Band Theory & Electrical Properties

Carriers & Mobility

Electrons, holes, drift, diffusion, and how fast carriers move

Electrons and Holes

Electrons and Holes

Current in semiconductors is carried by two types of charge carriers:

  • Electrons: Negatively charged, move in the conduction band. Dominant carriers in N-type silicon.
  • Holes: Positively charged "absences of electrons" in the valence band. Dominant carriers in P-type silicon.

In intrinsic (undoped) silicon at room temperature, the carrier concentration is about 1.5 × 10¹⁰ cm⁻³. This sounds large, but silicon has 5 × 10²² atoms/cm³, so only about 1 in every 10¹² atoms has a thermally generated free carrier.

Key Concept: Mass Action Law

In thermal equilibrium, the product of electron and hole concentrations is constant: n × p = nᵢ². If you increase electrons (N-type doping), the hole concentration automatically decreases, and vice versa. This is the mass action law.

Carrier Mobility

Carrier Mobility

Mobility (μ) measures how easily carriers move through the crystal in response to an electric field. Higher mobility = faster devices.

At room temperature in silicon:

  • Electron mobility: ~1400 cm²/(V·s)
  • Hole mobility: ~450 cm²/(V·s)

Electrons move about 3× faster than holes in silicon. This is why NMOS transistors (which use electron current) are faster than PMOS transistors (which use hole current).

Mobility depends on:

  • Temperature: Higher temperature → more lattice scattering → lower mobility
  • Doping: Higher doping → more impurity scattering → lower mobility
  • Electric field: At very high fields, carriers reach a maximum velocity (~10⁷ cm/s in Si)

Knowledge Check

Knowledge Check

1 / 2

Which carrier has higher mobility in silicon?