DTIC ADA596364: Laser Cooling of Solids

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Laser cooling of solids
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University of New Mexico,Department of Physics & REPORT NUMBER
Astronomy,Albuquerque,NM,87106
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14. ABSTRACT
We present an overview of solid-state optical refrigeration also known as laser cooling in solids by
fluorescence upconversion. The idea of cooling a solid-state optical material by simply shining a laser beam
onto it may sound counter intuitive but is rapidly becoming a promising technology for future cryocoolers.
We chart the evolution of this science in rare-earth doped solids and semiconductors.
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Laser&Photon.Rev.3,No.1–2,67–85(2009)/DOI10.1002/lpor.200810038 67
Abstract Wepresentanoverviewofsolid-stateopticalrefrig-
erationalsoknownaslasercoolinginsolidsbyfluorescence
upconversion.Theideaofcoolingasolid-stateopticalmaterial
bysimplyshiningalaserbeamontoitmaysoundcounterintu-
itivebutisrapidlybecomingapromisingtechnologyforfuture
cryocoolers.Wecharttheevolutionofthisscienceinrare-earth
dopedsolidsandsemiconductors.
Measured cooling efficiency as a function of the pump laser
wavelengthfora1.2%Tm+3 dopedBaY F crystalatroom
2 8
temperature.Thesolidlineiscalculatedusingtheabsorption
spectrum[30].
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
Laser cooling of solids
MansoorSheik-Bahae1,*andRichardI.Epstein1,2
1OpticalScienceandEngineering,DepartmentofPhysics&Astronomy,UniversityofNewMexico,Albuquerque,NM,USA
2LosAlamosNationalLaboratory,LosAlamos,NM,USA
Received:1August2008,Revised:8September2008,Accepted:10September2008
Publishedonline:27October2008
Keywords: Solid-statelasercooling,opticalrefrigeration,anti-Stokesfluorescence,luminescenceup-conversion,rare-earthdopedsolids,
directband-gapsemiconductors,all-solid-statecryocooler,externalquantumefficiency,GaAs,differentialluminescencethermometry.
PACS: 32.80.Pj,78.20.–e,78.55.Cr,78.66.Fd
1. Basicconcepts tialsimilaritiestoatomcooling:lightquantaintheredtail
oftheabsorptionspectrumareabsorbedfromamonochro-
Theterm“lasercooling”ismostoftenusedinassociation maticsourcefollowedbyspontaneousemissionofmore
withcoolingandtrappingofdilutegasesofatomsandions energetic(blue-shifted)photons.Inthecaseofsolids,the
to extremely low temperatures. This area of science has extraenergyisextractedfromlatticephonons,thequantaof
progressed rapidly in the last two decades and has facil- vibrationalenergyinwhichheatiscontained.Theremoval
itated the observation of Bose-Einstein condensates and of these phonons is equivalent to cooling the solid. This
manyrelatedphenomena[1,2].Itissurprisingthatnearly process has also been termed “anti-Stokes fluorescence”
halfacenturybeforeDopplercoolingofatomswasever and“luminescenceup-conversion”cooling.
contemplatedandmorethanthirtyyearsbeforeinvention Lasercoolingofsolidscanbeexploitedtoachievean
ofthelaser,GermanphysicistPeterPringsheim(Fig.1)pro- all-solid-state cryocooler [4–6] as conceptually depicted
posedcoolingofsolidsbyfluorescenceup-conversion[3]. in Fig.2. The advantages of compactness, no vibrations,
In the solid phase, atoms do not possess relative transla- nomovingpartsorfluids,highreliability,andnoneedfor
tionalmotion–theirthermalenergyislargelycontained cryogenicfluidshavemotivatedintensiveresearch.Space-
inthevibrationalmodesofthelattice.Thephysicsoflaser borneinfraredsensorsarelikelytobethefirstbeneficiaries,
coolingofsolids(oropticalrefrigeration)doeshaveessen- withotherapplicationsrequiringcompactcryocoolingreap-
*Correspondingauthor:e-mail:[email protected]
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
68 M.Sheik-BahaeandR.I.Epstein:Lasercoolingofsolids
beingcooled,theload,byathermallink;seeFig.2.This
Excited State
linksiphonsheatfromtheloadwhilepreventingthewaste
fluorescencefromhittingtheloadandheatingit.
Anotherpotentialapplicationoflasercoolingofsolids
istoeliminateheatproductioninhigh-powerlasers.Even
thoughlaseremissionisalwaysaccompaniedbyheatpro-
duction,Bowman[8,9]realizedthatinsomelasermaterials,
thepumpwavelengthcanbeadjustedsothatthesponta-
Ground State neous anti-Stokes fluorescence cooling compensates for
thelaserheating.Suchthermallybalancedlaserwouldnot
sufferthermaldefocusingorheatdamage.
