The eects of doping a grain boundary in ZnO withvarious concentrations of Bi

Johan M. Carlsson a,*, Bo Hellsing a, Helder S. Domingos b, Paul D. Bristowe b

a Experimental Physics, School of Physics and Engineering Physics, Chalmers University of Technology and Gooteborg University,SE-41296 Gothenburg, Sweden

b Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK

Abstract

We have made a systematic study of the Bi-decoration process in a R 13 [0 0 0 1] tilt grain boundary in ZnO byrst-principles calculations. This grain boundary is taken as a model system for studying the microscopic properties of

commercial Bi-doped ZnO-varistors. The calculations show that the decoration process is strongly site dependent and

that there is a considerable segregation energy for the Bi-atoms at low concentration. Increasing the concentration

lowers the segregation energy which sets an upper limit of approximately 32% for the Bi-concentration in this grain

boundary. This implies that the Bi-atoms stay in the grain boundary region rather than diusing into the ZnO grains

during the manufacturing process, but the maximum Bi-concentration is limited which is consistent with the experi-

mental observations. Bi-impurities in ZnO act as donors at low impurity concentration, but a localized BiBi-bond is

formed at higher Bi-concentration in the grain boundary. This Bi-state is located in the band gap of ZnO and it may be

responsible for the varistor eect observed in Bi-decorated grain boundaries.

2003 Elsevier Science B.V. All rights reserved.

Keywords: Grain boundaries; Zinc oxide; Interface states; Density functional calculations

1. Introduction

Zinc oxide is receiving increased interest today

due to its range of applications, but it is also

considered as a prototype material for studying the

properties of metal oxides. The wide direct optical

band gap makes single crystalline ZnO suitable for

optical applications [1] and the polycrystalline

form has been used for a long time in varistors [2].

A varistor is a voltage dependent resistor which

exhibits a highly non-linear IV characteristic [2].These devices are manufactured by liquid sinteringof ZnO mixed with a number of additives such as

Bi, Sb, Mo, Co and Cr [3]. The sintering produces

a polycrystalline ZnO material where the additives

accumulate in the grain boundaries [3,4]. It is as-

sumed that interface states in the grain boundaries

create a depletion region, which leads to the for-

mation of a double Schottky barrier (DSB) [2].

The barrier limits electron transport through thegrain boundary but an applied eld is able to

manipulate the population of the interface states.

The non-linearity is therefore the result of the

dramatic current increase when the DSB is re-

moved by the applied eld.

*Corresponding author. Address. FritzHaber -Institut der

Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin,

Germany, Tel.: +49-30-8413 4830; fax: +49-30-8413 4701.

E-mail address: johanc@fhi-berlin.mpg.de (J.M. Carlsson).

0039-6028/03/$ - see front matter 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0039-6028(03)00193-6

Surface Science 532535 (2003) 351358

www.elsevier.com/locate/susc

Bismuth is the most important additive which

contributes to the formation of the DSB [2]. A

majority of the Bi-atoms accumulate into Bi2O3-

phases at the triple junctions between the ZnO

grains in varistor materials [5] but the Bi-atoms

may also diuse out to become incorporated in thegrain boundaries. These Bi-atoms appear either as

isolated Bi atoms decorating the grain boundary

[6] or as a thin amorphous Bi2O3-layer [3] de-

pending on the cooling process [2]. It has been

debated in the literature which of these two types

of Bi congurations give rise to the most pro-

nounced non-linearity.

We have therefore studied the Bi-decorationprocess in a R 13 [0 0 0 1] tilt grain boundary inZnO by rst principles calculations. This particular

grain boundary is a convenient model system since

its atomic structure has been determined previ-

ously by both high resolution electron microscopy

(HREM) [7,8] and rst principles calculations [9].

The study involves a systematic investigation of

the most favourable substitution sites for the Bi-impurity atoms in the grain boundary and the Bi-

induced eects on the electronic structure.

2. Methods

The rst-principles calculations were based on

density functional theory (DFT) [10,11] using thePW-91 GGA exchange-correlation functional [12]

implemented in the Dacapo code [13]. A plane

wave basis set with an energy cuto of 300 eV was

used together with ultrasoft pseudopotentials [14].

