Native point defects in ZnO

Native point defects in ZnO

Anderson Janotti and Chris G.Van de Walle

Materials Department,University of California,Santa Barbara,California93106-5050,USA

?Received18April2007;published4October2007?

We have performed a comprehensive?rst-principles investigation of native point defects in ZnO based on density functional theory within the local density approximation?LDA?as well as the LDA+U approach for overcoming the band-gap problem.Oxygen de?ciency,manifested in the form of oxygen vacancies and zinc interstitials,has long been invoked as the source of the commonly observed unintentional n-type conductivity in ZnO.However,contrary to the conventional wisdom,we?nd that native point defects are very unlikely to be the cause of unintentional n-type conductivity.Oxygen vacancies,which have most often been cited as the cause of unintentional doping,are deep rather than shallow donors and have high formation energies in n-type ZnO?and are therefore unlikely to form?.Zinc interstitials are shallow donors,but they also have high formation energies in n-type ZnO and are fast diffusers with migration barriers as low as0.57eV;they are therefore unlikely to be stable.Zinc antisites are also shallow donors but their high formation energies?even in Zn-rich conditions?render them unlikely to be stable under equilibrium conditions.We have,however,iden-ti?ed a different low-energy atomic con?guration for zinc antisites that may play a role under nonequilibrium conditions such as irradiation.Zinc vacancies are deep acceptors and probably related to the frequently ob-served green luminescence;they act as compensating centers in n-type ZnO.Oxygen interstitials have high formation energies;they can occur as electrically neutral split interstitials in semi-insulating and p-type mate-rials or as deep acceptors at octahedral interstitial sites in n-type ZnO.Oxygen antisites have very high formation energies and are unlikely to exist in measurable concentrations under equilibrium conditions.Based on our results for migration energy barriers,we calculate activation energies for self-diffusion and estimate defect-annealing temperatures.Our results provide a guide to more re?ned experimental studies of point defects in ZnO and their in?uence on the control of p-type doping.

DOI:10.1103/PhysRevB.76.165202PACS number?s?:61.72.?y,71.55.Gs,61.72.Bb,66.30.?h

I.INTRODUCTION

Understanding the behavior of native point defects is es-sential to the successful application of any semiconductor. These defects often control,directly or indirectly,doping, compensation,minority carrier lifetime,and luminescence ef?ciency.They also assist the diffusion mechanisms in-volved in growth,processing,and device degradation.1–3 Doping forms the basis of much of semiconductor technol-ogy and can be drastically affected by native point defects such as vacancies,self-interstitials,and antisites.Such de-fects may cause self-compensation:for instance,in an at-tempt to dope the material p type,certain native defects which act as donors may spontaneously form and compen-sate the deliberately introduced acceptors.In ZnO,speci?c native defects have long been believed to play an even more important role.As-grown ZnO frequently exhibits high lev-els of unintentional n-type conductivity,and native point de-fects have often been invoked to explain this behavior.Oxy-gen vacancies and zinc interstitials have most often been mentioned as sources of n-type conductivity in ZnO.4–15 Nevertheless,most of the arguments have been based on circumstantial evidence,in the absence of unambiguous ex-perimental observations.The availability of higher-quality bulk crystals and epitaxial layers has contributed to signi?-cant progress in the experimental observation of point de-fects in the last few years.16–24However,the impact of indi-vidual defects on the electronic properties of ZnO is still a subject of much debate.

Besides knowing their electronic properties,it is also im-portant to know how native point defects migrate in the crys-tal lattice.Knowledge of migration of point defects greatly

contributes to the understanding of their incorporation during

growth and processing,and it is essential for modeling self-

diffusion and impurity diffusion,which is nearly always me-

diated by native https://www.wendangku.net/doc/a75486240.html,rmation about atomic diffusion

or migration of point defects in ZnO is currently limited.

Neumann has summarized experimental results for self-

diffusion in ZnO up to1981.25Activation energies of zinc

self-diffusion were reported to be in a range from

1.9to3.3eV,while activation energies for oxygen self-

diffusion were reported to span a much wider range,from

1.5to7.5eV.Interpreting these results or using them in a

predictive manner is not straightforward.The activation en-

ergy for self-diffusion?Q?is the sum of the formation energy of the defect that mediates the self-diffusion and its migra-

tion energy barrier:26

Q=E f+E b.?1?The migration energy barrier E b is a well de?ned quantity,

given by the energy difference between the equilibrium con-

?guration and the saddle point along the migration path,and

can be obtained with good accuracy from?rst-principles

calculations.27–31The?rst term in the activation energy,

namely,the formation energy of the defect?E f?,however, strongly depends on the experimental conditions,such as the

position of the Fermi level and the zinc or oxygen chemical

potentials.These parameters can cause large changes?by

several eV?in the formation energy.It is usually not straight-

forward to assess how the environmental conditions affect

PHYSICAL REVIEW B76,165202?2007?

the formation energy and hence the activation energy for self-diffusion.This explains the wide spread in the reported values and makes it dif?cult to extract values from experi-ment.

In addition to self-diffusion measurements,investigating the behavior of point defects through annealing can also pro-vide valuable information about their migration.17,23,32–35The point defects in such experiments are often deliberately in-troduced into the material through nonequilibrium processes such as electron irradiation or ion implantation.Once point defects are introduced,they can be identi?ed by their optical, electronic,or magnetic responses?signatures?.These signa-tures are then monitored as a function of annealing tempera-ture.Changes in defect signatures at a given annealing tem-perature indicate that the relevant defects have become mobile.In principle,one can perform a systematic series of annealing experiments at different temperatures,extract a time constant for the decay of the signal at each temperature,

and then perform an Arrhenius analysis.In the absence of

such elaborate studies,estimates for activation energies can

still be obtained by performing an analysis based on transi-

tion state theory.36All of these assume,of course,that the

observed changes in defect signatures are solely related to

defect migration and do not involve any other processes such

as formation of complexes,etc.

For all these reasons,systematic?rst-principles studies of

both migration and formation energies for all relevant defects

are very useful.As we will show,the calculated values can

be used to interpret results from self-diffusion measurements

and annealing experiments.A number of?rst-principles cal-

culations for point defects in ZnO,based on density func-

tional theory?DFT?and the local density approximation ?LDA?or the generalized gradient approximation?GGA?, have been reported in the last few years.37–45However,in-

terpretation of the results of these calculations is not straight-

forward.Calculations based on DFT-LDA or DFT-GGA suf-

fer from the well known band-gap error.In the case of ZnO,

the calculated band gap using LDA is only0.8eV,compared

to the experimental value of3.4eV.This error leads to large

uncertainties in the calculated position of the defect-induced

states in the band gap and,consequently,in the defect for-

mation energies and transition levels,precluding direct pre-

dictions or comparisons with experimental values.Various

attempts have been made to correct formation energies and

transition levels given by LDA.Some of these corrections

are based on empirical reasoning or on a rigid shift of the

conduction band;37–41others are based on non-self-consistent

approaches,38,42LDA+U,43,44or calculations using a hybrid

functional.45These various approaches have led different

groups to qualitatively different conclusions about the role of

individual point defects in ZnO.37–45

A comprehensive analysis of the electronic and structural

properties of native point defects requires a systematic,quan-

titative,and self-consistent approach for correcting formation

energies and transition levels.The reason LDA severely un-

derestimates the band gap of ZnO is partially related to the

underestimation of the binding energy of the zinc semicore

3d states.46In this work,we use the LDA+U approach to

correct for the position of the zinc d states in ZnO.As dis-

cussed in more detail elsewhere,46,47this leads to a system-atic improvement in the description of the physical proper-ties of the system.The LDA+U approach also produces a partial correction of the band gap.By combining self-consistent calculations based on LDA and LDA+U,we are able to calculate the dependence of transition levels on the theoretical band gap and extrapolate the results to the experi-mental band gap.The transition levels are thus corrected according to their valence-and conduction-band character in a consistent and quantitative fashion,distinguishing the ap-proach from previous studies based on LDA+U.43,44Based on this formalism,we investigate the electronic and struc-tural properties of all native point defects in ZnO.We ex-plore the local atomic relaxations and their effect on the elec-tronic structure of each defect.We also report results for previously unexplored con?gurations and present a compre-hensive study of migration barriers.Finally,we discuss the in?uence of native defects on the control of n-and p-type doping.

This paper is organized as follows.In Sec.II,we discuss the theoretical framework for studying native point defects in semiconductors.We describe the calculation of formation en-ergies,transition levels,and the correction scheme based on the LDA and LDA+U calculations.In Sec.III,we focus on the results for native point defects in ZnO.We report the calculated formation energies and discuss the electronic and geometric structure.We devote particular attention to the oxygen vacancy,which has frequently,but incorrectly,been invoked as the source of n-type conductivity in ZnO.We also report the results for diffusion mechanisms and the corre-sponding migration barriers for interstitials and vacancies. Section IV summarizes our results.

II.THEORETICAL APPROACH

Our?rst-principles investigations are based on density functional theory within the local density approximation.48 The DFT-LDA approach allows for calculations of total en-ergies of solids,molecules,and https://www.wendangku.net/doc/a75486240.html,ttice parameters, atomic positions,and forces?derivatives of total energy with respect to atomic positions?can be computed quite accurately;49the structural parameters are typically predicted to within a few percent of the experimental values.By using appropriate boundary conditions,such as supercells with pe-riodic boundary conditions,it is also possible to investigate the electronic and local lattice structure of defects in solids, search for equilibrium atomic positions of defects and the surrounding host atoms,and calculate migration energy bar-riers and migration paths.Formation energies of defects and impurities can be derived directly from total energies,allow-ing calculation of equilibrium concentrations.30

A.Technical details

We use the pseudopotential method to separate the chemi-cally inert core electrons from the chemically active valence electrons.Semicore states,such as the zinc3d states which are less than10eV below the valence-band maximum in ZnO,need to be treated explicitly as valence electrons.In the present work,we use the projector-augmented-wave pseudo-

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

potentials as implemented in the V ASP code.50,51The defects are simulated by adding ?removing ?host atoms to ?from ?a 96-atom supercell with periodic boundary conditions.We use a plane-wave basis set with a 400eV cutoff and a 2?2?2mesh of special k points for integrations over the Brillouin zone.Tests as a function of plane-wave cutoff and k -point sampling show that our results for neutral defects are nu-merically converged to within 0.1eV;somewhat larger er-rors may occur for charged defects due to defect-defect in-teractions in neighboring supercells.

B.Defect concentrations

The concentration of a point defect depends on its forma-tion energy.In thermodynamic equilibrium and in the dilute regime ?i.e.,neglecting defect-defect interactions ?,the con-centration of a point defect is given by

c =N sites exp ??E f

k B T

?

,?2?

where E f is the formation energy ,N sites the number of sites the defect can be incorporated on,k B the Boltzmann con-stant,and T the temperature.Equation ?2?shows that defects with high formation energies will occur in low concentra-tions.Here,we neglect the contributions from the formation volume and the formation entropy.The former is related to the change in the volume when the defect is introduced into the system;it is negligible in the dilute regime and tends to become important only under high pressure.The formation entropy is related mainly to the change in the vibrational entropy.Formation entropies of point defects are typically of the order of a few k B ,and therefore become important only at very high temperatures.Moreover,vibrational entropy con-tributions largely cancel out when comparing different de-fects or assessing solubilities.30

C.Formation energy of defects

The formation energy of a point defect is not a constant but depends on the growth or annealing conditions.30For example,the formation energy of an oxygen vacancy is de-termined by the relative abundance of Zn and O atoms,as expressed by the chemical potentials ?Zn and ?O ,respec-tively.If the vacancy is charged,the formation energy further depends on the Fermi level ?E F ?,which is the energy of the electron reservoir,i.e.,the electron chemical potential.Form-ing an oxygen vacancy requires the removal of one oxygen atom;the formation energy is therefore

E f ?V O

q ?=E tot ?V O q ??E tot ?ZnO ?+?O +q ?E F +E v ?,?3?

where E tot ?V O

q

?is the total energy of a supercell containing the oxygen vacancy in the charge state q ,E tot ?ZnO ?is the total energy of a ZnO perfect crystal in the same supercell,and ?O is the oxygen chemical potential.Expressions similar to Eq.?3?apply to all native point defects.

