$BSSJFSNPCJMJUZDPNQFOTBUJPO - MOVPE of GaSb-based materials and solar cell structures

*OUSPEVDUJPO

)NAPUREINTRINSICSEMICONDUCTORTHEFREEELECTRONANDHOLEDENSITIESAREEQUALÌT4+

THE&ERMIENERGYLIESMIDWAYBETWEENTHE VALENCE AND CONDUCTIONBAND EDGES 7ITH INCREASING TEMPERATURE IT MOVES SLOWLY TOWARDS THE BAND WITH THE SMALLER DENSITY OF STATES4HISSITUATIONCHANGESINASEMICONDUCTORDOPEDWITHACCEPTORSDONORSORBOTH ÌTVERYLOWTEMPERATURESL_#5ISLESSTHANTHEBINDINGENERGYSOTHATELECTRONS HOLESARE BOUND TO DONOR ACCEPTOR IMPURITIES AND MAKE RELATIVELY LITTLE CONTRIBUTION TO CONDUCTION)NTHISTEMPERATUREREGIONTHEMOBILECHARGECARRIERSARESAIDTOBEÂFROZEN OUTÀ7HENK4ISGREATERTHANTHEBINDINGENERGYBUTSTILLMUCHLESSTHANTHEENERGY GAP THE IMPURITIES ARE IONISED AND THE CARRIER CONCENTRATION IS ALMOST INDEPENDENT OF TEMPERATURE FYIBVTUJPOSFHJPO)FTHETEMPERATUREISINCREASEDFURTHEREVENTUALLYTHE EQUILIBRIUMDENSITYOFTHERMALLYGENERATEDELECTRONSANDHOLESWILLEXCEEDTHEEXCESSOF ELECTRONSHOLES DUE TO IMPURITIES AND THE MATERIAL WILL BE AN INTRINSIC SEMICONDUCTOR JOUSJOTJDSFHJPO

4HE&ERMILEVELINANNTYPE PTYPESEMICONDUCTORATLOWTEMPERATURESLIESNEARANDIF THE IMPURITY CONCENTRATION IS VERY HIGH WITHIN THE CONDUCTION VALENCE BAND ÌS THE TEMPERATUREINCREASESANDTHEINTRINSICREGIONISREACHEDTHE&ERMILEVELMOVESTOWARDS THECENTREOFTHEENERGYGAP7HENTHEDENSITYOFINTRINSICCARRIERSGREATLYEXCEEDSTHE

'JHVSF *ODPSQPSBUJPOCFIBWJPVSPGTJMJDPOJOUP(B4C

5IF TJMJDPO DPODFOUSBUJPO BT NFBTVSFE CZ 4*.4 JT DPNQBSFE UP UIF IPMF DPODFOUSBUJPOBU,

1E-4 1E-3 0.01 0.1

1E16 1E17 1E18 1E19

1E-4 1E-3 1E-2 1E-1 Silicon (SIMS)

<Si> = 3.36E19*[SiH4]/[TEGa]

Holes (Hall, 300K)

Concent rat ion [ c m

-3

]

Ratio of molar flow rates [SiH

₄

][/TEGa]

Hole concentration of typical not intentionally doped sample #757: 2.0E16

IMPURITYDENSITYTHEVARIATIONOFTHE&ERMILEVELWITHTEMPERATUREFOLLOWSTHATOFAPURE MATERIAL

)NTHEDESCRIPTIONOFTHECARRIERDENSITIESINDOPEDSEMICONDUCTORSTHE&ERMIENERGY%_&

CANBEELIMINATEDBYFORMINGTHEPRODUCTnp=ni²4HEINTRINSICCARRIERCONCENTRATIONO_J CAN BE CALCULATED IF THE EFFECTIVE MASSES IN ALL POPULATED VALLEYS OF VALENCE AND CONDUCTION BAND ARE KNOWN )N 'A3B THE , MINIMA IN THE CONDUCTION BAND LIE ENERGETICALLYVERYNEARTHE+MINIMUMTHECOMPLETEEXPRESSIONIS

(

^hh ^lh

)

