Physics for Information Science: Unit II: Semiconductor Physics
Carrier Concentration in p-Type Semiconductor
For p-type at absolute zero Ep will be exactly between E and E. At low temperatures some electron from valence band fills the holes in the acceptor energy levels.
CARRIER
CONCENTRATION IN p-TYPE SEMICONDUCTOR
For
p-type at absolute zero Ep will be exactly between E and E. At low temperatures
some electron from valence band fills the holes in the acceptor energy levels
as shown in Fig. 2.19.
We
know the density of holes in the valence band,
…….(1)
Let
Na be the number of acceptor energy levels per cm3 which
has energy Ea above valence band. If some electrons are accepted by
the acceptor energy levels from the valence band, say for example if two
electrons are accepted to fill the hole sites in the acceptor levels, then two
holes will be created in the valence band as shown in Fig. 2.19.
Therefore,
in general the electron density in the acceptor energy level can be written as
N
(Ea) dE = Z (Ea) dE • F (Ea)
i.e.,
ne = Na F (Ea) ………(2)
here
Since
Ea - EF >> KBT
………..(3)
Substituting
equation (3) in (2), we have
……….(4)
At equilibrium condition,
Equating
equation (1) and (4) we have
Taking
log on both sides
………..(5)
At
0K, i.e., when T = 0K, we can write equation (5) as
……(6)
Expression
for Density of Holes in Terms of Na
Substituting
equation (5) in (1) we get
……..(7)
Here
Ea - Ev = ΔE is known as ionisation energy of acceptors
i.e., ΔE represents the energy required for an electron to move from valence
band (Ev) to acceptor energy level (Ea).
Therefore
equation (7) becomes
………(8)
Physics for Information Science: Unit II: Semiconductor Physics : Tag: : - Carrier Concentration in p-Type Semiconductor
Physics for Information Science: Unit II: Semiconductor Physics
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