The chemical potential ?O depends on the experimental growth conditions,which can be either Zn rich,O rich,or anything in between.It should therefore be explicitly re-garded as a variable in the formalism.However,in thermo-

dynamic equilibrium,it is possible to place bounds on the chemical potential.The oxygen chemical potential ?O is sub-ject to an upper bound given by the energy of O in an O 2molecule,E tot ?O 2?,corresponding to extreme O-rich condi-tions;spin polarization is included in the energy of the mol-ecule.The calculated bond length of the O 2molecule of 1.22?is in good agreement with the experimental value of 1.21?.52Similarly,the zinc chemical potential ?Zn is sub-ject to an upper bound given by the energy of Zn in bulk zinc ??Zn =E tot ?Zn ??,corresponding to extreme Zn-rich condi-tions.It should be kept in mind that ?O and ?Zn ,which are free energies,are temperature and pressure dependent.

The upper bounds de?ned above also lead to lower bounds given by the thermodynamic stability condition for ZnO,

?Zn +?O =?H f ?ZnO ?,?4?

where ?H f ?ZnO ?is the enthalpy of formation of bulk ZnO ?negative for a stable compound ?.The upper limit on the zinc chemical potential then results in a lower limit on the oxygen

chemical potential:?O

min

=E tot ?O 2?+?H f ?ZnO ?.Conversely,the upper limit on the oxygen chemical potential results in a

lower limit on the zinc chemical potential:?Zn

min

=E tot ?Zn ?+?H f ?ZnO ?.The calculated enthalpy of formation of ZnO is ?H f ?ZnO ?=?3.5eV,compared to the experimental value of ?3.6eV.53The host chemical potentials thus vary over a range corresponding to the magnitude of the enthalpy of for-mation of ZnO.

The Fermi level E F in Eq.?3?is not an independent pa-rameter,but is determined by the condition of charge neu-trality.In principle,equations such as Eq.?3?can be formu-lated for every native defect and impurity in the material;the complete problem,including free-carrier concentrations in valence and conduction bands,can then be solved self-consistently,imposing charge neutrality.However,it is in-structive to examine formation energies as a function of E F in order to examine the behavior of defects when the doping level changes.We reference E F with respect to the valence-band maximum E v and allow E F to vary from 0to E g ,where E g is the fundamental band gap.Note that the valence-band maximum E v is taken from a calculation of a perfect-crystal supercell,corrected by the alignment of the electrostatic po-tential in the perfect-crystal supercell and in a region far from the defect in the supercell containing the defect,as described in Ref.30.No additional corrections to address interactions between charged defects are included here.It has become clear that the frequently employed Makov-Payne

correction 54often signi?cantly overestimates the correction,

30,55to the point of producing results that are less accurate than the uncorrected numbers.In the absence of a more rigorous approach,we feel that it is better to refrain from applying poorly understood correction schemes.

D.Defect transition levels

Defects often introduce levels in the band gap of semiconductors;1,2these levels involve transitions between different charge states of the same defect and can be derived from the calculated formation energies.The transition levels

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B 76,165202?2007?

are not to be confused with the Kohn-Sham states,which from now on we call states,that result from band-structure calculations.The transition level??q/q??is de?ned as the Fermi-level position for which the formation energies of charge states q and q?are equal.??q/q??can be obtained from

??q/q??=E f?D q;E F=0??E f?D q?;E F=0?

q??q

,?5?

where E f?D q;E F=0?is the formation energy of the defect D in the charge state q when the Fermi level is at the valence-band maximum?E F=0?.The experimental signi?cance of this level is that for Fermi-level positions below??q/q??, charge state q is stable,while for Fermi-level positions above ??q/q??,charge state q?is stable.Transition levels can be observed in experiments where the?nal charge state can fully relax to its equilibrium con?guration after the transi-tion,such as in deep-level transient spectroscopy?DLTS?.1,56 Transition levels correspond to thermal ionization energies. Conventionally,if a defect transition level is positioned such that the defect is likely to be thermally ionized at room tem-perature?or at device operating temperatures?,this transition level is called a shallow level;if it is unlikely to be ionized at room temperature,it is called a deep level.Note that shallow centers may occur in two cases:?rst,if the transition level in the band gap is close to one of the band edges?valence-band maximum?VBM?for an acceptor,conduction-band mini-mum?CBM?for a donor?;second,if the transition level is actually a resonance in either the conduction or valence band.In that case,the defect necessarily becomes ionized, because an electron?or hole?can?nd a lower-energy state by transferring to the CBM?VBM?.This carrier can still be Coulombically attracted to the ionized defect center,being bound to it in a“hydrogenic effective-mass state.”This sec-ond case coincides with what is normally considered to be a “shallow center”?and is probably the more common sce-nario?.Note that in this case,the hydrogenic effective-mass levels that are experimentally determined are not directly re-lated to the calculated transition level,which is a resonance above?below?the CBM?VBM?.

E.Local-density-approximation correction

Unfortunately,LDA seriously underestimates band gaps and therefore corrections are necessary to compare the cal-culated transition levels??q/q??with experimental results.In the case of ZnO,the error is particularly severe because LDA underestimates the binding energy of the zinc d electrons. The zinc d states form a narrow band that overlaps with the valence band in tetrahedrally bonded II-VI semiconductors. In ZnO,the zinc d states couple with the oxygen p states that form the top of the valence band.This coupling pushes the top of the valence band upward,reducing the band gap.57 This effect explains why ZnO has a smaller band gap than ZnS,despite being more ionic and having a smaller lattice constant:the lower-lying oxygen p states experience a stron-ger repulsion from the zinc d states than the sulfur p states.

In the LDA,the underbinding of the d states causes the p-d coupling to be unphysically strong,resulting in too large a reduction of the band gap.One way to correct for the underestimation of the binding energy of the Zn d electrons is by including an on-site Coulomb correlation interaction,as implemented in the LDA+U method.58In this approach an orbital-dependent correction that accounts for electronic cor-relations in the narrow bands derived from Zn d states is added to the LDA potential.This on-site Coulomb correla-tion corrects the position of the narrow bands derived from the Zn d states and affects both the valence-band maximum and conduction-band minimum.46It opens the band gap by shifting the valence band downward and the conduction band upwards.The LDA+U thus provides a partial correction of the band gap,the remaining correction arising from the in-trinsic LDA error in predicting the position of the conduction band.An important problem when applying the LDA+U ap-proach is how to choose the value of U.We have proposed an approach46to obtain U entirely from?rst principles by calculating U for the atom and screening this value by using the high-frequency dielectric constant??of the solid.Further discussion and justi?cation of this approach is contained in Ref.46.For ZnO,our procedure gives U=4.7eV for the semicore Zn d states.The difference in enthalpy of formation ?H f?ZnO?of ZnO between LDA and LDA+U is only 0.07eV.Note that in the LDA+U calculation of?H f?ZnO?, we take U=0for bulk zinc,consistent with our procedure of obtaining U as the atomic value divided by the high-frequency dielectric constant.

Although the LDA+U approach only corrects part of the band-gap error,it provides us with a basis for obtaining a full band-gap correction through a physically justi?ed extrapola-tion scheme.Point defects usually induce electronic states in the band gap of semiconductors and insulators.These states may be?fully or partially?occupied with electrons or empty, and the occupation of these states determines the charge state of the defect.The defect states exhibit a mixture of conduction-band and valence-band character.Since the LDA underestimates band gaps,the position of the defect states ?with respect to the valence-band edge?also tends to be un-derestimated.The greater its conduction-band character,the greater the error in the position of the defect state.As a consequence,the LDA also underestimates the formation en-ergy of defects that have occupied states in the band gap. Again,the error in the formation energy is expected to in-crease with the degree of conduction-band character in the defect state.

Our approach takes advantage of the fact that the extent to which transition levels??q/q??change in going from LDA to LDA+U re?ects their relative valence-band and conduction-band character.The procedure is to perform calculations us-ing the LDA,on the one hand,and the LDA+U,on the other hand,and then extrapolate to the experimental gap:

??q/q??=??q/q??LDA+U+

??

?E g

?E g expt?E g LDA+U?,?6?

with

??

?E g=

??q/q??LDA+U???q/q??LDA

E g LDA+U?E g LDA

.?7?

Here,E g LDA and E g LDA+U are the band gaps given by the LDA and LDA+U approximations and E g expt is the experimental

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

gap.59The coef?cient ??

?E g is the rate of change in the transi-tion levels with respect to the change in the band gap,and it is obtained by performing calculations using LDA and LDA+U ?Eq.?7??.The correction is in the spirit of schemes discussed by Zhang et al.38using different methodologies.It is important to note that this extrapolation is valid when the valence-and conduction-band character of the defect ?Kohn-Sham ?state does not change when the gap is corrected,and only the position of the state is shifted in the gap.The ex-trapolated values for the transition levels are very close to results obtained using self-interaction and relaxation-corrected pseudopotentials,60enhancing con?dence in the approach.

The corrections for transition levels enable us to also ap-ply corrections to formation energies.The procedure for do-ing so is more easily explained in the context of speci?c examples,after presenting some results for transition levels,and therefore we postpone this discussion to Sec.III B.

III.RESULTS AND DISCUSSION

A.ZnO perfect crystal

In Table I ,we list the calculated equilibrium lattice pa-rameters and band gaps using the LDA and LDA+U for ZnO.These calculations were performed for a four-atom primitive cell of the wurtzite structure and a 4?4?4Monkhorst-Pack special k -point mesh.For a detailed discus-sion of the effects of the on-site Coulomb correlation energy U on the electronic and structural properties of ZnO,we refer the reader to Ref.46.The defect calculations discussed in the next sections were performed at the theoretical equilibrium lattice parameters in the respective approximation ?LDA or LDA+U ?.Use of the theoretical lattice parameters is neces-sary in order to avoid spurious effects in the atomic relax-ations.Although the absolute value of the atomic displace-ments may differ between LDA and LDA+U ,we ?nd good agreement when displacements are expressed relative to the appropriate equilibrium Zn-O bond length.

B.Native point defects in ZnO

In this work,we consider all the possible native point defects in ZnO:oxygen and zinc vacancies ?V O and V Zn ?,interstitials ?O i and Zn i ?,and antisites ?O Zn and Zn O ?.Before giving detailed results for each point defect we discuss the LDA correction for defect transition levels and formation energies.

