---
title: "Band bending in semiconductors"
subject: "Electrical Engineering Material"
chapter: 6
key: "semester_3/electrical_engineering_material:band-bending"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/band-bending
site: BCT Engineering
---

# Band bending in semiconductors

Electrical Engineering Material · Chapter 6: Semiconductors

- Asked in: 2076 Chaitra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/band-bending
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-6

## Question

Explain how does the band bends in semiconductor.

## Short answer

Band bending is the spatial variation of energy bands (E_c, E_v) due to electric fields. In equilibrium, the Fermi level stays flat; doping or junctions create built-in potentials, so bands curve by e times the potential difference while the bandgap remains constant.

## Answer

**Band bending** is the curving of the energy bands ($E_c$, $E_v$, $E_{Fi}$) with position inside a semiconductor. It happens wherever there is an **electric field**, i.e. wherever the electrostatic potential $V(x)$ changes with position.

#### Why the bands bend

The energy of an electron at a point is its band energy plus its potential energy $-eV(x)$:

$$
E_c(x) = E_{c0} - eV(x)
$$

The field is $\mathcal{E} = -dV/dx$, so

$$
\mathcal{E} = \frac{1}{e}\frac{dE_c}{dx}
$$

- Where $\mathcal{E} = 0$ the bands are flat.
- Where a field exists, all three levels shift by the same amount, so the band gap $E_g$ stays constant but the bands tilt or curve.
- An electron "rolls down" the conduction band and a hole "floats up" the valence band.

#### Common cases

1. **Applied voltage on a uniform bar:** the field is uniform, so the bands tilt in a straight line. The Fermi level is no longer flat; current flows.
2. **pn junction (equilibrium):** electrons diffuse to the p side and holes to the n side, leaving fixed ion charges. These create a built-in field. Because the Fermi level must be the same throughout in equilibrium, the bands bend in the depletion region by $eV_0$.
3. **Non-uniform doping, metal–semiconductor contact, surface charges:** each creates a local space charge and field, so the bands bend near that region.

```text
 p side            n side
 Ec ----\
         \__________ Ec
 EF ------------------- EF (flat)
 Ev ----\
         \__________ Ev
       |<-W->|  depletion region
   bending = eV0
```

#### Key rule

In equilibrium the Fermi level is flat; any difference in doping is accommodated by bending of $E_c$ and $E_v$. The amount of bending equals $e$ times the potential difference across the region.

## Check yourself

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

1. What causes bands to bend?
   A. An electric field, i.e. a position-dependent potential V(x)
   B. A uniform temperature
   C. A change in the band gap
   D. Flat Fermi level alone with no charge
   Answer: A. E_c(x) = E_c0 - eV(x), so bending follows the potential. (Key point: Cause)

2. How is the field related to the band edge?
   A. E = e dEc/dx
   B. E = (1/e) dEc/dx; bands are flat where E = 0
   C. E = Eg/e
   D. Bands are flat where E is maximum
   Answer: B. Slope of the band edge is proportional to field. (Key point: Field relation)

3. What happens to Eg where the bands bend?
   A. It shrinks in proportion to field
   B. It doubles
   C. It stays constant because Ec, Ev and E_Fi all shift together
   D. It becomes zero at the bend
   Answer: C. A potential shifts all levels by the same amount. (Key point: Band gap)

4. Why do bands bend by eV0 at an equilibrium pn junction?
   A. E_F tilts instead of the bands
   B. Applied voltage forces it
   C. Electrons are removed from the n-side entirely
   D. Diffusion leaves fixed ions making a built-in field, and E_F must be flat in equilibrium
   Answer: D. A flat Fermi level forces the bands to bend across the depletion region. (Key point: pn junction)

## Related in Electrical Engineering Material

- [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
- [Band bending and Einstein relationship](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aband-bending-einstein) — Electrical Engineering Material, chapter 6, asked 2×
- [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
- [Fermi level at middle of band gap](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-level-middle-band-gap) — Electrical Engineering Material, chapter 6
- [Importance of Fermi energy in semiconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-energy-importance) — Electrical Engineering Material, chapter 6, asked 3×
- [Minority charge suppression in extrinsic semiconductors](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aminority-charge-suppression) — Electrical Engineering Material, chapter 6, asked 2×

## Related in other subjects

- [Microscopic and macroscopic bending losses](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amicrobend-macrobend-losses) — Propagation and Antenna, chapter 6