D - Mita

MOKSLO, INOVACIJŲ IR TECHNOLOGIJŲ AGENTŪRA
VILNIAUS UNIVERSITETAS
Projektas „Programos „Eureka“ mokslinių tyrimų ir technologinės plėtros projektų įgyvendinimas“
– EUREKA” (EUREKA)
Projekto kodas VP1-3.1-ŠMM-06-V-01-003
Poveiklė 1.2.1.14. "Eureka" projekto "OPTICAL DIAGNOSTICS Naujos optinės matavimo
technologijos ir įrenginiai puslaidininkių diagnostikai“ vykdymas “
2011-08-03 sutarties Nr. VP1-3.1-ŠMM-06-V-01-003
BAIGIAMOJI ATASKAITA
Projekto vadovas:
prof. habil. dr. Kęstutis Jarašiūnas
Atsakingas vykdytojas:Dr. Ramūnas Aleksiejūnas
Vilnius 2012
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Eureka Projekto partneriai
1. Projekto koordinatorius ir
vykdytojas
Vilniaus universitetas,
Taikomųjų mokslų institutas
Projekto vadovas:
Prof. habil. dr. Kęstutis Jarašiūnas
2. Partneris Lietuvoje
UAB Ekspla
Atsakingas uţ projektą:
Direktorius Kęstutis Jasiūnas
3. Partneris uţsienyje
Aixtron AG
Atsakingas uţ projektą:
Vice-president
for
Research
and
Development Prof. Dr. Mikhael Heuken
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Projekto vykdytojo darbo grupės sąrašas
1. Projekto vadovas, vyriausiasis mokslo darbuotojas prof. habil. dr. Kęstutis Jarašiūnas
2. Atsakingas vykdytojas, vyresnysis mokslo darbuotojas dr. Ramūnas Aleksiejūnas
3. Mokslo darbuotojas dr.Vytautas Gudelis
4. Jaunesnysis mokslo darbuotojas Patrik Ščajev
5. Jaunesnysis mokslo darbuotojas Saulius Nargelas
6. Projekto finansininkė Vida Lapinskaitė
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Projekto santrauka
Pagrindinis Eureka projekto tikslas – plėtoti tarpdisciplininius puslaidininkinių junginių
tyrimus, apjungiant netiesinės puslaidininkių optikos ir fotoelektrinių procesų sritis, tuo būdu tobulinti
netiesines optines matavimo technologijas ir jų pagrindu sukurti optinės diagnostikos įrenginius –
prototipus, skirtus plačiatarpių puslaidininkinių junginių charakterizavimui. Metodologinis darbo
naujumas yra tame, kad panaudojant šviesa sukeltą lūţio rodiklio bei sugerties koeficiento erdvinę bei
laikinę moduliaciją, tiriama nepusiausvyriųjų procesų dinamika ir nustatomi svarbūs puslaidininkių
parametrai, atspindintys medţiagos kokybę ir jos panaudojimo optoelektronikoje galimybes.
Darbe išplėtotos įvairios optinio „ţadinimo-zondavimo“ konfigūracijos bei stebėsenos metodai,
skirti rekombinacijos ir difuzijos procesų diagnostikai puslaidininkiuose plačiame laiko, suţadinimų ir
temperatūrų intervale. Metodai aprobuoti tiriant nitridinius puslaidininkių junginius, silicio karbidus bei
deimantus, uţaugintus įvairiomis technologijomis, ir paruošti parametrų nustatymo algoritmai
atitinkamoms tyrimo sąlygoms. Šios inovacijos, panaudojus difrakcinį šviesos pluoštelio daliklį
dinaminės gardelės uţrašymui, įdiegtos naujame HOLO-3 modulyje-prototipe, kuris skirtas
plačiatarpių puslaidininkinių junginių charakterizavimui ir pagal savo technines-eksploatacines
charakteristikas pranoksta anksčiau sukurtą ir įdiegtą modulį HOLO-2. Apart to, sukurtas kompleksinis
stendas krūvininkų gyvavimo trukmei matuoti plačiame laiko intervale – nuo dešimties pikosekundţių
iki kelių dešimčių mikrosekundţių dėka jame apjungto optinio ir elektrinio zonduojančio pluoštelio
uţlaikymo. Šie nauji techniniai sprendimai panaudoti daugelyje mokslinių publikacijų su paţangiais
uţsienio ir Lietuvos mokslo centrais ir perduoti UAB Ekspla, siekiant naujų matavimo modulių
komercializacijos.
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Ataskaitos turinys
1.
Įvadas. Projekto tikslai ir uždaviniai.
2. Taikomieji moksliniai tyrimai ir eksperimentinės plėtros darbai.
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2.1. Tyrimo metodai ir jų tobulinimas.
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2.2. Dinaminių gardelių ir diferencinio pralaidumo stendai.
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2.3. Moksliniai tyrimai su naujomis optinėmis matavimo schemomis.
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2.4. Gautų rezultatų reikšmė mokslo bei technologijų paţangai.
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3. Išvados, mokslinės rekomendacijos, siūlymai.
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4. Projekto rezultatų publikacijos.
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5.
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MTEP rezultatai.
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1. Įvadas. Projekto tikslai ir uždaviniai.
Vykdant projektą, buvo sprendţiami šie moksliniai-taikomieji ir matavimo technologijų uţdaviniai,
būtini mokslinių inovacijų sukūrimui ir jų perdavimui projekto partneriui komercializavimo tikslu.
I. Moksliniai-taikomieji uţdaviniai:
1.
Plėtoti tarpdisciplininius puslaidininkinių tyrimus, apjungiant netiesinės puslaidininkių optikos
ir fotoelektrinių procesų sritis, tuo būdu tobulinti netiesinius optinius metodus elektrinių
parametrų nustatymui.
2. Sukurtus matavimo metodus pritaikyti modernių medţiagų tyrimams plačiame optinių
suţadinimo tankio, spektro ir temperatūrų srityje (T=10-800 K). Krūvininkų dinamikos tyrimui
su reikiama laikine bei erdvine skyra panaudoti pramoninius pikosekundinius kietojo kūno bei
parametrinius lazerius, optinius kriostatus, duomenų surinkimo sistemas. Ištyrus įvairias
medţiagas, paruošti algoritmus fotoelektrinių parametrų nustatymui –gyvavimo trukmei,
difuzijos koeficientui, difuzijos ilgiui, jų priklausomybėms nuo injekcijos lygio.
3. Tyrimus atlikti įvairiose puslaidininkinėse medţiagose – nitridinių junginių sluoksniuose bei
daugialypėse kvantinėse sandarose, tūriniuose silicio karbido bei sintetinių deimantų
kristaluose, tame tarpe ir partnerio AIXTRON AG uţaugintuose nitridų sluoksniuose. Tuo
būdus pademonstruoti naujų matavimo būdų universalumą.
II. Technologiniai uţdaviniai siejami su matavimų įrangos modernizavimu:
1. Pritaikyti difrakcinius daliklius optinėse dinaminių gardelių uţrašymo konfigūracijose, išbandyti
holografinių daliklių matricas, apjungiančias kelis holografinius daliklius viename luste.
2. Panaudoti naujus techninius sprendimus - holografinių daliklių matricas diagnostiniame
modulyje HOLO-3.
3. Realizuoti optinį ir elektrinį zonduojančio pluoštelio uţlaikymą viename eksperimentiniame
stende krūvininkų gyvavimo trukmės stebėsenai plačiame laiko intervale – nuo dešimties
pikosekundţių iki kelių dešimčių mikrosekundţių.
4. Perduoti sukurtas technines inovacijas Projekto partneriui UAB Ekspla, o uţsienio partneriui
teikti informaciją apie jų auginamų medţiagų parametrus.
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2.Taikomieji moksliniai tyrimai ir eksperimentinės plėtros darbai.
2.1. Tyrimo metodai ir jų tobulinimas
Darbe buvo panaudotos „optinio ţadinimo - zondavimo“ schemos su koherentiniais šviesos
pluošteliais, kurios leido uţrašyti dinamines gardeles puslaidininkyje ir stebėti šviesa sukelto lūţio
rodiklio erdvinę ir laikinę moduliaciją n(x,t) per zonduojančio pluoštelio difrakciją, ir tuo būdu
matuoti krūvininkų difuzijos ir rekombinacijos spartą (nes n(x,t) irimas proporcingas generuotų
krūvininkų tankio moduliacijai N(x,t)). Dinaminės gardelės (DG) uţrašymui buvo panaudoti
difrakciniai optiniai elementai – įvairių periodų difrakcinės gardelės, išėsdintos kvarco padėkle. Šiame
etape buvo panaudota vienfotonė ir dvifotonė krūvininkų injekcija GaN ir deimantų kristaluose, tuo
būdu (i) išplečiant N intervalą, kuriame stebimi rekombinacijos-difuzijos procesai ir (ii) nustatant šių
procesų charakteringas vertes (difuzijos koeficientą D ir gyvavimo trukmę ), kurios priklauso nuo
injektuotų krūvininkų N koncentracijos bei temperatūros. Lyginant dvifotonio ir vienfotonio ţadinimo
eksperimentų duomenis, galima gauti vertingą informaciją apie medţiagas: įvertinti krūvininkų
sklaidos mechanizmus, legiravimo koncentraciją, defektų įtaką , netiesinės rekombinacijos spartą.
Kita tyrimų kryptis – lėtų rekombinacijos procesų optinis zondavimas, papildantis greitu
rekombinacijos komponenčių stebėseną DG metodu. Šiuo atveju zonduojamas diferencinio pralaidumo
kinetika, apspręsta zondo pluoštelio sugerties laisvaisiais krūvininkais (t.y. zonduojamas sugerties
koeficiento momentinis pokytis (t), proporcingas generuotam krūvininkų tankiui N(t). Tokiu būdu
per indukuotą laisvakrūvę sugertį (LKS) stebimos rekombinacijos kinetikos nuo kelių nanosekundţių
iki dešimčių-šimtų mikrosekundţių, kurios duoda įţvalgą į rekombinacijos procesų prigimtį , defektų ir
pernašos įtaka, defektų energetinius lygmenis ir jų terminę aktyvaciją.
Abiejų metodu – DG ir LKS panaudojimas – atveria naujas optinių netiesinių matavimo
metodų metrologines galimybes, ko ir buvo siekiama šiame projekto vykdymo etape. Ţemiau
pateikiamos optinės metodų konfigūracijos ir eksperimentiniai stendai jų realizavimui.
2.2. Dinaminių gardelių ir diferencinio pralaidumo stendai
I. DG schema su difrakciniu-holografiniu pluoštelio dalikliu ir stendas šios inovacijos realizavimui
pateiktas 1 paveiksle. Kairėje paveikslo pusėje pateiktas pikosekundinis lazerinis, generuojantis
pagrindinę 1064 nm harmoniką (kuri naudojama kaip zondas) ir aukštesnes harmonikas, kurios
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naudojamos krūvininkų generacijai tiriamajame bandinyje. Dešinėje pateiktas optinių-mechaninių
komponentų rinkinys sudaro diagnostinį modulį HOLO-3, kurio pagrindinis naujumas - holografinis
pluoštelio daliklis HPD ir jo matrica (2 pav.). Didelis difrakcinis efektyvumas (iki 60% pirmose
difrakcijos eilėse) daro difrakcinį elementą perspektyvų DG metodo realizavimui, tačiau difrakcinis
efektyvumas keletą kartų sumaţėja prie maţų periodų (<5 m), tuomet periodas maţinamas parenkant
maţesnį lęšio ţidinio nuotolį f2.
1 pav. Eksperimentis stendas DG metodo realizavimui su difrakciniu-holografiniu pluoštelio dalikliu (HPD)
ir pikosekundiniu lazeriu PL-2143 (UAB Ekspla).
2 pav. Holografinis pluoštelio daliklis HPD (su 10 m periodo gardele), suformuojantis koherentinius
pluoštelius DG uţrašymui ir elektro-mechaniškai valdoma HPD matrica su skirtingo periodo gardelėmis (nuo
10 iki 40 m), surinkta ant posūkio stalelio (UAB Standa).
II. Siekiant išplėsti diagnostinio HOLO-modulio galimybes, buvo surinktas eksperimentinis stendas,
apjungiantis abi metodikas (DG ir LKS) ir turintis papildomą galimybę panaudoti elektroninį zondo
uţlaikymą lėtų rekombinacijos procesų matavimui. Pastarajam tikslui panaudotas 2 ns trukmės
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impulsinis Nd-YAG lazeris (lazeriniais diodais kaupinamas UAB Ekspla modelis NL-202, kurio
impulso trukmė buvo sumaţinta iki 2 ns projekto reikmėms). Abu lazeriai (pikosekundinis ir
nanosekundinis) sinchronizuojami elektroniškai. Stendas leido atlikti LKS kinetikų matavimus nuo
kelių nanosekundţių iki dešimčių-šimtų mikrosekundţių. Šios matavimo sistemos leidţia matuoti
difrakcijos signalą, atitinkantį dinaminės gardelės difrakcinį efektyvumą 0.01%, o tai atitinka
suţadintų krūvininkų koncentraciją paviršiuje N 5×1017 cm-3. Tūrinio suţadinimo atveju jautris išauga
iki N1015 cm-3 vertės. Diferencinio pralaidumo kinetikos leido matuoti T/T1% pokyčius.
3 pav. Optinis stendas greitų ir lėtų procesų stebėsenai, besiremiantis šviesa sukelto lūţio rodiklio bei
sugerties koeficiento moduliacija ir tuo tikslu apjungiantis difrakcijos ir laisvakrūvės sugerties metodus su
optiniu ir elektriniu zonduojančio pluoštelio vėlinimu.
4 pav. HOLO-3 modulio su paraboliniais veidrodţiais optinė schema ir modulio prototipas.
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III. Siekiant išvengti optinių pluoštelių su skirtingais bangų ilgiais sferinės aberacijos optiniais
didelio skersmens lęšiais DG schemose (ypač uţrašant maţo periodo gardeles), buvo realizuota DG
uţrašymo ir zondavimo universali schema, naudojanti parabolinius veidrodţius (4 pav.). Ji buvo
surinkta kaip demonstracinis HOLO-3 modulis ir su ja atlikti testiniai difuzijos koeficiento matavimai
GaN epitaksiniame sluoksnyje su pikosekundinės trukmės lazerio impulsu. Čia abu pluošteliai
(ţadinantis ir zonduojantis) praeina HPD ir paraboliniais veidrodţiais nukreipiami į bandinį. Schema
ţenkliai palengvina difragavusiojo pluoštelio suradimą erdvėje (jis sklinda praėjusiojo zondo kryptimi)
ir atveria galimybę padidinti matavimo jautrį dėka difrakcinio signalo heterodininio stiprinimo (t.y.
difrgavusiojo ir praėjusiojo pluoštelio konstruktyvios interferencijos detektoriuje, kai jų tarpusavio
fazės parenkamos sinfaziškomis stumdant HPD-elementą gardelės vektoriaus kryptimi).
2.3. Moksliniai tyrimai su naujomis optinėmis matavimo schemomis.
Lentelėje pateikiama 2011-2012m. atliktų tyrimų suvestinė ir nuorodos į publikacijas.
Uţduotys
Tyrimo objektai
Rezultatai ir publikacijos
1. Difuzijos koeficiento
D ir gyvavimo trukmės
R
variacija
InGaN
sluoksniuose
50 nm storio
InGaN
epitaksinis sluoksnis su
13% In (pateiktas
AIXTRON AG)
Ištirtos nuo koncentracijos priklausančios difuzijos
koeficiento ir gyvavimo trukmės vertės lokalizuotose
ir laisvose būsenose, parodyta juostos renormalizacijos
efekto įtaka pernašai. Paruoštas pranešimas tarpt.
konferencijai ISSLED„2012 ( Berlynas) ir mokslinis
straipsnis (pateiktas į J. Appl. Physics 2012.12)
Nepoliniai GaN
2.Pernaša ir sugertis m- ir epitaksiniai sluoc-orientacijos
GaN ksniai ant mLiAlO2 padėklo
sluoksniuose
(AIXTRON AG)
ir tūrinis m-GaN
(Kyma Inc. JAV)
2. Defektiškumo bei optinių savybių anizotropijos
tyrimai
įvairiomis
optinėmis
metodikomis
(fotoliuminescencijos,
netiesinės
sugerties
ir
difrakcijos. Rezultatai atspausdinti ISI sąrašo
ţurnaluose Journal of Crystal Growth (329, 33-38
(2011)) ir Applied Physics Letters (100, 022112
(2012)).
2. Fotoelektrinių parametrų
nustatymas
vienfotonės ir dvifotonės
injekcijos sąlygomis
Nustatyta nepusiausvyriųjų krūvininkų gyvavimo
trukmė maţo defektiškumo GaN ir jos koreliacija su
D(T) kitimu, tuo pagrįstas difuzinės pernašos ribotas
rekombinacijos
mechanizmas.
Įvertinta
D(N)
priklausomybė leido nustatyti pusiausvyriąją elektronų
koncentraciją. Parodytas netiesinių optinių matavimų
pranašumas
lyginant
su
fotoliuminescencijos
kinetikomis GaN. Paskelbta straipsniuose Appl.
Phys.Lett. (98, 202105 (2011)), Journal of Appl. Phys.
1.1 Tūrinis GaN
(Kyma Inc, USA)
1.2.
Tūriniai
HPHT ir CVD
technologijų
deimantai
(Ukraina, Belgija)
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(111, 023702 (2012)), trys pranešimai tarpt.
konferencijose (kviestinis SPIE Photonics West 2011,
kviestinis MRS 2011 ir ţodinis SPIE Photonics West
2012).
Krūvininkų dinamika deimantuose dvifotonės
injekcijos sąlygomis ištirta pirmą karta, atvėrė naujas
galimybes nustatyti krūvininkų judrius, gyvavimo
laikų
sparčias-lėtas
kinetikas,
jų
netiesines
priklausomybes nuo koncentracijos ir temperatūros.
Paruoštas 1 pranešimas deimantų simpoziumui
(Belgija, 2012) ir paskelbtas mokslinis straipsnis
(Physica status solidi (a) 209, 1744–1749 (2012)).
2.4. Gautų rezultatų reikšmė mokslo bei technologijų paţangai.
Kadangi šiame projekte buvo sprendţiami moksliniai-taikomieji uţdaviniai, susiję su optinės
diagnostikos metodų pritaikymu kompleksiniam puslaidininkių charakterizavimui, pirmaeilės svarbos
tyrimo objektu buvo defektiškumo sąlygoti medţiagų elektriniai parametrai (nes būtent jie parodo
auginimo
technologijos
paţangą
ir
leidţia
prognozuoti
medţiagų
tinkamumą
taikymams
optoelektronikoje). Todėl poreikis išmatuoti elektrinius parametrus bekontaktiniais optiniais metodais
išlieka aktualus daugeliui medţiagų – GaN, InGaN, InN, bei SiC. Kita vertus, įgyta metodologinė
patirtis (optinės konfigūracijos, matavimo reţimai, algoritmai) šių medţiagų tyrimuose gali būti
panaudojami kitų medţiagų analizėje ( ZnO, AlGaN, deimantai).
Šiame projekto etape atliktuose tyrimuose buvo gauti rezultatai, liudijantys apie pikosekundinių
dinaminių gardelių metodo perspektyvumą pernašos ir rekombinacijos tyrimams InGaN epitaksiniuose
sluoksniuose bei kvantinėse sandarose, kurių auginimas plėtojamas VU Taikomųjų mokslų institute. Jų
fotoliuminescencijos efektyvumo įsotinimo mechanizmas stiprios injekcijos sąlygomis yra plačiai
tiriamas pasaulyje ir yra diskusijų objektas iki šiol, todėl naujų optinių metodų panaudojimas,
papildantis standartinius fotoliuminescencijos tyrimus, yra reikšmingas mokslui bei technologinės
plėtros įvertinimui. Be to, krūvininkų parametrų nustatymas dvifotonės injekcijos sąlygomis tūriniuose
GaN bei deimantų kristaluose suteikė papildomos informacijos apie dislokacijų sąlygotą
rekombinacijos spartą GaN bei sklaidos mechanizmų esminį indėlį judrio vertei deimantuose
(pataruoju atveju tai leidţia prognozuoti difuzijos lėkio esminį sumaţėjimą stiprios injekcijos
prietaisuose).
