Diffusion and Continuity Equations

Diffusion is a process, in which a particle tend to spread out a redistribute as a result of random thermal motion migrating from regions of high particle concentration to low particle concentration to produce uniform distribution.

Electrons and holes are charged so when they diffuse diffusion current.

Derivation of Diffusion current

Assumptions

.  One dimensional only

.  All carriers move with the same velocity (in practice a distribution of velocity)

.  The distance moved by carriers between collisions is a fixed length L. (L is actually mean distance moved by carrier between collisions).

Randomness of thermal motion equal no. of particles moving in +x and -x

Fig.9.1

Derivation

Within and section equal outflow of particles per second from any interior section to neighbouring sections on the right and left. But because of concentration gradient the no. of particles moving from right to left second is greater than no. of particles moving from left to right.

Fig.9.2

Of the holes in a volume LA on either side of x = 0

Will move in proper direction so as to cross x = 0 plane

= holes moving in +x which cross x=0 plane in time

  = holes moving in +x which cross x = 0 plane in time

But

= net no of +x directed holes with cross x = 0 plane in time

Net current cross x=0 plane.

We define

Generalizing

are constants in cm 2 /sec