Physics for Information Science: Unit II: Semiconductor Physics
Variation of Fermi Energy Level and Carrier Concentration with Temperature in an Intrinsic Semiconductor
For an intrinsic semiconductor number of electrons (i.e,) electron density will be the same as that of number of holes (i.e.,) hole density.
VARIATION
OF FERMI ENERGY LEVEL AND CARRIER CONCENTRATION WITH TEMPERATURE IN AN INTRINSIC
SEMICONDUCTOR
For
an intrinsic semiconductor number of electrons (i.e,) electron density will be
the same as that of number of holes (i.e.,) hole density.
(i.e.,)
ne=nh
Equating
equations (7) and (12), we can write
Taking
log on both sides we have
……..(13)
Equation
(13) becomes
……..(14)
i.e.,
the Fermi energy level lies in the midway between Ec and Ev
as shown
in
Fig. 2.9 (since at 0 K, T=0).
But
in actual case m*h >m *e and the Fermi energy level
slightly increases with the increase in temperature as shown in Fig. 2.9.
Density of electrons and holes interms of Eg
In
terms of energy gap (Eg) where Eg = Ec-Ev,
we can get the expression of nc and nh by substituting
the value of EF in terms of Ec and Ev.
Substituting
equation (13) in (7) we get
Since
Eg = Ec-Ev, we can write
………(15)
Similarly
by substituting equation (13) in (12) we get
………(16)
Thus,
it is found that ne = nh = ni where ni
is the intrinsic carrier concentration.
Results
•
In an intrinsic semiconductor the density of electrons in conduction band is
equal to the density of holes in valence band. (i.e.,) ne = nh
•
ne and nh increases exponentially as the temperature
increases.
Intrinsic Carrier Concentration
We
know that, ni = ne = nh where ni2 = ne . nh
Substituting
from equations (15) and (16), we have
………(17)
Physics for Information Science: Unit II: Semiconductor Physics : Tag: : - Variation of Fermi Energy Level and Carrier Concentration with Temperature in an Intrinsic Semiconductor
Physics for Information Science: Unit II: Semiconductor Physics
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Physics for Information Science
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