---
title: "Direct and indirect recombination"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:recombination-direct-indirect"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/recombination-direct-indirect
site: BCT Engineering
---

# Direct and indirect recombination

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2076 Chaitra, 4 marks
- Video: [L28 | Indirect Recombination; Trapping || Electronic Devices (AKTU)](https://www.youtube.com/watch?v=zeK9sQoSkx8) — Dr. Sapna Katiyar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/recombination-direct-indirect
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

Describe the Direct and indirect recombination process between an electron and hole in semiconductor with necessary diagrams.

## Short answer

Direct recombination: electron falls from conduction to valence band emitting a photon, occurs in direct-gap materials (GaAs). Indirect recombination: goes via deep-level traps releasing phonons, typical in Si and Ge, and determines minority carrier lifetime.

## Answer

**Recombination** is the process in which a conduction band electron falls into an empty state (hole) in the valence band, so a free electron–hole pair disappears. It balances thermal generation in equilibrium.

#### 1. Direct (band-to-band) recombination

The electron at the bottom of the CB falls straight into a hole at the top of the VB. Energy $\approx E_g$ is given out as a **photon** ($h\nu = E_g$).

- Possible only when CB minimum and VB maximum are at the same k (direct band gap: GaAs, InP).
- Rate is proportional to both concentrations: $R = Bnp$.
- Fast; used in LEDs and lasers.

```text
 Ec ----- e ---------
          |
          |  photon hv = Eg  ~~>
          v
 Ev ----- h ---------
```

#### 2. Indirect recombination (through recombination centres)

In indirect materials (Si, Ge) direct transition is very unlikely because momentum must also change. Instead recombination takes place through a **recombination centre** – an impurity (Au, Fe) or crystal defect – that creates a localised level $E_r$ deep in the gap.

Steps:
1. The centre captures a conduction electron; energy is given to lattice vibrations (phonons).
2. The trapped electron then drops into the valence band and fills a hole (or the centre captures a hole).
3. The centre is empty again and ready for the next event.

```text
 Ec ----- e ---------
          | (phonons)
 Er  ...  * ......... recombination centre
          | (phonons)
 Ev ----- h ---------
```

The energy is released mainly as **heat** in small steps. Minority carrier lifetime is set by the centre density: $\tau = 1/(C_r N_r)$ approximately.

#### Comparison

| Point | Direct | Indirect |
|---|---|---|
| Path | CB → VB straight | CB → centre → VB |
| Energy given as | Photon (light) | Phonons (heat) |
| Materials | GaAs, InP | Si, Ge |
| Lifetime | Short (ns) | Longer, set by impurities |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What happens in direct recombination?
   A. An electron drops from CB to a VB hole and emits a photon with hv = Eg
   B. The electron is trapped at a deep centre
   C. Energy is given only to phonons
   D. Holes are created
   Answer: A. Same k lets the transition conserve momentum, giving a photon. (Key point: Direct recombination)

2. What is the direct recombination rate proportional to?
   A. R = B n alone
   B. R = B n p, the product of electron and hole concentrations
   C. R = B (n - p)
   D. R = B / (np)
   Answer: B. Recombination needs an electron and a hole to meet. (Key point: Rate law)

3. How does indirect recombination occur in Si and Ge?
   A. Straight from CB to VB with a photon
   B. Through the band edge only
   C. Through a recombination centre near mid-gap, releasing energy as phonons
   D. Via a metal contact
   Answer: C. Momentum change makes direct transitions unlikely, so deep levels (Au, Fe, defects) mediate. (Key point: Indirect path)

4. Which is correct for lifetime and energy released?
   A. Direct: heat; indirect: light
   B. Both: short, light
   C. Indirect lifetime is fixed by Eg
   D. Direct: short lifetime, light; indirect: longer lifetime set by impurity density, heat
   Answer: D. tau for indirect is about 1/(C_r N_r). (Key point: Comparison)

## Related in Electrical Engineering Material

- [Compensated semiconductor: electron and hole concentrations](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acompensated-carrier-concentration) — Electrical Engineering Material, chapter 6, asked 4×
- [Degenerate semiconductors; direct vs indirect bandgap](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adegenerate-direct-indirect) — Electrical Engineering Material, chapter 6
- [Direct versus indirect band gap semiconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adirect-indirect-bandgap) — Electrical Engineering Material, chapter 6
- [Electron concentration in an extrinsic semiconductor](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aextrinsic-electron-concentration) — Electrical Engineering Material, chapter 6
- [Compensated semiconductor concentrations and conductivity](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acompensated-conductivity) — Electrical Engineering Material, chapter 6
- [Intrinsic Si concentration (hole mass 0.56me)](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aintrinsic-si-056) — Electrical Engineering Material, chapter 6, asked 6×

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