SIMULATIONOFZINCBLENDEGALLIUMNITRIDEHIGHELECTRONMOBILITYTRANSISTORSFORNORMALLY-OFF

OPERATION

By

RyanGrady

SeniorThesisinElectricalEngineering

UniversityofIllinoisatUrbana-Champaign

Advisor:CanBayram

May2017

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Abstract

Forhigh-power,high-frequencyapplications,siliconisbeingpushedtoitsphysicallimits.Inordertomeetdemandfordevicesinthisarea,newmaterialsystemsneedtobeconsidered.Galliumnitride(GaN)andrelatedalloysincludingaluminumgalliumnitride(AlGaN)arehighlysuitedtotheseapplications,butareyettomature.TheleadingissueinthedesignofGaNhighelectronmobilitytransistors(HEMTs)isensuringnormally-offbehavior.Herewepresentanewmethodforcreatingnormally-offGaNHEMTs:theuseofpolarization-freezincblende(ZB-)GaN.Inordertocreate theconductive two-dimensionelectrongas (2DEG)channel, carriersare introducedthroughδ–dopingoftheAlGaNlayer.WiththeuseofSentaurusTechnologyComputerAidedDesign(TCAD),weareabletoshowaworkingdesignforZB-GaNHEMTsandgiveguidelinestoensurenormally-offbehavior.Thisincludestuningthealuminummolefraction,gatemetalworkfunction,δ-dopingdensity,andAlGaNlayerthicknesses.Itisfoundthataluminumcontentlessthan 35% and δ-doping below 4 x 1012 cm-2 result in normally-off behavior.We are able todemonstrateturn-onvoltages(VT)greaterthan1V,and2DEGsheetdensityexceeding1013cm-2.Additionally,thebreakdownvoltage(VBR)andon-stateresistanceisprovidedtocharacterizeanoptimizeddevice.Subject Keywords: cubic, zincblende, AlGaN, high electron mobility transistor, technologycomputeraideddesign,on-stateresistance,breakdownvoltage

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Acknowledgments

Iwouldliketothankmyadvisor,Prof.CanBayram,forhisguidancewhileworkingonthisproject,and

hisgeneralhelpincraftingavisionofmyacademicfuture.IdonotbelieveIwouldbeonthetrajectoryI

amtodaywithouthishelp.IwouldalsoliketothankmyfellowICORLABmembersfortheirassistance

withbothresearch-relatedquestionsandtheoccasionallaugh.IwouldalsoliketothankICORLAB

alumnusPhilTsaiforhishelpinlearningtouseSynopsysSentaurus.Finally,Iwouldliketothank

StephanieHoldingfordealingwithmeonadailybasisandbeingsupercute,andmyfamilyforalways

believinginme.

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Contents

1.Introduction.............................................................................................................................................1

2.LiteratureReview.....................................................................................................................................2

3.DescriptionofResearchApproach...........................................................................................................6

a.DeviceDescriptionandFabricationStrategy.......................................................................................6

b.DevicePhysicsandSimulationParameters..........................................................................................8

c.SimulationApproach............................................................................................................................9

4.Results....................................................................................................................................................11

a.EffectsofAl-contentintheAlxGa1-xNbarrier.....................................................................................11

b.EffectsofAlxGa1-xNbarrierlayerthicknessesandδ-doping...............................................................12

c.Effectsofgatemetal...........................................................................................................................15

5.Conclusion..............................................................................................................................................19

References..................................................................................................................................................23

1

1.IntroductionSilicon-basedtransistorsarereachingmaturityasincreasinglymoreapplications(suchas

DC/DC power conversion, 5G networks) demand high power and high speed operation,

motivating new material and device structure investigations [1]. Gallium nitride (GaN) high

electron mobility transistors (HEMTs) are ideal candidates to address such emerging needs,

particularlyinhighpower(>10W)highfrequency(>10GHz)applications.Figuresofmeritfor

highpowerandhighfrequencyapplicationsshowGaNhavingavalueof790forJohnson’sfigure

of merit [2,3] (indicating high speed and high power capabilities) and 100 for Baliga’s high-

frequencyfigureofmerit[3,4]whennormalizedtothevaluesforSi.Thewidebandgap(~3.4eV),

high critical breakdown field (~3.5 MV/cm), and high two-dimensional electron gas (2DEG)

mobility (> 1000 cm2/V·s) all contribute to the promise of GaN devices in such operation

conditions [5]. A key issue in GaN HEMTs is normally-on operation. Due to the inherent

polarizationfieldsinhexagonal(h-)phaseGaN,conventionalh-GaNHEMTsarenormally-on.This

means a conductive 2DEG channel is formed in the AlGaN/GaN hetero-interfacewithout an

externalbias[5].Forsafetyandenergysavingsinhighpower/frequencyapplications,normally-

offHEMTsaredesired[6].Severalmethodsofimplementingnormally-offGaNHEMTshavebeen

exploredincludingfluorineimplantationbelowthegate[7],arecessedgateapproach[8],andp-

GaNgateinsertion[9].However,normally-offdevicesenabledbytheseapproachesareyetto

mature.Recently,ZB-GaNmaterialshasemergedinphotonicdeviceapplications[10,11].Here

weproposethisemergingnaturallypolarization-freezincblende(ZB-)phaseforthecreationofa

new electrical device: normally-off ZB-phase GaN HEMT. Using Technology Computer Aided

Design(TCAD)software{SynopsysSentaurus[12]},weexploredesignparameters inZB-phase

AlGaN/GaNHEMTsandinvestigatedesignguidelinesallowingforanormally-offoperation.