We illustrate the correction based on the LDA and LDA +U calculations with the detailed example of the oxygen vacancy.Figure 1shows the calculated formation energies for the oxygen vacancy using LDA and LDA+U .The re-moval of an oxygen atom from the lattice breaks four bonds.The four “dangling bonds”on the surrounding Zn atoms combine to form a fully symmetric a 1state in the band gap,and three almost degenerate states located above the CBM.In the neutral charge state of the oxygen vacancy,the a 1state is occupied with two electrons.The other three states above the CBM are always empty;we do not need to consider them further.In LDA,the a 1state is close to the VBM.As the band gap is corrected,the a 1state is shifted upward,as expected for a state that has signi?cant Zn ?and hence conduction-band ?character.Since the a 1state is occupied with two electrons,this shift increases the formation energy of the oxygen vacancy in the neutral charge state with re-spect to the positive charge states,as illustrated by compar-ing the LDA and LDA+U calculations in Fig.1.Because the LDA+U affects both the valence band and the conduction band,the shift in the a 1state ?and hence in the formation energy ?re?ects the correct physics,according to the relative amount of valence-versus conduction-band character in the state.It is noteworthy that these shifts could not simply be guessed based on the qualitative character of the defect state.Indeed,as noted above,the defect state for V O is made up largely of Zn dangling bands,and hence one might guess that it would exhibit mainly conduction-band character and shift rigidly with the conduction band when the band gap is cor-rected by 0.7eV ?from E g =0.8eV in LDA to 1.5eV in LDA+U ?.For a state occupied with two electrons,the for-

TABLE I.Calculated lattice parameters a ,c /a ,and u ,band gap E g ,and enthalpy of formation ?H f for ZnO using LDA and LDA +U .Experimental data were taken from Refs.59and 61.

LDA

LDA+U Expt.a ??? 3.195 3.148 3.249c /a 1.615 1.612 1.602u

0.3790.3790.381E g ?eV ?

0.80

1.51

3.43

LDA

LDA+U

Corrected

0.0

1.0

2.0

3.0Fermi level (eV)

-1.00.01.0

2.03.04.05.06.07.0F o r m a t i o n e n e r g y (e V )

2++

0.0

1.0

2.0

3.0Fermi level (eV)

-1.00.01.02.0

3.04.05.06.07.02+

+0

Fermi level (eV)

FIG.1.?Color online ?Calculated formation energies as a function of Fermi level for the oxy-gen vacancy in ZnO:?a ?LDA results,?b ?LDA +U results,and ?c ?extrapolated formation ener-gies.The zero of Fermi level corresponds to the valence-band maximum,and the dashed lines in ?a ?and ?b ?indicate the band gap in the respective calculations.

NATIVE POINT DEFECTS IN ZnO

PHYSICAL REVIEW B 76,165202?2007?

mation energy should therefore increase by1.4eV.Instead, Fig.1shows that the correction is less than half of that.The reason is twofold:?rst,the LDA+U shifts not only the con-duction band but also the valence band;second,evidently, the V O defect state is by no means purely conduction-band-like in character.

We note in Fig.1that the transition levels are shifted upward in the band gap going from LDA to LDA+U.Since the difference between LDA and LDA+U re?ects the correct physics of valence-band versus conduction-band character of the Kohn-Sham states,this justi?es the use of Eq.?6?to correct defect transitions levels??q/q???which are refer-enced with respect to the VBM?.The procedure above differs from the assumption made by Lany and Zunger in Refs.62 and44that the transition levels of the oxygen vacancy in ZnO are well described by the LDA+U and do not shift at all with the conduction band.In their paper,the conduction band is rigidly shifted to agree with the experimental band gap,while the transition level is kept?xed at the LDA+U values.We feel that Lany and Zunger’s assumption is unjus-ti?ed and inconsistent with their own results.The assumption that the transition levels associated with the oxygen vacancy do not shift when the conduction band is corrected is equiva-lent to saying that the a1state has purely valence-band char-acter.If this were true,then LDA and LDA+U would give the same values for the transition levels,which is clearly not the case.By increasing the band gap by going from LDA to LDA+U,the transition levels??2+/+?,??+/0?,and??2 +/0?all shift upward in the band gap,in accordance with the relative conduction versus valence-band character of the a1 state.

Figure2and Table II show the position of the corrected transition levels??q/q??in the band gap for all native point defects in ZnO.The justi?cation provided above applies to transition levels and therefore also to relative formation en-ergies.The correction of the absolute formation energies re-quires further considerations regarding the electronic struc-ture.First,we take note of the fact that the formation energies of charged defects depend on the position of the VBM,as evident from Eq.?3?.We already emphasized that the LDA+U approach shifts the position of the VBM as well as the CBM,and this effect will be felt in the formation energies as well.LDA+U of course does not fully correct the band-gap error;indeed,the usual errors intrinsic to the DFT-LDA are still present,and the LDA+U band gap ?1.51eV?is still signi?cantly smaller than the experimental gap?3.43eV?.To extrapolate to the experimental gap,we therefore need to make an assumption about the position of

O O i

Zn i i Zn

FIG.2.?Color online?Thermodynamic transition levels for de-

fects in ZnO.These values were corrected based on the LDA and

LDA+U calculations according to the procedure described in the

text.

TABLE II.Calculated transition levels??q/q???in eV?for native point defects in ZnO.LDA,LDA+U, and corrected values according to Eq.?6?are listed.The differences??=??q/q??LDA+U???q/q??LDA?in eV?

are also listed.

Defect q/q???q/q??LDA??q/q??LDA+U????q/q??

V O2+/+ 1.01 1.410.40 2.51

+/00.050.530.47 1.82

V Zn0/?0.080.110.030.18

?/2?0.290.450.160.87

Zn i2+/+ 1.41 2.010.60 3.65

+/0 1.44 2.060.62 3.75

O i?oct?0/?0.270.390.120.72

?/2?0.86 1.060.20 1.59

O i?split?2+/+?0.12?0.090.03?0.01

+/0?0.07?0.050.020.00

Zn O4+/3+0.330.750.42 1.88

3+/2+?0.250.090.34 1.01

2+/+ 1.59 2.210.62 3.91

+/0 1.62 2.250.63 3.97

O Zn0/?0.600.850.25 1.52

?/2?0.550.880.32 1.77

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

the valence band.Here,we assume that this position is given

by the value in the LDA+U approach and does not undergo

any further shifts when the band gap is corrected;i.e.,we

assume that all of the remaining correction occurs in the

conduction band.This approximation is justi?ed by studies

in which LDA band structures were compared with quasipar-

ticle calculations based on the GW approximation.63

Additional corrections to the formation energy occur,of

course,due to the correction in the position of the defect

states.In case the defect state is not occupied,this shift will

not affect the formation energy.Therefore,for charge states

in which the defect?Kohn-Sham?states are empty,the for-

mation energy of the defect should be well approximated by

its LDA+U value.In the case of the oxygen vacancy,this is

true for the2+charge state,for which the a1defect state is empty of electrons.The corrected formation energy for V O2+,

corresponding to the experimental band gap,is therefore

equal to its LDA+U value?see Fig.1?.Once we have an

absolute value for the2+charge state,we can then obtain

extrapolated values for the formation energies of the other

charge states??and0?as well,taking advantage of the fact

that our extrapolation scheme for transition levels?Eq.?6??

also provides corrected values for the differences between

formation energies of different charge states.

Some point defects are not stable in any charge state for

which all associated defect states are unoccupied,complicat-

ing the question of how to obtain an absolute formation en-

ergy.Indeed,for a charge state in which the defect state is

partially occupied,the shift in formation energy from LDA to

LDA+U contains contributions from both the shift in the

VBM and the shift in the defect state.Since further correc-

tion to the experimental gap should leave the VBM intact,

we need to somehow disentangle these two contributions.

Fortunately,this is also feasible by closer inspection of the

LDA and LDA+U results.Indeed,the part of the formation-

energy correction due to the shift in the Kohn-Sham state is

proportional to the number of electrons that are occupying

the defect state?s?.We can calculate this shift by looking at

the energy difference between two charge states q and q?and analyzing how this energy difference changes in going from

LDA to LDA+U.The energy difference between these

charge states is contained in the transition level??q/q??de-?ned in Eq.?5?.Therefore,we can identify the energy shift

in the Kohn-Sham state?s?as the shift of the calculated tran-

sitions levels between the LDA and LDA+U calculations in

Eq.?7????=??q/q??LDA+U???q/q??LDA?.Once we know the shift in the defect state?s?,we can extrapolate the absolute formation energies according to

E f=E f,LDA+U+?E g expt?E g LDA+U?

?E g LDA+U?E g LDA?

n??,?8?

where n is the occupancy of the defect states in the band gap for a given defect in charge state q.For example,in the case of the oxygen vacancy,n=0for q=2+,n=1for q=1+,and n=2for q=0;for the zinc vacancy,n=4for q=0,n=5for q=1?,and n=6for q=2?.Note that Eq.?8?correctly incor-porates our notion about the VBM position being?xed by the LDA+U calculation.As a check,our previous discussion of LDA+U giving the correct absolute formation energy for V O2+is also correctly re?ected by Eq.?8??since n=0?.For some defects,states with very different character or symme-try can simultaneously be occupied in certain charge states. In the case of the zinc antisite,the different??values can be explicitly evaluated?see Table II?and taken into account in the corrections for formation energies?Table III?.In other cases,one of the states is actually a deep resonance in the valence band?e.g.,the a1state of the zinc vacancy?,and hence it is not possible to obtain explicit information about the??value for this state.In such cases,we have assumed that the state has mostly valence-band character,and there-fore it follows the valence band and does not contribute to the correction in the formation energy as the band gap is corrected.In the case of the zinc vacancy,we have checked the effect of this assumption on the calculated formation en-ergies by also extrapolating formation energies based on in-cluding the electrons in the a1state in the electron count n; this corresponds to assuming that the a1state shifts up as much as the t2states,which would provide an upper limit to

the expected shift;even then,the results differed by less than

0.5eV,assuring us that our results are not very sensitive to

this approximation.

In Table III,we list the calculated LDA,LDA+U,and

corrected formation energies and the occupancy of the defect

states in the gap for each charge state.Our method for ex-

tracting??from the difference??q/q??LDA+U???q/q??LDA is not unique,since most defects can be stable in more than two

different charge states.Each combination of charge states q

and q?therefore,in principle,leads to a different value for ??.Fortunately,we?nd that all of these different evaluations provide very similar results,as illustrated by the values in

Table III for cases where q and q?differ by1.The values of ??extracted for different combinations of charge states agree with each other to better than0.1eV?the case of the Zn antisite re?ects different physics and will be discussed below?.This provides a con?rmation of the validity of our analysis of the various contributions to the formation energy and how they shift with the band-gap correction.For pur-poses of the extrapolation in Eq.?8?we use an average of the various??values for a given defect state,which we call??ˉ.

From the values of??ˉ,we can also extract a quantitative

measure of the relative amount of valence-band versus

conduction-band character.Defect states that have exclu-

sively conduction-band character should shift rigidly with the conduction band,i.e.,??ˉ=?E g.Conversely,defect states with exclusively valence-band character should not shift at all when the band gap is corrected,i.e.,??ˉ=0.This implies that the parameter??ˉ/?E g can be used as a measure of the amount of conduction-band character in the state?and1???ˉ/?E g as a measure of the amount of valence-band char-acter?.Inspection of the results in Table III indicates that these measures indeed agree with our intuitive expectations about the nature of the defect states.For instance,for zinc interstitials,the shift??ˉis almost equal to the band-gap correction given by LDA+U:??ˉ=0.61eV compared to ?E g=E g LDA+U?E g LDA=0.71eV.The resulting degree of conduction-versus valence-band character CB/VB,ex-pressed as percentages,is87/13.Similar results apply to the high-lying transition states of another donor,the zinc antisite.

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B76,165202?2007?

The oxygen vacancy,however,clearly exhibits a more com-plex behavior,with only62%of conduction-band character in its defect state.Defect states induced by acceptors,on the other hand,are expected to exhibit mainly valence-band character.For instance,for zinc vacancies??ˉ=0.09eV,re-sulting in87%valence-band character.This is consistent with the fact that the defect states of the zinc vacancy are composed of oxygen dangling bonds and are expected to follow the valence band.

