37
Review of Basic Device Physics
a semiconductor. This leads to an additional component of current in proportion to the concentration gradient and is called the diffusion current. Thus,
the diffusion is a gradient driven motion and occurs from high-concentration regions toward low-concentration regions as shown in Figure 2.8.
The diffusion flux is given by Fix’s first law,
F
D
dC
dx
= −
(2.39)
where:
F, D, and C are the flux of carriers, diffusion constant, and carrier density,
respectively
The negative sign is due to the fact that the carriers flow from the higher
concentration to lower concentration; that is, dC/dx is negative. If the carrier
flow in a semiconductor material is electron, then the diffusion current flow
due to the electron concentration gradient dn/dx is given by
J
qD
dn
dx
n diff
n
,
=
(2.40)
Similarly, the hole diffusion current due to hole concentration gradient dp/dx
is given by
J
q D
dp
dx
p diff
p
,
= −
(2.41)
where:
D n and D p are called the diffusivity or diffusion constants for electrons and
holes in the material, respectively
t 1 Flux of
diffusion
current
−x
x
0
Flux of
diffusion
current
Carrier
concentration
t 3
t 2
t 1
FIGURE 2.8
Diffusion of carriers from high concentration to low concentration due to concentration
gradient over different time intervals t 1   <  t 2   <  t 3 ; t 1 is the initial time and the background
concentration ≈ 0.