Figure1 (onlinecolorat:www.lpr-journal.org) In1929,Peter
Theprocessofopticalrefrigerationcanoccuronlyin
Pringsheimsuggestedthatsolidscouldcoolthroughanti-Stokes
specialhighpuritymaterials(seesectionIII)thathaveap-
fluorescenceinwhichasubstanceabsorbsaphotonandthenemits
oneofgreaterenergy.Theenergydiagramontherightshowsone propriatelyspacedenergylevelsandemitlightwithhigh
waythiscouldoccur.Anatomwithtwobroadlevelsisembedded quantumefficiency.Todate,opticalrefrigerationresearch
inatransparentsolid.Thelightsourceoffrequencyhν excites hasbeenconfinedtoglassesandcrystalsdopedwithrare-
atomsnearthetopofthegroundstateleveltothebottomofthe earth elements and direct-band semiconductors such as
excitedstate.Radiativedecaysoccurringafterthermalizationemit galliumarsenide.Lasercoolingofrare-earthdopedsolids
photonswithaverageenergyhν >hν. havebeensuccessfullydemonstrated,whileobservationof
f
netcoolinginsemiconductorshasremainedelusive.Fig.1
schematicallydepictstheopticalrefrigerationprocessesfor
ingthebenefitsasthetechnologyprogresses.Astudyby a two level system with vibrationally broadened ground
BallAerospaceCorporation[7]showsthatinlow-power, andexcitedstatemanifolds.Photonsfromalowentropy
space-borneoperations,ytterbium-basedopticalrefriger- lightsource(i.e.alaser)withenergyhν exciteatomsfrom
ation could outperform conventional thermoelectric and the top of the ground state to the bottom of the excited-
mechanicalcoolersinthetemperaturerangebetween80– state.Theexcitedatomsreachquasi-equilibriumwiththe
170K.Efficient,compactsemiconductorlaserscanpump latticebyabsorbingphonons.Spontaneousemission(flu-
opticalrefrigerators.Inmanypotentialapplications,there- orescence) follows with a mean photon energy hνf that
quirementsonthepumplasersarenotveryrestrictive.The is higher than that of the absorbed photon. This process
spectralwidthofthepumplighthastobenarrowcompared hasalsobeencalledanti-Stokesfluorescence.Therewere
tothethermalspreadofthefluorescence.Multimode,fiber initial concerns that the second law of thermodynamics
coupledlaserwithspectralwidthsofseveralnanometers mightbeviolateduntilLandauclarifiedtheissuein1946
wouldbeadequate.Inanopticalrefrigeratorthecooling byassigninganentropytotheradiation[10].
powerisoftheorder1percentofthepumplaserpower.For In the aforementioned simple model, the interaction
micro-coolingapplications,withmWheatlift,onlymodest ratebetweenelectronsandphononswithineachmanifold
lasersareadequate.Forlargerheatlifts,correspondingly isassumedtobefarfasterthanthespontaneousemission
more powerful lasers are needed. In all cooling applica- rate, which is valid for a broad range of materials and
tions,thecoolingelementhastobeconnectedtothedevice temperatures.Thecoolingefficiencyorfractionalcooling
thermal link (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:6)(cid:8)(cid:7)(cid:9)(cid:10)
Figure2 (onlinecolorat:www.lpr-
journal.org) Schematicofanoptical
(cid:18)(cid:5)(cid:12)(cid:9)(cid:5)(cid:6)(cid:19)(cid:4)(cid:15)(cid:17)(cid:14)(cid:6)(cid:10) (cid:14)(cid:9)(cid:15)(cid:12)(cid:5)(cid:16)(cid:14)(cid:7)(cid:17)(cid:7)(cid:6)(cid:4)(cid:8)(cid:9)(cid:9)(cid:15)(cid:17)(cid:13)(cid:7)(cid:4) refrigeration system. Pump light is
efficiently generated by a semicon-
ductordiodelaser.Thelaserlighten-
tersthecoolerthroughapinholein
(cid:11)(cid:12)(cid:13)(cid:5)(cid:9)(cid:11) onemirrorandistrappedbythemir-
rorsuntilitisabsorbed.Isotropicflu-
vacuum
orescenceescapesthecoolerelement
andisabsorbedbythevacuumcas-
heat sink
ing. A sensor or other load is con-
nected in the shadow region of the
high reflectivity mirrors secondmirror.Fig.2hasbeenrepro-
ducedfrom[6].
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.lpr-journal.org
Laser&Photon.Rev.3,No.1–2(2009) 69
energyforeachphotonabsorbedis (pumpphoton)of1eVfromroomtemperaturedemands
thatη η >97%.Althoughsuitablelaserswereavail-
ext abs
hν −hν λ
η = f = −1 (1a) ableintheearly1960’s,morethanthreedecadesofprogress
c hν λf inmaterialgrowthwereneededtosatisfythiscondition.