Figure3shows the corrected?i.e.,extrapolated to the ex-perimental gap?formation energies for the relevant native point defects in ZnO as a function of Fermi-level position. The kinks in the curves for a given defect indicate transitions between different charge states;the corresponding?cor-rected?transition levels??q/q??were shown in Fig.2.Note that the results presented in this work differ slightly from some values that were published in a preliminary account of our work.64The differences are related to the correction of absolute formation energies,where we now take into account the occupancy of the defect-induced states in the case of defects with partially occupied states in the band gap.

We now discuss the electronic structure and local atomic geometry of each point defect in more detail.For migration barriers,we found that the values calculated with LDA and LDA+U differed by less than0.1eV;the results quoted be-low are all obtained within LDA.

C.Oxygen vacancies

1.Formation energy and transition levels

Among the defects that behave as donors,oxygen vacan-cies have the lowest formation energy?see Fig.3?.Oxygen vacancies have frequently been invoked as the source of un-intentional n-type conductivity in ZnO.Our?rst-principles results indicate that this assignment cannot be correct.First, we note from Fig.3that the formation energy of V O is quite high in n-type material,even under extreme Zn-rich condi-tions?3.72eV?.This indicates that the V O concentration will always be low under equilibrium conditions.Even more im-portant,however,is that the oxygen vacancy is a deep rather

TABLE III.Calculated formation energies at E F=0for native point defects in ZnO under zinc-rich conditions.LDA,LDA+U,and corrected values are listed.The occupancy n of the defect states in the gap,

de?ned in the text,is also given.In the last column,we list the relative degree of conduction-band versus

valence-band character?CB/VB,expressed as percentages?for each defect state.The conduction-band char-

acter of the defect state is de?ned as CB=??ˉ/?E g,where?E g=E g LDA+U?E g LDA=0.71eV?see text?.All

energies are given in eV.

Defect q n E f,LDA E f,LDA+U E f?CB/VB??%?

V O2+0?0.37?0.60?0.60

?10.640.81 1.9162/38

020.69 1.34 3.72

V Zn04 5.94 6.397.38

?5 6.02 6.497.5513/87

2?6 6.31 6.948.43

Zn i2+0?0.10?0.45?0.45

?1 1.32 1.56 3.2087/13

02 2.76 3.62 6.95

O i?oct?04 6.36 6.838.54

?5 6.637.229.2623/77

2?67.498.2810.86

O i?split?2+2 5.13 5.12 5.25

?3 5.01 5.02 5.2403/97

04 4.93 4.97 5.24

Zn O4+00.14?0.31?0.31

3+10.480.44 1.5754/46

2+20.220.53 2.59

?3 1.81 2.74 6.4989/11

04 3.43 4.9810.47

O Zn049.9410.0413.15

?510.5310.8814.6841/59

2?611.0811.7616.45

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

than a shallow donor.Figure 1?c ?shows that the ??2+/0?transition level occurs at ?1eV below the conduction band.Therefore,it is clear that the oxygen vacancy cannot provide electrons to the conduction band by thermal excitation in steady state,and therefore it cannot be a source of the often-observed unintentional n -type conductivity.It should be noted that,whereas the formation energy of V O is very high in n -type ZnO,it is much lower in p -type ZnO,where V O assumes the 2+charge state.Thus,oxygen vacancies are a potential source of compensation in p -type ZnO.

2.Atomic geometry and negative-U character

We ?nd that the oxygen vacancy is a “negative-U ”center,implying that ??2+/+?lies above ??+/0?,with U =??+/0????2+/+?=?0.7eV,as seen in Fig.1?c ?.As the Fermi level moves upward,the thermodynamic charge-state transition is thus directly from the 2+to the 0charge state;the ?charge state is unstable for any position of the Fermi level.

Negative-U behavior is typically related to unusually large local lattice relaxations that stabilize particular charge states.For the neutral charge state,the four Zn nearest neigh-bors are displaced inward by 12%of the equilibrium Zn–O bond length,whereas for the ?and 2+charge states,the displacements are outward by 2%and 23%,as shown in Fig.4.The origin of these large lattice relaxations lies in the electronic structure of V O ,which was discussed in Sec.III B.In the neutral charge state,the a 1state is occupied by two electrons,and its energy is lowered as the four Zn atoms approach each other.In this case,the gain in electronic en-ergy exceeds the cost to stretch the Zn–O bonds surrounding the vacancy and the resulting a 1state lies near the top of the

valence band.In the V O

+

con?guration,the a 1state is occu-pied by one electron,and the electronic energy gain is too small to overcome the strain energy;the four Zn atoms are displaced slightly outward,moving the a 1state near the

middle of the band gap.In the V O 2+

con?guration,the a 1state is empty and the four Zn atoms strongly relax outward,strengthening the Zn–O bonds;the empty a 1state lies near the conduction band.These large relaxations signi?cantly re-duce the formation energies of V O

2+and V O 0relative to V O +

,making the oxygen vacancy a negative-U center.

https://www.wendangku.net/doc/a75486240.html,parison with experiment

Most of the experimental investigations of oxygen vacan-cies to date have relied on electron paramagnetic resonance ?EPR ?studies,which will be discussed in the next section.One group has studied oxygen vacancies with positron anni-hilation spectroscopy.35,65The samples were electron irradi-ated and had a Fermi level 0.2eV below the CBM after irradiation.The dominant compensating defect was found to be the zinc vacancy,consistent with the results presented in Sec.III D;however,the measurements also produced evi-dence for the presence of a neutral defect,which was pro-posed to be the neutral oxygen vacancy.These observations are fully consistent with our computational results,both re-garding the absence ?below the detection limit ?of oxygen vacancies in as-grown material and V O being present in the neutral charge state when E F =E c ?0.2eV.

4.Electron paramagnetic resonance studies of oxygen vacancies

Because of the negative-U character,the positive charge

state of the oxygen vacancy,V O

+

,is thermodynamically un-stable,i.e.,it is always higher in energy than either V O

2+or V O 0for any position of the Fermi level in the band gap.This has important implications for the characterization of oxygen va-cancies in ZnO.Only the positive charge state,with its un-paired electron,is detectable by magnetic resonance tech-niques.An EPR signal associated with V O should thus not be observed under thermodynamically stable conditions.It is,of course,possible to create oxygen vacancies in the ?charge state in a metastable manner,for instance,by excitation with

light.Once generated,V O

+

does not immediately decay into the 2+or 0charge state due to the existence of energy bar-riers associated with the large lattice relaxations that occur around the oxygen vacancy.We thus expect that at low

enough temperatures,EPR signals due to V O

+

may be ob-served upon excitation.When the excitation is removed and the temperature is raised,these signals will decay.In Ref.66,we reported that the thermal barrier to escape out of the 1+

0.0

1.0

2.0

3.0

Fermi level (eV)

-2.00.02.04.06.08.0

10.012.0F o r m a t i o n e n e r g y (e V )

0.0

1.0

2.0

3.0Fermi level (eV)

Zn-rich

O-rich

V O

V Zn

Zn i Zn O V Zn O i (oct)

V O

O i (oct)

O Zn

O i (split)

Zn i Zn O

O i (split)O Zn

FIG. 3.?Color online ?Formation energies as a function of Fermi-level position for native point defects in ZnO.Results for Zn-rich and O-rich conditions are shown.The zero of Fermi level corresponds to the valence-band maximum.Only segments corre-sponding to the lowest-energy charge states are shown.The slope of these segments indicates the charge state.Kinks in the curves indi-cate transitions between different charge states.

(a)V O 0

V O 2+

(b)

FIG.4.?Color online ?Local atomic relaxations around the oxy-gen vacancy in the ?a ?neutral and ?b ?2+charge states.In the

neutral charge state,the four Zn nearest neighbors are displaced inward by 12%of the equilibrium Zn–O bond length,whereas for the 2+charge states,the displacements are outward by 23%.

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B 76,165202?2007?

charge state is0.3eV,suf?cient to maintain an observable concentration of V O+during excitation and cause persistent photoconductivity at low temperature,but clearly too low to allow for persistent photoconductivity at room temperature.

We therefore disagree with Lany and Zunger’s44proposal

that persistent conductivity related to oxygen vacancies is

responsible for the unintentional n-type conductivity ob-

served in many ZnO samples.

In previous work,66we mapped out a complete

con?guration-coordinate?CC?diagram that allowed a direct

comparison with experimental results and provided a de-

tailed interpretation of recent optically detected EPR

experiments.24The key quantity for this interpretation is the

position of the??+/0?transition level in the band gap.Our results yield??+/0?=1.82eV,in contrast to the value of 1.2eV obtained by Zhang et al.38based on empirical correc-

tions,the value of?1eV obtained by Lany and Zunger44,62

using LDA+U,or the results of Kohan et al.37that?nd the ??+/0?in the valence band.From our calculated CC diagram in Ref.66,the peak for the optical transition V O0→V O+is 2.0eV.This value is in good agreement with the experimen-

tal value of2.3eV.67,68

Experimental reports of EPR measurements relating to

oxygen vacancies in ZnO are summarized in Table IV.They

fall into two categories,depending on the value of the g

factor.One set of reports associates oxygen vacancies with a

g value of?1.96,the other with g?1.99?see Table IV?.We feel that there is overwhelming evidence that it is actually the g?1.99line that can be consistently assigned to oxygen vacancies.This signal has only been observed after irradia-tion of the samples,clearly indicating it is related to a point defect?and also consistent with our calculated result that V O has a high formation energy and is thus unlikely to occur in as-grown n-type material?.Also,it has been found that illu-mination is necessary to observe the center,68–70consistent with our results that excitation is required in order to gener-ate the paramagnetic1+charge state.Further evidence for the identi?cation of the g?1.99line with the oxygen va-cancy came from the observations of hyper?ne interactions with the67Zn neighbors of the vacancy.68,69

On the other hand,no hyper?ne interactions were ob-served for the g?1.96line.It is likely that the g?1.96 signal is associated with electrons in the conduction band or in a donor band,as originally proposed by Müller and Schneider71and most recently con?rmed by Garces et al.22 The historical tendency for authors to assign the g?1.96line to V O was probably largely based on the prevailing hypoth-esis that oxygen vacancies were the donors responsible for the unintentional n-type conductivity.In a collection of ex-perimental results up to1970,Sancier72also favored assign-ing the g?1.96line to electrons in the conduction band.In a critical review of results up to1981,Neumann73observed that doping with Al,Ga,or In increases the intensity of the g?1.96signal.This behavior is consistent with the g ?1.96signal being due to delocalized electrons,but would be hard to reconcile with oxygen vacancies as the source.We

TABLE IV.Overview of electron paramagnetic resonance observations of donors in ZnO.

g value Sample Treatment Reported assignment Reference

g?=1.956,g?=1.955Single crystal1150°C,7h Electrons bound

at donors

74

g?=1.957,g?=1.956Powder900°C,2h V O75

g?=1.956,g?=1.955Single crystal Electrons in CB or

donor band

71

g?1.96Powder975°C,1–20h76

g=1.9539Powder V O77

g=1.9564,1.9600Powder575K,vac+O272

g?=1.9576,g?=1.9557Single crystal V O8

g=1.9557Powder V O78

g=1.956Powder V O79

g=1.955Powder930°C,H2then O2V O10

g?=1.9573,g?=1.9557Powder V O80and81

g=1.9564,g=1.9596Powder700–900°C,N2,H2V O96

g?=1.9570,g?=1.9551Single crystal Delocalized

electrons

21

g?=1.957,g?=1.956Single crystal Shallow

donors

22

g?=1.9948,g?=1.9963Single crystal Irradiation,illumination V O69

g?=1.9948,g?=1.9961Single crystal Irradiation V O86

g?=1.9945Single crystal Irradiation,illumination V O68

g?=1.9945Single crystal Irradiation,illumination V O70

g?=1.9948,g?=1.9963Single crystal Irradiation,illumination V O109and110

g?=1.9951,g?=1.9956Single crystal Irradiation,illumination V O-Li Zn109

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

note that the g ?1.96line has also been reported to be pho-tosensitive;in particular,the signal is enhanced after UV illumination.71,74,76–79,81This observation is of course consis-tent with the g ?1.96line corresponding to electrons in conduction-band states,since UV light can promote electrons into these states.

