Physics for Information Science: Unit II: Semiconductor Physics
Carrier Concentration in n-Type Semiconductor
At 0 K, EF will lie exactly between Ec and Ed, but even at low temperature some electrons may go from Ed to Ec.
CARRIER
CONCENTRATION IN n – TYPE SEMICONDUCTOR
The
energy band structure of n-type semi- conductor is as shown in Fig. 2.16.
At
0 K, EF will lie exactly between Ec and Ed,
but even at low temperature some electrons may go from Ed to Ec.
Let us assume that Ec-EF > KB T. Then the
density of electrons in conduction band can be written as
…………(1)
Let
Nd be the number of donor energy levels per cm3 (i.e.,)
density of state Z (Ed) dE, which has energy Ed below the
conduction band.
If
some electrons are donated from donar energy level to conduction band say for
example if two electrons goes to conduction band then two vacant sites (holes)
will be created in E, levels as shown in Fig. 2.16.
Thus,
in general we can write the density of holes in donar energy level as
N
(Ed) dE=Z (Ed) dE (1 - F (Ed))
i.e.,
nh = Nd (1-F (Ed) ……..(2)
we
know
………(3)
Since
EF -Ed>>KBT
(or)
Ed - EF <<KBT
(or)
Ed - EF / KBT <<1
(or)
e(Ed − EF)/KBT
<< 1
1
+ e(Ed − EF)/KBT≈ 1
Equation
(3) becomes
1
− F (Ed) = e(Ed − EF)/KBT
.....(4)
Substituting
equation (4) in (2)
nh
= Nd e(Ed − EF)/KBT
……(5)
At
Equilibrium condition
Number
of electrons per unit volume in conduction band (i.e. electron density) = Number
of holes per unit volume in donar energy level. (i.e., hole density)
Equating
equation (1) and equation (5) we get
Taking
log on both sides
………(6)
At
0K i.e, When T=0, we can write the above
equation as
EF=(Ec+Ed)/2
…...(7)
Equation
(7) shows that, at 0K, EF will lie exactly in the midway between Ecand
Ed
Expression
for Density of Electrons in Conduction Band in terms of Nd
Substituting equation (6) in (1) we get
Here
Ec-Ed=ΔE is called as Ionisation energy of donors (i.e.)
ΔE represents the amount of energy required to transfer an electron from donar
energy level (Ed) to conduction band (Ec).
We
can write
……..(8)
Physics for Information Science: Unit II: Semiconductor Physics : Tag: : - Carrier Concentration in n-Type Semiconductor
Physics for Information Science: Unit II: Semiconductor Physics
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Physics for Information Science
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