Optical properties of \textit{n}- and \textit{p}-type ZnO thin films -- two different approaches to the impurity distribution inhomogeneity

0.18 MB·English

by  Takayuki Makino

Opticalproperties ofn-and p-typeZnO thin films —two different approaches to the impurity
distribution inhomogeneity
7
0
0 Takayuki Makino
2 Department of Material Science,
University of Hyogo, Ako-gun, Hyogo, Japan;
n ∗
a
J
We investigated the optical properties of epitaxial n- and p-type ZnO films grown on lattice-matched
1 ScAlMgO4substrates.Chemicaldopingyieldedasevereinhomogeneityinastatisticaldistributionofinvolved
3
charged impurities. Two approaches areadopted to treatthe inhomogeneity effects; Monte Carlosimulation

techniqueforthen-dopedfilms,andthefluctuationtheoryforthep-ZnO.ThebroadeningofPLbandofn-ZnO
]
i wassignificantlylargerthanpredictedbytheoretical resultsinwhichthelinewidthsofeachindividual emis-
c sionshavebeendeterminedmainlyfromtheconcentrationfluctuationofdonor-typedopantsbythesimulation.
s
Moreover, theratherasymmetricallineshapewasobserved. Toexplainthesefeatures, avibronicmodelwas
-
l developed accounting for contributions from a series of phonon replicas. In case of p-type ZnO:N, analysis
r
t ofexcitation-intensitydependence ofthepeakshiftofdonor-acceptor luminescencewithafluctuationmodel
m
hasalsoproventheimportanceoftheinhomogeneityeffectofchargedimpuritydistribution,asinthecaseof
. ZnO:Ga.Weextractedtheinhomogeneityinthesampleandacceptoractivationenergypreparedunderthevar-
t
a iousgrowthconditions.Itisshownthatthetheoreticalresultsareingoodagreementwiththeexperimental5-K
m time-resolvedluminescenceforthesystemsinafluctuationfield.Finally,localized-statedistributionshavebeen
studiedinN-dopedZnOthinfilmsbymeansoftransientphotocurrentmeasurement.
-
d
n
o
c
[ I. INTRODUCTION

1
v AmongwidegapII-VIsemiconductors,ZnOseemstobeoneofthemostpromisingmaterialsforoptoelectronicapplications.
7 Thisisduetoitsstableexcitons,havingalargebindingenergyof59meV[1,2]. Itisalsodesiredtomoredeeplyunderstand
6
theunderlyingdopingphysics[3,4]fortheachievementofacompound-semiconductor-qualityp-njunction[5]. Inourprevious
7
work,wereportedtheobservationofintensenear-band-edgephotoluminescence(PL)forZnO:Gaatroomtemperature(RT)[6].
1
Itcanbeeasilyimaginedthatahighdopingleveltendstoyieldasevereinhomogeneityinastatisticaldistributionofinvolved
0
7 chargedimpurities. In this work, such an effectis characterizedwith the Monte Carlo simulation technique[7]. The phonon
0 interactionsarealsodiscussedwitha‘vibronic’model[8].
/ Donor-acceptorpair(DAP)photoluminescence(PL)bandshavebeenwidelyusedtocharacterizeacceptor-dopedsemiconduc-
t
a tors. Especially,inwide-gapsemiconductors,ithasbeendifficulttoobtainp-typedopedmaterials. However,thetime-resolved
m PLhasnothardlybeenstudied[9,10]forZnO:N.ForthecaseofZnO,alargeamountofnitrogenwellinexcessof1019cm−3
- hastobedopedtoachievep-typeconductivityevenusingoneofthebestgrowthtechniquesthathaveeverreported[arepeated-
d
temperature modulation (RTM) technique] [5]. It has become apparent that the “standard” theory formulated by Thomas,
n
Hopfield,andAugustyniak[11](hereafter,itiscalleda“standard”THAmodel)istotallyincapableofexplainingresultsofthe
o
DAPPLforheavilydopedmaterialsprobablybecausethisdoesnottaketheeffectsofinhomogeneityintoaccount.Inthiswork,
c
: toimplementtheeffectofthefluctuationfieldinherenttothedopedsamples,wesuccessfullygrewp-type-dopants-incorporated
v
films,whicharesuitablefortheexperimentalverificationoftherelevant“fluctuation”theory.