Leiter et al.82,83have performed photoluminescence and optically detected magnetic resonance experiments on a broad emission band around 2.45in as-grown ?i.e.,unirradi-ated ?single-crystal ZnO.They detect intense resonances which they attribute to a spin-triplet system ?S =1?with g ?=1.984and g ?=2.025.Based on analogies with anion va-cancies in other oxides,they attribute this signal to oxygen vacancies.This assignment clearly disagrees with the experi-ments cited above,which relate oxygen vacancies with g values of 1.99.In addition,the signal observed by Leiter et al.is present already in as-grown material,unlike the obser-vations of the g ?1.99signal,which all required irradiation.Moreover,the samples in Refs.82and 83are n type with residual donor concentration of ?1017cm ?3.Under these conditions,the formation energy of oxygen vacancies is at least 3.7eV,and therefore,the concentration of oxygen va-cancies is expected to be too low to be detectable.In Sec.III D 4,we will suggest that the triplet S =1EPR signal ob-served by Leiter et al.may be related to spin-dependent re-combination involving an S =1/2V Zn

?

defect exchange coupled to a S =1/2effective-mass donor.

5.Migration

Migration of oxygen vacancies occurs when a nearest-neighbor oxygen atom in the oxygen lattice jumps into the vacant site,leaving a vacancy behind.We obtained the mi-gration barrier of the oxygen vacancy by calculating the total energy at various intermediate con?gurations when moving an oxygen atom from its nominal lattice site adjacent to the vacancy along a path toward the vacancy,as schematically shown in Fig.5?a ?.The coordinate along the path is the distance between the intermediate position of the jumping atom and its original lattice site position.The oxygen va-cancy has 12next-nearest-neighbor oxygen atoms:six are located in the same basal plane as the vacancy and account for vacancy migration perpendicular to the c axis;the other six neighbors are located in basal planes above and below the basal plane of the oxygen vacancy and can account for vacancy migration both parallel and perpendicular to the c axis.We ?nd no anisotropy in the calculated migration bar-

rier for oxygen vacancies.That is,migration barriers involv-ing oxygen atoms from the basal plane of the vacancy and from planes above or below the basal plane of the vacancy have the same value.

However,the migration barrier does depend on the charge state of the oxygen vacancy.Here,we focus on the stable

charge states,namely,neutral and 2+?V O 0and V O 2+

,respec-tively ?.The former is relevant for migration of the oxygen vacancy in n -type samples and the latter for vacancy migra-tion in semi-insulating ?E F below 2.2eV ?or p -type samples.

We ?nd migration barriers of 2.4eV for V O

and 1.7eV for V O 2+

,as shown in Figs.5?b ?and 5?c ?.A possible qualitative explanation for this difference is that the saddle-point con-?guration may be regarded as a complex formed by an oxy-gen interstitial adjacent to two oxygen vacancies.For Fermi

energies where V O 0is stable,this complex is 2V O 0+O i 0,and for Fermi energies where V O 2+

is stable,this complex is 2V O 2+

+O i 2?.Because the distances between the vacancies and the interstitial are smaller than the distance between the two

vacancies,the complex 2V O 2+

+O i 2?can exhibit an attractive Coulomb energy which is absent in 2V O 0

+O i 0.Thus,the Cou-lomb interaction between the point defects that constitute the

saddle-point con?guration lowers the migration barrier for V O

2+compared to V O 0

.We note that a similar difference be-tween migration barriers for different charge states of the anion vacancy was found in the case of GaN.29

Erhart and Albe 43have also calculated migration barriers for the oxygen vacancy in ZnO.Contrary to our results,they ?nd differences as large as 0.7eV between migration barri-ers involving oxygen atoms from the basal plane of the va-cancy and from planes above or below the basal plane of the vacancy.They have reported energy barriers of 1.09and

1.49eV for migration of V O

2+

through out-of-plane and in-plane paths,respectively,and energy barriers of 2.55and

1.87eV for migration of V O

through out-of-plane and in-plane paths,respectively.Such large anisotropies in the mi-gration barriers are quite unexpected since the local geom-etry around the oxygen vacancy has almost tetrahedral symmetry.We suspect that the small supercells ?32atoms ?used in Ref.43are responsible for the discrepancies.In fact,calculated migration barriers for the nitrogen vacancy in GaN using 32-and 96-atom supercells differ by as much as 0.6eV due to the large relaxations around the nitrogen va-cancy that are not properly described in the 32-atom supercell.29More details about the effects of supercell size can be found in Ref.29.

x

(a)

x (?)

E n e r g y (e V )

x (?)

FIG.5.?Color online ??a ?Migration path for oxygen vacancies.Paths where an oxygen atom from an adjacent basal plane or from the same basal plane moves into the vacancy are shown.Both migration paths give quantitatively the same result.?b ?Calculated energy along the migration path for the neutral charge state of V O .?c ?Calculated energy along the migration path for the 2+charge state of V O .

NATIVE POINT DEFECTS IN ZnO

PHYSICAL REVIEW B 76,165202?2007?

D.Zinc vacancies

1.Formation energy and transition levels

Zinc vacancies in ZnO introduce partially occupied states in the band gap.These states are derived from the broken bonds of the four oxygen nearest neighbors and lie close to the VBM.They are partially ?lled and can accept additional electrons,thus causing V Zn to act as an acceptor.Since the formation energy of acceptor-type defects decreases with in-creasing Fermi level,zinc vacancies can more easily form in n -type samples.They are also more favorable in oxygen-rich conditions.Figure 3shows that zinc vacancies have exceed-ingly high formation energies in p -type ZnO,and therefore should exist only in very low concentrations.In n -type ZnO,on the other hand,zinc vacancies have the lowest formation energy among the native point defects.This energy is low

enough for V Zn

2?

to occur in modest concentrations in n -type ZnO,acting as a compensating center.Positron annihilation experiments 35,84have indeed identi?ed the presence of zinc vacancies in n -type ZnO.

We ?nd that zinc vacancies are deep acceptors with tran-sition levels ??0/??=0.18eV and ???/2??=0.87eV ?see Fig.2and Table II ?.These levels are too deep for the zinc vacancy to act as a shallow https://www.wendangku.net/doc/a75486240.html,bined with their very high formation energy in p -type materials,zinc vacan-cies are thus unlikely to play any role in p -type conductivity.Recently,it has been proposed that a complex formed by a column-V element ?As or Sb ?on a substitutional Zn site surrounded by two zinc vacancies could be responsible for p -type conductivity.85From our results,the formation energy of a single V Zn is 3.7eV under p -type conditions ?E F at the VBM ?,in the most favorable O-rich limit.The formation energy of an As Zn -2V Zn complex would then amount to 2?3.7eV plus the formation energy of substitutional As Zn ?or Sb Zn ?minus the binding energy of the complex.Assuming that the formation energy of As Zn ?or Sb Zn ?is about 1eV ?a very low value considering the chemical mismatch between Zn and As ?,a binding energy of more than 6eV would be required to stabilize these complexes at equilibrium condi-tions.This value is too large to be attainable,and indeed much larger than the value calculated in Ref.85.Therefore,we feel that these complexes cannot be responsible for p -type conductivity.

2.Atomic geometry

The oxygen atoms around the zinc vacancy exhibit large outward breathing relaxations of about 10%with respect to

the equilibrium Zn-O bond length,as shown in Fig.6.Simi-lar relaxations are observed for the three possible charge-state con?gurations,V Zn 0,V Zn ?,and V Zn 2?

.This indicates that the overlap between the oxygen 2p orbitals surrounding the zinc vacancy is too small to result in signi?cant chemical bonding between the oxygen atoms.Indeed,the calculated O-O dis-tances are about 3.5?,much larger than the sum of the covalent radii,which is 2?0.73?=1.46?.

Our calculations,using either LDA or LDA+U ,do not produce any low-symmetry Jahn-Teller distortions for V Zn in the 1?or neutral charge states,even though such distortions are known to occur.17,86,87Jahn-Teller distortions around cat-ion vacancies also occur in ZnSe,88and it is known that LDA calculations are unable to reproduce them.89,90In the case of ZnO,for a zinc vacancy in the 1?charge state,the hole is expected to be localized on one of the four nearest-neighbor oxygen atoms.The oxygen atom with the hole is expected to relax toward the vacancy,lowering the energy of the system.In the case of ZnSe,according to Vlasenko and Watkins,17

the Jahn-Teller effect lowers the energy of V Zn ?

by 0.35eV.Note that a lowering of the energy of the negative charge state would result in the ???/2??transition level shifting away from the VBM,i.e.,the tendency is toward making the level deeper.

3.Electron paramagnetic resonance studies of zinc vacancies

Several EPR observations of zinc vacancies in ZnO have been reported.Taylor et al.86reported EPR signals with g factors in the range 2.0018–2.056in irradiated single crys-tals.It was proposed that a subset of these lines would be due to Zn vacancies.Galland and Herve 87observed lines with g factors between 2.0024and 2.0165in irradiated single crys-tals,also attributing them to Zn vacancies.

4.Green luminescence

ZnO often exhibits green luminescence,centered between 2.4and 2.5eV.18,19,91,92This green luminescence has been observed in samples prepared with a variety of growth tech-niques,and it is important to point out that there may not be a single source for this luminescence.For instance,Cu has been suggested as a potential cause.93,94Still,not all ZnO samples contain copper.Native defects have also been sug-gested as a potential source.Reynolds et al.18,19and Kohan et al.37have suggested that the Zn vacancy can give rise to green luminescence.Indeed,our calculated transition level

V Zn 2-

(a)x (?)

FIG.6.?Color online ??a ?Local atomic geometry of the zinc vacancy in the 2?charge state ?V Zn 2??.?b ?Migration paths of V Zn 2?

:a zinc atom from an adjacent basal plane or from the same basal plane moves into the vacancy.?c ?Calculated migration energy barrier for the path where a zinc atom from an adjacent basal plane moves to the vacant site.The two migration paths give energy barriers that differ by less than 0.1eV.

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE

PHYSICAL REVIEW B 76,165202?2007?

between the1?and2?charge states occurs at0.9eV above the VBM,and hence a transition between the conduction band?or a shallow donor?and the V Zn acceptor level would give rise to luminescence around2.5eV,in good agreement with the observed transition energy.In addition to the agree-ment with the observed emission energy,the Zn vacancy is also a likely candidate because it is an acceptor-type defect: acceptor defects are more likely to occur in n-type material, and most ZnO materials to date have exhibited unintentional n-type conductivity.This proposed explanation for the green luminescence that is similar to the proposal that gallium va-cancies are the source of the yellow luminescence in GaN.95 Other explanations have been proposed for the green lu-minescence.Several groups have suggested that oxygen va-cancies are the source of green luminescence.38,82,96–99Van-

heusden et al.reported a correlation between the intensity of the green luminescence and the concentration of oxygen vacancies.96,99However,their assessment of the presence of oxygen vacancies was based on the observation of a line with g?1.96in EPR measurements;as discussed in Sec. III C4,this assignment is not correct,undermining the arguments made in Refs.96and99.Our calculated con?guration-coordinate diagrams for V O also do not show any transitions consistent with green luminescence.66Leiter et al.associated the emission band around2.45with oxygen vacancies based on optically detected magnetic resonance experiments.82,83As discussed in Sec.III C4,we consider it unlikely that the S=1center that they observed represents the oxygen vacancy.Instead,we suggest that V Zn may be the cause of the observed green luminescence in their experi-ments.Indeed,an S=1EPR signal related to V Zn has recently been proposed by Vlasenko and Watkins.17We suggest that the signal observed by Leiter et al.is associated with the spin-dependent process V Zn?+EM0→V Zn2?+EM+,where the exchange interaction between the localized V Zn?center and the delocalized effective-mass?EM?donor is large enough to produce the combined S=1spectrum.

