ANSWERS
PHYS1200
PHYSICS II
SPRING 2005
Class 25 Activity:
p
and
n
Semiconductors
Part 1.
Doping Silicon
 Making semiconductor devices
Pure silicon at room temperature has an electron number density in the conduction band of
about 5 ×10
15
m
3
and an equal density of holes in the valence band. Suppose that one of
every 10
5
silicon atoms is replaced by a phosphorus atom.
1.
What is the valence of silicon?
What is the valence of phosphorous?
Silicon is valence 4.
Phosphorous is valence 5
2.
Which type will the doped semiconductor be,
n
or
p
?
Si doped with P will be ntype.
3.
If silicon has a molar mass of 28.1 g/mol and a density of 2.33 g/cm
3
, how many silicon
atoms would there be in a unit volume (1 cubic meter) ?
Si atoms
=
6.02 x 10
22
Si atoms
x
1 mol Si
x
2.33 grams Si
x
100
3
cm
m
3
mol Si
28.1 grams Si
1 cm3
1 m
3
There are 5 x 10
28
atoms of Si in 1 m
3
4.
So, given that one of every 10
5
silicon atoms is replaced by a phosphorus atom,
what charge carrier number density will the phosphorus add?
5 x 10
28
/ 1 x 10
5
=
5 x 10
23
atoms added by phosphorous.
Each atom adds 1 electron, so an equal number of charge carriers are added.
5.
What is the ratio of the charge carrier number density (electrons in the conduction band
and holes in the valence band) in the doped silicon to that in pure silicon?
holes
Si
electrons
conduction
Si
electrons
P
Added
holes
Si
electrons
conduction
Si
PureSi
DopedSi
.
.
.
.
.
.
.
.
.
+
+
+
=
=
(5 x 10
15
+ 5 x 10
15
+ 5 x 10
23
) / (5 x 10
15
+ 5 x 10
15
)
=
5 x 10
7
It is important to include both Si electrons and holes in the numerator AND denominator
1
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 Spring '08
 PeterPersans
 Physics, Semiconductors, silicon atoms, carrier number density, charge carrier number, nonzero current values

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