A scanning tunnelling microscope sees atoms. Why does a tiny gap change so much?
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Answer: Exponential current
Exponential current ✓ — Correct. STM works because tunnelling current depends exponentially on the tip-sample distance, so an angstrom-scale height change can strongly change current. Some teaching texts estimate a 1 angstrom gap change can shift current by about an order of magnitude. That turns quantum leakage into a topographic ruler.
Surface heat damage — Heating the surface would usually be a nuisance, not the measurement principle. STM uses a small voltage and current feedback, and it needs conducting or semiconducting samples. The nice twist is that the microscope maps absence: a vacuum gap with no classical wire still carries a measurable quantum current.
Lens magnification — A normal lens is not what gives STM atomic sensitivity. The tip is brought extremely close to a conducting surface, and the electronics keep the tunnelling current near a target value. Unlike optical microscopy, the resolution comes from the steep distance dependence of electron tunnelling.
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