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2.LiteratureReviewToeffectivelyquantizetheperformanceenhancementpromisedbyGaN,severalfigures

ofmeritforhighpowerandhighfrequencyapplicationscanbeapplied.Johnson’sfigureofmerit

givestheproductofthemaximumappliedvoltageandtheswitchingfrequencyasproportional

totheproductofthecriticalelectricfieldandcarriersaturationvelocity[2].Thisfigureisbased

onmaterialparameters,andoffersanupper limit to thecapabilitiesofamaterial.Whenthe

valuesarenormalizedtothatofSi,wefindavalueof790forGaN[3].Foradditionalfiguresof

merit,GaNoffersan impressive910whennormalized toSi forBaliga’s figureofmeritwhich

indicateslow-frequencypowerlosses[3],andavalueof100onBaliga’shighfrequencyfigureof

meritwhich indicatesa reduction inswitching losses [3,4].Table1showsthevaluesof these

figuresGaNandtheclosestwideband-gapcompetitor,4H-SiC.Theexpressionforeachfigureis

givenaswell.

Table1:Figuresofmeritforpowersemiconductordevices[3]

Figure JFOM BFOM BHFFOM Expression 𝐸"𝑣$/2𝜋 𝜖𝜇𝐸*+ 𝑅-.𝐶0. 12 Si 1 1 1 GaN 790 910 100 4H-SiC 410 290 34

AkeyissueinGaNHEMTsisnormally-onoperation.Duetotheinherentpolarizationfields

in hexagonal (h-) phase GaN, conventional h-phase GaN HEMTs are normally-on,meaning a

conductive2DEGchannelisformedintheAlGaN/GaNhetero-interfaceevenundernoexternal

bias.Forsafetyandenergysavingsinhighpower/frequencyapplications,normally-offHEMTs

aredesired. Severalmethodsof implementingnormally-offGaNHEMTshavebeenexplored

includingfluorineimplantationbelowthegate[7],arecessedgateapproach[8],andp-GaNgate

insertion[9].However,normally-offdevicesenabledbytheseapproachesareyettomature.An

alternativemethodforcreationofanormally-offGaNHEMTdesigns isproposedhere,which

employstheuseofpolarization-freezincblende(ZB-)phaseGaN.

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Thedesignofanormally-off,orenhancementmode,HEMTusingfluorineimplantation

wasdemonstratedin2005[7].Thisprocessissimilartothethresholdadjustmentimplantation

performed on silicon MOSFETs. The implantation is typically performed using a CF4 plasma

treatment followed by rapid thermal annealing (RTA) [7]. The resulting devices have a high

density of fluoride ions near the 2DEG channel, which prevent the 2DEG formation under

equilibriumconditions.Thistechniquerequirescare,however,asthedevicescreatedusingthis

techniquecansufferfromareducedon-state𝐼45[13].

RecessedgateHEMTsaremadebyetching aportionofAlGaNand thus reducing the

distancebetweenthegatecontactandthe2DEGinaselectiveregion[8].Thisincreasestheturn-

onvoltage𝑉; ,whilemaintainingcharacteristicsofadepletionmode,ornormally-on,device.In

particular,theonresistance𝑅-.andbreakdownvoltage𝑉<= showasimilartrade-offrelationship

astheirnormally-oncounterpart[8].Theissuewiththisdesignisthat𝑉; canonlybeshiftedby

asmallamount,andsoachievinghighturn-onvoltagesisproblematicandlowleakagecurrents

atoperatingvoltagescanbedifficult.

Employment of a p-doped GaN gate contact has also been studied recently. This

approachavoids thepitfallsof the fluorine-treateddevicesand the recessedgatestrategy to

achievehighturn-onvoltagesofupto3V[14].Thebiggestproblemistheactivationofthep-

type dopants. Magnesium is typically used to achieve a p-doped GaN layer, but the large

activation energy (approximately 170 meV) leads to a much lower hole concentration than

chemicalconcentration[9].

Combinationsoftheaboveapproacheshavebeenused,inparticularthecombinationof

a recessed gate and fluorine treatment [15]. This approach aims to use the benefits of both

fluorinetreatmentandarecessedapproachwhilelimitingthedetrimentaleffectson𝐼45.Devices

fabricatedthiswayareabletopush𝑉;toaround2.5V[15].

TheuseofZB-GaNhasshownpromiseinsimulations,achievingturn-onvoltagesinthe

1.1Vrange.Thesedevicesalsofeaturea2DEGsheetdensity𝑛$ontheorderof1013cm-2,aligned

withmanyh-GaNdevices.Thebiggestdrawback is in thegrowthofZB-GaN,althoughrecent

breakthroughshavegreatlyreducedthisproblem[11].

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In the design of a power transistor, there are several quantities of interest. These

include𝑅-.,𝑉;,and𝑛$aswellasbreakdownvoltageandswitchingspeed.Inordertoaccurately

extractthesequantitiesfromsimulationdataandoptimizeadevice,themechanismsgoverning

foreachquantitymustbeunderstood.

