Yeah, this week I've restarted my scanning tunnel microscope that I'm failing to make work for years... The current one is a standard pair of long metal bars with the piezoelectric component on one end, with 2 screws, and a 3rd screw on the other end.
My problem is that it doesn't matter how I design the thing, either the screws offer too little precision so I can't help but to crush the tip into the sample every time, or too little travel distance so I can't help but crush the tip into the sample when adjusting the coarser screws near the tip. This is the kind of thing that looks like a non-problem on the web, because everybody just ignores this step.
It sounds like you need to add a "stage" to help position your sample. Flexures are systems that bend to perform motion, and can do surprising things that you can't do with joined together machined pieces.
Here's an open source stage project using flexures that will likely help
I'm a fan of this project, but flexures are antithetical to an STM assembly. And STM needs very rigid components, the smallest vibration can interact with the height adjustment and push the tip into the sample.
But it's a great assembly for anything that doesn't have a feedback on the positioning.
Adding another step (not a problem, just maybe a solution), a quick estimate says that if I place a few kHz signal at the sample, it will induce enough current at the tip to be detected by the preamp when the distance reaches the micrometers. That's the same range you want to stop the approximation, so it may be a nice proximity signal.
In the future, if you'd like even more precise measurements, theoretically you could use 2 different frequencies or a reflected source, and look at the interference or superposition of the waves.
I'm by no means an expert in this, but I've heard that optical measurement (eg: laser + Michelson interferometer) could theoretically take you down to the nanometer range.
Digital micrometers are expensive, but you can get analog ones on AliExpress [1] or other places for around $10. Of course, the precision may not be as good as name-brand (eg: Mitutoyo) tools.
If you have machining/fabrication skills, it might also be possible to buy a few worm gear sets and modify your micrometer to move really slowly but precisely.
My problem is that it doesn't matter how I design the thing, either the screws offer too little precision so I can't help but to crush the tip into the sample every time, or too little travel distance so I can't help but crush the tip into the sample when adjusting the coarser screws near the tip. This is the kind of thing that looks like a non-problem on the web, because everybody just ignores this step.