• Pixel-art sticker of Gapsy, personifying Band Gap, with the caption "Mind The Gap."

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Gapsy

Band Gap Physics

\[\lambda_{\max} = \frac{hc}{E_g}\]
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Meet Gapsy, who minds the gap: in a semiconductor, electrons need at least the band-gap energy to jump into the conduction band, and a photon with less energy does nothing. For silicon, a gap of about 1.12 eV means only light shorter than about 1.11 µm can lift an electron across. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Gapsy, a semiconductor with a gap she won't let small photons cross.

In a solid, electrons can only have energies inside allowed bands. In a semiconductor the valence band is nearly full and the conduction band nearly empty, and between them lies a forbidden band gap of energy E_g. To free an electron so it can carry current, something must lift it across that gap. A single photon can do it only if its energy hc/λ is at least E_g, so there is a longest useful wavelength, λ_max = hc/E_g.

For silicon, E_g is about 1.12 electronvolts at room temperature, which gives λ_max of about 1.11 micrometres, in the near infrared. Light at longer wavelengths passes through silicon without being absorbed this way.

This one number shapes a lot of technology: it sets which colours a silicon solar cell or camera sensor can use, and why LEDs made of different semiconductors glow in different colours.

Silicon's gap is indirect, which makes absorption near the edge weak, and the gap shifts slightly with temperature, so the cutoff is softer than a single number suggests.

Equations

\[\lambda_{\max} = \frac{hc}{E_g}\]
Symbols
SymbolMeaningUnit
\(\lambda_{\max}\) longest wavelength that can lift an electron across the gap \(\mathrm{m}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(E_g\) band-gap energy \(\mathrm{J}\)