EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
EE529 Semiconductor
Optoelectronics
Semiconductor Lasers
1.
2.
3.
4.
Optical gain spectrum
Laser threshold, power and efficiency
Modulation characteristics
Advanced laser structures
Reading: Liu, Sec. 13.3-13.4, 13.9-13.10
Ref: Bhattacharya, Sec. 6.7, 7.2, 7.13; Liu, Sec. 4.3, 5.1
Lih Y. Lin
EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Laser Operation
Lasing process in a ruby laser
Process:
1. Population inversion ― Through optical pumping or carrier injection.
2. Seed photons ― From spontaneous emission and initiate the stimulated emission process.
3. Optical cavity ― Resonant enhancement and define the output wavelength.
4. Gain saturation – Population inversion decreases as stimulated emission increases.
→ Steady state.
5. Output coupling ― Let some of the photons out at each round trip.
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Basic Semiconductor Laser Structure
p+
Junction
n+
Ec
Eg
Ev
EF p
eV o
Ho les in V B
Electro ns
Electro ns in C B
n+
p+
Ec
EF n
Ec
In v ers io n
reg io n
Eg
EF n
Ec
eV
EF p
Ev
(a)
(b)
Current
V
Photograph of an edge emitting laser
diode
Cleaved surface mirror
L
Electrode
GaAs
p+
L
n+
GaAs
Electrode
Active region
(stimulated emission region)
500 µm
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Different Regimes of Operation
Energy
Optical gain
EF n − EF p
CB
EF n
Ec
Pumped electrically or
optically until population
inversion happened.
→ Emission > Absorption.
Electrons
inCB
eV
hυ
0
Eg
Holes inVB
=Emptystates
Ev
EF p
At T >0
VB
At T =0
Optical absorption
Densityof states
Optical P ower
Laser
Optical Power
Optical P ower
LED
Stimulated
emission
λ
Optical P ower
Laser
Spontaneous
emission
λ
0
I
Ith
λ
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Optical Gain Spectrum
Optical gain coefficient g: Fractional change in
the light power (or intensity) per unit distance
g(ν)
1/2
2(mr* )3/2 c 2
h
ν
−
E
[ f c ( E2 ) − f v ( E1 )]
(
g)
2 2 2
n h ν τ sp
∆EF
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Threshold Gain gth
Shown on the right is a typical output power-Injection current
characteristics of a laser diode.
When does lasing happen?
Steady-state condition: Laser power is constant
→ Round-trip gain = Round-trip loss
Pf
Pi
Reflecting
Reflecting
surface
surface
E E
f
2
PO
Lasing
Ith → gth
I
i
SteadystateEMoscillations
R2
L
1
Cavityaxis
x
R1
Where does the loss come from?
Reflection loss at the mirrors. Losses in the cavity medium (scattering at defects, absorption
by impurities, absorption by free carriers …)
Pf
Pi R1 R2 exp[ g (2 L)]exp[−α(2 L)]
α : Loss coefficient of the laser medium
Pf = Pi → gth = α +
1  1 
ln 

2 L  R1 R2 
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Threshold Current and Efficiency
Laser diode active layer thickness = d
Determine Nth from the gain spectrum
edN th
J th =
ηinj τ s
or
J th =
edRsp ( N th )
ηinj ηi
Above threshold, under steady state,
(1 / 2 L)ln(1 / R1 R2 )
hν
P0ut = ηi ηinj
( I − I th )
α + (1 / 2 L)ln(1 / R1 R2 )
e
External quantum efficiency
d ( Pout / hν)
(1 / 2 L)ln(1 / R1 R2 )
ηe =
= ηi ηinj
d ( I − I th ) / e
α + (1 / 2 L)ln(1 / R1 R2 )
Slope efficiency
dP
hν
ηs = out =ηe
VdI
eV
n Po
nth
Threshold population
inversion
n
Power conversion efficiency
P
I th 
hν 
1
ηc = out =ηe
−
VI
eV 
I 
P o = Lasing output power
∝ Nph
Slope represents efficiency
I
Ith
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Exercise: Threshold Current Density of a
GaAs Laser
Calculate the threshold current of a GaAs laser with an undoped active region of width d = 0.2 µm
starting from g(E) and Rsp(E):
( E − E ) [ f ( E ) − f ( E )] cm
g( E ) =
3 × 10
1/2
g
4
E
c
2
v
1
−1
Rsp ( E ) =×
1.15 1029 E ( E − Eg )
1/2
f c ( E2 )[1 − f v ( E1 )] s −1cm −3 (eV) −1
Assuming the following parameters for the laser: L = 400 µm, R1 = R2 = 0.9, α = 103 cm-1, Γ = 0.95,
ηi = 0.9, ηinj=1 . Along your calculation, verify that you obtain the following results:
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Exercise: Efficiencies of an InP Laser
An InP Fabry-Perot laser emits at wavelength ~ λ =920 nm. It has an
injection efficiency ηinj =
90% and an internal quantum efficiency
ηi =95% . The voltage applied to the device is 2.5V. The reflectivity
of both cavity ends are R1 = 100% and R2 = 70% . The loss
coefficient of the laser medium is α =1cm-1. Its threshold current is
characterized to be I th = 1mA.
(a) The semiconductor laser has a cavity length L = 400 µm.
Assume the refractive index n = 3.3. What should be the exact
emission wavelength? At which longitudinal mode does lasing
occur?
(b) Calculate the photon extraction efficiency, external quantum
efficiency, and slope efficiency of the device.
(c) If the laser is operated at an injection level twice the threshold,
find its power conversion efficiency and output power.
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Transient Response
Transient phenomena occur because of the time required for the electron and photon
populations to come into equilibrium. As the photon population builds up rapidly, the
carrier density is depleted until it falls below transparency condition.  Photon population
decreases.  Carrier population starts to build up again, this time from a higher initial
value, and so does the photon population.
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Frequency Response under
Small-signal Modulation
As the initial oscillations cease, the situation becomes periodic small-signal modulation
of a laser.
mγ c γ n
Ω 2 − Ω 2r + iΩγ r
Complex response function:
r (=
eiϕ
Ω) | r |=
Modulation power spectrum:
m 2 γ c2 γ 2n
=
R( f ) r=
(f)
16π4 ( f 2 − f r2 ) 2 + 4π2 f 2 γ 2r
2
1/2
 2 γ 2r 
f pk  f r − 2 
Resonance peak: =
8π 

