Carrier Injection
we expect the minority carrier concentration on each side of a p-n junction to vary with the applied bias because of variations in the diffusion of carriers across the junction. The equilibrium ratio of hole concentrations on each side
equ (1)
becomes with bias
equ (2)
With this simplification we can write the ratio of Eq. (1) to (2) as equ (3)
We can easily calculate the excess hole concentration Δpn at the edge of the transition region xn0 by subtracting the equilibrium hole concentration from Eq. 3
equ (4)
and similarly for excess electrons on the p side, equ (5)
We can write the diffusion equation for each side of the junction and solve for the distributions of excess carriers (∂n and ∂p) assuming long p and n regions:
equ (6)
The hole diffusion current at any point xn in the n material can be calculated equ (7)
The total hole current injected into the n material at the junction can be obtained simply by evaluating equ (7)
By a similar analysis, the injection of electrons into the p material leads to an electron current at the junction of
This is the carrier injection for electron & holes.