Diffusion current

[1] It is necessary to consider the part of diffusion current when describing many semiconductor devices.

The diffusion constant for a doped material can be determined with the Haynes–Shockley experiment.

In a region where n and p vary with distance, a diffusion current is superimposed on that due to conductivity.

This diffusion current is governed by Fick's law: where: The diffusion coefficient for a charge carrier is related to its mobility by the Einstein relation: where: Now let's focus on the diffusive current in one-dimension along the x-axis: The electron current density Je is related to flux, F, by: Thus Similarly for holes: Notice that for electrons the diffusive current is in the same direction as the electron density gradient because the minus sign from the negative charge and Fick's law cancel each other out.

However, holes have positive charges and therefore the minus sign from Fick's law is carried over.

To derive the diffusion current in a semiconductor diode, the depletion layer must be large compared to the mean free path.

One begins with the equation for the net current density J in a semiconductor diode, where D is the diffusion coefficient for the electron in the considered medium, n is the number of electrons per unit volume (i.e. number density), q is the magnitude of charge of an electron, μ is electron mobility in the medium, and E = −dΦ/dx (Φ potential difference) is the electric field as the potential gradient of the electric potential.

For example, when a bias is applied to two ends of a chunk of semiconductor, or a light is shining in one place (see right figure), electrons will diffuse from high density regions (center) to low density regions (two ends), forming a gradient of electron density.