# Band gap A **band gap** is a range of energy in a solid for which no [[Electron|electron]] state exists. In a crystal the allowed energies form continuous bands, and the gap of interest is the one between the highest filled band and the lowest empty one; its width E_g, usually quoted in [[Electronvolt|electronvolts]], is the smallest energy that can lift an electron from the [[Electronic_band_structure|valence band]] into the conduction band and leave a mobile hole behind.[^openstax-v3-95] One number decides an unexpected amount: whether a material conducts at room temperature, what colour it is, what colour it emits, and what fraction of [[Sunlight|sunlight]] it can convert. In the microsim below the reader sweeps a photon-energy slider across the visible spectrum while a slab of material sits in the beam. Below its gap the slab is transparent, because no available transition can absorb the photon; above the gap it absorbs.[^spec-m39] The equation that answers is the absorption edge, `lambda_edge = h·c/E_g`, which in convenient units is 1,239.84 nm·eV divided by the gap in electronvolts.[^derived-bg][^openstax-v3-ch6] The presets are [[Silicon|silicon]] at 1.12 eV, gallium arsenide at 1.42, cadmium sulfide at 2.42, gallium nitride at 3.4 and [[Diamond|diamond]] at 5.5 eV, and their edges land at 1,107, 873, 512, 365 and 225 nm — opaque, opaque, yellow, colourless, colourless.[^derived-bg] A [[Light-emitting_diode|light-emitting diode]] reads the same equation backwards: an electron dropping across the gap emits a photon of that energy, so the emission colour is the gap. On the [[Materials_science]] flagship this article serves *The absorption edge* section of Part VII — Research, the third member of the shared C31 set: [[Electronic_band_structure|electronic band structure]] opens the gap, [[Doping_(semiconductor)|doping]] fills it with carriers, and this page turns its width into a wavelength. ## In semiconductor physics The gap is what separates the three electrical classes of solid, and it does so through an exponential rather than a threshold. The intrinsic carrier density carries E_g in the exponent, `n_i ~ exp(-E_g/(2·k·T))`, so a modest change in the gap is a vast change in conduction.[^openstax-v3-96] At 300 K the thermal energy kT is 25.9 meV, and the ratio E_g/kT is 43 for silicon and 213 for diamond; the exponential factor exp(−E_g/2kT) is 4×10⁻¹⁰ for silicon and 6×10⁻⁴⁷ for diamond.[^derived-bg] With a band-edge density of states of order 10¹⁹ per cubic centimetre, that leaves diamond one intrinsic carrier per 1.6×10²⁷ cubic centimetres — a cube some 12,000 kilometres on a side, comparable to the diameter of the Earth.[^derived-bg][^openstax-v3-appd] Nothing about diamond's bonding is qualitatively different from silicon's; the difference between an insulator and a semiconductor is a factor of five in one energy, amplified by an exponential. The same arithmetic explains why the semiconductor/insulator boundary is conventional rather than physical. A material with a gap of 3 eV is an insulator at room temperature and a semiconductor at 600 K; a material with a gap of 0.1 eV is a semiconductor at 300 K and nearly a metal. The [[Temperature|temperature]] at which a gap matters is the temperature at which kT becomes comparable to it, and for the gaps in ordinary use that temperature is far above room temperature — which is precisely why [[Doping_(semiconductor)|doping]], and not heating, is how carriers are put into a semiconductor. ### Direct and indirect band gap Where the valence maximum and the conduction minimum sit in the Brillouin zone matters as much as how far apart they are in energy. If both occur at the same wavevector, the gap is direct and a [[Photon|photon]] alone can carry an electron across it: photon momentum is negligible on the scale of the zone, so the transition is vertical on a band diagram and needs no third party. If the two extrema sit at different wavevectors the gap is indirect, and a photon cannot supply the momentum difference; a [[Phonon|phonon]] must be absorbed or emitted at the same time.[^openstax-v3-95] The consequence is a difference in rate, not in possibility. An indirect transition requires three bodies to meet instead of two, so it is orders of magnitude less probable, and the absorption edge of an indirect material rises gradually over hundreds of millielectronvolts instead of turning on sharply. Silicon is indirect and gallium arsenide is direct, and that single structural fact is why silicon dominates electronics and not [[Light-emitting_diode|light emission]]: an indirect material absorbs weakly, so a silicon cell must be hundreds of micrometres thick where a direct-gap cell needs a few, and it emits scarcely at all, because an excited electron in silicon has time to lose its energy as heat before it finds a phonon to help it radiate. The sim's presets do not distinguish the two cases — its edge is drawn as a step — and the article marks that simplification as ILLUSTRATIVE for the indirect materials in the list.