Bandgap (energy gap, E_g)

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:

Light with $\lambda > \lambda_g$ ($h\nu < E_g$) is transmitted; light with $\lambda < \lambda_g$ is absorbed. A semiconductor laser emits at a wavelength slightly longer than its bandgap-corresponding wavelength (due to Stokes shift and thermal effects).

Bandgaps and corresponding cutoff wavelengths at 300 K:

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:

where $\alpha$ and $\beta$ are material-specific. The decrease is typically 0.4 meV/K near room temperature, producing $\sim 0.3$ nm/K wavelength shift in semiconductor laser emission with temperature — the dominant mechanism behind laser wavelength drift with operating temperature.