Chemistry Reference
In-Depth Information
Show that if charge neutrality is maintained in the laser active region
(
n
=
p
)
then the peak gain depends on carrier density
n
as
G
0
1
exp
exp
2
n
m
v
kT
2
n
m
c
kT
−
π
−
π
g
max
=
−
−
Show that if
m
c
m
v
, then the transparency carrier density,
n
0
, (for
=
which
g
max
=
0
)
is given by
m
c
kT
π
n
0
=
ln 2
2
This shows that the transparency (and hence threshold,
n
th
) carrier
density increases with the band edge effective mass in a quantum
well laser, and also that
n
0
increases approximately linearly with
temperature.
Justify why the transparency carrier density will vary as
n
0
∼
2
in a
D
-dimensional structure, and hence why the threshold
current density is predicted to have a lower temperature dependence
as the dimensionality
D
is reduced in the active region of an ideal
semiconductor laser.
D
/
(
k
B
T
)
