Doping Rules and Doping Prototypes in A2BO4 Spinel Oxides

Home , Spinel group

www.afm-journal.de www.MaterialsViews.com FULL PAPER Doping Rules and Doping Prototypes in A2 BO4 Spinel Oxides Tula R. Paudel , Andriy Zakutayev , Stephan Lany , Mayeul d’Avezac , and Alex Zunger *

known spinels including ∼ 130 oxides, A2 BO4 spinels constitute one of the largest groups of oxides, with potential some of them explored previously for fer- applications in many areas of technology, including (transparent) conducting roelectricity, [ 4 ] ferromagnetism,[ 5 ] super- [6] [7–10] layers in solar cells. However, the electrical properties of most spinel oxides conductivity, thermoelectricity, and catalytic properties.[ 11,12 ] Only recently this remain unknown and poorly controlled. Indeed, a signifi cant bottleneck large group of materials has been tapped hindering widespread use of spinels as advanced electronic materials is the for its potential in electronic and opto- lack of understanding of the key defects rendering them as p-type or n-type electronic applications. [ 13–16 ] Such appli- conductors. By applying fi rst-principles defect calculations to a large number cations would require fi rst and foremost of spinel oxides the major trends controlling their dopability are uncovered. that these materials can be doped n-type and/or p-type, even though the perfectly Anti-site defects are the main source of electrical conductivity in these com- stoichiometric III2 -II-VI4 or II2-IV-VI 4 sys- pounds. The trends in anti-sites transition levels are systemized, revealing tems generally form a closed-shell octet, fundamental “doping rules”, so as to guide practical doping of these oxides. and hence tend to be insulators. Four distinct doping types (DTs) emerge from a high-throughput screening It is important to realize that doping of a large number of spinel oxides: i) donor above acceptor, both are in the in spinels can follow different rules from gap, i.e., both are electrically active and compensated (DT-1), ii) acceptor doping in traditional electronic materials, such as Si or GaAs. The main rea- above donor, and only acceptor is in the gap, i.e., only acceptor is electrically sons are that (a) spinels have both octa- active (DT-2), iii) acceptor above donor, and only donor is in the gap, i.e., only hedral and tetrahedral occupied cation donor is electrically active (DT3), and iv) acceptor above donor in the gap, i.e., sites, and (b) that spinels often contain both donor and acceptor are electrically active, but not compensated (DT-4). multivalent elements such as transition Donors and acceptors in DT-1 materials compensate each other to a varying metal ions. These ions (can) switch their valence when moved from one coordi- degree, and external doping is limited due to Fermi level pinning. Acceptors nation to another, and such a change in in DT-2 and donors in DT-3 are uncompensated and may ionize and create valence may lead to hyperdeep electrical holes or electrons, and external doping can further enhance their concentra- levels such as donors inside the valence tion. Donor and acceptor in DT-4 materials do not compensate each other, band and acceptors inside the conduction and when the net concentration of carriers is small due to deep levels, it can band. This is in contrast to the traditional be enhanced by external doping. semiconductors, in which acceptor levels usually lie in the lower part of the gap and donor levels usually lie in the upper part of the gap. Thus the doping physics of spi- 1. Introduction nels is more diffi cult and interesting compared to conventional [1] = [2,3] semiconducting materials. A2 BX4 spinels (X O, S, Se, Te) comprise a broad group of chalcogenides containing two metal atoms (A and B), being either III-valent and II-valent cations (giving the III2 -II-VI4 spinel 1.1. Recent Work on Spinel Doping group,e.g., Al2 MgO4 ) or II-valent and IV-valent cations (giving the II 2 -IV-VI4 spinel group,e.g., Cd 2SnO4. There are about 1000 Previous experimental[ 13 , 15–26 ] and theoretical attempts[ 22 , 27–31 ] to study doping of such oxides have revealed one interesting feature: Dr. T. R. Paudel , Dr. A. Zakutayev , Dr. S. Lany , Dr. M. d’Avezac even when a would-be dopant is successfully introduced, the Fermi National Renewable Energy Laboratory Golden level is often pinned in a narrow energy region in the gap and CO 80401, USA would not shift much when more dopants are added. Therefore, Prof. A. Zunger sightings of spinels that manifest some free carriers when off-stoi- University of Colorado chiometric or intentionally doped have been sporadic[ 13–15 , 18 , 20 , 32–38 ] Boulder, CO 80309, USA E-mail: [email protected] and unpredictable. Indeed, the type of conductivity (n or p or neither), and far more its magnitude, of the vast majority of spi- DOI: 10.1002/adfm.201101469 nels is still unknown, this being a major impediment for their

