Script Part4 Laser

8/10/2019 Script Part4 Laser

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Chapter 4: Stimulated emission and LASERS

Stimulated EmissionStimulated emission and photon amplificationStimulated emission rate and Einstein coefficients

Light amplificationRate equations for amplifiers

Laser Oscillation ConditionOptical threshold gainOutput characteristics

Semiconductor laser diodePrinciplesGain spectrum under forward biasHomojunction laser diodeHeterojunction laser diodeLaser diode layout and lateral mode confinementLaser diode characteristicsSteady state semiconductor rate equationsOptimal out-couplingDistributed bragg reflection for single mode lasersGain spectrum in QW lasersLow dimensional structures & threshold current reductionVertical cavity surface emitting lasersLate News: Ge electrically pumped laser

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Stimulated emission and photon amplification

Photon absorption excites electronfrom E1 E2.

Allowed process, if energy (insemiconductor: and momentum) isconserved (Ph =hPh =E2 E1).

Two possibilities for de-excitation:i) Spontaneous emission:Eventually, also the electrons in an isolated atom will return to

their ground state spontaneously, without external action (purely QM process), bothradiative (photon emission hPh =E2 E1) and non-radiative transitions [phononemission (lattice vibration) etc.] can occur.

ii) Stimulated emission: The interaction of the atoms excited electron with an EMradiation in resonance with the de-excitation energy E2 E1 triggers the de-excitation.A photon coherent with the incoming EM field (in phase and with same propagationdirection relative to incoming photons) is emitted [inverse process to (stimulated)

absorption]. Not considered until 1916 (Einstein), but required for an opticallypumped system to reach stationarity, since absorption rate depends on intensity, butspontaneous emission rate not.

Stimulated emission is the base process for light amplification.

Shown later: Light amplification requires more electrons in the excited state than inthe ground state(population inversion).

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Stimulated emission rate and Einstein coefficients

N [cm3] two level system in thermal equilibrium withradiation in black body (BB).

N1 in groundstate @ E1, N2 in excited state @ E2,N=N1+ N2.

Stimulated excitation (absorption) rate R12 proportional toN1, to the number of photons with h21=E2 E1 pervolume {i.e. to the energy density (h21), [] =Jsm

3}:

R12 =B12N1(h21), [B12] =m3J1s2

De-excitation rate R21 =Rstim21 +R

spont21

analog to absorption: Rstim21 =B21N2(h21) R

spont21 =A21N2, independent of number of photons, only

prop. to N2.

R21 =A21N2+ B21N2(h21)

Above equations define Einstein coefficients B12, B21, A21as proportionality factors for the rates.

Thermal equilibrium:a) R12 =R21.

b) Boltzmann statistics: N2/N1 = e(E2E1)/kBT = eh21/kBT.

c) Photon energy density in BB given by Plancks law: eq(h)= 8h3

c3

eh/kBT 1

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Stimulated emission rate and Einstein coefficients

Three equations for the three Einstein coefficients.

Dividea)byN1 and solve for N1/N2:N2

N1 =

B12(h21)

A21+ B21(h21) Using Boltzmann statisticsb)results in:

e21/kBT =

B12(h21)

A21+ B21(h21) (h21) =

A21/B21(B12/B21)e21/kBT 1

Comparision with Plancks lawc): Equal for all T only, if

B12 =B21 B and A21

B21= 8h

321

c3 (= h Photon DOS)

Interpretation: Stimulated emission and absorption are inverse processes and occur with equal

probability per available initial state (2 for stim. emission, 1 for absorption) population inversion (N2 >N1) can never be achieved by intense optical pumping a

two level sytem, at most transparancy (N1 = N2) is achieved. Spontaneous emission prop. and stimulated emission prop. are related, ratio

increases with 3, harder to construct x-ray lasers.

Rstim21R

spon21

= BA(h) = 1

h(h)

Photon DOS

Ratio increases with:i) # photons available optical resonator

ii) decreasing density of photon states optical resonatorTFH SS 2012 95
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Light amplification

Absorption law: dIdx

= I I(x) =I0ex exponential decay of intensity I.

For expressing via electron transition rates, we convert intensity I into photonflux , photon density nPh and : I = h=nPhch=c(h).

dI

dx =hd

dx =ch

dnphdx

=hdnph

dt =h(R12+ R21) = (N1 N2)hB(h).

dI

dx = (N1 N2)

hBc

I

negative for population inversion (N2 >N1) exponentially growing intensity,i.e. gain.

gain coefficient g= (N2 N1)nrefhB

c0

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Rate equations for amplifiers Which pump-rate is required to achieve

gain (i.e. population inversion)?

ideal pumping scheme involves 4 levels

Spontaneous transition rates lumpedtogether and are expressed as inverselifetimes (i.e. Rspon21 =

121,spon)

example: spontaneous lifetime of level 2: 12 =121 +

120 =

121,sp+

121,nr+ +

120

Rate equations [Wi = B(h12)]:

dN3

dt= R

N3

32

dN2

dt=

N3

32

N2

2 N2Wi+N1Wi

dN1

dt=

N2

21

N1

1+N2Wi N1Wi

dN0

dt= R+

N1

1+

N2

20

32 3x N3 = R32 dN2dt

= R N22 N2Wi+N1Wi

stationary solution d

dt= 0 :

N N2 N1 = R2(1 1/21)

1 + Wi[2+1(1 2/21)]

N0

1 + Wis

N

0

: pop. inv. in the absence of amplifier radiation.s: saturation time.

Non-linear gain , gain saturation.

typically: nonr. 2 1 decay rate negligible (21 =21,sp) && 20 21,sp 1, thus: N0 R21,sp, s 21,sp.

