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Diffusion Current

Diffusion current is current which occurs in response to concentration gradient. That is, diffusion current is the movement of charge carriers as a result of entropy ensuring that carriers move from a region of high concentration into regions of low concentration. This is in contrast to drift current which is a result of an applied electric field.

Overview[edit]

In a given material where particles are uniformly distributed within the lattice, charge carriers will roam around randomly due to thermal velocity of the material. However, due to the random collisions the net current will result in a net current of zero as the carriers do not really go anywhere.

diffusion current - uniform.svg

In a material where particles are not entirely uniformly distributed, entropy will ensure that carriers in region of high concentration will move to regions of low concentration. The diffusion current is therefore the movement of those charge carriers as they diffuse.

diffusion current - high con.svg

Diffusion vs Drift currents[edit]

See also: drift current
Diffusion current Drift current
Result of Having mass Having charge
Due to Carrier movement due to concentration gradient Carrier movement due to electric field applying a force
Obey Fick's law Ohm's law

Theory[edit]

Using Fick's law, we ca related the diffusive flux to the concentration.

Equation upper F equals minus upper D StartFraction d phi Over d x EndFraction

which, for electrons is

Equation upper F Subscript n Baseline equals minus upper D Subscript n Baseline StartFraction d n Over d x EndFraction

and for holes is

Equation upper F Subscript p Baseline equals minus upper D Subscript p Baseline StartFraction d p Over d x EndFraction

Where Equation upper D Subscript n is the electron diffusion coefficient and the Equation upper D Subscript p is the hole diffusion coefficient. Both are in cm2/s.

There are Equation n free electrons per cubic meter of this material, each with have an elementary charge Equation q .

Diffusion current density Equation upper J Subscript n Superscript diff due to free electrons

Equation upper J Subscript n Superscript diff Baseline equals q upper D Subscript n Baseline StartFraction d n Over d x EndFraction

While the current density Equation upper J Subscript p Superscript diff due to holes is

Equation upper J Subscript p Superscript diff Baseline equals minus q upper D Subscript p Baseline StartFraction d p Over d x EndFraction

See also[edit]