Adv. Funct. Mater. 2011, 21, 4493–4501 © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 4493 4494 FULL PAPER cause ofn-typeconductivity, n- orp-type.Itwasthoughtthat(i)oxygenvacancyV(O)isthe from thefewknownexamples,establishingwhatmakesaspinel ously made exploitation aselectronicmaterials.Attempts havebeenprevi- metal–metal bondingormetal–oxygenunderbonding, properties. are toughttobeunlikelyandhencedonotaffectitselectrical donor. iii)Interstitialdefectsintheclosedpackspinelstructure substitution isexpectedtobeanelectron-producing(hole-killing) n-typeness anddefeatp-typeness of thehigh-valentcation(e.g.,IIIin usually acceptors.Concomitantly, itwasthoughtthat(iii)excess as supportedbythegeneralknowledgethatcationvacanciesare (ii) cationvacancyV(A)orV(B)isthecauseofp-typeconductivity, oxygen defi tions little success.Previousfi and optimizationofdopedspinels,butwith principles havebeenguidingthesearch energetically theyarediffi Oxygen vacanciesarenottheleading i) principles toguidedopinginspinels. This fi in spinelsthanthevacanciesorinterstitials. that theanti-sitesaremuchmoreabundant we foundadifferentphysicalpicture,namely function oftemperatureandoxygenpressure, zation levels,andcarrierconcentrationasa culations ofdefectformationenergies,ioni- Using anextensivesetoffi 1.2. PresentRealizations eral rulesofdopinginthisfamilyoxides. far toextractgeneralunderstandingandgen- pounds, andnoattemptshavebeenmadeso wileyonlinelibrary.com www.afm-journal.de poor (reducing)conditions. oxygen vacanciesinfavorableoxygen- nels shownin the absolutemajorityoftypicalspi- is anoxidehavingasmany10 form oxygenvacancies.For example,ZnO oxides differgreatlyintheirpropensityto ing causeofp-typeconduction.Generally, spinels, norarecationvacanciesthelead- cause ofn-typeconductioninmostthe exceptions inFigure 1 thatdomanifest the availablenumberofsites. Theonly ways ofarrangingthedefectsamong rational entropythatarisesduetodifferent rium andtakingintoaccounttheconfi simulations assumingthethermalequilib- the fi tion energyofthedefectcalculatedusing ing condition,aspredictedbytheforma- 10 [ 22 16 nding impliesdifferentpracticaldesign , 28 cm rst principlesandthethermodynamic ] werelimitedtoafewspecifi ciency iscorrelatedwithelectronconductivity, andthat [ 40,41 − [ 13–15 3 oxygenvacancieseveninreduc- ] Extracationinaninterstitialpositionleadto ] todistill somephenomenologicalexpectations Figure rtpicpe calcula- rst-principle cult toform.These phenomenological

rst-principles cal- rst-principles 1 [ 14,15 havelessthan [ 43 [ , 28 37 ] Incontrast, , ] 39 assupportedbythefactthat ] of aspinelbecauseIII-on-II 19 c com- c cm gu- 2

-II-VI − © 3

2011WILEY-VCHVerlag GmbH&Co. KGaA,Weinheim 4 other compoundsitislimitedbyformation ofoneorboththemetalions. in themaximallyreducingcondition islimitedbyformationofCo defects insomecompoundssuchasRh with theoxgyenmoleculeisveryhardtorealize.Insuchoxidizingconditions cation-related that themostoxidizingconditionwhereinofcasescompound existinequilibrium (B) tothemostreducingconditionatatypicalgrowthtemperatureof 700 condition (compoundtobeinequlibriumwithbinaryoxidesofBcation) andthebottompanel pared tonumberofanti-sitesdefects.Thetoppanel(A)corresponds themostoxidizing 1. Figure that theyareinequilibriumwithone orbothofthemetalliccations.For example,theCo acceptor typeanti-siteB-on-A.Further, noteverycompoundexistinreducingconditionsuch donor typeA-on-Banti-sitedefects,howeveroveralldefectphysics remaindominatedby ) willenhance [ 42 ] hence hence Showing thenumberofdefects(logarithmicscale)A,B,andOvacanciescom- tion ofanti-sitedonorsareGa a highconcentrationofV(O),comparabletotheconcentra- oxygen, cationvacancies,andinterstitialdefectsarenotthe having charge donor (0/2 example,theV(O) isdouble in thesetwospineloxides(for vacancy isnottheleadingcauseofn-typeconductivity, even corresponding donorlevelsareenergeticallydeepsooxygen that oxygenvacanciesarenotthemaindefects. spinels, suchasFe V(A) andV(B)vacancyconcentrationsinFigure 1 . Inafew source ofp-typebehavior, ascanbeseenfromthesurveyof to theoxygenvacancy, cationvacanciesarenottheleading short-hand notationforconductionbandminimum).Similar E q meaning theenergywhereV(O)changesfromhavingcharge

= –2.4eV, whereas inCr 0to q

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FULL PAPER 4495

] 55 , in- ] 48 [ 50–54 [

]

57 [ O. or the unoccu- 2 c

E wileyonlinelibrary.com www.afm-journal.de nite-size supercell, nite-size , including a potential- and Cu v

] nite system. nite E 56 [ lling effect plays a role in , y how each of aforemen- y how each of 3 O 2 and the extension due to Mak- ] band ﬁ In 58 ] ] [ Further, the reference potential Further, ] 55 , 60 [ 61,62 48 [ [ nite supercell size effect and potential who suggested to include an additional term ] It has been shown by Lany and Zunger It has been shown by Lany and Zunger ] 59 [ 48 [ , and when charges are added to the system, as in , and when charges F

E above the top of valance band maxima (VBM), when above

F E that account for the interaction between the delocalized part that account for the interaction between point-charge of defect-induced charges with the screened between of images to fully take into account the interaction dielectric constant charges and their periodic images. The that determines screening is calculated by using density functional perturbation. that formations energies calculated in the fi including aforementioned corrections, accurately represent the formation energy of a defect in infi the determination of the formation energy for both charged and neutral defect. This effect arises due to electrons occupying the bottom of the conduction band (CBM) instead of the donor level, and holes occupying the top of the valence band maxima (VBM) instead of the acceptor level. This effect is in- cluded by taking the difference between the sums of energy of the occupied bands above the host CBM and between the cell containing the defect and the cell without a defect has been aligned explicitly considering the difference radii in the defect-free between the average potential at PAW host and defect-containing cell. alignment effect in the full Brillouin zone, as described by Lany and Zunger. pied bands below the host VBM and ov and Payne, ov and Payne, cluding ZnO and GaAs, and GaAs, cluding ZnO formation energy has been tested in serveal cases, in serveal cases, energy has been tested formation alignment effect: To accurately calculate the formation energy alignment effect: To defect concentra- for the charged defect in the limit of dilute to the formation tion we explicitly calculate the contribution its image in the energy due to interaction of a charge with energy of a use the screened Madelung periodic system. We as sug- point charge compensated by a jellium background, gested by Leslie and Gillian, In the following we discuss briefl In the following equilibrium with the rst considers a system in thermodynamic tioned quantities is computed including the correction beyond including the correction beyond tioned quantities is computed calculations. standard DFT total energy Enthalpy of the Formation 2.1. Calculation in supercell approach, one calculate the formation energy To fi it exchanges atoms to create defects. Then with which reservoir, of a neutral defect can be calculated as the the formation energy between total energy of a supercell sum of energy difference a defect, and the difference between with a defect and without the added atom. For the chemical potential of the removed and to be in equilib- charged defect we further assume the system then add sea. We i.e., the Fermi rium with the charge reservoir, the energy of Fermi the chemical potential of an electron, i.e., sea ii) The Moss–Burstein-type charges are removed from the system, as in the case of donors charges are removed from the system, as or subtract the case of the acceptors. The obtained formation energy of the the case of the acceptors. The obtained formation charged defect has to be corrected. i) Correction for the fi )