Attention: for strong pumping,Rnot independent of N because

N0+ N1+ N2+ N3 =Na (atom density) and N3 N1 0 N0 Na N2 Na NTFH SS 2012 97
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Laser oscillation conditionOptical threshold gain

gain coefficient (stim. em.)

g= (N2 N1)B21nrefh21

c0 loss:

abs : absorption: impurities in laser medium, non-inverted allowed transitions with similartransition energy, free carriers (semiconductors !!)

sc : scattering out of resonator mode: defects and inhomogeneities.Ri : Out-coupling losses, power reflection coefficient of cavity mirrors R1,R2 1

stationarity conditions: Pf!

=PiPf =PiR1R2e

2Lgthe2L(abs+sc)

gth =

abs+sc+ 12Lln( 1R1R2 ) threshold gain.Nth =gth

c0

B21nrefh0 threshold pop. inv.

Increase R(i.e N0): g remains clamped at gthafter stationary is re-established N= Nth

.

102

101

100

101

102

Wis =/s

0.0

0.2

0.40.6

0.8

1.0

N/N0

=

g/g0 laser turn-on

loss=gth

steady state

time

ph. fluxdensity

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Laser oscillation conditionOutput characteristics

Gain clamping: N= Nth

Nth = N0

1 +Wis

Wi = 1

s

N0

Nth 1

Wi(h12)

=s N

0

Nth 1, N0 >Nth

0, N0 Nth

steady-state laser-internalphoton-flux density

Spontaneous emission neglected. In addition: stationarity of phase

Fabry-Perot resonator modes.

Simplified description of a laser oscillator.

(N2 N1) and coherent output power P0

vs. pump rate Runder continuous wave

steady state operation.

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PrinciplesoftheLaserDiode

pn junctioninaDegenerate

Semiconductor

FermilevelinthepregionisbelowEv

FemilevelinthenregionisaboveEc

Withnoappliedvoltage, Efn=Efp yields

averynarrowdepletionregion

Thereisapotentialenergybarrier,eVothatpreventsnsideelectronsfrom

diffusingto

the

pside

and

vice

versa

Whenvoltageisapplied

ChangeintheFermilevelisthework

donebytheappliedvoltage,eV

Ifthejunctionisforwardbiased

suchthatEfnEfp =eV >Eg

Appliedbiasdiminishesthebuildin

potentialbarrier

Depletionregionisnolongerdepleted

Therearenowmoreelectronsinthe

conductionbandthaninthevalance

bandnearEv Populationinversion

p+ n+

EFn

(a)

Eg

Ev

Ec

Ev

Holes in VB

Electrons in CB

Junction

Electrons

Ec

p+

Eg

V

n+

(b )

EFn

eV

EFp

The energy band diagram of a degenerately dopedp-n with no bias. (b) Banddiagram with a sufficiently large forward bias to cause population inversion andhence stimulated emission.

Inversionregion

EFp

Ec

Ec

eVo

1999 S.O. Kasap,Optoelectronics(Prentice Hall)

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PrinciplesoftheLaserDiode

Populationinversionregionisa

layeralongthejunctioncalledtheinversionlayer(activeregion)

Anincomingphotonwithenergy

EcEvcannotexciteanelectronin

EvtoEcastherearehardlyany

presentinthevalanceband

withinthe

active

region

Hencethereismorestimulated

emissionthanabsorption

Theopticalgainpresentinthe

activeregionduetolackof

probabilityofvalanceelectron

absorption

h

Eg

Optical gainE

FnE

Fp

Optical absorption

0

Energy

Ec

Ev

CB

VB

(a) The density of states and energy distribution of electrons and holes inthe conduction and valence bands respectively at T 0 in the SCLunder forward bias such thatEFnEFp>Eg. Holes in the VB are empty

states. (b) Gain vs. photon energy.

Density of states

Electrons

in CB

Holes in VB

= Empty states

EFn

EFp

eV

At T> 0

At T= 0

(a) (b )

1999 S.O. Kasap,Optoelectronics(Prentice Hall)

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Gain spectrum under forward bias

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Evolution of the absorption andgain curves as a function if the

position of the quasi-Fermi level.The gray (dark) curvescorrespond t oa small (large)displacement from equilibrium.In this case, the medium absorbsall photons having energies inexcess of the bandgap. Once theenergy separation between thetwo quasi-Fermi levels exceedsthe bandgap, all photons withenergies between Eg andE

F,cE

F,v are amplified.

From E. Rosencher, B. Vinter,

Optoelectronics, Cambridge University

Press (2002)
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Gain spectrum under forward bias

From A. Yariv, Quantum Electronics, 3rd edition, John Wiley & Sons, (1989)

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ElectroopticalPerformanceofIII/VDiodes

injectionpumping: Opticalpumpingisachievedbyforward

diodecurrent

and

the

pumping

energy

is

an

external

battery

Forlaserwealsoneedanopticalresonatorcavity. Thisis

achievedthroughtheuseofaslabwaveguidewithahigh

indexcontrastattheemissionend

Wavelengthoftheradiationthatcanbuildupinthecavity

dependsonthelength(L)inhalf multiples

LElectrode

Current

GaAs

GaAsn+

p+

Cleaved surface mirror

Electrode

Active region(stimulated emission region)

A schematic illustration of a GaAs homojunction laserdiode. The cleaved surfaces act as reflecting mirrors.

L

1999 S.O. Kasap, Optoelectronics (Prentice Hall)

ypical output optical power vs. diode current ( I) characteristics and the correspondingutput spectrum of a laser diode.

