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.