On-stateresistance,𝑅-.,istheresistancefoundbetweenthesourceanddraincontacts

intransistorwhenthedeviceison.Thisresistancecanbebrokendownintoseveralcomponents,

withcontributionsfromthesourcecontact𝑅?5,thesourcedoping𝑅AB,thechannelresistance

𝑅?C, and drain contact resistance𝑅45 [16]. Source contact resistance𝑅?5 is from themetal

contactmadetothe𝑛Bsourceregion.Thisresistanceisdeterminedbytheworkfunctionofthe

contactandthedopinginthe𝑛Bregion,aswellasgeometry.Thedopingresistance𝑅ABisdue

toohmiclossesascurrentflowsthroughthesource,andisinverselyproportionaltodopinglevels

andhasageometricfactor.Channelresistanceisafunctionofthedevicegeometry,aswellas

biasandmaterialparameters.ForaMOSFET,itisfoundtoobey𝑅?C =EFG

HIJK?LM NO1NPG[16].For

the HEMT devices discussed, the channel resistance depends on𝑛$. This parameter,𝑅-., is

typicallymeasuredempiricallyastheinverseslopeofthe𝐼45vs.𝑉45relationshipmeasuredin

thesaturationregion.

Turn-onvoltageintheHEMTislargelydeterminedbythefabricationtechniques,andwill

vary for the methods of making normally-off devices discussed so far. For h-GaN devices

fabricatedusingfluorineimplantation,thethresholdvoltagedependsonthedensityoffluorine

implanted[13].Fortherecessedgateapproach,theAlGaNthicknessbelowtherecessedgateis

responsibleforthepositiveshiftin𝑉; [8].WhenemployingaZB-GaNapproach,𝑉; wasfound

todependonaluminumcontent,𝛿-dopinglevels,andAlGaNlayerthickness.

Sheet density, 𝑛$, has been thoroughly studied. For h-GaN structures, it is given by

𝑛$(𝑥) =U VW− YZY V

[W\𝑒Φ< 𝑥 + 𝐸` 𝑥 − Δ𝐸? 𝑥 [17].Forthisexpression,𝜎 𝑥 referstothe

polarizationinducedchargedensity,Φ<tothesurfacebarrierheight,𝐸` totheFermilevel,and

Δ𝐸? to the conductionbanddiscontinuity at theAlGaN/GaNheterojunction. For the ZB-GaN

structure, there isnopolarizationfieldandsoallcarrier inthe2DEGmustbeaddedusing𝛿-

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dopingtechniques.Thevalueof𝑛$wasstillfoundtobestronglycorrelatedtotheconduction

bandoffset.

Breakdownvoltageisthemaximumvoltagethatbeappliedbetweendrainandsource

while the device is in the off-state without allowing current to flow. This value is typically

measuredbypickingathresholdcurrentontheorderof100nAandmeasuringthevoltage𝑉45

forwhich 𝐼45 equals the threshold voltagewhen thedevice is in theoff-state (𝑉*5 = 0for a

normallyoffdesign,𝑉*5 < 𝑉; foranormallyondesign).Thisvalueisofparticularimportancefor

GaNpowerdevices,andthecurrentrecordisover3.3kV[18].InthetraditionalpowerMOSFET,

thebreakdownvoltageisprimarilyduetoavalanchebreakdowncausedbythelargeelectricfield

inthechannel[16].Duringavalanchebreakdown,carriersareacceleratedtohighvelocitiesand

eventuallyreachasaturationvelocity𝑣$.Theseelectronshaveenoughkineticenergytoionize

latticefixedatomsonimpact,referredtoasimpactionization.InthecaseofaHEMT,thecauses

of breakdown are thought to be due to a combination of factors including punch through,

breakdownofthegate-drainjunctionduetosurfaceconduction,andimpactionizationdueto

hotelectrons[19].

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3.DescriptionofResearchApproach

a.DeviceDescriptionandFabricationStrategyThe zincblende AlxGa1-xN/GaN HEMT structure under consideration consists of an

unintentionally doped (UID-) ZB-GaN substrate on which high quality intrinsic ZB-GaN is

epitaxiallygrown. Tomakecontacts to thedevice,a layerofn-typeGaN is thengrown,and

etchedbacktocreateanopening.Insidetheopening,anAlxGa1-xNlayerisgrownontopofthe

epi-GaN(Figure1(a)).ThegrowthofhighqualityZB-GaNhasbeenrecentlydemonstratedusing

Sisubstrates,indicatingthatthisisatechnologicallyfeasiblestructure[11].TheAlxGa1-xNbarrier

layeriscomposedofthreeparts:undopedlayersofAlGaN1andAlGaN3(withthicknessof𝑡2and

𝑡+) and δ-doped layer of AlGaN2 (with thickness of 𝑡f). The δ-doped AlGaN2 layer provides

carrierstothe2DEGchannelformedattheAlGaN/GaNhetero-interface,andthecorresponding

thickness𝑡fdeterminesthenetnumberofdopants introducedandthustheamountofband

bendingintheAlGaNlayer.Theδ-dopingisachievedbycreatingafewnanometersofhighly-

doped AlGaN via MOCVD or MBE processes [20], and these carriers then diffuse to the

AlGaN/GaNheterojunctiontoformthe2DEG.TheionizedimpuritiesremainintheAlGaN2layer

afterthecarriersaredepleted,leadingtostrongbandbendinginthisregion.Becausethecarriers

are depleted, we instead find the peak electron concentration at the AlGaN/GaN junction

corresponding to the 2DEGas opposed to the doped layer. TheAlGaN3 layer of thickness 𝑡+

separatesδ-dopedAlGaN2layerfromthechannelandreducestheimpurityscatteringeffects.

TheAlGaN1 layerwith corresponding thickness 𝑡2 distances thegate contact from the2DEG,

controllingthegate-contact-inducedelectricfieldeffectsonthe2DEGchannel.Finally,0.25μm

longsourceanddraincontactsareformedwiththen-dopedGaN.

