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Design of tunneling injection quantum dot lasers

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Design of tunneling injection quantum dot lasers

    Design of tunneling injection quantum dot

    lasers

    0mELECTR0NI(:SLETERSVo1.3No.1.15Jan.2007

    '一一????一..一?.Designoftunne?n!=lInIectionquantumdotlasers

    JIAGuo-zhi'.YAOJiang-hong.SHUYong-chun'.andWANGZhan-guo'-

    J.KeyLab.forWeak

    LightNonlinearPhotonicsMaterialsofEducationMinistryofChinaandKeyLab.of PhotonicsMaterialsandTechnologyforInformationScOnce,ofTianjinCity,TEDAAppliedPhysicsSchool

    NankaiUniversity,Tianjin300475,China

    2.KeyLaboratoryofSemiconductorMaterialsScience,InstituteoJ'Semiconductors,ChineseAcademyofSciences,

    Beijing100083,China

    (Received4September2006)

    Toimplementhighquafitytunnefinginjectionquantumdotlasers,effectsofprimaryfactorsonperformanceofthe

    tunnelinginjectionquantumdotlaserswereinvestigated.Theconsideredfactorsweretunnelingprobability,tun

    nelingtimeandcarriersthermalescapetimefromthequantumwel1.Thecalculationresultsshowthatwithincreas

    ingoftheground

    stateenergylevelinquantumwell,thetunnelingprobabilityincreasesandthetunnelingtime decreases,whilethethermalescapetimedecreasesbecausetheground

    stateenergylevelisshallower.Longitudinal

    opticalphonon

    assmtedtunnelingcanbeaneffectivemethodtosolvetheproblemthatboththetunnelingtimeand

thethermalescapetimedecreasesimultaneouslywiththeground

    stateenergylevelincreasinginquantumwell

    CLCnumber:TN365Documentcode:AArticlelDl1673.1905(2007)01-000403

    DOl10.1007/s1180100761O81

    Inrecentyears,semiconductorquantumdot(QD)lasers haveattractedconsiderableattentionduetotheirpotential applications".AlthoughQDlaserhasbeenpredictedcan havemoreexcellentperformancethanconventionalquan

    tumwell1aser.sofartemperatureinsensitiveQDlaserstill hasnotbeenreportedduetohotcarriereffectstandcarrier

    thermalescape[31.Inaddition,thecarrierrelaxationtimefrom thehighenergystatetogroundstatealsoplaysanimportant roleinobtaininghighperformanceQDlasers.Theoretically, ifelectronsareintroduceddirectlyintothelasingstatesby tunnelingandthetunnelingrateiscomparabletothestimu

    1atedemissionrate.thecarrierdistributionintheactiveregion willremain''cold"andhotcarriereffectsareminimizedt4]. ThegroundstateenergylevelofQDs.heightandwidth oftunnelingbarrierdirectlyaffectthecarriertunnelingand thermalescapeprobability.Thus.sufficientlytakingintoac

    counttheabovefactorswouldbeakeytoachievehighper

    formanceQD1asers.InthisPaper,wehavefocusedourre

    searchworkonthestudyofthetunnelingprobability,tun

    neffngtimeandthermalescapetimefortheelectronstunnd

    ingacrossathinpotentialbarrier.

    TheenergybanddiagramofatunnelinginjectionQD laserisillustratedinFig.1.Theinjectedcarriersarefirst ThisprojectissupportedbytheNationalNaturalScienceFoundation ofChina(GrantNo.60476042)andTianjinCityResearchFounda

    tionforKeyBasicResearch,China(GrantNo.06YFJZJC01100).

Email:yaojh@nankai.edu.cn

    collectedbythequantumwellA,followedbytunneling throughthethinbarrierlayerintotheQD.Here,wehaveas

    sumedarectangularpotentialbarrierofwidthl,heightB andthegroundstateenergylevelofquantumwellE.

    'I,'.

    Fig.1Energybanddiagramoftunnelinginjection quantumdotlaser.

    Thetunnelingprobabilitywasderivedbysolvingthetimein

    dependentSchr~klingerequationandgivenas: ~p

    {}

    whereqistheelectroncharge,mistheelectroneffective mass.andisPlanck'sconstant.Fig.2showsthetunneling probabifityoftheelectronsasafunctionofthepotentialbar

JIAPff

    rierwidthZ.Thegraphclearlyshowsthatthetunnelingprob- aNlityvariesrapidlyfordifferentpotentialbarrierwidthand canattainthevalueof0.8.Thetunnelingprobabilitycall keepsomeconstantattheextremelylargerangeofcarrier energy.believethatthetunnelingprobabilitycanbevar

    iedbytuningtheenergyofthegroundstateincollectedquan

    rumwell,becausethepotentialbarrierwidthneedstokeepa necessaryvalueduetotheexistingofwettinglayer. Energy(eV)

    Fig.2Tunnelingprobabilityvs.incidentenergywith differentpotentialbarrierwidth.

