széchenyi istván university győr hungary edge-emitting lasers and surface-emitting vertical...

Széchenyi István University

Győr

Hungary

Edge-Emitting Lasers and Edge-Emitting Lasers and Surface-Emitting Vertical Cavity Surface-Emitting Vertical Cavity

LasersLasers

Szilvia NagySzilvia Nagy

Department of TelecommunicationDepartment of Telecommunication

22ESM Lille 2007ESM Lille 2007

OutlineOutline

Operation of lasersOperation of lasersPropertiesProperties

applicationsapplications

Atomic energy levelsAtomic energy levels

Population inversion Population inversion

Energy bands in solid statesEnergy bands in solid states

Heterojunctions in semiconductorsHeterojunctions in semiconductors

Quantum well lasersQuantum well lasers

Vertical cavity surface emitting lasersVertical cavity surface emitting lasers


Properties of lasersProperties of lasers

Monochromatic light – small bandwidthMonochromatic light – small bandwidth

Small divergence – narrow and directed Small divergence – narrow and directed beambeam

Coherent beam – all photons have nearly Coherent beam – all photons have nearly the same phasethe same phase

Usually not too high power, but Usually not too high power, but

High power densityHigh power density

Not an effective energy transformerNot an effective energy transformer


Application of the lasersApplication of the lasers

Materials processing – cutting, drilling, Materials processing – cutting, drilling, welding, heat treating, …welding, heat treating, …

Reading optical signs – CD, barcode, …Reading optical signs – CD, barcode, …

Graphics – printers, color separators, Graphics – printers, color separators, printing plate makers, …printing plate makers, …

Laboratory, measurementsLaboratory, measurements

Medicine – bloodless scalpel, tumor Medicine – bloodless scalpel, tumor destroying, …destroying, …

Military – target designators, finders, …Military – target designators, finders, …

TelecommunicationsTelecommunications


optical power of the light before reflection: Pafter reflection:(1−1)P

Operation of lasersOperation of lasers

What is needed for laser operationWhat is needed for laser operation

Laser gain – an optical amplifierLaser gain – an optical amplifier

Optical resonator – positive feedbackOptical resonator – positive feedback

reflection






new photons arisereflection

optical gain in the amplifier: P g∙ℓ∙P






(1−2)P

2∙P



In equilibrium the gain and the losses have In equilibrium the gain and the losses have to be the same: the power of the light to be the same: the power of the light varies asvaries as

ℓ

P



The solution of the SchrThe solution of the Schröödinger equationdinger equation

results inresults in - quantized eigenenergies- quantized eigenenergies

- corresponding wave functions- corresponding wave functions

EH

E

ground state

1st excited state

2nd excited state



If a photon of energy If a photon of energy

interacts with an atom, an electron can be interacts with an atom, an electron can be excited from energy level excited from energy level EEmm to level to level EEnn

mn EEh

E

nE

mE

ephoton

photon absorption – relative rate:

hffB

r

nmmn

mn

1



An excited electron from energy level An excited electron from energy level EEmm can can relax to a lower from energy level relax to a lower from energy level EEnn, , releasing a photon of energyreleasing a photon of energy

mn EEh

E

nE

mE

ephoton – random direction

spontaneous emission – relative rate:

spontaneous lifetime

mnnmnm ffAr 1



If a photon corresponding to the energy If a photon corresponding to the energy

interacts with an atom which has an excited interacts with an atom which has an excited electron at energy level electron at energy level EEnn, it can stimulate , it can stimulate the electron to relax to level the electron to relax to level EEnn

mn EEh

E

nE

mE

photon

stimulated emission

2 photons – same direction, same phase

hffBr nmmnmn 1stim



Stimulated emission can take place long Stimulated emission can take place long before the spontaneous lifetime.before the spontaneous lifetime.