Metodikų plėtra buvo panaudota doktorantų moksliniuose tyrimuose (2012.12 apginta
S.Nargelo disertacija), o rezultatai apie ištirtas nitridinių junginių savybes (InGaN, InN) buvo perduoti
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projekto parneriui (AIXTRON, Vokietija), Hasselto universiteto Medţiagų mokslo institutui (Belgija),
bei JAV kompanijai Kyma (su visais paskelbtos bendros publikacijos). Naujos ţinios bus naudojamos
ir mokslinės grupės vykdomame ESF remiamame visuotinė dotacijos projekte „Optoelektronikos
poreikiams skirtų nitridinių junginių heterosandarų netiesinė optinė ex-situ diagnostika ir
optimizavimas (OPTO“ (2012-2015), Europos Komisijos BP7 M. Kiuri ITN projekte „Funkciniai
interfeisai SiC (NetFiSiC)“ ( 2011-2014), Lietuvos - Baltarusijos dvišalio bendradarbiavimo mokslo ir
technologijų srityje programos (2011-2012) projekte „Elektroninių ir šiluminių procesų dinamikos
tyrimai optiniais metodais skirtingos morfologijos CVD deimantuose“, bei Baltijos-Amerikos Laisvės
Fondo projektas „Krūvio pernaša ir rekombinacija optoelektronikai skirtuose nitridų junginiuose”
(2011.04 - 2012.04).
3. Išvados, rekomendacijos ir siūlymai.
Eureka projekto metu buvo tobulinami ir aprobuojami netiesinės optinės metrologijos metodai su
įvairiomis puslaidininkinėmis medţiagomis bei sandaromis, uţaugintomis Lietuvoje bei uţsienio
mokslo ir technologijų centruose. Todėl pasiekta paţanga didina Lietuvos mokslo tarptautinį prestiţą
(buvo skaityti du kviestiniai pranešimai tarptautiniuose JAV forumuose – Photonics West ir Materials
Research Society, 2012 m. paskelbti/paruošti 4 straipsniai). Tokia tarptautinė sklaida ir sukurtųjų
netiesinių matavimo technologijų papildomumo demonstravimas atţvilgiu plačiai naudojamo
standartinio fotoliuminescencijos metodo medţiagų charakterizavimui atlieka naudingą darbą mokslo
komercializacijai, siekiant kad projekto partneris UAB EKSPLA rastų uţsakovus naujo diagnostinio
modulio HOLO-3 gamybai.
Būtina paminėti, jog 2011m. pradėtas GaN sluoksnių bei InGaN kvantinių sandarų auginimas
Taikomųjų mokslų institute, todėl Eureka projekte išplėtoti optinės diagnostikos metodai padės šiai
technologinei grupei įvertinti MOCVD reaktoriaus auginimo reţimus, o esant poreikiui – testuoti ir
MBE technologija FTMC uţaugintus GaAsBi-GaAsN junginius .
12
4. Projekto rezultatų publikacijų sąrašas (su padėka Eureka Projektui).
Moksliniai straipsniai
1.
P. Ščajev, K. Jarašiūnas, Ü. Özgür, H. Morkoç, J. Leach, and T. Paskova, „Anisotropy of free-
carrier absorption and mobility in m-GaN“. Applied Physics Letters 100, 022112 (2012).
2.
K. Jarašiūnas, P. Ščajev, R. Aleksiejūnas, J. Leach, T. Paskova, S. Okur, Ü. Özgür, and H.
Morkoç. „Recombination and diffusion processes in polar and nonpolar bulk GaN investigated by
time-resolved photoluminescence and nonlinear optical techniques“, In: Gallium Nitride Materials and
Devices VII, edited by Jen-Inn Chyi, Y. Nanishi, H.Morkoç, J. Piprek, E. Yoon, Proc. of SPIE Vol.
8262, 82620G1-10, 2012, DOI: 10.1117/12.906303
3.
K. Jarašiūnas, R. Aleksiejūnas, T. Malinauskas, S. Nargelas and P. Ščajev, „Nonlinear Optical
Techniques for Characterization of Wide Band Gap Semiconductor Electronic Properties: III-Nitrides,
SiC, and Diamonds“ (Invited paper - MRS Fall meeting 2011), MRS Proceedings 2012 vol. 1396 (12
psl), Cambridge University Press, 2012, DOI: http://dx.doi.org/10.1557/opl.2012.497.
4.
K. Jarašiūnas, S.Nargelas R. Aleksiejūnas,, S. Miasojedovas, M.Vengris, S. Okur, U. Ozgir, H.
Morkoc, C.Giesen, O. Tuna, M. Heuken „Spectral distribution of excitation-dependent recombination
rates jn InGaN“ (straipsnio rankraštis pateiktas 2012.12.10 ţurnalui „Journal of Applied Physics”)
2011 metais, nors Projektas nebuvo tiesiogiai finansuojamas , vyko metodikų plėtros ir jų
aprobacijos darbai, bendradarbiaujant su uţsienio partneriu AIXTRON bei ankstesniųjų metų rezultatų
sklaida tarptautiniu lygiu. Šią veiklą liudija šios publikacijos (su padėka Eureka projektui):
1. S. Miasojedovas, C. Mauder, S. Krotkus, A. Kadys, T. Malinauskas, K. Jarasiunas, M. Heuken, and
H. A. Vescan, „High-excitation luminescence properties of m-plane GaN grown on LiAlO(2)
substrates“, J. Crystal Growth 329, 33-38 (2011).
2. P. Ščajev, M. Kato and K. Jarašiūnas, „A diffraction-based technique for determination of interband
absorption coefficients in bulk 3C-, 4H- and 6H-SiC crystals“, J. Phys. D: Appl. Phys. 44, 365402
(2011).
13
3. P. Ščajev, A. Usikov, V. Soukhoveev, R. Aleksiejūnas, and K. Jarašiūnas, „Diffusion-limited
nonradiative recombination at extended defects in hydride vapor phase epitaxy GaN layers“, Appl.
Phys. Lett. 98, 202105 (2011)
4. K. Jarašiūnas „Time-resolved nonlinear optical-holographic techniques for investigation of
nonequilbrium carrier dynamics in semiconductors“ (Invited paper, Photonics West 2011), in
ULTRAFAST PHENOMENA IN SEMICONDUCTORS AND NANOSTRUCTURE MATERIALS,
Proc. SPIE, vol 7937, 7937W1-17, 2011 (DOI: 10.1117/12.877108 ).
Tarptautinės konferencijos:
1. MRS Fall meeting (Bostonas JAV, 2011.12) kviestinis pranešimas: K.Jarašiūnas, R.
Aleksiejūnas, T. Malinauskas, S. Nargelas and P. Ščajev, Nonlinear Optical Techniques for
Characterization of Wide Band Gap Semiconductor Electronic Properties: III-Nitrides, SiC, and
Diamonds
2. SPIE Photonics West 2012 ( San Francisco, JAV, 2012.01), pranešimas K. Jarašiūnas, P.
Ščajev, R. Aleksiejūnas, J. Leach, T. Paskova, S. Okur, Ü. Özgür, and H. Morkoç.
Recombination and diffusion processes in polar and nonpolar bulk GaN investigated by timeresolved photolumines-cence and nonlinear optical techniques.
3. Internatinal symposium on semiconductor light emitting structures ( ISSLED, Berlynas,
2012.07), pranešimas K. Jarašiūnas, R. Aleksiejūnas, S.Nargėlas, T. Malinauskas, S.
Miasojedovas, A. Kadys, S. Okur, X.Li, U. Ozgir, H. Morkoc, O. Tuna, M. Heuken, „ On
injection activated nonradiative recombination in InGaN”.
14
Finansinių paraiškų teikimo, jų vertinimo, lėšų
skyrimo, ataskaitų teikimo ir vertinimo tvarkos aprašo
6 priedas
MOKSLINĖS/TECHNOLOGINĖS PRODUKCIJOS APŽVALGA
Poveiklė 1.2.1.14. OPTICALDIAGNOSTICS (VU)
Metai, uţ kuriuos teikiami duomenys: 2011-2012
Eil. Nr.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Produkcija
Sukurtų, paruoštų diegti ar įdiegtų naujų technologijų
skaičius
Sukurtų naujų gaminių skaičius
Pateiktų tarptautinių patentinių paraiškų pagal Patentinės
kooperacijos sutartį ir Europos patentų konvenciją
skaičius
Pateiktų nacionalinių patentinių paraiškų skaičius
Įgytų patentų skaičius
Publikacijų ţurnaluose, įtrauktuose į Mokslinės
informacijos instituto sąrašą (ISI), skaičius
Apgintų disertacijų skaičius
Sukurtų naujų darbo vietų verslo įmonėse skaičius
Sukurtų naujų darbo vietų mokslininkams ir tyrėjams
verslo įmonėse skaičius
Įkurtų naujų įmonių skaičius
Kiekis
2
Perskaitytų pranešimų konferencijose, seminaruose,
kituose renginiuose skaičius
Kiti projekto įgyvendinimo metu pasiekti rezultatai.
1
_____Kęstutis Jarašiūnas _________
Projekto vadovas (vardas, pavardė) (parašas)
0
0
0
0
4
1
0
0
2
_______________ 2012-12-31
(data)
15
PRIEDAI
-----------------------------------------------------------------------------------------------------------Priedas 1. 2012 m. paskelbtų straipsnių kopijos ir įteikto spaudai straipsnio rankraščio kopija.
Priedas 2. Projekto viešinimo plakato kopija.
Priedas 3. Projekto partnerio EKSPLA UAB raštas dėl sukurtų matavimo technologijų priėmimo.
16
Priedas 1. 2012 m. paskelbtų straipsnių kopijos ir įteikto spaudai straipsnio rankraščio kopija.
Anisotropy of free-carrier absorption and diffusivity in m-plane GaN
P. Ščajev, K. Jarašiūnas, Ü. Özgür, H. Morkoç, J. Leach et al.
Citation: Appl. Phys. Lett. 100, 022112 (2012); doi: 10.1063/1.3674306
View online: http://dx.doi.org/10.1063/1.3674306
View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v100/i2
Published by the American Institute of Physics.
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APPLIED PHYSICS LETTERS 100, 022112 (2012)
Anisotropy of free-carrier absorption and diffusivity in m-plane GaN
P. Ščajev,1,a) K. Jarašiūnas,1,2 Ü. Özgür,2 H. Morkoç,2 J. Leach,3 and T. Paskova3
1
Institute of Applied Research, Vilnius University, Saulėtekio Ave. 9 - III, Vilnius 10222, Lithuania
Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond,
Virginia 23284, USA
3
Kyma Technologies, Inc., 8829 Midway West Road, Raleigh, North Carolina 27617, USA
2
(Received 8 December 2011; accepted 13 December 2011; published online 13 January 2012)
Polarization-dependent free-carrier absorption (FCA) in bulk m-plane GaN at 1053 nm revealed
approximately 6 times stronger hole-related absorption for E\c than for Ejjc probe polarization
both at low and high carrier injection levels. In contrast, FCA at 527 nm was found isotropic at low
injection levels due to electron resonant transitions between the upper and lower conduction bands,
whereas the anisotropic impact of holes was present only at high injection levels by temporarily
blocking electron transitions. Carrier transport was also found to be anisotropic under two-photon
C 2012
excitation, with a ratio of 1.17 for diffusivity perpendicular and parallel to the c-axis. V
American Institute of Physics. [doi:10.1063/1.3674306]
Development of nonpolar and semipolar GaN-based devices has been gaining interest as the polarization induced fields
in the commonly employed polar c-plane orientation hamper
the efficiency of light emitters and brings about constraints on
the widths of quantum wells used in active regions. For device
designs utilizing nonpolar and semipolar orientations, it is imperative that anisotropy of optical and electrical properties of
wurtzite type nitrides is considered. However, the anisotropy
of carrier transport or polarization-dependent absorption have
not been investigated in sufficient detail, as the earlier studies
utilized relatively thin c-plane GaN platelets which restricted
the propagation of a probing optical beam along the symmetry
axis (kjjc, E\c). Heretofore, only the polarization-state of
emission in thin nonpolar m-plane GaN films has been investigated, confirming the polarization selection rules and revealing an anisotropic strain.1,2
Bulk nonpolar crystals allow coupling of an optical
probe conveniently along or perpendicular to the c-axis and
thus investigation of the anisotropic features. Indeed, a
strong anisotropy of free-carrier absorption (FCA) has been
observed in heavily doped hexagonal n-SiC polytypes due to
anisotropy of electron effective mass.3,4 In nitride semiconductors, the valence band splitting and spin-orbit interaction
lead to more favorable conditions for the hole-related FCA,5
and the indirect absorption processes have been numerically
analyzed for GaN/InGaN heterostructures in the 400-670 nm
spectral range.6 The latter calculations predicted up to two
times higher intraband absorption cross-section by holes for
light polarized perpendicular to c-axis (rh\) than that for the
parallel polarization (rhjj) and rather weak isotropic absorption by free electrons. The experimental value of FCA for
undoped c-GaN was reported for a bipolar free-carrier
plasma only for the E\c polarization, providing a crosssection of reh ¼ (2.5 6 0.3) 1017 cm2 at 1053 nm.7
Here, we report on an experimental study of free-carrier
absorption and carrier transport in a nonpolar m-plane bulk
GaN substrate using optical probes at kp ¼ 1053 and 527 nm.
a)
Author to whom correspondence should be addressed. Electronic mail:
patrik.scajev@ff.vu.lt. Telephone: þ370 5 2366036. Fax: þ370 5 2366037.
0003-6951/2012/100(2)/022112/4/$30.00
Taking advantage of the in-plane c-axis, we were able to
investigate the anisotropy by directing the linearly polarized
probe beam normal to the surface and rotating its polarization for full 360 . Measurements of polarization-dependent
FCA revealed nearly 6-times stronger hole-related absorption at 1053 nm for E\c as compared to that for Ejjc. Isotropic and rather strong FCA was measured at 527 nm which
we attributed to FCA in the conduction bands. The anisotropy of ambipolar and hole diffusivity was found to be much
less pronounced.
The measurements were carried out on a d ¼ 450 lmthick m-plane freestanding GaN wafer, sliced from a 7-mm
thick freestanding Hydride Vapor Phase Epitaxy (HVPE)
grown GaN boule (with an electron density of
9.5 1015 cm3, threading dislocation density varying from
1 106 cm2 at the edge side to 4 105 cm2 at the
front side of the boule). For carrier injection to the entire
bulk of the layer, we used two-photon (2P) excitation by
15 ps pulses at 527 nm from a neodymium-doped yttrium
lithium fluoride laser. Single-photon (1P) carrier injection at
351 nm was used to reach higher injected carrier densities, in
a photopumped slice of thickness d. Monitoring the probe
beam differential transmission, ln(T0/T) ¼ Dad, we measured
the FCA coefficient, Da, at kp ¼ 1053 nm and 527 nm probe
wavelengths and
determined the FCA cross-sections
Ð
reh ¼ ln(T0/T)/ DN(z)dz, where the injected carrier density
DN(z) is integrated over the sample thickness.5 By varying
the orientation of the linearly polarized probe beam with
respect to the c-axis, the anisotropy of reh was measured.
Carrier diffusivity was investigated by the light-induced
transient grating technique8 under two-photon injection conditions, providing DN ¼ 1016 – 5 1017 cm3. Two orthogonal orientations of the grating vector K with respect to the caxis were used to determine the diffusion coefficient D along
the two orthogonal directions (K\c and Kjjc) from the
diffusion-governed grating decay time.
In Fig. 1(a), we present the dependence of FCA on excitation energy density for 1053 nm probe. The FCA signal
increased almost linearly with carrier injection at 351 nm,
thus a constant reh value can be assumed in the range up to
100, 022112-1
C 2012 American Institute of Physics
V
Downloaded 03 Jan 2013 to 193.219.83.91. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
022112-2
Ščajev et al.
FIG. 1. (Color online) (a) Polarization-dependent FCA for a 1053 nm probe
beam: dependence on excitation energy density and (b) FCA decay kinetics
at high injected carrier density (5 1019 cm 3). The dashed lines are numerical fits and the inset in (b) shows FCA decay at low excess carrier density (1017 cm3).
7 mJ/cm2 (5 1019 cm3). The linear relationship allowed
us to determine reh values. A varying FCA signal strength
for different probe beam polarizations implies that reh is
strongly anisotropic [Fig. 2(a)]. The FCA cross-section as a
function of the polarization angle / was fitted using reh(/)
¼ reh \ – (reh \ – reh jj) cos2(/). For the 1053 nm probe, we
obtained reh\ ¼ 2.2 1017 cm2, rehjj ¼ 3.4 1018 cm2,
and an anisotropy ratio S ¼ r\/rjj ¼ 6.5. The same values of
reh and S were obtained under two photon excitation, i.e., in
the carrier density range from 1015 to 5 1017 cm3 [see
FIG. 2. (Color online) (a) Polarization dependence of FCA cross-section reh
for 1053 nm probe wavelength at high (351 nm) and low injection (527 nm)
conditions. (b) reh for 527 nm probe at low (DN 5 1017 cm3, external
circle) and high injection [two internal circles for reh at zero delay time (for
DN 5 1019 cm3) and at 4 ns delay time (for DN 2.6 1019 cm3)]. (c)
GaN energy band diagram with direct (vertical arrows) and indirect phononassisted intraband transitions (diagonal arrows) depicted (after Ref. 6).
Appl. Phys. Lett. 100, 022112 (2012)
Fig. 2(a)]. The injection-independent FCA at the given probe
wavelength can be attributed to the polar optical phonon
assisted FCA in valence bands,6 thus reh rh at 1053 nm.
Polarization-dependent FCA measurements with the
527 nm probe were performed at low and high carrier injection conditions (i.e., by using excitation wavelengths of
527 nm or 351 nm, respectively). At low excess carrier densities, the measurements yielded smaller reh values compared to those for the 1053 nm probe and no dependence on
polarization: reh\ ¼ rehjj ¼ 8 1018 cm2 [Fig. 2(b)]. This is
a clear signature that holes that are responsible for FCA anisotropy at 1053 nm do not contribute noticeably to FCA in
the visible spectral range, or at least at 527 nm. Therefore,
the electron-related transitions within the conduction band
must be invoked, contrary to the predictions.6 The measured
FCA cross-section that is more than an order of magnitude
larger than the predicted one re ¼ 4.6 1019 cm2 is
ascribed to the isotropic conduction bands.9 The contribution
of direct inter-valence-band hole transitions cannot be
observed at 527 nm due to absence of appropriate valence
bands [see Fig. 2(c)].6
At high injection levels, the measured FCA cross sections
for kp ¼ 527 nm revealed anisotropic features and much
smaller reh values with respect to those measured under low
injection [Fig. 2(b)]. We note that the high injection reh values
measured at zero delay [reh\ ¼ 1.2 1018 cm2, rehjj
¼ 6.7 1019 cm2, and S ¼ r\/rjj ¼ 1.8, see Fig. 2(b)] are
close to the theoretical values for holes (rh\ ¼ 1.5 1018
cm2, rhjj ¼ 6.2 1019 cm2, S ¼ r\/rjj ¼ 2.4),6 thus indicating that interband transitions in the conduction band are fully
suppressed at high excess carrier densities. Moreover, at longer probe delays, reh values slightly increased and became
more isotropic [Fig. 2(b)]: at 4 ns delay, reh\ ¼ 1.8 1018
cm2, rehjj ¼ 1.3 1018 cm2, and S ¼ r\/rjj ¼ 1.4.
To understand these observations, we analyzed the rate of
nonequilibrium processes and the influence of high excess carrier density on the intraband transitions within the conduction
bands. Single-photon excitation at 351 nm provides a carrier
density of up to DN 1020 cm3 within a very thin photoexcited layer, d ¼ 1/a ¼ 0.1 lm, but ongoing rather fast diffusion
processes as well as the plausible absorption bleaching for
351 nm wavelength may expand the excited layer thickness d
up to a few micrometers.8 The injection-density (DN) dependent room-temperature bandgap, according to Ref. 10 is given
by Eg,opt(DN) [eV] ¼ 3.452 – 4.27 108 DN1/3 þ 0.082
(DN/1019)2/3, where the second and the third terms on the
right hand side represent the band gap renormalization
(BGR) and band filling, respectively. Consequently, for the
employed excitation wavelength of 351 nm (hm3¼3.53 eV),
the injected average carrier density for I0¼7 mJ/cm2 fluence
is limited to N*¼4.81019 cm 3 [assuming that Eg,opt(N*)
¼ hm3], and, therefore, carriers are distributed over
d ¼ 2.6 lm depth, since N* d ¼ I0/hm3. In order to obtain
the carrier density at 4 ns delay time [Fig. 1(b)], we fitted the
FCA decay rate using the relationship 1/sR ¼ 1/snonR
þ B(DN) DN and the measured nonradiative carrier lifetime of snonR ¼ 49 ns at low injection (see inset in [Fig.