′ q / q and ( 4 E ects the ZnO ) enhances 2 4 In such condi- ] and therefore it ] -II-VI to be in equilib- 2 (where the most (where the 46 [ 2 4 , 4 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim GmbH & Co. 2011 WILEY-VCH Verlag spinel compounds: 20 ). The method of [ to be in equilibrium 4 ©

μ 4 , ), deep in the band gap ZnO T 4 2 MnO BO ( 2 2 F

in the band gap and the E MnO

F 2 ) of various point defects as ) of E ZnO μ 2 , (cf., Figure 4 , Figure 5 , and 5 , Figure 4 , (cf., Figure , ). This difference reﬂ ′ F

4 q E and Cr and Cr ( 4 H ned by Rh ned by Rh to realize in practice, and even cult MgO Δ and 2 and Rh ). We will explain these spinel doping ). We q ), cation vacancies becomes compara- ), cation vacancies 4 ZnO 4 3 2 O of the constituent elements 2 μ

ZnO MgO 2 , 4493–4501 2 and ZnO, and Cr and ZnO, and Cr The method that is used to calculate the 21 ] 2 , 49 [ and Cr and Cr 4 2011

and that for calculating equilibrium Fermi energy and that for calculating equilibrium Fermi ] O 3 ), whereas it has practically no effect in other classes ] 48 [ ), or shallow in the band gap but compensated by a 47 4 [ 4 MnO ZnO a function of the Fermi energy a function of the Fermi is energetically less costly to substitute one cation by the other is energetically less costly carrier than to create a metal vacancy and emit or absorb a bonds. In the most oxidizing condition, and to repair broken in compound like Rh and defect concentration has been described in detail by Biswas et al. chemical potential rium with RhO tions the number of cation vacancies decreases and anti-site tions the number of cation vacancies decreases B. When 1 in Figure defects becomes dominant as can be seen reside in the band the respective anti-site ionization levels of conductiv- gap, cation anti-site is also the main promoters anti-sites will be discussed in greater detail below. Cation ity. with Mn of atomic disorder in spinel. Figure 1 illustrates this doping this doping illustrates 1 disorder in spinel. Figure of atomic are more metal anti-sites showing that generally principle, One possible reason is that both prevalent than vacancies. similar orbital radii, cations in spinels have main defects that control the dopability of spinel oxides, they of spinel oxides, that control the dopability main defects this paper. discussed further in will not be calculating the formation energy is described by Lany and Zunger if one manages to achieve such condition by applying external if one manages to achieve such condition by by acceptor- pressure, then the overall defect is dominated typically these compounds are type anti-site B-on-A. However, binaries rather then grown often at higher temperature using the oxygen molecules and metallic ions. ble with donor-type anti-site defects, A-on-B. However such an anti-site defects, A-on-B. ble with donor-type diffi oxidizing condition is oxidizing condition is defi oxidizing condition is between charge states in Section 3.4. and 3.5); 6 Figure 2 2 These two new and surprising rules that emerge from thisThese two new study open the way to deliberate design and discovery of novelstudy open the way to deliberate design previously untappedelectronic materials from the large and example, we have shown that engineered group of spinels. For cation (e.g., II in III excess of the lower-valent Co ii) leading cause substitutions are the anti-site Metal-on-metal p-typeness in one class of spinels (for example Rh shallow acceptor (Al rules by means of detailed calculations in the rest of this paper. tendency of the donor level associated with substitution of thetendency of the donor level associated with cation to be insidehigh-valent cation on the site of the low-valent the valence band (Co We have used the supercell approach within the density func- We tional theory (DFT) to calculate for 40 A 2. Methods of Calculation 2. Methods of Calculation i) The formation enthalpy (Cr (Cr iii) the defect concentration (c.f. Figure 1 ) 1 the defect concentration (c.f. Figure iii) energy the equilibrium Fermi iv) ii) the associated acceptor and donor transition energies of spinels (for example Al www.MaterialsViews.com Adv. Funct. Mater. Funct. Adv. 4496 FULL PAPER trality inthesystemasdescribedbyBiswasetal. E consistently thenumberofdefects,equilibriumFermi energy by asupercellapproach.Our supercell consistsof at theequilibriumFermi energy is takenintoaccount.Thedefectconcentrations(cf.,Figure 1 ) ways ofarrangingdefectsamongtheavailablenumberssites and onlytheconfi defects, assuming free energyofdefectivecellswithrespecttotheconcentration Defect concentrationsarecalculatedbyminimizingtheGibbs 2.3. DefectConcentrations DFTbandgaperror: ItiswellknowninDFTthattheband ii) i TheassociatedacceptoranddonortransitionenergieE(q/q i) 2.2. AcceptorandDonorTransistion Energy of competingbinaries. such awaythatitcorrectlyreproducestherelativestability is usedwithPAW ally invariantGGA and correlationeffectsbeyondGGAaretreatedinarotation- the equilibriumFermi energy ionized defects,whichin-turnisdeterminedbytheposition of chemical potential.Thenumberofcarriersiscontributedbythe the functionofnumbercarriersatagiventemperatureand band structureapproachasimplementedinVASP code wileyonlinelibrary.com www.afm-journal.de

