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Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
3/16/2021 1
Arpan Deyasi, RCCIIT, India
Topic: Foundation of Optoelectronics
3/16/2021 2
Arpan Deyasi, RCCIIT, India
Optical Processes Absorption
Emission
stimulated absorption spontaneous
emission
stimulated emission
(generation) (recombination)
hν
hν
hν
3/16/2021 Arpan Deyasi, RCCIIT, India 3
Properties of Stimulated Emission
Emitted photons have same frequency
Emitted photons have specific propagation direction
Emitted photons are in phase
Emitted photons have same state of polarization
3/16/2021 Arpan Deyasi, RCCIIT, India 4
Recombination process
Radiative recombination
Nonradiative recombination
excess energy is dissipated in the form of phonon
excess energy is dissipated in the form of photon hν
3/16/2021 Arpan Deyasi, RCCIIT, India 5
Radiative recombination
alternatively called Luminescence
Cathodoluminescence occurs when an electron beam impacts
on a luminescent material such as a "phosphor"
Photoluminescence is caused by moving electrons to
energetically higher levels through the absorption of photons
Electroluminescence generates light in response to an
electric current passing through some material
3/16/2021 Arpan Deyasi, RCCIIT, India 6
Einstein’s relation
Ei
Ej Nj
Ni
Consider two-energy level system
Initially Ni>Nj
ρ: energy density at frequency ν
stimulated absorption rate
stimulated emission rate
spontaneous emission rate
. .
ij ij
N B
ρ
. .
ji ji
N B
ρ
.
ji ji
N A
3/16/2021 Arpan Deyasi, RCCIIT, India 7
Einstein’s relation
total downward transition rate
Under equilibrium
. . .
ji ji ji ji
N A N B
ρ
+
. . . . .
ij ij ji ji ji ji
N B N A N B
ρ ρ
= +
1
ji
ji
ij ij
ji ji
A
B
N B
N B
ρ
 
 
 
 
=
  
−
  
  
  
3/16/2021 Arpan Deyasi, RCCIIT, India 8
Einstein’s relation
Considering degeneracy factor
exp
ij i
ji j
N g h
N g kT
ν
   
=    
   
 
exp 1
ji
ji
ij i
ji j
A
B
B g h
B g kT
ρ
ν
 
 
 
 
=
    
−
    
    
  
3/16/2021 Arpan Deyasi, RCCIIT, India 9
Einstein’s relation
For blackbody radiation
3
3
8
exp 1
h
c
h
kT
π ν
ρ
ν
 
 
 
=
 
−
 
 
3/16/2021 Arpan Deyasi, RCCIIT, India 10
exp 1
ji
ji
ij i
ji j
A
B
B g h
B g kT
ρ
ν
 
 
 
 
=
    
−
    
    
  
3
3
8
exp 1
h
c
h
kT
π ν
ρ
ν
 
 
 
=
 
−
 
 
Einstein’s relation
i ij j ji
g B g B
=
3
3
8
ji
ji
A h
B c
π ν
=
3/16/2021` Arpan Deyasi, RCCIIT, India 11
Ratio of emission rate
ji
ji
A
R
B
ρ
=
3
3 3
3
exp 1
8
8
h
h kT
R
c h
c
ν
π ν
π ν
 
−
 
   
= ×
 
 
 
 
 
3/16/2021 Arpan Deyasi, RCCIIT, India 12
Ratio of emission rate
exp 1
h
R
kT
ν
 
= −
 
 
R>1 spontaneous emission dominates
0>R>1 stimulated emission dominates
3/16/2021 Arpan Deyasi, RCCIIT, India 13
Population Inversion
Ni
Nj
Ej
Ei
Ni
Ei
Ej
Nj
Ei
Ej Ni
Nj
Nj
Ni
Ei
Ej
3/16/2021 Arpan Deyasi, RCCIIT, India 14
Absorption Coefficient
Consider monochromatic beam
for incident radiation
( )
( )
dI z
I z
dz
α
= −
α: absorption coefficient
3/16/2021 Arpan Deyasi, RCCIIT, India 15
Absorption Coefficient
Net loss of photons per unit volume
i ij j ji
dN
N B N B
dt
ρ ρ
− = −
i ij j ji
g B g B
=
j
i j ji
i
g
dN
N N B
dt g
ρ
 
− = −
 
 
we neglect the effect of spontaneous emission
3/16/2021 Arpan Deyasi, RCCIIT, India 16
Absorption Coefficient
Intensity Nh c
I
n
ν
=
In
N
h c
ν
=
( )
n dI
dN z
h c dz
ν
= ∆
3/16/2021 Arpan Deyasi, RCCIIT, India 17
Absorption Coefficient
Rate of decay of photon density in a time interval ‘dt’
.
dN n dI dz
dt h c dz dt
ν
=
1
.
( / )
dN dI dz
dt h c n dz dt
ν
=
3/16/2021 Arpan Deyasi, RCCIIT, India 18
Absorption Coefficient
1 1
. .
( / )
dN dI dz
dt h dz c n dt
ν
=
1
dN dI
dt h dz
ν
=
3/16/2021 Arpan Deyasi, RCCIIT, India 19
Absorption Coefficient
1
( ( ))
dN
I z
dt h
α
ν
= −
1
dN Nh c
dt h n
ν
α
ν
 
= −  
 
3/16/2021 Arpan Deyasi, RCCIIT, India 20
Absorption Coefficient
1
dN c
dt h n
ρ
α
ν
 
= −  
 
1
j
i j ji
i
g c
N N B
g h n
ρ
ρ α
ν
   
− =
−
   
 
 