InFigure1(b),agenericbanddiagramforthestructureisgiven.Inthisplot,thedesign

parameters𝑡2,𝑡f,and𝑡+aremarked,aswellastheSchottkybarrierheight(𝜑h).TheSchottky

barrierensuresthatanelectricfield ispresentwhenthedevice isunbiased,preventing2DEG

formation,and𝜑hdeterminesthestrengthofthisfield.Thefinalparametersinconsiderationis

thealuminumcontent,𝑥ij,whichdeterminesthebandgapoffset,andthusdeterminesthedepth

ofthetriangularquantumwellintheconductionbandattheAlGaN/GaNjunction,aswellasδ-

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doping density (𝑁4) in the AlGaN2 layer, which both directly impact the number of carriers

presentinthe2DEG.

Figure1:(a)SketchoftheinvestigatedAlxGa1-xN/GaNHEMTstructure,consistingofanintrinsicunintentionallydopedZB-phaseGaNsubstrateonhighqualityintrinsicepi-GaNisgrown.OntopofthisisanAlxGa1-xNlayercomposedofthreeparts:undopedlayersofAlGaN1andAlGaN3(withthicknessoft1andt3,respectively)andδ-dopedlayerofAlGaN2(withthicknessoft2).Sourceanddrain contacts aremade ton-dopedGaNdirectly contacting the channel. (b)Ageneric band-diagram of Al0.25Ga0.75N/GaN HEMT (with Schottky barrier height 1.8 eVcorrespondingtoagatemetalof5.05eV;t1=15nm;t2=2nm;t3=3nm;δ-dopingof2E+12cm-2)throughthecross-sectionisshown.Themetal-semiconductorworkfunctiondifferenceisgivenby𝝋𝒃.Theregionst1,t2,andt3areseenintheirrespectivelocations.Thepositionx=0markstheAlxGa1-xN/GaNhetero-junction.

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b.DevicePhysicsandSimulationParametersFor simulating the band structure of the wide bandgap materials, the temperature

dependencegivenbytheVarshnimodel[21]𝐸* 𝑇 = 𝐸* 0 − o;\

pB;isused,withvaluesof𝛼, 𝛽

asgiveninTable2.Duringthesimulations,FermistatisticsareusedtoimproveaccuracyasFermi

energylevel(𝐸`)exceedsconductionbandenergylevel(𝐸?).Thermionicemissioncurrentsare

considered for electrons in order to accuratelymodel carrier flow along the heterojunction,

following the literature [22]. For carrier flowanddensities confinedalong the triangularwell

formed at the metallurgical junction {as in our AlxGa1-xN/GaN hetero-structure}, a quantum

potentialisconsidered.Thispotential,denoted𝛬.,addsquantizationtocarrierdensitiesinthe

quantum well according to 𝑛 = 𝑁?𝐹u\

vw,J1vF1xJy;J

without impacting simulation times

significantly[12]. Inthisequation,𝑁? istheeffectivedensityofstates,whileF1/2 istheFermi

integral of order 1/2. 𝛬.is obtained by solving 𝛬. = − zℏ\

2f|J 𝛻f 𝑙𝑛 𝑛 + 2

f𝛻 𝑙𝑛 𝑛 f =

− zℏ\

�|J

�\ ...Here𝛾isafitfactor,𝑛istheelectronconcentration,𝑚.istheelectronmassandℏ

isthereducedPlanckconstant.Theeffectsofbandgapnarrowingwithheavydopingisneglected,

basedonthedifficultyinactivatingdopantsinGaN.Carrierrecombinationiscomputedusinga

combination of Shockley-Hall-Read recombination, Auger recombination, and radiative

recombination models. While modeling the electrical behavior of the structure, the basic

transport equations are solved while the potential at various electrodes is swept. Transient

behaviorisignored,andonlyquasi-stationarysolutionsareused.Threeequationsaresolvedat

eachstepofthesimulation:Poisson’sequationandthecontinuityequationforbothelectrons

and holes. Poisson’s equation is given by𝛻 ⋅ 𝜀𝛻𝜙 = −𝑞(𝑝 − 𝑛 + 𝑁4B − 𝑁i1), where 𝜀 is the

materialpermittivity,𝜙referstotheelectrostaticpotential,𝑝and𝑛aretheholeandelectron

concentrations, and 𝑁4B and 𝑁i1 are ionized impurities. The continuity equation for both

electronsandholesisgivenby±𝛻 ⋅ 𝐽.,� = 𝑞𝑅��� + 𝑞�.,���

withthepositivetermcorresponding

to𝑛andthenegativeto𝑝,aswellasthequantumpotentialequations[12].Forthisequation,

𝑅��� denotes the net recombination rate, and 𝐽.,�is the respective electron or hole current

density.

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Table2:Thevaluesforsignificantmaterialparametersusedinthesimulations.TheVarshnimodelforthebandgapasafunctionoftemperatureisusedwithvaluesforbandgapat0K,𝜶,and𝜷asgivenforbothGaNandAlxGa1-xN.TherelativepermittivityforzincblendephaseAlNandGaNareusedtocalculatemole-fractiondependentpermittivitiesbylinearinterpolation.ElectronaffinitiesforAlNandGaNareusedinlinearinterpolationstodeterminebandoffsetsandtheSchottkybarrierheight.Elasticcoefficientshavebeenusedincalculatingthecriticalthickness. The doping in the n-GaN contact areas is provided, as well as the δ-dopingconcentration. Intrinsic concentrations in the substrateareextractedusing themass-actionlaw.

