properties of semiconductor laser

1. Course: Semiconductor
Optoelectronic Devices:
Properties of Semiconductor laser
Course Coordinator: Arpan Deyasi
1/13/2021 1Arpan Deyasi, RCCIIT, India
Dept of ECE, RCCIIT, Kolkata

2. 1/13/2021 Arpan Deyasi, RCCIIT, India 2
Condition of Lasing
R1 R2
P(0) P(L)
L
R1.P(L)
R1.P(2L)
R1.R2.P(2L)

3. 1/13/2021 Arpan Deyasi, RCCIIT, India 3
Condition of Lasing
1
( )
dP
k z
P dz
=Gain coefficient
( ) (0)exp( )P z P kz=
α: absorption coefficient
( ) (0)exp(( ) )P z P k zα= −

4. 1/13/2021 Arpan Deyasi, RCCIIT, India 4
Condition of Lasing
For each complete trip
(2 ) (0)exp(( )2 )P L P k Lα= −
Condition for self-sustained oscillation
1 2. . (2 ) (0)R R P L P≥

5. 1/13/2021 Arpan Deyasi, RCCIIT, India 5
Condition of Lasing
1 2
(2 )
. . 1
(0)
P L
R R
P
≥
1 2. .exp(( )2 ) 1R R k Lα− ≥
under threshold condition k = kth

6. 1/13/2021 Arpan Deyasi, RCCIIT, India 6
Condition of Lasing
1 2. .exp(( )2 ) 1thR R k Lα− ≥
1 2
1 1
ln
2 .
thk
L R R
α
 
= +  
 

7. Bulk LASER
Semiconductor LASER
Quantum LASER
Different types of LASER
1/13/2021 7Arpan Deyasi, RCCIIT, India

8. BulkLASER(3-level)
N0
N1
N2
E0
E1
E2
sp. emi
st. emi
N0>>N1, N2
hν1=E2-E0
st. abs
hν2=E2-E1
hν3=E1-E0
1/13/2021 8Arpan Deyasi, RCCIIT, India
N1>>N0

9. BulkLASER(4-level)
N0
N2
N3
E0
E2
E3
sp. emi
st. emi
N0>>N1, N2, N3
hν1=E3-E0
st. abs
hν2=E3-E2
hν3=E2-E0
N1
st. emi
hν4=E2-E1
E1
1/13/2021 9Arpan Deyasi, RCCIIT, India

10. SemiconductorLASER
Vbi
1/13/2021 10Arpan Deyasi, RCCIIT, India
EC
EFI
EV
Vbi -Vf
hν=EC-EV

11. Semiconductor LASER
For operation, both electrical and optical biases are required
g
f
E
V
q
≈
1/13/2021 11Arpan Deyasi, RCCIIT, India

12. 1/13/2021 Arpan Deyasi, RCCIIT, India 12
Threshold Population Inversion
j
j i ji
i
g h n
k N N B
g c
ν 
= − 
 
( )j
j i
i ji
g ck
N N
g B h n
ν
ν
 
− = 
 

13. 1/13/2021 Arpan Deyasi, RCCIIT, India 13
Threshold Population Inversion
( )j th
j i
i ji
g ck
N N
g B h n
ν
ν
 
− = 
 
under threshold condition
1 2
1 1
ln
2 .
j
j i
i ji
g c
N N
g B h n L R R
α
ν
    
− = +    
    

14. 1/13/2021 Arpan Deyasi, RCCIIT, India 14
Threshold Population Inversion
from Einstein’s relation
3
3 3
8
ji
ji
A c
B
h nπ ν
=
2 2
2
1 2
8 1 1
ln
2 .
j
j i
i ji
g n
N N
g A c L R R
πν
α
    
− = +    
    

15. 1/13/2021 Arpan Deyasi, RCCIIT, India 15
Threshold Population Inversion
1
ji
ji
A
τ
=
2 2
2
1 2
8 1 1
ln
2 .
j ji
j i
i
g n
N N
g c L R R
πν τ
α
    
− = +    
    

16. 1/13/2021 Arpan Deyasi, RCCIIT, India 16
Threshold Population Inversion
( )
2 3
2
1 2
8 1 1 1
ln
2 .
j
j i
i
ji
s
g
N N
g
n
c k L R R
πν τ
α
ν
 