i
X
r
a II. EXPERIMENTALPROCEDURES
We have grown gallium- and nitrogen-doped ZnO films grown by laser-molecular-beam epitaxy on lattice-matched
ScAlMgO4 substrates. The detailed methods of fabrication have been given elsewhere [5]. A very complicated growth se-
quence has been adoptedfor the nitrogen doping. We measured the photoluminescence(PL) of the doped ZnO layers in the
band-edgeregion. Theexperimentalprocedures[6]wereidenticaltothoseadoptedinourpreviousstudyandtheirdetailswere
reportedelsewhere[12]. Pulsedexcitationwasprovidedforthetime-resolvedexperimentswiththefrequencydoubledbeamof
apicosecondmode-lockedTi:sapphirelaser.
∗Electronicaddress:[email protected];Furtherauthorinformation:(SendcorrespondencetoT.M.)
T.Makino.:PartofthepresentworkwasperformedatthePhotodynamicsResearchCenter,TheInstituteofPhysicalandChemicalResearch(RIKEN),Sendai,
Japan.
2
III. RESULTSANDDISCUSSION
A. Opticalpropertiesofn-typedopedZnO
Figure1(a)showsPLspectraofZnO:Gaatfourdifferentdopinglevels(dashedlines).TheshapeofthePLbandisasymmet-
rical. Thelinewidthsof the PL increasefrom154to 195meV with an increasein Ga concentration(n ). The“theoretical”
Ga
broadeningfor the PL was evaluated in terms of potential fluctuationscaused by the randomdistribution of donorimpurities
(cf. Fig.3ofourpreviouspaper[6]). ThesevaluesarelistedinTableI.However,theexperimentallyobservedbroadeningare
greaterthanthecalculatedwidths(σ1).
(a) 1×1020 cm-3 n-type ZnO:Ga (b) 4×1018 cm-3
297 K
exp
195 meV s) fit 72 meV
nits) b. unit SLO = 0.65
TY (arb. u 4×1019 cm-3 186 meV NSITY (ar
TENSI INTE
N
L I
P 1×1019 cm-3 0
164 meV
2.6 2.8 3.0 3.2 3.4 3.6
PHOTON ENERGY (eV)
4×1018 cm-3
154 meV
2.6 2.8 3.0 3.2 3.4 3.6
PHOTON ENERGY (eV)
FIG.1:(a)Room-temperaturephotoluminescencespectra(dashedcurves)ofn-typeZnOdopedwithdifferentGaconcentrations.Alsoshown
aretheresultsofthefittothedatausinga‘vibronic’model(solidlines).(b)ThelowermostPLcurveofframe(a)withindividualcontribution
oftheemissionlines(dash-dottedlines).
TABLE I: Sample specification and main characteristics for the four n-ZnO samples. Ga concentration (nGa), theoretical broadening σ1,
broadeningevaluatedfromtheMonteCarlosimulationσ2,zero-phononpeakenergyE,andthededucedHuang-RhysfactorS.
nGa σ1 σ2 E S
(cm−3) (meV) (meV) (eV)
8.0×1018 77.7 73.5 3.277 0.64
2.0×1019 97.1 115 3.272 0.78
8.0×1019 150 139 3.297 1.1
1.5×1020 188 170 3.345 1.4
Itisthoughtthatthetheoreticalwidthsareexceedinglyunderestimatedbecausethemodelmightbetoomuchsimplified. We
hereadoptanotherapproachproperlytakingthemicroscopicfluctuationofdonorconcentrationintoaccount;thethermalization
redistributionmodeldevelopedbyZimmermannetal[13]. Accordingtothismodel,thereisarelationshipbetweentheStokes
shift and the full-width at half maximum (FWHM) of PL. One can estimate the energy scale of the band potential profile
fluctuationfromtheStokesshiftandpredictconsistentlytheFWHM.Figure2showsaStokesshiftoftheluminescenceplotted
3
0.25
ZnO:Ga
RT
0.20
Stokes shifts
)
V
e
hift ( 0.15
s
s
e 0.10
k
o
St
0.05
0.00
5 6 7 89 2 3 4 5 6 7 89 2 3
19 20
10 10
-3
Gallium concentration n (cm )
Ga
FIG.2:ThePLStokesshifts(closedsquares)plottedagainsttheGaconcentration.ThemeasurementswereperformedatRT.
