Ab-initio studies on Li doping, Li-pairs, and complexes between Li and intrinsic defects in ZnO

Transcription

1 Ab-nto studes on L dopng, L-pars, and complexes between L and ntrnsc defects n ZnO R. Vdya, P. Ravndran, and H. Fjellvåg Ctaton: Journal of Appled Physcs 111, (2012); do: / Vew onlne: Vew Table of Contents: Publshed by the AIP Publshng Artcles you may be nterested n Magnetsm of Cr-doped ZnO wth ntrnsc defects J. Appl. Phys. 111, (2012); / Effect of L-dopng on the magnetc propertes of ZnO wth Zn vacances J. Appl. Phys. 111, (2012); / The orgn of p-type conducton n L-N codoped ZnO: An ab nto calculaton study J. Appl. Phys. 110, (2011); / Electronc structures of defects n ZnO: Hybrd densty functonal studes J. Chem. Phys. 129, (2008); / Ab nto study of magnetc nteracton of Fe doped ZnO wth ntrnsc vacances Appl. Phys. Lett. 90, (2007); /

2 JOURNAL OF APPLIED PHYSICS 111, (2012) Ab-nto studes on L dopng, L-pars, and complexes between L and ntrnsc defects n ZnO R. Vdya, 1,a) P. Ravndran, 1,2 and H. Fjellvåg 1 1 Center for Materals Scence and Nanotechnology and Department of Chemstry, Unversty of Oslo, Box 1033 Blndern, N-0315 Oslo, Norway 2 Central Unversty of Taml Nadu, Thanjavur Road, Thruvarur, Taml Nadu, Inda (Receved 6 March 2012; accepted 17 May 2012; publshed onlne 22 June 2012) Frst-prncples densty functonal calculatons have been performed on L-doped ZnO usng allelectron projector augmented plane wave method. L was consdered at sx dfferent ntersttal stes (L ), ncludng ant-bondng and bond-center stes and also n substtutonal stes such as at Zn-ste (L zn ) and at oxygen ste (L o ) n the ZnO matrx. Stablty of L Zn over L s shown to depend on synthetc condton, vz., L Zn s found to be more stable than L under O-rch condtons. Hybrd densty functonal calculatons performed on L Zn ndcate that t s a deep acceptor wth (0/-) transton takng place at 0.74 ev above valence band maxmum. The local vbratonal frequences for L-dopants are calculated and compared wth reported values. In addton, we consdered the formaton of L-par complexes and ther role on electronc propertes of ZnO. Present study suggests that at extreme oxygen-rch synthess condton, a par of acceptor type L Zn -complex s found to be stable over the compensatng L þ L Zn par. The stablty of complexes formed between L mpurtes and varous ntrnsc defects s also nvestgated and ther role on electronc propertes of ZnO has been analyzed. We have shown that a complex between L Zn and oxygen vacancy has less formaton energy and donor-type character and could compensate the holes generated by L-dopng n ZnO. VC 2012 Amercan Insttute of Physcs. [ I. INTRODUCTION Fabrcaton of optoelectronc devces such as blue and UV lasers and lght emttng dodes (LEDs) s one of the most attractve applcatons of wde-gap semconductors. ZnO wth ts wde band gap (3.37 ev at room temperature) and large excton bndng energy (60 mev) has receved much attenton as a promsng materal for optoelectronc devces such as LEDs and laser dodes. The possblty of growng many dfferent ZnO nanostructures has opened up a wde range of hgh technology applcatons. 1 In addton, among the tetrahedrally bonded semconductors, ZnO s found to have the hghest pezoelectrc tensor. 2 Ths unque combnaton of pezoelectrc, conductve, and optcal propertes of ZnO made t useful n many devces such as ultrasonc transducers, surface-acoustc-wave devces, and chemcal sensors. A p-n homojuncton usng a wde-gap semconductor has wde applcatons such as functonal wndow to transmt vsble lght and generate electrcty n response to the absorpton of UV photons. However, unlke the slcon technology t s very dffcult to make a p-n homojuncton usng wde-gap semconductors. It s well known that nomnally undoped ZnO exhbts n-type conductvty. To realze the optoelectronc devces, an mportant ssue s the fabrcaton of lowresstance p-type ZnO wth hgh hole concentraton. However, the realzaton of low-resstvty p-type ZnO has thus far proven dffcult due to reasons such as self-compensaton, a) Electronc address: vdya.ravndran@kjem.uo.no. deep acceptor level, and low solublty of the acceptor dopants. As large number of canddates receve partcular attenton for ntroducng p-type conductvty n ZnO, the optmal choce of acceptor speces remans to be determned. N substtutng for O appears promsng, whle other group-v dopants such as P and As have also been nvestgated. Unfortunately ther acceptor levels are dentfed to be deep. For example, a recent densty-functonal study 3 on N-doped ZnO usng an accurate hybrd-functonal calculaton that reproduced expermental band-gap has shown that N o s n fact a deep acceptor. Moreover Group-V dopants have qute low solublty lmts and the relablty of the resultng p-type behavor s stll the man ssue. Among Group-I elements, L-dopng has receved partcular attenton, manly because, L s the most common unntentonal dopant n hydrothermally grown ZnO. 4 Recently, p-type ZnO was reported to be achevable wth L mpurtes, although p-type conducton s hghly senstve to the growth condtons. 5 Moreover, L exhbts amphoterc behavor n ZnO, vz., the type of charge carrers generated by L-dopng depends mostly on the ste at whch L occupes. For example, f L occupes an ntersttal ste t acts as a donor; n contrast, substtutonal L (L Zn ) acts as an acceptor. Even though the solublty 6 of L n ZnO can be up to around 30 at. %, L dopng typcally ncreases the resstvty of n-type ZnO leadng to sem-nsulatng samples. Though the ncrease n electrcal resstvty by the ntroducton of L ons s detrmental for electrcal conductvty, t could be useful for measurng delectrc propertes /2012/111(12)/123713/10/$ , VC 2012 Amercan Insttute of Physcs