Parameter Symbol Value GaN bandgap at 0 K 𝐸*,*�A 3.299 eV [23] AlN bandgap at 0 K 𝐸*,ijA 6.00 [23] Varshni coefficients 𝛼*�A 5.93 × 10-4 eV/K [23] 𝛽*�A 6.00 × 102 K [23] 𝛼ijA 5.93 × 10-4 K [23] 𝛽ijA 6.00 × 102 K [23] Relative permittivity 𝜀�,*�A 9.7 [24] 𝜀�,ijA 9.14 [25] Electron affinity 𝜒ijA 0.6 V [24] 𝜒*�A 4.1 V [24] Elastic coefficients 𝑐22 25.3 × 1011 dyn/cm-2 [5] 𝑐2f 16.5 × 1011 dyn/cm-2 [5] n-GaN dopant concentration 𝑁4 1 × 1019 cm-3 i- GaN carrier concentration 𝑛0 6.23 × 10-9 cm-3

c.SimulationApproachTheZB-phaseAlxGa1-xN/GaNtransistorissimulatedasAl-contentintheAlxGa1-xNbarrier

(𝑥ij)(from0.10to0.40),gateSchottkybarrierheight(𝜑h)(from1.2to2.0eV),andAlGaN1,2,3

thicknesses(𝑡2 from10to35nm,𝑡ffrom1to5nm,and𝑡+from2to10nm)arevaried.Asthe

AlxGa1-xNelectronaffinity(𝜒5)changeswithaluminumcontentaccordingtoVegard’slaw,barrier

heightactsasabetterexperimentalcontrolandthuswevarythegateSchottkybarrierheight

(𝜑h){opposedtovaryingtheworkfunctionofthegatemetal(Φ�)}.Whilestudyingeffectsof

eachvariable{𝑥ij,𝜑h,𝑡2,𝑡f,𝑡+}ontheHEMT,eachvariableisvariedindependentlywhilethe

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otherparametersareheldatcontrolvalues(Table3).Thecriteriafornormally-offbehavioris

taken to be the formation of the 2DEGwhen the Fermi level exceeds the conduction band

minimumattheAlGaN/GaNhetero-interface.Thisdefinitionofnormally-offisjustifiedbythe

correspondingelectronconcentration.Theelectronconcentrationnear theheterointerface is

dictatedbythetriangularquantumwellformedalongtheinterface.As𝐸` and𝐸? coincide,the

probabilityoffindingelectronsintheavailablewellstatesbeginstoincreaseaccordingtothe

Fermi-Diracdistribution, leadingtoformationofthe2DEGandthusnormally-onbehavior. In

Figure 6, this phenomenon is shown as the electron density increases by several orders of

magnitudewhen𝐸` approaches𝐸? .

Table 3:While studying effects of each variable {Al-content in the AlxGa1-xN barrier (𝒙𝑨𝒍),Schottkybarrierheight(𝝋𝒃),AlGaN1layerthickness(𝒕𝟏),AlGaN2layerthickness(𝒕𝟐),AlGaN3layerthickness(𝒕𝟑)}ontheZB-phaseAlxGa1-xN/GaNHEMT,eachvariableisvariedoneatatimeastheotherparametersareheldatvaluesshownasinthistable.

Parameter Value 𝑥ij 0.25 𝑡2 15 nm 𝑡f 2 nm 𝑡+ 3 nm 𝜑h 1.8 eV δ-doping (in AlGaN2) 2× 1012 cm-2

Total AlGaN thickness (𝑡2 +𝑡f +𝑡+)

20 nm

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4.Results

a.EffectsofAl-contentintheAlxGa1-xNbarrierFigure2showsthebanddiagramacrosstheHEMTaswevary𝑥ij from0.10to0.40.This

range of Al-content can be attained despite latticemismatch, and doping of high Al-content

AlGaNhasbeendemonstrated [26,27].Additionally,deviceswithhighAl-contenthaveshown

promisingperformance,asthe2DEGisintheGaNlayerandunaffectedbypossibledislocations

intheAlGaNlayers.Inordertomaintainaconstant𝜑hof1.8eV,Φ�isallowedtochangewith

𝑥ij. CorrespondingvaluesofΦ� are calculatedusing𝜑h = 𝑞(Φ� −𝜒5) andwrittennext to

eachband.As𝑥ij increases,theconductionbandminimumapproachestheFermilevel.For𝑥ij

below 0.35, the HEMT is normally-off. This shows good agreement with existing literature,

indicatingnormally-offdevicesareattainablefor𝑥ij of0.33forsimilarrangesofcontrolvariables

inthisstudy[28].Itshouldbenotedthattoensureasufficientlyhighturnonvoltage(dependent

Figure2:Theequilibriumbandstructureisshownextendingfromthegatecontactto30nmbelowtheAlxGa1-xN/GaNjunction.Theinsetshowsthevaluesof𝒕𝟏,𝒕𝟐,and𝒕𝟑.Thevalueof𝝋𝒃hasbeensetto1.8eV,correspondingtochanging𝜱𝑴foreachvalueof𝒙𝑨𝒍.As𝒙𝑨𝒍increasesfrom0.10to0.40,thedeviceisseentoremainnormally-offforvaluesof𝒙𝑨𝒍lessthan0.35.