A strong argument in favor of zinc vacancies being the source of green luminescence has been provided by the ex-periments of Sekiguchi et al.,who have reported strong pas-sivation of the green luminescence by hydrogen plasma treatment.100This observation is consistent with the green luminescence being caused by zinc vacancies,which act as acceptors;these acceptors can be passivated by hydrogen, which acts as a donor.101,102In fact,the same passivation effect was observed by Lavrov et al.,who simultaneously observed an increase in vibrational modes associated with hydrogenated zinc vacancies.102We note that the passivation of the green luminescence by hydrogen is very plausible if the green luminescence is caused by zinc vacancies;hydro-gen atoms passivate zinc vacancies by forming strong O-H chemical bonds.102

5.Migration

Migration of zinc vacancies occurs when a nearest-neighbor zinc atom moves into the vacant site leaving a va-cancy behind,as schematically shown in Fig.6?b?.For the calculation of the migration energy barrier,we have focused on the most relevant2?charge state;zinc vacancies in the neutral and1?charge states have very high formation ener-gies and are therefore very unlikely to occur under equilib-rium conditions.The calculated migration energy barrier for the zinc vacancy in the2?charge state is1.4eV,as shown in Fig.6?c?.We also?nd that migration paths involving zinc atoms in adjacent basal planes or in the same basal plane of the zinc vacancy give almost the same result,differing by less than0.1eV.We thus predict that the migration of zinc vacancies in ZnO is isotropic,similar to the case of oxygen vacancies discussed above.

E.Zinc interstitials

1.Formation energy and atomic geometry

There are two distinct types of interstitial sites in the wurtzite structure:the tetrahedral site?tet?and the octahedral site?oct?.The tetrahedral site has one zinc and one oxygen as nearest-neighbor atoms,at a distance of about?0.833d0, where d0is the Zn-O bond length along the c axis.Thus,a zinc atom placed at this site will suffer severe geometrical constraints.The octahedral site is in the interstitial channel along the c axis.It is equidistant from three zinc and three oxygen atoms by1.07d0.From the distances above,one can expect the Zn i interstitial to prefer the octahedral site where the geometrical constraints are less severe.Indeed,we?nd that the octahedral site is the stable site for Zn i.The zinc interstitial at the tetrahedral site is0.9eV higher in energy and unstable:it spontaneously relaxes to the octahedral site, and therefore may play a rule in Zn i migration,as discussed below.Moreover,instead of occupying the ideal octahedral site,we observe a large displacement of the Zn i along the c axis.The resulting relaxed geometry has an increased Zn i-Zn distance of1.22d0and a decreased Zn i-O distance of1.02d0; it is depicted in Fig.7.Similar displacements along the c axis were also observed for Ga i in GaN.29

Figure3shows that under n-type conditions,i.e.,for Fermi-level positions near the conduction band,Zn i has a high formation energy.This is true even under extreme Zn-rich conditions,where the value is?6eV.Zinc interstitials are thus unlikely to be responsible for unintentional n-type conductivity,since they will be present in very low concen-trations in n-type ZnO.On the other hand,the formation energy of Zn i2+decreases rapidly when the Fermi level de-

(a)Side

view

(b)Top

view

Zn i2+

Zn i2+

FIG.7.?Color online?Local atomic geometry of the zinc inter-stitial in the2+charge state?Zn i2+?at the stable octahedral site.?a?Side view perpendicular to the c axis.?b?Top view parallel to the c axis?along the?0001ˉ?direction?.

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B76,165202?2007?

creases toward the VBM;zinc interstitials are thus a poten-

tial source of compensation in p-type ZnO.

2.Transition levels

The zinc interstitial introduces an a1state with two elec-

trons above the CBM.These two electrons can be transferred

to conduction-band states;indeed,we?nd that the zinc in-

terstitial occurs exclusively in the2+charge state,with the ??2+/+?and??+/0?levels above the conduction-band mini-mum,as listed in Table II.The zinc interstitial will always

donate electrons to the conduction band,thus acting as a

shallow donor.These electrons can,of course,be bound to

the defect center in hydrogenic effective-mass states,so that

effectively the observed defect levels would be the effective-

mass levels below the CBM.

However,because of their high formation energy?see

above?,zinc interstitials will not be present in ZnO under

equilibrium conditions.It has been suggested that zinc inter-

stitials can be observed in n-type ZnO under nonequilibrium

conditions.Thomas6reported the introduction of shallow do-

nors when ZnO crystals were heated in Zn vapor followed by

a rapid quench,and Hutson5observed the appearance of a

shallow donor with ionization energy of51meV in Hall

measurements.Look et al.20conducted high-energy electron

irradiation experiments and identi?ed a shallow donor with

ionization energy of30meV.Based on the much higher pro-

duction rate of this defect for the Zn?0001?face than for the O?0001ˉ?face,the donor was suggested to be related to a Zn-sublattice defect,either the Zn interstitial itself or a Zn-interstitial-related complex.Because of the high formation energies of Zn i and its high mobility even a low temperatures ?as discussed in Sec.III E3below?,we do not believe that isolated Zn i were the observed species in the above experi-ments.

3.Migration

We have considered migration paths for Zn i2+parallel and

perpendicular to the c axis.A“natural”migration path for the

zinc interstitial would be along the hexagonal interstitial

channel,parallel to the c axis?perpendicular to the plane of

Fig.7?b??.Along this path,the interstitial has to pass through

a plane containing three zinc atoms with relatively short Zn i-Zn distances,leading to a barrier of0.78eV.At the saddle point,the Zn i is in the same plane as the three Zn nearest neighbors,which are pushed apart,leading to a Zn i-Zn distance of about1.2d0?.This path can account for migration only along the c axis.

We have also considered a path where the interstitial Zn atom moves through the unstable tetrahedral site,resulting in diffusion perpendicular to the c axis.At the saddle point,the Zn i atom is at the tetrahedral site,repelling the Zn nearest neighbor by increasing the Zn i-Zn distance from?0.833d0 to1.12d0.The migration barrier for this path is0.90eV, which is the energy difference between the octahedral and the tetrahedral con?guration.

In addition,we have considered a kick-out?or intersti-tialcy?mechanism,as shown in Fig.8.In this mechanism, the interstitial Zn atom moves in the direction of a substitu-tional Zn and then replaces it.The former substitutional zinc atom moves to an adjacent octahedral interstitial site,which can be either in the same basal plane or in a basal plane adjacent to that of the original interstitial?Fig.8?.At the saddle point,the substitutional site is shared by two Zn i at-oms in a rather symmetric con?guration as shown in Fig. 8?b?.Surprisingly,we?nd that the kick-out mechanism gives the lowest migration barrier:0.57eV?see Fig.9?.The dif-ference in the energy barriers for migration paths parallel and perpendicular to the c axis is smaller than0.05eV.There-fore,the migration of the zinc interstitial is also predicted to be isotropic.The low migration barrier implies that zinc in-

(a)(b)(c)

Side view Side

view

Side

view

Top view Top

view

Top

view

FIG.8.?Color online?Migration path of Zn i2+

in the kick-out mechanism,where a zinc intersti-

tial exchanges places with a zinc atom on a sub-

stitutional lattice site.Upper panels show side

views,whereas lower panels show top views.?a?

Starting con?guration,?b?saddle point,and?c?

?nal con?guration where the new zinc interstitial

is in a basal plane adjacent to the basal plane of

the original interstitial

atom.

x(?)

E

n

e

r

g

y

(

e

V

)

FIG.9.Calculated migration energy barrier for Zn i2+in the kick-

out mechanism illustrated in Fig.8.The coordinate x is the sum of

the distances between the intermediate positions of the two Zn at-

oms and their respective initial positions.

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

terstitials are mobile below room temperature.

The calculated energy barrier of0.57eV is in very good agreement with experimental measurements by Thomas,6 who reported a migration barrier of0.55eV for zinc intersti-tials based on experiments involving heating crystals in Zn vapor followed by rapid quenching.Despite this low migra-tion barrier,the activation energy for Zn self-diffusion medi-

ated by Zn interstitials is still quite high in n-type samples,

since we have to add the formation energy of Zn i?see Eq.?1??.The fact that Zn interstitials migrate by exchanging po-sitions with Zn atoms at regular lattice sites should be taken

into account when interpreting the migration of Zn intersti-

tials in ZnO crystals using Zn isotopes.103,104As a Zn isotope

is introduced into ZnO,it promptly exchanges positions with

Zn atoms in the lattice site via the kick-out mechanism.Fur-

ther diffusion of these isotopes then has to occur through a

self-diffusion mechanism,which can be mediated either by

zinc interstitials or by zinc vacancies;these mechanisms

have much higher activation energies than the migration bar-

rier of zinc interstitials by themselves.

It is worth noting that their low migration barrier implies

that zinc interstitials are very unlikely to occur as isolated

interstitials;they will have a high tendency to either diffuse

out of the sample or to bind with other defects or impurities.

Combined with the high formation energy of Zn i in n-type

material,this renders it unlikely that zinc interstitials contrib-

ute to unintentional n-type conductivity in ZnO.Even when

zinc interstitials are formed under nonequilibrium conditions,

such as irradiation,they will be unlikely to remain present as

isolated interstitials;the fact that they are mobile at tempera-

tures below room temperature implies that they will either

diffuse out of the sample,recombine with Zn vacancies,or

form complexes with other defects or impurities.

It is conceivable that the high diffusivity of Zn i would

cause it to?nd sites?defects or impurities?to which it is

attracted and with which it can form a complex with a posi-

tive binding energy.If this binding energy is suf?ciently

high,and if the resulting complex still acts as a shallow

donor,this may yet provide a mechanism for the zinc inter-

stitial to play a role in the unintentional n-type conductivity

of ZnO.However,we feel that under equilibrium conditions,

this is quite unlikely.Consider,for example,the seemingly

favorable scenario of Zn i binding to an impurity that acts as

a single acceptor.Since Zn i is a double donor,the resulting

complex is expected to still act as a single donor.However,

the formation energy of the isolated Zn interstitial is so high

that the binding energy of the complex would need to be

unreasonably high in order for the complex to occur in ob-

servable concentrations.We can illustrate this with the ex-

ample of a zinc interstitial bound to a nitrogen acceptor,

which was proposed in Ref.105.Under n-type and Zn-rich conditions,Look et al.105calculated a formation energy for the?N O-Zn i?+complex of3.4eV.This high value renders it very unlikely that this complex would form during growth of the material.Such complexes would have a higher chance of occurring if the interstitials were created under nonequilib-rium conditions such as irradiation,as discussed in Ref.105.

