Self-passivation of vacancies in α-PbO
aa r X i v : . [ c ond - m a t . m t r l - s c i ] F e b Self-passivation of vacancies in α -PbO. J. Berashevich, J.A. Rowlands
Thunder Bay Regional Research Institute, 290 Munro St., Thunder Bay, ON, P7B 5E1, Canada
A. Reznik
Thunder Bay Regional Research Institute, 290 Munro St., Thunder Bay, ON, P7B 5E1, Canada andDepartment of Physics, Lakehead University, 955 Oliver Road, Thunder Bay, ON, P7B 5E1
We introduce a self-passivation of single lead (Pb) and oxygen (O) vacancies in the α -PbO com-pound through formation of a Pb-O vacancy pair. The preferential mechanism for pair formationinvolves initial development of the single Pb vacancy which, by weakening the covalent bonding,sets up the crystal lattice for an appearance of the O vacancy. Binding of the Pb and O vacanciesoccurs through the ionization interactions. Since no dangling bonds appear at the Pb-O pair site,this defect has a minor effect on the electronic properties. In such, vacancy self-passivation offers apractical way to improve the transport properties in thermally grown PbO layers. Polycrystalline Lead Oxide (PbO) is one of the fewphotoconductive materials with a long- more than 60years - history of employment in imaging devices. Al-though PbO is extensively used as a photoconductor,very little is known about the electronic properties andcharge transport in this material. It is generally believedthat transport in PbO is controlled by trapping in de-fects and that trapping is a cause of low mobility-timeproduct [1]. However, the nature of defects is not fullyunderstood. Emerging applications of PbO in the directconversion flat panel radiation medical imaging detectorsrevived the interest in studying defects in this material asdefects can significantly affect imaging performance [2].Our recent modeling of the native point defects in α -PbO [3] has shown that thermally deposited PbO layersshould contain a significant concentration of single va-cancies due to their moderate formation energies. Singlevacancies are amphoteric defects appearing in the dif-ferent charge states. In the neutral charge state, theO vacancy ( V O(0) )) holds two electrons and forms thedeep donor level. The neutral Pb vacancy ( V Pb(0) )) isfilled with holes, and is a shallow acceptor. It was estab-lished that these vacancies prefer to appear doubly ion-ized, V Pb(2 − ) and V O(2+) , acting as compensating cen-tres to each other. Indeed, two compensating vacancieshave a lower formation energy than neutral ones, such as∆ E f ( V Pb(0) + V O(0) )- ∆ E f ( V Pb(2 − ) + V O(2+) )=0.78 eV[3].The fact that vacancies prefer to appear in chargestates suggests that we have to consider the ionizationinteractions between them and the formation of a neutralvacancy pair V Pb-O instead of two separate compensat-ing vacancies. This should further decrease the formationenergy, approximately speaking, the free energy requiredto insert a defect in a lattice is reduced by the energyliberated due to ionization of the donor and acceptor.Indeed, the formation of the defect complexes in favorover the single defects is often observed during materialdeposition [4]. In this work, we present our study of theformation mechanism of V Pb-O pair in PbO layers andits effect on the electronic properties. Analysis of the formation of V Pb-O vacancy pair wasperformed using the density functional theory (DFT)available in the Wien2k package [5] which utilizes the full-potential augmented plane-wave method. The Perdew-Burke-Ernzerhof parameterization [6] of the generalizedgradient approximation (GGA) to DFT has been imple-mented. We assigned only 5 p , 5 d , 6 s and 6 p electrons ofthe Pb atom and 2 s and 2 p electrons of the O atom to thevalence states, while the lower energy electrons were in-cluded into the core shells. The supercell approach wasapplied in which the supercell was taken of 120 atomsize (5 × × × × RK max =7(product of the atomic sphere radius and the plane-wavecut-off in k-space), and standard Monkhorst-Pack meshof size 4 × × α -PbO singlecrystals [8], we have considered it as a model compound.The α -PbO single crystal is of the tetragonal symmetry(129P4/nmm), its crystal structure is layered and thelayers are held together due to interlayer orbital overlapof the Pb:6 s lone pairs [9]. The detailed information onstructure and parameters used in our investigation of thevacancy defects can be found elsewhere [3].Upon formation of the vacancy pair, deficiency of twoelectrons at the Pb vacancy is compensated by two elec-trons occupying the O vacancy and dangling bonds areclosed on each other. Since Pb vacancy state is delocal-ized beyond the vacancy site (its wavefunction is spreadover at least five nearest-neighbours), it is not requiredfor O and Pb vacancies to be located at the nearest sitesto form a pair: schematic presentation of a position ofthe interacting vacancies relative to each other is shownin Fig. 1 (b). The electronic interactions between va-cancies are calculated as function of separation distance.Our analysis has revealed that an extra electron or holeadded to the pair is delocalized implying that V Pb-O has
