Transport Mechanisms

• Drift: Occurs due to an applied electric field, causing carriers to move in response to the field.
• Diffusion: Occurs due to a concentration gradient, leading to carriers moving from regions of high to low concentration.

Drift Velocity and Scattering

• Carriers attain an average drift velocity when subjected to an electric field, influenced by scattering events (like lattice scattering and impurity scattering).
• For low electric fields, the drift velocity is linearly proportional to the applied field, but it reaches a saturation limit at high fields, around $10^7$ cm/s.

Carrier Mobility

Defined as the ratio of drift velocity to the applied electric field $$\mu = v_d

• It depends on temperature and ionized impurity concentration.
• Electron and hole mobilities affect how easily carriers can move through the semiconductor.

Drift Current Density

$$ J_{drift} = \sigma E $$

• Conductivity is determined by the carrier concentrations and their mobilities
• Resistivity is the inverse of conductivity

Diffusion Current Density

$$ J_{diffusion} \propto \=D \cdot \nabla n $$

Einstein Relation

• Relates the diffusion coefficient and mobility:

  $$ D = \mu \frac{kT}{q} $$

Hall Effect