3 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) Moreover, L-dopng s shown to nduce ferroelectrc phase sutable for optcal memory devces. 8,9 Therefore, understandng the effects of L dopng n ZnO s mmnent for devce applcatons. In ths work, we have attempted to analyze the effects of L-dopng n ZnO by ntroducng varous defects and defect complexes through super-cell approach and performed structural optmzaton usng accurate densty-functonal calculatons. Interestngly, L-doped ZnO has been prepared by many dfferent synthetc technques and the propertes are shown to vary sgnfcantly dependng on growth condtons. Zeng et al. 11 have prepared p-type ZnO by mono-dopng of L usng dc magnetron sputterng. They have shown that p-type conducton s senstve to the substrate temperature as well as L-concentraton. 12 At 550 C, more L atoms substtute for Zn, whch act as an effectve acceptor and thus the optmzed p-type conducton s acheved. The acceptable p-type conducton dentfed by room temperature and temperaturedependent Hall-effect measurements was electrcally stable over a month. When substrate temperature s reduced to 450 C, redundant L atoms are ncorporated n the matrx, however the hole concentraton s decreased. On the contrary, the ZnO flms prepared by pulsed laser deposton (PLD) method showed 14 maxmum hole concentraton and lowest resstvty at 450 C. When the substrate temperature s reduced to 400 C the solublty of L atoms or L 2 O molecules n ZnO s low and also, when the temperature s ncreased to 600 C the amount of L-acceptor s reduced due to re-evaporaton of L from ZnO lattce. However, L-doped ZnO thn flms prepared by the same PLD method, but eptaxally grown on LNbO 3 substrates, have shown 15 n-type conductvty wth carrer densty of cm 3. Lu et al. 5 have prepared L-doped ZnO by PLD and shown that the type of carrer can be controlled by adjustng the growth condtons. They used an onzaton source so that the oxygen chemcal potental s ncreased snce excted O radcal speces are created n an onzed oxygen atmosphere, whch provdes an oxygen-rch condton for producng ZnO. They have shown that f the onzaton source s off, the ZnO flms grown n a conventonal O 2 atmosphere wthout ntentonal dopng shows n-type conductvty. On the other hand, f the onzaton source s on, p-type conductvty s obtaned n undoped ZnO due to the creaton of Zn vacances. Moreover, for ZnO:L flms prepared wthout usng the onzaton source the n-type conductvty s monotoncally reduced when the L content ncreases. Further, for ZnO:L flms prepared n the onzed oxygen atmosphere, the p-type conductvty s evdently enhanced wth the ncorporaton of L. L-doped ZnO also receves attenton as ferroelectrc actvty was found 11 n L-doped ZnO, although no phase transton had been reported by L dopng at atmospherc pressure. It s beleved that the large dfference n onc rad between the host Zn (0.74 Å) and the dopant L (0.60 Å) s very mportant for the appearance of ferroelectrcty n Ldoped ZnO. 12 Wang et al. 16 have prepared L-doped ZnO usng PLD and measured ts ferroelectrc and optcal propertes. They proposed that the off-centered postons of L substtutng Zn atoms lead to ferroelectrc dstorton. So, t s nterestng to study the local structural relaxaton by the substtuton of L at the Zn ste n ZnO. L-doped ZnO thn flms were prepared by sol-gel method 7 and the hole concentraton was shown to be low at 10 or 12.5 at. % of L, as holes are compensated by natve defects such as V o and Zn. However, f 15.0 at. % or more L atoms entered nto the ZnO crystal lattce, L atoms occupy Zn stes (ndcated by the decrease n c-axs length). Therefore, stable and optmzed p-type conducton was obtaned by around 15.0 at. % of L dopng. However, on further ncrease n L concentraton, the electrcal conductvty s decreased, may be because some L atoms do not occupy the Zn ste, nstead assemble at the crystal gran boundary whch could act as a scatterng center, thus deteroratng the p-type electrcal conductvty. Further, L-doped ZnO powders obtaned by ball-mllng of L 2 O wth ZnO showed ncrease n electrcal conductvty by ncrease n L concentraton and ths s attrbuted to the possble formaton of ntrnsc defects such as vacances. 17 In order to have mcroscopc understandng about the role of hgh concentraton of L on electrcal conductvty n ZnO detaled electronc structure studes n hgh concentraton of L-doped ZnO are needed. A frst-prncples calculaton showed 19 that L co-doped wth cobalt leads to room-temperature ferromagnetsm n ZnO whch has been confrmed n low-temperature sol-gel syntheszed ZnO:Co,L samples. Recently ferromagnetsm n L-doped ZnO nanorods has been observed 18 wth Cure temperature up to 554 K, ndcatng that t can be a promsng dlute magnetc semconductor useful for spntronc devces. Lee et al. 20,21 proposed a L-H codopng method for fabrcatng low-resstvty p-type ZnO. They have shown that co-dopng H severely suppresses the formaton of ntersttal donors and the solublty of L-dopants can be enhanced by the formaton of hydrogen-acceptor complexes. 22 However, expermentally t has been shown that 30% of Zn stes can be substtuted by L n sngle crystals. 