^E ^k^T

T Lk L B

B gap

B m m m e

e h m

n k ³^/² ³^/² ³^/² ²

2 / 3 2

2 2

− Γ

∆Γ

3/2 − ⋅ + ⋅



 



 +

 ⋅



 



 ⋅

⋅

= π

ÌCCEPTINGTHEEFFECTIVEMASSESGIVENIN;=THERESULTINGINTRINSICCARRIERCONCENTRATION AT + IS ni =1.7⋅10¹² cm^-3 5SING np=ni² TOGETHER WITH CHARGE NEUTRALITY

− = +

+N_A p N_D

n USEFULAPPROXIMATIONSCANBEGIVENFOREACHOFTHEABOVEMENTIONED TEMPERATUREREGIONS

ÌT VERY LOW TEMPERATURES K4 IS COMPARABLE TO THE MAJOR IMPURITY¾S BINDING ENERGY 7ITHOUT PROOF THE ELECTRON DENSITY IN THIS REGION CAN BE APPROXIMATED TO BE



 

−

⋅ kT

N E

n _D ^D

exp 2

~ WHERE&_%ISTHEBINDINGENERGY OF THE DONOR MEASURED FROM THE EDGE OF THE CONDUCTION BAND 3IMILAR EXPRESSIONS APPLY TO PTYPE MATERIAL ÌT HIGHER TEMPERATURES EYIBVTUJPO SFHJPO ONE CAN ASSUME THAT ALL IMPURITIES ARE IONIZED IE

A N

N⁻ = AND ND⁺ =ND 3UBSTITUTING THIS TOGETHER WITHnp=ni² INTO n+N⁻A = p+NA⁺

AND THEREBY ELIMINATING THE MINORITY CARRIER CONCENTRATION THE RESULT FOR A PTYPE SEMICONDUCTORISTHEQUADRATICEQUATION^p² ⁺ ^p

(

^N^D ⁻^N^A

)

⁻ⁿⁱ² ⁼⁰4HESOLUTIONIS

2 2

2 ⁱ

A D D

A N N N n

p N +



 −

− ±

)N THE EXHAUSTION REGION ONE CAN NEGLECTO_J AND GET p=NA −ND AS THE SOLUTION (OWEVER THE ASSUMPTIONS ND⁺ =ND AND ESPECIALLY NA⁻ =NA ARE NOT STRICTLY TRUE

0LOTTING 



 

−

⋅ kT

N E

p _A ^A

exp 2

~ AGAINST5FORDIFFERENT%_ÌSHOWSTHATTHERECANSTILL BE A CONSIDERABLECONCENTRATIONOFNEUTRALACCEPTORSPRESENTATLIQUIDNITROGENTEMPERATURE ÌSnp=ni² ANDni FOR 'A3B ISn_i(300K)=1.7⋅10¹² cm^-3 IT FOLLOWS THAT THE MINORITY CARRIERCONCENTRATIONOINPTYPE'A3BATLIQUIDNITROGENTEMPERATUREWILLBENEGLIGIBLE COMPARED TO THE MAJORITY CARRIER CONCENTRATIONQ )N (ALLMEASUREMENTS THE GENERAL EXPRESSIONFORTHE(ALLCOEFFICIENT

( )

2 2

n p

H e p n

n R p

µ µ

⋅ +

⋅

−

= ⋅ CANTHEREFOREBESIMPLIFIEDTO

p R_H e

= ⋅1

ORR_H e n

− ⋅

= 1

FORPORNTYPEMATERIALRESPECTIVELY

ÌT HIGHER TEMPERATURES ONE CAN APPROXIMATE n_i >> N_D − N_A AND

2 2

2 ⁱ

A D D

A N N N n

p N +



 −

− ±

= GIVES ^p=ⁿi

( )

=ⁿ )N THIS TEMPERATURE REGION BOTH CARRIERTYPESAREPRESENTANDTHEINTERPRETATIONOF(ALLMEASUREMENTSBECOMESDIFFICULT BECAUSETHEGENERALIZEDFORMULAFOR3₎MUSTBEUSED(OWEVERSEVERALHUNDREDl#ARE NECESSARYTOGENERATESUFFICIENTLYHIGHCONCENTRATIONSOFINTRINSICCARRIERSIN'A3B;=