F.Oxygen interstitials

1.Formation energy,atomic geometry,and transition levels

Excess oxygen atoms in the ZnO lattice can be accommo-dated in the form of oxygen interstitials.The oxygen atoms can occupy the octahedral or tetrahedral interstitial sites or form split interstitials.We?nd that the oxygen interstitial at the tetrahedral site is unstable and spontaneously relaxes into a split-interstitial con?guration in which it shares a lattice site with one of the nearest-neighbor substitutional oxygen atoms.In Fig.10?a?,we show the local lattice relaxation around the oxygen split interstitial,O i?split?.The calculated O-O bond length is1.46?,suggesting the formation of an O-O chemical bond,and the Zn-O distances are about3% smaller than the equilibrium Zn-O bond length in ZnO.Re-cently,Limpijumnong et al.proposed that other?rst-row el-ements can also form“diatomic molecules”in ZnO.106Our results agree with theirs,and we also?nd two almost degen-erate and completely?lled states in the band gap that re-semble the antibonding pp?*state from a molecular orbital description of the isolated O2molecule.However,in the iso-lated molecule,the pp?*molecular orbital?MO?is occupied by two electrons with parallel spins,resulting in a triplet S =1ground state.In the solid,the four zinc nearest neighbors provide two additional electrons,and the pp?*-like MO is completely occupied.This explains the signi?cantly longer O-O bond length in the split interstitial?1.46??compared to that of the isolated O2molecule?1.22??.Our calculations show that the oxygen split interstitial is electrically inactive, i.e.,it is neutral for any Fermi-level position,with the calcu-lated donor transition levels??+/0?and??+/2+?occurring below the VBM.

We also?nd a metastable con?guration for the oxygen split interstitial,O i0?split?*,with formation energy?0.2eV higher than the lowest-energy con?guration O i0?split?.Its lo-cal atomic geometry is shown in Fig.10?b?.The O-O bond length is1.51?.The existence of these two almost degen-erate con?gurations with very different O-Zn-O bond angles reinforces the picture of the oxygen split interstitial as an O2 molecule embedded in the ZnO crystal.

Erhart and Albe43also reported on the O i?split?and its metastable con?guration O i0?split?*.They referred to them as “dumbbell con?gurations,”and they found that these defects

(a)(b)(c)

O i0(split)O i0(split)*

O i2-(oct)

FIG.10.?Color online?Local atomic geom-

etry of electrically inactive oxygen split intersti-

tial?a?in the most stable con?guration?O i0?split??

and?b?in a metastable con?guration?O i0?split?*?.

?c?Local atomic geometry of electrically active

oxygen interstitial at the octahedral site

?O i2??oct??.

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B76,165202?2007?

are electrically active with acceptor transition levels close to the CBM.Our results do not support this assignment.We suggest that the acceptor charge states found by Erhart and Albe are a result of occupying extended bulk states near the CBM,and not defect-induced states.This explains why Er-hart and Albe?nd acceptor transition levels slightly above the CBM.According to our results,these two con?gurations are both dimers as previously reported in Ref.106.The in-teraction between Zn-O i is much less strong than that be-tween O-O,resulting in similar formation energies despite the very different O-Zn-O bond angles in these two compet-ing con?gurations.

Oxygen interstitials can also exist as electrically active interstitials occupying the octahedral site,O i?oct?,as shown in Fig.10?c?.Interstitial oxygen at the octahedral site intro-duces states in the lower part of the band gap that can accept two electrons.These states are derived from oxygen p orbit-als and result in deep acceptor transition levels??0/??and ???/2??,at0.72and1.59eV above the VBM.Figure3 shows that interstitial oxygen can exist either as electrically inactive split interstitials O i0?split?in semi-insulating and p-type materials or as deep acceptors at the octahedral inter-

stitial site O i2??oct?in n-type materials?E F?2.8eV?.Note that for both forms,the formation energies are very high ?except under extreme O-rich conditions?,and we do not expect oxygen interstitials to be present in signi?cant con-centrations under equilibrium conditions.

The relaxation pattern around the oxygen atom at the oc-tahedral interstitial site is the reverse of the pattern around the zinc interstitial.The oxygen interstitial is displaced along the?0001ˉ?direction toward the basal plane formed by the three zinc nearest neighbors,as shown in Fig.10?c?.For the most relevant2?charge state,the resulting O i-Zn distances are almost equal to d0and the O i-O distances are about 1.2d0.The relaxation pattern is opposite to that of the zinc interstitial,which is displaced slightly toward the oxygen plane.

2.Migration

The migration path and calculated energy barrier for the oxygen split interstitial O i0?split?are shown in Fig.11?a?,and for the interstitial oxygen at the octahedral site O i2??oct?in Fig.11?b?.For the split interstitial O i0?split?,we focused on migration of the lowest-energy con?guration only?Fig. 10?a??;the calculated migration barrier is0.9eV.For the octahedral-site interstitial O i?oct?,we considered only the migration in the most relevant2?charge state.The migration barrier for O i2??oct?through the hexagonal channel along the c axis is1.1eV.Migration through the kick-out mechanism is a high-energy path,because the saddle point of the kick-out process involves a con?guration similar to the split inter-stitial;since the split interstitial is not stable in the2?charge state,this is a high-energy con?guration.

G.Zinc antisites

1.Formation energy,atomic geometry,and transition levels

Zinc antisite defects nominally consist of a zinc atom sit-ting on the“wrong”lattice site,i.e.,on an oxygen site?Zn O?.We?nd that zinc on an oxygen site signi?cantly lowers its

energy by assuming a lower-symmetry off-site con?guration.

The zinc atom is displaced by more than1?from the sub-

stitutional lattice site toward two next-nearest-neighbor oxy-gen atoms along the?101ˉ0?direction,as shown in Fig.12. The resulting Zn O-O interatomic distances are only8%

larger than the equilibrium Zn-O bond length.At this equi-

librium con?guration,we?nd three Zn O-Zn distances of ?2.4?and one Zn O-Zn distance of?2.8?.One can think of this low-symmetry con?guration of Zn O as a complex of a

zinc interstitial and an oxygen vacancy.We?nd a doubly

occupied a1state in the lower part of the band gap that re-

sembles the a1state of the oxygen vacancy,and another dou-

bly occupied state resonant in the conduction band that re-

sembles the a1state of the zinc interstitial.The very different

character of these defect states leads to quite different??values for different charge states?see Table II?,which are consistently taken into account in the corrections for forma-tion energies in Table III.

We?nd that the3+charge state is not stable for any

position of the Fermi level in the band gap,with the??

4

x(?)

E

n

e

r

g

y

(

e

V

)

(a)

(b)

x

x

FIG.11.?Color online??a?Migration path and calculated energy barrier of oxygen split interstitial O i0?split?.?b?Migration path and calculated energy barrier of interstitial oxygen at the octahedral site O i2??oct?.

(a)(b)

Side

view

Top

view

Zn O2+

Zn O2+

FIG.12.?Color online?Local atomic geometry of the zinc an-tisite in the2+charge state?Zn O2+?,showing a large displacement off the substitutional site.?a?Side view perpendicular to the c axis.?b?Top view parallel to the c axis?along the?0001ˉ?direction?.

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

+/2+?at1.45eV above the valence-band maximum.The ?nite size of the supercell,in principle,requires corrections

due to charged defect-defect interactions.For reasons dis-

cussed in Sec.II C,such corrections are not included here.

Since such corrections scale with q2,they could become sig-

ni?cant for a charge state as high as q=4.These corrections can be expected to increase the formation energy of Zn O4+and

therefore to lower the position of the??4+/2+?in the band gap.Because of these uncertainties,we indicate the forma-tion energy of Zn i4+as dotted lines in Fig.3.

The two electrons in the a1state resonant in the conduc-

tion band can occupy the CBM and cause the zinc antisite to

act as a shallow donor,i.e.,it is stable in the2+charge state Zn O2+?see Fig.3?and the??2+/+?and??+/0?transition levels are located above the CBM?Table II?.However,zinc

antisites have very high formation energies,as shown in Fig.

3;they are thus very unlikely to occur under equilibrium

conditions in ZnO for any position of the Fermi level in the

band gap.

First-principles calculations by Kohan et al.37and by

Zhang et al.38have also found Zn O antisites to be higher in

energy than the other donor-type native defects?V O and Zn i?. The calculations of Oba et al.39found Zn O to be comparable

in energy to V O under Zn-rich conditions.All calculations

agree that zinc antisites behave as shallow donors.However,

none of the earlier studies revealed the off-site relaxation of

Zn O.

2.Migration

Migration of the antisite in effect involves splitting the

defect into its Zn i and V O constituents.The question then is

whether these constituents remain bound and move in con-

cert or whether they move independently;in the latter case,it

is unclear whether the antisite can actually reform.A com-

prehensive investigation of these mechanisms is beyond the

scope of the present work,but a reasonable estimate of the

dissociation barrier can be obtained as follows.In n-type ZnO,the calculated binding energy of Zn O2+,i.e.,the energy required to separate Zn O2+into Zn i2+and V O0,is0.7eV?see Table III?.If we add the migration barrier of interstitial zinc ?0.6eV?,the estimated dissociation energy of Zn O2+is1.3eV. We therefore expect Zn O2+to be stable at temperatures of up to?500K.This suggests that Zn O2+may cause n-type con-ductivity if intentionally introduced under nonequilibrium conditions such as high-energy electron irradiation.20Indeed, recent experiments on electron-irradiated ZnO reported that the donor defects created by irradiation anneal out at 400°C.105This result is consistent with the stability of Zn O2+.

H.Oxygen antisites

Formation energy,atomic geometry,and transition levels

Finally,we have investigated oxygen antisites,where an oxygen atom wrongly occupies a site on the zinc sublattice ?O Zn?.O Zn is an acceptor-type point defect with very high formation energy,even under the most favorable O-rich con-ditions?see Fig.3?.This makes it very unlikely that O Zn would be present in equilibrium.However,oxygen antisites could potentially be created under nonequilibrium conditions

such as under irradiation or ion implantation.We?nd that

oxygen on the ideal zinc site is unstable and spontaneously

relaxes to an off-site con?guration,as shown in Fig.13.The oxygen atom is displaced along the?0001ˉ?direction by more than0.7?and forms a chemical bond with one of the oxy-

gen nearest neighbors.The O-O bond length is1.46??ex-

actly twice the covalent radius?in the2?charge state and

1.42?in the neutral charge state.

The distances between the oxygen antisite and the other

nearby oxygen atoms are?2.0?,much larger than twice the

oxygen covalent radius of0.73?,thus indicating the ab-

sence of bonding.Our results indicate that oxygen antisites

are deep acceptors with transition levels??0/??and ???/2??at1.52and1.77eV above the VBM.

Similar to zinc antisites,an investigation of migration

paths for oxygen antisites would be quite complicated.We

did not consider this effort warranted for a defect with such

high formation energies.Qualitatively,we expect the migra-

tion barrier to be higher than that of vacancies or interstitials.

Lin et al.92have suggested that the green luminescence in

ZnO corresponds to deep levels induced by oxygen antisites.

They observed that the intensity of the green emission in-

creases with oxygen partial pressure in thin?lms annealed at

high temperatures.Based on previous LDA calculations of

the defect transition levels,they ruled out zinc vacancies and

oxygen interstitials.According to our results,oxygen anti-

sites have much higher formation energies than oxygen in-

terstitials and zinc vacancies,and are therefore unlikely to be

present in signi?cant concentrations under equilibrium con-

ditions.As discussed in Sec.III D4,we feel that zinc vacan-

cies are more likely to be the cause of the observed green

luminescence in ZnO,and equally consistent with the results

of Lin et al.85

https://www.wendangku.net/doc/a75486240.html,parison with previous calculations

First-principles calculations based on DFT-LDA or DFT-

GGA for native point defects in ZnO have been reported by

a number of groups.37–43However,the severe underestima-

tion of the band gap in LDA or GGA calculations leads to

O Zn2-

FIG.13.?Color online?Local atomic geometry for the oxygen antisite O Zn in the2?charge state,showing a large displacement off the substitutional site.

