Drift velocity

The drift velocity is the flow velocity that a particle, such as an electron, attains due to an electric field. It can also be referred to as axial drift velocity. In general, an electron will propagate randomly in a conductor at the Fermi velocity. An applied electric field will give this random motion a small net flow velocity in one direction.

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

Because current is proportional to drift velocity, which in a resistive material is, in turn, proportional to the magnitude of an external electric field, Ohm's law can be explained in terms of drift velocity.

The most elementary expression of Ohm's law is:

$u= \mu E ,$

where u is the drift velocity, μ is the electron mobility (with units m²/(V⋅s)) of the material and E is the electric field (with units V/m).

Experimental measure

The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by:

$u = {j \over n q} ,$

where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.

In terms of the basic properties of the right-cylindrical current-carrying metallic ohmic conductor, where the charge-carriers are electrons, this expression can be rewritten as:

$u = {m \; \sigma \Delta V \over \rho e f \ell} ,$

where

• u is again the drift velocity of the electrons, in m⋅s⁻¹
• m is the molecular mass of the metal, in kg
• ΔV is the voltage applied across the conductor, in V
• ρ is the density (mass per unit volume) of the conductor, in kg⋅m⁻³
• e is the elementary charge, in C
• f is the number of free electrons per atom
• ℓ is the length of the conductor, in m
• σ is the electric conductivity of the medium at the temperature considered, in S/m.

Numerical example

Electricity is most commonly conducted in a copper wire. Copper has a density of 8.94 g/cm³, and an atomic weight of 63.546 g/mol, so there are 140685.5 mol/m³. In one mole of any element there are 6.02×10²³ atoms (Avogadro's constant). Therefore in 1 m³ of copper there are about 8.5×10²⁸ atoms (6.02×10²³ × 140685.5 mol/m³). Copper has one free electron per atom, so n is equal to 8.5×10²⁸ electrons per cubic metre.

Assume a current I = 3 amperes, and a wire of 1 mm diameter (radius = 0.0005 m). This wire has a cross sectional area of 7.85×10⁻⁷ m² (A = π × (0.0005 m)²). The charge of one electron is q = −1.6×10⁻¹⁹ C. The drift velocity therefore can be calculated:

$\begin{align} u &= {I \over nAq}\\ u &= \frac{3}{\left(8.5 \times 10^{28}\right) \left(7.85 \times 10^{-7}\right) \left(-1.6 \times 10^{-19}\right)}\\ u &= -0.00028 \end{align}$

Dimensional analysis:

$u = \dfrac{\text{A}}{\dfrac{\text{electron}}{\text{m}^3}{\cdot}\text{m}^2\cdot\dfrac{\text{C}}{\text{electron}}} = \dfrac{\dfrac{\text{C}}{s}}{\dfrac{1}{\text{m}}{\cdot}\text{C}} = \dfrac{\text{m}}{\text{s}}$

Therefore in this wire the electrons are flowing at the rate of −0.00028 m/s.

By comparison, the Fermi flow velocity of these electrons (which, at room temperature, can be thought of as their approximate velocity in the absence of electric current) is around 1570 km/s.

In the case of alternating current, the direction of electron drift switches with the frequency of the current. In the example above, if the current were to alternate with the frequency of F = 60 Hz, drift velocity would likewise vary in a sine-wave pattern, and electrons would fluctuate about their initial positions with the amplitude of:

$A = \frac{1}{2F} \frac{2\sqrt{2}}{\pi} |u| = 2.1\times10^{-6} \text{ m}$

See also

• Flow velocity
• Electron mobility
• Speed of electricity
• Drift chamber
• Guiding center

External links

• Ohm's Law: Microscopic View at Hyperphysics