FIG. 1: Colour on-line. (a) The crystal structure of α -PbO isshown for supercell of size 5 × ×
2. (b) Scheme demonstratesa position of the O vacancy (numbers 1,2,3 and 4) relative tothe Pb vacancy to generate the V Pb-O vacancy pair. only zero charge state for which the formation energy is[10]:∆ E f ( V Pb-O ) = E tot ( D ) − E tot ( X ) + µ (O) + µ (Pb) (1)where E tot ( D ) and E tot ( X ) are the total energy of thesystem containing the defect and defect-free, respec-tively; µ (O) = E tot (O) + µ ∗ (O) and µ (Pb) = E tot (Pb) + µ ∗ (Pb) , are the chemical potentials of removed atoms(O and Pb atoms) where µ ∗ i is the energy required tomove atom from vacuum to the conditions of growth( µ ∗ (Pb) + µ ∗ (O) = ∆ f H (PbO) =-2.92 eV [3] is definedfor the stable compound).To account for ionization interactions between vacan-cies we have analyzed the non-interacting and interact-ing vacancies. For non-interacting case, V O and V Pb have been placed into the same supercell, but in differ-ent layers. The interactions between such vacancies areabsent and each vacancy creates its own localized state, V O(0) and V Pb(0) . The formation energy under typicalgrowth conditions ( µ ∗ (Pb) + µ ∗ (O) =-2.92 eV) is found tobe ∆ E f ( V O(0) + V Pb(0) )=5.41 eV. To initiate the inter-action between vacancies, they have been placed in thesame supercell and the same layer. The formation ener-gies of the vacancy pair ∆ E f ( V Pb-O ) as function of thevacancy separation are presented in Fig. 2 (a) (in thefollowing we assume that ∆ E f ( V Pb-O ) is saturated atposition 4).The total lowering in the formation energy upon va-cancy binding is found to be E bind =-1.47 eV (vacanciesare located next to each other) which suggests that V Pb-O
FIG. 2: The formation energy of the vacancy pair as a func-tion of the vacancy separation ( V O position is referred topositions 1,2,3 and 4 in Fig. 1 (b)): (a) formation of the V Pb-O vacancy pair. (b) binding of V O to previously formed V Pb ( V O → Pb ). (c) binding of V Pb to already existing V O ( V Pb → O ). The formation energy of the single charged vacan-cies are calculated elsewhere [3]. is extremely energetically favored. There are two primaryparts contributing to E bind : interaction energy E int andlattice relaxation E lat . The E int is the energy changeinduced by the electron exchange between V O(0) and V Pb(0) causing their ionization to V Pb(2 − ) and V O(2+) states which is followed by lattice relaxation E lat . Thevalue of E int can be determined through the differencebetween the considered position and the point of satura-tion (position 4 is considered here to be the saturationpoint), is equal to 0.55 eV for V O in position 1. E int gradually decreases as oxygen vacancy is moved away(see Fig. 2 (a)) thus increasing the formation energy ofa pair. The magnitude of E int =0.55 eV is foreseen to beunderestimated because the state formed by the V Pb va-cancy is largely delocalized and when V O is placed at po-sition 4, it already may interact with the periodic copiesof V Pb . To eliminate this effect, the supercell of largersize has to be implemented which is not computationallyaffordable for us. For all positions depicted in Fig. 1 (b), E lat is constant and equals to 0.92 eV as the charge statewithin V Pb is not changed.Although vacancy binding lowers the formation en-ergy, its value is still high ( ≥ V Pb → O when V Pb isformed nearby existing V O , and V O → Pb for the oppositecase. The formation energies are:∆ E f ( V O → Pb ) = E tot ( D ) − E tot (Pb) + µ (O) (2)∆ E f ( V Pb → O ) = E tot ( D ) − E tot (O) + µ (Pb) (3)where E tot (Pb) and E tot (O) are the total energy of thesystem containing the single vacancy V Pb or V O , respec-tively.We have plotted the results on the formation energy ofthe vacancy pairs, V O → Pb and V Pb → O , in Fig. 2 (b) and(c), respectively. The different growth conditions havebeen considered: µ ∗ (Pb) =0.0 eV and µ ∗ (O) =-2.92 eV aredefined for Pb-rich/O-poor limit, while µ ∗ (Pb) =-2.92 eVand µ ∗ (O) =0.0 eV for Pb-poor/O-rich limit [3]. There isa very important trend to be observed in Fig. 2 (b) and(c): the values of ∆ E f ( V Pb → O ) and ∆ E f ( V O → Pb ) aresignificantly lower than the formation energy of the cor-responding single vacancies in their doubly ionized state[3]. Taking into account that binding energy is only E bind =-1.47 eV, this trend indicates that the lattice distor-tion induced by the single vacancy reduces the energyrequired