The R 13 [0 0 0 1] tilt grain boundary was con-structed in the supercell using two unit cells of the

coincidence site lattice (CSL) in which the crystals

were misoriented by 32.2. The supercell thereforecontains 104 atoms and the periodic boundary

condition produces two grain boundaries per su-

percell. The Brillouin zone was sampled at 3 k-points along the c-axis parallel to the grain

boundary plane according to the MonkhorstPack

scheme [15]. The electronic population factor was

smeared by 0.01 eV [16] to improve convergence

and the atomic relaxation was performed using theBFGS-algorithm until the forces on the atoms

were less than 0.05 eV/AA. The projected density of

states (PDOS) was calculated by projecting the

wavefunctions on the atomic orbitals provided by

the ultrasoft pseudopotentials.

The formation energy of a defect is dened as

the change in Gibbs free energy due to the inclu-

sion of the defect in the system [17]. The formationenergy of the Bi impurity is therefore:

Eform EZnO : nBi EZnO nlZn lBi nele; 1

where n is the number of substituted atoms and lBiand lZn indicate the chemical potentials of the Biand Zn atoms respectively. The number of elec-

trons added to or removed from the impurity is

denoted ne and le is the electron chemical poten-tial. However, in the present work we have not

varied the charge state of the impurity and there-

fore the last term in Eq. (1) is zero. The segregation

energy Eseg is the dierence in formation energy ofthe impurity in the grain boundary and in the bulk:

Eseg EGBZnO : nBi EGBZnO nEbulkZnO : Bi EbulkZnO; 2

where the impurities in bulk are considered in the

dilute, non-interacting limit.

3. Results and Discussion

The results and discussion are divided into two

sections. The atomic structures and segregation

energies for the Bi impurities in the grain bound-

ary are presented rst. This is followed by a de-

scription of the impurity induced eects on theelectronic structure of the system.

3.1. Segregation

The calculated R 13 grain boundary structurewhich most closely matches the observed structure

[7,8] consists of a zig-zag chain of structural units

in the form of 10 atom rings [9]. These structuralunits contain two 3-coordinated neck sites and

eight 4-coordinated Zn-sites per atom ring and

there are two structural units per CSL-cell as can

be seen in Fig. 1. Two of the atoms in each

structural unit are common to both rings giving a

352 J.M. Carlsson et al. / Surface Science 532535 (2003) 351358

total of 16 Zn-sites per CSL-cell in the core of the

R 13 grain boundary. The substitution of one Biatom in the supercell then corresponds to

1=16 6:25% Bi-concentration in the grainboundary.

Three dierent substitution sites, denoted by A,B and C in Fig. 1 have been considered for the Bi-

substitution. A is the 3-coordinated site at the neck

of the structural unit, where one of the tetrahedral

bonds is broken and B and C are two dierent 4-

coordinated sites. Fig. 2 shows that the segregation

energy of one Bi atom in the grain boundary fa-

vours the 3-coordinated A site whereas the segre-

gation energy for B and C-sites is close to zero.This can be understood from the fact that the 4-

coordinated B and C-sites have maintained the

tetrahedral coordination of the bulk lattice giving

a more or less bulk like environment. The relax-

ation of the atoms in the grain boundary results in

a lattice expansion around the Bi-atom occupying

B or C-sites in the same way as was observed forBi-doping in the bulk [18]. The 3-coordinated A-

site, on the other hand, permits an asymmetric

relaxation into the structural unit. The Bi-atom in

the A-site utilized this freedom to move 0.7 AA inthis direction [18] resulting in large strain relief.

Increasing the Bi-concentration results in

stronger BiBi interaction. Previous bulk calcula-

tions [18] indicate a repulsive Bi impurityimpurityinteraction which suggests that the Bi atoms would

prefer a dispersed or dilute phase in the grain

boundary thus maximizing the BiBi distance.

Comparing the segregation energy in Fig. 2 for the

dispersed phase to the clustered phase where two

Bi atoms occupy the adjacent 3-coordinated neck

sites in the same structural unit also shows that the

dispersed phase is more favourable at 12.5% Bi-concentration. Another indication of the repulsive

BiBi interaction is that the segregation energy at

12.5% Bi-concentration is less than double the

value at 6.25%, which would be the case for two

non-interacting Bi-atoms.