8 On the other hand, Wardle et al. 23 suggested that p-type dopng may be lmted by the formaton of complexes, such as L Zn -L and L Zn -H. So, t s nterestng to study the stablty and nature of charge carrers of L-par complexes n ZnO by ab-nto calculaton. L dopng was shown 25 to typcally ncrease the resstvty of ZnO whch had otherwse very good n-type conductvty. Further, t has been theoretcally predcted 26 that p-type dopng n ZnO ncreases the Madelung energy, whch could nduce the localzaton of the acceptor states. 27 In the present work we report results of accurate total energy calculatons based on densty functonal method by consderng L at substtutonal stes (L Zn and L O ). In addton, we have also consdered sx dfferent ntersttal postons (Fg. 1) n order to fnd out the most preferable ntersttal ste for L n ZnO. The ntrnsc defects are known to nduce non-stochometry n ZnO at ambent condtons. Moreover, n hydrothermally grown ZnO samples, L concentraton of cm 3 s found, 28 whch can account only for 25% 65% of acceptors obtaned from Hall measurements and moblty smulatons. The remanng acceptors are suggested to have resulted from the coexstence of ntrnsc defects and L-mpurtes. As defect

4 Vdya, Ravndran, and Fjellva g J. Appl. Phys. 111, (2012) FIG. 1. The dfferent ntersttal postons for L n ZnO (.e., L) consdered for the total energy calculatons such as (a) Loct, (b) ABO;?, (c) ABZn;?, (d) ABO;k, (e) BCk (along c-axs), and (f) BC? (perpendcular to c-axs). The atom labels are gven n (a). complexes formed between ntrnsc defects and L-mpurtes have receved lttle attenton,23 we have carred out detaled nvestgaton on ntrnsc defect complexes wth L mpurtes and analyzed the energy levels nduced by such complexes. II. COMPUTATIONAL DETAILS Frst-prncples calculatons have been performed usng the projected augmented plane-wave (PAW)29 method as mplemented n the Venna ab nto smulaton package (VASP).30 We have performed calculatons for supercells wth 192 and 256 atoms. The defects are smulated by addng and/or removng consttuent atoms to/from the supercell. As the calculated formaton energy does not vary very much for 192 and 256 atoms supercells, we used the 192 atom supercells for smulatng defect complexes. We have tested the total energy convergence wth respect to k-ponts and plane wave energy cutoff. For the sake of more accurate results we used plane-wave energy cutoff of 550 ev. Brlloun zone samplng was done n the Monkhorst-Pack scheme wth k-pont mesh of for supercells wth 192 atoms. The optmzaton of the atomc geometry was performed va a conjugate-gradent mnmzaton of the total energy, usng Hellmann-Feynman forces on the atoms and the stresses n the unt cell. Durng the smulatons, atomc coordnates and axal ratos were allowed to relax for dfferent volumes of the unt cell. Convergence mnmum wth respect to atomc relaxatons was attaned when the energy dfference between two successve teratons was less than 10 6 ev per unt cell and the forces actng on the atoms were less than 1 mev A 1. For charged defects a jellum background charge was used. Exchange and correlaton effects are treated under the generalzed-gradent-approxmaton (GGA)31 ncludng the Perdew-Burke-Ehrenkof (PBE) functonal. The defect formaton energy s calculated as descrbed n Refs We have calculated the formaton energy of L-based defects by dervng chemcal potental of L from metallc L. The formaton energy derved from chemcal potental of L from L2O and L2O2 s 3.14 and 3.46 ev hgher n energy, respectvely. The dpole correcton to the formaton energy s ncluded by calculatng the correcton terms for 72 and 192 atom supercells. These values are extrapolated to nfnty wth respect to 1/L where L s the lnear length of the supercell. It s well known that present type of densty-functonal calculatons underestmate the band-gap sgnfcantly and therefore many correcton schemes are adapted dependng upon the type of the defect. One of the common correcton methods s to perform scssor operaton whch shfts

5 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) theoretcal conducton band mnmum (CBM) to match wth the expermental band-gap value. As the densty-functonal theory (DFT)-based calculatons severely underestmate band-gap [E g ; that obtaned by GGA s 0.88 ev], the transton levels are shown wth respect to corrected E g values. The correcton has been carred out by performng GGA þ U calculaton that provded an E g of 1.84 ev wth the valence band maxmum (VBM) pushed downwards. Then, a scssor operaton was performed to push the CBM upwards to match wth the expermental value. In order to fnd out the defect level nduced by L Zn whch s a polaranc defect, we have performed structure optmzaton and electronc structure calculaton usng the Heyd-Scusera-Ernzerhof (HSE) hybrd functonal 32 n neutral and 1 charge states. A screenng parameter of a ¼ was used whch reproduced expermental parameters for ZnO and provded a band-gap of 3.34 ev. Moreover, we have calculated bndng energy of a defect-complex (AB) formed between ndvdual defects A and B usng the followng conventon: Bndng energy E b (AB) ¼ E f (A) þ E f (B) - E f (AB), where E f (A), E f (B), and E f (AB) are formaton energy of defect A, defect B, and defect-complex AB, respectvely. Therefore, a postve bndng energy represents a bound system. In order to dentfy pont defects expermentally, vbratonal modes are often used to characterze varous defects. Therefore, we have calculated the vbratonal