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Lecture 1

ECE331 Lecture Notes - Lecture 1: Charge Carrier, Indium Phosphide, Indium


Department
Electrical and Computer Engineering
Course Code
ECE331
Professor
C.R.Selvakumar
Lecture
1

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E&CE 231 Majority and Minority Carrier Density Page 1/3 C.R.Selvakumar
How to determine the thermal equilibrium Majority and
Minority Carrier Densities in extrinsic semiconductors ?
We want to consider a general situation in which we assume that both ND donors
and NA acceptors per unit volume are present in the extrinsic semiconductor. We
want to know how many electrons (n0) and how many holes (p0) per unit volume
will be there in this extrinsic semiconductor. This is easily determined by solving
two key equations: law of mass action and charge neutrality equations. Thus
solve the following two equations simultaneously to determine n0 and p0:
np n
i00 2
= (1)
nN pN
AD00
+=+
-+
(2)
nn
p
n
pNpN
pNNpn
p
i
iAD
AD i
0
2
0
2
00
0
202
0
0
=
+=+
-- -=
-+
-+
Substitute in (2):
Collecting the terms,
Solving for
()
,
pNN NN
AD AD022
1
2
1
24=-+ -+
-+ -+
()()n
i
---- (3)
The above equation is required to be used to calculate hole density only
in the rare cases where the doping density is so low as to be comparable to
intrinsic carrier density ni
Approximations
For example consider the case of silicon. The doping densities range usually
between 1015 to 1020 cm-3 . Clearly these dopant densities are much greater than
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