# Capacitance per unit area and CMOS case

In a modern 0.35μm CMOS processor, the gate oxide thickness is around 80Å = 8nm. This gives us a capacitance per unit area of $430nF/cm^2$

I am not getting how one gets this capacitance per unit area. Can anyone explain this? (i.e. how formula are constructed and used.)

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Perhaps electronics.stackexchange.com is a better home? –  Qmechanic Jan 13 '13 at 7:52

Capacitance of area A, dielectric thickness d is, $$C=\frac{\epsilon_{0}\epsilon_{r}A}{d}$$ where permittivity of free space is $\epsilon_{0}=8.85\times 10^{-12} {\rm~F/m}$ and the relative permittivity of silicon dioxide is $\epsilon_{r}=4.5$ at $f=1{\rm~kHz}$ (Kaye and Laby 14th edition). Put $A=1{\rm~cm}^{2}$, $d=8{\rm~nm}$ and one gets $C=498{\rm~nF}$. I guess the overestimate is because the relative permittivity is less at higher frequencies typical of ICs.