modes by obtanng second-dervatve of the total energy wth respect to dsplacement. The phonon frequences are derved from frozen-phonon calculatons,.e., dstortons consstent wth the symmetry of the mode are ntroduced and the correspondng total energy s calculated. In the present computatons, the second dervatves requred for the force-constant matrx elements were obtaned by calculatng the forces exerted on all atoms when one or two of the atoms are dsplaced n the a, c drecton. Both postve and negatve dsplacements were consdered to take nto account possble anharmonc effects. For all the frozen-phonon calculatons, we have used respectve supercells (wth 192 atoms). The coeffcent a2 n the second-order term n the followng equaton s the harmonc contrbuton to the total energy, naturally referred to as a force constant. Knowng ths, we then obtan the phonon frequency as ¼ð2pLÞ 1 a2 1=2 ; (1) 2l where l s the mass of the atom whch s nvolved n a gven phonon mode. From the second dervatve of the total energy or the frst dervatve of the force wth respect to the dsplacement of respectve atom, we have calculated the A1 and E phonon frequences. More detals of these calculatons are gven elsewhere. 36 III. RESULTS AND DISCUSSION A. L at ntersttal stes Many dfferent ntersttal stes for H at ZnO matrx have been dscussed n the lterature, 37 vz., dfferent antbondng and bond-center stes. Smlar to the H case, we have consdered L at sx dfferent ntersttal stes n ZnO as shown n Fg. 1. Among these ntersttal stes consdered (as seen from Table I), L prefers to occupy the octahedral ntersttal ste (L oct ) at whch t forms sx bonds wth neghborng atoms (three L-O bonds have 2.14 Å and three Zn-O bonds have 2.30 Å bond-lengths). Upon relaxaton, ths atom has dsplaced 0.1 Å closer to O atoms and 0.27 Å away from Zn atom does not nfluence dsplacement of neghborng host atoms from ther equlbrum postons. Ths could explan why ths ste confguraton has lower formaton energy compared to other confguratons consdered. The next hgher energy L (AB Zn;? ) ste s a dstorted tetrahedral ste at whch L forms 3 bonds wth O atoms (wth lengths rangng from 1.79 to 2.35 Å) and1bondwthazn atom at a dstance of 2.32 Å). The occupaton of L at L (AB Zn;? ) ste dsplaced neghborng Zn atom from ts equlbrum poston. Smlarly, the L at AB O;k poston also nfluences dsplacements of neghborng oxygen atoms from ther equlbrum postons. Ths ntersttal L atom also forms dstorted tetrahedral ste wth one oxygen atom at 1.62 Å and remanng three O atoms at a dstance of 2.15 Å. However, unlke H ntersttal, L does not prefer to take up the bondcenter postons (BC k and BC? ) and ths may be due to consderably larger covalent rad of L (1.28 Å) compared wth that for H (0.38 Å). It may be noted that the formaton of L s ndependent of Zn or O partal pressures. As seen from Tables I, the 1 þ charge state (donor) of L s lower n energy than neutral state for all ntersttal postons consdered, except for BC? poston. The acceptor-type charge state (1 ) s approxmately 0.30 ev hgher n energy than the neutral state. However, for the BC? poston the donor-type state s 2.55 ev hgher n energy than the neutral state. If the calculatons are atoms. Moreover, ths L oct TABLE I. Energy of formaton of L n dfferent possble ntersttal stes (notatons are as gven n Fg. 1). The L chemcal potental s derved from metallc L. The values correspond to the Ferm energy at valence band maxmum. Defect Charge state Formaton energy (ev) L oct þ L (AB Zn;? ) þ L (AB O;k ) þ L (AB O;? ) þ L (BC? ) þ L (BC k ) þ

6 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) performed wth constranng L to be at the BC? poston, the host atoms up to thrd nearest-neghbor postons undergo sgnfcant dsplacements from ther equlbrum postons and occupy the ntersttal stes. Therefore, even f L 1 state s acheved by placng L at BC? poston by some means, the crystal structure would not be stable. Ths mples that L atom occupyng an ntersttal ste can never have an acceptor-type character. s a shallow donor, n agreement wth prevous theoretcal studes. 20,23 As a shallow donor level s ntroduced below CBM by L, t can be taken as an ndcaton of decrease n E g, n good agreement wth the reducton n E g (from 3.37 ev to 3.25 ev) observed by absorpton band-edge from optcal measurements. 7 Moreover, photolumnescence (PL) spectra shows 47 an emsson band at 0.15 ev below E g (at 3.15 ev). (However, t may be noted that the concentraton of L n our smulaton s sgnfcantly lower than that n expermental observatons). L oct s-states are more prevalent n conducton band than n valence band, as expected and are energetcally well dspersed. A real-space frst-prncples calculaton 48 also found that the defect wave Densty of states (DOS) analyss shows that L 1þ functon arsng from L oct s not spatally bound to the defect atom. The hyperfne splttngs of 7 L n L-doped ZnO nanopartcles are measured 49,50 to be much smaller than that for atomc L, ndcatng that defect levels ntroduced are shallow and weakly bound. Ths s consstent wth the present observaton of formaton of shallow donor by L oct n ZnO. The energetcally well dspersed L 1þ s-orbtal DOS could also explan why L donor-type character (.e., n-type conductvty) s more domnant than the L Zn acceptor-type character n ZnO. As at CBM (n-type condton) the acceptor-type L Zn s havng lower energy than the donortype L, the holes would compensate the