1(b)]). The modeling of vertical carrier diffusion with varying diffusivity D(DN) and bimolecular recombination coefficient B(DN) values for the degenerate carrier plasma11,12
Downloaded 03 Jan 2013 to 193.219.83.91. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
022112-3
Ščajev et al.
provided a density of 2.6 1019 cm3 and an instantaneous
lifetime of 11 ns at 4 ns delay. As the hole effective mass is
some 10 times higher than that for electrons,10 band filling
and BGR impact the conduction band more by lifting it up
by 233 meV and shifting down by 155 meV, respectively,
[obtained from Eg,opt(DN) at DN ¼ N*]. Assuming that
higher energy electrons mostly contribute to interband transitions leads to detuning of the resonance transition energy
between lower and upper conduction bands at 2.5 eV (Ref.
6) and to vanishing electron-related contribution to reh (see
Fig. 2(c)). At longer probe delays, the impact of many-body
effects decreases with decreasing carrier density causing the
FCA cross-section to increase. Eventually, at the low injection limit (1017 cm3), the measured reh ¼ 8 10 18 cm2
value involves contributions from the isotropic electron
cross-section, re ¼ 7 1018 cm2, and the much smaller anisotropic hole cross-section, rh (1.2-0.7) 1018 cm2,
measured at zero delay [see Fig. 2(b)].
The fitting of rh in the 527-1064 nm range uncovered a
tendency of its fast increase in accordance with the relationship rh ! k-p, accounting both the anisotropy in effective
masses and relaxation times.6 Here, scattering by polar optical phonons would lead to p ¼ 2.5 (Ref. 13) whereas our fitting provided p values of 4.0 and 2.5 for E\c and Ejjc
polarizations, respectively. The discrepancy with the theory
for E\c polarization can be explained by band nonparabolicities and/or hole intervalence band transitions for 1053 nm.6
Injection independent rh at 1053 nm is verified by a linear
dependence of FCA vs. injection [as predicted theoretically13
and confirmed by our data, Fig. 1(a)] and vs. temperature (as
reported for E\c (Ref. 7)).
For measurements of the diffusivity, D, the carriers were
injected by two-photon interband transitions at 527 nm providing equal density of electrons and holes. The sample was
rotated by 90 to obtain the orthogonal or parallel orientations
of the grating vector K ¼ 2p/K (which is in the plane of grating recording beams) with respect to the c-axis. The refractive index spatial modulation Dn(x) by the injected carrier
density DN(x) ¼ N02P(1 þ cos(Kx))2, where x is the in-plane
spatial coordinate, creates a transient phase grating [Dn(x) !
DN(x)], on which the probe beam at 1053 nm diffracts and its
efficiency decays with g(t)! DN2 exp(-2 t/sG).14 The measured exponential grating decay time sG is used to obtain the
diffusive decay time sD ¼ 1/K2D through the relationship
1=sG ¼ 1=sR þ 1=sD for the given diffusion coefficient D,
grating period K ¼ 1.74 lm and a very long nonradiative carrier lifetime sR snonR ¼ 49 ns. Two-photon band-to-band excitation created holes and electrons with equal densities
DN ¼ DNn ¼ DNh, and the injected average carrier density
Nav ¼ 1.5 N02P was calculated according to Ref. 14. The
electrons and holes diffused together with the ambipolar diffusion coefficient given as:15 D(DN) ¼ (n0 þ DNn þ DNh)DnDh/
[(n0 þ DNn)Dn þ DNhDh], where n0 is the doped electron density and Dh and Dn are the hole and electron diffusivities,
respectively. Assuming that Dh Dn for GaN due to the large
hole effective mass, we determined the Dh value at low injections (DN n0) and the ambipolar diffusivity Da 2Dh at
DN n0. A fitting of experimental diffusivity data (Fig. 3) as
a function of Nav provided an average doping density of
n0 ¼ 2 1016 cm3 as well as hole diffusion coefficients of
Appl. Phys. Lett. 100, 022112 (2012)
FIG. 3. (Color online) Anisotropy of diffusivity in bulk m-GaN. For comparison, the D values for free-standing c-GaN (with dislocation density
5 105 cm2) revealed a slightly higher Dh\ ¼ 0.81 cm/s value due to lower
doping (n0 ¼ 8 1015 cm3).
Dh\ ¼ 0.76 cm2/s and Dhjj ¼ 0.65 cm2/s. For modeling the diffusivity at low injections, Dn values of 36 and 26 cm2/s were
used for c-plane and m-plane samples, respectively, based on
the reported electron mobilities16 and their relationship to diffusivity, Dn ¼ kTle/e.15 The experimental data provided a
17% anisotropy of the room-temperature hole mobility in
m-plane GaN for two orthogonal in-plane orientations. The
rather small anisotropy of mobility can be attributed to the opposite anisotropy of the light-hole and split-off valence
bands.9 In the m-plane GaN sample investigated, the acoustic
phonon scattering is dominant at room temperature, as the ionized impurity scattering reduces the mobility in m-GaN with
respect to c-GaN only by 7% based on the doping levels.
Thus, according to Ref. 17, a ratio of D\/Djj ¼ 1.35 was calculated, using the GaN valence band parameters.9 The calculated diffusion anisotropy is in satisfactory agreement with the
experimentally obtained value of D\/Djj ¼ 1.17.
In conclusion, we investigated the FCA anisotropy and
diffusivity in bulk m-plane GaN under low and high carrier
injection conditions. A strong hole-related FCA anisotropy
was observed at 1053 nm probe wavelength with the crosssection ratio of r\/rjj ¼ 6.5. FCA at 527 nm probe wavelength was isotropic and related to electron-transitions
between the lower and upper conduction bands. Strong
blocking of electron transitions at high injections due to
band filling and renormalization revealed the anisotropic features of hole-related FCA at 527 nm. Small anisotropy of
hole and ambipolar diffusivity was attributed to the opposite
anisotropy of the light-hole and split-off valence bands.
The research was sponsored by the Baltic-American
Freedom Foundation and Eureka E!4473 Project. Work at
VCU was supported by Grants from NSF and AFOSR.
1
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023705 (2010).
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022112-4
6
Ščajev et al.
E. Kioupakis, P. Rinke, A. Schleife, F. Bechstedt, and C. G. Van de Walle,
Phys. Rev. B 81, 241201(R) (2010).
7
P. Ščajev, A. Usikov, V. Soukhoveev, R. Aleksiejūnas, and K. Jarašiūnas,
Appl. Phys. Lett. 98, 202105 (2011).
8
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T. Malinauskas, K. Jarašiūnas, M. Heuken, F. Scholz, and P. Brukner,
Phys. Status Solidi C 6, S743 (2009).
Appl. Phys. Lett. 100, 022112 (2012)
For modeling, a lower B ¼ 0.3 1011 cm3/s was used with respect to a
low-injection one, B ¼ (2-5) 1011 cm3/s.
13
B. K. Ridley, Quantum Processes in Semiconductors (Clarendon, Oxford,
1999).
14
P. Ščajev, V. Gudelis, E. Ivakin, and K. Jarašiūnas, Phys. Status Solidi A
208, 2067 (2011).
15
J. F. Schetzina and J. P. McKelvey, Phys. Rev. B 2, 1869 (1970).
16
D. Huang, F. Yun, M. A. Reshchikov, D. Wang, H. Morkoç, D. L. Rode,
L. A. Farina, ç. Kurdak, K. T. Tsen, S. S. Park et al., Solid State Electron.
45, 711 (2001).
17
T. Kinoshita, K. M. Itoh, M. Schadt, and G. Pensl, J. Appl. Phys. 85, 8193
(1999).
12
Downloaded 03 Jan 2013 to 193.219.83.91. Redistribution subject to AIP license or copyright; see http://apl.aip.org/about/rights_and_permissions
Mater. Res. Soc. Symp. Proc. Vol. 1396 © 2012 Materials Research Society
DOI: 10.1557/opl.2012.497
Nonlinear Optical Techniques for Characterization of Wide Bandgap Semiconductor
Electronic Properties: III-nitrides, SiC, and Diamonds
Kęstutis Jarašiūnas1, 2, Ramūnas Aleksiejūnas1,Tadas Malinauskas1, Saulius Nargelas1, and
Patrik Ščajev1
1
Department of Semiconductor Optoelectronics, Institute of Applied Research, Vilnius
University, Saulėtekio al. 9-III, Vilnius, LT-10222 Lithuania
2
Department of Electrical and Computer Engineering, Virginia Commonwealth University, 601
W. Main Str., Richmond, Virginia 23284 USA
ABSTRACT
Combining interdisciplinary fields of nonlinear optics, dynamic holography, and
photoelectrical phenomena, we developed the optical measurement technologies for monitoring
the spatial and temporal non-equilibrium carrier dynamics in wide bandgap semiconductors at
wide range of excitations (1015 to 1020 cm-3) and temperatures (10 to 800 K).
We explored advantages of non-resonant optical nonlinearities, based on a short laser
pulse induced refractive or absorption index modulation (Δn and Δk) by free excess carriers. This
approach, based on a direct correlation between the electrical and optical processes, opened a
possibility to analyze dynamics of electrical phenomena in “all-optical” way, i.e. without
electrical contacts.
Carrier diffusion and recombination processes have been investigated in various wide
band gap materials - differently grown GaN, SiC, and diamonds - and their key electrical
parameters determined, as carrier lifetime, diffusion coefficient, diffusion length and their
dependences on temperature and injected carrier density. The studies provided deeper insight
into nonradiative and radiative recombination processes in GaN crystals, revealed diffusiondriven long nonradiative carrier lifetimes in bulk GaN and SiC, disclosed impact of
delocalization in InGaN layers, and suggested a trap-assisted Auger recombination in highlyexcited InN. Injection and temperature dependent diffusivity revealed a strong contribution of
carrier-carrier scattering in diamond and bandgap renormalization in SiC.
INTRODUCTION
During the last two decades, a significant progress in growth techniques paved a way for
development of novel device-quality wide bandgap semiconductors. The most prominent among
them are III-nitrides [1], silicon carbide [2], and diamond [3], all featuring some superior
characteristics for high power optical or electronic devices. Unfortunately, growth of these
materials up to now remains challenging, which inevitably leads to relatively high defectiveness
of the layers. Point and extended defects affect the dynamics of excess carriers, hence degrading
performance and reliability of devices. In spite of a huge experimental and theoretical effort,
many peculiarities of carrier recombination and transport processes remain unclear; especially
this is true for highly excited semiconductors, when conditions are similar to those in operating
high power devices.
In this article, we address this problem in III-nitride, SiC, and diamond semiconductors
by using two pump-probe optical techniques – Free Carrier Absorption (FCA) and Light Induced
Transient Grating (LITG). They are based on correlation between instantaneous density of
excess carriers and nonresonant modulation of complex refractive index; as a result, they allow a
direct and contactless observation of temporal and spatial evolution of injected carrier pattern.
Combined with versatility of nowadays lasers, pump-probe approach offers great flexibility of
experimental conditions, like a wide range of excitation wavelengths, delay times, excess carrier
density, etc. Exploiting the mention strengths of FCA and LITG, we managed to get a deeper
insight into nonradiative and radiative recombination and transport processes GaN, SiC and
diamond semiconductors. We also demonstrate a promising potential for investigation of carrier
dynamics in InGaN layers for light-emitting diode applications.
SAMPLES AND TECHNIQUES
The samples used in this study cover a wide range of wide bandgap materials grown in
different labs worldwide. A set of GaN layers with thickness d ranging from 10 to 145 μm was
grown on sapphire by hydride vapor phase epitaxy (HVPE) technique at TDI Inc.[4]. GaN layers
of d=80 μm on sapphire [5] and free standing one d=200 μm [6] were used to determine
nonradiative carrier lifetimes and their dependence on dislocation density, temperature, and
injected carrier density.
A 200 μm thick free standing cubic SiC layer was grown non undulant Si in a cold wall
low pressure reactor. The 3C layer was removed from the Si substrate by mechanical polishing
and chemical etching. The background carrier density was ~1017 cm-3 [7]. A low nitrogen-doped
3C layer (n0=1014–15 cm-3) with thickness of ~60 µm was grown on nominally on-axis 4H-SiC
substrate using the horizontal hot-wall chemical vapor deposition reactor at Linköping university
[8]. The grown-in ~30 mm2 size 3C-SiC islands were revealed by room temperature PL under
strong picosecond pulse excitation at 351 nm.
The 0.9 mm thick HPHT diamond layer [9] was of II a type with concentration of
nitrogen below 1017 cm-3, according to absence of characteristic absorption bands in 1000–
1500 cm-1 spectral range. The another sample was CVD grown 0.67 mm thick layer with very
low residual nitrogen density of about 5×1014 cm-3 [10].
A set of InGaN/GaN QWs was grown on c-plane sapphire by metal-organic chemical
vapor deposition (MOCVD). The nominal thickness of wells and barriers was 6 nm and 10 nm,
correspondingly. The ratio of TMIn/TMGa was varied from 0.5 to 2.6 for the growth of QWs
with different In content. In content in QWs was estimated from PL emission spectra and XRD
measurements and varied from 3% to 16% in different samples. The reference sample was grown
without In in the wells but keeping the same growth conditions. All samples were annealed insitu at 820 0C temperature for 20 minutes.
InN layers of 0.6 μm and 2.3 μm thickness were grown by molecular beam epitaxy
(MBE) on sapphire substrate [11] and typically had high background carrier density, (1–4)×1018
cm-3. The absorption spectra provided the bandgap values of 0.66 eV and 0.72 eV.
For investigation of carrier dynamics and determination of recombination rates and
diffusion coefficients in wide excitation range, we used powerful picosecond lasers. The Nd:YLF
and Nd:YAG lasers operating at 10 Hz repetition rate (Ekspla Co., LT) provided 12 ps and 25 ps
pulses at fundamental emission lines (10 mJ @ 1053nm and 30 mJ @ 1064 nm) as well as the
higher harmonics, up to the 5th one with 2 mJ @ 213 nm. The harmonics were used to realize an
interband carrier photoexcitation in GaN and SiC at λ3h=351/355 nm or λ4h=266 nm wave-
lengths, as well in diamonds at λ5h=213 nm. The high power of pulses allowed two-photon
excitation of bulk GaN and diamond crystals at λ2h =527 nm and λ3h=351 nm, correspondingly.
Time-resolved FCA [7–10], LITG [4–6,12] (Fig. 1) and standard photoluminescence
techniques were applied for investigation of spatial and temporal carrier dynamics. The LITG
technique paves the way for the determination of carrier diffusion coefficient and mobility, while
the FCA decay provides the carrier recombination times. The recombination and diffusion
processes were monitored by a delayed probe beam at longer wavelengths (1053 or 1064 nm).
The optically delayed (up to 4 ns) picosecond probe pulse at λ1=1053 nm was used to measure
the fast decay transients. For the measurement of longer relaxation tails (up to hundreds of ns in
the used crystals), an electronically delayed ~2 ns duration probe pulse from a diode-pumped
Nd:YAG was used [7]. The measurements were performed in the 80–800 K range.
Figure 1. Experimental setups of (a) LITG and (b) FCA techniques. For grating recording, a
holographic beam splitter (HBS) and lenses with focal lengths f1and f2 were used.
Light-induced transient grating technique
For grating recording, the excitation beam at wavelength λ2h,3h passed a diffractive
optical element (a permanent diffraction grating with a fixed spatial period), and the two first
order diffracted beams, intersecting at an angle Θ, provided an interference pattern with a period
Λ≈λ2h,3h/sin(Θ) in the sample [13]. The pump beam penetration depth under a single photon
excitation (1P), α-11P, was determined by the interband absorption coefficient, and the carrier
density near the surface was calculated as N01P=α1PI0/hν, where α is the interband absorption
coefficient, I0=(1–R)Iinc is the excitation energy density in the sample (in mJ/cm2), R is the
reflection coefficient, Iinc is the incident excitation density, and hν is the photon energy. Under
two photon excitation (2P), a value of two-photon coefficient β [cm/GW] and the excitation
beam instantaneous power density P(t)=2I0exp(-4t2/τ22h)π-1/2τ2h-1 [GW/cm2] determine the
+∞
generated carrier density N02P= ∫− ∞ βP(t )2 dt / 2hν =bI02/2hν. The factor b = β /(τ 2h π / 2 ) describes
a decrease of the incident fluence I(z) during propagation inside the crystal solely due to 2P
absorption:
I ( x, z ) =
I (x )
,
1 + bzI (x )
(1)
where I (x ) = I 0 [1 + cos(2πx / Λ )] (x is the direction of the grating vector K = 2π/Λ). Consequently,
the injected carrier density ΔN(z) slightly decreases with the depth z:
ΔN (x, z ) =
N 02 P [1 + cos(2πx / Λ )]2
(1 + bzI (x )) 2
.
(2)
The above relationships allowed us to calculate an average carrier density
Nav=1.5N02P/[1+bdI0] for various excitation power densities I0. The carrier density equals to N01P
and 1.5N02P near the excited surface (at 1P and 2P injection condition, respectively), and the
factor 1.5 is due to the nonsinusoidal profile of the grating at 2P excitation (see Eq. 2).
The generated carriers lead to a refractive index change, Δn=nehΔN, according to Drude*
Lorentz model [13], where neh = −e 2 λ12 / 8π 2 c 2 n1ε 0 meh
× E g2 / E g2 − (hc / λ1 )2 is the refractive index
(
(
)
)
change per one electron-hole pair, n1 is the refractive index for probe wavelength λ1, ε0 is the
vacuum permittivity, Eg is the GaN bandgap, and m*eh is the reduced electron-hole effective mass
[ 1 / m *eh = (1 / m *e + 1 / m *h ) ]. The following values were calculated for wide bandgap crystals for
nonresonant probing at λ1=1053 (or 1064) nm: for GaN, neh=-1.36×10-21 cm-3 using averaged
me=0.2 m0 and mh=1.5 m0, for diamond, neh=-5.8×10-22 cm3 using me=0.48 m0, mh=1.4 m0, and
for SiC, neh=-8.7×10-22 cm-3 using its reduced optical mass meh=0.24.
The refractive index spatial modulation Δn(x) creates a phase grating in the GaN crystal, on
which the probe beam diffracts with efficiency η(t):
2
⎛ 2t ⎞
⎛ 2πn eh N 02 P d ⎞
⎟⎟ exp⎜⎜ − ⎟⎟
η (t ) = ⎜⎜
λ1
⎝
⎠
⎝ τG ⎠
(3)
and provides the grating decay time τG:
1
τG
=
1
τR
+
1
τD
,
(4)
where τR and τD=Λ2/4π2D are the carrier lifetime and diffusive decay time for the given diffusion
coefficient D and grating period Λ. Equation 3 slightly overestimates the diffraction efficiency η
due to depletion of pump beam (i.e. I(z) and ΔN(z) ∝ I(z)2 vary with depth at two-photon
absorption conditions, see Eqs. 1 and 2); therefore, numerical calculations provided the η
decrease (with respect to Eq. 3) of more than 50 % at excitations above 15 mJ/cm2. The exact
value of the first order diffraction efficiency at arbitrary modulation profile Δn(x,z,t) was
calculated numerically according to relationship (5) [13] and used for fitting the measured
dependence η(I0).
2π
2
Λd
⎛ 2πx ⎞
η (t ) =
Δn(x, z , t )dz cos⎜
⎟dx .
∫
∫
λ1 0 0
⎝ Λ ⎠
(5)
For determination of D, the grating decay rates 1/τG were measured at least for two
different but small grating periods (Λ=1.74 μm and 7.8 μm) in order to separate the diffusive and
the recombinative contributions. The diffusive decay is always dominant at Λ=1.74 μm period
(according to Eq. (4)) and the corresponding τD≈0.3–1 ns was much shorter than the measured
carrier lifetime τR ≈ 10 - 100 ns for bulk GaN at 10–800 K, i.e. condition τR>>τD was satisfied,
leading to τG=τD. Moreover, the measured η value at a fixed excitation fluence (η∝ΔN2) allowed
determination of the two-photon absorption coefficient (see Eqs. (3) and (5)).