Laser

LaserOptical Power

Optical Power

I0

LEDOptical Power

Ith

Spontaneous

emission

Stimulated

emission

Optical Power


2criticalcurrentidentifiers

Transparency current: Currentabove

whichno

net

photon

absorption

occurs

Threshold current:currentabove

whichopticalgainovercomesall

photonlossesinthecavity

Lnm =

2

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R = (nGaAs1

nGaAs+1)2 35%

typically: Jth = 500 Amm2 for

homojunction LD !!
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Heterojunction LaserDiodes

Mainissuewithhomojunction diodesis

that

the

laser

threshold

current

density

istoohighforpracticaluses.

Ex.Jth =500A/mm2 forGaAs at300K

Heterostructured diodesreducethesecurrentdensitiesbyordersofmagnitude

Thisisachievedthroughacombinationofcarrierconfinement(mismatchedmaterials),andphotonconfinement(geometric

shape

of

the

waveguide)

Doubleheterojunction (DH)deviceswithnpp layersallowfordesignedconfinementoftheactiveregion

LowerrefractiveindexoftheAlGaAsenhancesthemodeconfinementincomparisontoahomoorsimple

heterojunction device Significantlyreducesthresholdcurrent

density

Refractiveindex

Photondensity

Active

region

n~ 5%

2 eV

Holes in VB

Electrons in CB

AlGaAsAlGaAs

1.4 eV

Ec

Ev

Ec

Ev

(a)

(b)

pn p

Ec

(a) A doubleheterostructure diode hastwo junctions which arebetween two dif ferentbandgap semiconductors(GaAs and AlGaAs).

2 eV

(b) Simplified energyband diagram under alarge forward bias.Lasing recombinationtakes place in the p-GaAs layer, theactive layer

(~0.1 m)

(c) Higher bandgapmaterials have alower refractiveindex

(d) AlGaAs layersprovide later al opticalconfinement.

(c )

(d)


GaAs

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Photonics,6thedition Yariv andYeh

igure 15.10 A typical double heterostructure GaAs/GaAlAs laser. Electrons and holes are injected into the active GaAs layer from the

and p GaAlAs. Photons with frequencies near =Eg/h are amplified by stimulating electronhole recombination.

Cc 2007Photonics,6thedition Yariv andYeh (OxfordUniversityPress

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Photonics,6thedition Yariv

andYeh 11

Figure 15.12 The magnitude of the energy gap in Ga1x

AlxAs as a function of the molar fraction x. For x > 0.37 the bandgap is indirect.

(After Reference [11].)


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Heterojunctions Laser Heterojunction diode: different materials for n & p


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Heterojunction diode: different materials for n & p

Different materials: significantly different index n

Also different lattice constants

Important point: want the lattice matched at layer boundary

Use mixed alloy: eg GaAs and AlAsAlxGa1-1As

x = mole fraction of Aluminum

1-x = mole fraction of Gallium

Heterojunctions Laser Single Heterojunctions: one sided confinement
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Single Heterojunctions: one sided confinement

p-GaAlAs: p-GaAs: n-GaAs

Better confinement means lower threshold current for lasing

Thus operates in pulsed mode at room temperature

Double Heterojunction lasers: confines both top & bottom

p-GaAlAs: GaAs: n-GaAlAs: n-GaAs

Double Heterojunctions Laser Has both Band and Index steps on both top & bottom
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Has both Band and Index steps on both top & bottom

Doubly confines light: creates a waveguide as cavity

Requires much less threshold current

Thus CW operation now possible at room temperature

Comparison of Homo/Hetero/D-Heterojunctions Lasers As add index steps get smaller light spreading
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As add index steps get smaller light spreading

Single hetrojunction threshold current ~5x < homojunction

Double hetrojunction threshold ~50-100x


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j

Surrounded both vertical & horizontal by lower material

1-2 microns wide: high efficiency, low threshold

Channeled Substrate

Etch channel in substrate: isolate active area

Low loss

Buried Crescent

Fill grove to get crescent shaped active strip

Heterojunctions with WaveguidesRidge Waveguide
http://goforward/http://find/http://goback/


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Etch away a mesa around active region

confines current flow to 2-3 micron strip

Double-channel planar buried heterostructure

Isolate active with mesa, then fill with lower index

used with very high power InGaAsP lasers


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EdgeEmittingLasers

VerysimilartoELEDdevicespresentedinchapter3

AdditionalcontactinglayerofpGaAs nexttothep=AlGaAs providesbettercontactingandavoidsSchottky junctionwhichwouldlimitthecurrentinthedevice.

pandnAlGaAs layersprovidecarrierandopticalconfinementintheverticaldirection

LaseremissionintheactivepGaAs(oradifferentAlGaAs constitution)regionisbetween870900

nm

depending

on

doping.

Schematic illustration of the the structure of a double heterojunction stripecontact laser diode

Oxide insulator

Stripe electrode

SubstrateElectrode

Active region where J> Jt h.