3FTVMUT

.OWTHEABOVECONSIDERATIONSCANBEAPPLIEDTO3IDOPED'A3BÌSSHOWNIN'A3B WAS DOPED WITH 3ILICON TO VARIOUS DIFFERENT DOPING LEVELS AND A RELATED PTYPE CONDUCTIVITY WAS ACHIEVED )T IS OF PARTICULAR INTEREST TO FIND OUT THE DEGREE OF COMPENSATION OF 3ILICON IN 'A3B AS THIS IMPURITY IS USUALLY INCORPORATED AS DONOR IN 'AÌSAND)N0)NADDITIONTHEINTERPRETATIONOF0,SPECTRAOF3IDOPED'A3BDEPENDS STRONGLY ON THE BACKGROUND DONOR CONCENTRATION 4WO DIFFERENT METHODS HAVE BEEN USEDINORDERTOESTIMATETHEDEGREEOFCOMPENSATIONINTHESAMPLES

^TUBQQSPBDINPCJMJUZWFSTVTIPMFDPODFOUSBUJPO

)N ;= HOLEMOBILITIES FOR 'A3B ARE CALCULATED AS A FUNCTION OF THE FREE HOLE CONCENTRATION AT + AT VARIOUS COMPENSATION RATIOS (OWEVER SOME EFFECTS WERE EXCLUDED FORM THE CALCULATIONS INCLUDING SCATTERING AT DISLOCATIONS WHICH MUST BE EXPECTED FOR A LATTICE MISMATCH BETWEEN 'A3B AND 'AÌS AND HOPPING CONDUCTIVITY AT LOW TEMPERATURES AND HIGH IMPURITY CONCENTRATIONS .EGLECTING THESE EFFECTSTHEMOBILITIESOFSILICONANDZINCDOPEDSAMPLESCANNOWBECOMPAREDTOTHE CALCULATED MOBILITIES IN ;= IN ORDER TO OBTAIN THE COMPENSATION RATIOS &IGURE

1E15 1E16 1E17 1E18 1E19

100 1000

Silicon, 300K Silicon, 77K Zinc, 300K Zinc, 77K

native acceptors, 300K native acceptors, 77K

M o b ility [c m

/V *s e c ]

Doping [cm

^-3

]

'JHVSF .PCJMJUZWFSTVTIPMFDPODFOUSBUJPOGPSTJMJDPO[JODBOEUIFOBUJWFBDDFQUPS

SHOWSTHEHALLMOBILITIESOFTHESAMPLESASAFUNCTIONOFTHEFREEHOLECONCENTRATION

#OMPARINGTHEMEASURED(ALLMOBILITIESPRESENTEDINTHEABOVEFIGURETOTHECALCULATED VALUESTAKENFROM;= WHICHUNFORTUNATELYHAVEONLYBEENCALCULATEDFORRATHERLOW DOPINGLEVELSTHEMEASUREDMOBILITIESCORRESPONDTOVERYHIGHCOMPENSATIONRATIOSFOR SAMPLESWITHDOPINGLEVELSINTHECMRANGEREACHINGAPPROXIMATELYFORANOT INTENTIONALLYDOPEDSAMPLEWITHP₊^%CM&ORHIGHER3IDOPINGLEVELSINTHEMID CMRANGE A CAUTIOUS EXTRAPOLATION OF THE CALCULATIONS GIVEN IN ;= SUGGESTS A MUCHLOWER COMPENSATION RATIO OF

D N

N ^ 4HIS RANGE OF HIGHER DOPING LEVELSWILLBEANALYSEDINMOREDETAILBY3)-3MEASUREMENTSDESCRIBEDINTHEFOLLOWING TEXT4HEDATAWILLBESUMMARIZEDINFIGURE

3AMPLE WHICH WAS CHOSEN FOR A DETAILED ANALYSIS OF THE OPTICAL PROPERTIES OF MODERATELY3IDOPED'A3BINSECTIONISNOTINCLUDEDINFIGUREBECAUSEITWAS GROWNUNDERSLIGHTLYDIFFERENTGROWTHCONDITIONS)TSHOWSAFREEHOLECONCENTRATIONOF ECMANDACORRESPONDINGCOMPENSATIONRATIOOFAPPROXIMATELY