A deeper analysis of the FCA and LITG kinetics at injected carrier densities high excitations
was undertaken by the numerical solution of the nonlinear continuity equation [7]:
∂N (z , t )
ΔN (z , t )
= D(ΔN )∇ 2 ΔN (z , t ) −
− BΔN 2 (z , t ) − CΔN 3 (z , t ) + G (z , t ) ,
∂t
τR
(6)
delay, ps
20
200
1000
3400
7200
17
-3
ΔN (cm )
10
16
10
15
10
14
10
(a)
0
1
z (μm)
2
3
PL intensity/carrier density (a. u.)
where G(z,t) is the carrier generation rate, B and C are the bimolecular and Auger recombination
coefficients. The carrier density and its evolution was calculated assuming carrier injection by a
~20 ps laser pulse at 351 nm and using the boundary condition Da δΔN(0,t)/δz=SΔN(0,t) at the
front surface (z=0) and the determined D(ΔN) and τR values. The instantaneous carrier spatial
profiles ΔN(z) (see Fig. 2a) provide impacts of carrier diffusion and surface recombination.
(b)
τ = 40 ns
τ = 3.2 ns
0
10
FCA at 527 nm
LITG at 351 nm
PL at 266 nm
τ = 1.1 ns
-1
10
0.0
0.5
1.0
Delay (ns)
1.5
Figure 2. (a) Evolution of carrier depth profiles in bulk GaN after carrier injection to a thin
surface layer at 266 nm wavelength. Surface recombination velocity S=1.1×104 cm/s and D value
varying from the ambipolar D=1.6 cm2/s to the minority carrier one Dh=0.8 cm2/s were used for
calculations. (b) Comparison of carrier decay transients revealed by various optical techniques at
single photon (PL and LITG) and two-phonon (FCA) excitation conditions. The LITG decay is
given for grating period Λ=7.8 μm at high injection conditions, 2×1019 cm-3 at t=0, and leads to
decay time of 3.2 ns at t=1 ns (red dashed line). For comparison, FCA decay at 2P injection
conditions (1017 cm-3) indicates 40 ns lifetime (black dashed line, determined from FCA decay in
200 ns range [6]).
Diffusion expands the spatial profile up to 1–2 μm, thus surface-related recombination can be
seen as a fast initial transient in the measured FCA and LITG decay. Surface recombination is
strongly pronounced in GaAs and AlGaAs [14], where the S value reaches up to 5×105 cm/s. In
case of GaN and SiC, S impact is much smaller and overlaps with the contribution of
bimolecular recombination, also seen as the initial non-exponential decay. We note that the used
FCA and LITG techniques exploit infrared probe beam to integrate the carrier density over the
thickness, thus making them insensitive to diffusion coefficient value. On the other hand, timeresolved photoluminescence in direct bandgap materials is very strongly influenced both by
diffusion and surface recombination, if a very thin surface layer is photoexcited. The TR PL
technique also integrates the PL signal (Eq. 7), but reabsorption of emission allows only a thin 1–
2 μm layer contribute to the measured PL signal IPL:
d
I PL ∝ ∫ ΔN p (ΔN n + n0 ) exp(− α R z )dz .
(7)
0
Therefore, carrier escape by diffusion away from the PL controlled layer (in case the carrier
lifetime ensures the large diffusion length) is one of the main factors leading to fast PL decay
initial transients, which often are present in TRPL kinetics [15–17].
Free-carrier absorption technique
The FCA decay kinetics at 2P injection were used to determine carrier lifetime values τR
at various temperatures and excitation densities. The carriers were injected by a single Gaussian
beam, and the induced absorption transient, Δα(t)=σehΔN(t), was monitored via the
measurements of IR probe beam differential transmission [T0-T(t)]/T0∝1-exp[-Δα(t)d] [7]. At
two photon excitation, the following general equation describes the FCA decay:
ln(T0 / T (t )) = σ eh d
N 02 P exp(− t / τ R )
.
1 + bdI 0
(8)
The dependence of FCA signal on the injected carrier density (at t*=2τ3h≈24 ps, following
the excitation pulse) allowed determination of the free carrier absorption cross section
σeh=ln[T0/T(t=t*)]/(N02Pd). This relationship is valid for relatively low fluences (I0<10 mJ/cm2)
when the factor bdI0<<1. At higher I0, the depth-averaged carrier density for both FCA
(N*=N02P) and LITG (N*=1.5N02P) techniques was calculated taking into account the beam
depletion, as given above by Eq. 2 at 2P carrier injection.
EXPERIMENTAL RESULTS
The experimental investigations had a common goal to investigate fast nonequilbrium
processes in different materials, determine carrier recombination rates and diffusion coefficients
at various injected carrier densities and temperatures, and eventually disclose the factors which
govern these parameters in wide excitation and temperature range. Therefore, we used singlephoton (1P) and two-photon (2P) carrier excitation conditions in order to study carrier dynamics
in the ΔN~5×1017–5×1019 cm-3 (1P) and the 1015–3×1017 cm-3 (2P) ranges, correspondingly. The
thickness of the photoexcited region δ under 2P excitation was three orders of magnitude larger
(δ =α-12P ≈100 μm at 1 GW/cm2 power density) when compared to the 1P injection case (δ =α-11P
≈100 nm at 351 nm with a diffusion-expanded photoexcited region of a few micrometers, see
Fig.2a). Consequently, two-photon excitation increased the photoexcited thickness δ and ensured
detection of ΔN×δ , which is the measured quantity by these techniques. Thus, low excess carrier
densities at 2P excitation allowed to study nonradiative recombination processes and avoid
impact of many body effects, which may cause lifetime and diffusivity dependence on carrier
density. The latter dependences were studied at 1P injection conditions.
The measured dependences and determination of photoelectric parameters
80 K , τR = 9.8 ns
-1
10
300 K, τR = 40 ns
ln(T0/T)
800 K, τR = 122 ns
-2
10
(a)
0
100 200 300 400
Electrical Delay (ns)
Diffraction efficiency (a. u.)
The standard kinetics of induced FCA absorption and LITG efficiency decay are single
exponential and provide carrier lifetime values and diffusivity (see Eqs 4 and 6). In Fig. 3, we
present these kinetics in bulk GaN at different temperatures. In this way, the carrier lifetimeτR
dependence on T was determined in GaN (Fig. 5) as well in diamonds [9,18] at 2P excitations
and in bulk SiC at 1P excitation [8]). We note that an electronically delayed 2 ns duration probe
was used to measure FCA decay times above 5 ns (see Fig. 3a), whereas the optically delayed
picosecond pulses probed the fast decay transients (see Fig. 7). The LITG decay at small grating
periods (e.g. for Λ=1.74 μm in Fig. 3b) ensured solely diffusive grating decay with time
τD=Λ2/4π2D<<τR, which led to D value (as well its dependence on T or N, see Fig. 6).
80 K , τG = 0.24 ns
-2
300 K, τG = 0.50 ns
10
800 K, τG = 1.05 ns
17
Nav = 1.3×10 cm
-3
10
-3
Λ = 1.74 μm
-4
10
(b)
0
1
2
Optical delay (ns)
3
Figure 3. Kinetics of FCA decay (a) and LITG diffraction efficiency decay (b) in free standing
200 μm thick GaN under two-photon carrier injection.
Another characteristic of these nonlinear techniques is the dependence of the induced
optical signal (η or ln(T0/T)) on excitation beam energy density I0. These dependences in log-log
plot are power functions with a slope index γ, which points out to carrier generation rate (see Fig.
4): the FCA slopes are linear (γ=1, SiC) and quadratic (γ=2, GaN) at 1P and 2P carrier excitation,
while the γ values become doubled in diffraction characteristics, η vs I0. Moreover, the absolute
values of η(I0) allowed determination of the injected carrier density ΔN, based on the calculated
modulation coefficient neh (see Eq. 3). In turn, the FCA cross section σeh values were determined
by fitting the measured ln (T0/T) dependences for known ΔN values. The determined σeh value
for GaN and SiC and are given in Fig. 4.
0
GaN
γ = 1.95
-2
10
-3
10
1
(a)
cm
-17
cm
σeh=(2.5±0.5)×10
-5
10
-21
neh =1.34×10
2
I0 (mJ/cm )
-2
10
β =15 cm/GW
10
-1
10
γ = 3.6
-4
10
Diffraction efficiency, ln(T0/T)
Diffraction efficiency, ln(T0/T)
-1
10
-18
σeh (4H)=10x10
-18
σeh (3C)=4.1x10
2
cm
2
300 K
3C-SiC
4H-SiC
-3
γ=2
-4
neh (4H)=8.9x10 cm
-22
3
neh (3C)=8.5x10 cm
10
10
2
γ=1
FCA
10
3
cm
-22
LITG
1
(b)
2
I0 (mJ/cm )
3
10
Figure 4. Dependences of light-induced diffraction efficiency, η, and differential transmission
DT on excitation energy fluence, I0, in GaN under two-photon carrier injection and in 3C-/4HSiC at interband injection. neh, σeh stand for the refractive index and absorption coefficient
changes under carrier injection. The indices γ are the slopes of the curves in the log-log scale.
Lifetime and diffusivity dependences on temperature and injection
The very long lifetime values τR in bulk GaN at RT can be qualitatively attributed to very low
dislocation density in this crystal (5×105 cm-2 [19]), while the unusual lifetime dependence τR(T)
required a novel insight into the mechanism on nonradiative recombination (thermally activated
lifetime would lead to an opposite tendency). The monotonous increase in lifetime with
τR (ns)
γ=
15
1.
τinter
τdiff
d = 145 μm
d = 90 μm
d = 10 μm
γ = 0.93
10
τR ×10
τdiff=23/Da(T)
1
10
(a)
100
-3
cm
16
-3
ΔN = 3×10 cm
τinter + τdiff
τR (ns)
17
ΔN = 5×10
2
10
-3
τinter=4.1×10 T
2
10
2
a /Da(T) fits
3/2
3
T (K)
10
(b)
10
2
3
T (K)
10
Figure 5. Dependences of carrier lifetime on temperature in the bulk GaN at for two different
injection conditions: (a) at 2P injection providing low carrier density, indicated on the plot and
(b) at 1P injections for three different thickness HVPE layers. Fittings of τR(T) are shown,
accounting contribution of diffusion (τdiff∝1/D(T)) and interface defects (τinter∝T 3/2).
increasing T was observed in different quality GaN layers on sapphire [4], as well in thick cubic
SiC [8]. The observed inverse correlation between the measured τR(T) and D(T) (see Fig. 6a)
pointed out to impact of diffusion-limited recombination in bulk semiconductors. Numerical
fitting of these dependences by surface-limited lifetime (inversely dependent on D) at high
excitations [4] and of interface recombination (τinter∝1/S) at lower injections [6] confirmed that
the diffusive flow of carrier to internal grain boundaries of GaN hexagonal grains and subsequent
interface recombination at dislocations determine the nonradiative recombination rate in lowdefect density GaN. The extremely high carrier density ΔN resulted in enhanced recombination
rate due to bimolecular recombination (1/τR∝BΔN2) and revealed the enhanced carrier diffusivity
due to plasma degeneracy in GaN [5]. The experimental D(N) dependence was approximated by
D(N)=D0(1+N/N0) and parameters N0=2.2×1019 cm-3, D0=1.5 cm2/s [5]. Moreover, at moderate
injections, the decrease of D was observed in SiC and especially in diamonds (Fig. 6b). This
peculiarity was attributed to many-body effects which known to cause an enhanced carrier
scattering and bandgap shrinking, resulting in decrease of D in SiC [20,21]. D(N) dependence for
diamonds in wide excess carrier range (1015 to 1017 cm-3) was monitored under 2P carrier
injection at 351 nm and explained the observed nearly 10-fold decrease of D in diamonds at high
interband injections (using 213 nm wavelength [9,18]). In this way, LITG technique allowed
contactless measurements of high mobility values in diamond, previously accessed only by
electrical time-of-flight method.
1
2
10
0.1
(a)
D (cm /s)
2
Da (cm /s)
100
17
T = 300 K
10
15
n0= 6 x 10 cm
-3
-3
GaN, ~10 cm
16
-3
3C-SiC, ~10 cm
15
-3
HPHT diamond, ~10 cm
2
10
CVD diamond
HPHT diamond
3C-SiC
GaN
1
15
3
T (K)
10
15
n0= 9 x 10 cm
(b)
10
16
10
17
10
-3
18
-3
10
ΔN (cm )
19
10
Figure 6. Dependences of ambipolar carrier diffusivity in GaN, 3C-SiC, and diamond on
temperature (a) and injection (b). The modeled solid curves in (a) take into account only phonon
and defect scattering while in (b) also many body effects were included.
The low-injection conditions were found useful to get deeper insight into mechanisms of
carrier recombination in diamonds. The exponential FCA decays in 80–800 K range provided
carrier lifetimes increasing with temperature and saturating at 360 ns at T ≥300K [9].The latter
value was attributed to minority carrier lifetime governed by nitrogen defect with density
NN=3×1015 cm-3. Fast FCA decay transients were measured at relatively low injections, 1016 to
1017 cm-3 (Fig.7a), exhibiting a linear decrease of carrier lifetime with injected carrier density.
This feature of nonlinear recombination, (1/τ=B*(N0+ΔN)), was fitted with the coefficient
B*=4×10-9 cm3/s value at 800 K. Thus, the observed nonlinear recovery of traps recharged by
optical illumination follows the trap-assisted Auger recombination process (TAAR) with
coefficient B*=BTAAR= CTAAR×NTrap,, which requires presence of active deep trap density in mid1015 cm-3 [9] (origin of the traps needs further studies). Similarly, carrier dynamics in InN
revealed very fast nonradiative mechanism of recombination [11] which also followed the
similar tendency as in HPHT diamond. The measurements of FCA decay at various
photoexcitation densities ranging from 80 μJ/cm2 to 1.4 mJ/cm2 exhibited density-dependent
17
800 K
-1
Normalized ln(T0/T)
ln(T0/T)
τ=0.76 ns
10
-3
3.0x10 cm
16
-3
9.9x10 cm
16
-3
4.2x10 cm
16
-3
1.1x10 cm
τ=2.5 ns
τ=6.4 ns
0
(a)
1
2
2
18
-3
n0 = 1.4×10 cm
I (mJ/cm )
0.08
0.24
0.44
0.72
1.44
0.1
τ=23 ns
-2
10
InN
1
3
4
Optical Delay (ns)
*
-10
3
B = 4×10 cm /s
τ = 1.45 ns
0
(b)
150
300
450
Probe delay (ps)
Figure 7. Light induced absorption kinetics in HPHT diamond (a) and InN (b) layers under
interband carrier injection conditions
10
0
10
-1
10
-2
(a)
InxGa1-xN
2
excitation 50 μJ/cm
Λ=9.6 μm
3.56 ns
2.79 ns
2.71 ns
x=16%
x=15%
x=10.8%
x=7.9%
x=3.4%
x=0 %
0
1
2
3
Probe delay (ns)
2.17 ns
Lifetime (ns)
1
2
10
D (cm /s)
Normalized η (a. u.)
carrier lifetimes. Linear decrease of excess carrier lifetime with increase of photoexcited carrier
density allowed us to determine nonlinear recombination coefficient B. The measured
temperature dependence of B by using LITG has not revealed a feature of the bimolecular
recombination mechanism, for which the B value must follow T-3/2 law. The data obtained by
FCA and LITG techniques allowed us to propose that plausibly TAAR is the dominant
mechanism, which governs carrier recombination in highly excited InN layers at room
temperature. We note that the determined B* values varied with intrinsic carrier density N0 and
were equal to 4×10-10 cm3/s (in a sample with N0=3×1018 cm-3) and 3×10-9 cm3/s in another
sample with N0=4.7×1018 cm-3.
1.29 ns
1.06 ns
(b)
3
1
x=15%
x=10.8%
x=3.4%
1
0.1
0.1
12
Excitation energy density (mJ/cm )
Figure 8. LITG kinetics in InGaN QWs with different In content (a) and the determined values of
lifetime and D at various excitation fluences (b).
Fig. 8 (a) shows LITG kinetics recorded in InxGa1-xN quantum wells (QW) with varying
In content x. With increasing x, exponential decay with τR~1 ns for x=0.03 is gradually replaced
by non-monotonous one with fast and slow components. Intuitively, the latter tendency could be
attributed to longer carrier lifetime in high In-content QWs. However, more thorough analysis
proves that non-exponential decay is caused by carrier localization (and, probably, internal
electric fields), so the fast and slow components are related to recombination of carriers from
extended and localized states, respectively [22]. As a proof, Fig. 8 (b) shows diffusion coefficient
and lifetime measured in QWs of various x, as a function of excitation energy (i.e. excess carrier
density). For the lowest excitation, diffusivity drops and lifetime increases with growing In
content (e.g. compare D and lifetime at 0.05 mJ/cm2), as more carriers are captured into localized
states. Low mobility of these carriers prevents them from moving around and finding a nonradiative recombination center, which causes an increase in lifetime. As pump is increased,
localized states get gradually saturated and free carriers start to play relatively larger role in
recombination. At high pump, shorter lifetime in high In content QW reflects higher
recombination rate of free carriers due to higher concentration of defects. It has to be mentioned,
though, that internal electrical fields would give qualitatively similar tendencies as carrier
localization, thus these processes can not be fully distinguished by a single technique.
CONCLUSIONS
We reviewed time-resolved measurement techniques based on free carrier nonlinearities
and their implementation to monitor carrier lifetimes, diffusion coefficients, and ambipolar
diffusion length LD in various wide bandgap semiconductors. The latter value at room
temperature varied from ~35–70 μm (in HPHT and CVD diamonds) and 6–17 μm (in 4H- and
3C-SiC) to LD =2.4 μm in bulk GaN and LD = 0.8 μm in InN layers. Long nonradiative lifetimes
of ~40 ns in GaN were assigned to diffusion-limited recombination at internal grain boundaries
of hexagonal grains. Two-photon carrier injection allowed studies of carrier dynamics in wide
injection range and revealed density-dependent mobility decrease in SiC, and especially in
diamond. Linearly increasing with excitation recombination rates in diamond and InN were
attributed to trap-assisted Auger recombination process. Carrier transport features in LEDstructures is a promising area for studies by these time-resolved optical techniques. The
performed investigations confirmed a high capability of time-resolved optical techniques for
investigation of temporal and spatial carrier redistribution in advanced materials for electronics
and optoelectronics.
ACKNOWLEDGMENTS
The authors acknowledge fruitful collaboration with advanced research and technological
centers of wide bandgap materials at Linkoping University (Sweden), Ulm University
(Germany), TDI Inc. and Virginia Commonwealth University (USA), Nagoya Technical
University (Japan), Institute of Physics (Belorus), and Hasselt University (Belgium). Kęstutis
Jarašiūnas acknowledges financial support of the Baltic-American Freedom Foundation.
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Recombination and diffusion processes in polar and
nonpolar bulk GaN investigated by time-resolved
photoluminescence and nonlinear optical techniques
Kęstutis Jarašiūnas1, Patrik Ščajev1, Saulius Nargelas1, Ramūnas Aleksiejūnas1, Jacob Leach2,
Tania Paskova2, Serdal Okur3, Ümit Özgür3, and Hadis Morkoç3
1
Department of Semiconductor Optoelectronics, Institute of Applied Research, Vilnius
University, Saulėtekio Ave. 9, Bld.3, Vilnius, LT-10222 Lithuania
2
Kyma Technologies, Inc. 8829 Midway West Road, Raleigh, NC 27617, USA
3
Department of Electrical and Computer Engineering, Virginia Commonwealth University,
Richmond, VA 23284, USA
ABSTRACT
Optically-injected carrier dynamics were investigated in bulk polar and nonpolar GaN in 1015-to-1020 cm-3 carrier
density range, exploring single- and two-photon photoexcitation conditions. The excitation decay and recombination
rates were monitored by time-resolved photoluminescence and free-carrier absorption techniques, while diffusivity
was investigated by light-diffraction on transient grating technique. Carrier dynamics in c- and m-plane thick
freestanding HVPE GaN revealed nearly linear increase of carrier lifetime with temperature in the 80 - 800 K range
whereas the bipolar carrier diffusivity decreased with temperature. This feature suggests that the measured long
lifetime values of 40-50 ns at RT result from diffusion-governed carrier flow to interface defects at GaN hexagons,
which act as centers of nonradiative recombination. The fast PL transients under carrier injection to submicrometer
thick layer were fitted by using the determined diffusivity and lifetime values and revealed a strong impact of
vertical carrier diffusion, surface recombination, and reabsorption processes. Radiative and nonradiative emission
rates were analyzed by various optical techniques to discriminate contribution of excitons and free carriers at various
temperatures and injected carrier densities.