F ( Computationalparameters: T edge andthetransitionlevelwillremainconstant. move upinsuchawaythatthedifferencebetweenband expected toremainthesame,whereasshallowdonorswould the realbandgapcorrectionis,deeptransitionlevelsare for movingupCBMisunphysical.Howevernomatterwhat CBM. Here, wewouldliketostressthattheshiftemployed in theGGA with theconductionband.Deepdonorsareleftascalculated Thus, weshiftthetransitionlevelsofshallowdonorsalong Moss–Burstein shift,astheyareexpectedtofollowCBM. affects shallowdonorsthatareusuallyassociatedwiththe in ourwork.Thisa-posterioricorrectionofCBMmostly tion ofGGA resents thetypicalmagnitudeofbandgapunderestima- top ofGGA by introducinga-posteriorianarbitraryshiftof1eVonthe to thetransitionmetald-orbitalandapproximateCBM position ofVBMtoalargeextentbyaddingHubbard “U” too lowwithrespecttovacuumconditions.We correctthe lies toohighandtheconductionbandminimum(CBM) gap isunderestimated,asthevalencebandminimum(VBM) GGA transition levelstakingintoaccounttheDFTbandgaperror Paudel andLambrecht. two chargedefectsbytheirdifference,asdescribed the differencebetweendefectformationenergies cell, thetransitionenergycanbeeasilycalculatedbydividing tion energyiscalculatedforeachchargestateofadefectin between twochargestatesqand , μ

), andthecarrierdensitybyrequiringoverallchargeneu- + U approximation. U + + + U level,astheyarenotexpectedtofollowthe U CBM.Theshiftofthe CBMby1eVrep- U calculationsforthecompoundsconsidered Δ gurational entropyresultingfromdifferent [ H 53 + isindependentofthedefectconcentration, ] U formalism, U andPBEpseudopotential. [ 56 ] [ Defectcalculationsareperformed 63 ] We thencorrectthepositionof Densityfunctionaltheory(DFT) E F

( T E , F

μ [ 55 ( ′ ). Hence, wecalculateself- T : Oncetheaccurateforma- ] , withUdeterminedin μ

54 ] Exchange N (A 2 BO [ 51,52 4 ′ ) ) ]

2 Monkhorst-Pack such asCo 340 eVandoxygensoftpseudopotentials.Inafewmaterials, inverse (P4 general formula[A to disordered-dual(bothFd3m but by second-orderphasetransitionfromthedisordered-inverse and A-on-T equally betweentheT cells includingcorrectionsand4 convergence oftheformationenergyusing112atomsuper- tain compensatedandnoncompensated defects( substitutions canbeclassifi Our calculationsshowthatdopingbehaviorduetocross- Uncompensated Spinels 3.2. Two broaddopingclasses:Compensated vs. with disorderinthecationsub-latticesatfi whether thecompoundisnon-stoichiometricorstoichiometric doping inthematerials.We focus onthedoping,irrespective where theA:B:Oratioisalteredfrom2:1:4. 2/3). Thesecondchannelofdisorderischangestoichiometry, position ofoxygenatomswithrespecttotheirneighboringcations. minimization ordiffractionexperiments),thatalsodecidesthe by the“anion displacementparameter” ence betweenordered-normalandordered-inverseisdetermined the formationenergyofadefecttoconvergewithin0.01eV. cations areswappedbetweenO stoichiometry: InthiscasetheA:B:Oratioisstill2:1:4,but disorder. Thefi the octahedral(O group Fd3m) theA-cation (high–valentin–outnotation)resideson are foundinorderedphase.Intheordered-normalphase(space tural form.At lowtemperature,bothnormalandinversespinels inverse spinel(spacegroupP4 this structurethesystemisaclosed-shellinsulator. Intheordered- T At 3.1. StructuralConsiderations Results 3. cubic unitcellswith Fd3m but transition betweenordered-normaltodisordered-dual(both depending onthestartingconfi different order–disorderphasetransitionsatperfectstoichiometry respectively. Thisconfi and roundbracketsdenote[octahedral](tetrahedral)sites, resides ontheO tetrahedral (T whereas theB-cation(low-valentinournotation)resideson the occupancyofO (0 < Both thecationdisorderandnon-stoichiometrycancause fi At λ

< = 1), where 0KA nite temperature,there are twodifferentchannelsof λ

1 d 22) todisordered-inverse(Fd3m). Here 2 structures);b)ﬁ increasesfromzerotowards2/3,creatingB-on-O 2 ZnO d BX ) sitethatiscoordinatedbyfouroxygenatoms.In rst istheconﬁ h 4 site.Ithasrecentlybeen shown

λ spinelsappearineithernormalorinversestruc- h 4 deﬁ ) sitethatiscoordinatedbysixoxygenatoms, 2 − , Rh , [ 56 λ

B ]

d nes thedegreeofinversionandsquare N andO k λ 2 h -points withakineticenergycutoffof gurational entropyeffectcausestwo ](A ZnO

sitesgetrandomized.Thisisfollowed = 8(atotalof56atoms)and2 λ ed intotwobroadgroupsthatcon- B rst-order transitionfromordered- 4 h 1 − , andAl sites,whereasalloftheB-cation gurational disorderwithperfect λ

1 )O 22) theA-cation isdistributed h Adv. Funct. andT 4 × withaninversionparameter

λ 4 guration: a)continuous decreasesfrom1towards u 2 MgO × (obtainablefromenergy 4 d , asdescribedby the www.MaterialsViews.com

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-on-T -on-T + 3 towards the CBM and thus cause formation towards the CBM , thereby reducing their numbers. The shaded, thereby reducing their numbers.