A D

N ^

ÌTTENTIONMUSTBEDRAWNTOTHEFACTTHATLATTICEMISMATCHANDTHERESULTINGDISLOCATION DENSITYMIGHTLEADTOADEGRADATIONOFTHEHOLEMOBILITY4HISEFFECTWASNOTINCLUDEDIN THE CALCULATIONS IN ;= )T SHOULD HAVE A GREATER IMPACT ON LIGHTER DOPED SAMPLES BECAUSEIONIZEDIMPURITYSCATTERINGWILLBEMOREDOMINANTATHIGHERDOPINGLEVELS)TCAN THEREFORE BE SUSPECTED THAT THE COMPENSATION RATIO OF APPROXIMATELY FOR THE .Ì BACKGROUND DOPED SAMPLE IS POSSIBLY OVERESTIMATED TO A CERTAIN EXTENT 4HIS ASSUMPTIONISCONFIRMEDBYCOMPARINGTHERESULTSIN;=TOTHEDATAGIVENIN;=4HE LATTER PRESENTS A THOROUGH ANALYSIS OF TEMPERATURE DEPENDENT (ALLMEASUREMENTS ON DIFFERENT NOT INTENTIONALLY DOPED 'A3B LAYERS THEREBY GIVING AN INDEPENDENT DETERMINATION OF DONOR AND ACCEPTOR CONCENTRATIONS 4HE AUTHORS¾ RESULTING COMPENSATION RATIOS ARE INDEED SOMEWHAT LOWER COMPARED TO THE VALUES THAT THEIR MOBILITYVERSUSCONCENTRATION DATA WOULD GIVE IN THE MODEL OF ;= .EVERTHELESS

"OSACCHI ET AL STILL FIND A FAIRLY CONSTANT COMPENSATING DONOR CONCENTRATION OF APPROXIMATELY % CM AND GET COMPENSATION RATIOS BETWEEN AND DEPENDINGONTHEGROWTHCONDITIONS7HILEONTHEONEHANDTHEABOVECOMPENSATION RATIOOFINDEEDAPPEARSTOBESLIGHTLYOVERESTIMATEDTHEMINORDEVIATIONFROMTHE TRUEVALUEWILLNOTBESIGNIFICANTWITHRESPECTTOTHECONCLUSIONSDRAWNINSECTION 4HE NATURE OF THE COMPENSATING DONOR IN THE NOT INTENTIONALLY DOPED SAMPLES HAS TO REMAINUNCLEAR

ÌS A CONCLUSION THE ABOVE FINDINGS SUGGEST THAT NOTINTENTIONALLY DOPED AND SLIGHTLY SILICON DOPED 'A3B ISHIGHLY COMPENSATED BY AN UNKNOWN DONOR )N CONTRAST SILICON DOPED 'A3B AT HIGHER DOPING LEVELS SHOWS SIGNIFICANTLY LOWER COMPENSATION RATIOS (ERE THE CORRESPONDING DONOR WILL BE IDENTIFIED TO BE AMPHOTERIC SILICON IN THE FOLLOWINGTEXT

)T SHOULD BE NOTED THAT 3IDOPED SAMPLES WITH HIGHER DOPING LEVELS TEND TO SHOW COMPARABLE FREE HOLE CONCENTRATIONS AT + AND + WHILE AT LOWER DOPING CONCENTRATIONSTHEMEASUREMENTSAT+GIVEINCREASINGLYSMALLERHOLECONCENTRATIONS THANAT+4HISBEHAVIOURCANBEQUALITATIVELYUNDERSTOODBYTAKINGINTOACCOUNTTHE TWOFOLLOWINGPOINTS&IRSTLYTHEMATERIALCANBEEXPECTEDTOSHOWMETALLICCONDUCTION

AT PDOPING LEVELS ABOVE APPROXIMATELY 1⋅10¹⁸cm⁻³ ;= 3ECONDLY THERE ARE TWO ACCEPTORSINVOLVEDWHICHHAVEDIFFERENTIONIZATIONENERGIES)NTHELOWERDOPEDSAMPLES WHICH ARE DOMINATED BY THE NATIVE ACCEPTOR WITH A HIGH BINDING ENERGY OF APPROXIMATELYME6;=THEIONIZATIONOFTHEACCEPTORSISFARFROMCOMPLETEAT+