againstthe galliumconcentration. Obviously,the shiftenergyincreaseswith incorporationof the donordopants. The energy
scaleofthebandpotentialprofilefluctuationcanbeevaluatedfromtheStokesshiftandpredictconsistentlytheFWHM.AStokes
shiftoftheluminescenceisplottedagainstthegalliumconcentrationasshowninFig.2. Atsufficientlyhightemperatures,the
above-mentioned relationship is indicated as E = −σ2/kT. The nomenclatures (k and T) take their conventional
Stokes B
meanings. Forexample,theStokesshiftforthesamplewith then of8.0×1018 cm−3 is22meV, leadingtoσ of24meV.
Ga
Italso yieldsthetemperatureindependentvalueof2σ (ln4) ≃ 46meVintheFWHM, whichcanbealsosupportedbythe
MonteCarlosimulation.
p
Miller-Abraham’srateforphonon-assistedcarriertunnelingbetweentheinitialandfinalstatesiandjwiththeenergiesofE
i
andE wasadoptedtosimulatethehoppingeventsofphoto-createdcarriers:
j
2r (ε −ε +|ε −ε |)
νij =ν0exp − ij − i j i j . (1)
α 2kT
(cid:18) (cid:19)
Here rij is the distancebetweenthe localizedstates, α isthe decaylengthof the wave function,andν0 isthe attempt-escape
frequency.HoppingwassimulatedoverarandomlygeneratedsetoflocalizedstateswiththesheetdensityofN. Dispersionof
thelocalizationenergieswasinaccordancewithaGaussiandistribution,
2 2
g(ε)∝exp(−(ε−E0) /2σ ). (2)
WiththepeakpositionedatthemeanresonantenergyE0 andthedispersionparameter(theenergyscaleofthebandpotential
−1
profilefluctuation)σ. Theradiativerecombinationeventwiththeprobabilityτ terminatesthehoppingprocess.Theemission
0
energyatthetime of recombinationis scoredto theluminescencespectrum. By implementingthe thermalbroadeningeffect,
theoverallFWHMofthePLbandisgivenby:
FWHM(σ2)≈[(2σ (ln4))2+(1.8kBT)2]1/2. (3)
Figure 3 represents, with a solid line, the simulated resuplt obtained for the following values of parameters: Nα3 = 0.1,
τ0ν0 = 104, and σ ≃ 24 meV. The lineshape of resulting spectrum was independent of the choices of the Nα3 and τ0ν0
parameters. ThesimulatedcurvecouldbewellapproximatedbytheGaussianfunction,whichisnotsurprisingif considering
themeasurementtemperature(300K).TheFWHMs (σ2)ofthesimulatedPL spectraforthesamplesatfourdifferentdoping
levelsarecompliedinTableI.
Thesimulatedbroadening(σ2)issmallerthanthatofexperimentsasinthecaseofthesimplertheoreticalconsideration.This
differenceisprobablyduetothecontributionofthephononreplicas.Inaddition,thesimulatedline-shapeisrathersymmetrical,
whichisingreatcontrasttotheasymmetricalshapeobservedintheexperimentalspectra. Wethinkthatthezero-phononpeak
and its phononreplicas are not spectrally resolved well, leading to the larger experimentalbroadening. It is inferredthat the
couplingwithlongitudinal-optical(LO)phononisrelativelystrong.ZnOmayhavecouplingconstantsignificantlystrongerthan
thatofGaNorofZnSe[14].