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upontheapplication),itisdesirabletokeep𝑥ij small.However,as𝑥ij decreases,conduction

bandoffset(Δ𝐸?)alsodecreasesadverselyimpactingthe2DEGsheetdensity(𝑛$).Thisinturn

limits theoutputpower.Overall,byvarying𝑥ij,onecantrade-off turn-onvoltageand𝑛$ for

specific applications.Wehavechosen𝑥ij of0.25 for the restof this study to study trade-off

amongstotherdesignparameters.

b.EffectsofAlxGa1-xNbarrierlayerthicknessesandδ-dopingFigure3showsthebanddiagramacrosstheHEMTaswevary𝑡2 from10nmto25nm.

For a fixed 𝑥ij (0.25), as 𝑡2 is increased, the conduction band minimum decreases. This is

attributedtotheincreasedseparationbetweenthegatecontactandthe2DEG.Weobservethat

bylimitingthethicknessof𝑡2(inthiscasebelow25nm),normally-offHEMTsareenabled,which

isinagreementwithstudiesshowingnormally-offdevicesfor10nmofequivalentAlGaN3layers

[28].Thisapproachhastheadditionalbenefitofreducinglattice-mismatchrelateddislocation

Figure3:BanddiagramacrosstheHEMTisshownas𝒕𝟏 isvariedfrom10nmto25nm(forafixed𝒙𝑨𝒍(of0.25)).Theinsetshowsthevaluesof𝒙𝑨𝒍,𝒕𝟐,and𝒕𝟑.Arrowsindicatethedirectionofincreasing𝒕𝟏.Therelationshipbetween𝒕𝟏thicknessandtheminimumofconductionbandedgeindicatesthatathinner𝒕𝟏willleadtonormally-offbehavior.

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formationintheAlGaNbarrier,asthecriticalthickness(ℎ")ofZB-phaseAl0.25Ga0.75NonZB-phase

GaNpredictedbytheMatthews-Blakesleeequationis9.18nm[29].Wehaveset𝑡2to15nmfor

theremainderofthisstudy.WhilethisvalueresultsinatotalAlGaNthicknessexceedingℎ",it

allowssufficientroomforfullinvestigationoftherelationshipbetweenthevariousparameters

andthenormally-offbehavior.

Figure4showsthebanddiagramacrosstheHEMTaswevary𝑡ffrom1nmto5nm.For

fixed𝑥ij (0.25)and𝑡2(15nm),whentheAlGaNbarrierthicknessiskeptat20nm,thedevice

remainsnormally-off for𝑡flessthan4nm,which isslightlysmallerthansimilarexperimental

workusing6nmdopedlayers.Thisisexplainedbytheincreaseddopinglevelinthepresent

Figure4:BanddiagramacrosstheHEMTisshownast2isvariedfrom1to5nm(forafixed𝒙𝑨𝒍(of0.25)and𝒕𝟏(of15nm)).Thedopingdensityofthe𝜹-dopedlayeriskeptconstant(as2×12cm-2).Theinsetshowsthevaluesof𝒙𝑨𝒍,𝒕𝟏,and𝒕𝟑.Arrowsindicatethedirectionofthebandshiftsforincreasing𝒕𝟐.TheundopedAlxGa1-xNbarrierthickness(𝒕𝟏 +𝒕𝟑)iskeptfixedas20nmbykeepingthe𝒕𝟑 barrierlayerconstantandadjusting𝒕𝟏appropriately.Minimizing𝒕𝟐 isshowntoimprovethenormallyoffbehavior.

14

work.Tomaximizethedensityofthe2DEG,maximizing𝑡fandsubsequentlythenumberof

carriersintroducedwhileretainingnormally-offbehaviorandpreventingadverseimpactsonthe

channelmobilityisideal.

Fixing𝑥ij (as0.25),𝑡2(as15nm),𝑡f(as2nm),andthedopingdensity(as12×102fcm-2),

wehavealsostudiedtheeffectof t3 (Figure5).It isshownthat t3hasminimal impactonthe

normally-offoperationof theHEMT.ThisAlGaN3 layerprimarily serves to keep theδ-doping

impuritiesfurtherawayfromthe2DEGinordertominimizeimpurityscatteringeffects.

Figure5:Effectsof𝒕𝟑barrierlayerthicknessontheconductionbandedgearereported.TotalAlxGa1-xNlayerthickness(𝒕𝟏 + 𝒕𝟐 + 𝒕𝟑)hasbeenkeptconstantas20nmwhere𝒕𝟐iskeptat2nmand𝒕𝟏and𝒕𝟑areadjustedaccordingly.ThebandminimumcanbeseentomoveclosertotheFermilevelwithincreasing𝒕𝟑.Duetoitsscatteringlimitedimpactonthebanddiagram,𝒕𝟑shouldbelargeenoughtominimizeimpurityandsmallenoughtodiffusecarriersfromdopedlayer𝒕𝟐totheAlxGa1-xN/GaNhetero-interface.

TheeffectofthedopingdensityisstudiedandshowninFigure6,asacomplementtothe

studyof𝑡f.Weshowthatforidenticalvaluesof𝑥ij andt1(0.25and15nm,respectively),with

𝑡ffixedto2nm,thedeviceremainsnormally-offwhenthedopingdensityis4×1012cm-2orless.

15

Thisvaluealignswithexistingexperimentalworkshowingnormally-offcubicGaNdeviceswith

equivalentδ-dopingdensityof2.4×1010cm-2[28].Theelectrondensityhasbeenincludedas

well,asthecarriersinthe2DEGareprovidedbytheδ-doping.Thisbringsanewdesigntrade-off

between𝑛$and𝑉;.

