1
ECE 315 Homework 2
Due 12noon, Sept. 6, 2007
in the drop box
1.
(Compensational doping)
For a piece of homogeneous semiconductor under equilibrium at
room temperature with
n
i
=1.5
×
10
10
cm
3
,
find the electron and hole concentrations for
the
semiconductor contains
both N
A
=10
18
cm
3
and
N
D
=10
15
cm
3
:
(a)
Use the charge neutrality condition and
np=n
i
2
to obtain the exact solution of
n
and
p
(4 pts)
(b)
Explain why
p = N
A
– N
D
is a good approximation for the majority carrier here (4 pts)
(c)
Repeat (a) and (b) for
N
A
=10
18
cm
3
and
N
D
=10
17
cm
3
.
(4 pts)
(d)
If you are asked to calculate the electrostatic potential for the case in (a), will you use
p
or
N
A
?
What is the potential in relation to the intrinsic level? (4 pts)
(e)
If we build a resistor with this semiconductor, how will you compare the mobility for
the compensational doping with both
N
A
=10
18
cm
3
and
N
D
=10
17
cm
3
and the mobility
for
the case with only N
A
=9
×
10
17
cm
3
?
Briefly explain. (4 pts)
2.
(Carrier concentration in different temperatures)
The intrinsic silicon has
E
gap
=
1.1eV
and
n
i
= 1.5
×
10
10
cm
3
at 300K.
If we assume
E
gap
and the dopant (impurity that is either
donor or acceptor) ionization are temperature insensitive, given that
n
i
∝
exp(
E
gap
/2kT
),
(a)
What will be the intrinsic concentration at 250K and 400K? (4 pts)
(b)
If the silicon piece is doped with
N
D
= 10
16
cm
3
, find the electron and hole
concentrations at 250K and 400K. (4 pts)
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 Fall '07
 SPENCER
 Semiconductors, Microelectronics, Electric charge, Pn junction, Egap, Compensational

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