Hi,

There are 2 effects that come into play:

1. The charge fluctuations in the channel due to trapping may be referred to the gate, thus dividing the current power
spectral density by Cox^2 when you try to obtain input-referred voltage power spectral density of the noise. More
W*L => more Cox.

2. As the gate area increases, more and more traps are active in contributing 1/f noise. Thus, the 1/f noise as an ensemble
average is reduced compared to the noise of a single trap.  Thus, for most cases excepting extremely tiny gate areas, the
noise contribution will smoothly go down as gate area is reduced. For the limiting case of a very small gate area, if there
is no trap, there will be absolutely no noise due to trapping, and if there is a single trap, then its noise will be higher than what
you may expect from the standard formula.

Note that the exact origins of 1/f noise are not completely understood. Some people (foundries) will give you a formula
for 1/f where the noise goes down only as 1/L, and not as 1/sqrt(W.L). Also note that the happy situation of reduced 1/f noise
(gate-referred) as more and more traps contribute is not seen in the time domain. You can average for all you want without
reducing 1/f noise.

Regards
Vivek

Hi F117,

I am not sure if I understand your statement correctly, but here is an attempt to answer it:

1. Each trap operates independent of all the others. Hence, the overall effect is ensemble averaged. For instance, not
all traps may be trapping and releasing the charges at the same time. The trap density is typically constant for a given
process and so for moderate-large gate areas, increasing the overall gate area gradually increases number of traps. As
the trap action can be considered as charge fluctuations in the channel, these can be referred back to the gate.
In summary:

in^2 = K. (WL), where K is some constant
vn^2 (at gate) = in^2/Cgate^2 => vn^2 = K/(W.L)

This is the principal reason why you have smaller 1/f voltage noise when the gate area is increased.

2. For very small gate area, there may be no trap. However, if there is a single trap for a very small gate, it causes
more noise. For example, if the trap density is 2 traps/10 (um)^2, then the average number of traps for a 1 (um)^2 gate
would be 0.2 . However, for any specific gate, you will either have a trap or not have a trap (assuming no more than 1 trap
for a small gate). Thus, the noise from having a trap is higher than the average prediction. Note that the numbers quoted here
are not realistic.

3. To remove 1/f noise, you need to use some form of autozeroing such as correlated double sampling or chopper stabilization,
both of which will result in circuit overhead and more thermal noise.

You can find more information by searching for these topics in the previous posts.

Regards
Vivek