where λ = c/ν is the wavelength. The invention of the
laser in 1960 prompted several unsuccessful attempts to
observelasercoolingofsolids[11–13].In1995,netcool- 2. The4-levelmodelforopticalrefrigeration
ingwasfirstachievedbyworkersatLosAlamosNational
Laboratory[14].Twotechnicalchallengeswereaddressed
Considerthe4-levelsystemofFig.3inwhichtheground
andovercomeintheseexperiments.TheLosAlamosre-
statemanifoldconsistoftwocloselyspacedlevelsof|0(cid:105)
searchershadtohaveasysteminwhichi)thevastmajority
and|1(cid:105)withanenergyseparationδE .Theexcitedmani-
of optical excitations recombine radiatively and ii) there g
foldconsistsoftwostates|3(cid:105)and|2(cid:105)withanenergysepara-
isaminimalamountofparasiticheatingduetounwanted
tionδE .Laserexcitationathν istunedtobeinresonance
impurities.Bothofthesecriticalengineeringissuesareig- u
withthe|1(cid:105)–|2(cid:105)transitionasshownbythesolidredarrow.
noredintheidealizedsituationdescribedbyEq.(1a),but
The double-line arrows depict the spontaneous emission
arekeytoexperimentalsuccess.
transitionsfromtheupperleveltothegroundstateswith
It is also important that spontaneously emitted pho-
arateofW ;thisrateisassumedtobethesameforall
tonsescapethecoolingmaterialwithoutbeingtrappedand rad
fourtransitions.Thenonradiativedecayrates(indicatedby
re-absorbed,whichwouldeffectivelyinhibitspontaneous
the dotted lines) are also assumed to be equal and given
emission[15,16].Thisisacriticalissueforhighindexsemi-
byW Thepopulationineachmanifoldreachesaquasi-
conductorswheretotalinternalreflectioncancausestrong nr.
thermalequilibriumviaanelectron-phononinteractionrate
radiationtrapping.Intheabsenceofradiationtrapping,the
givenbyw andw forlowerandupperstates,respectively.
fractionofatomsthatdecaytothegroundstatebythede- 1 2
Therateequationsgoverningthedensitypopulations
siredradiativeprocessisknownasthequantumefficiency,
N ,N ,N ,andN are:
η =W /(W +W )whereW andW areradia- 0 1 2 3
q rad rad nr rad nr
tiveandnonradiativedecayrates,respectively.Includinga
(cid:18) (cid:19)
dN g I R
fltuumoreesfficecniecneceysc(aEpQeEe)f:ficηieexntc=yηηeedWefirande/s(aηneWexrtaedrn+alWqunarn)-, dt1 =−σ12 N1− g21N2 hν + 2 (N2+N3)
whichassumesthefluorescenceisre-absorbedwithinthe (cid:18) (cid:19)
g
excitationvolume(seesectionIV).Thisdescribestheef- −w N − 1N e−δEg/kBT , (3a)
1 1 g 0
ficiency by which a photo-excited atom decays into an 0
escaped fluorescence photon in free space. In a similar dN (cid:18) g (cid:19) I
2 =σ N − 1N −RN
fashion,anabsorptionefficiencyηabs = αr/(αr+αb)is dt 12 1 g 2 hν 2
2
definedtoaccountforthefractionofpumplaserphotons
(cid:18) (cid:19)
that are engaged in cooling [6,17]. Here αr is the reso- +w N − g3N e−δEu/kBT , (3b)
nantabsorptioncoefficientandα istheunwantedparasitic 2 3 g 2
b 2
(background) absorption coefficient. As will be derived
insectionsIIandIV,thecombinationofalltheseeffects
re-definesthecoolingefficiencyas: |3>
(cid:3)E w
λ u 2
η =η η −1 (1b) |2>
c ext absλ
f
wheretheproductη η indicatestheefficiencyofcon-
ext abs
vertinganabsorbedlaserphotontoanescapedfluorescence
photon. Note that ηabs is frequency-dependent and falls h(cid:2) Wrad W
offrapidlybelowphotonenergyhν −k T wherek is nr
f B B
the Boltzmann constant and T is the lattice temperature.
At pump photon energies much more than k T below
B
hν ,η istoosmalltomakeη >0andlasercoolingis
f abs c |1>
unattainable.Theaboveanalysisdefinestheapproximate (cid:3)E w
conditionneededforlasercooling[6,17].: g 1
|0>
k T
η η >1− B (2)
ext abs hν Figure3 (onlinecolorat:www.lpr-journal.org) Thefour-level
f
energymodelforopticalrefrigerationconsistingoftwopairsof
Thisrelationquantifiestheneededefficiencies:coolinga closelyspacedlevels:|0(cid:105)and|1(cid:105)inthegroundstateand|2(cid:105)and
materialfromroomtemperaturewithanominalenergygap |3(cid:105)intheexcitedstatemanifolds.
www.lpr-journal.org ©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
70 M.Sheik-BahaeandR.I.Epstein:Lasercoolingofsolids
(cid:18) (cid:19)
dN g
3 =−RN −w N − 3N e−δEu/kBT (3c) meansthatifw <R,decayoftheexcitedstatecanoccur
dt 3 2 3 g 2 2
2 beforethermalizationwiththelattice,whichresultsinno
fluorescence upconversion and no cooling [18]. This ex-
N +N +N +N =N (3d)
0 1 2 3 t tremelimitofcoldelectronrecombinationisanissuefor
whereR = 2Wrad +2Wnr isthetotalupperstatedecay semiconductorsatverylowtemperatureswheretheelec-
rate, σ12 is the absorption cross section associated with tronsinteractwiththelatticeprimarilybyrelativelyslow
|1(cid:105)–|2(cid:105)transition,I istheincidentlaserirradianceandthe acousticphonon[15].