A Bi-concentration of 18.75% results in more

than one Bi-atom in every second structural unit.

The additional Bi-atom, occupying either a 3- or a

Fig. 1. The relaxed geometry for the Bi-doped R 13 [0 0 0 1]tilt grain boundary at a Bi-concentration of 18.75%. The Bi

substitution sites are indicated by the letters A, B and C and the

encircled A marks the Bi atom for which the PDOS is shown in

Fig. 3. The 3-coordinated sites are indicated by A and the two

dierent 4-coordinated sites are marked by B and C. The da-

shed lines indicate the limits of the supercell and the dash-

dotted line indicates the grain boundary plane.

5 10 15 20 25 30 35 402

1.5

1

0.5

0

0.5

Bi-conc [% Bi/Zn-sites]

E seg

[eV

]

A

BC

AA

(AA)

A(AB)

A(AA)

A(AB)C

(AA)(AA)

(AA)B(AA)

(AA)B(AA)B

Fig. 2. The variation of the segregation energy for Bi-atoms in

a R 13 [0 0 0 1] tilt grain boundary in ZnO. The letters refersto the substitution sites indicated in Fig. 1 and AAr indicatesthat a BiBi bond is formed. The solid line shows the lowest

energy conguration at each doping concentration.

J.M. Carlsson et al. / Surface Science 532535 (2003) 351358 353

4-coordinated site, forms a bond with the 3-coor-

dinated Bi-atom on the opposite side of the

structural unit which will be discussed in detail

below. The 3-coordinated site remains more fa-

vourable than the 4-coordinated site, but the gain

upon adding a second Bi-atom in the structuralunit is much less than occupying the rst 3-coor-

dinated sites as can be seen in Fig. 2. This is related

to the fact that the Bi-atoms restrict the freedom

for the other Bi atoms to relax. The presence of

another Bi atom in the structural unit reverses the

movement of the Bi-atoms back towards the initial

Zn-sites due to the repulsive BiBi interaction.

This can be seen by comparing the relaxation ofthe Bi atoms in the structural unit containing one

or two Bi atoms in Fig. 1. The reversal of the re-

laxation is particularly evident at 25% Bi-concen-

tration where the most favourable conguration

corresponds to lling all 3-coordinated sites. The

Bi-relaxation at this concentration is less than 0.1AA with respect to the initial Zn-positions in theundoped grain boundary for all four Bi-atoms.The relaxed BiBi distance across the structural

unit is 2.93 AA which is very close to the corre-sponding ZnZn distance of 2.91 AA in the undopedgrain boundary.

The segregation energy starts to decrease as the

Bi concentration approaches 25%. The BiBi in-

teraction is then so strong that the energy gain in

substituting the Bi-atoms in 3-coordinated sites issubstantially reduced by the repulsive interaction.

A further increase in the impurity concentration

beyond 25% in addition means that the less fa-

vourable 4-coordinated sites have to be occupied.

The segregation energy at 31.25% is consequently

close to zero which indicates that the repulsive Bi

Bi interaction completely outweighs the energy

gain due to the improved bonding environment inthe grain boundary. Around 32% is therefore the

limit when further increase of the Bi-concentration

is no longer favoured compared to substitution in

the bulk.

The bismuth decoration process can be sum-

marized as strongly site dependent. The 3-coordi-

nated sites are the preferred substitution sites and

the repulsive BiBi interaction strives to maximizethe BiBi distance. This means that the 3-coordi-

nated sites are populated by placing one Bi atom in

each structural unit before another Bi atom can be

placed in the same structural unit. However, the

increased Bi-concentration forces the Bi-atoms to

occupy the adjacent 3-coordinated neck sites in

spite of the strong BiBi repulsion. Twenty ve

percent Bi-concentration marks the limit when all3-coordinated sites are populated and going be-

yond this concentration results in a signicant

decrease in segregation energy. There is a maxi-

mum Bi-concentration in the boundary of ap-

proximately 32% and this is consistent with

experimental measurements on doped ZnO poly-

crystals which report upper limits that are less than

a complete monolayer of Bi [4].