[^spec-m39] ### Light-emitting diodes and laser diodes An LED is a [[P–n_junction|p–n junction]] driven so that electrons and holes are pushed into the same region and recombine there. Each recombination across a direct gap releases a photon of energy close to E_g, so the emission wavelength is hc/E_g and the colour is chosen by choosing the material.[^spec-m39] The design problem is therefore a materials problem: red needs a gap near 1.9 eV, green near 2.3, blue near 2.7, and each must be a direct-gap crystal that can be grown well enough, and doped both ways, to make a junction. Gallium nitride, with a gap of 3.4 eV in the ultraviolet, became important because alloying it with indium tunes the gap down through blue and green while keeping the gap direct; a white LED is then a blue emitter behind a phosphor that converts part of the blue to longer wavelengths. A laser diode is the same junction with two additions: enough carrier density that the population across the gap is inverted, so stimulated emission outruns absorption, and an optical cavity to feed the emitted light back through the gain region. Both additions reward a direct gap for the same reason the LED does, and the threshold current is the price of reaching inversion. ### Photovoltaic cells In a solar cell the gap sets two losses that pull against each other. Every photon with energy below E_g passes through unabsorbed and is lost entirely; every photon above E_g is absorbed, but the excess above E_g is given up to the lattice as heat within picoseconds, so only E_g of each absorbed photon's energy is available. Raising the gap therefore increases the energy recovered per photon while decreasing the number of photons collected, and lowering it does the reverse.[^spec-m39] The optimum for a single junction lies in the near infrared, where silicon's 1.12 eV and gallium arsenide's 1.42 eV both sit; silicon's absorption edge at 1,107 nm marks exactly where its collection stops.[^derived-bg] The way past the trade-off is to stop using one gap. A tandem cell stacks a wide-gap material on top of a narrow-gap one, so the top cell takes the blue photons at their full value and passes the red ones through to the cell beneath, and each junction sees only the part of the spectrum it handles well. The same logic sets the research interest in materials whose gap can be tuned continuously by composition, since a tunable gap is what makes a matched stack possible at all. ### List of band gaps The values below are the sim's presets, with the absorption edge computed from each.[^spec-m39][^derived-bg] The colour column is what the gap alone implies for a pure, defect-free crystal: the visible band runs from about 1.65 eV at 750 nm to 3.26 eV at 380 nm, so a gap below 1.65 eV absorbs the whole visible range and a gap above 3.26 eV absorbs none of it.[^derived-bg] | Material | E_g (eV) | λ_edge (nm) | Edge lies in | Appearance implied | |---|---|---|---|---| | Silicon | 1.12 | 1,107 | near infrared | opaque, metallic grey | | Gallium arsenide | 1.42 | 873 | near infrared | opaque | | Cadmium sulfide | 2.42 | 512 | green | yellow–orange | | Gallium nitride | 3.4 | 365 | ultraviolet | colourless | | Diamond | 5.5 | 225 | deep ultraviolet | colourless | Cadmium sulfide is the instructive row: its edge falls inside the visible band, so it absorbs violet, blue and green and transmits the rest, which is why the gap alone predicts a yellow crystal. Real specimens depart from the table wherever defects, dopants or colour centres add states inside the gap — the reason a diamond can be yellow or blue while its gap stays 5.5 eV. ## Optical versus electronic bandgap The two are not the same quantity, and the difference is an exciton. The electronic, or transport, gap is the energy to create a free electron and a free hole that no longer feel one another: it is what a measurement of conduction or of photoemission reports. The optical gap is the lowest energy at which a photon is absorbed, and the state a photon creates first is a bound electron–hole pair, held together by their mutual Coulomb attraction. The optical gap is therefore smaller than the electronic gap by the binding energy of that pair. How much smaller follows the same hydrogenic arithmetic as a shallow donor, with the reduced mass of the pair in place of the electron's mass: the binding energy scales as the reduced mass divided by the square of the relative permittivity. In a high-permittivity inorganic crystal that puts it in the tens of millielectronvolts at most — with silicon's conduction-band effective mass of 0.26 electron masses and a permittivity near 12 the estimate is about 25 meV, some two per cent of the 1.12 eV gap, so the distinction is usually ignored.