Figure6:BanddiagramacrosstheHEMT{forafixed𝒙𝑨𝒍(of0.25),𝒕𝟏(of15nm),𝒕𝟐(of2nm),𝒕𝟑(of3nm),and𝚽M(of5.05eV)}isshownaswevariedthe𝜹-dopingdensityfrom2E+12cm-2

to1×1013cm-2inuniformsteps.Itisshownthatforadopingdensityof4×1012cm-2andlessthedeviceremainsnormally-off. Additionally,theelectrondensity isplottedasthedopingdensitywillimpact𝒏𝒔inthe2DEG,indicatingadesigntrade-offbetween𝑽𝑻and𝒏𝒔.

c.EffectsofgatemetalFigure7showsthebanddiagramacrosstheHEMT{forafixed𝑥ij (of0.25),𝑡2(of15nm),𝑡f(of

2nm),and𝑡+(of3nm)}aswevariedΦ�torepresentcommongatemetalsandalloysolutes

(e.g.platinum,iridium,nickel,copper,tungstenandtitanium)enablingawiderangeof𝜑h.For

Φ�greaterthan4.55Vthedeviceexhibitsnormally-offbehavior.Bypickingagatemetalwitha

sufficientlylarge�thedevicewillexhibitnormally-offbehavior.Examplesofsuchmetalsare

16

platinum[30],gold-platinumalloys[31],andnickel[30].Experimentalresultsshowingnormally

offdeviceswithPd/Ni/Au{𝛷�(Pd)=5.22eV}gatecontactsexhibitingnormallyoffbehaviorfor

similarrangesofcontrolvaluescorroboratethisresult[28].

Figure7:BanddiagramacrosstheHEMT{forafixedxAl(of0.25),t1(of15nm),t2(of2nm),andt3(of3nm)}isshownaswevaried𝜱𝑴torepresentcommongatemetalsandalloysolutes(e.g.platinum,iridium,nickel,copper,tungstenandtitanium)enablingawiderangeof𝝋𝒃.TheinsetshowstheHEMTstructure.Thearrowindicatesthedirectionofdecreasinggateworkfunction.AlargeSchottkybarrierisdesirablefornormally-offbehavior.

Itisimportanttounderstandthebreakdownmechanismsinthedevicetomaximizethe

blockingvoltage.Forthisstudy,breakdownvoltageisfoundbymeasure𝑉45where𝐼45=100nA

while𝑉*5=0V.Thedominantbreakdownmechanismintheproposeddeviceispunch-through,

whichagreeswiththeliteratureonbreakdownintraditionalh-GaNHEMTs[19].InFigure8,the

currentdensityinsidethedeviceisshown.Forthissimulation,allparametersweresettovalues

indicatedinTable3.Thegatelength𝐿* wasfixedtobe1𝜇m,with250nmspacingbetweenthe

sourceelectrodeandthegateelectrodeandatotaldrain-sourcespacing𝐿45 of2𝜇m.Thepunch-

througheffectmanifests inthe𝐼𝑉characteristicsasaslowlyincreasingcurrent,basedonthe

17

highlyresistivenatureoftheintrinsicGaNlayerasopposedtothesharpincreaseincurrentseen

inavalancheorZenerbreakdowns.Thecorresponding𝐼𝑉curveisgiveninFigure9.

Figure8:CurrentdensityheatmapfortheZB-GaNHEMTduringelectricalbreakdown,with𝑽𝑮𝑺=0V,𝑽𝑫𝑺=69.68V.Thecurrentisseentobeisolatedtothe2DEGinareaswhicharenotgated,whilethecurrentbelowthegateextendsintotheepitaxiallygrownZB-GaNlayer,indicatingpunch-throughtobethedominantbreakdownmechanismfortheproposeddevice.

Figure9:Draincurrentvs.drainvoltageforthedeviceuptoelectricalbreakdownasseeninFigure8.Thedraincurrentreaches100nAat81.5V,indicatingbreakdown.

18

Inordertooptimizethebreakdownvoltageofthedevice,theimpactofxAlandsource-

drainseparationLSDwasstudied.Punchthroughrequiresthermionicemissioncurrentstoinject

carriers across the heterojunction and in to the substrate. Thermionic emission currents for

electronsaregivenby𝐽. = 2𝑞 𝑣.,*�A𝑛*�A −|O­®|¯°O­®

𝑣.,ij*�A𝑛ij*�A exp´vF

y;J,¯°O­®,where𝑞is

the elementary charge, 𝑣.is the emission velocity given by 𝑣. = y;Jfµ|J

, 𝑛 is the electron

concentration,𝑚iseffectivemass,𝛥𝐸? istheconductionbanddiscontinuity,𝑘istheBoltzmann

constant, and𝑇is the carrier temperature [12]. This exponential dependence on𝛥𝐸? would

implythatlargeraluminumcontentwouldincreasebreakdownvoltage.However,theimpactof

𝑥ij on𝑉; offsetsthisimpact,asthelowerthresholdvoltagemeansalowerbreakdownvoltage.

TheseresultsareshowninFigure10.Theminimumwithrespectto𝐿54near3.5𝜇misnotyet

understood.

Figure10:Breakdownvoltageasafunctionof𝒙𝑨𝒍and𝑳𝑺𝑫.

19

For power applications, on-resistance 𝑅-. is another important parameter. Resistive

losseswhentheHEMTfunctionsforpowerswitchingareproportionalto𝑅-.,andsokeeping

𝑅-.assmallaspossibleisbeneficialtoperformance.InFigure11,𝑅-. isplottedagainst𝑉*5 for

adevicewithparametersasgiveninTable3,with𝐿54setto2𝜇mand𝑉45at10V.𝑅-.isseen

todropsignificantlyas𝑉*5beginstoexceed𝑉;.As𝑉*5increasesandthe2DEGbeginstosaturate,

𝑅-.reachesapproximately1𝛺/𝜇m.