4
n-type ZnO
s) 297 K
t
ni simul.
u

b. 8×1018 cm-3
r
a
(

Y
T 73.5 meV
I
S
N
E
T
N
I

L
P

2.6 2.8 3.0 3.2 3.4 3.6
PHOTON ENERGY (eV)
FIG.3:SimulatedPLspectrumunderstationaryexcitation.TheGaconcentrationisshowninthefigure.
Onlythetermsoflongitudinaloptical(LO)phononsaretakenintoaccount[15],whoseinteractionisknowntobethestrongest.
Insuchacase,thetransitionenergyofthereplicaswillbe¯hω = EZPL−ηLOELO,whereELO=72meVinZnO,EZPL isthe
energyofthezero-phononpeakandηLO isaninteger.AGaussianfunctionwithwidthσ1(cf. TableI)modeledeachindividual
emissionlinein thespectrum. Theprobabilityofa givenphononemissionisproportionalto (SLηOLO/ηLO!), whereSLO is the
Huang-RhysfactorfortheLOphononsandηLO thenumberofphononsemittedinatransition.ThesolidlinesinFigs.1(a)and
(b)wereobtainedby summingallofthe linesusinganappropriateset ofparameters. TableI summarizesthedonor-impurity
concentrations (nGa), zero-phononpeak energies (E), and S-factors. The respective contributions whose peak positions are
shownbyfivedash-dottedcurvesinFig.1(b),withequidistantpeaksbytheELO of72meV.We cansayfromthisfitthatthe
asymmetricalandbroadPLbandcanbeexplainedbythecontributionofLOphononreplicas.Itshouldbenotedthat,eveninthe
undopedZnO, the zero-phononemissionbecomesweaker thanLO-phonon-assistedannihilationprocessesatelevatedsample
temperatures.
B. Opticalpropertiesofp-typedopedZnO
ThinZnOfilmsareknowntobegrownmoreorlessunderresidualn-type. Thetrialofthep-typedopingoftenresultsinan
observationof theradiativerecombinationfromdonor-acceptorpairs(DAPs). Monte-Carlosimulation[7] cannotbe usedfor
the analysis of such a DAPsystem because the photo-carriersin these structurescannotbe regardedas a single particle. The
experimentalPLfeaturescannotbeexplainedwiththesimpleTHAmodelinthecaseofourN-dopedZnOsamples.Symbolsin
Fig.4(a)showasetof5-KPLdecaycurvestakenatthreedifferentemissionenergies,whilethecorrespondingtime-integrated
PLisgiveninFig.4(b). Wefirstremarkthatthedecaytimeconstantsforalltheenergiesaresimilarwithrespecttoeachother
andthedecaycurvesarenon-exponential. Thissimilarity isdifficulttobe predictedin theframeworkofTHAtheory. Inthis
model,usingthepairdistance(R)betweendonorsandacceptors,theemissionenergy(hν)isgivenby[11]:
2 2
hν =hν∞+e /ǫR=(EG−EA−ED)+e /ǫR, (4)
wheretheothersymbolstaketheirconventionalmeanings.Equation(4)givesauniquerelationbetweenhνandR.Theradiative
recombinationkineticsof DAPs is predominantlydeterminedby the pair distance, R. Itis well-knownthatthe decaytime is
stronglydependentonR,andhenceonhν. Thisstrong“dispersion”effectisinapparentcontradictionwithourobserveddata.