[^likharev-qm-meff][^derived-bg] In a molecular solid the permittivity is several times smaller, and because it enters squared, a threefold reduction multiplies the binding energy by nine. The optical and electronic gaps of an organic semiconductor then differ by several tenths of an electronvolt, which is far too large to ignore: a device designed from an absorption spectrum alone will have the wrong energy levels, and the pair must be separated at an interface before any current flows. ## Band gaps for other quasi-particles Nothing in the argument for a gap is specific to electrons. A gap opens whenever a wave of any kind propagates through a periodic medium and its wavelength comes into register with the period, so that forward and backward waves interfere and no travelling solution survives in a band of frequencies. Any periodic structure has gaps somewhere in its spectrum. A [[Photonic_crystal|photonic crystal]] has a periodic refractive index and therefore a range of optical frequencies that cannot propagate through it: light in the gap is reflected however thick the crystal, which is how a defect line in such a structure can guide light around a sharp bend that no ordinary waveguide would survive. A phononic crystal does the same for elastic waves, giving a band of frequencies at which [[Sound|sound]] and [[Vibration|vibration]] will not pass, with applications in isolation and filtering; the [[Debye_model|phonon spectrum]] of an ordinary crystal has gaps of the same origin, set by the [[Bravais_lattice|lattice]] and the masses on it. Magnonic crystals do it for spin waves, and superconductors have a gap of a different kind, opened not by periodicity but by pairing, whose width measures the energy needed to break a pair rather than the energy needed to cross a zone boundary.[^openstax-v3-95] ## Materials A gap is not a free parameter: it is fixed by which atoms are present and how they are bonded. Within a column of the periodic table the gap falls as the atoms grow heavier and the bonds lengthen and weaken, so diamond, silicon and germanium run 5.5, 1.12 and about 0.7 eV; across the [[Electronegativity|electronegativity]] scale it rises with ionicity, so the III–V and II–VI compounds isoelectronic with a group IV element have larger gaps than it does. That pair of rules organizes most of the table of known semiconductors and explains why the wide-gap materials are also the hard, refractory ones — the same strong bonds do both jobs. Alloying gives the continuous tuning that discrete compounds do not. Mixing two compounds with a common sublattice generally moves the gap smoothly between the endpoints, so composition becomes a dial for wavelength, and it is that dial, not the discovery of new compounds, that supplies most of the LEDs and detectors in use. Outside the crystalline semiconductors the gap concept still applies: an amorphous solid has no Brillouin zone but retains a range of energies with very few states, a mobility gap; a molecular solid's gap is the separation between the occupied and unoccupied orbitals of the molecule, shifted by its neighbours; and in a [[Quantum_dot|quantum dot]] the gap depends on the particle's size, because confinement adds a term that grows as the inverse square of the radius. ### List of electronics topics The gap is the parameter along which the electronics landscape is naturally ordered, and reading it that way makes the field's divisions look less arbitrary. Narrow gaps, below about 0.5 eV, belong to infrared detectors and thermal imaging, where the point is to absorb photons too weak for anything else. The 1 to 1.5 eV band holds the workhorses — [[Transistor|transistors]], [[Integrated_circuit|integrated circuits]], [[Solar_cell|solar cells]] — where the gap is large enough to keep intrinsic carriers negligible at operating temperature and small enough to absorb sunlight. From 2 to 3.5 eV are the visible emitters and the transparent conductors. Above 3 eV sit the wide-gap power devices, chosen because a wide gap means a high breakdown field and a high operating temperature, and above 5 eV the ultraviolet detectors and the insulators that separate everything else. A list of electronics