Lecture 13: Semiconductors lasers

1
Lecture 13 Semiconductors lasers

• Quasi-Fermi levels
• Optical properties
• pn junctions

2
Announcements

• Optical soliton talks next week
• Schedule for rest of quarter (extra credit talks)

3
Last time
n-type
p-type
energy
energy
EFermi
EFermi
1
1
P(E)
0
P(E)
0
4
Electron P(E)
Quasi-Fermi levels
Fn
energy
Ec
EFermi
energy
energy
Ev
Fp
1
P(E)
0
r(E)
Hole P(E)
If we achieve this, electrons would spontaneously
emit photons and tend to make FnFp.By
injecting electrons from the n-side of a p-n
diode, we can pump electrons into the system,
thus maintaining the population inversion.
5
Optical absorption
?
1
Transmission
0
Frequency
1
0
6
Optical absorption
energy
1
Transmission
0
1
0
Frequency
7
Optical absorption (?)
Pump
?
1
Transmission
0
Frequency
1
0
8
Recall TiSapphire
2Eg
Fast decay
Pump
Stimulated emission
T2g
Fast decay
9
Optical absorption (?)
energy
Fast decay
Pump
Fn
Ec
Pump
Ev
Fp
r(E)
Discuss diagram in detail, including overlay
of density of states, photon energy, and
10
Optical absorption (?)
Pump
Log(Iout/Iin)
0
frequency
Red equilibrium Blue pumped
Discuss log scaleon board (0).
Our goal in the next slides is to calculate
quantitatively the blue curve.
11
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
12
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
13
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
14
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
15
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
16
Optical emission
energy
Pump
E2
Ec
emission
Ev
E1
r(E)
E2 and E1 are not centered around midgap.
17
Optical emission
energy
Pump
E2
dE2
dE1 and dE2?
Ec
Ev
E1
dE1
r(E)
18
Optical emission
E
0
electrons
dE2
holes
dE1
19
Optical emission
E
dk
dE2
dE1
20
So far
energy
Pump
E2
dE2
So far, we have assumed
Ec
What if the incoming intensity is distributed in
frequency such that I(n)dn is the intensity
between n and ndn?
Ev
E1
How many states are there such that an incident
intensity with total intensity I(n)dn
participates?
dE1
r(E)
21
So far
22
So far
23
So far
24
So far
Power emitted hn number of transitions/time
hn (R21-R12)
25
So far
Power emitted hn number of transitions/time
hn (R21-R12)
26
So far
Power emitted hn number of transitions/time
hn (R21-R12)
27
So far
Three cases 1) hn lt Egap 2) Egap lt hn lt Fn-Fp 3)
hn gt Fn - Fp
28
Case one hn lt Egap
No absorptionNo emissiong0
29
Case two Egap lt hn lt Fn-Fp
energy
Fn
Ec
Ev
Fp
GAIN
r(E)
30
Case three gt Fn-Fp
energy
Fn
Ec
Ev
Fp
LOSS
r(E)
31
Optical absorption (?)
Pump
Log(Iout/Iin)
0
frequency
Red equilibrium Blue pumped
Our goal in the next slides is to calculate
quantitatively the blue curve.
32
Optical absorption (?)
Pump
From Verdeyen
33
Optical absorption (?)
Pump
Discuss log scaleon board (0).
From Fukuda, Optical Semiconductor Devices
34
Drude model Drift current
Electric field E
e-
random scattering centers
35
Drude model Drift current
Electric field E
e-
random scattering centers
36
Drude model Drift current
Electric field E
e-
random scattering centers
37
Drude model Drift current
Electric field E
e-
random scattering centers
38
Drude model Drift current
Electric field E
e-
m
random scattering centers
39
Drude model Drift current
Electric field E
e-
m
random scattering centers
40
Diffusion current
41
Total current
E, n can depend on x!
Holes
42
Diffusion equation
Cross section area of length dx (draw on board)
43
Diffusion equation
Cross section area of length dx (draw on board)
44
Diffusion equation
Cross section area of length dx (draw on board)
45
Diffusion equation
Cross section area of length dx (draw on board)
46
Steady state
47
Steady state
48
Steady state
49
Steady state
50
Last time
n type
p type
energy
energy
EFermi
EFermi
1
P(E)
0
1
P(E)
0
What if we bring n and p type together? p n diode
51
p n diode
n type
p type
holes
energy
EFermi
EFermi
electrons
52
p n diode
p type
n type
EFermi
energy
53
p n diode
n type
p type
eVo
EFermi
-
p type
n type

-

-

-

-

-

potential
54
Forward bias
n type
p type
e(Vo-Vf)
EFermi
EFermi
p
x
55
Laser diode
56
Laser diode
57
Threshold current

• Injected electrons current
• Recombination rate n p
• Need input current recombination rate (steady
  state)
• Need n,p 1018 cm-3
• J 10 kA/cm2 VERY BIG!

58
p n diode