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7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
The Carrier Density (1)The Carrier Density (1)
How do you calculate EFN and EFP?
For a non-degenerate semiconductor we can write :
By non-degenerate we mean that
( )dEEfEgp
dEEfEgn
FpVV
FnCC
)(1)(
)()(
=
=
degerate-Non)(
exp
)(exp
=
=
KT
EENp
KT
EENn
VFPV
FNC
C
V
C
Np
Nn
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
The Carrier Density (2)The Carrier Density (2)
Unfortunately, semiconductor lasers behave like degeneratesemiconductors, and thus we must perform the Fermi-Dirac integrals.
Fortunately, nice approximations have been developed for handling
all of interest.
In general, the carrier densities in terms of Fermi-Dirac integrals:
where,
)(FNp(FNn i/V/C == 2121 ),
KT
E
KT
EE gi
CFN =
= ,
)exp(27.01
)exp()21
(F /
+
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
The Wavelength of EmissionThe Wavelength of Emission
From the Eq. that , we seethat it is possible to choose the frequency of emission by using theproper bandgaps.
Some of the more useful semiconductor materials are :
hEf g/=)(Lasing FPFNg EEfhE
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Calculations of Threshold Current Density (1)Calculations of Threshold Current Density (1)
The first type of semiconductor lasers consisted of a simple p-njunction device.
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Calculations of Threshold Current Density (2)Calculations of Threshold Current Density (2)
Band Diagram
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Calculations of Threshold Current Density (3)Calculations of Threshold Current Density (3)
The region t where the population inversion occurs is of the order of adiffusion length, LD
A typical dimension for GaAs :
The ratio of electron to hole current is :
mDL sD 5~1=
p
n
p
n
p
n
D
D
J
J
constantMobility:
constantDiffusion:where
D
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
: generation rate of electronics in the upper level state byway of a forward biased current
: Spontaneous recombination
: Stimulated emission
stim
s
RnGdt
dn =
22
s
n
2
G
stimR
Rate Equations for Electrons (1)Rate Equations for Electrons (1)
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Some assumptions for the eq
Homogeneous medium
.
The optical mode interacts with the entire volume of carriers whichare recombising
Steady state case
eq can be expressed as
s
nG
=
02 =dt
dn
0stimR
Rate Equations for Electrons (2)Rate Equations for Electrons (2)
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
: internal efficiency of converting injected electrons to electronswhich recombine
: number of injection electrons / sec
: volume of the recombination region
Vq
IG I
=
V
I
q
I
Rate Equations for Electrons (3)Rate Equations for Electrons (3)
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (4)Rate Equations for Electrons (4)
DLLWV =
DqL
JG
=
AIJ =
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (5)Rate Equations for Electrons (5)
We can calculate n2th using eqn. and
From our previous discussion
sD
th
th qL
Jn
=
2
2/12
0
2
2
1
2
2/12
0
2
12
21
8)1(
218
)(
ff
C
n
n
n
ffCnnG
sp
sp
=
=
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (6)Rate Equations for Electrons (6)
Equation can be expressed as
: strong function of temperature
RLff
CTnG s
spthth
1ln
121
8)(
2/12
0
2
2 +=
=
)(T
7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-2
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (7)Rate Equations for Electrons (7)
Where, for a homojunction laser
Eq
Case : GaAs semiconductor Laser
( )
+
=RL
ft
Tc
fqJ sth
1ln
1
2)(
118 2/12
20
dLt=
sec/105 122/1 =f1)( =T
m 84.00
sec/103 140 =f
1201
ln1 + cm
RL
35.3=n
kT = 0;
mLD 2
;;
;;
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (8)Rate Equations for Electrons (8)
Eq
The important parameters for reducing the threshold current density
Reduce t
Reduce the linewidth , by possibly reducing the temperature
Decrease the absorption losses,
In most good lasers,
23 /1050~20 cmAJth
2/1f
1
kT = 300
s
2/140 cmAJA
Ith
th =kT = 0
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (9)Rate Equations for Electrons (9)
reducing the threshold current density in a semiconductor laser; Lower power consumption
The degradation rate was strong correlated to the thresholdcurrent density
The several problem areas which prevented researchers fromachieving low threshold current density
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
Rate Equations for Electrons (10)Rate Equations for Electrons (10)
A confinement factor,
Where, is the perpendicular intensity to the junction
The expression for the gain
=dxxI
dxxIt
)(
)(0
)(xI
2/1
2
0
2 2
8)(
ff
cT
qt
JG
=
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
DoubleDouble HeterostructureHeterostructure DiodeDiode
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
DoubleDouble HeterojunctionHeterojunction Stripe Contact Laser DiodeStripe Contact Laser Diode
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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.
BuriedBuried HeterostructureHeterostructure Laser DiodeLaser Diode