Does such a device exists to measure voltage and current in 14nm and below semiconductors?
Yes, this is SEM (scanning electron microscope) equipped with 3-axis nanomanipulator(s). They are commercially available as together with SEM, as as separate module.
\$\begingroup\$ Do the nanomanipulators need to be adjusted to the process size eg. 14, 12, 7, 5 or 3 nm? \$\endgroup\$ Jul 24, 2022 at 11:35
2\$\begingroup\$ those numbers are just numbers they don't actually measure anything. \$\endgroup\$ Jul 24, 2022 at 12:08
4\$\begingroup\$ Minimum contact pad size which it can probe depends on mover accuracy and probe (needle) tip radius. You can easily find these parameters in catalogues. In usual integrated circuits there are no suitable parts less than about 50-100 nm, i think, because usually we probe metallic tracks an pads (very large), not FET gates which are passivated by silicon oxide layer(s). \$\endgroup\$– VladimirJul 24, 2022 at 12:42
There is a product called a "picoprobe" which has very fine tungsten needles with a tip that is about 1 um in diameter. This is moved with a 3-axis "micromanipulator" to touch the desired point on a chip.
The desired point is usually covered in oxide (SiO2) or other non-conductive material and this has to be scratched off first. This is sometimes possible by 'hammering' on it or scratching with the tungsten needle, but in newer technologies (< 250 nm) the dimensions are so small that this is not practical.
Note that frequently the node that you want to measure is buried below other metal layers and not frequently accessible. A Focused Ion Beam (FIB) machine can mill away portions of the upper layers (metal and oxide) to expose the node; it can the deposit metal and a larger pad to allow the microprobe to connect.
This allows voltages to be measured. Many circuits cannot drive even the tiny loading that such a probe adds, so there are limitations on the capability. Current could be measured by using 2 connections, but this is cumbersome.