555 timer to measure variable capacitance
Your measurement problem requires more precision that a 555 with any real-world capacitances and any real-world silicon tolerances will offer. So, I'm afraid this approach is a dead end.
Much, much worse:
When trying to measure femtofarad, you'll have to learn that basically anything you can do to connect your measurement device to the object under test will have its own capacitance that is unknown and orders of magnitude larger in its uncertainty than what you want to measure. You can't (usually, without knowing a lot more) even calibrate that.
So, your &quot;I insert a signal externally&quot; approach, no matter how fast a pulse you can generate, can't work (and no, your 555 + Arduino approach isn't even remotely appropriate for short pulses).
I've seen the same being done for Terahertz-absorbing Bolometers, to measure the changing parameters of teeeny tiny pieces of material.
You rely on the parasitic inductance due to your &quot;thing's&quot; (whatever you want to measure) geometry, and then observe how dampened their oscillating response is to RF energy.
That's the kind of ideas you need to come up with. You need to ask much &quot;higher-up&quot; questions, like, &quot;how does one measure femtofarad capacitances of {describe your thing}&quot;, not &quot;can I use a shovel and a duck to measure femtofarad capacitances of this thing I do not mention&quot;.
To give you a bit of relation:
DRAM cells, which just measure whether a capacitor is charged or not, are in your order of capacitance. To enable that, you need to basically combine the readout transistor with the capacitance in a single, sub-micrometer structure on a silicon die. That thing can't estimate the capacitance by any means, it will just tell you whether the charge exceeded a relatively unclear threshold.