F d E gap. External dopants will also behave similar dopants will also gap. External adding example, dopants. For as the intrinsic dopants to the T external n-type B of additional that an equal amountthere is no requirement of A T change in response to external n-type dopingchange in response to energy of A would even raise the formation 3.3. Heuristic Relation Between the and the Electrical Character Valence of Anti-Site-Substitution green region in Figure 2 a, right panel illustrate 2 green region in Figure which such pinning canthe narrow range over comparable formationoccur in a material with levels of both donors andenergy and transition in the energetic proper- acceptors. Asymmetry this narrow region toties of defects may cause evenmove closer to one of the band edges or inside of the band, as will be discussed below in more details. In the case of acceptor-above- level b, right panel), the Fermi 2 donor (Figure call movement is essentially unrestricted. We materials such materials doping-type 4 (DT-4) ). It is also possible that one defect 3 (see Figure is compensated and the opposite-charge defect is uncompensated. In these cases, the Fermi bylevel movement is only partially restricted either electrically active acceptors or electrically p-type materials make good active donors. Such or n-type semiconductors, and we call them Four ), respectively. doping-type 3 (DT-3) and doping-type 2 (DT-2) 3 materials (see Figure indoping types of spinels are summarized in more details and will be discussed 3 Figure in the following sections. site, then such a substitution to A d rst group rst site, then such cross-substitution to A to a T to a T d h mal spinel) remains high-valent when it is moved from an O donor level, capable of releasing electrons. O electrically neutral. a T a T ii) when it is moved from an if A lowers its valence Conversely, The defect energy levels in Figure 3 are related to the ability are related to the ability 3 Figure The defect energy levels in of atoms to switch their valence when moved from their home base. The atoms that do switch their valence have extremely deep energy levels that are electrically neutral (for example The atoms in DT-4). or both acceptors in DT-3, donors in DT-2, that do not switch their valence have much shallower energy levels, capable of releasing electrons or holes and capable of compensating other charged defects (for example acceptors in The chemical heuristics or both in DT-1). donors in DT-3, DT-2, that decides the electrical character of the anti-site defect levels are based on the valence of atoms is as follows: i) (which is high-valent on its O If the A-cation iii) Similarly, if the B-cation, (which is low-valent on its T if the B-cation, (which is low-valent on its T Similarly, iii)

d d -on-T -on-T -on-T -on-T

in the + + 3 3 up due to lowering h 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim GmbH & Co. 2011 WILEY-VCH Verlag © in the band gap. Con-

-on-O + 2 down can be moved above CBM (good for n-type doping). can be moved above CBM (good for n-type doping). the gap, but this will cause the easier F E in the gap, causing an easier formation of down

F , 4493–4501 up E 21 , acceptors), thus shifting the Fermi level acceptors), thus shifting the Fermi h can be moved all the way below VBM (good for p-type doping), similarly if the F

2011

-on-O + ). Compensated defects occur in materials where cross- Two broad groups due to relative position of anti-site transition levels. In the ﬁ broad groups due to relative position of anti-site Two 2 3

Figure due to lowering of their formation energy (and a less-easy formation of B donors), thus shifting the Fermi energy donors), thus shifting the Fermi versely, intentional attempts of p-type doping of such a material versely, would initially shift of their formation energy (and a less-easy formation of A acceptor level is above CBM, is further subdivided into four doping types, depending on the positions of the defect energy levels with respect to band edges ( Figure 2 . fromation of native electron-producing donors such as A (a), the Fermi level is pinned to a narrow region by a negative feedback mechanism, while in the level is pinned to a narrow (a), the Fermi level is unrestricted to a wide region. If donor level second group (b) the movement of the Fermi is below VBM, substitution causes the donor level to be above the acceptor level a), and uncompensated defects occur when the acceptor 2 (Figure b). In the former case of 2 level is above the donor level (Figure energy can be pinned a), the Fermi 2 (Figure donor-above-acceptor into a narrow range because of a negative feedback mechanism call materials with pinned that counteracts intentional doping. We a, 2 materials. As shown in Figure level doping-type 1 (DT-1) Fermi materials, intentional n-type doping will initially right panel, in DT-1 level shift the Fermi native hole-producing acceptors such as B www.MaterialsViews.com Adv. Funct. Mater. Funct. Adv. 4498 FULL PAPER i) F iv) using DFT, weﬁ In DT-1, formanydifferentspinelscalculated 3.4. DonorAboveAcceptor:Doping Type 1 counterpart ofthechemicalheuristicrules. inactive. Thesearetheﬁ the conductionbandthenitisalsoelectrically tive. Ifanacceptortransitionlevelsfallsinto into thevalencebandthenitiselectricallyinac- stated above.Ifadonortransitionlevelsfalls without relyingonthechemicalheuristicrules calculations ofthedonorandacceptorlevels B donor inthegaplocatedenergeticallyabove however, doesnotmeanthatthere couldbeno shown inFigure 2 a. Such Fermi level locking, via compensation,asexplainedaboveand causes pinning(“locking”) oftheFermi level donor-above-acceptor orderofenergylevels acteristics being “compensated” (c), p-type (p), n-type (n), or intrinsic (i). acteristics being“compensated”(c),p-type(p),n-type(n),orintrinsic(i). wileyonlinelibrary.com 3. Figure (red) andtheacceptorB-on-O www.afm-journal.de 2 + In theremainingpartofthispaperwewilluseDFT -on-O could leadtoanacceptorlevel,capableofreleasingholes. from aT base inanormalspinel)remainslow-valentwhenitismoved neutral. neutral. O inally, ifBraisesitsvalencewhenitismovedfromaT h site,thensuchsubstitutiontoB h Schematic depictionoftheenergeticorderdonorA-on-T acceptor, asshownin d toanO nd thatA h site,thensuchasubstitutiontoB rst-principles physical physical rst-principles h (blue).ThisleadstofourDTs withdopingchar- 3 + -on-T