)NCONTRASTTHEHIGHERDOPEDSAMPLESAREDOMINATEDBYSILICONACCEPTORSWHICHHAVEA MUCH LOWER BINDING ENERGY SEE SECTION ÌS A RESULT THEIR DEGREE OF THERMAL ACTIVATIONDOESNOTCHANGESIGNIFICANTLYBETWEEN+AND+

^OEBQQSPBDI4*.4WFSTVT)BMM

ÌSSUMINGTHAT3ILICONISMAINLYINCORPORATEDSUBSTITUTIONALLYTHECOMPENSATIONRATIOCAN ASWELLBEESTIMATEDBYCOMPARING3)-3DATATOTHEFREEHOLECONCENTRATION(OWEVER THIS IS COMPLICATED BECAUSE THE HOLE CONDUCTIVITY IN 'A3B AT LOW DOPING LEVELS IS SIGNIFICANTLY INFLUENCED BY THE BACKGROUND CONCENTRATION OF NATIVE ACCEPTORS 4HE EXPERIMENTALDATAWERETHEREFOREANALYSEDINTHEFOLLOWINGWAY

ÌSSHOWNINSECTIONTHESILICONCONCENTRATION4JIN'A3BASMEASUREDBY3)-3 CAN BE DESCRIBED AS A LINEAR FUNCTION OF THE RATIO OF THE MOLAR FLOW RATES ;3I(= AND

;4%'A= [ ]

] 4 10 [

36 .

3 ¹⁹ ³

TEGa cm SiH

Si>= ⋅ ⋅

< ⁻ 4HEFREEHOLECONCENTRATIONASMEASURED

BY(ALLCANNOWBEDESCRIBEDASAFUNCTIONOFTHESILICONCONCENTRATION3I&IRSTLYITIS ASSUMED THAT THE PTYPE CONDUCTIVITY AT DOPING LEVELS MUCH HIGHER THAN THE .Ì CONCENTRATION IS DOMINATED BY 3ILICON ACCEPTORS )T FOLLOWS THAT THE PERCENTAGE OF 3I ATOMS THAT ARE ELECTRICALLY ACTIVE AS ACCEPTORS IS N_A_,_Si =0.56⋅<Si> ÌSSUMING COMPLETEIONISATIONOFTHEACCEPTORSAT + LEADS TO p_Si =0.56⋅<Si> 3ECONDLY IT IS ASSUMEDTHAT3ILICONACCEPTORSANDNATIVEACCEPTORSBOTHCONTRIBUTEEQUALLYTOTHETOTAL ACCEPTOR CONCENTRATION AT LOWER DOPING LEVELS NA =NA_,Si +NA_,NA ÌGAIN COMPLETE IONISATIONAT+GIVESp= pSi + pNAÌSARESULTONEGETSTHEFOLLOWINGEXPRESSIONFOR THEFREEHOLECONCENTRATION p=0.56⋅<Si>+pNA4HISFUNCTIONISPLOTTEDINFIGURE

1E16 1E17 1E18

p as measured by Hall p = <Si>*0.56 + 1.6E16

H o le co nc en tr at ion p [ c m

-3

]

Silicon concentration <Si> [cm

^-3

]

'JHVSF )PMF DPODFOUSBUJPO WFSTVT TJMJDPO DPODFOUSBUJPO JO (B4C 5IF HJWFO NPEFM DBOEFTDSJCFUIFIPMFDPODFOUSBUJPOTPWFSUIFFOUJSFEPQJOHSBOHF

ACCEPTING pNA =1.6⋅10¹⁶CM AND [ ] ]

4 10 [

36 .

