[quantum electronics] ch-9 semiconductor laser-2

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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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 /

+


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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


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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.


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Band Diagram


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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


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: 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)


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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



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: 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



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DLLWV =

DqL

JG

=

AIJ =


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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

=

=


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Equation can be expressed as

: strong function of temperature

RLff

CTnG s

spthth

1ln

121

8)(

2/12

0

2

2 +=

=

)(T


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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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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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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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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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DoubleDouble HeterostructureHeterostructure DiodeDiode


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DoubleDouble HeterojunctionHeterojunction Stripe Contact Laser DiodeStripe Contact Laser Diode


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BuriedBuried HeterostructureHeterostructure Laser DiodeLaser Diode

[quantum electronics] ch-9 semiconductor laser-2

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