electrons generated by donor-type defects whch may explan the reason for ncrease n resstvty 25 at n-type condton due to L-dopng. B. Role of L substtuton at Zn (L Zn ) and oxygen (L O ) stes As the formaton of L at Zn and O stes requres formaton of Zn-vacancy(V Zn ) and Oxygen-vacancy (V O ), respectvely, they depend on the oxygen partal pressure. Between extreme Zn-rch and O-rch condtons, the oxygen chemcal potental vares by 3.38 ev. Ths varaton s gven as percentage of O-partal pressure n Fg. 2. As can be seen, L s the predomnant defect under Zn-rch condton. It can be noted that under O-rch condton the formaton energy of L Zn s very much lower than that of L at Zn-rch condton. Therefore, L Zn readly forms under O-rch condton, especally above 62% 64% of oxygen partal pressure. Below that value and under equlbrum condton, L s the domnant defect. Especally L has ca. 0.5 ev lower formaton energy than L Zn from L 2 O whch s the most common L source. L O s n a donor state (1þ state s 1.98 ev lower n energy than neutral state) and t has hgher formaton energy under both Zn-rch and O-rch condtons as well as at equlbrum. Hence, L O s not a stable defect and we have not consdered t for further dscussons. Formaton energy (ev) The L Zn defect has ca. 0.2 ev lower formaton energy for acceptor (1 ) state than the neutral state. Our structural relaxaton shows that f L s placed n the vcnty of a V Zn t relaxes down to the V Zn ste. Ths ndcates that L Zn can be stablzed n ZnO f one could dope L n ZnO samples that contan V Zn. Our prevous work 35 and other theoretcal studes 45,46 have shown that V Zn s the domnant defect under O- rch condton. The present observaton of the formaton of acceptor states by L Zn s consstent wth expermental results from Lu et al. 5 who showed that, upon usng onzng oxygen gas whch ncreases oxygen chemcal pressure, the p-type conductvty n ZnO s enhanced wth the ncorporaton of L at the Zn vacancy stes. For ZnO:L flms prepared wthout usng the onzaton source, a sharp decrease n electron concentraton was observed as compared wth the undoped ZnO flm. The n-type conductvty s monotoncally reduced as the L content ncreases, demonstratng that L compensates electrons n ZnO. Moreover, t may be noted that ZnO samples have Zn-termnated face (wth negatve surface polarty) and O-termnated face (wth postve surface polarty). When the L-doped ZnO sample s heat treated n ar, the concentraton of V Zn at the O-face s ncreased because of low Zn partal acceptors towards the oxygen face s enhanced durng the heat treatment. 4,38 L Zn receves partcular attenton not only for p-type conductvty but also for ferroelectrcty. Expermental studes 8,10 12 suggest that ZnO exhbts ferroelectrcty when L occupes the Zn ste, owng to the msmatch between ther onc rad. The nteratomc dstance between Zn and O n pure ZnO s Å and Å along ab plane and along c-axs, respectvely. The correspondng dstances for L-O s Å and Å, respectvely. Accordng to our calculatons based on PBE functonal, pressure. Therefore, transport of L 1 Zn L 1 Zn Oxygen partal pressure (%) FIG. 2. Formaton Energy of L oct,l Zn, and L O calculated as a functon of oxygen partal pressure. Zn-rch condton corresponds to 0% and Oxygenrch to 100% of Oxygen partal pressure. Chemcal potental of L s from metallc L. states occur at the top of VBM, ndcatng that t s a shallow acceptor, n agreement wth prevous studes If the Madelung correcton of ev s ncluded, the (0/1-) transton s found to take place at 0.05 ev above VBM. A study based on ultra-soft psuedopotentals has also found 24 localzed peak close to VBM whch has been assgned to L 2s and 2p orbtals. However, recent calculatons based on more accurate methodology 40 and hybrd-functonal calculatons have L L Zn L O

7 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) TABLE II. Local vbratonal frequences (n cm 1 ) of L-mpurtes n ZnO. Frequency Defect Mode 6 L 7 L L oct A 1 (along c) E (? to c) L Zn A 1 (along c) E (? to c) shown 41,42 L Zn to be a deep acceptor. In order to fnd out the (0/-) transton level of L Zn accurately, we have performed complete structural relaxaton usng hybrd (HSE) functonals as mplemented n the VASP program for a 72-atom supercell. In contrast to the PBE calculatons, the L-O dstances for L Zn are reduced by 2.14% and 2.53% along ab plane and c-axs, respectvely. All the four O atoms surroundng the L Zn have a unform bond-length of Å. Moreover, the L atom s slghtly dsplaced from ts ntal poston and moved towards the axal O atom along c-axs, could be due to the localzaton of hole at the axal O atom It may be noted that a decrease n c-axs length by L-dopng s also put forth by expermental studes. For example, a slght change s lattce parameters are observed n L-doped ZnO thn flms for L content of 4 at. %. 13 Our HSE calculatons provde the (0/-) transton level of L Zn to be at ev above VBM, n good agreement wth expermental value of 0.8 ev, 43 mplyng that L Zn s a deep acceptor. A recent electron paramagnetc resonance and PL spectroscopy study 44 on L-doped ZnO nanocrystals has also dentfed L acceptor wth an acceptor energy of 0.8 ev. As descrbed n Sec. II, the local vbratonal (LV) mode frequences for L are calculated and shown n Table II, are n good agreement wth earler theoretcal values. 