topics is, read in this light, largely a list of gap values. ## See also - [[Light-emitting_diode]] — the equation read backwards, emission colour from E_g - [[Direct_and_indirect_band_gaps]] — where the extrema sit, not just how far apart - [[Quantum_dot]] — the gap as a function of size - [[Transparency_and_translucency]] — what a gap above 3.26 eV looks like - [[Electronic_band_structure]] — the parent sim that opens the gap - [[Doping_(semiconductor)]] — filling the gap with carriers - [[Semiconductor]] - [[Solar_cell]] ## References [^openstax-v3-95]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3* (OpenStax). Chapter 9, "Condensed Matter Physics" (pp. 393–440), §9.5 Band Theory of Solids: the valence and conduction bands, the gap between them, and the classification of metals, semiconductors and insulators by its width; §9.8 for the superconducting gap (page to pin). https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 [^openstax-v3-96]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3* (OpenStax). Chapter 9, §9.6 Semiconductors and Doping: the intrinsic carrier density and its exponential dependence on E_g/(2kT) (page to pin). https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 [^openstax-v3-ch6]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3* (OpenStax). Chapter 6, "Photons and Matter Waves" (pp. 241–294): the photon energy E = hf = hc/λ that converts a band gap into an absorption wavelength; constants from Appendix C, "Fundamental Constants" (pp. 549–550) (page to pin). https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 [^openstax-v3-appd]: Sanny, Jeff; Ling, Samuel (2016). *University Physics Volume 3* (OpenStax). Appendix D, "Astronomical Data" (pp. 551–552), for the diameter of the Earth used in the comparison (page to pin). https://open.umn.edu/opentextbooks/textbooks/university-physics-volume-3 [^likharev-qm-meff]: Likharev, Konstantin (2013). *Essential Graduate Physics, Part QM: Quantum Mechanics*. Chapter 2, effective mass `1/m_ef = (1/hbar^2)*d2E/dq2`; silicon 0.26 mₑ in the conduction band and 0.39 mₑ in the valence band (pp. 87–89). https://open.umn.edu/opentextbooks/textbooks/part-qm-quantum-mechanics [^si-2019]: Bureau International des Poids et Mesures. *The International System of Units (SI Brochure)*, 9th edition, 2019: h, c and e are exact defined values, so the product hc/e is exact. https://www.bipm.org/en/publications/si-brochure [^spec-m39]: Matter & Energy Cluster contract, `_registry/plans/MATERIALS_SCIENCE_SECTIONS.md` row M39: new sibling of `Electronic_band_structure`, a photon-energy slider sweeping the visible with the material transparent below its gap and absorbing above it, `lambda_edge = h·c/E_g` (1,240 nm·eV/E_g), presets Si 1.12, GaAs 1.42, CdS 2.42, GaN 3.4 and diamond 5.5 eV reading opaque / yellow / colourless, and the LED as the same equation read backwards. [^derived-bg]: Computed for this article. With the 2019 SI values h = 6.62607015×10⁻³⁴ J·s, c = 299,792,458 m/s and e = 1.602176634×10⁻¹⁹ C, all exact, hc/e = 1,239.841984 eV·nm exactly.[^si-2019] Dividing by the gaps of [^spec-m39] gives λ_edge = 1,107.0, 873.1, 512.3, 364.7 and 225.4 nm for Si, GaAs, CdS, GaN and diamond. The visible band 380–750 nm corresponds to 3.263–1.653 eV. With k = 8.617×10⁻⁵ eV/K, kT = 25.9 meV at 300 K, so E_g/kT = 43.3 (Si) and 212.7 (diamond), and exp(−E_g/2kT) = 3.9×10⁻¹⁰ and 6.3×10⁻⁴⁷. Taking a band-edge density of states of 10¹⁹ cm⁻³ — a round order of magnitude, ILLUSTRATIVE, not read from a Portal Book — diamond's intrinsic density is 6×10⁻²⁸ cm⁻³, one carrier per 1.6×10²⁷ cm³, a cube 1.16×10⁴ km on a side. ILLUSTRATIVE: the exciton estimate 13.6 eV·(m*/m)/ε_r² = 25 meV uses m* = 0.26 mₑ from [^likharev-qm-meff] with a relative permittivity taken as 12; only its order, its 2 % share of the 1.12 eV gap and the factor of 9 from a threefold smaller permittivity are claimed. ## External links - The Wikipedia pair's *External links* section lists band-gap tables and semiconductor parameter databases; the Portal Book chapters above are the sources of this page. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Band_gap.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Band gap* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Band_gap.html" data-title="Band gap"></div> *Built from `MICROSIM_GUIDE/specs/sims/Band_gap.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Band_gap) : [Wikitube](https://en.wikitube.io/wiki/Band_gap) · pinned revision [1369611095](https://en.wikipedia.org/w/index.php?oldid=1369611095) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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