Keywords: gallium nitride, two-photon carrier generation, diffusion, recombination, free carrier absorption,
photoluminescence, transient gratings
1. INTRODUCTION
A reliable determination of nonradiative and radiative recombination rates remains an open question for
development of III-nitride materials even after decades of intensive studies. To address this very issue, investigation
of carrier dynamics as well the relevant optical techniques able to characterize fast electronic properties are on
demand. A wide arsenal of lasers with carrying pulse duration and wavelengths is available not only to generate
excess carriers, but also monitor their decay in different ways - by recording photoluminescence (PL) transients or
applying optical “pump-probe” techniques. The latter nonlinear optical techniques, based on strong correlation
between the electrical and optical phenomena open a possibility to analyze electrical processes with high temporal
resolution and without electrical contacts. Among various time-resolved “pump-probe” techniques, the light-induced
transient gratings (LITG) [1-3] and free-carrier absorption (FCA) [4,5] techniques have been found most
advantageous, as enabled access to carrier diffusion and recombination processes as well provided the direct and
reliable relationships between the measured nonlinear optical response of a material and the electrical parameters of
a semiconductor.
Particular interest in polar and nonpolar GaN stems from the wide range of application of nitrides in high
efficiency ultraviolet to green light emitting diodes and laser diodes, and high power/high frequency robust
electronics. In this work, investigation of carrier dynamics was performed on c-plane-200-μm and m-plane-450-μm
Gallium Nitride Materials and Devices VII, edited by Jen-Inn Chyi, Yasushi Nanishi,
Hadis Morkoç, Joachim Piprek, Euijoon Yoon, Proc. of SPIE Vol. 8262, 82620G
© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.906303
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thick freestanding HVPE GaN for a wide range of excitation intensities and temperatures. The excitation decay was
monitored by photoluminescence and free-carrier absorption (FCA) techniques, while diffusivity was investigated
by light-diffraction on transient grating technique (LITG). Interband carrier excitation was realized by laser pulses
at 266 and 351 nm (photon energy hν > bandgap Eg, single excitatation conditions) and at 527 nm (hν < Eg, two20
photon excitation conditions). In this way, injection range varied from 1015 to 10 cm-3, paving the way for study of
monopolar to bipolar carrier diffusivity as well as monomolecular (defect governed) and bimolecular interband
recombination processes. The temperature dependences of carrier lifetime and diffusivity were investigated by
different optical techniques to discriminate radiative and nonradiative recombination rates and get a deeper
understanding of the origin of the fast PL transients. Numerical modeling was found helpful to reveal a strong
impact of in-depth carrier diffusion, surface recombination, and reabsorption processes to the subnanosecond PL
transients. The value of bimolecular recombination coefficient B was determined from the carrier-density dependent
FCA decay. Radiative exciton lifetime, its temperature dependence, and dynamic interaction between the exciton
and electron subsystems is analyzed experimentally.
2. TECHNIQUES AND BULK GAN SAMPLES
For investigation of carrier dynamics and determination of recombination rates and diffusion coefficients in a wide
excitation range, we used powerful picosecond and femtosecond lasers. The Nd:YLF and Nd:YAG lasers operating
at 10 Hz repetition rate (Ekspla Co., LT) provided 12 ps and 25 ps pulses, respectively, at fundamental emission
lines (1053 nm and 1064 nm, respectively) as well as the higher harmonics. The harmonics were used to realize a
single interband carrier photoexcitation (at λ3h= 351/355 nm or λ4h=266 nm wavelengths) as well the interband twophoton excitation at λ2h =527 nm in GaN. For TRPL study, a standard setup of time-resolved PL spectroscopy was
employed using ~150 fs frequency tripled pulses from a Ti-Sapphire laser at λ=266 nm along with a Hamamatsu
streak camera.
Time-resolved FCA, LITG (Fig. 1a,b) and standard photoluminescence techniques (Fig. 1c) were applied for
investigation of spatial and temporal carrier dynamics. The LITG technique paves the way for the determination of
carrier diffusion coefficient and mobility, while the FCA decay provides the carrier recombination times. The
recombination and diffusion processes were monitored by a delayed probe beam at weakly absorbed longer
wavelengths (1053 or 1064 nm). The optical delay (up to 4 ns) of the picosecond probe pulse was used to measure
the fast decay transients. For the measurement of longer relaxation tails (up to a hundred of ns for the GaN samples
investigated here), an electronically delayed ~2 ns duration probe pulse from a diode-pumped Nd:YAG was used
[5]. The measurements were performed in 10–800 K range.
(c)
Fig.1. Experimental setups of LITG (a), FCA (b), and TRPL (c) techniques. For grating recording, a holographic
beam splitter (HBS) and lenses with focal lengths f1 and f2 were used. FCA setup explores an additional pulsed
Nd:YAG laser for probing slow decay components in carrier dynamics.
The measurements were carried on two thick freestanding HVPE-grown GaN wafers. A d = 450 μm-thick mplane sample was sliced from a 7-mm thick boule with an electron density of n0= 9.5 × 1015 cm-3 and threading
dislocation density NTD varying from ~1 x 106 cm-2 at the edge side to ~4 × 105 cm-2 at the front side of the boule.
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The second one was a d = 200 μm thick c-GaN sample with electron concentration n0 = 1.3×1016 cm-3 and mobility
μn = 1200 cm2/Vs.
In the case of interband carrier generation the light was strongly absorbed in a thin surface layer of thickness d=
1/α (approx ~100 nm in GaN) and the carriers have a strong gradient towards the depth, N(z). For two photon
excitation (2P), light at 527 nm was weakly absorbed and its large penetration depth d= 1/α2P ≈100-200 μm allowed
to neglect the near-surface effects. A numerical solution of the continuity equation (1) was used to calculate spatiotemporal non-equilibrium carrier dynamics N(x, z, t) at single and 2P-injection conditions and fit the PL, FCA and
LITG decay kinetics:
∂N ( x, z, t )
ΔN ( x , z , t )
= D(ΔN )∇ 2 ΔN ( x, z, t ) −
− BΔN 2 ( x, z , t ) + G ( x, z, t ) ,
∂t
τR
(1)
where G is the carrier generation rate, D is the diffusion coefficient, and A=1/ τR and B are the coefficients of linear
and bimolecular recombination, respectively.
3. EXPERIMENTAL RESULTS
3.1 Carrier lifetime measurements
The explored time-resolved FCA and LITG techniques monitor the dynamics of injected carrier density N(z),
integrated over the photoexcited layer of thickness z=δ (i.e. ∫ N(z)dz= N*(t)δ(t), which cause temporary changes of
absorption coefficient Δα =σeh N* and refractive index spatial modulation Δn(x) = neh N*(x). Consequently, the
probe beam monitors the differential transmission, ln(T0/T), or the diffraction efficiency of the grating (η (t) ∝
Δn(x,t)2 ∝ ΔN*2). In most experiments, the interband carrier injection by strongly absorbed beam was used and
provide a high value of N (up to 1020 cm-3) whereas in a very thin layer δ (below 1 μm in direct bandgap
materials). Τwo-photon (2P) absorption allows to increase the photoexcited depth thickness significantly, up to few
hundred μm. The increased δ value compensates the decreased N value at 2P conditions, which is a few orders of
magnitude lower, thus the integrated product N*(t)δ(t) provides high enough sensitivity of FCA an LITG
techniques to monitor carrier dynamics at low injections as well.
The used 2P carrier injection at 527 nm excitation wavelength provided carrier densities in the range 1015 to
1017 cm-3. Varying the probe-laser trigger delay Δt up to 300 ns electronically (see Fig. 1b), we measured FCA
decay kinetics, and the plot of ln(T0/T) vs. Δt (see inset in Fig. 2a) provided a carrier lifetime of 50 ns for bulk mGaN crystal at room temperature (RT). Similar lifetime values of 24-40 ns at RT were reported for bulk c-GaN
crystals [6,7] and attributed to nonradiative carrier capture by defects, located at internal boundaries of GaN
hexagonal grains. Temperature dependence of lifetime for m-GaN (Fig. 2a) revealed nearly linear increase in the 80800K range, at both low injection 2P excitation (527 nm) and single photon injection conditions (351 nm). In the
latter case, the injected carrier density was higher, but the slow FCA decay component also exhibited the lifetime
increase with temperature. The observed peculiarity of a steep increase of lifetime in m-GaN at T > 600 K (with
respect to c-GaN) is probably related to passivation of interface traps at grain boundaries, leading to a decrease of
interface recombination velocity. We note that this feature was not present at 351 nm excitation in m-GaN, as the
higher injected carrier density within a thin layer provided favorable conditions for the surface and bimolecular
recombination [8].
The fast recombination transients were investigated by LITG technique using optical delay of the picosecond
probe beam. The carrier dynamics at large grating period of Λ= 11.4 μm (see Fig. 2b) are governed by
recombination as the measured decay time of 6-8 ns is a few times shorter than the estimated diffusive decay time
of τD = Λ2/4π2D=20-24 ns. The initial decay component of 2 ns was observed in case of carrier injection to a very
thin layer (δ = 0.1−0. 2 μm at 266 nm) and can be ascribed to contribution of surface recombination time, τs= δ/S,
with the estimated upper limit of surface recombination coefficient S = 104 cm/s. Carrier diffusion from the surface
to the bulk will increase the depth and diminish the surface impact with time. At higher excitations, the even faster
initial decay component emerges; here, due to the linear increase of recombination rate with excitation this feature
can be attributed to the bimolecular recombination. Numerical fitting of carrier dynamics using Eq. (1) provided the
values of S=6×103 cm/s and bimolecular recombination coefficient B=6×10-12 cm3/s in GaN at RT.
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3.2 Optical measurements of carrier diffusion
For measurements of the diffusivity by LITG technique, we explored advantage of 2P interband carrier injection
providing equal density of electrons and holes (ΔN = ΔNn = ΔNh) and rater low injected carrier concentration (ΔN <
n0). The probe beam diffraction efficiency on the grating decays according to a simple relationship η (t) ∝ ΔN2 exp(2t/τG) [3] with rate 1 / τ G = 1 / τ R + 1 / τ D , reflecting both carrier lifetime τR and diffusive decay time τD = Λ2/4π2D.
Conditions of our experiment (grating period of Λ = 1.74 μm and a very long nonradiative carrier lifetime of τR ≈
τnonRad = 50 ns) ensured solely the diffusive grating decay (τD << τR) and a simple determination of D = Λ2/4π2τG.
ln(T 0/T)
-2
300 K
λex = 527 nm
10
τR, ns
100
-3
10
0
50 100 150 200
Delay, ns
γ
.1
=1
5
c-GaN, 527 nm
m-GaN, 527 nm
m-GaN, 351 nm
10
(a)
m-GaN
τ = 50 ns
Diffraction efficiency, a. u.
-1
10
100
T, K
1000
10
1
10
0
10
-1
10
-2
10
-3
m-GaN, Λ =11.4 μm, 266 nm
I0, mJ/cm
1.7
2
0.77
0.35
0.16
0.073
0.033
0.015
3
S = 6× 10 cm/s, B = 6× 10
0
(b)
1
2
Delay, ns
-12
3
cm /s
3
Fig. 2. (a) Temperature dependence of nonradiative carrier lifetime determined by FCA technique at various
excitation conditions. The inset in (a) shows FCA decay in m-GaN sample at two-photon carrier generation. (b)
LITG kinetics at 266 nm excitation for different excitation levels I0, modeled by using continuity Eq. (1) and S, B
values as given on the plot.
In the bipolar plasma, the electrons and holes diffuse together with the ambipolar diffusion coefficient [9]:
D(ΔN) = (n0+ΔNn+ΔNh)DnDh [(n0+ΔNn)Dn+ΔNhDh],
(2)
where n0 is the doped carrier density. Noting that the hole diffusivity is much smaller than that of electrons (Dh <<
Dn), the measurements in high excitation regime (ΔN >> n0) provided an ambipolar diffusion coefficient Da while at
low injection conditions (ΔN << n0) the measured value was very close to the minority carrier (hole) diffusivity Dh.
The experimental diffusivity data for the c- GaN and m-GaN samples (Fig. 2a) and the fitting as a function of
ΔN provided an average doping density n0 of 8×1015 and 2×1016 cm-3 for c- and m-GaN, respectively. At high
excitations, the bipolar diffusion coefficient of Da ≈ 2Dh= 1.6 cm2/s and hole mobility value μh = eDh/kT = 31 cm2/s
were determined. We note that the m-plane layer allowed variation of the grating vector orientation with respect to
the c-axis and determine the diffusion coefficient Da along the two orthogonal directions. Consequently, hole
diffusion coefficients of Dh⊥= 0.76 cm2/s and Dh||= 0.65 cm2/s were measured in m-GaN for diffusion perpendicular
to or parallel to the c-axis, respectively. A slightly higher Dh⊥=0.8 cm/s value in c-GaN is probably due to its lower
doping (n0 = 8×1015 cm-3) and lower dislocation density (5×105 cm-2). The experimentally measured diffusion
anisotropy ratio of 1.17 was found in satisfactory agreement with the calculated one of 1.35 in m-GaN [10].
A striking difference between these two bulk samples was a decrease of D value below the minority diffusivity
at low injected carrier density (see Fig. 3a). Our previous study of bulk crystals at carrier generation from deep level
states (e.g. EL2 in GaAs, vanadium in CdTe, etc [11,12]) have revealed a similar tendency of carrier diffusivity drop
down to value by an order of magnitude smaller than the Da. Photoexcitation of donor type traps by light
interference pattern and the electron diffusion along the grating vector creates a space-charge field between the
mobile carriers and recharged traps. This field opposes carrier diffusion, and thus, the grating diffusive decay by
drift current. At bipolar excitation conditions, the space charge field is formed between the electrons and holes and
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the carrier modulation decay is governed by bipolar diffusion (as the former built in field between mobile carriers
and ionized trap is screened). These processes seems to take place in m-GaN crystal and indicate presence of deep
midgap traps with a density of about (2-3)×1015 cm-3. Understanding the origin of these traps need more detail
studies. We note that presence of these traps was found also in intentionally doped HVPE grown n+ type bulk GaN
crystals, when 532 nm wavelength was used for carrier photogeneration [13].
1.6
1.4
⊥c
1.2
1.0
0.8
0.6
0.2
14
(a)
15
10
16
10-3
Nav, cm
2.4
1.8
c-GaN
17
-3
Da at 10 cm
15
-3
Da, theor at 10 cm
0.0
10
2Dnpo
2Dac
1.2
m-gan
c-gan
fits
0.4
2Dpop + npo
2
D, cm /s
||c
2
D, cm /s
4.8
4.2
3.6
3
T = 300 K
0.6
17
10
100
T, K
1000
(b)
Fig. 3. (a) Dependence of carrier diffusivity on injected excess carrier density (symbols- experimental data, lines – a
numerical fitting by Eq (2). (b) The measured temperature dependence of diffusivity D (symbols) and the modelled
one (red line). Theoretically calculated dependences for ambipolar diffusivity (Da = 2Dh, theor) account for acoustic
(ac), polar (pop) and nonpolar (npo) optical phonon scattering (black dashed curves).
For modeling of the measured diffusivity dependence on temperature (Fig. 3b), the equilibrium carrier densities
were calculated using a previously determined concentration of donors (1×1016 cm-3) and acceptors (2.4×1015 cm-3)
[14] with activation energies ED = 25 meV and EA = 140 meV. The concentration of free electrons vs. T was
calculated accordingly [15], revealing its decrease to 3.2×1015 cm-3 at 80 K and saturation above RT at n0 = Nd – Na =
8×1015 cm-3. In order to fit the dependence Da(T), temperature-dependent scattering rates (see Dh,theor in Eq. 3) were
used for acoustic, polar and nonpolar optical phonon scattering, according to equations [16] and appropriate
parameters for GaN [17,14] were used for Dh,theor calculation: static and optical dielectric constants εr(0) = 10.4,
εr(∞) = 5.43, density ρ = 6.1 g/cm3, longitudinal velocity v|| = 8 km/s, heavy and light hole density of states effective
masses mHH/LH = 1.9/0.33 m0 [18], polar and nonpolar optical phonon energies 91 meV and 80 meV, respectively
[19], and the acoustic and optical inter/intra-valley deformation potentials, Ca = 9.6 eV and Dii+jj = 1.34×109 eV/cm,
respectively. The dependence Da =2 Dh,theor was fitted by the empirical relationship 1/Dh,theor = 1/Dap+ 1/Dop, where
the Dap = 19.1×T -1/2 and Dop = 3.6×10-4×T[exp(–Eph/kT) – 1] correspond to acoustic and optical phonon (Eph = 91
meV) contributions, respectively.
At temperatures T < 150 K the spatial bandgap renormalization (BGR) created periodic potential for carriers
[20] and thus hindered carrier diffusion, leading to lower than calculated Da values (Fig. 3), as the given Dh, theor (T)
calculations do not account for contribution of BGR. The experimental data pointed out that BGR at 1017 cm-3
carrier density may create barriers of 12 meV, which hinder the diffusion at low temperatures. At very high
injections, the BGR in wide bandgap crystals may peak up to 100 meV at RT [21].
3.3. Comparison of temporal and spatial carrier dynamics
Comparison of Da(T) and τR(T) dependences (see Figs. 2a and 3b) pointed out strong correlation between the
diffusion and recombination processes in bulk GaN: a decrease of D led to increase of carrier lifetime. This
behavior was also observed in cubic SiC crystals, for which the extended defects are limiting the carrier lifetime
values [22]. In GaN, threading dislocations (TD) are well known as centers for nonradiative recombination, and a
correlation between the TD density and recombination rate was verified from carrier dynamics in epitaxial layers,
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grown on different substrates (Si, SiC, and sapphire) [8]. That study provided nearly linear dependence of carrier
lifetime on distance between the dislocations in highly defective layers with TD density > 108 cm-2 (Eq. 8).
τ R [ns ] ≈ 2.6 ⋅ 10 4 / N TD [cm −2 ]
(3)
The observed inverse correlation between D and lifetime resembles the case of diffusion-limited surface
recombination in a thin layer, when lifetime τS is dependent on the rate at which carriers diffuse from the
photoexcited layer of thickness 2d* to the surface (τdiff ∝ d*2/Da) and recombine there with rate 1/τsurf ∝S/d* (S is
the surface recombination velocity) [5]. Nevertheless, estimations for the studied 200-400 μm-thick layer provided
τdiff ≥ 100 μs which is far from reality for GaN with low diffusivity (Da = 1.6 cm2/s [10]). Therefore, diffusion to the
internal boundaries of GaN hexagonal grains [23] (assumed to be cylinders of radius rc for simplicity) must be
considered, and τsurf should be replaced with τinter, which depends on the interface recombination velocity Sinter.
Using this model wherein τSinter=τinter + τdiff = π-1/2rc/Sinter +π-3/2rc2/Da [6], the fit of the measured τR value at RT for cGaN provided rc = 3.6 μm and an effective interface recombination velocity of Sinter = 9500 cm/s at RT. Following
this model, we fitted the experimentally measured temperature dependence of lifetime (τR ∝ T 1.15), inclusive of the
defect related part, τinter ∝ T 3/2 , which corresponds to a capture of carriers by charged defects with their cross section
strongly dependent on temperature, σc ~T -2 [24]. Consequently, the interface recombination rate rapidly decreases
with temperature, 1/τinter =σcvthNtr ~ T -3/2, where vth ~T 1/2 is the carrier thermal velocity and Ntr is the interface trap
density. Therefore, the extended defects (dislocations) and associated point defects near the grain boundaries must
be assumed as effective “interface” centers of nonradiative recombination for the carriers reaching them by
diffusion. Further investigations of carrier dynamics with the technologically modified point defects at grain
boundaries will elucidate a way to passivate the dislocation-related centers of nonradiative recombination in GaN.
