Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics
Density of holes in Valence Band of Intrinsic Semiconductor (Derivation)
We know that if an electron is transferred from valence band to conduction band, a hole is created in valence band
Density of holes in Valence Band of Intrinsic Semiconductor (Derivation)
We
know that if an electron is transferred from valence band to conduction band, a
hole is created in valence band.
Let
dp be the number of holes per unit volume in valence band between the energy E
and E + dE.
dp
= Z (E) (1 − F (E)) dE .................(1)
where
Z (E) dE → Density of states in the energy range E and E+ dE.
Since
F (E) is the probability of electron occupation 1 - F(E) is the probability of
an unoccupied electron state, i.e., (a) g probability of presence of hole.
Since
E is very small when compared to EF, in valence band (E – EF)
is a negative quantity. Therefore, 
is very small and it is neglected
in the denominator term of eqn (2).
Density
of states in valence band,
Here,
mh is the effective mass of the hole in valence band.
Ev,
top of energy level in valence band is the potential energy of a hole at rest.
Hence, (Ev - E) is the kinetic energy of the hole at level below Ev.
So the term E in eqn (4) is replaced as (Ev - E).
The
number of holes in valence band for the entire energy range is obtained by
integrating eqn (6) between limits - ∞ to Ev.
To
evaluate the integral in eqn (7), let us assume,
Substituting
these values in eqn (7), we have
[-ve
sign is omitted by interchanging the limits]
Using
the gamma function, it is shown that
Substituting eqn (10) in eqn (9), we have
The
equation (11) is the expression for the concentration of holes in valence band
of intrinsic semiconductor.
Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics : Tag: : - Density of holes in Valence Band of Intrinsic Semiconductor (Derivation)
Physics for Electronics Engineering: Unit III: Semiconductors and Transport Physics
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Physics for Electronics Engineering
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