Figure d formsa 3

+ 4 -on-O

. The The .

d Calculated anti-sitetransitionlevelsinvariousspineloxidesbelongingtoclassDT-1. toan

h d

as itpromotesBsubstitutingAinO be enhancedbygrowingthecompoundsinaB-richenvironment, more, extrinsic doping in these spinels is unlikely to be effective: more, extrinsicdopinginthesespinelsisunlikelytobeeffective: i IfthenumberofA i) behaviors: respect tothebandedges.We distinguishthefollowinggeneric of thetwoanti-sitesandonpositiontheirenergylevelswith p-type orviceversa,dependscriticallyontherelativeconcentration free carriers However, ifthenumberdonordefectsfarexceeds ii) substituting BinT growing thecompoundsinanA-rich environment,asitpromotesA n-Typeness inthisfamilyofcompoundscanbeenhancedby is reallydeepasexemplifi Ga Ga if itisrelativelydeepcomparedtothedonor, asexemplifi exemplifi tors arecomparablethan:a)oneexpectsnetn-typebehavioras is shallow, asexemplifi of acceptors:a)netn-typebehaviorisexpectedwhenthedonor an electricallyinactiveintrinsiccompensatedspinel. Sc and exemplifi than thatneededtoionizethedonor, (acasewecallDT-1(p)), CBM, signalingthattheenergytoionizeacceptorissmaller acceptor levelliesclosertoVBMthanthedonoris is totheVBM.Thesearen-typecompensatedspinels.b)If if thedonorlevelliesclosertoCBMthanacceptor either aroundthebandedges,asexemplifi ly equaltotheacceptorlevelpositionofVBMandiftheylie c) Finally, ifthedonorlevelpositionofCBMisapproximate- expected. We callthesematerialsp-typecompensatedspinels. ceptor isshallow, asexemplifi donors, then:c)netp-typebehaviorisexpectedwhentheac- similarly, ifthenumberofacceptorsfarexceeds insulating behaviorisexpectedwhendonorreallydeep;and or evenifitisrelativelydeepcomparedtotheacceptor; b)net 2 2 CdO FeO 4 4 ; andd)insulating behaviorisexpectedwhenacceptor ed bymaterialslikeIn , oratthemidgap,exemplifi . Thebalanceof carriers,whethern-typeprevailsover ed byCo d sites,creatingelectrons.Similary p-typenesscan ed byFe 2 FeO 3 ed byGa +

-on-T 4 , anetp-typebehaviormightbe ed byIn 2 d 2 Adv. Funct. ZnO donorsandB CdO h sites,creatingholes.Further- 2 MnO 4, 4 edbyFe Fe Fe andGa 2 FeO www.MaterialsViews.com

4 Mater. 2 andSc MgO ed byAl 4 andGa

2 2011 ZnO 2 4 2 CoO andIn + 2

-on-O MnO , 21 2 4 MgO (Figure 4 ) 4) (Figure 4 , 4493–4501 , wehave 2 FeO h 4 2 . accep- MnO

ed by 4 and and 4 , or or , 4 , FULL PAPER 4499 the donor 4 nd materi- nd CuO home site but 2 d wileyonlinelibrary.com www.afm-journal.de cult to ﬁ to cult and Co and Co 4 in energy to ciently high on their T on their T CdO CdO + 2 sites. First-principles calcula- sites. First-principles h nd rigorous examples of DT-3 of DT-3 nd rigorous examples ed, it would be very good n-type rst principles calculations are shown in on the O + and illustrate some DT-4 cases. This behavior leads to and illustrate some DT-4 6

no electrical compensation and unrestricted movement of the no electrical compensation and unrestricted tions were so far unable to fi within the indium- (n) within the spinels studied here, even in wide band gap based spinels. The reason is probably that semiconductors, such as spinels, it is diffi als with acceptor states that are suffi such a spinel with a be resonant with the conduction band. If low-lying CBM can be identifi conductor. the acceptor level fact so deep that the donor level lies below band and that both of them are far from the corresponding edges. Results of the fi Figure become effectively 3 correspond to B-cations that are 2 iii) In DT-4 both donor and acceptor levels are very deep, in both donor In DT-4 iii) Calculated anti-sites transition levels for various spinel oxides of DT-2. The VBM of Calculated Calculated anti-site transition levels of various spinel oxides of the DT-4. The VBM of anti-site transition levels of various spinel oxides Calculated

Figure 6 . each of the compound is set to zero in the plot. Note that in Ir level lies just below the acceptor level, close to VBM. They indeed are the borderline compounds and could easily be either DT-2, if donor levels would be slightly deeper and fall below VBM, or DT-1, if the donor level would be slightly shallower and lie above the acceptor level. Figure 5 . each of the compound is set to zero in the plot. 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim GmbH & Co. 2011 WILEY-VCH Verlag Mg, Zn, Cd. Mg, Zn, Cd. © =

on + + 2 on their (crossing + 4 is a hole-pro-

] CdO CdO

47 2 [ . acceptor level is 4 donor lies not only below the accep- donor lies not only below the h d -on-O

+ 2 ZnO Al, Ga, In, and B In, and Al, Ga, . Materials with high-lying VBM energies with . Materials on-T on-T 2 DT-1 spinels have both DT-1 = 5 , , and Ga , and Ga -on-O