3.4. Analysis of fast decay transients probed by different optical techniques
Two sets of measurement were performed by TRPL technique in bulk GaN. For comparison of carrier dynamics in
the same crystals by different techniques, TRPL kinetics were measured at ~ 1018 cm-3 carrier injection by ~150 fs
pulses of 267 nm wavelength. The PL transients at RT revealed very fast initial decay (about 150 ps) which became
slower after 0.5- 1 ns. TRPL kinetics were compared with LITG decay at the same excitation wavelength while
using ~20 ps duration pulses, providing carrier densities up to 2 × 1019 cm-3. The experimental data are presented in
Fig 4a. Investigation of carrier dynamics under 266 nm injection was undertaken with the help of the numerical
solution of the Eq.(1) , using the boundary condition Da δΔN(0,t)/δz = SΔN(0,t) at the front surface (z = 0) and the
determined D(N) and τR values. The instantaneous carrier spatial profiles ΔN(z) are shown in Fig. 4b, providing
impact of carrier diffusion and surface recombination. For calculation of the PL transients, the intensity of the PL
emission was integrated over the excited layer thickness taking into account reabsorption of light emission αR [25]:
d
I PL ∝ ∫ ΔN p (ΔN n + n0 ) exp(− α R z )dz .
(4)
0
Comparison of carrier decay transients at single and two-phonon excitation condition indicates that only FCA at
2P excitation conditions directly provide carrier lifetime in the bulk. The LITG decay at 1P excitation conditions,
being insensitive to carrier diffusion to the depth (as the probe beam monitors the excess carrier density integrated
over the photoexcited layer thickness, which increases with time, see Fig 4b) reveals mainly the contribution of
bimolecular recombination, while the impact of surface recombination may also become noticeable at high injection
conditions, plausibly due to surface potential screening (in GaN, it may be as large as 1 eV [26]. Indeed, modeling
of LITG decay in m- and c-GaN revealed faster decay in c-GaN because of higher surface recombination coefficient
S= 6×103 cm/s.
PL decay was found very sensitive to both surface recombination and carrier diffusion to the depth, as PL signal
originates from the carriers located nearby the surface (in 1-1.5 μm thick layer), while the carriers brought by
diffusion to the larger distance from the surface become “invisible” to the PL technique due to reabsorption of
emission (see Eq. 3). Much slower decay rate of PL in m-GaN is attributed to its high surface quality achieved by
advanced chemical mechanical polishing, while the long-term self-oxidation of c-GaN surface after its growth
resulted in a higher S value (1.1×104 cm/s). We note that different surface recombination rates obtained from the
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3
τ = 40 ns
10
16
-1
0.0
c-GaN:
LITG
TRPL
0.8
Delay, ns
-3
16
10
τ = 1.1 ns
m-GaN:
TRPL
LITG
FCA
20
250
500
1000
2000
4000
n0=2×10 cm
-3
τ = 6.4 ns
10
Δt, ps
τ=50 ns
τ = 4.1 ns
-2
(a)
10
τ = 9.2 ns
0
10
S=6×10 cm/s
2
Dh=0.75 cm /s
17
ΔN, cm
PL intensity/carrier density, a. u.
modeling of carrier dynamics at different injected carrier densities (comparing LITG and TRPL decays) suggests
possibility of surface potential screening [5, 26] at injections above 1018 cm-3 in the case of LITG. Contribution of
bimolecular recombination at excess carrier density of 2×1019 cm-3 also lead to decreasing LITG decay time (τRad =
1/BΔN ) with excitation and its impact is clearly seen at excitations above 0.77 mJ/cm2 (see Fig. 2b).
15
10
1.6
0
(b)
1
z, μm
2
Fig. 4. (a) Comparison of TRPL, LITG and FCA decays. (b) Modeled carrier in depth distribution profiles at
different delays and TRPL excitation level I0 =1 mJ/cm2 For modeling , the following parameters were used: for mGaN, τnonr=40 ns, Da = 1.5 cm2/s, B= 6×10-12 cm3/s, S= 6×103 cm/s (for LITG decay) and S= 1.1×103 cm/s (for
TRPL); for c-GaN: τnonr=40 ns, Da = 1.6 cm2/s, B= 6×10-12 cm3/s, S= 4×104 cm/s (for LITG) and S= 1.1×104 cm/s
for TRPL. In m-GaN, impact of carrier density accumulation was taken into account via modeling TRPL decay after
8 excitation pulses with 12 ns repetition time (i.e. at conditions typical for Ti-sapphire laser operation).
These studies revealed the specificity of the PL kinetics, being strongly influenced by diffusion, reabsorption of
emission, and surface recombination (in case of not properly processed surface). These peculiarities may mask the
excitonic emission features which should be directly observed in PL kinetics even at RT. Therefore, we performed
further TRPL studies in the bulk m-GaN layer in wide excitation and temperature ranges for study of exciton-related
radiative emission features.
3.4. Analysis of PL decay transients
In order to study radiative decay in m-plane GaN, temperature and excitation intensity dependent TRPL
measurements were performed under 267 nm excitation (see Fig. 1c). Figure 5 shows PL kinetics at various
temperatures for the excitation energy density of 4µJ/cm2, providing 1018 cm-3 injected carrier density at the surface.
PL transients are composed of the fast initial component (~ 0.15 ns) which is followed by the slower decay, being
temperature dependent. The fast PL decay has been observed in previous TRPL studies of HVPE GaN performed at
similar conditions (267 nm excitation) and attributed to the surface recombination [27] or tentatively to diffusion of
free excitons away from the surface [28]. In this study, we show essential impact of free carrier diffusion in m-GaN
on fast PL decay transient (see Fig 4a). Fitting the PL longer decay transient by numerical modeling ( Eqs. 1 and 4),
the PL decay time τPL = 6.4 ns was obtained. Assuming that relationship (4) is valid, this value correspond to
radiative lifetime τRad = 2 τPL = 13 ns at RT.
We note that radiative PL decay times measured at two-photon injection conditions (using 527 nm for injection
of carrier density of 1016 cm-3 in the bulk) have been reported to be longer and varied from 2 to 17 ns at RT [29]. As
the latter measurements eliminated the impact of diffusion and surface recombination, these PL decay values at low
excitations were attributed to the exciton-related recombination mechanism. On the other hand, the reported
experimental value of lifetime τPL= 17 ns at RT was much shorter than the calculated one, τRad = 1/BN > 2 μs,
assuming a recombination coefficient of excitons B= (0.2-0.5) 10-10 cm3/s [17] and an exciton density of N =
1016cm-3.
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Moreover, the expected dependence of τRad on temperature, τRad ∝T3/2, in accordance to B(T) dependence [17,
27], has not been observed in time-resolved measurements up to now, thus questioning the origin of PL at RT
(except for Ref [27] providing the calculated τRad(T) dependence at T>50K, where the impact of bound excitons can
be neglected). Absence of a clear signature of excitonic emission in a wide range of temperatures may result from
exciton dissociation at elevated temperatures, screening of Coulomb potential by high carrier density at interband
injection conditions, as well as impact of shallow donor-like defects that may lead to dominating radiative
transitions involving free carriers (electrons and non-equilibrium holes). Our measurements of PL transients at
different excitation densities (0.04, 0.4 and 4 µJ/cm2) and two temperatures (10 and 300 K) were approximated by
double exponential decays (Fig. 6) and exhibited monotonous increase of τPL from 1.5 ns at 10 K to 4 ns at RT. The
increase of τPL ∝ τRad with increasing excitation followed a power function with index of 0.2, which can be attributed
to exciton screening at reaching carrier densities above Mott transition. The ratio of lifetimes for the highest and the
lowest excitation was equal to 1.90 at 10 K and 1.68 at 300 K, thus indicating that exciton screening is more
pronounced at lower temperatures. Comparison of PL spectra at 1018 cm-3 (4 µJ/cm2) and at ~ 15 times higher
injection by 20 ps laser pulse at 266 nm (see inset in Fig 6b) has not revealed spectral features confirming the
exciton-like recombination at 300K, whereas the bandgap renormalization pointed out to dominance of interband
free carrier recombination.
350 K (4.0 ns)
350K
300K
250K
200K
100K
50K
10K
PL Intensity (a.u.)
10 K (1.5 ns)
system
response
0
2
4
Delay Time (ns)
6
8
Figure 5. Temperature dependent time-resolved PL decay in m-GaN at 4 µJ/cm2 excitation density. System response
of 40 ps is also shown in the figure.
300 K
PL Intensity (arb. u.)
10 K
2
4 μJ/cm
2
0.4 μJ/cm
2
0.004 μJ/cm
2
4 μ J/cm
60 μ J/cm2
3.3
3.4 3.5
Photon
P hotonenergy
Energy ( eV) (eV)
2.9 ns
τPL=1.3 ns
2.3 ns
0.7 ns
0.8 ns
0
3
τPL=1.7 ns
6
0
3
Delay Time (ns)
6
Figure 6. Excitation density-dependent TRPL kinetics in bulk m-GaN at 10 K and 300 K. The inset in Fig 6(b)
shows PL spectra at 4 μJ (1018 cm-3) and 60 μJ (~1019 cm-3) excitations where the latter exhibits a ~11 meV red shift.
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CONCLUSIONS
Using various optical techniques we studied carrier dynamics in bulk c-plane and m-plane GaN at single- and twophoton carrier injection conditions. The photoelectric parameters, such as carrier lifetime, diffusion coefficient,
bipolar and monopolar mobility, and carrier diffusion length were determined for a wide range of excitation
densities and temperatures. The extremely long carrier lifetimes, varying from 40-50 ns at 300K and further
increasing with temperature up to ~100 ns correlated well with the diffusivity decrease, thus justifying diffusionlimited recombination rate in the bulk at grain boundaries of the extended defects. The unexpected drop of
diffusivity below its monopolar value indicated presence of residual deep defects in m-GaN. The subnanosecond PL
transients were found less pronounced in m-GaN with respect to c-GaN due to lower surface recombination, while
the initial fast decay in both crystals reveals unavoidable impact of diffusion at surface excitation conditions.
Temperature and excitation intensity dependent photoluminescence decay times have not provided evidence of
excitonic-related radiative decay at single-photon carrier injection conditions.
ACKNOWLEDGMENTS
Research at Vilnius University was partially funded by VU budget and Eureka Project E!4473. Virginia
Commonwealth University acknowledges support from AFOSR and NSF grants. K.J. acknowledges sponsorship of
the Baltic- American Freedom Foundation (BAFF). The authors are thankful for Dr. Miasojedovas at Vilnius
University for photoluminescence spectra measurements at very high injections.
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Spectral distribution of excitation-dependent recombination rate
in InGaN
K. Jarašiūnas*1, S. Nargelas1, R. Aleksiejūnas1, S. Miasojedovas1, M. Vengris2, S. Okur3,
Ü. Özgür3, H. Morkoç3, C. Giesen4, Ö. Tuna4,5, and M. Heuken4,5
1
Institute of Applied Research, Vilnius University, Vilnius 10222, Lithuania
Laser center of Vilnius University, Vilnius 10222, Lithuania
3
Department of Electrical and Computer Engineering, Virginia Commonwealth University,
Richmond, VA 23284, USA
4
AIXTRON SE, Kaiserstr. 98, 52134 Herzogenrath, Germany
5
GaN Device Technology, RWTH Aachen University, 52074 Aachen, Germany
2
Time-resolved optical techniques of photoluminescence (PL), light-induced transient grating
(LITG), and differential transmission (DT) spectroscopy were used to investigate carrier
dynamics in a single 50-nm thick In0.13Ga0.97N epilayer at high photoexcitation levels. Data in
wide spectral, temporal, excitation, and temperature ranges revealed novel features in spectral
distribution of recombination rates as follows: at low injection levels, an inverse correlation
of carrier lifetime increasing with temperature and diffusivity decreasing with temperature
confirmed a mechanism of diffusion-limited nonradiative recombination at extended defects.
Carrier dynamics in the spectral region below the absorption edge but ~70 meV above the PL
band revealed a recombination rate that increased with excitation, while recombination rate in
PL emission band (420–430 nm) decreased after saturation of trapping centers. Monitoring of
spectrally-integrated carrier dynamics by LITG technique allowed us to ascribe the enhanced
recombination rate to bimolecular recombination and determine its coefficient
B=7×10-11 cm3/s. Complementary measurements unveiled the cause of PL efficiency
saturation at injection levels above 5×1018 cm-3, attributable to bandgap renormalization in
the extended states above the PL emission band which encumbers carrier transfer from highto-low energy states. These results provided insight that spectrally-resolved carrier
generation-recombination rates are excitation-dependent and would play a critical role in
saturation of internal quantum efficiency in InGaN alloys used in light emitters, such as light
emitting diodes.
Keywords InGaN, carrier dynamics, recombination, diffusivity, photoluminescence,
transient gratings, differential transmission, bandgap renormalization.
*
Corresponding author: e-mail kestutis.jarasiunas@ff.vu.lt, Phone: +370 5 2366036, Fax: +370 5 2366037
1
I.
INTRODUCTION
Study of carrier dynamics in InGaN alloys and heterostructures allows determination
of recombination parameters in part in response to the fact that the origin of
photoluminescence efficiency degradation at relatively high optical (electrical) injections still
remains an object of studies. This is a rather complicated task due to overlapping effects of
carrier localization phenomena, presence of piezoelectric field, carrier leakage, and others in
effect. They collectively lead to injection-dependent interplay of radiative and nonradiative
recombination rates. Heretofore studies have been undertaken predominantly in InGaN/GaN
light-emitting diode (LED) structures to understand “efficiency droop” which has been
attributed to impact of Auger recombination, carrier delocalization, electron leakage out of
active region, and carrier asymmetry (for a brief review see [1-4]). While the two latter
effects seem to be more important for biased device structures, the two former ones may take
place under optical carrier injection, when carriers reside mainly in the wells. Consequently, a
more detailed study of carrier dynamics with temporal, spatial and spectral resolution is
required to reveal recombination and diffusion processes in InGaN alloys and
heterostructures under high injection.
To date, time-integrated (TI) and time-resolved photoluminescence (TRPL)
techniques have mostly been used for monitoring radiative recombination pathways and
evaluation of internal quantum efficiency in semiconductor heterostructures. The advantage
of PL based techniques that provide easy access to spectral features of emission is
encumbered by rather vexing interpretation of TRPL decay kinetics as their non-exponential
transients vary with injection and temperature because of simultaneous overlapping of
different recombination mechanisms (excitonic and free carrier, radiative and nonradiative).
A recent study of carrier dynamics in InGaN quantum wells using a number of optical timeresolved techniques has demonstrated the validity of excitation-enhanced nonradiative
recombination of delocalized carriers, while the impact of this effect to PL efficiency was not
disclosed [5]. Therefore, a deeper insight into any correlation of structural, optical, and
photoelectrical properties of nitride semiconductors requires not a single, but several
complementary spectrally, spatially, and time-resolved optical techniques for monitoring both
the radiative and nonradiative recombination mechanisms, carrier diffusion, and features of
these processes in a wider spectral region than the PL does, which is the subject matter of the
present manuscript.
Defect-insensitive emission has been intensively studied mainly in quantum well
structures of InGaN [6,7], wherein many factors contribute to enhancement of PL efficiency
(localization of holes and probably electrons at nanometer scale, screening of quantumconfined Stark effect, QCSE). At the same time, highly defective thick epitaxial InGaN films
(where polarization field is negligibly weak and indium fluctuation at the few nanometer
scale is unlikely) also exhibited high PL efficiency [8] and long nonradiative carrier lifetimes
[9]. In these quasi-bulk layers, studies of carrier dynamics have been limited, while their
investigation may clarify impact of larger scale inhomogeneities to PL efficiency
enhancement and its gradual loss at high injections.
Therefore, in this work, we focused on a detailed study of carrier dynamics in a single
InGaN layer. We applied linear and nonlinear optical techniques to investigate excitationdependent recombination rates in a 50-nm thick epitaxial layer of In0.13GaN alloy. Timeintegrated PL and TRPL spectroscopy allowed measurement of PL efficiency as well as PL
2
decay kinetics at various injected carrier densities. By exploring time-resolved DT spectra,
the narrow spectral range accessible by PL was extended well above the lowest band tail
states of InGaN alloy. LITG technique was used to probe spectrally-integrated carrier
dynamics with spatial and temporal resolution, thus providing directly the values of carrier
lifetime and diffusion coefficient. Consequently, a full set of data from complementary
optical techniques provided excitation energy density, spectral position, and temperature
dependent recombination rates in the epitaxial InGaN layer, allowed direct determination of
the bimolecular recombination coefficient, and unveiled causes of efficiency saturation of the
main PL emission band.
II.
SAMPLE AND TECHNIQUES
A 50-nm thick In0.13Ga0.87N epilayer was grown on a few-micrometer thick GaN-onsapphire template by using AIXTRON 3×2 Close-Coupled Showerhead reactor. A substrate
temperature of 732 oC and a chamber pressure of 200 mbar were used for InGaN growth.
Structural properties and the strain were studied by means of X-Ray diffraction (XRD),
Rocking curve and reciprocal space mapping (RSM) of (10–15) reflection, respectively.
Atomic force microcopy (AFM) was used for surface morphology investigation. The In
content of the layer was determined through XRD ω-2θ measurement with the aid of
simulations. The XRD spectra exhibited a sharp InGaN peak with very clear Fabry-Pérot
interfaces and with a narrow full width at half maximum (FWHM) of 400 arcsec for the
symmetric diffraction of (0002) revealing the high crystal quality of the InGaN layer. RSM
confirmed that the InGaN layer is fully strained. Simulation of XRD data yielded an In
content of 13%. The strain state of the InGaN layer was taken into consideration during the
simulation of XRD ω-2θ scan in order to achieve reliable In content. The AFM measurements
revealed a surface morphology dominated by terraces with a roughness of 0.8 nm and V-pits
with density of about 2.5×108 cm-2. The latter value for InGaN is comparable with that in
GaN layers suggesting that not many dislocations are formed at the InGaN/GaN interface
which propagate through the InGaN layer and manifest themselves as V-pits on the surface.
A standard PL spectroscopy setup was employed using ~150 fs pulses at 375 nm
wavelength (the 2nd harmonic of an 80 MHz repetition rate Ti-Sapphire laser) for selective
excitation of the InGaN layer. Using a spectrometer and a Hamamatsu streak camera, PL
spectra and kinetics were measured for injected carrier densities in the range of ~1016 to
1018 cm-3. To reach higher injections, e.g. up to 5×1019 cm-3, another setup with 20 ps pulse
duration at 266 nm (model PL2143, Ekspla) was used. In the latter setup, TRPL
measurements with 25 ps temporal resolution were performed using a Kerr shutter with
toluene.
The experimental setup for time-resolved DT is based on a commercial Ti:Sapphire
femtosecond amplifier (SuperSpitfire, Spectra Physics) delivering 800 nm pulses of 120 fs
duration at 1 kHz repetition rate. The output of the amplifier was split into two equal parts.
One was used to pump the optical parametric amplifier (TOPAS, Light Conversion) that
provided 120 fs pulses set to 330 nm wavelength (3.75 eV). The second beam was delayed
and used to generate white light continuum in a CaF2 window. The DT technique provided
means to observe evolution of DT spectra in 380–480 nm range with high temporal resolution.
LITG technique explores for excitation an interference pattern of two coherent beams
of a YLF:Nd3+ laser (PL2243, Ekspla) emitting 8 ps duration pulses at 1053 nm or a
3
YAG:Nd3+ laser (PL2143, Ekspla) emitting 25 ps duration pulses at 1064 nm. The 3rd or 4th
laser harmonics were used for recording the transient spatially-modulated free carrier pattern
N(x)=N0+N[1+cos(2x/ with spacing , which modulates the refractive index
n(x)N(x) and diffracts a delayed probe beam at 1053 nm. Diffraction efficiency of the
grating, , and its decay, (t)=(2nehNd/probe)2exp(-2t/G), where neh is the refractive index
change per one electron-hole pair and d is the layer thickness, provided a convenient way to
discriminate the recombination-governed grating decay time R and the diffusive decay time
D, according to the relationship 1/G=1/R+1/D. Measurements of grating period
dependent diffusive decay time D=2/(42Da) were used for determination of the bipolar
diffusion coefficient Da [10]. The measurements were performed at various photoexcited
carrier densities (~1018–5×1019 cm-3) and temperatures (80 to 300 K).