    ,-,

    ?

    o

    Fig.3Therelationshipbetweentunnelingtimeand incidentenergyinquantumwel1.

    Thetunnelingtimeisanimportantparametertoobtaina highperformancetunnelinginjectionquantumdotlaser.If thetunnelingtimeistoolong,anumberofcarrierscanbe consumedinthepotentialbarrierlayerandproducesmany negativeeffects.Thetunnelingtimemustbesufficiently shorterthanthecarrierrecombinationtimeinquantumdots, whichisanessentialconditiontomaintaintI1etunnelingin. jectionquantumdotlaseraction.Basedontheconceptof theprobabilityandmadeuseofthefirstorderwavefunction andcontinuityofdifferentialcoefficient,thetunnelingtime canbeexpressedas:

    ml[

    Optoelectron.Lett.Vo1.3No.1?0005?

    sin(2Kl1/2KlCOS2

    lCOS26

    (2)

    where,k=?2E,K:42m(~bBE)/,andtan=K/k

    Fig.3showstherelationshipbetweentunnelingtimeandthe incidentenergyinquantumwel1.Wecanseefromthegraph thatthetunnelingtimequicklydecreasesasthecarrieren- ergyincreases.

    Whenthecarriersaregeneratedinthecollectedquantum welltheycaneithertunnelorthermallyescapeoverthe barriers.Theprocessofcarrierescapingfromthequantum wel1dependsontheconfinedcarrier'senergydistribution.It

    isessentialtodesignanefficientconfinementofcarriersin thecollectedquantumwellinordertosuppressthethermally escapingofthecarriers.Weassumethattheescapetimeis dominatedbythermalemissionanddependsontemperature andthecarrierenergy:

    pf_.(3)

    where"isthecarrierradiativerecombination1ifetimeand R

    isBoltzmann'sconstant.Thecalculationresultsoftheelec- tronescapetimeasafunctionofelectronenergyisshownin Fig.4.entheCarTierthermalescapetimeisclosetothecar- riertunnelingtime,theperformanceoftheQDlasercan sharplydeclineduetothattheradiativerecombinationin QDsisnotenough.Itisshownthatthecarriertherma1es. capetimequicklydecreaseswithcarrierenergyincreasing. Energy(eV)

    Fig.4Therelationshipbetweencarriersescapetime andenergyinquantumwel1.

    Inviewoftheabove,thereisacontradictionbetween carriertunnelingandescape.Asthecarrierenergyislow,the tunnelingparticlesexperiencearectangularbarrierwitha smalltunnelingprobabilityandalongtunnelingtime,though afewcarriersescapefromthecollectedquantumwelldueto alargeenergydifference(B-betweenthegroundstateof thecollectedquantumwellandthepotentialbarrier.whiCh HIo00盆一一0?州

    一?II一—II;0?0?

    resultsinalowefficiencyforlaseraction.However,asthe carrierenergyincreases,thetunnelingprobabilityincreases

aswellasthetunnelingtimereduces,whileanumberofcar

    tierscanescapefromthecollectedquantumwellduetoen- ergydifference(E)decreases.WeCankeepalargeen-

    ergydifference(8-ingraph1andincreasethecarriers energybylongitudinalopticalphonon-assisted,whichisan effectivemethodtosolvetheproblem}5J,becausealargeell

    ergydifferencebetweenthequantumwellandthepotential barriercanreducethecarrierthermalescape,andthephonon- assistedtunnelingincreasesthecarriertunnelingprobability. Here,althoughwedon'tIreatofapracticalmaterial,thequaff- tativeanalysishasveryimportantmeaningtodesignahigh performancetunnelinginjectionQDlaser.

    Insummary,effectsofprimaryfactorsonperformance ofthetunnelinginjectionquantumdotlaserwereinvestigated. Thecalculationandanalysisresultsshowthatwiththein

    Optoelectron.Lett.Vo1.3No.1

    creasingofthegroundstateenergylevelinquantumwell,

    thetunnelingprobabilityincreasesandthetunnelingtime decreases,whilethethermalescapetimedecreases.In addition,theresultsalSOindicatethataphonon.assistedtun. nelingcanbeaneffectivemethodtosolvetheproblemthat boththetunnelingtimeandthethermalescapetimedecrease simultaneously.

    References

    1YArakawaandH.Sakaki,App1.Phys.Lett,40(1982),939. 2M.Wi1atzen,Takahashi,andY.Arakawa,IEEE

    PhotonicsTechno1.Lett.,4(1992),682.

    3NagarajanR.,IshikawaM.,andFukushimaIEEEJ.Quan- rumElectron,28(1992).1990.

    4M.Kucharczyk,M.S.Wartak,andP.Weetman,J.App1.Phys., 86(1999),3218.

    5S.Ghosh,S.Pradhan,andP.Bhattacharya,App1.Phys.Lett, 81(2005),3055.

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