Drift velocity

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The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. Since particles can accelerate arbitrarily close to the speed of light in the absence of other forces, the term "drift velocity" can only really apply to carriers in materials, and not to particles in a vacuum. Particles in solids, for example, actually collide or scatter with the crystal lattice (or phonons), which slows them down. Drift velocity is non-uniform as it involves electric field as an externally accelerating agent.

In a semiconductor, the two main carrier scattering mechanisms are ionized impurity scattering and lattice scattering.

$J_{drift} = \rho \cdot \nu_{avg}$ where ρ is charge density in units $C / c m 3$ , and ʋavg is the average velocity of the carriers

$\nu_{avg} = \mu \cdot E$ where μ is the mobility of the carriers $\frac{cm^2}{V-s}$ and E is the electric field (V/cm)

[edit] Derivation

To find an equation for drift velocity, one can begin with the very definition of current:

$I = \frac{\Delta Q}{\Delta t}$

where

ΔQ is the small amount of charge that passes through an area in a small unit of time, Δt.

One can relate ΔQ to the motion of charged particles in a wire by:

$Δ Q$	$= \left( \mathrm{number \ of \ charges} \right) \times \left( \mathrm{charge \ per \ particle} \right)$
	$= \left( n A \Delta x \right) q$

where

n is the number of charge carriers per unit volume

A is the cross sectional area

Δx is a small length along the wire

q is the charge of the charge carriers

Now, normally particles move randomly, but under the influence of an electric field in the wire, the charge carriers gain an average velocity in a specific direction. This is what's called drift velocity, v_d. And since Δx = v_d Δt, we can plug it into the above equation.

$\Delta Q = \left( n A v_d \Delta t \right) q$