III. RESULTS AND DISCUSION
A. Characterization by PL techniques.
Time-integrated room-temperature PL spectra were measured at low excitations
(I0≈6–10 J/cm2) using selective excitation at 375 nm (150 fs pulses) or at 266 nm (25 ps
pulses). The emission line for the InGaN alloy with 13 % In content was positioned at
424±6 nm at FWHM (2.922±0.040 eV). TRPL kinetics at relatively weak selective excitation
of the InGaN layer (in the 1016 to 1018 cm-3 range) revealed increasing PL decay times with
increasing injection (Fig. 1), thus indicating a gradual saturation of nonradiative
recombination centers. This tendency was also verified by a change of the power index, of
PL intensity dependence on excitation density, IPLI0. Its plot in log-log scale (Fig. 2)
revealed the change from  to 2 at a carrier density of 1017 cm-3 at room temperature.
After the saturation of trapping centers, the nonradiative carrier lifetime became constant and
PL intensity increased quadratically with injection ( The latter value is indicative of
the fact that the injected electron and hole density Ne,p is larger than the residual electron
concentration n0, thus Ne=Np>n0 and PL intensity increase follows the relationship
IPL(n0+Ne)NpI02. We note that at 10 K the change of index  (from ~1.5 to 1, see Fig. 2)
takes place also at the same carrier density as for RT (i.e. after the trapping centers – the
residual acceptors with density of about 1017 cm-3 become saturated). At these conditions,
two factors ensured the radiative PL emission being dominant: (i) the coefficient of radiative
recombination B essentially increases at low temperatures (BT –3/2) [11] and (ii) excitonic
nature of emission dominates due to relatively high exciton binding energy, leading to
IPL~Bexnex [12] and thus providing the typical slope value.
Excitation of the sample by picosecond pulses at 266 nm wavelength enabled us to
reach excess carrier peak densities up to 1020 cm-3. At these high-excitation conditions, the
backscattered PL spectra revealed only the features of spontaneous emission, while the
underlying GaN layer showed both the spontaneous (at ~3.4 eV) and stimulated emission
(SE) at ~3.32 eV. The absence of a clear SE peak from InGaN layer is typical for
luminescence in case of spatial fluctuations of In content [13], thus only a slight narrowing of
the emission peak above a threshold density of 0.33 mJ/cm2 was observed. Nevertheless, a
very fast decay transient of PL (temporal shape of which repeated the laser pulse) confirmed
the presence of SE. Further measurements of InGaN luminescence were performed using thin
stripe excitation and edge emission detection [13]. The dependence of PL intensity on
4
excitation (Fig. 3) revealed the presence of SE with its threshold at I0≈0.1 mJ/cm2. The
increase of up to 3.7 was observed at an excitation density above the SE threshold, while
further increase in excitation led to saturation of luminescence intensity due to limited
number of excited states. 
Knowledge of the SE threshold allowed us to limit the further measurements of carrier
dynamics in InGaN epilayer up to this level (0.1 mJ/cm2), until the non-equilibrium processes
reveal the peculiarities of spontaneous emission. We present below investigation of the
recombination and transport features by using techniques of differential transmission (DT)
and light-induced transient gratings (LITG).
B. Differential transmission spectroscopy
The PL spectroscopy allows access only to the limited spectral region of radiative
emission from localized states, while a large Stokes shift in InGaN epilayers and QWs,
linearly increasing with In content [14] suggests that there is a broad spectral distribution of
localized and extended states. For the In0.13GaN layer investigated here, a 125 meV Stokes
shift is expected [14]. Consequently, the emission peak at 2.922 eV predicts an effective
bandgap energy of EB≈3.05 eV for this alloy. As PL emission originates from the lowest
energy states near the band tail, where the density is lower than that in the extended states,
the spectrally and temporally resolved DT measurements are needed to reveal the excitation
relaxation dynamics of all available states, and especially of the states above the mobility
edge, which will be occupied after filling the band tail states under strong excitation
conditions (but still below the SE threshold).
To explore the full spectral range and determine spectrally-dependent relaxation rates,
we performed spectrally and temporally resolved DT measurements in wide spectral (390 to
440 nm) and excitation range (4 to 520 J/cm2). In Fig. 4 we present DT spectra measured at
10 ps and 1 ns after photoexcitation. The DT spectra are blue shifted with respect to those
obtained by PL. This shift is ascribed to relatively larger density of higher energy states
contributing to the absorption bleaching. The FWHM of DT spectra is rather narrow
(~60 meV), but it broadens towards the blue energy wing due to temporary filling of
extended states at higher excitations. The spectral broadening is followed by faster relaxation
rates, and the DT spectra becomes symmetric after 1 ns (Fig. 4). Spectrally-integrated DT
kinetics within 390–440 nm range exhibit faster decays with increasing excitation fluence (I0).
The fast decay transient lasts only 1–2 ns and follows 1/I0 dependence, thus indicating shorter
average carrier lifetimes in higher energy extended states than in the lower ones. The
question then is whether the increasing decay rate is caused by transfer of delocalized and
thus more mobile carriers to lower energy states or whether it is due to increasing
recombination rate in extended states with excitation. In order to entertain an answer, we
determined decay times of DT spectral components as well as their injection-dependences. In
Fig. 5 we present spectrally-resolved DT kinetics at various excitation energy densities (in the
range from 10 to 300 J/cm2) for two spectral positions, corresponding to the central line of
PL peak (425 nm) and of DT blue wing (414 nm). In the spectral range of PL, the lowinjection DT decay is fast but slows and saturates with excitation, exhibiting DT=1.5 ns
decay time (similarly to PL decay times at RT, see Fig. 1). Despite the fact that the DT
measurements were performed at excitation energy densities up to 300 J/cm2 (i. e. by more
5
than an order of magnitude higher than the selective photoexcitation of PL up to 17 J/cm2),
the DT kinetics did not reveal any faster recombination transient at 425 nm, which would
confirm the PL radiative recombination being dominant. The observed long DT decay at the
blue wing (at low excitations DT equals to 6–8 ns, which is 10-times longer with respect to
DT decay in the PL window) does not support the common tendency of increasing PL decay
rate at the high energy wing. Moreover, the DT decay time at the blue wing decreases with
injection in the 30–100 J/cm2 range. Fig. 5c summarizes the variation of carrier lifetimes in
the spectral range from the PL emission band up to absorption edge and their dependence on
injected carrier density. The data clearly show that the spectral interval of ~415 nm (i.e.
~70 meV above the PL peak) is favorable for carrier accumulation at low injections.
Consequently, prolonged carrier lifetime in the blue-wing of extended states and their
subsequent faster decay at higher injections may strongly impact the PL characteristics
indirectly. Namely, at low injections this wing plays the role of a reservoir to accumulate
injected carriers to be transferred to the lower energy states responsible for the PL emission,
while at higher injections the fast recombination rate in this wing consumes the carriers
locally and diminishes their delivery to the PL band most likely due to bandgap
renormalization, as will be discussed below. It is worth to note that the injection-enhanced
DT decay at blue wing starts at I0=20–33 J/cm2 (5×1018 cm-3) (as can be seen both in
spectrally-resolved kinetics (Fig. 5a,b) and spectrally-integrated ones) and lasts for about 1 ns,
while at later times it slows to values typical for low-injection (6–8 ns for N1018 cm-3). As
the DT technique in the vicinity of absorption edge monitors the overall decay rate, which is
equal to the sum of the recombination rate and carrier transfer rate to the lower energy states
[15], it is difficult to judge about the mechanism for enhanced decay rate in the blue wing. In
general, the faster decay at high injection is attributed to increasing radiative recombination
rate of localized carriers or excitons (especially in QWs [16]). Hypothesis of excitationenhanced defect related recombination has also been provided [4] within the framework of
carrier delocalization in QWs. Moreover, screening of the potential barriers around deep
charged defects [7] at high injections may reduce the effective barrier for diffusive carrier
flow to electrically active dislocations. Therefore, for a deeper understanding of carrierdensity dependent effects in InGaN alloy we performed complementary measurements of
carrier recombination and diffusivity in a wide excitation and temperature range, using the
picosecond light-induced transient grating (LITG) technique.
C. Characterization by light-induced transient gratings (LITGs)
Time-resolved LITG technique allows direct monitoring of excess carrier dynamics
and determination of excitation-dependent carrier recombination rates. It provides nonresonant probing of light-induced refractive index modulation, n, at wavelength well below
the bandgap (1064 nm) [17]. Under these conditions, linear dependence of n on spectrallyintegrated nonequilibrium carrier density N makes the analysis of LITG characteristics
relatively simple [18]. The probe beam diffraction efficiency  of the TG depends
quadratically on injected carrier density, N2(t)×exp(-2t/G). Single exponential kinetics
of LITG at various grating periods allow determination of the carrier lifetime R and diffusion
coefficient D. If, however, the lifetime or diffusivity is dependent on carrier density, the
grating decay becomes nonexponential [19]. Another measurable characteristic is the
6
dependence of grating diffraction efficiency  on the excitation energy density, I0. The
latter dependence is a power function with the index value which equals to 2 at linear
generation and recombination rates. However, excitation-dependent changes in carrier
generation or recombination rates will lead to change of the index value [20].
Decay kinetics of LITG (at =12 mfor excitation energy densities in the range of
10–300 J/cm2 revealed a nearly single exponential decay with a characteristic time
G=R=1.55 ns only at the lowest injection used (10 J/cm2). At higher excitation levels
(above 5×1018 cm-3 at the front surface of the layer), the fast decay transient emerges in 1–
2 ns time interval characterizing the excitation-enhanced recombination rate. At
I0=300 J/cm2, a very fast decay component appears which follows the laser pulse of width
25 ps, thus indicating stimulated decay of emission (SE). The latter feature was also observed
in PL decay at similar injection levels.
Comparison of excitation dependences for InGaN/GaN layers at various delay times
t (Fig. 6) revealed some important features in injection-dependent recombination rate. For
the InGaN layer under investigation, gradually decreasing index value γ in the I0= 10–
100 J/cm2 range points out that the carrier lifetime in InGaN becomes dependent on injected
carrier density. In contrast, the index value γ=2 for underlying GaN layer (in the range
I0=0.4–1 mJ/cm2) remains constant up to the threshold of stimulated emission (5×1019 cm-3).
This behavior has been observed in other MOCVD-grown GaN layers as well [21] and can be
explained as follows: the radiative recombination rate rad=1/BN in GaN increases with
excess carrier density, but its impact is masked by a faster nonradiative recombination rate.
Thus more sensitive response of InGaN layer to the excitation suggests a higher radiative
recombination rate and requires numerical modeling of carrier dynamics.
In order to carry out the above mentioned numerical modeling, the excess carrier
density and the absorption coefficient at 355 nm for the InGaN layer are needed. The latter
was determined from the measured dependence of (I0) (Fig. 6). Here, the diffraction
efficiency from InGaN layer saturates near the SE threshold, and the subsequent increase of 
at I0>300 J/cm2 is due to contribution of the grating recorded in the underlying 2 m-thick
GaN layer (we note that the diffraction efficiency from the GaN layer, GaN, also saturates
when the SE threshold of 1.5 mJ/cm2 is reached). Extrapolation of GaN(I0) to the low
injection range (see the solid line in the inset of Fig. 6) characterizes the ratio of diffraction
efficiencies from both InGaN and GaN layers (InGaN/GaN=1/2=5.2) as well the ratio of
excess carrier densities (InGaN/GaN=2.3), integrated over the depth of the layer. From these
results, an absorption coefficient of 1.6×105 cm-1 was calculated at 355 nm and used for
calibration of the excess carrier density in InGaN: for I0=10 J/cm2, NInGaN is equal to 2
×1018 cm-3 at the front surface of the layer.
A deeper insight into the enhanced recombination mechanisms requires measurements
of temperature-dependent recombination rate and diffusivity in the InGaN layer. The LITG
decay was measured at small grating periods to ensure diffusive grating decay and determine
the values of D and lifetime R at carrier densities as low as 2×1018 cm-3. An inverse
correlation between the decreasing bipolar diffusion coefficient (DT-1/2) and increasing
lifetime with T (RT1/2) is observed (Fig. 7a), confirming that the nonradiative lifetime
values of 0.15–1 ns in the 50 nm-thick InGaN layer are determined by carrier diffusion to
7
dislocations and associated point defects. Similar mechanism of diffusion-limited
recombination rate was observed in HVPE-grown GaN layers, leading to nonradiative carrier
lifetimes in range from 0.4 to 40 ns at 300 K [10,22]). We note that the typical recombination
rate via point defects would follow the relationship 1/RT1/2, according to Shockley-ReadHall (SRH) recombination model: 1/R=NTvth, where vthT1/2. The observed opposite
tendency in the investigated InGaN layer strongly supports the dominant role of extended
defects, as centers of nonradiative recombination. As for the mobility, its temperature
dependence followed the well-known relationship T-1.45, confirming the mechanism of
carrier scattering by acoustic phonons. At half injection level (30 J/cm2) the decreased
power index (T-1.2) indicates contribution of additional scattering, presumably by charged
defects. Our observations suggest that screening of charged defects at relatively higher
injection levels may lead to enhanced diffusivity, and thus to shorter nonradiative lifetimes
(according to the dependence displayed in Fig. 7). Note that we experimentally observed
decreasing lifetimes with excitation at RT (Fig. 8) but not an increase of D vs N (Fig. 7b).
Absence of the latter dependence is probably due to compensation by a more dominant effect
such as the bandgap renormalization (BGR), which is the strongest in the induced grating
peaks and spatially modulates the bandgap Eg, thus diminishing the D value (Eg may reach
18 meV in GaN at 1019 cm-3 [10]). On the other hand, increase of both carrier diffusivity and
bimolecular recombination rate may take place when the degenerate plasma density limit is
reached [19].
D. Determination of InGaN bimolecular recombination coefficient
Contribution of bimolecular recombination was analyzed by numerical fitting of the
experimentally measured set of LITG decay kinetics at various injected carrier densities
(Fig. 8) and temperatures in the 10–300 K range (Fig. 9). For modeling of spatial and
temporal carrier distribution, we refer to the continuity equation [23]
N x, z, t 
 DN  2 N x, z, t   AN x, z, t   BN 2 x, z, t   Gx, z, t 
t
(1)
where G(x, z, t)=I0(1-R)×exp(-z) is the carrier generation rate in InGaN layer, D is the
ambipolar diffusion coefficient, A=1/R and B are the SRH and bimolecular recombination
coefficients. The required modeling parameters 1/R(T) and D(T) for the investigated InGaN
layer were measured at low injections (Fig. 7a), and the absorption coefficient
=1.6×105 cm-1 at the excitation wavelength of 355 nm was determined as described above
from the data in Fig. 6. Therefore, only one adjustable parameter, B, was used to fit the sets
of LITG decay rates. Numerical solution of N(x, z, t) was used to calculate instantaneous
profiles of N(z, t) and diffraction efficiency (t)=N2(t)dz, which in turn was
experimentally measured. The data of (t) vs I0 provided B=7×10-11 cm3/s value at RT and its
temperature dependence BT –3/2 in 100–300K range. The determined B value is slightly
larger than that for bulk GaN (B=2–5×10-11 cm3/s) but very close to those for InGaN quantum
wells (B=(7–10)×10-11 cm3/s) with 10% of In [16, 24]. The decreased value of B at T<100K
(see inset in Fig. 9) can be a consequence of many-body effects in high-density carrier plasma
which are more pronounced at low temperatures and may lead to saturation of radiative
recombination rate at densities above 1018 cm-3 [16, 25].
8
E. Analysis of carrier dynamics measured by different techniques
To reiterate measurements by TRPL and DT techniques under selective excitation of
InGaN layer allowed comparison of nonequilibrium processes in various spectral regions
below the absorption edge. Let us discuss first the processes in the PL spectral window,
which are commonly investigated for evaluation of the internal quantum efficiency. Gradual
saturation of the nonradiative recombination centers at injections up to 30 J/cm2 was
verified by longer decay times of PL and DT@425nm (nevertheless, NonRad<<Rad remained
valid). The decreased nonradiative recombination rate was favorable for increase of PL
efficiency up to the threshold of stimulated emission, while the PL increase was linear up to
20 J/cm2 (Fig. 2) and sublinear up to SE threshold (Fig. 3). It is important to note that
DT@425nm decay time of 1.5 ns saturated at I0=30 J/cm2 (i.e. at a similar level as that for
PL) and did not decrease with increasing excitation energy density up to I0=300–520 J/cm2.
Under these conditions, the estimation based on the determined value of B=7×10-11 cm3/s and
excess carrier density of 3–5×1019 cm-3 resulted in Rad=1/BN=0.3–0.6 ns and, thus, predicted
the subnanosecond DT@425nm decay time at 300–520 J/cm2: DT=1/(1/NonRad+1/Rad).
This discrepancy calls for the need for a more explicit approach to evaluate the spectral
density of excess carriers at excitations above 30 J/cm2. After filling of the lowest states in
the conduction and valence bands (this is clearly seen from DT broadening towards the highenergy wing in Fig. 4a), the absorbed fluence starts to create carriers in a much wider spectral
range. Therefore, generation rate to PL spectral window is expected to decrease gradually
with excitation. To verify this premise, we compared dependences of DT signal on excitation
density (IDTI0, Fig. 10), spectrally-integrated over the PL spectral range (420–430 nm,
DTPL) and over all the spectral range of photoexcited states (390–430 nm, DTfull). The
decreasing ratio of DTPL/DTfull at I0>33 J/cm2 (N>6.7×1018 cm-3) pointed out to decrease
in carrier density available for PL emission, which may cause the gradual saturation of PL
intensity vs excitation. Comparison of the calculated DTPL integral with experimentally
measured dependence of PL intensity on excitation energy density (Fig. 2) discloses rather
similar features such as the initial steep increase of IPL with excitation (due to trap saturation),
then quadratic increase of PL (=2 in Fig. 2, which corresponds to the linear growth of DTPL)
[26], and the ongoing slower growth IPLI01.5 at high injections (Fig. 3).
The observed decrease in the carrier generation rate in the spectral region of PL
emission is critical for understanding the origin of PL saturation at high injections, i.e. what
eventually leads to lower IQE values. This drawback is a consequence of nonequilibrium
processes in extended states above the PL emission band, which are expected to transfer the
photoexcited carriers without significant losses to the lower energy PL states. The reason that
the carriers cannot be transferred efficiently to the PL states is probably hidden in the BGR
for the occupied higher energy states: as the BGR effect grows with excitation, an additional
potential barrier is built and adds to the likely existing potential fluctuations (thus blocking
carrier transport to lower energy states). Assuming that holes are strongly localized in the
InGaN alloy [7, 27] and their decreased diffusivity Dh limits the bipolar diffusion coefficient,
Da≈2Dh, we can estimate a value of the valance band renormalization according to the
following relationship [28]
Ev(N)=Z[3 meV (N/1018)1/3+19 meV (N/1018)1/4]
(2)
9
with a material dependent parameter Z=0.48 for GaN [10]. The renormalization value Ev
varies from 13 to 23 meV for injected carrier densityN=2×1018–2×1019 cm-3 and adds to the
initial localization energy. The impact of BGR is proved by decreasing with injection carrier
diffusivity (see Da≈1 cm2/s within the interval I0=20–80 J/cm2 in Fig. 7c) while in highly
excited GaN epilayer the Da value doubles with excitation (from 1.5 to ~3 cm2/s [19]).
The above described observations of spectrally-dependent diffusivity and
recombination rate seem feasible as the higher energy states (regions with lower In content)
are spatially displaced from the lowest energy states (regions with high In content) and - what
is upmost important- the photoexcitation creates very strong potential barrier between these
regions which are retained up to SE threshold. This peculiarity allows carriers to be bunched
in spectral region 415–420 nm and recombine here without transfer to the PL band. This is
very different from the low injection regime, which does not block the injected carrier
transfer from the high energy wing of PL to the low energy states, leading to enhanced PL
efficiency.