(Emission region)

p -GaAs (Contacting layer)

n -GaAs (Substrate)

p -GaAs (Active layer)

Current

paths

L

W

Cleaved reflecting surfaceEllipticallaser

beam

p -AlxGa

1- xAs (Confining layer)

n -AlxGa

1- xAs (Confining layer)

12 3

Cleaved reflecting surface

Substrate


AlGaAs andGaAs havenegligiblelattice

mismatchyieldingveryfewdefectsin

thecrystalthatwouldleadtoexcessive

thresholdcurrents

Also,thestripe electrodeacrossthetop

confinestheelectricfieldandthusthe

opticallyactive

region

providing

additionalgeometricalconfinement

Suchlasers arecalledgainguided,b/c

thecurrentdensitygeneratedisguided

bytheelectricfieldbetweenthestripe

electrodeandthebottomelectrode

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BuriedHeterostructure LDs

Figure

from

Chapter

15

Photonics,

6th

edition

Yariv and

Yeh 2007

Oxford

University

Press

Althoughthestripeelectrodegeometryprovides

some

geometric

confinement,

it

is

more

advantageoustorestrictlateralgeometryphysically

throughtheuseofconfininglayersalongtheside

ofthediode

Creationofaopticalwaveguideinbothverticaland

horizontaldirectionsaidsinreducingopticalcavity

modes

and

promotes

confinement Significantlyreducescurrentdensityrequiredfor

stimulatedemission

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ElementaryLaserDiode(LD)Characteristics

Longitudinalmode:lengthdetermined

Lateral

mode:

width

determined

Emissioniseithermultimodeorsingle

modedependingontheopticalresonating

structureandthepumpingcurrentlevel

Height,HWidth W

Length,L

The laser cavity definitions and the output laser beamcharacteristics.

Fabry-Perot cavity

Dielectric mirror

Diffraction

limited laser

beam


778 780 782

Po= 1 mW

Po= 5 mW

Relative optical power

(nm)

Po= 3 mW

Output spectra of lasing emission from an index guided LD.At sufficiently high diode currents corresponding to highoptical power, the operation becomes single mode. (Note:Relative power scale applies to each spectrum individually annot between spectra)


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Steady state semiconductor rate equations
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S y q

Current (I) pump rate: R= IedLW

Photon loss rate: dNph

dt =

Nphph

, where ph is

average time for a photon to be lost from

lasing cavity mode due to transmission at end facets,scattering and absorption in the semiconductor

Use rate equ. results (p. 97 f): assume a) 2 =21 =21,sp; b) 1 0 N1 0

N= N01+Wis

N2 R21,sp1+Wi21,sp

; in particular Nth Nth2 =Rth21,sp

Stimulated emission rate: dN2dt

st

= N2Wi

at threshold: dNth2

dt

st

= dNthph

dt

Nthphph

=Nth2 Wth

i =Nth2 CN

thph

Nth2 = 1Cph

, where

C =Bh21/and B is the Einstein coefficient.

Jth = Ith/LW = ed Rth =ed/ Cph21,sp

gain clamping: N2 = Nth2 R21,sp

1+CNph21,sp= Rth21,sp

Nph = 1

C21,sp( R

Rth 1) =

Jthphed

( JJth 1) =

phed

(J Jth)

Half of the cavity photons move towards out-couple mirror, a fraction (1 Rm) Tmescapes during the transversal time in this direction

Pout= (0.5Nph )(Cavity Volume) (Photon energy)

time for photon to transverse cavity length (1 Rmirror) = hc20ph W(1Rmirror)

2enref (J Jth)TFH SS 2012 119

Sketch of BHJ laser diode layer structure

Optimal out-coupling I


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p p g

Tm = 1 Rm transmission coefficient

Pout NphTm Tm( RRth 1)= Tm(R Cph21,sp1)

Photon lifetime Ph includes out-coupling losses, i.e Ph =Ph(Tm)

each photon escapes with probability T within round-trip time 2nL/c0.

dNph

dt =

dNphdt

loss

+ dNph

dt

gain

=

dNph

dt

loss,out

+ dNph

dt

loss,else

+

dNphdt

gain

= [

1/ph (Tm )

( T

mc0

2nL + 1

loss) +N2C]Nph

maximize Poutwith respect to Tm:

dPout

dTm

d

dTm[Tm(R C21,sp

2nLlossTmc0loss+ 2nL

1)] 0

Toptm = 2Lnc0loss

+ 2Lnc0 C R21,sp N0N02

2Lnc0loss

Floss,int+g0Floss,int

Floss,int internal loss fraction (probability) per round trip.

g0 open-loop photon multiplication fractor per round trip.

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Optimal out-coupling II
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p p g

From A. Yariv, Quantum Electronics, 3rd edition, John Wiley & Sons, (1989)

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Distributed

Bragg

Reflection

for

Single

Mode

Lasers

Ensure

single

mode

radiation

in

the

laser

cavity

is

to

use

frequency

selective

mirrors

at

the

cleavedsurfaces

Distributed

Bragg

reflector

is

a

mirror

that

has

been

designed

a

reflective

Bragg

grating

Reflectedwaveoccursonlywhenthewavelengthcorrespondstotwicethecorrugation

periodicity,

.

The

diffraction

order

of

the

reflector

is

integer,

q

=

0,1,2,

N=refractiveindexofthemirror

Bragg

wavelength

of

the

mirror

output

is

B

Corrugated

dielectric structure

Distributed Bragg

reflector

(a) (b)

A

B

q(B/2n) =

Active layer

(a) Distributed Bragg reflection (DBR) laser principle. (b) Partially reflected wavesat the corrugations can only constitute a reflected wave when the wavelengthsatisfies the Bragg condition. Reflected wavesAandBinterfere constructive whenq(B/2n) =.


= 2

n

q B

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n
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DistributedFeedbackLaser(DFB)

InaDFBlaser,thecorrugatinggratingiscalledtheguidinglayerandrestontopofthe

activelayer.

ThepitchofthecorrugationprovidesopticalgainattheBraggwavelength,B.

Travelingwavesareexcitedbytheactivelayerandcoupletotheguidinglayerasthey

reflectbackandforthacrossthegratingtogenerateallowedDFBmodesthatarenot

exactlymatchedtotheBraggwavelength,butareplacedsymmetricallyjustofftheideal

modeoftheguidinglayeratm.