3/16/2021 Arpan Deyasi, RCCIIT, India 21
Absorption Coefficient
j
i j ji
i
g h n
N N B
g c
ν
α
 
= −
 
 
Gain coefficient
j
j i ji
i
g h n
k N N B
g c
ν
 
= −
 
 

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Foundation of Optoelectronics

  • 1. Course: Electronic Devices paper code: EC301 Course Coordinator: Arpan Deyasi Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India 3/16/2021 1 Arpan Deyasi, RCCIIT, India Topic: Foundation of Optoelectronics
  • 2. 3/16/2021 2 Arpan Deyasi, RCCIIT, India Optical Processes Absorption Emission stimulated absorption spontaneous emission stimulated emission (generation) (recombination) hν hν hν
  • 3. 3/16/2021 Arpan Deyasi, RCCIIT, India 3 Properties of Stimulated Emission Emitted photons have same frequency Emitted photons have specific propagation direction Emitted photons are in phase Emitted photons have same state of polarization
  • 4. 3/16/2021 Arpan Deyasi, RCCIIT, India 4 Recombination process Radiative recombination Nonradiative recombination excess energy is dissipated in the form of phonon excess energy is dissipated in the form of photon hν
  • 5. 3/16/2021 Arpan Deyasi, RCCIIT, India 5 Radiative recombination alternatively called Luminescence Cathodoluminescence occurs when an electron beam impacts on a luminescent material such as a "phosphor" Photoluminescence is caused by moving electrons to energetically higher levels through the absorption of photons Electroluminescence generates light in response to an electric current passing through some material
  • 6. 3/16/2021 Arpan Deyasi, RCCIIT, India 6 Einstein’s relation Ei Ej Nj Ni Consider two-energy level system Initially Ni>Nj ρ: energy density at frequency ν stimulated absorption rate stimulated emission rate spontaneous emission rate . . ij ij N B ρ . . ji ji N B ρ . ji ji N A
  • 7. 3/16/2021 Arpan Deyasi, RCCIIT, India 7 Einstein’s relation total downward transition rate Under equilibrium . . . ji ji ji ji N A N B ρ + . . . . . ij ij ji ji ji ji N B N A N B ρ ρ = + 1 ji ji ij ij ji ji A B N B N B ρ         =    −         
  • 8. 3/16/2021 Arpan Deyasi, RCCIIT, India 8 Einstein’s relation Considering degeneracy factor exp ij i ji j N g h N g kT ν     =           exp 1 ji ji ij i ji j A B B g h B g kT ρ ν         =      −             
  • 9. 3/16/2021 Arpan Deyasi, RCCIIT, India 9 Einstein’s relation For blackbody radiation 3 3 8 exp 1 h c h kT π ν ρ ν       =   −    
  • 10. 3/16/2021 Arpan Deyasi, RCCIIT, India 10 exp 1 ji ji ij i ji j A B B g h B g kT ρ ν         =      −              3 3 8 exp 1 h c h kT π ν ρ ν       =   −     Einstein’s relation i ij j ji g B g B = 3 3 8 ji ji A h B c π ν =
  • 11. 3/16/2021` Arpan Deyasi, RCCIIT, India 11 Ratio of emission rate ji ji A R B ρ = 3 3 3 3 exp 1 8 8 h h kT R c h c ν π ν π ν   −       = ×          
  • 12. 3/16/2021 Arpan Deyasi, RCCIIT, India 12 Ratio of emission rate exp 1 h R kT ν   = −     R>1 spontaneous emission dominates 0>R>1 stimulated emission dominates
  • 13. 3/16/2021 Arpan Deyasi, RCCIIT, India 13 Population Inversion Ni Nj Ej Ei Ni Ei Ej Nj Ei Ej Ni Nj Nj Ni Ei Ej
  • 14. 3/16/2021 Arpan Deyasi, RCCIIT, India 14 Absorption Coefficient Consider monochromatic beam for incident radiation ( ) ( ) dI z I z dz α = − α: absorption coefficient
  • 15. 3/16/2021 Arpan Deyasi, RCCIIT, India 15 Absorption Coefficient Net loss of photons per unit volume i ij j ji dN N B N B dt ρ ρ − = − i ij j ji g B g B = j i j ji i g dN N N B dt g ρ   − = −     we neglect the effect of spontaneous emission
  • 16. 3/16/2021 Arpan Deyasi, RCCIIT, India 16 Absorption Coefficient Intensity Nh c I n ν = In N h c ν = ( ) n dI dN z h c dz ν = ∆
  • 17. 3/16/2021 Arpan Deyasi, RCCIIT, India 17 Absorption Coefficient Rate of decay of photon density in a time interval ‘dt’ . dN n dI dz dt h c dz dt ν = 1 . ( / ) dN dI dz dt h c n dz dt ν =
  • 18. 3/16/2021 Arpan Deyasi, RCCIIT, India 18 Absorption Coefficient 1 1 . . ( / ) dN dI dz dt h dz c n dt ν = 1 dN dI dt h dz ν =
  • 19. 3/16/2021 Arpan Deyasi, RCCIIT, India 19 Absorption Coefficient 1 ( ( )) dN I z dt h α ν = − 1 dN Nh c dt h n ν α ν   = −    
  • 20. 3/16/2021 Arpan Deyasi, RCCIIT, India 20 Absorption Coefficient 1 dN c dt h n ρ α ν   = −     1 j i j ji i g c N N B g h n ρ ρ α ν     − = −        
  • 21. 3/16/2021 Arpan Deyasi, RCCIIT, India 21 Absorption Coefficient j i j ji i g h n N N B g c ν α   = −     Gain coefficient j j i ji i g h n k N N B g c ν   = −    