It is seen that in conductor current flow is due to the free electrons.
When conductor is subjected to an external voltage, free electrons move
from negative to positive terminal with a steady velocity constituting a
current. Such a current is called drift current which is due to
drifting of free electrons under the externally applied voltage.

In addition to the drift current, there may exist an additional current
due to the transport of charges in a semiconductor. Such an additional
current is due to the phenomenon called diffusion. This is the
characteristic of semiconductor and can not be observed in conductors.
The current due to the diffusion is called diffusion current. Basically
it is due to nonuniform concentration of charged particles in a
semiconductor.

**Note**: Diffusion is observed in non uniformly doped semiconductors and not in the conductors.

Consider a p-type semiconductor bar which is nonuniformly doped. Along
its length, in the direction of x as shown in Fig. 1(a), there exists a
nonuniform doping. As x increases, the doping concentration decreases.

To form p-type semiconductor, acceptor impurity is added which creates
holes as the majority charged particles. Let p be the concentration of
holes. But due to nonuniform doping it is not constant but is changing
with respect to x.

Let concentration of holes at x = 0 is P = P(0) and is maximum as bar
is heavily doped at x = 0. As x increases, the concentration of holes
decreases. The nature of the variation in p against distance x is shown
in the Fig. 1(b).

The slope of the graph can be observed from the Fig. 1(b) is the ratio
of change in concentration to change in distance. It is called rate of
change of concentration or concentration gradient.

**.**

^{.}. Slope of graph = Concentration gradient = dp/dx ................ (1)
Hence nonuniform doping produces a concentration gradient in a
semiconductor. Due to such concentration gradient, holes move from the
higher concentration area to the lower concentration area to adjust the
concentration. Such a movement of holes, due to the concentration
gradient in a semiconductor is called diffusion. Due to the movement of
holes, current is constituted in a bar which is called diffusion
current. There exists such a diffusion current in n-type semiconductor
if it is nonuniformly doped, due to movement of electrons which are
majority carriers.

**Note**: Nonuniform doping creats concentration gradient, due to which diffusion of charge carriers exists.

__1.1 Diffusion Current Density__

The diffusion current density is proportional to the concentration
gradient, which is responsible for the diffusion and hence the diffusion
current.

**.**J

^{.}._{p}α dp/dx ............ (2)

where J

_{p}= Diffusion current density due to holes

Hence the diffusion current density is expressed by,

J

_{p}= q D

_{p}dp/dx

where D

_{p}= Diffusion constant for holes expressed in square meters per second (m

^{2}/sec).

**Note**: The current due to holes is in the direction of the conventional current and hence treated as positive. But slope of the graph i.e. dp/dx is negative giving the negative diffusion current density for holes. But to get positive sign for holes, an additional negative sign is used to compensate for negative sign of dp/dx. Hence diffusion current density for holes is mathematically expressed as,

_{p}= - q D

_{p}dp/dx ............. (3)

In case of n-type bar, such diffusion current is due to the electrons.
Current due to the electrons is in opposite direction to the
conventional current and mathematically treated to be negative. The
concentration gradient dn/dx is negative where n is concentration of
electrons.

Hence diffusion current density to electrons is expressed by,J

_{n}= + q D

_{n}.............. (4)

where D

_{p}= Diffusion constant for electrons in square meters per second (m

^{2}/sec).

The Fig. 2(a) shows the direction of diffusion of holes and
corresponding diffusion current density. The Fig. 2(b) shows the
direction of diffusion of electrons and corresponding diffusion current
density.

Fig. 1 Diffusion current densities |

Observe that the charge carriers whether it is hole or electron, always
move from high concentration area towards low concentration area. Hence
direction of diffusion is same in both the cases. But resulting current
densities have opposite direction.

__1.2 Total Current Density Due to Drift and Diffusion__

We have seen that the drift current is due to the applied voltage while
the diffusion current is due to the concentration gradient. But in
semiconductor it is very much possible that both the types of currents
may exist simultaneously. In practice is such situation there exists
four components of current as the drift current due to electrons and due
to holes, while the diffusion current due to electrons and due to
holes.

Drift current density due to the electrons and holes can be expressed from equations (3) and (4) as,J

_{n}= n q E and J

_{p}= p q E

Diffusion current density due to the electrons and holes can be expressed from equations (3) and (4) as,

J

_{n}= + q D

_{n}dn/dx and J

_{p}= - q D

_{p}dp/dx

Total current density due to the electrons can be expressed as,

J

_{n}= n q μ

_{n }E + q D

_{n}dn/dx .............. (5)

and Total current density due to the holes can be expressed as,

J

_{p}= p q μ

_{p }E + q D

_{p}dp/dx .................. (6)

And hence the total current density due to the electrons and holes (drift + diffusion) is,

J = J

_{n}+ J

_{p}................. (7)

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