23 As expermental determnaton of these frequences nvolves Lsotopes, the sotopc mass s taken nto account n the present calculaton. The LV frequences for L oct ndcate sgnfcant dfference n the bond strengths between bonds along c and perpendcular to c-axs. In contrast, the L Zn bonds have smlar strengths along c-axs and perpendcular to the c- axs. The Raman spectra measured for L-doped ZnO thn flms show two peaks at 438 and 579 cm 1 assgned to the longtudnal vbraton modes E2 and E1, respectvely. 39 Moreover, the L-doped flms exhbted hgh conductvty. Therefore, the expermentally observed E2 peak can be attrbuted to L whch acts as a donor and expected to ncrease conductvty. C. L-par complexes Many studes have found that the p-type conductvty decreases when the concentraton of L ncreases n ZnO. As the probablty to form L-pars s more by ncreasng the concentraton of L dopng n ZnO, we have carred out calculatons for pars of L,L Zn, and L þ L Zn (Fg. 3) to understand ther stablty and role n the electronc propertes n ZnO. For the case of L par, one L s placed at the octahedral ntersttal and another at AB Zn;?, as ths ntersttal ste s next hgher n energy. We found that the formaton FIG. 3. Formaton energy of L-par complexes as a functon of oxygen partal pressure; Zn-rch (0%) O-rch (100%). energy s 5.68 ev for the neutral state and as expected, the double donor state s 2.20 ev lower n energy (the values are calculated from chemcal potental of metallc L). When L 2 O s used as the source for L, and under O- rch condton, L Zn pars are more probable to form accordng to the followng equaton: L 2 O þ 2V Zn! 2L Zn þ O0 þ 2h: (2) The formaton of L Zn -par requres 7.02 ev/par n Zn-rch condton and only 0.26 ev/par under O-rch condton. The 2 charge state s found to be 0.12 ev/par lower n energy than the neutral state. As V Zn s less probable to form under Zn-rch condton, the formaton of L Zn par under ths condton requres a large energy. Ths par has a bndng energy of 5.58 ev. Smlar to the case of sngle L Zn defect the PBE functonal shows that the L Zn par s also a shallow acceptor, wth 2- to 0 transton takng place exactly at the VBM. Ths suggests that p-type conductvty n ZnO can be nduced, f the ZnO samples are prepared n oxygen-rch condton wth hgh concentraton of L,.e., by ntroducng L Zn -pars. In order to fnd out the poston of defect level nduced by the L Zn -par more accurately, computatonally demandng HSE functonal-based calculatons are requred. To understand the nteracton between L at the ntersttal and substtutonal postons n ZnO we have also nvestgated the (L þ L Zn ) par complex. As we have shown that the L oct has the lowest formaton energy than L at other ntersttal postons, we have smulated the (L oct þ L Zn ) par by placng a L atom at L oct and another L at Zn ste at a dstance of Å and made complete structural relaxaton. The formaton energy of (L þ L Zn ) s 4.34 ev/par and 0.96 ev/par under Zn-rch and O-rch condtons, respectvely. Interestngly, the neutral state s ev lower n energy than the 1 state. Therefore, ths par could compensate charges on ncreasng the L-content as suggested

8 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) FIG. 4. The formaton energy of L-par complexes as a functon of Ferm energy under Zn-rch and O-rch condtons. earler. 23 Moreover, the bndng energy for L þ L Zn par s also more (7.13 ev) compared to other L-pars ndcatng that ths par s more stable. It may be noted that, though L þ L Zn par s more probable to form n ZnO, t wll not contrbute to the electrcal conductvty owng to the fact that neutral state s more stable for ths defect. As seen from Fg. 3, the double-donor L -par s stable n a narrow wndow under extremely Zn-rch condtons. On the other hand, the double-acceptor L Zn s stable above 80% of oxygen partal pressure. The compensatng (L þ L Zn )pars stable for most of the growth condtons as well as at equlbrum condtons. Under equlbrum condton, the compensatng (L þ L Zn ) par s ca. 1 ev/par lower n energy than the double acceptor 2L Zn. However, under extreme O-rch condton and upto 80% of oxygen partal pressure, 2L Zn becomes stable. Therefore, f one could produce L-doped ZnO at O- rch condton, the p-type conductvty can probably be acheved even for hgher concentratons of L. The above dscusson corresponds to the Ferm energy (E F ) at the VBM whch can provde a clue for syntheszng L-doped ZnO. As the energetcs can become dfferent for E F values greater than VBM, the formaton energy of L-par complexes under Zn-rch and O-rch condtons are shown as a functon of E F n Fg. 4. Under extreme Zn-rch condton, the double donor L par s stable up to E F ¼ VBM þ 0.5 ev. Then, the compensatng (L þ L Zn ) becomes stable for E F up to 1.5 ev. The double acceptor L Zn par s stable for the remanng E F values and ths could explan the ncrease n resstvty as the L concentraton ncreases n some samples snce these acceptors wll compensate the donors created by other defects. Unlke the Zn-rch stuaton, f L-dopng s carred out under O-rch condton, the double acceptor 2L Zn s stable for all E F values from VBM to CBM. When a sngle L atom occupes Zn-ste (L Zn ) n ZnO lattce, the E F s pnned at 2.2 ev and 0.48 ev at Zn-rch and O-rch condtons, respectvely, due to self-compensaton. However, Fg. 4(b) clearly shows that the self-compensaton can be avoded f a 2L Zn s created under extreme O-rch synthetc condton. However, whether 2L Zn leads to p-type conductvty n ZnO can be ascertaned only from accurate HSE-based hybrd functonal calculatons. D. Complexes between L and ntrnsc defects Expermental studes based on Secondary Ion Mass Spectroscopy (SIMS) proflng, scannng spreadng resstance measurements, and postron annhlaton spectroscopy ndcated that L mpurtes are electrcally passvated through trappng by vacancy clusters whch are generated by on mplantaton and subsequent flash annealng. 