The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. In Physics, velocity is defined as the rate of change of Position. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In general, an electron will rattle around in a conductor at the Fermi velocity randomly. 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 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. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that

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. Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the

Drift velocity is expressed in the following equations:

• $J_{\it drift} = \sigma \cdot v_{\it avg}$, where Jdrift is the current density ,σ is charge density in units C/m3, and vavg is the average velocity of the carriers(drift velocity);
• $v_{\it avg} = \mu \cdot E$, where μ is the electron mobility in m2/(V·s) and E is the electric field in V/m. The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International In Physics, electron mobility (or simply mobility) is a quantity relating the Drift velocity of Electrons to the applied Electric field

## 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. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere.

One can relate ΔQ to the motion of charged particles in a wire expecting a dependence on the number density of the charge carriers and using dimensional analysis:

 ΔQ $= \left( \mathrm{number \ of \ charged \ particles} \right) \times \left( \mathrm{charge \ per \ particle} \right)$ $= \left( n A \Delta x \right) q$
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. In Physics, Astronomy, and Chemistry, number density is an Intensive quantity used to describe the degree of concentration of Countable Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand In Geometry, a cross section is the intersection of a body in 2-dimensional space with a line or of a body in 3-dimensional space with a plane etc This is what's called drift velocity, vd. And since Δx = vd Δt, we can plug it into the above equation.

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

Putting that back into the original equation and re-arranging to solve for the drift velocity:

 $v_d = \frac{I}{n q A}$
Alternative derivation

Using the definition of current density:

$J_{drift} = \sigma \cdot \nu_{drift}$

where σ is the density of charge per volume and the fact that

$J= \frac{I}{A}$

We can simply express:

$\sigma = n \cdot q$

to get

$\frac{I_{drift}}{A} = n \cdot q \cdot \nu_{drift}$

and the same result as above:

$v_d = \frac{I}{n q A}$