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3-7 Extra Carriers in Semiconductors:
The semiconductor is often used in the extrinsic case and in a situation
of loss of equilibrium in the concentration of the carriers. In equilibrium, the
generation (G) and the recombination (R) of the carriers are equal and the
product of the majority carriers and the minority carriers is constant, for
example, in a p-type crystal, the number of the holes ( p ) and the number of
the electrons ( n ) is constant where ( p  n ) and ( 2
i np  n ) and the
generation (the electron-hole pair generation) is equal to the recombination
(G = R).
In the loss of equilibrium situation, the concentration of the carriers
changes due to an external factor which generates extra carriers above the
equilibrium concentration level, for example, if light is applied on the
semiconductor then the generation of the carriers will increase, for p-type
semiconductor, which contains at equilibrium ( p ) holes and ( n ) electrons,
now assume that this semiconductor from the time instant ( t  0 ) is
subjected to an external stimulus (light) which generates extra holes and
electrons with a concentration ( n  p ) because each generated electron
generates a hole, so the number of holes becomes:
p p p total   
And the number of electrons:
n n n total   
In this case, ( ni n p 2  ) where ( ni n p 2  ) and the semiconductor is
called unstable semiconductor.
When the stimulus disappears, the equilibrium level returns to its
original level after a short period. Assume that the number of extra electrons
2
Ali Farooq Electronic Physics Control & Systems
Lecture 7 First Year
at ( t  0 ) is ( o n ) and the number of extra holes at this moment is ( o p ),
then the disappearance of the external stimulus (light) at this moment results
in the decreasing of the number of the extra carriers with time, the decrease
is exponential where the number of the remaining extra electrons is given by
the following equation:
e
o
n n t


   exp
Where:
n : The number of the remaining extra electrons after time ( t ) from the
moment of turning off the light source.
o n : The number of the extra electrons generated at the moment of turning
off the light source ( t  0 ).
e  : Life time of the electron. ( e  ) represents the time average in which the
electron remains free before it recombines.
Similarly, for the holes:
p
o
p p t


   exp
p  : Life time of the hole.
Example (3-6): The conductivity of a piece of n-type silicon increased from
( 5104 (.cm)1 ) to ( (0.3.cm)1 ) when exposing this piece to a light source.
Calculate the number of the excited electrons across the energy gap.

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انا أتآآآمر من زمان هذه اللحلها قصة ع 8 أجزاء....

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