to generate another vacancy nearby. The singlevacancy disturbs the lattice periodicity that alters theatomic forces between atoms and weakens the covalentbonds around the vacancy site.Therefore, the Pb vacancy sets up a lattice to accom-modate the O vacancy, thus causing a reduction in theformation energy ∆ E f ( V O(2+) ) − ∆ E f ( V O → Pb )=4.52 eV( V O is in position 1). Negative ∆ E f ( V O → Pb ) means thatthe lattice containing V Pb tends to ”suck in” O vacancyand formation of V O → Pb pair becomes spontaneous. Weexpect the Pb vacancies to be completely passivated by Ovacancies, as even for O-rich limit the formation energy∆ E f ( V O → Pb ) is close to zero. Similarly, the formation ofPb vacancy in close proximity to pre-existing O vacancyis energetically more favorable than single double ionized V Pb(2 − ) . However, the gain in energy is smaller than inthe previous case: ∆ E f ( V Pb(2 − ) ) − ∆ E f ( V Pb → O )=1.96eV and because ∆ E f ( V Pb → O ) >
0, the lattice distortioninduced by O vacancy is not sufficient to make a processof origin of the Pb vacancy spontaneous.To understand an effect of passivation on the transportproperties, the next step is to examine alteration in theelectronic properties induced by the neutral vacancy pair.We found, since the uncompensated dangling bonds areabsent at the V Pb-O defect site, the vacancy pair has a lit-tle effect on the band formation as shown in Fig. 3. Thevacancy pair does not seems to generate any localizedstate within the band gap, but rather induces a slightmodification into the band behavior. The top valenceband and its dispersion are almost unaffected by the ap-pearance of the vacancy pair and, therefore the hole mi-croscopic mobility is predicted to remain the same (it isalready low as a result of heavy holes m ∗ h =2.44 m [11]).In the conduction band, the vacancy pair induces a shiftof the lowest band down on the energy axis. This bandis a product of closing of the dangling bonds of vacancieson each other, i.e. its antibonding orbital. Moreover, itshows a slightly weaker dispersion at the M ∗ point that isanticipated to cause a reduction in the electron mobility.To gain insight the band behaviour we have plottedthe electron density map for bottom of the conductionband ( E C ) and top of the valence band ( E V ) in Fig. 4 FIG. 3: Band diagram for ideal supercell (black solid line)and for the same supercell containing the V Pb-O defect (reddashed line).FIG. 4: Colour on-line. The electron density map (e/A )plotted with XcrySDen [12] for 3 × × E C +0.076 eV), (b) thevalence band ( E V -0.076 eV). (a) and (b), respectively. The O vacancy was creatednext to the Pb vacancy. The electron density map isplotted for the narrow energy range ( E C +0.076 eV) and( E V -0.076 eV) to catch E C and E V in vicinity of the M ∗ and Γ points, respectively. For the conduction band, theelectron density shows the pronounced localization in thelayer containing V Pb-O and, in particular, on the atomsaround the defect site: continuity of the electron networkis disturbed that should affect the electron microscopicmobility. For the valence band, an alteration in the elec-tron density is confined entirely to the vacancy site wheredensity vanishes. Although such hole in the electron den-sity can affect the carrier transport locally in the vicinityof the defect, beyond that density remains undisturbed,suggesting that the hole mobility is not altered.From our study, one can conclude that Pb vacanciesin PbO layers are passivated by O vacancies to form theneutral vacancy pair. It seems reasonable to assume thatnegative effect of the vacancy pairs on the transport prop-erties of PbO photoconductive layers would be minimizedas the V Pb-O pair can not act as trapping center (dan-gling bonds are absent and extra electron or hole is delo-calized). Moreover, as pair formation involves merging ofsingle Pb and O vacancies ( E bind =-1.47 eV) which other-wise are active traps, it is foreseen to suppress the carriertrapping. As the concentration of O vacancies is higherthan that of Pb vacancies, the large fraction of V O(0) is left uncompensated to be filled with two electrons [3].The experimental evidence of n -type conductivity in PbOlayers [13] supports this observation. Our finding offer apractical way to improve the transport properties of ther-mally deposited PbO layers. The post-growth annealing (in vacuum or oxygen atmosphere) would initiate migra-tion of the O vacancies towards Pb vacancies with drivingforces defined by the vacancy interaction E int =0.55 eVand facilitates their merging. This is expected to reducean amount of ionized centres in PbO thus improving driftmobilities of electrons and holes as well suppressing re-combination. I. ACKNOWLEDGEMENT
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