Stimulated emission:Stimulated emission:

one photon in one photon in two photons outtwo photons out

The The optical amplifieroptical amplifier can be a collection of can be a collection of atoms with lots of electrons excited to the atoms with lots of electrons excited to the same state (with long spontaneous lifetime).same state (with long spontaneous lifetime).



LLight ight AAmplification by mplification by SStimulated timulated EEmission mission of of RRadiationadiation

The resonator is usually much longer than The resonator is usually much longer than the wavelength.the wavelength.

E

Upper Laser Level

Lower Laser Level



In equilibrium, the relative rates In equilibrium, the relative rates

Thus the photon density at energy Thus the photon density at energy hh

stimnmnmmn rrr

nm

mn

nmmn

nm

Bffff

B

Ah

11

relative occupation probability


Population inversionPopulation inversion

In thermodynamical equilibrium, the In thermodynamical equilibrium, the population of the states follow Boltzmann’s population of the states follow Boltzmann’s lawlaw

TkE

iB

i

eNN

0

TkEE

B

mn exp

the relative occupation probability is

nmTk

EEmn

nm

BBA

hB

mn exp

thus



Comparing the resulting photon density Comparing the resulting photon density with the black body radiationwith the black body radiation

nmmn BB

1 exp

4

2

3

Tkh

c

hh

B

nm

B

mnmn

nm

BTkEE

B

Ah

exp 2

34ch

BA

nm

nm



In thermodynamical equilibrium, the In thermodynamical equilibrium, the population of the states follow Boltzmann’s population of the states follow Boltzmann’s lawlaw

TkE

iB

i

eNN

0

iE

iNmE

nE

If Bmn=Bnm, the relative , the relative rate of absorption in rate of absorption in equilibrium is much equilibrium is much higher than that of higher than that of stimulated emissionstimulated emission



Somehow the number of electrons in the Somehow the number of electrons in the upper laser level is increasedupper laser level is increased

population inversionpopulation inversion occurs. occurs.

iE

iNmE

nE

The particles are not in thermodynamical equilibrium



Population inversion is generated by Population inversion is generated by

exciting the electrons to a exciting the electrons to a level with short spontaneous level with short spontaneous lifetime above the upper lifetime above the upper laser level: laser level: pumpingpumping

from the from the ppumping umping llevel the evel the electrons relax to the electrons relax to the uupper pper llaser aser llevel, which has longer evel, which has longer spontaneous lifetimespontaneous lifetime

electrons accumulate at the upper electrons accumulate at the upper laser levellaser level

E

ULL

LLL

PL

GS



Three-level laser Three-level laser Four-level laserFour-level laser

EE

upper laser level

lower laser level =

pumping level

ground state

upper laser level

lower laser level

pumping level

ground state

short spontaneous lifetime



Inverse population can be generated by Inverse population can be generated by

special filtersspecial filters

electrical pumpingelectrical pumping direct electrical dischargedirect electrical discharge

radio frequency fieldradio frequency field

electron beamelectron beam

p-n heterostructurep-n heterostructure

optical pumpingoptical pumping

chemical pumpingchemical pumping

nuclear pumpingnuclear pumping



In solids the atomic niveaus broaden In solids the atomic niveaus broaden energy bands are formedenergy bands are formed

vibrations (and rotations) in the crystalvibrations (and rotations) in the crystal momentum dependence of energy levelsmomentum dependence of energy levels splitting of degenerate states, …splitting of degenerate states, …

E

valance band

conduction band

bandgap – no electrons are allowed



The Fermi level is the highest energy level The Fermi level is the highest energy level occupied by electrons:occupied by electrons:

Fermi level in the conduction bandFermi level in the conduction band metalmetal

Fermi level in the gap Fermi level in the gap insulator insulatorE E

FE

FE

metal insulator (semiconductor)



At non-zero temperature, the Fermi level is At non-zero temperature, the Fermi level is not strict, the occupation probability will not strict, the occupation probability will follow Fermi-Dirac statisticsfollow Fermi-Dirac statistics