3 ¹⁹ ³

TEGa cm SiH

Si>= ⋅ ⋅

< ⁻ 4HE VALUE OF

1016

6 . 1 ⋅

NA =

p IN THE FUNCTION IS IN GOOD AGREEMENT WITH THE VALUE OF pNA =2⋅10¹⁶ WHICHWASMEASUREDFORATYPICALNOTINTENTIONALLYDOPEDSAMPLE

)NORDERTOCONFIRMTHATTHESILICONINCORPORATIONANDACTIVATIONINTOHOMOEPITAXIALAND HETEROEPITAXIAL 'A3B IS INDEED COMPARABLE #6MEASUREMENTS WERE PERFORMED ON HOMOEPITAXIALLY GROWN PNJUNCTIONS )N WELLSUITED SAMPLES I E SAMPLES WHERE THE DOPINGRATIOSWERESUCHTHATTHECORRESPONDINGDEPLETIONWASALMOSTENTIRELYINTHEP TYPEMATERIALTHERESULTINGHOLECONCENTRATIONSWEREINVERYGOODAGREEMENTWITHTHE HOLE CONCENTRATION DETERMINED IN (ALL MEASUREMENTS ON HETEROEPITAXIAL SAMPLES 4HIS RESULTCONFIRMSTHEVALIDITYOFTHEMETHOD

4HE ABOVE RESULTS CAN NOW BE USED TO DETERMINE THE COMPENSATION RATIO OF SILICON DOPED 'A3B AT HIGHER DOPING LEVELS WHERE p= pSi /N THE ONE HAND THE HOLE CONCENTRATIONINTHEEXHAUSTIONREGIONCORRESPONDSTOp= pSi =NA −ND/NTHEOTHER HANDONECANASSUMETHATSILICONISMAINLYINCORPORATEDSUBSTITUTIONALLYANDTHEREFORE

A N

N Si>= +

< AND p= p_Si =0.56⋅<Si> 0UTTING THESE RESULTS TOGETHER ONE GETS

(

A D

)

D A

Si N N N N

p= = − =0.56⋅ + WHICH GIVES A COMPENSATION RATIO OF

A D

N ^

4HIS VALUE IS IN GOOD AGREEMENT WITH THE RESULT OBTAINED ABOVE USING THE THEORETICALHALLMOBILITIES4HATAPPROACHSUGGESTED

A D

N ^FORTHESAMPLES

INWHICHTHE.ÌCANBENEGLECTED IEABOVEP₊^Ü¹⁶cm^-3-OREOVERTHERESULTIS INGOODAGREEMENTWITH;=WHERECOMPENSATIONRATIOSOFUPTOWEREREPORTED FOR3IDOPED'A3BGROWNONSEMIINSULATING'AÌS

4VNNBSZ

4WODIFFERENTAPPROACHESHAVEBEENUSEDINORDERTOFINDTHEDEGREEOFCOMPENSATION FORSILICONDOPEDPTYPE'A3B&ORLIGHTLYDOPEDSAMPLESTHEMEASUREDMOBILITIESWERE COMPARED TO CALCULATED ONES WHEREAS FOR HIGHER DOPING LEVELS 3)-3 AND (ALL MEASUREMENTS WERE COMPARED )N THE TRANSITION REGION BOTH APPROACHES ARE IN GOOD AGREEMENT )N SUMMARY THEY GIVE THE FOLLOWING PICTURE .OTINTENTIONALLY DOPED AND LIGHTLY SILICON DOPED 'A3B IS HIGHLY COMPENSATED BY AN UNKNOWN DONOR 4HE CORRESPONDING (ALL MOBILITY SUGGESTS A COMPENSATION RATIO OF APPROXIMATELY FOR A NOTINTENTIONALLYDOPEDSAMPLE)NCONTRASTSILICONDOPED'A3BATHIGHERDOPINGLEVELS SHOWS SIGNIFICANTLY LOWER COMPENSATION RATIOS IN THE RANGE (ERE 3)-3 MEASUREMENTSSUGGESTTHATTHEAMPHOTERICNATUREOFSILICONLEADSTOACERTAINAMOUNT OF 3IIMPURITIES INCORPORATED ON DONOR SITES RESULTING IN A PARTLY SELFCOMPENSATING BEHAVIOUR4HERESULTSFORLAYERSGROWNUNDERSIMILARCONDITIONSARESUMMARIZEDINTHE FOLLOWINGFIGURE

Im Dokument MOVPE of GaSb-based materials and solar cell structures (Seite 80-86)