Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics
Concentration of Holes in Valence Band of p-type Semiconductors
Derivation
In p-type semiconductor, acceptor energy level is just above valence band
CONCENTRATION OF HOLES IN VALENCE BAND OF P-TYPE SEMICONDUCTORS
[Derivation]
In
p-type semiconductor, acceptor energy level is just above valence band (fig.
3.10).
Density
of holes per unit volume in valence band is given by
Ev → Energy corresponding to
top most level of valence band.
Density
of ionised acceptors = Na F(Ea)
N-the
number of acceptor atoms per unit volume.
Ea-
acceptor energy level
Here, F(Ea) is probability for finding electron in acceptor energy level ie., ionised acceptor.
The
eqn (1) becomes, density of ionised acceptors
is a large quantity and thus '1' from the (a) e denominator of R.H.S. of eqn
(2) is neglected.
Now,
the eqn (2) is modified as,
Density
of ionised acceptors 
At
equilibrium,
Taking
log on both sides in eqn (5), we have
Rearranging,
Substituting
eqn of EF from (7) in (1), we get
where
∆E = Ea – Ev is the ionisation energy of acceptors.
Results
i.
Density of holes in valence band is proportional to the square root of acceptor
concentration.
ii.
At high temperature, we must take into account the intrinsic carrier concentration
of semiconductor due to breaking of covalent bond along hole concentration
produced by acceptor impurity.
iii.
At very high temperature, intrinsic carrier concentration over takes holes due
to acceptor concentration.
iv.
i.e., At very high temperature, p-type semiconductor behaves like an intrinsic
semiconductor and acceptor concentration becomes insignificant.
Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics : Tag: : Derivation - Concentration of Holes in Valence Band of p-type Semiconductors
Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics
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Physics for Electronics Engineering
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