g termsrepresentdegeneracyfactorsforeachlevel.The DividingtheEq.(5)bythetotalabsorbedpowerden-
i
weightingfactorintheelectron-phononinteractionterms sityP = (α+α )I givesthecoolingefficiencyη =
abs b c
(w1 andw2)maintainstheBoltzmanndistributionamong −Pnet/Pabs:
eachmanifoldatquasiequilibrium.Thenetpowerdensity hν
η =η η f −1, (8)
depositedinthesystemisthedifferencebetweenabsorbed c q abs hν
andout-radiatedcontributions:
whichissimilartoEq.(1.b)notincludingtheluminescence
(cid:18) (cid:19)
g N trapping.Themostusefulfeatureofthe4-levelmodelisits
P =σ N 1− 1 2 I
net 12 1 g N descriptionofthetemperature-dependenceofthecoolingin
2 1
aphysicallytransparentmanner.Asthetemperatureislow-
−Wrad[N2(E21+E20)+N3(E31+E30)] ered,red-shiftingofmeanfluorescencewavelengthcom-
binedwiththereductionoftheresonantabsorptionreduces
+α I, (4)
b
thecoolingefficiency.AttemperatureT =T thecooling
m
wherethefirsttermisthelaserexcitation(|1(cid:105)-|2(cid:105)transition) stops(i.e.ηc(Tm)=0).Thisminimumachievabletemper-
andsecondtermincludesthespontaneousemissionterms ature(Tm)canbeloweredbyreducingthebackgroundab-
fromlevels|2(cid:105)and|3(cid:105)withtheirrespectivephotonenergies. sorption(higherpurity),increasingthequantumefficiency,
Wehavealsoincludedatermthatrepresentsparasiticab- andenhancingtheresonantabsorption(e.g.choosingama-
sorptionofthepumplaserwithanabsorptioncoefficientof terialwithanarrowgroundstatemanifold).Theeffectof
α .Itisstraightforwardtoevaluatethesteady-statesolution fluorescencetrappinganditsconsequentre-absorptionby
b
totheaboverateequationsbysettingthetimederivatives bothresonantandparasiticprocesseswillfurtherdiminish
tozero.Toemphasizecertainfeatures,weignoresaturation thequantumefficiency.Wewilldiscussthisindetailwhen
andassumeunitydegeneracyforalllevels.Thenetpower weanalyzeoflasercoolinginsemiconductorswheretotal
densityisthenobtainedas: internalreflectionleadstosubstantialtrapping.
(cid:18) (cid:19)
hν
P =αI 1−η f +α I, (5)
net q hν b 3. Coolingrare-earth-dopedsolids.
whereηq = (1+Wnr/Wrad)−1isthe(internal)quantum Theadvantagesofrare-earth(RE)dopedsolidsforlaser
efficiencyandhνf denotesthemeanfluorescenceenergy coolinghadbeenforeseenfordecades.Kastler(1950[11]
ofthefour-levelsystemgivenby: andYatsiv(1961[13]suggestedthesematerialscouldbe
used for optical cooling. The key optical transitions in
δE δE
hν =hν+ g + u (6) RE-doped ions involve 4f electrons that are shielded by
f 2 1+(1+R/w2)eδEu/kBT the filled 5s and 6s outer-shells, which limit interactions
withthesurroundinglattice.Non-radiativedecaysdueto
Thegroundstateresonantabsorptionαisgivenby:
multi-phononemissionarethussuppressed.Hostswithlow
(cid:16) (cid:17)−1 phononenergy(e.g.,fluoridecrystalsandglasses)further
α=σ12Nt 1+eδEg/kBT (7) diminishnon-radiativedecayandhenceboostquantumeffi-
ciency.In1968,KushidaandGeusic[12]attemptedtocool
Despite its simplicity, the four level model reveals es- a Nd3+:YAG crystal with 1064nm laser radiation. They
sential features of solid-state optical refrigeration: First, reported a reduction of heating, but no cooling; it is un-
Eq.(7)exhibitsdiminishingpumpabsorptionduetother- clearwhethertheyobservedanyanti-Stokescoolingeffects.
maldepletionofthetopgroundstateatlowtemperatures, Lasercoolingofasolidwasfirstexperimentallydemon-
k T < δE . This implies that the width of the ground- stratedin1995withtheytterbium-dopedfluorozirconate
B g
state manifold (δE ) must be narrow to achieve cooling glassZBLANP:Yb3+[14].Laser-inducedcoolinghassince
g
atlowtemperatureswithreasonableefficiency.Thisissue beenobservedinarangeofglassesandcrystalsdopedwith
willberevisitedwhendiscussingsemiconductorsinsec- Yb3+(ZBLANP[19–22],ZBLAN[23,24],CNBZn[9,25]
tionIV.Second,Eq.(6)showsthatthemeanfluorescence BIG[25,26],KGd(WO ) [9],KY(WO ) [9],YAG[27],
4 2 4 2
photon energy is red shifted at low temperatures, which Y SiO [27], KPb Cl [25,28], BaY F [29–31], and
2 5 2 5 2 8
furtherlowersthecoolingefficiency.Thisshiftwouldbe YLF[32,33]).
enhanced if the electron-phonon interaction rate (w ) is Fig.4 shows the cooling and heating of a sample of
2
smallerthantheupperstaterecombinationrate(R).This Yb3+dopedZBLANPforarangeofpumpwavelengths[5].