Active layer

Corrugated grating

Guiding layer

(a)

(a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c)Typical output spectrum from a DFB laser.

Optical power

(nm)

0.1 nm

Ideal lasing emission

B(b) (c)


( )12

2

+= mnL

BBm

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CleavedCoupledCavityLaser

Device

has

two

different

optical

cavities

of

length

L

and

D.

Each

laser

cavity

is

pumped

by

a

different

current

Onlymodesresonantinbothcavitiesareallowedtoresonatethroughtheentiredevice,

allowingtheengineertotuneoutcertainmodesfromoneorbothindependentlaser

diodes

Whypumpboththecavities? Ans. Allowedmodesinanunpumped cavitywillundergo

recombinationifthedeviceisnotdriven.

Active

layer

L D

(a)

Cleaved-coupled-cavity (C3) laser

Cavity Modes

InL

InD

In bothLandD

(b)


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QuantumWell(QW)Devices

Devicewithanultrathin(50nm)narrowbandgap activeregionbetweentwowiderbandgap

semiconductors AssumethatinQWdevicesthatthelatticematchsothatallthesemiconductors havethesame

latticeconstantasothatcrystallinedefectsareminimized

Badgap changesattheinterfacearethereforeonlyduetodiscontinuitiesbetweenEcandEvofthedifferingmaterialsyieldingdiscreteallowablequantumstatesthatcanbesolvedasparticleinaboxtypeproblems.

A quantum well (QW) device. (a) Schematic illustration of a quantum well (QW) structure in which athin layer of GaAs is sandwiched between two wider bandgap semiconductors (AlGaAs). (b) Theconduction electrons in the GaAs layer are confined (by Ec) in thex-direction to a small length dso

that their energy is quantized. (c) The density of states of a two-dimensional QW. The density of statesis constant at each quantized energy level.

AlGaAs AlGaAs

GaAs

y

z

x

d

Ec

Ev

d

E1

E2

E3

g(EDensity of states

E

BulkQW

n= 1

Eg2Eg1

E n= 2Ec

BulkQW

Ev

(a) (b) (c)

Dy

Dz


[ ]

,...3,2,1,,

888

0)(2

2*

22

2*

22

2*

22

2

2

=

+++=

=+

zy

zeyee

c

e

nnn

Dm

nh

Dm

nh

dm

nhEE

xVEm

x

zy

h

Note:potentialenergybarrierofthe

conductionbandisdefinedbyw.r.t.Ec

Energy

in

a

quantum

well

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EnergySpectruminaQuantumWell(SQW)

Ec

Ev

E1

E1

h=E1E

1

E

In single quantum well (SQW) lasers electrons areinjected by the forward current into the thin GaAslayer which serves as the active layer. Populationinversion betweenE1andE1 is reached even with

small forward current which results in stimulatedemissions.


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Example:AGaAs QW

GaAs QW

Effective

electron

mass

is

me*=0.07me

WhatarethefirsttwoelectronenergylevelsforaQW

ofthickness10nm?

WhatistheholeenergybelowEviftheeffective

electronmassofthehole,mh*=.5me?

Whatistheemissionwavelengthw.r.t.bulkGaAs

whichasanenergybandgap of1.42eV?

Differenceinemissionwavelengthbetweenabulk

GaAs LDandaQWLDis35nm

Figure 16.1 Thelayeredstructureandthebandedges ofa

GaAlAs/GaAs/GaAlAs quantum

well.

Cc

2007

Photonics,

6th

edition

Yariv and

Yeh (Oxford

University

Press

( ) nm

eVnmeV

Ehc

nmeV

nmeV

E

hc

eVdm

nh

eVdm

nh

nng

QW

g

g

h

n

e

n

8390075.00527.042.1

1240

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0537.08

'

2*

22

'

2*

22

=

++

=

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=

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==

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TFH SS 2012 128

Gain spectrum in QW lasers
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Gain in a QW laser:

a) The Fermi inversionfc(n, ) fv(n, ) at two carrier

densities n2 >n1 for QW thicknessLz= 200A.

b) The gain vs. at n1 and n2.

c) The same as in a) for narrower QW(Lz= 100 A).

d) The same as in b) for narrower QW(Lz= 100 A).

e) The same as in a) for a bulksemiconductor.

f) The same as in b) for a bulksemiconductor.

The energy Ef in a) and c) corresponds tothe photon energy for which fc fv = 0which is the transparency condition

TFH SS 2012 129

Diff t Q t W ll T

DOS f 0 1 2 di i l
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Different

Quantum

Wells

Types

BasedonGeometry

ImagefromChapter16,ofFundamentalsofPhotonics,2nd ed.BySaleh andTeich cc2007 WileyInterscience

TFH SS 2012 130

DOS for 0,1,2 dimensional quantum

confined structures

Low dimensional structures & threshold current reduction
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from Z. Alferov, Nobel lecture Dec. 2000

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VerticalCavitySurfaceEmittingLasers(VCSELs)

Alternatinglayersoflowandhighindexaboveandbelow

theQWregion createsadistributedBraggreflectorof

dielectricmirrors

Themirrorsareneededtomatchtheopticalgainlostby

theshortcavitylength. Thuswiththemirrorsthelight

passesthroughthecavitysome2030timestoobtaina

desiredreflectanceof99%

Thehighreflectanceincreasesthegeometriccomponent

ofthegainrequiredforlaseremission

A simplified schematic illustration of a vertical cavitysurface emitting laser (VCSEL).

