band gap
The band gap Eg is the energy separation between the top of the valence band and the bottom of the conduction band, and it is the single parameter that decides whether a crystal behaves as an insulator, a semiconductor, or effectively a metal at practical temperatures. In semiconductor metrology and device engineering the number quoted for a material, such as 1.12 eV for silicon or 1.42 eV for gallium arsenide, is only the headline; the shape of the bands in momentum space, the temperature dependence of the gap, and whether the transition across it needs a phonon all change how a device built from that material actually performs. This entry works through the E-k picture of the gap, the direct-versus-indirect distinction, the wide-bandgap material family, and the alloying and strain techniques used to engineer Eg for LEDs, power devices, HEMTs, and photodetectors.
**Read the E-k diagram before quoting a single Eg number.**
The conduction-band minimum and valence-band maximum are each a point in E-k space, and Eg is simply the vertical energy distance between them at whatever k each extremum occupies. In gallium arsenide both extrema sit at the zone center, so an electron near 1.42 eV can drop straight down into a hole state at the same k with no exchange of crystal momentum. In diamond-structure hosts such as Si and Ge, the conduction minimum lies away from the zone center, spread across roughly 6 equivalent valleys along the 100-type directions for Si, and that offset forces every band-to-band transition to trade momentum with the lattice. This distinction is why compound direct-gap semiconductors dominate light-emitting and laser applications while silicon, despite dominating logic and power switching, needs an assist from other materials for efficient light emission.
**Separate direct-gap absorbers from indirect-gap phonon-assisted materials.**
A direct transition needs only a photon, so absorption and emission near the edge are strong and fast; GaAs absorbs strongly within about 1 µm of the surface. An indirect transition needs a photon plus a phonon to conserve momentum, so the process is weaker and slower; silicon needs tens of µm of thickness before it absorbs as completely, because the phonon-assisted step lowers the absorption coefficient near the edge. InGaAs spans roughly 0.75 eV to 1.42 eV as indium content changes, letting designers place the absorption edge where the application needs it. That physics is why LEDs and laser diodes lean on GaAs, InGaAs, GaN, and related direct-gap alloys rather than silicon, and why silicon photodetectors roll off in responsivity beyond about 1100 nm while InGaAs detectors extend the cutoff past 1600 nm for fiber-optic receivers.
```flowchart
Start from the intrinsic band structure of the host lattice
-> identify direct or indirect character at the conduction minimum
-> select alloy composition to tune Eg for the target wavelength or voltage
-> apply strain or heterostructure confinement to fine-tune band offsets
-> verify Eg and defect levels with ellipsometry, XPS, SIMS, and DLTS
-> validate carrier transport with Hall effect and four-point probe measurements
-> qualify the wide-bandgap or narrow-bandgap device for its target application
```
**Reach for wide-bandgap materials when the application needs voltage and frequency headroom.**
SiC at 3.26 eV, GaN at 3.4 eV, AlN at 6.2 eV, and diamond at 5.5 eV push the gap well past the roughly 1 eV to 1.5 eV range of Si and GaAs, and a wider gap raises the critical electric field before avalanche breakdown, often by a factor of 10 x over silicon at comparable doping. That headroom lets a SiC or GaN power device block hundreds of V with a drift layer only a fraction of the thickness silicon would need, cutting on-resistance and switching loss; commercial SiC MOSFETs commonly qualify near 650 V blocking with turn-off under 50 ns. GaN HEMTs pair the wide gap with polarization-induced charge to sustain a dense two-dimensional electron gas, supporting switching well past 100 kHz and RF power amplification into the MHz range, while diamond and AlN remain mostly developmental power players limited by doping and substrate cost.