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.lpr-journal.org
Laser&Photon.Rev.3,No.1–2(2009) 71
tumefficiency[36,37].Thisisalsothecasewithcooling
ofTm3+[34],
The initial proof-of-principle experiments in
ZBLANP:Yb3+ achieved cooling by an amount 0.3K
below ambient temperature [14]. The LANL group has
sincecooledZBLANP:Yb3+to208Kstartingfromroom
temperature [22] as shown in Fig.5. Although progress
is being made, optical refrigerators need to be more ef-
ficient and operate at lower temperatures, below about
170K,tobecompetitivewithothersolid-statecoolerssuch
as thermoelectric (Peltier) devices. Several studies have
shownthatytterbium-orthulium-dopedsolidsshouldbe
capableofprovidingefficientcoolingattemperatureswell
below100K[4,27,38].
Figure4 (onlinecolorat:www.lpr-journal.org) Thetempera-
turechange(normalizedtoincidentpower)inytterbium-doped
ZBLANP glass as a function of pump wavelength. When the
pump wavelength is considerably longer that the mean wave-
lengthofthefluorescenceλ (verticaldashedline),theescaping
F
lightcarriesmoreenergythantheabsorbedlaserlightandthe
glasscools.Heatingatwavelengthsgreaterthanλ isduetoim-
F
perfectquantumefficiencyofthefluorescenceandnon-resonant
lightabsorption[5].
Forwavelengthsshorterthanthemeanfluorescencewave-
lengthλ (verticaldashedline)thesampleheatsbecause
F
of the Stokes shift as well as by non-radiative processes.
Atlongerwavelengths,anti-Stokescoolingdominatesand
coolingaslargeas25Kperwattofabsorbedlaserpoweris
measured.Atstilllongerwavelengths,absorptionbyimpu-
ritiesorimperfectionsdominates,andthesampleheats.
In2000,lasercoolinginTm3+ dopedZBLANPwas
reportedatλ∼1.9µm[34].Thesignificanceofthisresult
wastwo-fold:First,itverifiedthescalinglawofEq.(1.a,b)
bydemonstratingnearlyafactoroftwoenhancementinthe
coolingefficiencycomparedtoYb-dopedsystems.,Theen-
hancementscalesastheratioofthecorrespondingcooling
transitionwavelengths.Second,itwasthefirstdemonstra-
tionoflasercoolinginthepresenceofexcitedstateabsorp-
tion. A record cooling power of ∼73mW was obtained
inthismaterialbyemployingamultipassgeometry[35].
Morerecently,coolingofEr3+dopedglass(CNBZn)and
crystal (KPb Cl ) at λ ∼ 0.870µm were reported by a
2 5
Spanishgroup[36].Itisinterestingtonotethatthecooling
Figure5 (onlinecolorat:www.lpr-journal.org) Panel(a)shows
transitionusedintheseexperimentsisbetweentheground recordcoolingto208KwithZBLANP:Yb3+.Thetemperatures
stateandthefourthexcitedstate(4I9/2)ofEr3+,notthe aremeasuredwiththermocouplesonthesampleandchamber;the
firstexcitedstateasillustratedinFig.1.High-energytran- internaltemperatureoftheglassisinferred[22].Panel(b)com-
sitionshavelowercoolingefficiency(Eq.1)butpotentially paresthecoolingefficienciesofavailablethermoelectriccoolers
higherquantumefficiencyduetotheirlownonradiativede- (TECs)withZBLANP:Yb3+-basedopticalrefrigerators.Devices
cayratestothegroundstate.Thepresenceofhigherexcited based on materials with low parasitic heating will outperform
states in Er3+ may prove advantageous since the energy TECsbelow200.Coolersmadefromcurrentmaterialsareless
upconversion transitions (i.e. at the cooling wavelengths efficientthanTECsatalltemperatures[39].Fig.5(a)hasbeen
ofthemaintransition)areendothermicwithahighquan- reproducedfrom[22]
www.lpr-journal.org ©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
72 M.Sheik-BahaeandR.I.Epstein:Lasercoolingofsolids
10
m]
p Cr3+
n [p 1 Ti3+
o
ati OH
r
nt V3+
e
c Ni2+
n 0.1
o Co2+
C
d Fe2+
ol Figure 6 (online color at: www.lpr-journal.org)
sh Calculatedimpuritythresholdconcentrations.Ifthe
re 0.01 impuritylevelsofanionisabovethelevelshown
h
T Cu2+ here,thecoolingefficiencyoftheZBLAN:1%Yb3+
%
willbelessthan90%ofitsidealvalueandrapidly
0
9 convertedintoheat.SeethedetailedstudybyHehlen
0.001 etal.[39].