Contact

Surface emission

Dielectric mirror

Contact

Substrate

/4n1

Active layer

/4n2 Dielectric mirror


Figure 16.14 Thefielddistributionofthelasermodeinsideavertical

cavitylaserwithL=/nwiththreequantumwells.Notethe

evanescentdecayofthefieldenvelopeinsidetheBraggmirrorsand

theconstantamplitudestandingwavebetweenthemirrors.


22211

=+ dndn

Constructiveinterferenceofpartiallyreflectedwaves

Ofwavelength,,attheinterface

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VCSELAttributes

VCSELactive

layers

are

generally

very

thin

0.1umandcomprisedofMQWforimprovedthresholdcurrent

Thedeviceiscomprisedofepitaxially depositedlayeronasuitablesubstratewhichistransparentintheemissionwavelength

Ex.980nmVCSELdevices

InGaAs istheactivelayer

GaAs isthesubstrate

AlGaAs withdifferentcompositionscomprisethedielectricmirrorstack

ThetopstackisthenetchedafterallthelayershavebeendepositedtocreatetheinvertedTshape

presentedin

the

previous

slide

Inpractice,currentflowingthroughthedielectricmirrorsgivesrisetoanundesiredvoltagedropthatmakesthedeviceVERYsensitivetofailurefromelectrostaticdischarge. Infact,thisisthemostcommonfailuremodeduringVCSELoperationandinstallation.

Theverticalcavity andthustheemittedbeamisgenerallycircularincrosssection

Theheightoftheverticalcavityisseveralmicrons. Thusthelongitudinalmodeseparationissufficientlylargetoallowonlyonemodeofoperation. Howeverlateralmodesmaybepresentincertaincavitygeometries

InpracticeVCSELShaveseverallateralmodesbutthespectralwidthisonlynmwhichissubstantiallylessthanthelongitudinalmodesofaDFBorELD.

Also,

VCSELS

have

an

average

beam

divergence

of

about

812o depending

on

their

fabrication

and

materialsused

DualwavelengthVCSELemissionisobtainedbyoperatingathighcurrents.

TFH SS 2012 133

Late News: Ge electrically pumped laser
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T.-H.Cheng et al., Appl. Phys.

Lett. 96, 211108 (2010).

An electrically pumped germanium laser

Rodolfo E. Camacho-Aguilera,1Yan Cai,

1Neil Patel,

1Jonathan T. Bessette,

1

Marco Romagnoli,1,2

Lionel C. Kimerling,1and Jurgen Michel

1,*

1Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA

2PhotonIC Corporation, 5800 Uplander Way, Los Angeles, CA 90230, USA*[email protected]

Abstract: Electrically pumped lasing from Germanium-on-Silicon pnn

heterojunction diode structures is demonstrated. Room temperature

multimode laser with 1mW output power is measured. Phosphorous doping

in Germanium at a concentration over 4x1019

cm3

is achieved. AGermanium gain spectrum of nearly 200nm is observed.

2012 Optical Society of America

OCIS codes: (140.2020) Diode lasers; (140.3380) Laser materials; (140.5960) Semiconductor

lasers; (160.3130) Integrated optics materials.

References and links

1. D. J. Lockwood and L. Pavesi, Silicon Photonics(Springer-Verlag, 2004).

2. M. E. Groenert, C. W. Leitz, A. J. Pitera, V. Yang, H. Lee, R. Ram, and E. A. Fitzgerald, Monolithic integration

of room-temperature cw GaAs/AlGaAs lasers on Si substrates via relaxed graded GeSi buffer layers, J. Appl.

Phys. 93(1), 362367 (2003).3. H. Park, A. Fang, S. Kodama, and J. Bowers, Hybrid silicon evanescent laser fabricated with a silicon

waveguide and III-V offset quantum wells, Opt. Express 13(23), 94609464 (2005).

4. J. Liu, X. Sun, D. Pan, X. Wang, L. C. Kimerling, T. L. Koch, and J. Michel, Tensile-strained, n-type Ge as a

gain medium for monolithic laser integration on Si, Opt. Express 15(18), 1127211277 (2007).

5. J. Liu, X. Sun, Y. Bai, K. E. Lee, E. A. Fitzgerald, L. C. Kimerling, and J. Michel, Efficient above-band-gap

light emission in germanium, Chin. Opt. Lett. 7(4), 271273 (2009).

6. J. Liu, X. Sun, R. Camacho-Aguilera, L. C. Kimerling, and J. Michel, Ge-on-Si laser operating at room

temperature, Opt. Lett. 35(5), 679681 (2010).

7. G. Shambat, S.-L. Cheng, J. Lu, Y. Nishi, and J. Vuckovic, Direct band Ge photoluminescence near 1.6 m

coupled to Ge-on-Si microdisk resonators, Appl. Phys. Lett. 97(24), 241102 (2010).

8. S.-L. Cheng, J. Lu, G. Shambat, H.-Y. Yu, K. Saraswat, J. Vuckovic, and Y. Nishi, Room temperature 1.6m

electroluminescence from Ge light emitting diode on Si substrate, Opt. Express 17(12), 1001910024 (2009).

9. M. O. E. Kasper, T Aguirov, J. Werner, M. Kittler, J. Schulze, Room temperature direct band gap emission

from Ge p-i-n heterojunction photodiodes, in Proceedings of Group IV Photonics 2010 (2010).

10. X. Sun, J. Liu, L. C. Kimerling, and J. Michel, Room-temperature direct bandgap electroluminesence from Ge-

on-Si light-emitting diodes, Opt. Lett. 34(8), 11981200 (2009).

