Glossary entry

Bandgap (energy gap, E_g)

The energy separation between the top of the valence band and the bottom of the conduction band in a semiconductor. Determines the longest wavelength a material can emit or absorb.

Optics fundamentals Lasers & gainUpdated October 2026

The bandgap is the forbidden energy region between the valence band and conduction band of a crystalline solid. Electrons cannot have energies within the gap; transitions across the gap require absorbing or emitting an energy quantum equal to or greater than $E_{g}$ .

For optical transitions, the bandgap sets the cutoff wavelength:

λ_{g} = \frac{h c}{E_{g}} \approx \frac{1.24 [μ m \cdot eV]}{E_{g} [eV]} .

Light with $λ > λ_{g}$ ( $h ν < E_{g}$ ) is transmitted; light with $λ < λ_{g}$ is absorbed. A semiconductor laser emits close to its bandgap wavelength: band filling puts the gain peak slightly above $E_{g}$ in energy, and quantum confinement in a quantum well shifts it further toward shorter wavelength.

Bandgaps and corresponding cutoff wavelengths at 300 K:

Material	$E_{g}$ (eV)	$λ_{g}$
AlN	6.0 – 6.2 (reported values vary)	200 – 207 nm
Diamond	5.47	227 nm
GaN	3.39	366 nm
ZnSe	2.70	459 nm
GaP	2.26	549 nm
AlAs	2.16	574 nm
GaAs	1.424	871 nm
InP	1.344	923 nm
Si	1.12	1107 nm
InGaAs (lattice-matched to InP)	0.75	1650 nm
Ge	0.66	1880 nm
InAs	0.354	3500 nm
HgCdTe (cryogenic IR)	tunable 0.05 – 1.5	830 nm – 25 μm

Direct vs indirect bandgap. In a direct-bandgap semiconductor, the conduction-band minimum and valence-band maximum occur at the same crystal momentum. Photon emission can occur in a single step. In an indirect-bandgap semiconductor (Si, Ge, GaP), the minimum and maximum are at different momenta, so emission requires phonon participation, drastically reducing efficiency. This is the fundamental reason silicon is a poor light emitter despite being an excellent waveguide material.

Bandgap engineering. In ternary and quaternary alloys (AlGaAs, InGaAs, InGaAsP, InGaAlAs), the bandgap can be tuned continuously between the constituent binary values. Quantum confinement in thin layers (quantum wells) further increases the effective bandgap by quantizing carrier energies. These two mechanisms together allow precise wavelength engineering in III-V laser design.

Temperature dependence. Bandgap decreases with temperature according to the Varshni equation:

E_{g} (T) = E_{g} (0) - \frac{α T^{2}}{T + β},

where $α$ and $β$ are material-specific. The decrease is typically 0.25 to 0.45 meV/K near room temperature, moving the gain peak by about 0.25 to 0.5 nm/K depending on material. This dominates the wavelength drift of Fabry-Perot lasers; a laser whose wavelength is set by a grating follows the refractive index instead, at 0.06 to 0.09 nm/K (see wavelength temperature coefficient).