50 100 150 200 250 300
Temperature [K]
Thereareseveralfactorsthatlimitthecoolingofrare- quencies;thiseffectisillustratedinthefour-levelsystem
earth-dopedsolidsinavailablematerials.Themostsignifi- discussedabove.Theneteffectisthatatlowtemperatures
cantfactoristhechoiceoflasercoolingmedium.Theideal thenumeratorofEq.(2)becomessmallandcoolingeffi-
coolingefficiency(Eq.1)showsthatthereisanadvantage ciencygoestozero;seeEq.(1b).Thewidthoftheground
ofpumpingwithlowerenergyphotons.Thisincreasedeffi- statemanifoldistypicallytheresultofcrystalfieldsplitting
ciencywaspartofthemotivationforinvestigatingthulium- anddependsonboththedopantionandthehostmaterial.
dopedcoolingmaterials,sincetheirground-andexcited Bychoosingionsandahostthatgivenarrowground-state
state manifolds are separated by about 0.6eV compared manifolds,thematerialcancooltolowertemperaturesbe-
to1.2eVinytterbium-dopedsolids.Thereareobstacles, forethelow-frequencytransparencyconditionsetsin.
however,ingoingtolongerwavelengths.Firstisthemore Forthematerialsystemsstudiedsofar,coolingisnot
limitedchoicesofpumplaserssincetherearefeweravail- limited by the reasons outlined above. It is most likely
ablenear0.6eVthannear1.2eV.Whilenotafundamental hindered by parasitic heating in the bulk of the cooling
consideration,itneedstobekeptinmindfornear-termcom- material or on its surface. As one can see in Fig.5b, the
mercialization.Asecondandmoregeneralreasoninvolves coolingefficienciesofcurrentlyavailableZBLANP:Yb3+
the ratio of radiative to non-radiative relaxation decays. are far below that for an ideal material with no parasitic
The rate of non-radiative, heat-producing, multi-phonon heating.Oneimportantsourceofheatinginthismaterial
decaydecreasesexponentiallywiththeseparationbetween isquenchingofexcitedytterbiumionsbyimpuritiessuch
the ground- and first excited-state manifolds; this is the asironandcopper.Theradiativedecaytimeofanexcited
well-knowenergy-gaplaw.Inpracticalterms,thismeans Yb3+ ion is about 1ms. During this time, the excitation
that because of the relatively large energy of the excited migratesthroughtheglassbytransferringenergytoneigh-
level in ytterbium-doped materials, non-radiative decays boringions.Iftheexcitationencountersanimpurityatom,
donotsignificantlydecreasethequantumefficiency.For theenergycanbetransferredtothisatomandrapidlycon-
purethulium-dopedmaterial,non-radiativedecaycanover- verted into heat. A detailed study by Hehlen et al. [39]
whelmanti-Stokescooling,dependingonthepropertiesof foundthattheidealcoolingefficiencycanbeapproached
thehostmaterial.Formaterialswithlowmaximumphonon whenconcentrationofimpuritiessuchasCu2+ islessthan
energies, such as ZBLANP and other fluoride hosts, the 0.01ppmandthatforFe2+isbelow0.1ppm;seeFig.6.
non-radiative decays are relatively slow. Many thulium-
Anadditionalsourceofparasiticheatingisabsorption
dopedoxidecrystalsandglasseshaverapidnonradiative
inthemirrorsthattrapthepumpradiationinthecooling
decayratesthatpreventlasercooling.
element.IntheLANLexperiments,thecoolingglasshasa
Anotherconsiderationinthechoiceofcoolingmedium pairofhigh-reflectivitymirrorsdepositedontwosurfaces,
is the width of the ground state manifold. According to asdepictedinFig.2.Pumplightisreflectedmultipletimes
Boltzmannstatistics,lowerenergylevelsinthemanifold byeachmirror,sothatthatevenrelativelylowabsorptionof
aremorepopulatedthanhigherones.Asthetemperature 0.0001persurfaceproducessignificantheating.Depositing
fallsandk Tbecomessmallcomparedtotheenergywidth higherqualitydielectricmirrormayobviatethisproblem.
B
oftheground-statemanifold,theupperlevelsbecomede- An alternative approach is to avoid dielectric mirrors all
populatedleadingtoincreasedtransparencyatlowerfre- togetherandexploitthetotal-internalrefectioninsidethe
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.lpr-journal.org
Laser&Photon.Rev.3,No.1–2(2009) 73
a b
Figure7 (onlinecolorat:www.lpr-
journal.org) (a) Cooling cycle in
GaAs
T=300 K laserrefrigerationofasemiconduc-
torinwhichabsorptionoflaserpho-
tons with energy hν creates a cold
distributionofelectron-holecarriers
(onlyelectrondistributionisshown
h(cid:2) h(cid:2)f forclarity).Thecarriersthenheatup
by absorbing phonons followed by
anup-convertedluminescenceathν .
