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Drift Velocity

Drift velocity ( Equation v Subscript d ) is the average net velocity of a charge carrier in the direction of the electric field. Drift velocity is expressed in cm/s.

Overview

Without an electric field being applied, electrons in a material move about randomly due to the thermal velocity of the material. Despite moving at very high velocities, with lots of random collisions, the mean free path ends up being roughly zero. That is, the electrons do not go anywhere. When an electric field is applied across the material, there is a new net force on the carriers.

Equation upper F equals plus-or-minus q upper E

In between collisions, the carriers accelerate in the direction of the electrostatic field. We can use the equation for the velocity at constant acceleration to model this.

Equation v left-parenthesis t right-parenthesis equals a t

Where the acceleration Equation a , from Newton's second law of motion is:

Equation upper F equals m a , therefore
Equation a equals StartFraction upper F Over m EndFraction

Therefore we can say that the velocity of the carriers are:

Equation StartLayout 1st Row 1st Column v left-parenthesis t right-parenthesis 2nd Column equals a t 2nd Row 1st Column Blank 2nd Column equals StartFraction upper F Over m EndFraction t 3rd Row 1st Column Blank 2nd Column equals plus-or-minus StartFraction q upper E Over m Subscript n comma p Baseline EndFraction t EndLayout

Where Equation m Subscript n comma p is the mass of an electron or a hole.

The problem is that electrons do not just drift through, they also collide very frequently. Let Equation tau Subscript c represent the average time interval between collisions, then the average net velocity, or the drift velocity, in the direction of the electric field will depend on the mean time the carrier travels.

Equation v Subscript d Baseline equals plus-or-minus StartFraction q upper E Over 2 m Subscript n comma p Baseline EndFraction tau Subscript c Baseline equals plus-or-minus StartFraction q tau Subscript c Baseline Over 2 m Subscript n comma p Baseline EndFraction upper E

Where

Equation mu Subscript n comma p Baseline equals StartFraction q tau Subscript c Baseline Over 2 m Subscript n comma p Baseline EndFraction

is the carrier mobility.

Note that the equation can be expressed in the form of Ohm's law.

Equation v Subscript d Baseline equals mu Subscript n comma p Baseline upper E

Where,

  • Equation v Subscript d is the drift velocity [cm/s]
  • Equation mu Subscript n comma p is the carrier mobility [cm2/Vs]
  • Equation upper E is the magnitude of the electric field being applied to a material.

Therefore the drift velocity for electrons is:

Equation v Subscript dn Baseline equals minus mu Subscript n Baseline upper E

and for holes:

Equation v Subscript dp Baseline equals mu Subscript p Baseline upper E
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