Week 3 HW
Week 3 HW
Week 3 HW
Lundstrom 09/04/2014
HW3
(continued):
5) For
each
of
the
cases
(a-‐e)
in
Prob.
3,
calculate
the
Fermi
level
position,
with
respect
to
the
intrinsic
level
( E F − Ei ) .
Note
that
you
need
to
consider
the
sign.
6) For
each
of
the
cases
(a-‐e)
in
Prob.
3,
calculate
the
Fermi
level
position,
with
respect
to
the
bottom
of
the
conduction
band
(EF
-‐
EC).
Note
that
you
need
to
consider
the
sign.
7) For
the
case
of
problem
4),
calculate
the
Fermi
level
position,
with
respect
to
the
intrinsic
level
( E F − Ei ) .
Note
that
you
need
to
consider
the
sign.
8) Your
textbook
defines
a
non-‐degenerate
semiconductor
as
one
for
which
the
Fermi
level
is
at
least
3k BT
below
the
conduction
band
edge
and
at
least
3k BT above
the
valence
band
edge.
What
is
the
largest
electron
density
for
non-‐degenerate
Si?
9) For
each
case
below,
explain
physically
(i.e.
in
words
in
no
equations)
whether
the
intrinsic
level
is
above
or
below
the
middle
of
the
gap,
then
compute
the
location
of
the
intrinsic
level
relative
to
the
middle
of
the
bandgap,
Emid = ( EC + EV ) 2
.
a) Silicon
at
T
=
300K
with
mn* = 1.18m0
and
m *p = 0.81m0 .
b) GaAs
at
T
=
300K
with
mn* = 0.067m0
and
m *p = 0.524m0 .
10) A
semiconductor
(not
necessarily
Si)
is
doped
at
N D = 2 × 1014 cm -3 and
N A = 1.2 × 1014 cm -3 .
The
thermal
equilibrium
electron
concentration
is
found
to
be
n = 1.1 × 1014 cm -3 .
Assume
complete
ionization
of
dopants,
and
compute
the
intrinsic
carrier
concentration
and
the
equilibrium
hole
concentration.
11) Answer
the
following
questions
about
resistivity
at
T
=
300K.
a)
Compute
the
resistivity
of
intrinsic
Si,
Ge,
and
GaAs.
b)
Compute
the
resistivity
of
n-‐type
Si,
Ge,
and
GaAs
doped
at
N D = 1019 cm -3 .
Assume
complete
ionization
of
dopants.
HW3
(continued):
12) You
are
given
a
10
Ohm-‐cm
silicon
wafer
at
300
K.
12a)
If
it
is
n-‐type,
What
is
the
electron
density?
12b)
If
it
is
p-‐type,
what
is
the
hole
density?
13)
Assume
a
hypothetical
semiconductor
with
the
following
properties:
EG = 1 eV N C = NV = 1 × 1019 cm -3
EC − EF = 0.4 eV
T = 600 K
Answer
the
following
questions.
13a)
What
is
the
equilibrium
electron
density?
13b)
What
is
the
equilibrium
hole
density?
13c)
What
is
the
intrinsic
carrier
concentration,
ni ?
13d)
What
is
the
net
doping
density,
N D − N A ,
assuming
that
the
dopants
are
fully
ionized?
13e)
Where
is
the
intrinsic
level
located
with
respect
to
the
conduction
band?
(Note:
You
can
simply
write
down
the
answer
without
any
work,
if
you
explain
your
reasoning.
14)
For
the
energy
band
diagram
sketched
below,
answer
the
following
questions.
14a)
Sketch
the
electrostatic
potential,
V ( x ) ,
vs.
position,
x.
14b)
Sketch
the
electric
field,
E ( x ) ,
vs.
position,
x.
14c)
Sketch
the
electron
density,
n ( x )
vs.
position,
x.
14d)
Sketch
the
hole
density,
p ( x ) ,
vs.
position,
x.