E E

FE FE

T = 0 K

T > 0 K

f(E)

TkB

TkEE

B

fEf

exp1

1

f(E)



So if an insulator has a bandgapSo if an insulator has a bandgap

considerable amount of electrons can be considerable amount of electrons can be present in thepresent in the conduction conduction band: band:

E

,roomTkB

E

FE roomTkB

conduction band

conduction bandgap

semiconductor insulator



In a crystal the energy levels depend on the In a crystal the energy levels depend on the electron’s wave number electron’s wave number k k (quasi momentum):(quasi momentum):

E

v.b

c.b

indirectgap

k

E

v.b

c.b

direct gap

kmomentum conservation

no photon emissionno momentum to be taken photon emission


Heterojunctions in Heterojunctions in semiconductorssemiconductors

Charge carriers can be injected to semi-Charge carriers can be injected to semi-conductors by conductors by dopingdoping: :

group V atoms: electrons group V atoms: electrons n-typen-type

group III atoms: holes group III atoms: holes p-typep-type

conduction band

valance band

E

FEp-

type

E

FE

n-type

localized acceptor/donor levels



If n-type and p-type doped semiconductorIf n-type and p-type doped semiconductor

layers are brought in contact, layers are brought in contact,

the positive and negative charge carriers the positive and negative charge carriers near the junction can recombine near the junction can recombine

photons can be emittedphotons can be emitted

potential barrier buildspotential barrier builds

barrierUe

no recombination

FE

x



If n-type and p-type doped semiconductorIf n-type and p-type doped semiconductor

layers are brought in contact, layers are brought in contact,

the recombination stops, unless external the recombination stops, unless external bias is appliedbias is applied LEDsLEDs

externalUeFpE

FnE

x

recombination possible active region



The simple heterojunctions have some The simple heterojunctions have some disadvantagesdisadvantages

due to the relative large spatial dimension, due to the relative large spatial dimension, high current is needed for creating high current is needed for creating sufficient population inversionsufficient population inversion

the heat generated by the current is very the heat generated by the current is very high, destroys the devicehigh, destroys the device

Solution: Solution: restrict the high current density region into restrict the high current density region into small regionsmall region double heterojunctiondouble heterojunction



1

active layer

The double heterojunction localizes the population The double heterojunction localizes the population inversion into a small region of space applying inversion into a small region of space applying two different materials with different bandgaps two different materials with different bandgaps 11 and and 22

22

x



1n

active layern

The semiconductors of the double hetero-The semiconductors of the double hetero-junction have different refractive indices junction have different refractive indices nn11 and and nn22 (not just different bandgaps (not just different bandgaps 11, , 22))

2n

x

the laser beam is also localized in direction x



The double heterojunction localizes the The double heterojunction localizes the population inversion and the laser beam into population inversion and the laser beam into a small region of spacea small region of space less heatless heat

substrate, p-type substrate, p-type dopeddoped

p-type, p-type, 22

n-type, n-type, 22

substrate substrate (n-type/undoped)(n-type/undoped)

electrodeelectrode

electrodeelectrode

x

active layer, active layer, 11



Materials grown upon each other should have Materials grown upon each other should have similar grid distance in order not to produce similar grid distance in order not to produce strain or dislocations in the crystal.strain or dislocations in the crystal.

x

p-GaAs, p-InGaAsP,…

p-Ga0,7Al0,3As, p-InP,…Ga0,95Al0,05As, InGaAsP,…n-Ga0,7Al0,3As, n-InP,…n-GaAs, n-InP,…

exampleexampless



Thin layers of semiconductors have to be Thin layers of semiconductors have to be grown on each other with very accurate grown on each other with very accurate layer thickness:layer thickness:

metal-organic chemical vapor depositionmetal-organic chemical vapor deposition

molecular beam epitaxymolecular beam epitaxy


The mirrors placed parallel to the plane The mirrors placed parallel to the plane plottedplotted the light propagates the light propagates parallel to the layerparallel to the layer


x

lighlightt

The optical properties The optical properties of the cleaved of the cleaved facelets are not facelets are not controllable during controllable during the fabrication the fabrication processprocess

The cleaved facelets The cleaved facelets of the stripe are of the stripe are usually sufficient usually sufficient reflectors.reflectors.



