The Tunnelling Microscope

Plate 38 speaks for itself: “Ten times less current per tenth of a nanometre.”

The Physics

Electrons tunnel through the vacuum gap between a sharp tip and a surface. The current falls exponentially with the gap, so a tenth of a nanometre changes it about tenfold, giving atomic resolution.

I ∝ e^(−2κd), κ = √(2 m_e φ) / ħ

• I: tunnelling current, A
• κ: decay constant, m⁻¹
• d: tip–sample gap, m
• m_e: electron mass, kg
• φ: work function (barrier height), J (quoted in eV)
• ħ: reduced Planck constant, J s

φ = 4–5 eV: ×8 to ×10 per 0.1 nm. Binnig & Rohrer, IBM Zürich, 1981–82.

Honest caveat: 'Ten times' is the round figure; for a 4 eV barrier the factor is nearer eight.

Sources

• G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Phys. Rev. Lett. 49, 57 (1982).

On the poster

Plate 038, “The Tunnelling Microscope”: the pixel-art plate with its slogan “Ten times less current per tenth of a nanometre.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.