*Drift and Diffusion *

The current that flows across a semiconducting crystal has two components :

1. Drift current

2. Diffusion current

In a perfect crystal, the periodic electric field enables electrons and holes to move freely as if it
in a vacuum. In this case, the wave model of the electron is more appropriate
than the particle model. The defects in real crystals cause the periodic
electric field to be distributed and for

In the absence of any
extremely applied electric field, the random motion of free carriers within a
crystal does not result in a net transfer of charge since charge movement in
any direction is balanced by charge movement in any other direction.

Where

whereis the relaxation time between collisions.

Thus

OrIf the material is a semiconductor, the current flow would be done electron and hole movement. Correspondingly the current densities due to electron drift and hole drift are

Respectively, these
charge movement are in opposite directions, the electron movement is negative
charge movement while the hole component is positive charge movement and so the
total drift current is the sum of the two components, thus

i.e.

Comparison withshows that the conductivity of a semiconductor is given by

For an intrinsic
semiconductor, conductivity is given by

Conductivity is a
function of temperature. If an increase of temperature cause an increase in
free charge, the conductivity odf the material is increased. However,
temperature increase also cause increased vibration of the lattice which causes
increased scattering, reduced carriers mobility and hence reduced conductivity.
The variation of conductivity of a material with temperature depends on which
of these effect dominates. For a conductor there is not a significant increase
in free charge with increase of temperature and therefore the increased
scattering causes the conductivity of a conductor to fall as the temperature
increases. Alternatively, the free carrier density of a semiconductor increases
rapidly with temperature resulting in increased conductivity. A conductor is
said to have a positive temperature coefficient resistant since its resistance
increases with temperature while a semiconductor has a negative coefficient.

At normal operating
temperature an extrinsic semiconductor has properties similar to these of a
conductor. An increase of temperature does not significantly change the free carrier
density. Since most of the dopant atoms are already ionized, thus increased
scattering causes conductivity to fall. However, as the transition temperature
is approached, the generation of electron-hole pairs does cause the free
carrier density to increase significantly and the material takes on intrinsic
properties. Thus an extrinsic semiconductor has a positive temperature
coefficient of resistance at normal temperature changing to a negative
coefficient near the transition temperature.

__Diffusion Current__In addition the drift
motion of the carriers under the influence of an electric field the carriers in
semiconductors may move by diffusion. Diffusion occurs whenever there is a
non-uniform concentration of charge carriers at some places of the crystal. The
free electron density in a homogeneous semiconductor in the absence of an
applied electric field is uniform at equilibrium due to a combination of the
random thermal motion of the electrons and the repulsive force between them
caused by their like charge. If excess carrier are introduced locally within
such a semiconductor, either by causing carrier generation by heating or
incident radiation or by injecting carriers into the material via a surface
contact, a non-uniform distribution is created. Ignoring the process of
recombination which is an additional phenomenon, the excess carriers move from
the region of higher density to regions of lower density tending to produce a
uniform distribution. The transport mechanism is called diffusion and it take
place in addition to drift caused by an applied electric field.

Let us suppose that the
concentrationof electrons varies with distance x in the
semiconductor, the concentration of gradient being

Partial derivatives are used here asis a function of both time and distance. Fick’s law states that the rate at which carriers diffuse is proportional to the density gradient and the movement is in the direction of negative gradient, the rate of flow of electrons is proportional to

From which the rate of
flow across unit area is equal to

Whereis the diffusion coefficient for electrons in
the semiconductors concerned. This flow constitutes an electron diffusion
current density and since conventional current is the rate of positive charge

If an excess hole
concentration is created in the same region, hole diffusion takes place in the
same direction at a rate per unit area

Resulting in a hole
diffusion current density

Whereis the hole diffusion coefficient.

If there is an electric
field E and a concentration gradient in the x-direction, the total hole-current
is the sum of the drift currentand the diffusing current given by eq. (4)

Thus

Similarly for the
electrons, the total current density

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