effectively the channel resistance) is not affected by scaling both the width and length simultaneously.

$i_D=0.5\dfrac{W}{L}k_n^'(V_{GS}-V_{th})^2$

As a result, scaling reduces the total circuit capacitance while maintaining equivalent drive strength. Note the (used to) in the Wikipedia article - as the feature sizes have shrunk to about 90 nm, this relationship with oxide thickness has become more complicated.

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 +1- that is great. Thank you. – Abid Rahman K Aug 5 '12 at 4:15