4 Moreover, n a L-doped ZnO thn flm prepared by sol-gel method, a peak centered at 385 nm n PL spectra s assgned to Lacceptor-bound-excton. 7 The monovalent L ons can create some compensatng oxygen vacances n the ZnO lattce. Further, f the most common source of L (L 2 O) s used to dope L nto ZnO, some ntrnsc defect formaton s possble based on the followng equatons: L 2 O! 2L 1 Zn þ O0 O þ V2þ O ; (3) L 2 O þ O 2þ L 2 O! 2L 1þ! 2L 1 Zn þ 2O0 O ; (4) þ O 2 ; (5) L 2 O! L 1 Zn þ L1þ þ O 0 O : (6) Therefore, we have modelled L-mpurtes together wth some of the predomnant ntrnsc defects under Zn-rch as well as at O-rch condtons. The L -ntrnsc defects complex formaton energy s gven n Table III. The formaton energy of L depends on the L-chemcal potental nvolved durng the L dopng process. Moreover, the formaton of ntrnsc defects depends on the Zn and O chemcal potentals. Therefore formaton energy of complexes s gven at Zn-rch and O-rch condtons. From Table III, t s clear that the complexes between L and the domnant ntrnsc defects (vz., V O,Zn, and Zn O ) at Zn-rch condtons have lower formaton energes. As these defects are stable at 2 þ charge state, ther complexes wth L have lower energy at 3þ charge state. Among these defect complexes (L þ V O ) has negatve bndng energy, ndcatng the nstablty of ths complex. The (L þ Zn O ) 3þ complex has the lowest formaton energy and hghest bndng energy at Zn-rch condton.

9 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) TABLE III. The calculated formaton energes of defect complexes between L and ntrnsc defects. The L chemcal potental s derved from metallc L. The formaton energy estmated from the chemcal potental of L 2 O and L 2 O 2 s 3.14 and 3.46 ev hgher n energy, respectvely. The values correspond to the Ferm energy at valence band maxmum. The values n brackets are bndng energy of the defect complexes n ev. Formaton energy (ev) Defect complex Charge state Zn-rch O-rch L þ V O þ 5.25 ( 1.77) þ L þ Zn þ þ þ 5.14 (0.14) 8.52 L þ Zn O þ þ þ 4.71 (0.49) L þ V Zn þ (0.94) L þ O þ (2.91) 2þ L þ O Zn þ Snce the doubly onzed Zn has delocalzed electrons at the CBM, charge can be transferred from Zn to the empty L 1þ states smlar to the case wth Co þ Zn complex n Co-doped ZnO. 51 As noted n our prevous work, 35 O has lower energy under neutral state at O-rch condton. Therefore, (L þ O ) 1þ complex has domnant donor character. As mentoned earler L wll relax down to V Zn f kept closer and unconstraned. Therefore, the (L þ V Zn ) s modelled by performng constraned calculatons. Even though 1 state of (L þ V Zn ) complex has lower energy of formaton, the bndng energy of ths complex s small compared to that of the donor-type (L þ O ) complex. In order to understand the behavor of defect complexes under p-type(at VBM) and n-type (at CBM) condtons and charge transtons caused by defect complexes, the formaton energy of more domnant complexes s shown as a functon of Ferm energy under Zn-rch and O-rch condtons n Fgs. 5(a) and 5(b). If one compares the stablty of L þ ntrnsc defect complexes under Zn-rch condton, the donor type complexes such as L þ Zn and L þ Zn O are stable at VBM and up to E F values of 1.2 ev. For the hgher E F values, the acceptor-type L þ V Zn becomes the domnant defect complex. On the other hand, under O-rch condton, the acceptor-type (L þ V Zn ) complex s stable for the entre E F range. E. Complexes between L Zn and ntrnsc defects We have shown n Sec. III B that L Zn has the possblty of stablzaton n a narrow wndow of hgher oxygen partal pressure. Therefore, formaton of complexes of L Zn wth natve defects s studed and the formaton energes are gven n Table IV. Even though the (L Zn þ O ) has the hghest bndng energy under O-rch condton, t has hgher formaton energy than the donor-type (L Zn þ V O ) complex. Moreover, the acceptor-type (L Zn þ V Zn ) has very lttle bndng energy n spte of havng almost the same formaton energy as that of (L Zn þ V O ). The formaton of the donor-type (L Zn þ V O ) complex may compensate the few holes generated by L Zn at O-rch condton and ths could also explan the dffculty n obtanng p-type conductvty. Formaton energy of complexes between L Zn and ntrnsc defects as a functon of E F s gven n Fg. 6. The present study suggests that, under Zn-rch condton, donor-type defects are predomnant. Even for L Zn whch has acceptor character, when t forms complexes wth donor defects such as V O,Zn, and Zn O, the donor character becomes predomnant. The defect complexes such as (L þ Zn O ) and (L Zn þ Zn O ) are found to be shallow donors, smlar to natve Zn O defect. As shown before 35 the V 2þ O has defect levels deep nsde E g and ths defect forms a complex wth L Zn gves rse to the 1þ!0 transton of L Zn þ V O deep nsde the band-gap. In contrast to Zn-rch condton, under O-rch condton, the acceptor-type defects are more predomnant. FIG. 5. Formaton energy of defect complexes formed between L and ntrnsc defects under (a) Zn-rch and (b) O-rch condtons. The dots ndcate charge-transton ponts and the charge states are gven on the llustraton.