IV. CONCLUSIONS
Complementary studies of spectral and spatial carrier dynamics in wide excitation and
temperature ranges revealed novel features in recombination rates and diffusivity in an
InGaN epilayer. We found an inverse correlation i.e. a carrier lifetime increasing with
temperature and a diffusivity decreasing with temperature, which confirmed a mechanism of
diffusion-limited nonradiative recombination at extended defects. At higher injections,
monitoring of spectrally-integrated carrier dynamics by transient gratting technique alowed
us to ascribe the enhanced recombination rate to bimolecular recombination and determine its
coefficient B=7×10-11 cm3/s at room temperature. Increase of carrier recombination rate and
decrease of diffusivity in the spectral interval above the PL emission band (415–420 nm),
observed by differential transmittivity and transient grating techniques, was attributed to
bandgap normalization effect in extended states. Impact of bandgap normalization increased
with excitation, building an additional potential barrier for carriers in addition to the already
existing potential fluctuations. In this scenario carrier transfer from high-to-low energy states
is inhibited and even blocked, leading to efficiency saturation of the PL band (420–430 nm)
at injection levels above 5×1018 cm-3. Based on these complementary results, we underscore
the importance of spectrally-dependent carrier generation rate which unveiled the causes for
efficiency saturation of the main PL emission band in 3D InGaN layer. The latter effect of
saturation is seen already at 10 ps after photoexcitation in spectrally integrated DT signal,
which in fact reflects the excitation dependence of PL band. Consequently, similar studies of
PL efficiency together with spatial, spectral, and temporal carrier dynamics in InGaN
quantum wells may provide deeper understanding of processes leading to saturation of
internal quantum efficiency of LEDs.
ACKNOWLEDGMENTS
The work at VU is supported by the European Social Fund and Lithuanian Science
Council. VCU team acknowledges support from NSF (Grant No EPMD 1128489).
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[10] P. Ščajev, K. Jarašiūnas, S. Okur, Ü. Özgür, and H. Morkoç, J. Appl. Phys. 111, 023702
(2012).
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J Appl. Phys. 107, 033510 (2010).
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Leszczynski, P. Perlin, and T. Suski, Journal of Crystal Growth 281, 183 (2005).
[14] R.W. Martin, P.G. Middleton, and K. P. O’Donnell, Appl. Phys. Lett. 74, 263 (1999).
[15]. A. Satake, Y. Masumoto, T. Miyajima, T. Asatsuma, F. Nakamura, and M. Ikeda, Phys.
Rev. B 57, R2041 (1998).
[16] A. David, M. J. Grundman, Appl. Phys. Lett. 96, 103504 (2010).
[17] H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings (Springer,
Berlin, 1986).
[18] K. Jarašiūnas, Procedings of SPIE, 7937, 79371W (2011).
[19] T. Malinauskas, K. Jarašiūnas, M. Heuken, F. Scholz, and P. Bruckner, Phys. Status
Solidi C 6, S743 (2009)
[20]. K. Jarašiūnas and H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
[21] T. Malinauskas, R. Aleksiejūnas, K. Jarašiūnas, B. Beaumont, P. Gibart, A. Kakanakova,
E. Janzen, D. Gogova, B. Monemar, and M. Heuken, J. Cryst Growth 300, 223 (2007) .
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11
[26] Power index  of IPL  I0dependence is doubled with respect to index  of IDT  I0
dependence because of bimolecular origin of photoluminescence ( ).
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12
List of Figure captions
FIG. 1. PL decay kinetics measured using femtosecond pulses at 375 nm wavelength and
various excitation densities I0, corresponding to injected carrier densities from 5×1016 to
1018 cm-3.
FIG. 2. Dependence of time-integrated PL intensity on excitation energy density using
femtosecond pulses at 375 nm. The curves can be approximated by a power-function IPL~I0
with slope values  as indicated on the plot.
FIG. 3. Dependence of time-integrated PL intensity on excitation energy density using edge
emission geometry. PL spectra at injection levels below and above SE threshold are given in
an inset.
FIG. 4. DT spectra at various excitation energy densities I0 (here I0=4 J/cm2). The spectra
are taken at 10 ps (a) and 1 ns (b) after photoexcitation by 200 fs duration laser pulses at
375 nm. For comparison, PL spectra at 20 J/cm2 (375 nm excitation) and 100 J/cm2
(266 nm excitation) are shown in (a).
FIG. 5. Spectrally resolved DT kinetics (a, b) for two spectral lines which correspond to blue
wing of DT at 414 nm and PL emission at 425 nm at various excitation energy densities
I0=10 J/cm2 (1), 33 J/cm2 (2), 100 J/cm2 (3), and 300 J/cm2 (4). In (c), spectral
distribution of the initial DT decay time is plotted for various I0.
FIG. 6. Dependence of diffraction efficiency  on excitation energy density I0 for different
delay times t of a probe beam. The dependence at t=0 ps can be approximated by a power
function I0 with slope value , as indicated in the plot. An inset shows enlarged view of
(I0) for comparison of  values from the InGaN layer (1) and GaN layer (2).
FIG. 7. (a) Temperature dependences of diffusion coefficient D and lifetime R in InGaN
layer at excess carrier density N=2–3×1018 cm-3 and (b) dependence of D on excitation
energy density I0 (here, average excess carrier density at I0=10 J/cm2 corresponds to
N=2×1018 cm-3 for used 266 nm excitation wavelength).
FIG. 8. LITG decay kinetics in InGaN layer at various excitation energy densities I0, which
extend over the excess carrier density range from 2×1018 to 3.2×1019 cm-3 (symbols) and their
numerical fitting (lines) using parameters given in the legend.
FIG. 9. Temperature-dependent LITG decay kinetics (symbols) at N=4×1018 cm-3 and their
fitting (lines) using BT-3/2 dependence. The fitting provided value of
B(300 K)=7×10-11 cm3/s.
FIG. 10. Dependence of spectrally-integrated DT signal IDT on excitation energy density. The
slope values  correspond to approximation by a power function IDTI0 and are in relation
13
with slope values  of IPLI0dependence as  DT spectra are taken at 10 ps after
photoexcitation, thus impact of recombination to DT value and slope is negligible.
14
FIG. 1. PL decay kinetics measured using femtosecond pulses at 375 nm wavelength and
various excitation densities I0, corresponding to injected carrier densities from 5×1016 to
1018 cm-3.
FIG. 2. Dependence of time-integrated PL intensity on excitation energy density using
femtosecond pulses at 375 nm. The curves can be approximated by a power-function IPL~I0
with slope values  as indicated on the plot.
15
FIG. 3. Dependence of time-integrated PL intensity on excitation energy density using edge
emission geometry. PL spectra at injection levels below and above SE threshold are given in
an inset.
FIG. 4. DT spectra at various excitation energy densities I0 (here I0=4 J/cm2). The spectra
are taken at 10 ps (a) and 1 ns (b) after photoexcitation by 200 fs duration laser pulses at
375 nm. For comparison, PL spectra at 20 J/cm2 (375 nm excitation) and 100 J/cm2
(266 nm excitation) are shown in (a).
16
FIG. 5. Spectrally resolved DT kinetics (a, b) for two spectral lines which correspond to blue
wing of DT at 414 nm and PL emission at 425 nm at various excitation energy densities
I0=10 J/cm2 (1), 33 J/cm2 (2), 100 J/cm2 (3), and 300 J/cm2 (4). In (c), spectral
distribution of the initial DT decay time is plotted for various I0.
FIG. 6. Dependence of diffraction efficiency  on excitation energy density I0 for different
delay times t of a probe beam. The dependence at t=0 ps can be approximated by a power
function I0 with slope value , as indicated in the plot. An inset shows enlarged view of
(I0) for comparison of  values from the InGaN layer (1) and GaN layer (2).
17
FIG. 7. (a) Temperature dependences of diffusion coefficient D and lifetime R in InGaN
layer at excess carrier density N=2–3×1018 cm-3 and (b) dependence of D on excitation
energy density I0 (here, average excess carrier density at I0=10 J/cm2 corresponds to
N=2×1018 cm-3 for used 266 nm excitation wavelength).
FIG. 8. LITG decay kinetics in InGaN layer at various excitation energy densities I0, which
extend over the excess carrier density range from 2×1018 to 3.2×1019 cm-3 (symbols) and their
numerical fitting (lines) using parameters given in the legend.
18
FIG. 9. Temperature-dependent LITG decay kinetics (symbols) at N=4×1018 cm-3 and their
fitting (lines) using BT-3/2 dependence. The fitting provided value of
B(300 K)=7×10-11 cm3/s.
FIG. 10. Dependence of spectrally-integrated DT signal IDT on excitation energy density. The
slope values  correspond to approximation by a power function IDTI0 and are in relation
with slope values  of IPLI0dependence as  DT spectra are taken at 10 ps after
photoexcitation, thus impact of recombination to DT value and slope is negligible.
19
Priedas 2. Projekto viešinimo plakato kopija.
Naujos optinės matavimo technologijos ir įrenginiai puslaidininkių diagnostikai
Eureka projektas E!4473 “Optical diagnostics” (VP1-3.1-ŠMM-06-V-01-003)
Projekto vykdytojai:
Partneriai:
UAB “Ekspla”
Savanorių pr. 231, Vilnius
Tel. +370 264 9631
K. Jarašiūnas, V. Gudelis, R. Aleksiejūnas, S. Nargelas, P. Ščajev, V. Lapinskaitė
10-2
MOCVD/Al2O3: 1.1 ns
GaN/SiC: 0.35 ns
10-3
GaN/Si: 0.15 ns
0.0
0.5
1.0
2.0
10
100
10-1
1.1 ns
Storis
d = 145 m
d = 90 m
d = 41 m
d = 17 m
d = 10 m
10-2
10-3
0.0
0.5 ns
0.4
0.8
1.2
1.6
2.0
Velinimas (ns)
3 pav. Dinaminių gardelių difrakcijos efektyvumo kinetikos bei nustatytieji parametrai skirtingo
defektiškumo GaN sluoksniuose, užaugintuose įvairiomis technologijomis: MOCVD būdu
epitaksiniuose sluoksniuose ant Si, SiC, Al2O3 padėklų, panaudojus ELO kaukę, bei tūriniuose
skirtingo storio HVPE kristaluose.
0.1
1015
1016
1017
10-2
1018
1019
0.0
0.1
0.2
0.3
0.4
4 pav. (Kairėje viršuje) Difuzijos koeficiento
D ir gyvavimo trukmės  temperatūrinė
priklausomybė 50 nm storio InGaN
sluoksnyje (MOCVD, AIXTRON Co.);
(kairėje apačioje) D priklausomybė nuo
sužadinimo energijos tankio InGaN/GaN
kvantiniuose lakštuose (MOCVD, VU) ir
(dešinėje) nuo injektuotų krūvininkų tankio
tūriniuose deimanto (HPHT, CVD), SiC
(CVD) bei GaN (HVPE) kristaluose.
(ns)
1
In0,15Ga0,85N
In0,10Ga0,90N
In0,03Ga0,97N
213,266,355 nm
1 pav. HOLO-3 prototipo optinė schema. Pikosekundinio lazerio PL2143 (Ekspla) spinduliuotės aukštesnės harmonikos
(355nm, 266 nm, 213 nm) naudojamos žadinimui, o pagrindinė harmonika (1064 nm) - zondavimui. Gardelės užrašymui
naudojami pirmųjų difrakcijos eilių pluošteliai.
D (cm2/s)
PL2143
Ekspla
L2
1.1
5
=
1
1
0.1
0.1
2
Energijos tankis (mJ/cm )
exc = 527 nm
10
Difrakcijos efektyvumas (snt. vnt.)
3
HPD
2
0.5
Elektrinis velinimas (s)
L1
3
N (cm-3)
Temperatura (K)
f2
n0= 9 x 1015 cm-3
100
2
1
100
10-1
1
80 K , G= 0.24 ns
300 K, G = 0.50 ns
800 K, G = 1.05 ns
10-2
-3
1
2
-3
1000
T (K)
7 pav. Laisvųjų krūvininkų rekombinacijos ir difuzijos procesai,
išmatuoti laisvakrūvės sugerties (kairėje viršuje) ir dinaminių
gardelių (kairėje apačioje) metodais tūriniame GaN kristale
dvifotonės injekcijos sąlygomis. Tuo būdu gauta D ir  R
priklausomybė (dešinėje) atskleidžia R prigimtį, siejamą su
krūvininkų difuzijos pernaša į rekombinacijos centrus GaN
kristalitų ribose.
10-4
0
17
N = 10 cm
100
Nav = 1.31017 cm-3
 = 1.74 m
10
Da (cm /s)
10
80 K , R= 9.8 ns
300 K, R = 40 ns
800 K, R = 122 ns
80
-0.
D

10
T = 300 K
n0= 6 x 1015 cm-3
R (ns)
1
CVD diamond
HPHT diamond
3C-SiC
GaN
6 pav. Optinė schema greitų (iki keletos nanosekundžių) ir lėtų (iki dešimčių mikrosekundžių) procesų stebėsenai,
besiremianti šviesa sukelto lūžio rodiklio bei sugerties koeficiento moduliacija.
ln(T0/T)
DT
T1/2
-1/2
D (cm2/s)
10
Optinė vėlinimo linija
f1+f2
1.5
Velinimas (ns)
1
f1
Difrakcijos efektyvumas (snt. vnt.)
ELO: 2.8 ns
HVPE GaN serija
4.2 ns
3.1 ns
2.6 ns
1
=
Naujame HOLO-3 modulyje panaudota tobulesnė dinaminių gardelių užrašymo schema su difrakciniais optiniais elementais
lazerinio pluoštelio padalinimui ir žadinančiojo interferencinio pluoštelio suformavimui. Šioje optinėje schemoje (1 pav.) du
pluošteliai, difragavę nuo difrakcinio-holografinio pluoštelio daliklio HPD, lęšių L1 ir L2 dėka labai paprastai ir patikimai
sutapatinami laike ir erdviškai, sukurdami interferencines linijas bandinio plokštumoje. Tokiu būdu puslaidininkyje indukuotos
dinaminės gardelės periodas pakeičiamas automatiškai, pasirenkant reikiamo periodo HPD. Patogumo dėlei skirtingų periodų
HPD rinkinys sumontuojamas ant skritulio (2 pav.), kuris elektromechaniškai valdomas kompiuterio programa. HPD
panaudojimas leido atsisakyti papildomų komponenčių ir procedūrų, kurios buvo būtinos HOLO-2 modulyje pasirinkus naują
gardelės periodą, t.y. optinio vėlinimo linijos interferuojančių pluoštelių laikinei sichronizacijai bei elektromechaniškai valdomų
veidrodžių erdviniam pluoštelių sutapatinimui bandinio plokštumoje.
Naujas sprendimas leidžia paprastai ir pakartotinai suformuoti reikiamo periodiškumo interferencinį pluoštelį, jį panaudoti
difuzijos ir rekombinacijos procesų vienalaikiam tyrimui. Optiškai vėlinamo zonduojančio pluoštelio difrakcija nuo dinaminės
gardelės panaudota tirti vyksmams, kurių trukmė kinta nuo ~10-11 iki 10-8 s. Tokia sparta būdinga rekombinaciniams procesams
nitridiniuose junginiuose - skirtingų technologijų GaN, InGaN ir InN sluoksniuose, InGaN bei AlGaN kvantinėse sandarose bei
difuzinei krūvio pernašai SiC ir deimantuose.
10-1
 (ns)
Naujieji techniniai sprendimai HOLO-3 modulyje
HVPE: 5 ns
2
Pagrindinis Eureka projekto tikslas - tobulinti netiesines optines matavimo technologijas, jų pagrindu sukurti optinės
diagnostikos įrenginius-prototipus, skirtus plačiatarpių puslaidininkinių junginių charakterizavimui bei jų gamybos technologijų
įvertinimui. Tokių tyrimų ir taikymų poreikis siejamas su naujais puslaidininkiniais junginiais, kurių optinės bei elektrinės savybės
valdomos technologiškai. Nauji matavimo būdai panaudoja lazerio spinduliuotės sąveiką su puslaidininkiu, kai jo optinės ir
elektrinės savybės moduliuojamos optiškai injektuotais krūvininkais. Tuo būdu tiriama erdvinė ir laikinė nepusiausvyriųjų
procesų dinamika N(x,z,t), bekontaktiniu būdu nustatomi svarbūs puslaidininkio parametrai, atspindintys medžiagos kokybę ir
jos panaudojimo galimybes optoelektronikoje bei elektronikoje.
Tarpdisciplininiais tyrimais buvo sukurtos ir išplėtotos įvairios optinio „žadinimo-zondavimo“ konfigūracijos bei metodai
rekombinacijos ir difuzijos procesų stebėsenai. Šios inovacijos buvo įdiegtos holografiniame diagnostikos modulyje HOLO-2,
perduotos UAB Ekspla, kuri pagamino holografinį diagnostikos kompleksą Rensselaer Politechnikos Institutui JAV. Tačiau šis
modulis reikalavo sudėtingų dinaminę gardelę užrašančių pluoštelių valdymo procedūrų.
0
10
D (cm /s)
Eureka projekto tikslai
Difrakcijos efektyvumas (snt.vnt.)
Vilniaus Universitetas
Saulėtekio al. 9-III, LT-10222, Vilnius
AIXTRON Co.
Kackerstr. 17-2, Aachen,
52072 Germany
Phone/Fax +49 241 8909 154
3
Optinis velinimas (ns)
Difrakciniai pluoštelio dalikliai
HPD
HPD
PV1
FD3
FD2
Praėjęs
450
400
350
250
PV2
0
10
20
30
Bandinys
OVL
V8
40
HPD pozicija (m)
2 pav. HPD blokas su elektromechaniniu-programiniu valdymu
(kairėje), difragavusio nuo kvarcinio HPD pluoštelio vaizdas ekrane
(viduryje) ir registruojamo difrakcijos signalo priklausomybė nuo HPD
poslinkio gardelės vektoriaus kryptimi (dešinėje).
400 x 600 mm
5 pav. HOLO-3 modulio su paraboliniais veidrodžiais optinė schema ir prototipas. Šioje schemoje abu pluošteliai (gardelę
užrašantis ir zondojantis) difraguoja nuo HPD ir paraboliniais veidrodžiais nukreipiami į bandinį.
2
 = 9.2 ns
0
10
 = 4.1 ns
 = 6.4 ns
10-1
10-2
V9
300
200
PV2
1
 = 40 ns
FD3
PV1
Difragavęs
Signalas (snt. vnt.)
Registruojamo signalo intensyvumą fotodetektoriuje įtakoja fazių skirtumas tarp koheretinių pluoštelių patenkančių į detektorių:
difragavusiojo ir bandinio išsklaidytos šviesos. Signalo vertė gali būti valdoma HPD poslinkiu gardelės vektoriaus
kryptimi (pakeičiama Idifr fazė). Tai atveria galimybes registruoti
difrakcijos signalą, mažesnį nei fono lygis bei stebėti lūžio rodiklio
pokyčio ženklo kitimą difrakcijos signalo kinetikose.
FD2
FD1
Signalas (snt. vnt.)
Pluoštelio dalikliai (difrakcinės gardelės) buvo suformuoti kvarco padėkle (10x10 mm), panaudojus fotolitografijos ir joninio
ėsdinimo technologijas. Gardelių erdvinis profilis leidžia pasiekti, kad 60-70% pluoštelio energijos būtų sukoncentruota pirmose
difrakcijos eilėse.
 = 1.1 ns
c-GaN:
TRPL
LITG
FCA
0.0
0.5
3
m-GaN:
LITG
TRPL
1.0
1.5
2.0
Velinimas, ns
8 pav. Įvairių optinio charakterizavimo metodų palyginimas, nustatant rekombinacijios
spartą GaN tūriniuose kristaluose: 1- laisvųjų krūvininkų rekombinacijos procesai,
išmatuoti laisvakrūvės sugerties būdu dvifonio sužadinimo sąlygomis; 2 - difrakcijos nuo
dinaminių gardelių būdu paviršinio žadinimo sąlygomis (355 nm) kristaluose su
skirtinga paviršiaus kokybe; 3 - liuminescencijos gesimo kinetika paviršinio žadinimo
sąlygomis (266 nm), įtakota difuzijos į gylį ir skirtingos paviršinės rekombinacijos
spartos.
Priedas 3. Projekto partnerio EKSPLA UAB raštas dėl sukurtų matavimo technologijų priėmimo.