--- title: "Direct versus indirect band gap semiconductors" subject: "Electrical Engineering Material" chapter: 6 key: "semester_3/electrical_engineering_material:direct-indirect-bandgap" source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/direct-indirect-bandgap site: BCT Engineering --- # Direct versus indirect band gap semiconductors Electrical Engineering Material · Chapter 6: Semiconductors - Asked in: 2078 Kartik, 4 marks - Video: [Direct Bandgap Semiconductors and Indirect Bandgap Semiconductors | Electronics Devices and Circuits](https://www.youtube.com/watch?v=hEYs-utWe7E) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/direct-indirect-bandgap - Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6 ## Question Differentiate between direct and indirect band gap semiconductors with examples. ## Short answer Direct band gap: conduction band minimum and valence band maximum at same crystal momentum k. Electron-hole recombination emits a photon efficiently (e.g., GaAs, InP). Indirect band gap: band edges at different k; recombination requires a phonon for momentum conservation, making light emission poor (e.g., Si, Ge). ## Answer A semiconductor is **direct band gap** if the minimum of the conduction band and the maximum of the valence band occur at the **same crystal momentum k**; it is **indirect band gap** if they occur at **different k values**. ```text Direct (GaAs) Indirect (Si) E E | \ / CB | \ / CB | \_/ | \_/ | | hv | ___ ^ | /^\ | / \ phonon | / \ VB |/ \ needed +---------- k +------------ k same k k(max) != k(min) ``` #### Comparison | Point | Direct band gap | Indirect band gap | |---|---|---| | Band edges | CB min and VB max at same k | At different k | | Transition | Electron drops straight down | Needs a change in momentum | | Third particle | Not needed | Phonon (lattice vibration) needed | | Recombination | Radiative: energy out as photon | Mostly non-radiative: energy out as heat | | Recombination rate | High, short lifetime (ns) | Low, long lifetime (µs–ms) | | Light emission | Efficient | Very poor | | Absorption edge | Sharp, strong | Gradual, weak | | Uses | LEDs, laser diodes, photodetectors | Diodes, transistors, ICs, solar cells | | Examples | GaAs (1.42 eV), InP, GaN, CdS | Si (1.1 eV), Ge (0.66 eV), GaP | #### Key point In a direct gap material an electron at the bottom of the CB can recombine with a hole at the top of the VB and give out a photon of energy $h\nu \approx E_g$ while conserving momentum. In an indirect material the photon carries almost no momentum, so a phonon must take part; this three-body process is unlikely, which is why silicon cannot be used to make efficient LEDs or lasers. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What defines a direct band gap semiconductor? A. CB minimum and VB maximum at the same k B. CB minimum and VB maximum at different k C. A band gap of exactly 1.1 eV D. No valence band maximum Answer: A. Same crystal momentum allows a transition without a momentum change. (Key point: Definition) 2. Why is a phonon needed in an indirect semiconductor? A. To supply the band gap energy B. The photon carries almost no momentum, so the lattice must supply the momentum change C. To create more electrons D. To increase the photon energy Answer: B. A three-body process of electron, photon and phonon is unlikely, hence poor emission. (Key point: Phonon role) 3. Which pairing is correct? A. Si for laser diodes; GaAs for ICs only B. Ge and GaP are direct C. GaAs for LEDs and lasers; Si for ICs and solar cells D. Direct materials are used only for transistors Answer: C. Efficient light emission needs a direct gap. (Key point: Applications) 4. How do recombination and lifetime compare? A. Direct: heat, long lifetime B. Both radiative with equal lifetime C. Indirect: radiative, ns D. Direct: radiative, short lifetime (ns); indirect: mostly non-radiative, long lifetime (us-ms) Answer: D. Direct recombination is fast and emits photons. 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