Imagine two cross section areas of a semiconductor

at distances zero and x. If the number of either electrons or holes is greater in one

area compared to another area, then carriers tend to move from the region of higher concentration

to the region of lower concentration, even in the absence of an applied voltage. This

process is called diffusion and the electric current, produced due to this process, is

known as diffusion current. For example, in this picture, the concentration

of electrons in the area at x equal 0 is greater than the concentration of electrons at distance

x. So dn/dx which is the concentration gradient is not zero. Therefore, electrons diffuse

from x0 area to x area so that the concentration gradient dn/dx becomes 0. The diffusion current is proportional to the

cross section Area (A), charge of the electron or hole (q) and the concentration gradient

which is dn over dx or dp over dx. We can convert this proportion to equality by adding

diffusion constant which is shown by the capital D with subscript n for electrons and with

subscript p for holes. So the diffusion current equals cross section

area (A) times charge of an electron or hole (q) times diffusion constant Dn for electrons

or DP for holes times the concentration gradient dn over dx for electrons or dp over dx for

holes. Current density can be easily obtained by dividing the current by the cross section

area. There is an important relationship which relates

diffusion constant to the mobility. This relation is known as Einstein’s relationship for

a semiconductor. According to Einstein’s relationship, the ratio of diffusion constant

to the mobility of the charge carriers is constant and is equal to the volt-equivalent

of temperature VT which equals K T over q. Where K is the Boltzmann constant, T is the

temperature, and q is the charge. The value of VT is approximately 26mV at 300ºK or room

temperature.

## No Comments