− 
 
  
+  
  
Considering the spectral broadening of a particular transition

17. 1/13/2021 Arpan Deyasi, RCCIIT, India 17
Threshold Population Inversion
( )
1
sk ν
ν
=
∆
Spectral broadening can be written as
( )2 2
2
1 2
8 1 1
ln
2 .
j
j i
i
ji
g
N N
g
n
c L R R
πν τ ν
α
 
− 
 
 ∆  
+  
  

18. 1/13/2021 Arpan Deyasi, RCCIIT, India 18
Threshold Population Inversion
( )2 2
2
1 2
8 1 1
ln
2 .
ji
th
n
N
c L R R
πν τ ν
α
 ∆  
+  
  

19. 1/13/2021 Arpan Deyasi, RCCIIT, India 19
Threshold Current Density
( )2 2
2
1 2
8 1 1
ln
2 .
ji
th
n
N
c L R R
πν τ ν
α
 ∆  
+  
  
d: thickness of active region
dm: thickness due to mode extension

20. 1/13/2021 Arpan Deyasi, RCCIIT, India 20
Threshold Current Density
( )2 2
2
1 2
8 . 1 1
ln
. 2 .
ji m
th
n d
N
c d L R R
πν τ ν
α
 ∆  
+  
  
J: current density of the diode
no. of electrons injected per unit time per unit volume of
the active region is (J/qd)

21. 1/13/2021 Arpan Deyasi, RCCIIT, India 21
Threshold Current Density
If these no. of electrons are removed, rate equation becomes
dN J N
dt qd τ
= −
then in steady state,
0
dN
dt
=
th thJ N
qd τ
=

22. 1/13/2021 Arpan Deyasi, RCCIIT, India 22
Threshold Current Density
th
th
N qd
J
τ
=
( )2 2
2
1 2
8 . 1 1
ln
2 .
ji m
th
n dq
J
c L R R
πν τ ν
α
τ
 ∆  
+  
  
1 11
r nrτ τ τ− −−
= +where

23. 1/13/2021 Arpan Deyasi, RCCIIT, India 23
Power Output
J: operating current density of the laser diode (J>Jth)
( ) i
tot th
h
P A J J
q
η ν
= −
A fraction of total output power is coupled out as useful laser
output and rest is used to overcome losses within cavity

24. 1/13/2021 Arpan Deyasi, RCCIIT, India 24
Power Output
1 2
1 2
1 1
ln
2 .
( )
1 1
ln
2 .
i
out th
L R Rh
P A J J
q
L R R
η ν
α
  
  
  = −
  
+   
  

25. 1/13/2021 Arpan Deyasi, RCCIIT, India 25
Efficiency
Differential quantum efficiency (ηd) is the increase in light
output due to an increase in drive current
( )
out
d
th
P
d
h
A
d J J
q
ν
η
 
 
 =
 
− 
 

26. 1/13/2021 Arpan Deyasi, RCCIIT, India 26
1 1
ln
( )
1 1
ln
i
out th
h L R
P A J J
q
L R
η ν
α
  
  
  = −
  +   
  
Efficiency
for R1 = R2 =R

27. 1/13/2021 Arpan Deyasi, RCCIIT, India 27
1 1
ln
1 1
ln
d i
L R
L R
η η
α
  
  
  =
  +   
  
Efficiency

28. 1/13/2021 Arpan Deyasi, RCCIIT, India 28
Efficiency
out
P
f
P
V AJ
η =
Power conversion quantum efficiency (ηP)
1 1
ln
( )
1 1
ln
th i
P
f
J J h L R
J qV
L R
η ν
η
α
  
  −   =
  +   
  

29. 1/13/2021 Arpan Deyasi, RCCIIT, India 29
For high injection condition
Efficiency
fqV hν=
1 1
ln
( )
1 1
ln
th
P i
J J L R
J
L R
η η
α
  
  −   =
  +   
  

30. 1/13/2021 Arpan Deyasi, RCCIIT, India 30
Efficiency
Also for high injection
thJ J>>
1 1
ln
1 1
ln
P i
L R
L R
η η
α
  
  
  ≈
  +   
  

31. 1/13/2021 Arpan Deyasi, RCCIIT, India 31
Efficiency
For optimum light coupling
1 1
ln
L R
α
 
<<  
 
P iη η≈

32. Semiconductor LASER: Drawbacks
Improper depletion width ---- ill-defined active region
---- carrier confinement is not possible
Improper modal volume
---- mode confinement is not possible
Larger active region --- higher threshold current
density ------- continuous room temperature operation
is not possible
1/13/2021 32Arpan Deyasi, RCCIIT, India