4 + + + , 4493–4501 3 2 3 is an electron-producing 21 d , Figure 2011

-on-T -on-T + , Ga2ZnO 3 being electrically inactive could 4 h c order, as discussed above. They can c order, site without donating the difference sites are electrically inactive and could sites are electrically d d MgO home-site but become effectively 2 2 h not only above the donor level, but is actually resonant in the conduction band. Thus, A charge to the conduction band. This effect was recently experimentally studied on the example of Co in Co tor, but the donor is actually resonant within the valence band, tor, as shown in (relative to vacuum), such as those that have nonbonding char- (relative to vacuum), such as those that have behavior where acter of the VBM, are more likely to show DT-2 the donor is swamped by the valence band. p-type materials are likely to be good Such B conductors. In DT-2, of donor and acceptor formation energies, acceptor formation of donor and compensating), the intrinsic 2 cf., Figure spontaneously and an- anti-site defect forms extrinsic doping.nihilates the effect of band, the intrin- the conduction or valence large and extrinsic sic doping is already doping is less relevant. ducing acceptor, unopposed by a compen- ducing acceptor, materials with A Heuristically, sating donor. on T the T the T correspond to A-cations that are 3 that correspond to A-cations O gap as shown in many spinels including in many spinels gap as shown Al donor, unopposed by a compensating ac- donor, with low-lying CBM (rela- Materials ceptor. tive to vacuum), such as indium-containing materials, are more likely to be DT-3, as the conduction band can swamp the ac- materials with ceptor level. Heuristically, B-on-O Overall, theoretically donor and acceptor anti-sites levels in the gapdonor and acceptor anti-sites in a specifi insulating, and externalbe n-type, p-type, or car- doping would have a limited effect on the level pinning. rier concentration due to Fermi spinels belonging to this group Heuristically, are distinguished by two cations that preserve they are on. Examplestheir valences irrespective of the lattice sites of such cations are A ii) If the Fermi level pinning occurs inside level ii) If the Fermi 3.5. Acceptor Above Donor: Doping Types 2, 3, and 4 3.5. Acceptor Above Donor: Doping Types locked to a level is not Fermi and DT4, the DT-3, In DT-2, levels is unable to narrow region, because one of the defect energy being, compensate the other on account of its ionization of energy states, for example, resonant within the continuum and thus the defect is electrically inactive. i) (p), the A DT-2 In i) the pinning occurs inside level If the Fermi ii) In DT-3 (n) the B ii) In DT-3 www.MaterialsViews.com Adv. Funct. Mater. Funct. Adv. 4500 FULL PAPER design a material with desired electrical properties. design amaterialwithdesiredelectricalproperties. response ofsystemtotheexternaldopingprovideasimpleway simple classifi number ofcarriersupondopingwiththesuitabledopants.These tion, whereasinDT-2, DT-3, andDT-4 itleadtoenhancementin (DT-4). ExternaldopingintheDT-1 materialsleadstocompensa- both donorandacceptorareelectricallyactivebutnotcompensated iv) theacceptor-above-donor typeinwhichbotharethegap,i.e., is inthegap,i.e.,onlydonorelectricallyactive(DT-3); and (DT-2); iii)theacceptor-above-donor typeinwhichonlythedonor acceptor isinthegap,i.e.,onlyelectricallyactive sated (DT-1); ii)theacceptor-above-donor typeinwhichonlythe both areinthegap,i.e.,electricallyactiveandcompen- four dopingtypes(DTs): i)thedonor-above-acceptor typeinwhich in thespinel.We foundthatspineloxidescanbecategorizedinto their transitionslevelsandfoundrulesthatdeterminethedoping Figures withcolorversions. Please note:ThisarticlewasamendedonDecember6,2011toreplace and VladanStevanovicforimportantinputusefuldiscussions. Zhang forsharinganunpublishedelementalchemicalpotentialtable Energy, Offi ce ofScience,BasicEnergySciences.We thankXiuwen Energy Frontier ResearchCenter fundedbytheU.S.Departmentof This workwassupportedthroughtheCenter forInverse Design,an Acknowledgements properties inA manner, weshowthattheanti-sitedefectscontrolelectrical By usingfi Conclusion 4. P Blzr H Lhan M Rbis Robbins, Tokura M. , Y. Lehmann, H. Arima, Baltzer , T. P. He, [5] J.-P. Kaneko, Y. Miyasaka, Gibbs, S. V. Yamasaki , Y. G. Craig , [4] R. J. Hill, J. R. Zunger [ 3 ] , A. Zhang, X. [2] wileyonlinelibrary.com formula chemical spinel the writing of way used widely Another [1] I Hs , .ih Iea N Siaaa J K Saik Stalick, K. J. Shirakawa, N. Ikeda, S.-ichi Hase, I. [6] www.afm-journal.de ie, respectively. sites, their oxidationstatesto2 behavior isexpectedwhenbothA in principlebedopedbothn-andp-type.Heuristically, DT-4 Fermi level,asshowninFigure 2 b, andsuchmaterialscould in differentstructuretypesincludingolivineFe Phys.Rev. Lett. 317. Zunger is AB formal cationvalencies is tobenotedthattheA La larger projectthattreatsallA 2003 2 CuO , , 2 131 O [2] rst-principle defectcalculationinahigh-throughput 4 4 forwhichA mainlybecausetheworkpresentedhereispartofa . Here,wechoosetouseA , 269. , cation combinedwiththeinformationabout 2 BO

2006 4 spinels.We systematizethemaccordingto , , 2 96 Adv. Funct. Mater. BX , 207204. , Z 4 2 A

isthegenerallyusednotation.Further it BO

= + 2and and3 4 notationiscommonforspinels with 2 BX Published online:October24,2011 4 Z compounds(notonlyspinels) + B

, whenmovedtoT Phys. Rev. Lett.