The population inversion can be restricted in The population inversion can be restricted in the other dimension, too:the other dimension, too:

electrodeelectrodestripe electrode stripe electrode restricts the current restricts the current flowflow

x

the population the population inversion takes place inversion takes place in a small stripe in a small stripe inside the active inside the active layerlayer



With special geometry the laser beam can With special geometry the laser beam can be localized, as well as the population be localized, as well as the population inversioninversion

x

the n-p junctions do the n-p junctions do not allow current not allow current outside of the stripeoutside of the stripe

n-typen-typen-typen-type

p-typep-typep-typep-type

refractive index refractive index nn<<nn11 the low refractive the low refractive index regions index regions restrict the beam: restrict the beam: the high refractive the high refractive index field is a index field is a waveguidewaveguide



With special geometry the laser beam can With special geometry the laser beam can be localized, as well as the population be localized, as well as the population inversioninversion

x

elliptical elliptical beambeam

the thinner the the thinner the layer, the layer, the less less modesmodes can can propagatepropagate

the thinner the the thinner the layer, the layer, the less less currentcurrent is needed is needed for sufficient for sufficient amount of inverse-amount of inverse-population charge population charge carrierscarriers



For proper optical confinement single For proper optical confinement single waveguide mode is neededwaveguide mode is needed the the higher order modes have to be cut off.higher order modes have to be cut off.This requires thicknessThis requires thickness

222 cg nnd

or less. For or less. For = the1.3 = the1.3 m, m, dd<0.56 <0.56 m.m.

((nngg and and nncc are reflective indices of are reflective indices of wavewavegguide and the uide and the ccladding)ladding)



If the waveguide is too thin, the light spreads out of If the waveguide is too thin, the light spreads out of itit the loss increases.the loss increases.

For confining the population inversion thinner For confining the population inversion thinner layers would be needed.layers would be needed.

Solution: the waveguide and the active layer are Solution: the waveguide and the active layer are not the same – not the same – SSeparate eparate CConfinement onfinement HHeterostructure (SCH)eterostructure (SCH)

active layeractive layer

waveguidewaveguide



If the waveguide is too thin, the light spreads out If the waveguide is too thin, the light spreads out of itof it the loss increases.the loss increases.

For confining the population inversion thinner For confining the population inversion thinner layers would be needed.layers would be needed.

Solution: the waveguide and the active layer are Solution: the waveguide and the active layer are not the same – not the same – GRGRaded aded ININdex SCH (GRINSCH)dex SCH (GRINSCH)

active layeractive layer

waveguidewaveguide



If the active region is thin enough, If the active region is thin enough, 10 nm10 nm

only few layers of atoms in the active only few layers of atoms in the active regionregion

quantum wellquantum well is formed is formed

The solution of the Schrödinger equation of The solution of the Schrödinger equation of quantum wells:quantum wells:

I.I. electron in a potential well in the electron in a potential well in the xx directiondirection

II.II. free electron gas solution in the free electron gas solution in the yzyz plane plane

m

kkE zy

2

222

k



The solution of the 1D potential well The solution of the 1D potential well problem:problem:

xV

x2/w2/w

x2 x1 x3



The solution of the 1D potential well problem:The solution of the 1D potential well problem:

the Schrthe Schröödinger equationdinger equation

2

2

2w

2

2

2

2

33032

2

222

2

11012

2

wxxExVx

xm

xw

xExxm

wxxExVx

xm



the boundary conditions:the boundary conditions:

xV

x2/w2/w

22

22

21

21

wx

wx

ww

22

22

32

32

wx

wx

ww



The solution of the differential equation The solution of the differential equation system:system:

xkbxkax cossin 222

xAx exp11

xAx exp33

EVm 02

mE

k2

withwith

andand



For V0=1 a.u., w=40 a.u., E=0.0029 a.u.:For V0=1 a.u., w=40 a.u., E=0.0029 a.u.:

xkbxkax cossin 222

xAx exp11 xAx exp33




xAx exp11 xAx exp33

xkbxkax cossin 222



k

The energy versus quasi momentum The energy versus quasi momentum function:function:

