Carrier Transport: Drift, Diffusion, and Mobility

Manual: General · Subject: Semiconductor Science

Analyze how carriers move under electric fields and concentration gradients.

How Carriers Move in Real Devices

Drift transport

Under an electric field $E$ , carriers acquire a drift velocity $v_d = \mu E$ , where $\mu$ is mobility. The resulting current density is $J_{\text{drift}} = qn\mu_nE + qp\mu_pE$ .

Diffusion transport

When carrier concentration varies with position, carriers diffuse from high concentration to low concentration. Electron and hole diffusion currents are proportional to concentration gradients, with $J_{n,\text{diff}} = qD_n\frac{dn}{dx}$ and $J_{p,\text{diff}} = -qD_p\frac{dp}{dx}$ under common sign conventions.

ℹ️

Mobility is not constant in practice

Mobility decreases with lattice scattering, ionized impurity scattering, and high electric field effects, so temperature and doping both influence transport.

Transport concepts

Concept	Driving force	Typical expression
Drift	Electric field	$v_d = \mu E$
Diffusion	Concentration gradient	Fick's-law based current
Mobility	Material response to field	Higher mobility means easier motion
Diffusion length	Recombination-limited spread	Related to lifetime and diffusivity

What primarily drives diffusion current in a semiconductor?

Electric field only Concentration gradient Crystal color Band gap size alone

Write the drift velocity relation for carriers in an electric field.

Solving simple transport problems

1

Identify whether drift, diffusion, or both are present.
2

Write the correct current-density expression.
3

Substitute carrier density, mobility, and field or gradient values.
4

Check sign conventions carefully for electrons and holes.

Drift vs diffusion

Drift

Caused by electric field
Can produce current even in uniform carrier density

Diffusion

Caused by concentration gradient
Can occur even with zero electric field

Which factor generally reduces mobility in a doped semiconductor?

Reduced scattering Ionized impurity scattering Fewer lattice vibrations always Perfect crystal order

Name one physical mechanism that limits mobility at higher temperatures.

Neuroanatomy Explorer

Memory Deck

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Concept Constellation