AccordingtothetreatmentofKuskovskyandhiscoworkers[16]inwhichthefluctuationeffectsareaccountedfor,anequation
describingthetime-dependentPLintensityisnowquitedifferentfromthatinitscounterpart[11]. Byaveragingoverallpossible
realizationofthefluctuationpotential,transientintensityI (t)atanenergyEis:
E
I (t˜)∝ Wmaxn˜ξ3 exp −n˜t˜ ∞dx x3exp(−x−t˜exp(−x)) ∞ du u5/2
E
4 6 0 0 u−1+exp(−u)
(cid:20) Z (cid:21)Z
p
5
3
200x10
102 (DaA) PZnO:N ( b 5)ZKnO:N D0X
units) 101 33..220296 eeVV units) 150 [N] = 6x1018cm-3
b. 3.240 eV b.
ar ar
sity ( 100 3.263 eV sity ( 100 DSAP-LO D↓SAP
n n
e e ↓
PL Int10-1 PL int 50 DSAP-2LO↓
10-2 5 K
0
0 5 10 15x10-9 2.9 3.0 3.1 3.2 3.3 3.4
Time (sec) Photon energy (eV)
FIG.4: (a): Comparisonoftheexperimentaltime-resolvedPLonZnO:Natthreedifferentemissionenergieswithafluctuationtheory. Open
circles are the experimental data, while the solid curves are the theoretical fits with parameters of ξ = 13, η = 0.036, n˜ = 0.011, and
Wmax = 3×1010 s−1. ThePLintensitieswerenormalizedandeachcurvewasverticallyshiftedforclarity. Themeasurementtemperature
is5K.Secondary-ionmassspectroscopy(SIMS)wasusedforthedeterminationsofthetotalNconcentrations([N]≈ 6×1018 cm−3). Its
conductivityisnotyetp-type.Alsoshownin(b)isthecorrespondingtime-integratedPL.
(E˜u−1)2
×exp (−ξu)−t˜exp[−ξu]−η . (5)
u(u−1+exp[−u])
" #
The zero energy as hν∞, defining an effective emission energy corresponds to E = hν −hν∞. We have introduced a di-
mensionless time t˜ = Wmaxt and energy E˜ = εRsE/e2, as well as parameters ξ = 2Rs/RB, η = e2/(4kTgεRs), and
n˜ = π(N −N )R3,whichhaveallowedustohaveallintegralsasdimensionlessfactor. Here,N andN aretheacceptor
A D B A D
anddonorconcentrations,R isthescreenradius,andT isthefrozentemperature.WiththeuseofEq.(5),itispossibletoshow
s g
thatthedecayisnon-exponential,relativelyclosetostretched-exponential,orevenslower,particularlyatverylowtemperatures.
ThesolidcurvesofFig.4(a)refertotheresultsoftheoreticalfitatdifferenthν accordingtoEq.(5). Forthecalculation,all
theparametersexceptE˜ werekeptfixed(ξ = 13,η = 0.036,n˜ = 0.011,andWmax = 3×1010 s−1). Thesevaluesarequite
reasonable,assumingR =23A˚ (whichcorrespondstothedonordepthof30meV)andR =150A˚.Asseenfromthefigures,
B s
thetheoryresultsinreasonablysatisfactoryfitsforallhν’s. Thefittingprocedureissensitivetothevaluesofthenetacceptor
concentration(NA−ND)andofWmax.
Although the experimentalverification for this theory has been performed in N-doped ZnSe, it should be emphasized that
only samples influenced by the very strong fluctuation fields have been analyzed [17, 18]. In regard with this theory, wide
applicabilityonthemagnitudeoffluctuationshasnotbeenyetverified,whichisthemainfocusofthepresentwork.Thistheory
introducesaconceptofscreeningradius(R )whichisintimatelyrelatedtothedegreeoffluctuations(smallerR corresponds
s s
tothesevererfluctuations).
We discuss the time-integrated PL [cf. Fig. 4(b)] from the viewpoint of excitation-dependentshift to quantify R of our
s
sample. ThePLisdominatedbytheDSAPrecombination(DS meansashallowerdonor)at3.235eV.TheDSAPbandexhibits
no detectable shift with a change in excitation, suggesting very large radius: R > 100 A˚. We confirmed that the use of
s
R = 150 A˚ gives the well-reproduced excitation-intensity dependence of hν. Here, we used a value of 3.228 eV [19] as
s
hν∞ =EG−EA−ED.EG =3.428eV,EA =170meV[20],andED =30meV[21]. Ontheotherhand,thesimilaranalysis
forZnSe:Nyieldedin: R ∼ 20A˚,indicatingthatoursampleisappropriatetoverifywhetherthistheorycanalsobeusedto
s
analyzethesystemwithsignificantlylargerR .