11. J. Liu, X. Sun, L. C. Kimerling, and J. Michel, Direct-gap optical gain of Ge on Si at room temperature, Opt.

Lett. 34(11), 17381740 (2009).

12. R. E. Camacho-Aguilera, Y. Cai, J. T. Bessette, D. Kita, L. C. Kimerling, and J. Michel, High active carrier

concentration in n-type, thin film Ge using delta-doping, submitted for publication (2012).13. G. Scappucci, G. Capellini, W. M. Klesse, and M. Y. Simmons, Phosphorus atomic layer doping of germanium

by the stacking of multiple layers, Nanotechnology22(37), 375203 (2011).

14. R. E. Camacho-Aguilera, Y. Cai, J. T. Bessette, L. C. Kimerling, and J. Michel, Electroluminescence of highly

doped Ge pnn diodes for Si integrated lasers, Proc. 8th IEEE Intern. Conf. GFP, Vol. 190,

10.1109/GROUP1104.2011.6053759 (2011).

15. S. Xiaochen, L. Jifeng, L. C. Kimerling, and J. Michel, Toward a Germanium Laser for integrated silicon

photonics, IEEE J. Sel. Top. Quantum Electron. 16(1), 124131 (2010).

1. Introduction

It has been long acknowledged that a monolithically integrated laser for silicon (Si) based

photonic circuits would be an enabling technology that could accelerate the implementation of

silicon photonics significantly [1]. Early attempts to integrate III-V semiconductor lasers on a

silicon platform had only limited success [2, 3]. More recently, germanium (Ge) has been

suggested as a gain medium for lasing on Si [4]. Using a combination of tensile strain and n-

type doping, efficient direct bandgap emission of Ge can be achieved [5]. Optically pumped

#164840 - $15.00 USD Received 19 Mar 2012; revised 24 Apr 2012; accepted 27 Apr 2012; published 2 May 2012

(C) 2012 OSA 7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 11316TFH SS 2012 134

lasing in Ge was demonstrated using a Ge waveguide with polished facets [6]. Furthermore,
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as g Ge was de o st ated us g a Ge wavegu de w t po s ed acets [6]. u t e o e,

attempts in electrically injection have demonstrated pin and pnn Ge diodes emitting between

1590 and 1700nm [710]. Here we present an electrically pumped pnn Ge diode laser that can

be monolithically integrated into a CMOS process. These first laser devices produce more

than 1 mW of output power and exhibit a Ge gain spectrum of over 200nm.

2. Experiments and results

Initial estimates of gain in n-type Ge based on experimental results showed that an n-type

doping level of 1x1019cm3would yield a gain of about 50 cm 1[11]. Such a gain can lead to

lasing when pumped optically because optical losses are mainly limited to facet losses and

free carrier losses in Ge. For electrical pumping, additional losses due to the electrical

contacts, free carrier losses in doped poly Si and losses due to the interaction with the contactmetal, have to be overcome. Modeling of mode propagation in Ge waveguides with electrical

contacts shows that these additional losses are >100 cm1.To overcome by these losses, the Ge

gain must be increased by increasing the n-type doping to a level of 3-5x10 19 cm3 [2].

Recently, we achieved n-type doping levels of > 4x1019cm3 by using a delta-doping

technique during epitaxial growth of Ge [12]. By correlation of photoluminescence (PL)

intensity, n-type doping level, and measured material gain, we have determined that an n-type

doping level of 4x1019cm3corresponds to a material gain of >400cm1, enough to overcome

the losses in an electrically pumped laser device.

Ge waveguides of 1m width were fabricated by selective growth of n-type Ge-on-Si in

silicon oxide trenches using Ultra-High Vacuum Chemical Vapor Deposition (UHV-CVD)

[3]. A delta-doped Ge layer was grown on top of the n-type Ge to serve as a phosphorousdiffusion source [12, 13]. The delta-doping technique inserts monolayers of P in the Ge film

at low temperatures by alternating the phosphine and germane gas flow in the CVD reactor.

After thermal annealing to drive the phosphorous into the n-type Ge layer, the delta-doped Ge

layer was removed during planarization using chemical mechanical polishing (CMP), to reach

a uniform doping concentration in the gain medium. The remaining thickness of the Ge

waveguide after CMP varied between 100 and 300nm depending on wafer and location on thewafer. Due to severe dishing of the waveguides after CMP the supported optical modes in the

waveguides could not be determined exactly. Up to six cavity modes can be supported in the

largest waveguides. An 180nm thick amorphous-Si film was then deposited via a Plasma-

Enhanced CVD process and subsequently phosphorus-implanted to a doping level of

1020cm3. After a dopant activation anneal at 750C, a metal stack, consisting of Ti and Al

was deposited for top and bottom contacts. The oxide trench provides excellent current

confinement. In order to assure even carrier injection into the n-type Ge, the top contact metal

was deposited on top of the waveguide. After dicing, the waveguides were cleaved to expose

the Ge waveguide facets. A thin oxide layer was deposited on the facets to protect against

contamination and catastrophic optical mirror damage which was observed in devices that did

not have oxide protection.


(C) 2012 OSA 7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 11317

Fig. 1. Schematic of the measurement set-up.

The waveguide emission was measured using a Horiba Micro PL system equipped with acooled InGaAs detector with lock-in detection. The emission power measurement was

calibrated using light from a commercial 1550nm laser that was coupled into a single mode

optical fiber with the fiber end at the sample location. In the calibration we verified that the

detection was linear with input power. The electrical pumping was supplied by a pulse

generator with current pulse widths in the range of 20 s to 100 ms. The duty cycle was

varied between 2 and 50%, typically 4% to reduce electrical current heating effects. The laserwas contacted with metal probes and the current was measured using an inductive sensor

placed directly in the biasing circuit. The experimental set-up is shown in Fig. 1.

