In one line
In a direct band gap semiconductor the conduction band minimum and valence band maximum occur at the same crystal momentum \(k\), so electrons can recombine by emitting light directly; in an indirect one they occur at different \(k\), so recombination needs a phonon and mostly releases heat.
Explained simply
Picture two floors connected by stairs. In a direct gap material the lowest point of the upper floor is right above the highest point of the lower floor, so an electron simply drops straight down and gives out a photon. In an indirect gap material the lowest point of the upper floor is shifted sideways, so the electron must also "move sideways" (change momentum). A photon carries almost no momentum, so a lattice vibration (phonon) must help, which makes light emission rare.
How it works
- Band diagrams are drawn as energy \(E\) against wave vector \(k\) (crystal momentum \(\hbar k\)).
- In any transition both energy and momentum must be conserved.
- Direct gap: CB minimum and VB maximum are at the same \(k\). An electron falls from CB to VB and emits a photon of energy \(E_g\). Recombination is fast and efficient. Examples: GaAs (about 1.43 eV), InP, GaN.
- Indirect gap: CB minimum and VB maximum are at different \(k\). The transition needs a phonon to supply the momentum change, a three-particle process that is much less likely. Energy is mostly released as heat. Examples: Si (1.12 eV), Ge (about 0.67 eV).
| Direct | Indirect |
|---|---|
| Same \(k\) for CB min and VB max | Different \(k\) |
| Photon emitted | Phonon involved, mostly heat |
| Short carrier lifetime | Long carrier lifetime |
| LEDs, laser diodes | ICs, transistors, rectifier diodes, solar cells |
| GaAs, InP, GaN | Si, Ge |
Key formula
Wavelength of emitted light: \(\lambda = \dfrac{hc}{E_g}\), or \(\lambda\,(\text{nm}) \approx \dfrac{1240}{E_g\,(\text{eV})}\). \(E_g\): band gap energy.
Quick example
GaAs, \(E_g = 1.43\) eV: \(\lambda = 1240/1.43 \approx 867\) nm (near infrared), used in TV remote LEDs and laser diodes. Silicon, with an indirect gap, is not used for LEDs, but works well for chips and solar cells.
Common mistakes
- Saying indirect semiconductors cannot absorb light; they absorb, just less sharply near the band edge.
- Drawing the energy band diagram against distance instead of against \(k\) when showing direct/indirect gaps.
- Listing Si as a direct gap material.
How MU asks it
Asked as "Differentiate between direct and indirect band gap semiconductors" (3 to 5 marks). Draw the two E-k diagrams with photon and phonon arrows, give a table of at least four points, and name two examples of each.