E



If the free electron gas is restricted to two or If the free electron gas is restricted to two or less dimensions, the density of states less dimensions, the density of states behaves different from the 3D casebehaves different from the 3D case

3D3D

jEEdEdN

Eg

E

Eg




2D2D

.constdEdN

ED

E

EDpositions adjustable positions adjustable via via d d (well thickness)(well thickness)




1D1D

jEEdE

dNE

1

E

E

positions adjustable positions adjustable via via d d (well thickness)(well thickness)



The absorption spectrum is also different for The absorption spectrum is also different for 2D electron systems from the bulk case:2D electron systems from the bulk case:

3D:3D:

2D:2D:the absorption spectrum is steplike with the absorption spectrum is steplike with resonances at the frequencies resonances at the frequencies corresponding to the energy differencescorresponding to the energy differences

better absorption spectrum, transparency.better absorption spectrum, transparency.

h



Usually a single quantum well (SQW) is too Usually a single quantum well (SQW) is too thin for confining the lightthin for confining the light

multiple quantum wells (MQW) with barrier multiple quantum wells (MQW) with barrier layers can be applied:layers can be applied:

x x

GRINSCHGRINSCHMQWMQW

SCH-MQWSCH-MQW



The quantum well lasers have higher The quantum well lasers have higher threshold than the bulk lasers, but they threshold than the bulk lasers, but they also have higher gain, better transparency.also have higher gain, better transparency.

Quantum wells based on GaAs perform well, Quantum wells based on GaAs perform well, low loss, high gainlow loss, high gain

Quantum wells based on InP have higher loss Quantum wells based on InP have higher loss (Auger recombination,…)(Auger recombination,…)a a strainstrain in the QW layers improves the in the QW layers improves the performance of QW InGaAsP lasersperformance of QW InGaAsP lasers



k

EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other electron, which other electron, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)

e.g. CCCH e.g. CCCH processprocess

C.B.C.B.

HH.B.HH.B.

LH.B.LH.B.SO.B.SO.B.



k

EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other hole, which other hole, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)

e.g. CHHL e.g. CHHL processprocess

C.B.C.B.

HH.B.HH.B.




k

EIn the Auger In the Auger recombination the recombination the energy which is energy which is released via an released via an electron-hole electron-hole recombination is recombination is absorbed by an absorbed by an other hole, which other hole, which dissipates the dissipates the energy by energy by generating lattice generating lattice oscillations oscillations (phonons)(phonons)

e.g. CHHS e.g. CHHS processprocess

C.B.C.B.

HH.B.HH.B.




k

EQuantum wellsQuantum wells cause splitting in the cause splitting in the conduction band, lift conduction band, lift the degeneracy of the degeneracy of the heavy hole and the heavy hole and light hole bands, and light hole bands, and distort the shapedistort the shape

Similar effective Similar effective mass (curvature) means mass (curvature) means more effective more effective population inversion population inversion (smaller threshold)(smaller threshold)

e.g. CCCHe.g. CCCH

k

C.B.C.B.

HH1HH1

LH.B.LH.B.SO.B.SO.B.HH2HH2



k

EQuantum wells + Quantum wells + tensile straintensile strain lifts the lifts the light hole bandslight hole bands

TM mode TM mode

The split off band is The split off band is also depressed also depressed

less Auger less Auger recombination, recombination, higher carrier higher carrier density is possibledensity is possible

e.g. CCCHe.g. CCCH

k

C.B.C.B.