Figure11:On-stateresistanceplottedagainst𝑽𝑮𝑺 forthenormally-offZB-GaNHEMT.

20

5.ConclusionBased on preceding design guidelines, a normally-off zincblende (ZB-) phase

AlxGa1-xN/GaNhighelectronmobilitytransistors(HEMTs)isproposed.Figure12showsthe𝐼4vs.

𝑉45responseoftheHEMTwith𝑥ij setto0.25,𝑡2setto15nm,𝑡fsetto2nm,𝑡+setto3nm,

and𝛷� set to 5.05 V, verifying the normally off behavior by showing that no current flows

throughthedevicewhenthegateisgroundedforvaluesof𝑉45upto10Vwhileincreasingthe

gatevoltageto4Vallowscurrentsof3mA/μm.Itisworthnotingthatthiscurrentexceedsmost

existentGaNHEMTdevicesbasedonwurtzicGaNbynearlythree-fold.Thisisduetoavarietyof

reasons,includingtheassumptionofperfectcontactstothesourceanddrainregions,aswellas

thelackoftrapsandotherinterfacestatesattheGaN/AlGaNheterojunctiontodiminishmobility

andthus𝐼45.

Figure12:𝑰𝑫vs.𝑽𝑫𝑺 responseissimulatedforgatebiasesbetween0and4V,demonstratingthattheproposeddeviceisnormally-off.Whenthegateisunbiased,nocurrentflowsfromthesourceasVDSrunsfrom0to10V.As𝑽𝑮𝑺increasesabovethresholdvoltage,𝑰𝑫vs.𝑽𝑫𝑺curvesfollowthosefromtypicallyfieldeffecttransistors.Thissimulationisrunusingthecontrolparameters(listedinTable2)andshowscurrentsontheorderof3mA/µmata4Vgatebias.Increasing𝑽𝑮𝑺willincrease𝒏𝒔andhencethecurrent.

21

Tailoring HEMT performance to specific applications requires investigation of key design

parameterssimultaneously.𝑥ij isanidealchoiceforexplorationduetoitspositivecorrelation

to𝑛$andinversecorrelationtoturn-onvoltage𝑉;.Todemonstratethedesignspaceavailablein

zincblendeAlxGa1-xN/GaNHEMTs,thedeviceissimulatedviavarying𝑥ij and𝑡2as𝑉; isextracted

fromthe𝐼4vs.𝑉* curves.Plottedasacontourmap,theresultingvaluesof𝑉; areseeninFigure

13(a).ThedashedlinemarksMatthews-Blakesleecriticalthickness(ℎ"),20witha20%margin

oferrorconsidered.FortheregionsofthedesignspacethatfeatureanAlxGa1-xNthicknessbelow

Figure13:(a)Turn-onvoltageasafunctionof𝒙𝑨𝒍and𝒕𝟏.Thecriticalthickness(𝒉𝒄)iscalculatedbyMatthews-Blakesleeformula[29]anddrawnafteraccountingforthelayers𝒕𝟐and𝒕𝟑(witha20%errormargin). (b) 2DEGdensity (𝒏𝒔) plottedas a functionof𝒙𝑨𝒍and𝑽𝑮𝑺.As𝑽𝑮𝑺 isincreasedfrom0Vto10V,𝒏𝒔increases.

22

ℎ", thethresholdvoltage isthe largestofferingstablenormally-offdesign.Asboth𝑡2and𝑥ij

increase,thevalueof𝑉; isshowntobecomenegativeindicatingthetransitionfromnormally-

offtonormally-onbehavioriscontrolledbytheproperlyselectingtheHEMTdeviceparameters.

Experimentaldataintheliteratureshowingnormally-offbehaviorwith𝑉; of0.6Vfor𝑥ij =0.33

and𝑡2=10nmshowexcellentagreementwithourresults[28].

Thevalueof𝑛$ isofparticularrelevance inHEMTdevicesforpowerapplications. It is

directlyrelatedtotheconductionbandoffset,whichisinturninfluencedby𝑥ij.Basedonthis

fact,𝑛$isplottedasafunctionofaluminumcontentand𝑉*5inFigure13(b).Thesheetdensity

iscalculatedbyintegratingthecarrierdensityalongthedepth.Thesheetdensityisseentoscale

withbothaluminumcontentandgatebias.Weseethatfor𝑉*5near10Vand𝑥ij near0.40,𝑛$

achievesvaluesnear2.75×1013cm-2.Previousstudiesshowing𝑛$=1.7×1012cm-2for𝑉*5=0.3

Vand𝑥ij =0.33areingoodagreementwithourdata[28].

In summary,we report the normally-off operation regime of ZB-phase AlxGa1-xN/GaN

HEMTsviavaryingkeydesignparameters(𝑥ij, 𝑡2, 𝑡f, 𝑡+,δ-dopingamount,and𝛷�).Particularly,

weconsiderandreportthetrade-offsbetween𝑥ij, 𝑡2,and𝛷�(viaitsimpactas𝜑h)tomaximize

𝑉; and𝑛$. ConsideringMatthews-Blakeslee critical thickness, we offer design guidelines for

maximizing 𝑉; while minimizing defectivity. Our results provide encouraging results for the

employment of ZB-phase GaN HEMTs, given the wide-range tenability in 𝑉; and 𝑛$, under

normally-offoperation.

23

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