3.2. Electronic structure

The isolated Bi-impurity acts as a donor in bulk

ZnO, since it donates a signicant fraction of its p-

electrons to the neighbouring O-atoms. The be-

haviour is similar when the Bi-atom resides in a

grain boundary at low impurity concentrations[18]. In order to investigate the eect of increasing

Bi-concentration in the grain boundary, the cal-

culated PDOS for a Bi-atom has been plotted for a

variety of Bi-concentrations in the range 6.25

37.5% in Fig. 3. The dispersive conduction band

unfortunately appears as isolated peaks instead of

a continuous region due to the nite k-pointssampling. The position of the bottom of the con-duction band at each Bi-concentration is therefore

indicated by the dashed dotted vertical line in Fig.

3. The gure shows that no Bi-induced states ap-

pear in the band gap of ZnO at 6.25% and 12.5%

Bi-concentration. Instead, a majority of the p-

states on the Bi atom are located in the conduction

band and these p-states have energies well above

the conduction band minimum. The Fermi levelfor these systems is consequently located in the

conduction band resulting in metallic character for

the system but it is expected that the metallicity is

localized in the grain boundary plane.

Increasing the Bi-concentration beyond 12.5%

forces the Bi atoms to start occupying both of the

3-coordinated neck sites in the structural units.

The PDOS for 18.75% Bi-concentration (Fig. 3)shows that some Bi-induced p-states then appear

in the bandgap of ZnO and the donation from the

354 J.M. Carlsson et al. / Surface Science 532535 (2003) 351358

Bi-atom decreases. This behaviour is most pro-nounced at 25% Bi-concentration when all 3-co-

ordinated neck sites are occupied. Analyzing the

variation of the PDOS for the atoms in the su-

percell as a function of the distances from the grain

boundary shown in Fig. 4 reveals that the Bi-in-

duced states are localized both in space and in

energy. The dispersion of the Bi-induced state is

limited and the energy lies within the bandgap ofZnO. The weight of the PDOS is concentrated to

the Bi-atoms and the closest neighbours in the

grain boundary region. The corresponding wave

function shown in Fig. 5 furthermore reveals that

these states are, in fact, associated with a BiBi

bond. This bond comes from the Bi 6p-electrons

associated with the two Bi atoms in the 3-coordi-

nated neck sites which pair up across the structuralunit. The wave function shown in Fig. 5 has the

character of a r-bond and the large amount ofelectric charge in between the two Bi-atoms sug-

gest that it has bonding character. The electron

transfer from the Bi-atoms is concentrated into ther-bonds at 25% Bi-concentration which meansthat donation to the conduction band of the sur-

rounding atoms reaches a minimum. The Fermi

level in Fig. 4 is accordingly positioned between

the energy level of the r-bond and the conductionband minimum which gives the material semicon-

ducting character. Photoemission experiments for

a Bi-covered ZnO-surface have revealed a state 0.9eV above the valence band maximum [19]. It was

interpreted as an acceptor state connected to an

oxygen vacancy but in the light of the of present

calculations it seems as likely that the observed

state is a BiBi bond in the Bi-adlayer.

Increasing the Bi-concentration further leads to

the occupation of 4-coordinated sites. These addi-

tional Bi-atoms are not taking part in the r-bondbut instead donate a fraction of their p-electrons to

the conduction band which again gives the material

metallic character in the grain boundary plane. In

addition, the 4-coordinated Bi-impurities contribute

1 0 1 20

0.5PD

OS

CBi=6.25%

1 0 1 20

0.5

PDO

S

CBi=12.5%

1 0 1 20

0.5

PDO

S

CBi=18.75%

1 0 1 20

0.5

PDO

S

CBi=25%

1 0 1 2 30

0.5

E Ev [eV]

PDO

S

CBi=31.25%

1 0 1 2 30

0.5

E Ev [eV]

PDO

S

CBi=37.5%

Fig. 3. The PDOS for the Bi-atom indicated by a circled A in Fig. 1 as function of Bi-concentration CBi, in the R 13 tilt grainboundary in ZnO. The dashed and solid lines indicate the s- and p-components, respectively. The top of the valence band in the

dierent systems are taken as the reference of the energy scale. The vertical solid and dash dotted lines mark the position of the Fermi

level and the bottom of the conduction band at the various Bi-concentrations.

