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Intrinsic material, Electrical Engineering
Int
r
insic Material
A perfect semiconductor crystal with no impurities or lattice defects.
No carriers at 0 K, since the valence band is completely full and the conduction band is completely empty.
For T > 0 K, electrons are thermally excited from the valence band to the conduction band (EHP generation).
EHP generation takes place due to breaking of covalent bonds => required energy = Eg.
The excited electron becomes free and leaves behind an empty state (hole).
Since these carriers are created in pairs, the electron concentration (n/cm
^{3}
) is always equal to the hole concentration (p/cm
^{3}
), and each of these is commonly referred to as the intrinsic carrier concentration
(n
_{i}
).
Thus, for intrinsic material n = p = n
_{i}
.
These carriers are not localized in the lattice; instead they spread out over several lattice spacings, and are given by quantum mechanical probability distributions.
Note: n
_{i }
= f (T).
To maintain a steadystate carrier concentration, the carriers must also recombine at the same rate at which they are generated.
Recombination occurs when an electron from the conduction band makes a transition (direct or indirect) to an empty state in the valence band, thus annihilating the pair.
At equilibrium, r
_{i}
=g
_{i}
, where g
_{i}
and r
_{i }
are the generation and recombination rates respectively, and both of these are temperature dependent.
g
_{i}
(T) increases with temperature, and a new carrier concentration ni is established, such that the higher recombination rate r
_{i}
(T) just balances generation.
At any temperature, the rate of recombination is proportional to the equilibrium concentration of electrons and holes, and can be given by r
_{i}
= α
_{r}
n
_{0}
p
_{0}
= α
_{r}
n
_{i}
^{2}
=gi(5) where α
_{r}
is a constant of proportionality (depends on the mechanism by which recombination takes place).
Posted Date: 1/11/2013 4:42:03 AM  Location : United States
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