HH1HH1

LH.B.LH.B.

SO.B.SO.B. HH2HH2



k

EQuantum wells + Quantum wells + compressive straincompressive strain depresses the light depresses the light hole bands, and hole bands, and further reduce the further reduce the heavy hole band’s heavy hole band’s curvaturecurvature

TE modulation TE modulation and further decrease and further decrease in threshold levelin threshold level

e.g. CCCHe.g. CCCH

k

C.B.C.B.

HH1HH1


HH2HH2


VCSELsVCSELs

The high gain of quantum wells make The high gain of quantum wells make possible to place the resonator above and possible to place the resonator above and under the active region:under the active region:

Bragg Bragg reflectorsreflectors(multiple) (multiple) quantum well quantum well structurestructure

electrodeselectrodes

apertureaperture


VCSELsVCSELs

The confinement of population inversion in The confinement of population inversion in the y and z dimensions is necessarythe y and z dimensions is necessary

aperture usually at aperture usually at the bottomthe bottom

n n DBRDBR

p p DBRDBR

etched mesa/air post etched mesa/air post VCSELVCSEL


VCSELsVCSELs

The confinement of population inversion in The confinement of population inversion in the y and z dimensions is necessarythe y and z dimensions is necessary

the etched regions the etched regions are regrown are regrown epitaxiallyepitaxially

(e.g., high index nipi (e.g., high index nipi layers – passive layers – passive antiguide region)antiguide region)

n n DBRDBR

p p DBRDBR

buried regrowth buried regrowth VCSELsVCSELs


VCSELsVCSELs

Since the reflectors are grown upon the diode Since the reflectors are grown upon the diode structurestructure

the resonator length is much shorter than the resonator length is much shorter than the edge emitting lasers’ cavity (less modes)the edge emitting lasers’ cavity (less modes)

the properties of the reflectors can be the properties of the reflectors can be monitored during the growthmonitored during the growth

very good reflectance can be very good reflectance can be producedproduced

it is easier to couple the VCSEL’s light into it is easier to couple the VCSEL’s light into an optical fiberan optical fiber

laser arrays can be producedlaser arrays can be produced


Fiber Optic Handbook, Fiber, Devices, and Systems for Optical Fiber Optic Handbook, Fiber, Devices, and Systems for Optical Communications,Communications,editor: M. Bass, (associate editor: E. W. Van Stryland)editor: M. Bass, (associate editor: E. W. Van Stryland)McGraw-Hill, New York, 2002.McGraw-Hill, New York, 2002.J. L. Miller, and E. Friedman,J. L. Miller, and E. Friedman,Photonics Rules of Thumb, Optics, Electro-Optics, Fiber Optics, Photonics Rules of Thumb, Optics, Electro-Optics, Fiber Optics, and Lasers, and Lasers, McGraw-Hill, New York, 1996.McGraw-Hill, New York, 1996.P. C. Becker, N. A. Olsson, and J. R. Simpson,P. C. Becker, N. A. Olsson, and J. R. Simpson,Erbium-Doped Fiber Amplifiers, Fundamentals and Technology,Erbium-Doped Fiber Amplifiers, Fundamentals and Technology,Academic Press, San Diego, 1999.Academic Press, San Diego, 1999.J. Singh,J. Singh,Semiconductor Optoelectronics, Physics and Technology,Semiconductor Optoelectronics, Physics and Technology,McGraw-Hill, New York, 1995.McGraw-Hill, New York, 1995.J. Singh,J. Singh,Optoelectronics, An Introduction to Materials and Devices, Optoelectronics, An Introduction to Materials and Devices, McGraw-Hill, New York, 1996.McGraw-Hill, New York, 1996.C. R. Pollock,C. R. Pollock,Fundamentals of OptoelectronicsFundamentals of OptoelectronicsIrwin, Chicago, 1995.Irwin, Chicago, 1995.

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