MSE 302 Problem Set 2 Solutions (32 Points)
1.
(6 Points)
a.
d
o
Aug
o
r
d
Aug
r
p
p
τ
α
α
τ
τ
τ
τ
τ
+
+
=
1
1
1
1
1
1
2
+
+
=
b.
The Auger and defect rates will be equal when
3
16
2
10
6
.
8
...
1
−
×
=
=
cm
p
p
o
o
Aug
d
α
τ
(
**note
, this rate coefficient is ~100x too high, so
a more realistic p
o
for the point when the Auger
rate dominates would be ~10
18
cm
-3)
At this dopant concentration, the radiative decay rate is slower than the
Auger or defect rates.
c.
Using the Einstein relation and mobility data for
electrons
q
kT
L
n
n
τ
μ
=
At p
o
=10
15
cm
-3
, the defect rate dominates
m
q
s
kT
Vs
m
L
n
μ
420
10
5
.
4
15
.
0
5
2
=
×
⋅
⋅
=
−
At p
o
=10
19
cm
-3
, the Auger process dominates and
s
9
10
3
.
3
−
×
≈
τ
m
q
s
kT
Vs
m
L
n
μ
93
.
0
10
3
.
3
01
.
0
9
2
=
×
⋅
⋅
=
−
2.
(12 Points)
a.
Remember that EQE is the number of electrons out of your device divided by the
number of photons that strike your device. In part a) we have assumed no
reflection or recombination losses and complete absorption so the EQE should be
perfect starting from wavelengths equal to the bandgap energy. I have included
this EQE curve below.

This ** preview** has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*