What is mobility of charge carriers and what factors affect it?

In one line

Mobility is the drift velocity acquired by a charge carrier per unit electric field, \(\mu = v_d/E\), and it measures how easily carriers move through a material.

Explained simply

Two people walk through the same crowded market with the same push from behind. The one who bumps into fewer people moves forward faster. Mobility measures how freely a carrier moves for a given "push" (electric field). Fewer collisions mean higher mobility.

How it works

1. Definition: \(\mu = \dfrac{v_d}{E}\), unit m²/V s.
2. Using \(v_d = eE\tau/m\): \(\mu = \dfrac{e\tau}{m^*}\), where \(m^*\) is the effective mass. Longer time between collisions or lighter effective mass gives higher mobility.
3. Electrons vs holes: electrons usually have higher mobility because holes move via valence-band electrons and have larger effective mass. In Si, \(\mu_e \approx 0.135\) and \(\mu_h \approx 0.048\) m²/V s.
4. Temperature: higher temperature makes lattice vibrations stronger, increasing scattering, so mobility decreases.
5. Impurities (doping): ionised impurity atoms scatter carriers, so heavy doping lowers mobility.
6. Crystal defects: dislocations and grain boundaries also reduce mobility.
7. Conductivity links to mobility: \(\sigma = ne\mu\) (one carrier type) or \(e(n\mu_e + p\mu_h)\).

Key formula

\(\mu = \dfrac{v_d}{E} = \dfrac{e\tau}{m^*} = \dfrac{\sigma}{ne}\). \(\mu\): mobility (m²/V s), \(v_d\): drift velocity (m/s), \(E\): field (V/m), \(\tau\): relaxation time (s), \(m^*\): effective mass (kg), \(\sigma\): conductivity (S/m), \(n\): carrier concentration (m⁻³).

Quick example

Copper: \(\sigma = 5.8\times10^7\) S/m and \(n = 8.5\times10^{28}\) m⁻³. \(\mu = \sigma/(ne) = 5.8\times10^7/(8.5\times10^{28}\times1.6\times10^{-19}) \approx 4.3\times10^{-3}\) m²/V s. Silicon electrons (0.135) are about 30 times more mobile, but copper conducts far better because it has vastly more free electrons.

Common mistakes

• Saying higher mobility always means higher conductivity; carrier concentration matters too.
• Writing the unit as m/V s or m²/V; it is m²/V s.
• Claiming mobility increases with temperature in lattice-scattering-dominated materials.

How MU asks it

Asked as "Define mobility and state the factors affecting it" (3 marks), or with conductivity numericals (find \(\mu\) from \(\sigma\) and \(n\), or \(v_d\) from \(\mu\) and \(E\)). Give the definition, unit, \(\mu = e\tau/m\), and list three factors with reasons.