J.M. Carlsson et al. / Surface Science 532535 (2003) 351358 355

to a less localized state in the grain boundary which

overlaps both the 3- and 4-coordinated Bi-atoms.

This state is just visible near the Fermi level at

31.25% Bi-concentration as seen in Fig. 3.

Fig. 4. The PDOS for the individual atoms in the supercell as function of the perpendicular distance z, to the R 13 [0 0 0 1] tilt grainboundary in ZnO doped with 25% Bi. The solid line indicates the Fermi level and CB denotes the conduction band edge. The arrow

labeled Bi shows the position of the BiBi-r bond in the bandgap.

Fig. 5. The amplitude of the wave function jwj2 for the BiBi-r bond in the grain boundary containing 25% Bi, indicated by the Bi-arrow in Fig. 4. The wave function is shown as an isodensity surface at an electron density of 5 103 [eAA3]. The dashed lines indicatethe limits of the supercell and the dashed dotted line shows the position of the grain boundary plane.

356 J.M. Carlsson et al. / Surface Science 532535 (2003) 351358

The transfer of electrons from the Bi impurity

and its dependence on the Bi-concentration could

be described by a simple model for impurities in

semiconductors. The most convenient way of in-

corporating Bi atoms into ZnO at low concentra-

tion is by donating the excess charge of theimpurities to the conduction band of the sur-

rounding material. However, increasing the

Bi-concentration enhances the repulsive BiBi in-

teraction due to the dierent charge on the impu-

rity compared to the cations (Zn) in the lattice.

The Bi atoms are then trying to counteract the

electrostatic interaction by lowering their ionic

charge. The p-states of the Bi-atoms are thereforerepopulated. When both of the 3-coordinated neck

sites in the structural unit are occupied by Bi-

atoms, these atoms get close enough for the

wavefunctions to overlap. It is then favourable to

form a BiBi bond which diminishes the electro-

static repulsion between the two neighbouring

impurity atoms. This diers from the undoped

grain boundary where the electron density insidethe structural unit is very low because no ZnZn

bond is formed. The absence of a ZnZn bond is

probably connected to the fact that the ZnZn

distance is 1.5 times the ZnO distance in ZnO, but

also to the spherical symmetry of the 4s valence

electrons which limits the tendency to form direc-

tional bonds. It is therefore more favourable to

enforce the three remaining ZnO bonds than toform a ZnZn bond across the structural unit.

4. Conclusions

The segregation of Bi-impurities to the R 13tilt grain boundary in ZnO is strongly site depen-

dent. The 3-coordinated sites are favourable forsegregation since they provide large freedom for

relaxation. Higher Bi-concentrations increase the

repulsive BiBi interaction which counteract the

energy gain from the improved bonding environ-

ment in the grain boundary. The BiBi interaction

therefore sets an upper limit for the Bi-concentra-

tion in the grain boundary, which is estimated from

Fig. 2 to be 32% in the R 13 tilt grain boundary.In addition, the BiBi interaction also forces the

neighbouring Bi atoms to form a BiBi bond

across the structural unit. This BiBi bond con-

stitutes a state highly localized to the grain

boundary region and the energy of this state is

located in the band gap of ZnO. It is therefore

possible to manipulate its population by varying

the stoichiometry of the system or by applying anexternal eld. The occupation and depletion of this

BiBi state may then be related to the varistor

eect observed in Bi-decorated grain boundaries

[6]. The relatively high Bi-concentration needed in

the grain boundary to form the Bi-bond is also

consistent with the observation of a threshold for

the onset of the non-linearity as function of the

impurity concentration [3]. An investigation of theinteraction between the Bi-impurities and native

defects in the grain boundary is under way, which

aims at further clarifying the role of Bi in the

varistor materials.

Acknowledgements

J.C. has been supported by the Swedish Natural

Science Research Council and HSD acknowledges

grant PRAXIS XXI/BD/13944/97. The calcula-

tions were performed using the UNICC resourcesat Chalmers, Gothenburg, Sweden.

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358 J.M. Carlsson et al. / Surface Science 532535 (2003) 351358

The effects of doping a grain boundary in ZnO with various concentrations of BiIntroductionMethodsResults and DiscussionSegregationElectronic structure

ConclusionsAcknowledgementsReferences