s
Oneofthe reasonsforthe unexpectedlyshortdecaycomparedtothose inothersemiconductors[9]is thedifferencein R ,
s
becausethedecaybecomesslowerwithincreasingfluctuation. TheotheroneispresumablyrelatedtotheWmax,whichisone
order of magnitudelarger than that for ZnSe, and may be inherentto ZnO. Xiong and coworkers[10] have also reported the
DAPPLlifetimeofaZnO:Nbulkcrystalshorterthanmanyothersemiconductors. TheprobabilityWmax isrepresentedbythe
followingequation:
Wmax = 1328e2mµh0¯hν∞2cE3p ×(cid:20)aaDA(cid:21)3, (6)
whereµistheindexofrefraction,m0istheelectronmass,cisthevelocityoflight,Episabandparameterthathasbeencalcu-
latedbyLawaetzusingak·panalysis,andtheresultforZnOis28eV,andtheothersymbolstaketheirconventionalmeanings.
6
ThecalculationusingtheeffectivemasstheoryforeffectiveBohrradiiofdonorsandacceptorsevaluatedthetheoreticalWmax
tobe:Wth =4×109s−1,whichisoneorderofmagnitudesmallerthantheexperimentalvalue.Itshouldbe,however,noted
max
thatthistheoreticalevaluationsensitivelydependsonthechoiceofZnO materialparametersadoptedin thecalculationof the
Bohrradiiofdonorsandacceptors. We wouldliketosaythattheexperimentalvalueofE islikelytobegreaterthan28eV,
p
thecontentionofwhichisbasedonthecomparisonofthevalueswithothersemiconductorsandthestrongexcitoniceffectsof
ZnO.Note,E isrelatedtothematrixelementbetweentheconductionandthevalencebands.
p
C. PhotoconductivityspectroscopyofN-dopedZnO
TheZnO:Nfilmsshowacomplicatedtransientbehaviorofthephotoconductanceinreachingtheirrespectivedarkorillumi-
natedequilibriumconductionstate. Figure5(a)showsatypicalcurrentbuildupanddecayilluminatedwithsub-band-gaplight
of384nmfor∼20minutes.Thephotoexcitationaswellasthedecayofphotoexcitedcarriersareveryslow.
After turning off the light, the photo-induced conductivity is observed to prevail for very long times. It is evident that
the decay is not essentially exponentialfor ZnO:N; a rather common feature for persistent photo-current(PPC) experiments,
implyinginteractionbetweenthephoto-carriersandlocalizedstatesduringthedecayprocesses. IfthePPCiscomingfromthe
AX-center-likedefects,therisingbehaviorattheedgeinPPCexcitationspectrummusttaketheformof(h¯ω−¯hωth)1.5 where
¯hωthdenotesthethresholdenergy.
1018
-6
2.b units)0x110.5 ←Light OFF (RaT) ZnO:N -3-1meV) 1016 eTff .= t e3m87p .K (RbT) Zn deOex:pdN.u fcited g
current (ar 10..05 ↑ OS g(E), (c 11001124 0
oto Light ON D
Ph 0.0 1010
0.0 0.2 0.4 0.6 0.8
0 20 40 60 80 100 120
Time (min) Energy E0' (eV)
FIG.5: (a)RiseanddecaytransientsofthecurrentinZnO:Nat293K.Thedashedlinestandsforasaturatedcurrent. (b)Densityofstates
obtainedfromthePPCtransientusingahigh-resolutionLTM(opencircles)inwhichthedarkcurrentwassubtracted. Thecontinuousline
correspondstotheresultoffittothesecircles.