3-dB modulation bandwidth:
1/2
f3dB
γ 2r 
1/2  2
=
(1 + 2)  f r −

8 2π2 

Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Exercise: Modulation Characteristics
A GaAs QW VCSEL has the following parameters: Emission wavelength = 850 nm,
refractive index n = 3.52 , gain overlap factor Γ =0.2 , threshold gain coefficient
gth 8.16 × 104 m −1 , excess carrier spontaneous lifetime τ s =3.02 ns , gain cross-section
=
σ
= 2.2 × 10−19 m 2 .
(a) Find the values of spontaneous carrier relaxation rate γ s and cavity decay rate γ c .
What is the photon lifetime τc ?
= 4.74 × 10−18 m3 ,
(b) If the laser output power =
Pout 60.6 µW , the mode volume Vmode
the emitted and photon extraction efficiency ηt =89% . Find the intracavity photon
density S0 .
(c) Find the values of differential gain parameter g n . Assume the nonlinear gain
parameter g p = − g n , find the values of differential carrier relaxation rate γ n and
nonlinear carrier relaxation rate γ p .
(d) Find the values of relaxation resonance frequency f r and total carrier relaxation rate
γr .
(e) Find the resonance peak of the modulation spectrum f pk . What is the 3-dB
modulation bandwidth f 3dB ?
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Heterojunction Lasers
p
n
G aA s
A lG aA s
(a)
p
Ith for homostructure laser diode extremely high
→ Not practical for room temperature operation
A lG aA s
( ~ 0 . µm
1 )
E le c tr o n s i n C B
∆Ec
Ec
Ec
Heterostructure laser: Enhance carrier
confinement and photon confinement
2 eV
1.4 eV
2 eV
(b)
Cleaved reflecting surface
W
Ev
Ev
H o l e s in V B
R e fra c t iv e
in d e x
(c)
P h o to n
d e n s i ty
L
Stripe electrode
A c t iv e
r e g io n
∆n ~ 5 %
Oxide insulator
p-GaAs (Contacting layer)
p-Al xGa1-xAs (Confining layer)
p-GaAs (Active layer)
n-Al xGa1-xAs (Confining layer)
n-GaAs (Substrate)
(d)
Elliptical
laser
beam
2
1
Current
paths
Substrate
3
Substrate
Electrode
Cleaved reflecting surface
Active region where
(Emission region)
J > Jth.
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
DBR Laser and DFB Laser
Optical Power
Laser
Output spectrum of a typical Fabry-Perot (F-P) laser
2L
=q
L
λ
→ Many wavelengths are possible, as
long as they are within the gain spectrum
λ
How do we obtain single-frequency semiconductor lasers?
Distributed Bragg reflector (DBR) laser
Λ
DistributedBragg
reflector
q(λB /2 n)= Λ
A
B
Corugated
dielectricstructure
Activelayer
(a)
(b)
ν m ≈ ν B ± ( m + µ)
Distributed feedback (DFB) laser
Λ
Corrugatedgrating
Opticalpower
Ideallasingemission
Guidinglayer
Activelayer
c
2nB l
0.1nm
(a)
(b)
λB
λ
λ (nm)
(c)
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Typical Grating Coupler Structure
and Coupled-Mode Theory
Coherent coupling between forward- and
backward-propagating waves results in
selection of longitudinal modes.
δ = β B − β(ω)
R=
(
sinh 2 | κ | L 1 − δ / κ
(
cosh 2 | κ | L 1 − δ / κ
2
)
2
)
− δ/κ
2
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Exercise: DBR Laser
A DBR laser has gain section of length l = 400 µm and two identical DBRs as
= 150 µm . The grating period of the DBR is
end mirrors, each of length lDBR
Λ =225 nm . The effective indices for the laser modes are n=
N=
3.45 .
β
β
The DBR coupling coefficient is | κ |=50 cm −1 . The gain spectrum peaks
~1550 nm.
(a) Find the Bragg wavelength and frequency near the gain peak.
(b) Find the peak reflectivity and the bandwidth of the two DBRs.
(c) Find the effective phase length of the DBRs and that of the DBR laser to
determine the longitudinal mode spacing of the laser.
(d) Assume the gain bandwidth is much broader than the DBR frequency
bandwidth, how many longitudinal modes can exist?
(e) If the laser is pumped right at the threshold, only one mode can oscillate.
What’s its wavelength? Calculate the DBR reflectivity at this lasing
wavelength.
Lih Y. Lin
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EE 529 Semiconductor Optoelectronics
– Semiconductor Lasers
Vertical Cavity Surface Emitting Laser
(VCSEL)
Dielectric mirrors → Distributed Bragg reflector structures
A 1st-order square grating of a 50% duty factor has the largest coupling coefficient
2∆n
| κ |=
λ
Λ = λ B / 2n
Contact
λ/4n 2
λ/4n 1
Dielectric mirror
Active layer
Dielectric mirror
Substrate
Contact
Surface emission
SEM (Scanning electron micrograph) of a VCSEL array.
Lih Y. Lin
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