Drift velocity
Encyclopedia
The drift velocity is the average velocity
that a particle, such as an electron
, attains due to an electric field
. It can also be referred to as Axial Drift Velocity since particles defined are assumed to be moving along a plane. In general, an electron will 'rattle around' in a conductor
at the Fermi velocity
randomly. An applied electric field will give this random motion a small net 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 is, in turn, proportional to the magnitude of an external electric field, Ohm's law
can be explained in terms of drift velocity.
Drift velocity is expressed in the following equations:
, where 
is the current density, 
is charge density in units C/m3, and vavg is the average velocity of the carriers (drift velocity);
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 1 mole
of any element there are 6.02×1023 atoms (Avogadro's constant). Therefore in 1m³ 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 m³.
Assume a current I=3 amperes, and a wire of 1 mm diameter (radius in meters = 0.0005m). This wire has a cross sectional area of 7.85×10-7 m2 (A= π×0.00052). The charge of 1 electron
is q=-1.6×10−19 Coulombs. The drift velocity therefore can be calculated:
Analysed dimensionally:
[V] = [Amps] / [electron/m3] × [m2] × [Coulombs/electron]
Therefore in this wire the electrons are flowing at the rate of -0.00029 m/s, or very nearly -1.0 m/hour.
By comparison, the Fermi 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 case of the 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
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
that a particle, such as an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
, attains due to an electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
. It can also be referred to as Axial Drift Velocity since particles defined are assumed to be moving along a plane. In general, an electron will 'rattle around' in a conductor
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...
at the Fermi velocity
Fermi energy
The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature....
randomly. An applied electric field will give this random motion a small net velocity in one direction.
In a semiconductor
Semiconductor
A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...
, the two main carrier scattering mechanisms are ionized impurity scattering
Ionized impurity scattering
Ionized impurity scattering is the scattering of charge carriers by ionization in the lattice. The most primitive models can be conceptually understood as a particle responding to unbalanced local charge that arises near a crystal impurity; not dissimilar to an electron encountering an electric field...
and lattice scattering
Lattice scattering
Lattice scattering is the scattering of ions by interaction with atoms in a lattice. This effect can be qualitatively understood as phonons colliding with charge carriers....
.
Because current is proportional to drift velocity, which is, in turn, proportional to the magnitude of an external electric field, Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
can be explained in terms of drift velocity.
Drift velocity is expressed in the following equations:
, where is the current density, is charge density in units C/m3, and vavg is the average velocity of the carriers (drift velocity);
-
, where μ is the electron mobilityElectron mobilityIn solid-state physics, the electron mobility characterizes how quickly an electron can move through a metal or semiconductor, when pulled by an electric field. In semiconductors, there is an analogous quantity for holes, called hole mobility...
in (m^2)/[V.s]) and E is the electric fieldElectric fieldIn physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
in VVoltThe volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
/m.
Numerical example
Electricity is most commonly conducted in a copper wire. CopperCopper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
has a density of 8.94 g/cm³, and an atomic weight
Atomic weight
Atomic weight is a dimensionless physical quantity, the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12...
of 63.546 g/mol, so there are 140685.5 mol/m³. In 1 mole
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...
of any element there are 6.02×1023 atoms (Avogadro's constant). Therefore in 1m³ 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 m³.
Assume a current I=3 amperes, and a wire of 1 mm diameter (radius in meters = 0.0005m). This wire has a cross sectional area of 7.85×10-7 m2 (A= π×0.00052). The charge of 1 electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
is q=-1.6×10−19 Coulombs. The drift velocity therefore can be calculated:
Analysed dimensionally:
[V] = [Amps] / [electron/m3] × [m2] × [Coulombs/electron]
- = [coulombs] / [seconds] × [electron/m3] × [m2] × [Coulombs/electron]
- = [meters] / [second]
Therefore in this wire the electrons are flowing at the rate of -0.00029 m/s, or very nearly -1.0 m/hour.
By comparison, the Fermi 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 case of the alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
, 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
External links
- Ohm's Law: Microscopic View at Hyperphysics