---
title: "Conductivity vs temperature"
subject: "Electromagnetism"
chapter: 2
key: "semester_3/electromagnetism:conductivity-vs-temperature-metals"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/conductivity-vs-temperature-metals
site: BCT Engineering
---

# Conductivity vs temperature

Electromagnetism · Chapter 2: Electric field

- Asked in: 2067 Shrawan, 3 marks
- Video: [How conductivity changes with temperature | How Resistivity changes with temperature](https://www.youtube.com/watch?v=0ARx6pY0mv8) — Kota_Physics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/conductivity-vs-temperature-metals
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-2

## Question

Explain how the conductivity of metals and semi-conductors changes with increase in temperature.

## Short answer

In metals, free electron density is nearly constant, but lattice vibrations reduce mobility as temperature rises, so conductivity decreases. In semiconductors, carrier concentration increases exponentially with temperature, dominating the slight mobility decrease, so conductivity increases.

## Answer

Conductivity σ = n e μ, where n is the density of free charge carriers, e the electron charge and μ their mobility.

#### Metals
In a metal the number of free electrons is fixed by the atoms and does not change with temperature. When the temperature rises, the lattice atoms vibrate more strongly, so electrons collide more often and their mobility μ falls. Hence **conductivity decreases and resistivity increases** with temperature. Over normal ranges ρ = ρ₀[1 + α(T − T₀)] with a positive temperature coefficient α. Copper and silver are common examples.

#### Semiconductors
In a semiconductor, few carriers exist at low temperature. Heat breaks covalent bonds and generates more electron-hole pairs, so n rises very rapidly (exponentially). The fall of mobility due to lattice vibration is much smaller than this rise. Hence **conductivity increases** with temperature, and resistivity decreases (negative temperature coefficient). Silicon and germanium are examples.

| Property | Metal | Semiconductor |
|---|---|---|
| Carrier density n | Almost constant | Rises exponentially |
| Mobility μ | Decreases | Decreases slightly |
| Conductivity σ | Decreases | Increases |
| Temperature coefficient | Positive (resistance) | Negative |

At very low temperatures, σ of a pure semiconductor approaches zero, while that of a metal rises to a high value limited by impurities and defects (a superconductor's resistance drops to zero below its critical temperature).

## Check yourself

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

1. Conductivity depends on:
   A. σ = n/μ
   B. σ = e/n μ
   C. σ = n e μ (carrier density, charge, mobility)
   D. σ = nμ/e
   Answer: C. σ = n e μ. (Key point: Conductivity expression)

2. In metals, conductivity decreases with temperature because:
   A. Carrier density falls
   B. Mobility falls as lattice vibrations cause more collisions
   C. Electrons are lost
   D. Charge e decreases
   Answer: B. n is nearly fixed while μ falls. (Key point: Metals)

3. In semiconductors, conductivity increases with temperature because:
   A. Carrier density rises exponentially, outweighing the small fall in mobility
   B. Mobility rises strongly
   C. Atoms stop vibrating
   D. Charge increases
   Answer: A. More electron-hole pairs are generated by heat. (Key point: Semiconductors)

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