| Material | Gap type | Eg at 300 K | Representative use |
|---|---|---|---|
| Ge | Indirect | 0.66 eV | IR detectors, SiGe HBTs |
| Si | Indirect | 1.12 eV | CMOS logic, power MOSFETs |
| GaAs | Direct | 1.42 eV | Laser diodes, HEMTs |
| InGaAs | Direct | 0.75 to 1.42 eV | Photodetectors, fiber receivers |
| SiC | Indirect | 3.26 eV | High-voltage power devices |
| GaN | Direct | 3.4 eV | Power HEMTs, blue LEDs |
| AlN | Direct | 6.2 eV | Deep-UV LEDs, substrates |
| Diamond | Indirect | 5.5 eV | Extreme power and frequency |
**Engineer the gap deliberately through alloying.**
AlGaAs spans roughly 1.42 eV to 2.16 eV as aluminum content rises, letting epitaxial designers set a laser or LED wavelength without leaving the arsenide family. InGaAs lowers the gap from the 1.42 eV GaAs value toward 0.75 eV as indium content increases, which is why 1.55 µm telecom photodiodes and avalanche detectors are built from an indium fraction tuned for that specific cutoff. SiGe alloys shrink silicon's gap by roughly 0.4 eV at high germanium fraction, a trick used to raise base transit speed in SiGe heterojunction bipolar transistors and to extend photodetector response beyond silicon's native 1100 nm edge without abandoning a silicon-compatible process flow.
**Add strain to shift the gap without changing composition.**
Compressive or tensile strain moves the band extrema without touching the alloy composition at all. A few tenths of a percent of biaxial strain in a SiGe or strained-Si channel can move Eg by roughly 0.05 eV and split degenerate valleys, which is exactly the mechanism strained-channel MOSFETs use to raise carrier mobility. Quantum wells add a further confinement shift, so a strained InGaAs well embedded in a HEMT structure has an effective gap distinct from either bulk constituent, and that distinction is central to setting threshold voltage and two-dimensional electron gas density in the channel. Process control of strain therefore belongs on the same metrology plan as composition, since a 0.1 % strain error can move Eg as much as a measurable alloy drift.
**Track Eg against temperature before trusting a datasheet number.**
Eg falls as the lattice warms because thermal expansion softens the bonding and electron-phonon coupling shifts the band extrema; the familiar trend takes Si from roughly 1.17 eV near 4 K down to 1.12 eV at 300 K, and GaAs shows a comparable roughly 0.05 eV to 0.06 eV drop over the same range. A laser diode qualified at 25 °C will drift in emission wavelength if the junction heats to 85 °C in service, and a photodetector's dark current climbs steeply as Eg narrows with self-heating, so thermal design and Eg temperature coefficients belong in the same qualification plan rather than separate documents. Wide-bandgap parts are not exempt; a GaN HEMT running near its 150 °C junction limit still loses a measurable fraction of an eV of headroom relative to its cold-plate rating.
**Match the metrology technique to the physical question about the gap.**
ellipsometry extracts the optical constants and absorption edge that give the optical Eg directly from a reflected polarization change, often resolving film thickness to well under 1 nm in the same measurement. Hall effect measurements return carrier type, density, and mobility that define the transport gap indirectly through carrier freeze-out behavior, while a four-point probe or a Keithley source-measure unit tracks sheet resistance to correlate with alloy composition and strain state. DLTS locates trap levels such as a state near 0.30 eV below the conduction edge that would otherwise masquerade as a shifted gap in a careless measurement, and XPS confirms surface chemistry and stoichiometry, useful when a Si 2p core level near 99.4 eV signals unwanted oxide or contamination on a test structure. SIMS profiles alloy composition with depth to confirm the graded aluminum, indium, or germanium fraction that a bandgap-engineered structure is supposed to have, AFM checks that strained or graded layers have not relaxed at the surface, and Keysight and Semilab corona-Kelvin tools add complementary electrical and surface-photovoltage cross-checks. NIST-traceable reference materials anchor the whole chain so an Eg extracted from one instrument can be compared honestly against a value pulled from another.
Viewed through an energy-band-design lens, the number quoted for Eg is a starting point rather than a specification. Whether the extrema sit at the same k or different k, whether a material's native gap of 1.12 eV or 3.4 eV suits the target voltage or wavelength, and how alloying or strain can move that gap by a few tenths of an eV together decide whether an LED emits efficiently, a power device blocks its rated V with margin, a HEMT sustains gain past 100 kHz and into the MHz range, or a photodetector reaches the required cutoff wavelength.