F
(b)Typicalanti-Stokesluminescence
E
observedinGaAs/GaInPdoublehet-
k erostructure[6].
coolingmediumforcirculatingthepumpbeam[40].An- Nosuchlimitationexistsinpure(undoped)semiconductors
othermethodofenhancingpumpabsorptionisusingreso- –temperaturesaslowas10Kmaybeachievable[47].
nantcavityeffects.Bothintra-laser-cavity[24]andexternal Semiconductorsshouldachievehighercoolingpower
resonant-cavity[41]geometrieshavebeendemonstrated. densitycomparedtoRE-materials.Themaximumcooling
Thelatterapproachhasbeencapableofachievingpump power density (rate of heat removal) is ≈ N ×k T/τ ,
B r
absorption exceeding90% [41].Most recently, usingac- whereN isthephoto-excitedelectron(-hole)densityand
tive stabilization, this method was employed to achieve τ istheradiativerecombinationtime.Insemiconductors
r
∆T ≈ 70K in a Yb:YLF crystal [33]. This is a highly the optimal density N is limited due to many-body pro-
promisingresultconsideringthatitwasobtainedwithfull cessesanddoesnotexceedthatofmoderatelydopedRE
black-bodythermalloadwhichisnearly5timeshigherthan systems.Wecangain5–6ordersofmagnitudeincooling
thatreportedin[22].Ithasalsobeenproposedthatphoton powerdensitybecausetheradiativerecombinationratesin
localization in nanocrystalline powders can be exploited semiconductorsaremuchfasterthaninREions.
toenhancelaserpumpabsorptionincoolingofrare-earth Laser cooling of semiconductors has been examined
dopedsystems[42]. theoretically[15,44,45,47–52]aswellasinexperimental
studies[46,53–56].Afeasibilitystudybytheauthorsout-
linedtheconditionsfornetcoolingbasedonfundamental
4. Prospectsforlasercooling materialpropertiesandlightmanagement[15].Researchers
insemiconductors attheUniversityofArizona[47,50]studiedluminescence
upconversioninthepresenceofpartiallyionizedexcitons,
Researchers have examined other condensed matter sys- whichmustbeunderstoodtoattaintemperaturesapproach-
tems beyond RE-doped materials, with an emphasis on ing10K.Theroleofbandtailstates[52],thepossibleen-
semiconductors [17,43–46]. Semiconductor coolers pro- hancementoflasercoolingbyincludingtheeffectsofpho-
vide more efficient pump light absorption, the potential tondensityofstatesaswellasnovelluminescencecoupling
of much lower temperatures, and the opportunity for di- schemesbasedonsurfaceplasmonpolaritons[57,58]were
rectintegrationintoelectronicandphotonicdevices.These recentlyintroducedbyKhurginatJohnsHopkinsUniver-
materialsprovidetheirownsetofengineeringchallenges, sity.Here,weexpandonthebasicmodelof[15]andpresent
however, and no net cooling has been observed yet. The thetheoreticalfoundationoflasercoolinginsemiconduc-
essentialdifferencebetweensemiconductorsandRE-doped tor structures with an arbitrary external efficiency. This
materialsisintheircoolingcycles.Inthelatter,thecooling treatmentaccountsfortheluminescencered-shiftdueto
transition occurs in localized donor ions within the host re-absorption,theeffectparasiticabsorptionofthepump,
materialwhiletheformerinvolvestransitionbetweenex- luminescencepower,andband-blockingeffects.Wethen
tendedvalenceandconductionbandsofadirectgapsemi- discussthelatestexperimentalresultsattemptingtomake
conductor(seeFig.7a).Indistinguishablechargecarriersin thefirstobservationoflasercoolinginasemiconductorma-
Fermi-Diracdistributionsmayallowsemiconductorstoget terial.
muchcolderthanREmaterials.Thehighestenergylevels Weconsideranintrinsic(undoped)semiconductorsys-
ofthegroundstatemanifoldintheRE-dopedsystemsbe- temuniformlyirradiatedwithalaserlightatphotonenergy
comelesspopulatedasthetemperatureislowered,dueto hν. Furthermore, we assume that only a fraction η of
e
Boltzmannstatistics.Thecoolingcyclebecomesineffective thetotalluminescencecanescapethematerialwhilethe
whentheBoltzmannconstanttimesthelatticetemperature remainingfraction(1-η )istrappedandre-cycled,thuscon-
e
becomescomparabletothewidthofthegroundstate(see tributingtocarriergeneration.Fornow,wewillignorethe
previoussectiondescribingthe4-levelmodel).Thissetsa parasiticabsorptionofluminescencebutwilllaterconsider
limitofT ∼ 100KformostexistingRE-dopedsystems. itsimplications.Foragiventemperature,therateequations
www.lpr-journal.org ©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
74 M.Sheik-BahaeandR.I.Epstein:Lasercoolingofsolids