Fig. 2. Ge laser emission spectrum before (a) and after (b) threshold. The cavity length of thewaveguide is 333m and the waveguide height about 100nm. Current injection employed pulse

widths of 50s at 800Hz and 15C. The detector spectral resolution was 1.2nm.

Figure 2 shows the spectrum of an electrically pumped Ge laser below and above

threshold. The broad, direct band gap related electroluminescence spectrum, observed for

highly doped n-type Ge LEDs, has been reported earlier [14]. The spectra in Fig. 2 employed

short integration times to assure wide spectrum analyses. Measurement time for these large

laser devices is ultimately limited by metal contact breakdown due to the high current flow.Figure 2(a) shows no spectral features above the noise floor. When the injection current

density is increased above threshold, sharp laser lines appear, as shown in Fig. 2(b). The

observed linewidth of the individual lines is below 1.2nm, the spectral resolution of the

measurement set-up. All measurements were performed with the samples mounted on a

thermo-electric cooler at 15C. Local device temperatures, however, are likely higher due tothe high current injection but could not be reliably determined.



TFH SS 2012 135

devices, the Ge waveguide height is directly related to the modal loss. Since Ge has the
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Fig. 3. L-I curve for a 270m long waveguide device. 40s electrical pulses were used at

1000Hz. Measurement temperature was 15C.

Figure 3 shows the L-I spectrum for a typical electrically pumped Ge waveguide laser.

The lasing threshold at about 280kA/cm2is clearly visible. This measurement was taken with

the set-up in Fig. 1 using a wide instrumental spectral resolution of 10nm, at a wavelength of

1650nm, monitoring a single laser line. The number of datapoints is limited by metal contact

breakdown at high current level. The optical emission power of about 1 mW corresponds to

Fig. 3. Occasionally we observed up to 7 mW. The spectrum in Fig. 2 shows two lines. Theestimate of the cavity free spectral range is 1nm, and the line spacing in Fig. 2, 3nm, is a

possible multiple of the FSR.

These lasers show a dependence of emission wavelength on threshold current density that

is consistent with the expected modal loss variation and that confirms the theoretical

conclusions that the gain spectrum of Ge for the given doping level and strain reaches over

more than 100nm spectral width [15]. For high doping levels of 4x1019

cm3

, and tensile strain

of ~0.2%, we observed lasing in the range from 1520nm to 1700nm. Figure 4 shows selectedlaser lines between 1576nm and 1656nm for different Fabry-Perot cavities of the same gain

material.

Fig. 4. Spectra of Ge lasers with different Ge waveguide heights. The measured laser line

wavelengths are (a) 1576nm, (b) 1622nm, and (c) 1656nm.

The CMP-induced variation in cavity height provides self-consistent evidence of the wide

gain spectrum and the gain clamping condition by lasing. Under lasing action optical gain

(and population inversion) is clamped at exactly the value of the resonant cavity losses. In our



g g y

highest refractive index in our device structure, thinner Ge layers expel more of the resonant

mode into the highly-doped poly-Si cladding and into the lossy metal contacts. The

wavelength corresponding to the Ge gain peak (the threshold injection level) and the cavity

loss is the expected emission wavelength of the device. As the modal confinement decreases

with decreasing Ge layer thickness, modal loss and correspondingly threshold current

increases and the emission wavelength blue shifts. In Fig. 5, we show spectral threshold

conditions for two different modal cavity losses using a parabolic band model as described in

[8].

A Ge waveguide of 300nm thickness has a modal loss of about 90 cm1

due to losses in

the doped poly Si and the metal electrode (solid line). A Ge waveguide of 100nm thickness,

however, has a modal loss of about 1000cm 1due to the closer proximity of the mode to theelectrode (dashed line). To overcome the high losses of the thin Ge waveguide, a relatively

high carrier injection level is needed. Lasing is therefore expected at around 1520nm, close to

what we find in Fig. 2. For lower loss waveguides we expect lasing to occur at longer

wavelengths as shown in Fig. 4.

Fig. 5. Simulation of gain clamping condition for two different Ge waveguide thicknesses

(100nm: solid line; 300nm: dashed line). The axes plot the corresponding modal loss and gainspectrum for the two different injection levels that are needed to overcome the respectivemodal losses and to achieve lasing.

3. Conclusions

We have observed lasing from electrically pumped n-type Ge Fabry-Perot cavities. The

threshold current densities decrease with increased modal confinement. The emission

linewidth is less than the 1.2nm resolution of our measurement. Laser emission wavelengths

were observed between 1520nm and 1700nm with a variation consistent with the gain

clamping condition for each device. Measured output powers greater than 1 mW at room

temperature were measured. Improvements in the Ge growth, electrical contacts, and in modal

loss reduction will decrease the lasing threshold to values comparable with Fabry-Perot diode

lasers. The high power and observed gain spectrum of nearly 200nm indicate that the Ge lasercould be used for WDM applications. Since the laser can be monolithically integrated into any

CMOS process flow, novel device applications and systems can be developed.

Acknowledgments

This work was supported by the Fully Laser Integrated Photonics (FLIP) program under APIC

Corporation, supervised by Dr. Raj Dutt, and sponsored by the Naval Air Warfare Center -

Aircraft Division (NAWC-AD) under OTA N00421-03-9-002. R.E.C.-A. was supported by a

NSF Graduate Research Fellowship award number 1122374.



TFH SS 2012 136
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