[Quantum Electronics] Ch-9 Semiconductor Laser-1

7/30/2019 [Quantum Electronics] Ch-9 Semiconductor Laser-1

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COMMUNICATION RESEARCH LAB.COMMUNICATION RESEARCH LAB.

SEMICONDUCTOR LASERSEMICONDUCTOR LASER

Division of Electrical and Computer EngineeringDivision of Electrical and Computer EngineeringHanyangHanyang UniversityUniversity

http://http://oeic.hanyang.ac.kroeic.hanyang.ac.kr


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General Properties (1)General Properties (1)

Gain and Absorption in Semiconductor

E-K diagram


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Density of electron states in the conduction & valence bands

( )

( ) bandvalencethein;2

2

1

bandconductionthein;2

2

1

21

23

2

*

2

21

23

2

*

2

EEm

EEm

vv

v

c

c

c

=

=

h

h

(1)

(2)


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Fermi-Dirac function,

Quasi-fermi functions in a nonequilibrium condition

Density of electrons & holes over an energy band dE

( )Ef

( ) levelFermi:,exp11

FF

EKT

EEEf

+= (3)

(4)

( )

( )1

1

exp111

exp1

+=

+=

KT

EEEf

KT

EEEf

FPv

FNc

( ) ( ) ( )( ) ( ) ( )( )dEEfEgEdp

dEEfEgEdn

vvv

ccc

=

=

1(5)


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Gain

gapvc EEE =


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Energy of an electron in a solid

bandvalenceandbandconductionin

electrontheofmassEffective:m,m; *v*c

bandvalencetheinmomentum:

bandconductiontheinmomentum:since

''

''

vv

cc

KP

KP

h

h

=

=

*

2'2'

*

2'2'

2,

2 v

vvv

c

ccc

m

KEE

m

KEE

hh=+= (7)

bandvalencethein;2

bandconductionthein;2

*

2

'

*

2'

v

v

v

c

c

c

EmPE

Em

PE

+=

+=

(6)


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We assume that only direct optical transitions occurto satisfy the conservation of momentum i.e.,

Conservation of energy relationship

Rewrite eqs. 7 ~ 9

freq.inputtheiswhere:'' fhfEE vc =

massreduced:where

2

**

**

*

22''

vc

vcr

r

gvc

mm

mmm

m

KEhfEE

+

=

+==h

(10)

(9)

KKK vc =='' (8)


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Number of transitions

Upward transition

Downward transition

[ ] ( )[ ]

( ) ( )sec#1)(1)()()(

312

1212

=

=

cmdEffB

dEdEEfEEfEBdN

vccv

cvccvv

[ ] ( )[ ]

( ) ( )sec#1)(1)()()(

321

2121

=

=

cmdEffB

dEdEEfEEfEBdN

vcvc

cvvvcc


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Net number of transitions Net downward rate, R

when

( )1221 NN

2

2/3

2

12

=

h

rmK

(11)

( )

( ) ( )[ ]

( )( ) 2/1021

21

1221

11

gvc

vccvvc

EEffKB

dEffffB

dNdNR

=

=

=

( )hfEE = 120


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Rate of change of photon density

The intensity is expected to have the form,inside the semiconductor thus,

hfx

IR

hft

11

==

(13)

(14)[ ] ( ) ( ) ( )

c

I

Ic

BEhfKffhfhfRdx

dI

gI

dx

dI

gvc

00

01221`

usedhavewewhere

1

thus,

=

==

=

( )gxexp


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Absorption coefficient for a semiconductor

( ) ( ) ( )c

BKKffEhfhfKg vcg

12`

21, == (15)


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What is Required fWhat is Required fnn Gain ? (1)Gain ? (1)

Since absorption and gain are really same process the onlydifference being in whether the upper state is more populated thanthe lover state.

For a gain we must have a population inversion which implies in thecase of a semiconductor

Good Lasing materials have high absorption.

absorption)(

gain)(

>

>

cv

vc

ffb

ffa


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What is Required fWhat is Required fnn Gain ? (2)Gain ? (2)

Let us look at the condition a little more closely :

For then we must have :

Since and the minimum frequency fn lasing emission

is determined by

KT

EEf

FPV )(

exp1

1

1 +=

KT

EEf

FNC )(

exp1

1

2 +=

KT

EE

KT

EEFPFN)()(

12

[Quantum Electronics] Ch-9 Semiconductor Laser-1

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