fortheelectron-holepairdensity(N)isgivenby[15]: parasiticabsorptiveprocesses.Thesecondtermisthees-
capedluminescencepowerdensityatameanluminescence
dN αI
dt = hν −AN −BN2−CN3+(1−ηe)BN2 (9) energyhν˜f definedas
(cid:82)
S(ν)R(ν)hνdν
Hereα(ν,N)istheinterbandabsorptioncoefficientthatin- hν˜f = (cid:82) . (15)
S(ν)R(ν)dν
cludesmany-bodyandblockingfactors.Therecombination
processconsistsofnonradiative(AN),radiative(BN2),and
Notethattheescapedmeanluminescenceenergycandevi-
Auger(CN3)rates.Alltheabovecoefficientsaretempera-
ate(i.e.redshift)fromitsinternalvalue(S=1)depending
turedependent.ThelasttermrepresentstheincreaseinN
onthethicknessorphotonrecyclingconditions.Withthe
fromthere-absorptionoftheluminescencethatdoesnot
aidofEq.(9),werewriteEq.(14)as:
escape,assumingthere-absorptionoccurswithinthelaser
excitation volume. The density-dependence of α results P =η BN2(hν−hν˜ )+ANhν
net e f
frombothCoulombscreeningandband-blocking(satura-
+CN3hν+∆P . (16)
tion)effects.Thelattercanbeapproximatedbyablocking
factorsuchthat[59,60]:
Eq.(16)rigorouslydescribeslasercoolingofasemiconduc-
torinacompactandsimpleform.Itaccountsforthepracti-
α N,hν)=α (N,hν){f −f }, (10)
( 0 v c calconsiderationsofluminescencetrappingbyintroducing
where α0 denotes the unsaturated absorption coefficient. aninhibitedradiativerecombination(ηeB)andashifted
The strongly density-dependent blocking factor in the meanphotonenergyhν˜f fortheescapedluminescence.For
brackets[61]containsFermi-Diracdistributionfunctions highexternalefficiencysystemswhereS(ν)=1,Eq.(16)
forthevalence(fv)andconduction(fc)bands. approachesthatdescribedintheliteraturewithηe =1and
Under steady-state conditions, Eq.(9) can be re- ν˜f = νf with νf denoting the mean fluorescence energy
writtenas producedinternallyinthesemiconductor[44–46].Eq.(16)
indicatesthatlasercoolingoccurswhenP <0,requir-
net
α(ν,N)
0= I−AN −η BN2−CN3. (11) ingadominantcontributionfromtheradiativerecombina-
hν e tionwithhν < hν˜ .Thecoolingefficiencyη isdefined
f c
astheratioofcoolingpowerdensityP (=−P )tothe
This indicates that the fluorescence trapping effectively c net
absorbedlaserpowerdensity(P =αI+∆P).Withthe
inhibits the spontaneous emission as it appears through abs
aidofEq.(11),thisefficiencycanbeexpressedas
η Bonly.Thisresulthasalsobeenshownpreviouslyby
e
Asbeck [16]. It is important to note that ηe is itself an η BN2(hν−hν˜ )+ANhν+CN3hν+∆P
averagedquantityovertheentireluminescencespectrum. η =− e f .
c η BN2hν+ANhν+CN3hν+∆P
e
(cid:82) (17)
S(ν)R(ν)dν
ηe = (cid:82) R(ν)dν . (12) Ignoringthe∆Pcontributionsforthemoment,ηc canbe
writtenmoresimplyas:
Here S(ν) is the geometry-dependent escape probabil- ν˜
ity of photons with energy hν and R(ν) is the lumines- ηc =ηext νf −1, (18)
cence spectral density that is related to the absorption
coefficientthroughreciprocityusinga“non-equilibrium” where ηext describes the external quantum efficiency
vanRoosbroeck-Shockleyrelation(alsoknownasKubo- (orEQE):
Martin-Schwinger(KMS)relation[59,62]:
η BN2
η = e ≈(η )1/ηe, (19)
8πn2ν2 (cid:26)f (1−f )(cid:27) ext AN +η BN2+CN3 q
R(ν,N)= α ν,N) c v , (13) e
c2 ( f −f
v c withη = BN2/(AN +BN2 +CN3)denotingthein-
q
wherecisthespeedoflightandnistheindexofrefraction. ternal quantum efficiency [46,63] as also defined more
NotethattheradiativerecombinationcoefficientBisob- generallyfollowingEq.(5).Theapproximateequalityin
tainedbyBN2 =(cid:82) R(ν)dν whichresultsinanegligible Eq.(19)isvalidonlyforηext nearunity(>0.9).Onesim-
dependenceofBonNatthecarrierdensitiesofinterest. ple consequence of Eq.(19) is that there is an optimum
Thenetpowerdensitythatisdepositedinthesemiconduc- carrier density Nop = (A/C)1/2 at which ηext reaches
toristhedifferencebetweenthepowerabsorbedfromthe amaximum: √
2 AC
laser(Pabs)andthatoftheluminescencethatescapes(Ple): ηmax =1− (20)
ext η B
e
P =P −P =[αI+∆P]−[η BN2hν˜ ], (14)
net abs le e f Includingbackgroundparasiticabsorption(∆P=α I),re-
b
sultsinmoregeneralformofcoolingefficiency:
where the absorbed power density includes the resonant
absorption(αI)andaterm∆P thataccountsfortheun- ν˜
desirableeffectssuchasfree-carrierabsorptionandother ηc =ηabsηext νf −1, (21)
©2009byWILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.lpr-journal.org