Introduction: Seeing Atoms
The Scanning Tunneling Microscope (STM), invented in 1981, uses quantum tunneling to image surfaces at atomic resolution. It earned Binnig and Rohrer the 1986 Nobel Prize.
How It Works
- Sharp metal tip brought within ~1 nm of surface
- Voltage applied between tip and sample
- Electrons tunnel through vacuum gap
- Tunneling current measured: \(I \propto e^{-2\kappa d}\)
- Feedback loop adjusts tip height to maintain constant current
- Tip height recorded as surface topology
The Sensitivity
Current changes by factor of ~10 for each 0.1 nm change in gap!
This extraordinary sensitivity comes from the exponential dependence of tunneling.
Worked Example
With work function \(\phi \approx 4\) eV (typical metal):
\[\kappa \approx \frac{\sqrt{2m\phi}}{\hbar} \approx 10^{10} \text{ m}^{-1}\]For \(d = 0.5\) nm: \(I \propto e^{-10} \approx 5 \times 10^{-5}\)
For \(d = 0.6\) nm: \(I \propto e^{-12} \approx 6 \times 10^{-6}\)
Current drops 10× for 0.1 nm change!
The Quantum Connection
The STM is quantum mechanics made practical. It images individual atoms, can manipulate single atoms, and probes electronic structure. The famous IBM logo made of individual xenon atoms was created using STM atom manipulation. Quantum tunneling went from theoretical curiosity to revolutionary technology.