Tosupportthis,wecalculatethespectraldistributionofthetrapdensity-of-statesusingthemultipletrappingmodel.Resulting
rate-equationsaregivenasfollows;
m
dn(t) dn (t) n(t)
=− i − +n0δ(t), (7)
dt dt t
i
X
dn (t)
i =ω n(t)−γ n (t), (8)
i i i
dt
wherenisfreecarrierdensity,n iscarrierdensitycapturedatthei-thlocalizedstate,τ isradiativerecombinationtimeforfree
i
carriers,n0isphotoexcitedcarrierdensity,ωi(∝g(Ei)×∆E)isacapturerateofcarrier,γiisareleasingrate,Ei isanenergy
ofi-thlocalizedstate,andgisdensityofstate.
BysolvingtheLaplace-transformedrateequationsanalytically,oneobtainsrelationshipofg(E′)withtheLaplacetransform
0
ofthePPCtransientIˆ(t,s):
I(0) Iˆ(s)Kˆ(s)−2[Jˆ(s)]2
′ 2
g(E )= s , (9)
0 σvkBT [Iˆ(s)]3
2ν
′
E0 =kBT ln( ), (10)
s
7
where σ is a capturing cross section, v is thermal velocity, s is a Laplace variable, ν is a detuning frequency, J(t) = tI(t),
K(t) = t2I(t), and E′ is the trap energybelow the mobility edge. The other symbols used in the equations have the usual
0
meaning.
TheLTMthusgivesaviewofthedensity-of-statedistributiong,aswasshowninFig.5(b). Thespectrallineshapefollows
an exponentiallydecayingfunction. The former componentwas fitted using an exponentialfunctionof the exp(−¯hω/kBT0)
type, where T0 meansthe characteristic temperature. The other symbols have the usualmeanings. The best fit to our data is
obtainedforT0 = 387K.ComparingwiththeresultsonapolycrystallineZnOfilms[22],deducedspectraldistributionofg in
ourcaseiscompletelydifferentfromthatofthepolycrystal. Inthelattercase,g hadapeak-likedistributionwithamaximum
neartheone-thirdoftheenergygap. Thiscanbeattributedtothelargedifferenceinthedensityofgrainboundaries[23]. The
characteristictemperatureT0deducedfromFig.5(b)is387K.
IV. SUMMARY
Gallium and nitrogen were successfully applied as sources of donor and acceptor impurities in the laser molecular-beam
epitaxygrowthofn-typeZnO,respectively.Theiropticalpropertieshavebeeninvestigatedintermsoftheireffectofinhomoge-
neousdopantdistributionandtheirphononinteraction.WealsodiscussedthePLshiftingbehaviorinZnO:Nandcomparedthem
withthecontrolsgrownbytheconventionalmethod.Wehaveexplainedhowthedegreeofdopantdistributioninhomogeneityis
extractedfromtheresultsofopticalcharacterization.Theactivationenergyofacceptorshasbeenevaluatedbypropermodeling
tobe≃170meV,whichisindependentofnitrogenconcentration.Wehaveobservedtransientbehaviorofphotoexcitedcarriers
insemi-insulatingN-dopedZnOusingphotocurrentspectroscopy.Theobtainedpersistentphotocurrentshowsdecaytimespre-
vailingoverhours. We obtainthespectraldistributionofdensity-of-statedistributionofthelocalizedstates. Thelineshapeof
thespectrumsuggestsanexistenceoflocalizedexcitonstates. Theexponentialfit[exp(−¯hω/kBT0)]deducedacharacteristic
temperatureT0of387K.
Acknowledgments
TheauthorsarestronglythankfultoC.H.ChiaandY.Segawaforthefruitfuldiscussionsandforprovidingtheexperimental
data analyzed in this work. Thanks are also due to S. Yoshida, A. Tsukazaki, K. Tamura, A. Ohtomo, M. Kawasaki, and H.
Koinumaforprovidingusthesamplesandfortheencouragethroughoutthepresentwork.Thisworkwaspartiallysupportedby
MEXTGrant-In-AidForScientificResearch18760017,theAsahiGlassFoundation,IketaniScienceandTechnologyFoundation
(undercontractNo. 0181027-A),andtheMurataScienceFoundation(undercontractNo.A64104),Japan.
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