10 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) TABLE IV. Formaton energes of defect complexes between L Zn and ntrnsc defects. The L chemcal potental s derved from metallc L. The formaton energes derved from chemcal potental of L 2 O and L 2 O 2 are 3.14 and 3.46 ev hgher n energy, respectvely. The values lsted are correspondng to the Ferm energy at valence band maxmum. The values n brackets are bndng energy n ev. Formaton energy (ev) Defect complex Charge state Zn-rch O-rch L Zn þ V O þ (0.33) 3þ L Zn þ Zn þ (0.90) 2þ L Zn þ Zn O þ 6.17 (1.16) þ L Zn þ V Zn (0.01) L Zn þ O þ (5.85) L Zn þ O Zn However, at VBM the acceptor-type (L Zn þ V Zn ) and donortype (L Zn þ V O ) have almost the same energy of formaton ndcatng that the probablty of compensatng the holes created by (L Zn þ V Zn ) s hgh. The p-type dopng usng L speces causes a remarkable ncrease n the Madelung energy, 52 resultng n the nstablty of onc charge dstrbutons n ZnO: L. Therefore, the formaton of V O n the vcnty of the mpurty L Zn stes s energetcally favorable n ZnO: L. Ths means that the dopng of L gves rse to bad crystallnty due to the compensaton by V O. As a result, ZnO: L crystals or thn flms probably exhbt hgh resstvty by ncrease of electron scatterng by poor crystallnty. The (L Zn þ Zn ) complex also has donor-type character wth bndng energy of 0.90 ev whch s found to be consstent wth the calculated value of 1.09 ev reported earler. 53 The (L Zn þ V Zn ) complex n 2 charge state s havng lower energy than the (L þ L Zn ) under the O-rch condton. Unfortunately, the (L Zn þ V O ) n donor state s very much lower n energy than the double acceptor (L Zn þ V Zn ). As V Zn and V O are nvolved n the (L Zn þ V O ) complex, ts formaton energy s ndependent of oxygen chemcal potental. The results from our structural optmzaton ndcate that the reducton n c-axs of L-doped samples may not be attrbuted to the sngle L Zn defect. We have shown earler 37 that a sngle V 2þ O actually reduces volume by 0.4%. As the L Zn þ V O has lower formaton energy than L Zn, the decrease n c-axs length can be attrbuted to ths defect complex. However, t may be noted that the complexes formed between L Zn wth V O and V Zn have very small bndng energy compared to that of the compensatng (L þ L Zn )complex. IV. SUMMARY We have performed densty-functonal calculatons for L-doped ZnO usng large supercells. Among the octahedral, ant-bondng, and bond-centered ntersttal postons consdered, L at the octahedral (L oct ) ntersttal ste s found to be more stable. L at oxygen ste behaves as a donor; however, t s not stable compared to L and L at Zn ste (L Zn ). Whle the donor-type L s stable at Zn-rch and equlbrum condtons, the acceptor-type L Zn becomes stable at oxygen-rch condtons (.e., above 62% of oxygen partal pressure). The s-electrons of L s energetcally well dspersed compared to that of L Zn whch s one of the reasons for more stablty of L.AsL Zn n 1 state s domnant at n-type condtons, the holes may compensate the electrons generated by ntrnsc defects and other mpurtes, thus ncreasng the resstvty of the sample at n-type condton. The calculated vbratonal frequences ndcate that L Zn has almost smlar bondstrengths along c and perpendcular to c drectons. Moreover, the hybrd functonal calculatons ndcate that L Zn s a deep acceptor wth the defect level at 0.74 ev above valence band maxmum. FIG. 6. Formaton energy of defect complexes formed between L Zn and ntrnsc defects under (a) Zn-rch and (b) O-rch condtons. The dots ndcate charge-transton ponts and the charge states are gven on the llustraton.

11 Vdya, Ravndran, and Fjellvåg J. Appl. Phys. 111, (2012) We have consdered L-mpurty pars n ZnO, vz., 2L, 2L Zn, and L þ L Zn. Whle the double-donor 2L s stable only at extreme Zn-rch condton, the double-acceptor L Zn par s stable at extreme O-rch condton. However, the (L þ L Zn ) whch s stable n neutral state s domnant n equlbrum condton. The complexes formed between L-mpurtes and ntrnsc defects are also consdered and we found that the L þntrnsc-defect complexes are more predomnant than L Zn þntrnsc-defect complexes. The L þntrnsc-defect complexes are stable n donor states and have reasonable bndng energes under both Zn-rch and O-rch condtons, whch could cause dffculty n obtanng p-type conductvty n L-doped ZnO. Among the L Zn þntrnsc-defect complexes consdered, the donor-type (L Zn þ V O ) s stable under Zn-rch condton and acceptortype (L Zn þ V Zn ) s stable under O-rch condton. 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