Phys. Chem.Miner. =

3 4,suchasMg 2010 2 + BO

andB Received: June30,2011 Revised: August9,2011 4 , , followingZhangand © 20 2011WILEY-VCHVerlag GmbH&Co. KGaA,Weinheim 2 , 1944. , SiO 2 J. LowTemp. Phys. + atomsswitch

4 1965 , , 2 β TiO -K , , 2 d

15 SO 4 andO 1979 . [65] , 493. , 4 , and ,

, , 4 h ,

0] . asuinHdv , . asm N H Pry A R Nagaraja, R. A. Perry , H. N. Wansom , S. Mansourian-Hadavi, N. [20] Y Ihd , . aa R Euh , . asnm , . auh , . Chainani, A. Taguchi , M. Matsunami, M. Eguchi, R. Baba, T. Ishida, Y. [7] 3] . ea T Oaa N Hkm , . ea H Mzgci T Hasimoto, T. Mizoguchi, H. Ueda, K. Hikuma, N. Omata, T. Ueda, N. Weimer , W. [13] A. Li , J. Scheffe, R. J. [12] 2] . padiaa , Appandairajan, N. [32] 3] . erc H Ln , Ling , H. Petric, Wang , A. H. Deutsch, [23] G. T. Huda, N. M. Shet, S. Ahn, K.-S. Walsh , A. Paranthaman, P. [22] M. Payzant, Andrew E. Zhu, J. Lu, Z. [21] Mason, O. T. Dorris, E. S. [19] 4] . ijd P d Mer , . acﬁ l , . ogiu , . Laügt, S. Bougrioua, Z. Lanceﬁeld, D. Mierry , de P. Tinjod, F. [ 34 ] Mizoguchi, H. Ueda, K. Hikuma, N. Ueda, N. Omata, T. [14] Kurosaki, K. Kobayashi, H. Yamanaka , S. [8] 3] . iouh , . iao S Fjtu T Tkuh , . Ueda, K. Takeuchi , T. Fujitsu , S. Hirano, M. Mizoguchi, H. [33] Dang, C. K. Nga, K. N. [11] 7] . ozaa J Peht , Piechota , J. Łodziana, Z. [27] Angelov , S. Zhecheva, E. Stoyanova, R. [26] Angelov , S. Stoyanova, R. Zhecheva, E. [25] Angelov , S. Stoyanova, R. Zhecheva, E. [24] 7] . iaaa R Nsio T Oaa K Ud , . Kawazoe, H. Ueda, K. Ogawa, T. Noshiro, Exarhos, R. J. Miyakawa, G. Ferris , M. F. [ 17 ] K. Windisch, F. C. [16] Kawazoe, H. Ueda, K. Ueda, N. Omata, T. [15] 5] . ekr , . ines D H A Bak Blank, A. H. D. Rijnders, G. Dekkers, M. [35] Katayama, S. Shiono, O. Hamamoto, Takayama-Muromachi , E. Arai, M. Isobe, K. M. [10] Fujishiro , Y. [9] 8] . . hn , .H Wi Wei , S.-H. Zhang, B. S. [28] 8] . . ame , . . ao , . . opemir Poeppelmeier , R. K. Mason, O. T. Kammler , R. D. [18] 9] . . xro , . . idsh r , . . ers R R Oig , Owings, R. R. Ferris , F. K. Jr. , Lee , Windisch F. G. C. Exarhos, C. J. G. Kim, [39] U. D. Choi, H. Koo, H. B. Kumar , R. Kumar , S. [36] 1] . oiae I Tnk , . b , . oaa H Adachi, H. Koyama, Y. Oba, F. Tanaka , I. Moriwake, H. Wei [31] , S.-H. Al-Jassim, M. M. Yan , Y. Walsh , Recio, A. M. J. [30] Sampath, K. S. Gale , D. J. Pandey , R. [29] 8] . . ors T O Msn Mason, O. T. Dorris, E. S. [38] Kim, J. H. [37] . . ao , Mason, O. T. . eb , . hsi Y Oaoo H Tkg , . hn Shin, S. Takagi , H. Okamoto, Y. Ohashi, H. Senba, Y. . aao , . ahmt , Hashimoto, T. Kawazoe, H. 3333. 336. . . unr S-. e , . a , . . lJsi , Al-Jassim, M. M. Yan , Y. 2009 Wei , S.-H. Turner , A. J. Soc. . otra , . oezn , . hnt E Vry M R Kokta, R. M. Virey , Pauwels, E. D. Chenot, Stone-Sundberg, S. L. Lorenzini, J. P. Tottereau , O. Kawazoe, H. Hashimoto, T. 2009 . ooo Hosono, H. 38 239. 361. 351. . ha M Oia M Hrn , . ooo Hosono, H. Hirano, M. Orita, M. Ohta, H. A 1077. 450. Awano , M. 321. 2112. A J.Ceram. Soc.Jpn. 021903. Int.J.QuantumChem. 112 2004 2000

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, 344 . , 415 . the two- coordination shells will be M-(A shells will the two- coordination high-symmetry Wyckoff positions other then 8a, 16d lead to noni- high-symmetry Wyckoff to produce favorable bonding leading deal bonding and are unlikely positions. to occupation of interstitial 81 81 T. Mason , J. , Bettinger Y. Shi , M. , Toney Other lower-symmetry Wyckoff positions convert themselves to Other lower-symmetry positions for certain values of high symmetry Wyckoff occupying 16c(0,0,0), leads to a M-(B leads to a M-(B occupying 16c(0,0,0), 064109 . D. , S.Ginley Y. Shi , J. S. , Bettinger M. F. , Toney [ 40 ] C.-J. Ting , metal ion(M), 3/8, 3/8) position with occupying 8b(3/8, example H.-Y. For , Lu ] [ 41 ] 42 [ R. J. Bratton , [ 43 ] S. , Lany A. , Zunger [ 44 ] R. Dieckmann , H. Schmalzried , [ 45 ] R. Dieckmann , H. Schmalzried , [ 46 ] T. , Paudel S. , Lany M. , D’Avezac A. , Zunger N. , Perry A. Nagaraja , [ 47 ] J. D. Perkins , T. R. Paudel , A. , Zakutayev P. Ndione , P. A. Parilla , S. , Lany [ 48 ] S. , Lany A. , Zunger www.MaterialsViews.com Adv. Funct. Mater. Funct. Adv.