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B76,165202?2007?

uncertainties in formation energies and transition levels,and

the lack of a systematic way to interpret or correct the LDA

or GGA results has led to signi?cant differences in the con-

clusions drawn from such calculations.Zhang et al.38re-

ported a strong asymmetry in the formation energies for

donor-type?V O,Zn i,and Zn O?and acceptor-type?V Zn,O i, and O Zn?defects,with donor-type defects having signi?-cantly lower formation energies.No such asymmetry was

observed by Kohan et al.37or Oba et al.,39and neither is it

evident in our present work;in fact,acceptors seem to po-

tentially exhibit lower formation energies in these studies ?depending on stoichiometry conditions,of course?.Lee et al.40and Kohan et al.37found that Zn i is a deep donor with transition levels??2+/+?and??+/0?at?0.5eV above the VBM,whereas Oba et al.39found the donor transition level ??2+/0?at?1.2eV?i.e.,above the calculated CBM?,and Zhang et al.38found that Zn i is a shallow donor.

In an attempt to correct for the LDA de?ciency in predict-

ing band gaps,Zhang et al.38tested a series of empirical and

non-self-consistent approaches to correct their LDA results. The lack of self-consistency and the scattered data from dif-ferent correction methods resulted in signi?cant uncertainties in their calculated formation energies for different charge states of a given defect.One of their results was that zinc vacancies do not introduce transition levels in the band gap, in contrast with our present results as well as the results of other groups,37,39,40and also con?icting with recent experi-mental evidence.23

Erhart et al.41,43performed calculations for vacancy mi-gration barriers and found a large anisotropy.As noted in Sec.III C5,we feel that these large anisotropies are an arti-fact of their use of a fairly small?32-atom?supercell.Previ-ous work by Limpijumnong and Van de Walle has shown that32-atom supercells are not suf?cient for calculations of migration barriers in wurtzite-phase semiconductors.29

Lany and Zunger44performed calculations using LDA and LDA+U.Although their LDA+U results are similar to ours, their analysis and interpretation differ signi?https://www.wendangku.net/doc/a75486240.html,ny and Zunger assume that LDA+U only changes the position of the valence band in ZnO.We have previously shown that LDA+U actually affects both the valence band and conduc-tion band.46Lany and Zunger also assume that when further corrections are applied to bring the band gap in agreement with experiment,transition levels remain unaffected,i.e., they remain pinned to the valence band.We strongly feel that this assumption is not justi?ed.Indeed,most defect levels exhibit both conduction-and valence-band character.This should be clear on general grounds?e.g.,based on the nature of the hybrid orbitals that combine to form the defect states?, and it also directly follows from a comparison of the LDA and LDA+U results,as extensively discussed in Secs.II E and III B and illustrated in Tables II and III.The Kohn-Sham states and transition levels for most defects exhibit signi?-cant shifts?in fact,shifts that are larger than the valence-band offset?E v=0.34eV between LDA and LDA+U that was calculated in Ref.46?,clearly indicating that the states exhibit a?nite amount of conduction-band character.Further corrections to the conduction-band position should therefore also lead to further shifts in the transition levels,and indeed we have taken advantage of the information contained in the shift from LDA to LDA+U to calculate the magnitude of this correction?Eq.?6??.

Lany and Zunger’s approach44leads them to conclude that oxygen vacancies should exist in ZnO in concentration of up to1017cm?3under equilibrium conditions.If this were the case,then oxygen vacancies should be readily observable in magnetic resonance experiments.In fact,as discussed in Sec. III C4,an unambiguous EPR signature of the oxygen va-cancy has been identi?ed,and this signature has never been observed in as-grown material,but only in samples subjected to high-energy electron irradiation?where vacancies can be formed in nonequilibrium concentrations?.This result is con-sistent with the high formation energy of oxygen vacancies as found in our present study and demonstrates the shortcom-ings of Lany and Zunger’s approach for calculating forma-tion energies.

Recently,Patterson45performed DFT calculations using a hybrid functional approach that yields a calculated band gap of3.34eV.While such calculations are valuable,Patterson’s analysis of the position of transition levels is unfortunately ?awed.Instead of calculating the transition levels from total-energy differences?see Eq.?5??,Patterson related their posi-tion directly to the position of the Kohn-Sham states.This procedure leads to large errors when the different charge states exhibit large and different local lattice relaxations as in the case of V O.However,an analysis of Patterson’s“raw data”is informative:the calculated band structure in Ref.45 shows that the position of the a1state of V O0is1eV higher in the hybrid functional calculation than in LDA.This shift is in very good agreement with our extrapolation scheme.

J.Activation energies for self-diffusion Now that we have presented our results for formation en-ergies,migration paths,and energy barriers for point defects in ZnO,we can discuss possible mechanisms for self-diffusion and their respective activation energies.Although activation energies Q can be easily computed based on the calculated formation energies and migration barriers using Eq.?1?,the comparison with experimental measurements is far from straightforward.Formation energies of point defects and,consequently,also activation energies depend on the chemical potential?Zn?or?O?and can also depend on the position of the Fermi level,i.e.,Q=Q??Zn,E F?.?Zn can vary from?Zn=E tot?Zn??extreme Zn-rich conditions?to ?Zn=E tot?Zn?+?H f?ZnO?=E tot?Zn??3.6eV?extreme O-rich

conditions?,and E F can vary from E F=0?p type?to E F =E g=3.4eV?n type?.On the experimental side,it is usually not straightforward to assign speci?c chemical potential val-ues to the growth or annealing conditions,and often the ex-act position of the Fermi level has not been established.A direct comparison between experimental and theoretical val-ues of self-diffusion activation energies thus,in principle, requires a major experimental effort to perform measure-ments under controlled and well de?ned conditions.Never-theless,it is possible to draw some important conclusions based on the calculated activation energies and relate them to the available experimental data.

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

Most of experiments so far have been performed on n-type or semi-insulating ZnO.In Table V,we list the calcu-lated diffusion activation energies for the vacancy-and interstitial-mediated mechanisms for three representative doping conditions:n type,where we assume the Fermi level to be at the CBM?E F=E g?,semi-insulating,where we as-sume the Fermi level to be midgap?E F=E g/2?,and p type,

where we assume the Fermi level to be at the VBM?E F

=0?.We have omitted cases where the formation energy is

negative because such negative energies indicate that the de-fect would form in such abundance that the Fermi level would be moved to a different position where the formation energy is positive.By inspecting Fig.3,we believe that most experiments are performed under conditions that are close to Zn rich.Otherwise,the samples would be heavily compen-sated by zinc vacancies.Therefore,we assume Zn-rich con-ditions in the following analysis.Values for other conditions or other doping levels can be easily obtained by referring back to Eq.?3?.

Zinc self-diffusion in ZnO can be mediated by Zn vacan-cies or Zn interstitials.In n-type ZnO,we note from Table V that despite the low-energy barrier for the interstitial-mediated mechanism,Zn self-diffusion is predicted to be mediated by Zn vacancies due to the signi?cantly lower for-mation energy of the vacancies.This result agrees with ex-periments by Tomlins et al.107who reported an activation energy of3.86eV for Zn self-diffusion in ZnO and sug-gested that it is controlled by a vacancy-mediated mecha-nism.Similar to other compound semiconductors,29,32,33the migration barrier for the cation vacancies is higher than for interstitials.However,the formation energy of the zinc va-cancy?an acceptor?is much lower than that of the zinc in-terstitial?a donor?under n-type conditions.Table V shows that zinc interstitials will play a more important role in Zn self-diffusion in semi-insulating and p-type ZnO where the formation energy of Zn interstitials is quite low and that of Zn vacancies is quite high.

Oxygen self-diffusion in ZnO can be mediated by O va-cancies or O split interstitials?O i?split??.Although oxygen interstitials at the octahedral site?O i?oct??have a low migra-tion barrier,they do not contribute to self-diffusion.In order to contribute to self-diffusion,the interstitials would ulti-mately need to become substitutional again,by exchanging positions with oxygen atoms at the regular lattice sites.As already discussed in Sec.III F2,our calculations indicate that this process involves a high energy barrier.

In n-type ZnO,our calculations indicate that both V O0and O i?split?will“equally”contribute to oxygen self-diffusion with activation energies of6.08and6.11eV,respectively. On the other hand,in semi-insulating and p-type ZnO,oxy-gen self-diffusion will be mediated by V O2+,since the forma-tion energy of V O2+decreases with the Fermi-level position. Our calculated activation energy in this case is4.53eV,in reasonable agreement with the experiments by Tomlins et al.,16who reported an activation energy between3.6and 4.2eV for oxygen self-diffusion in semi-insulating ZnO crystals.

K.Defect-annealing temperatures

Based on our results for migration paths and energy bar-riers for point defects in ZnO,we can also discuss the tem-peratures at which we expect individual defects to become https://www.wendangku.net/doc/a75486240.html,parison of these temperatures with experimental observations of changes brought about by annealing can aid in the identi?cation of speci?c defect species.According to transition state theory,36an atom near a vacancy can jump to the vacancy?or an interstitial can jump to the next interstitial site?over an energy barrier E b with a frequency

?=?0exp??E b k B T

?,?9?

where the prefactor?0is the ratio of the vibrational frequen-cies at the initial con?guration to the frequencies at the saddle point,k B is the Boltzmann constant,and T is the tem-perature.A reasonable estimate of the temperature at which a defect becomes mobile can be obtained by taking the usual de?nition of the activation temperature,i.e.,the temperature at which the jump rate?in Eq.?9?is1/s.Detailed calcula-tions of the prefactor are beyond the scope of the present investigation,but to a good approximation?0can be taken as a typical phonon frequency,i.e.,1013s?1.Therefore we can use?=1s?1,?0=1013s?1,and the calculated E b values for each defect to estimate an annealing temperature based on Eq.?9?.Comparison with established cases indicates that this method for estimating the annealing temperature typically slightly overestimates the temperature at which defects be-come mobile.

In Table VI,we list the estimated annealing temperatures for the various point defects in ZnO for which we computed the migration barriers.Only the lowest migration barrier for a given defect is considered here.We see that the low migra-tion barrier of zinc interstitials results in very low annealing temperatures,well below room temperature,in good agree-ment with recent experimental data from low-temperature irradiation experiments.17,23,34During low-temperature elec-tron irradiation,Frenkel pairs?zinc interstitial+zinc va-cancy?are created;these have been observed to annihilate at temperatures between100and200K in optically detected

TABLE V.Calculated migration barriers E b and activation en-ergies Q=E f+E b for possible self-diffusion mechanisms of zinc and oxygen species in ZnO.The formation energies E f are taken from Fig.3.Activation energies are given for Zn-rich conditions and for three possible values of the Fermi level:E F=E g for n-type,E F =E g/2for semi-insulating,and E F=0for p-type material.Absence of a value indicates that the particular charge state is not stable under those conditions.

Mediating defect E b?eV?

E F=E g

Q?eV?

E F=E g/2E F=0

Zn i2+0.57 6.98 3.55

V Zn2? 1.40 2.97 6.40

V O0 2.36 6.08

V O2+ 1.70 4.53

O i0?split?0.87 6.11 6.11 6.11

O i2??oct? 1.14 5.148.57

NATIVE POINT DEFECTS IN ZnO PHYSICAL REVIEW B76,165202?2007?

electron paramagnetic resonance?ODEPR?measurements by Watkins and co-workers.17,23Our results clearly indicate that the zinc interstitial is the mobile species responsible for the healing of the crystal at low temperatures.108

Our results also indicate that oxygen interstitials can diffuse at modest temperatures and are the mobile species responsible for defect recombination on the oxygen sub-lattice.Oxygen and zinc vacancies become mobile only at higher temperatures,in agreement with experimental observations.17,24Indeed,Vlasenko and Watkins have reported that oxygen vacancies are stable up to?670K.17 Nikitenko et al.110reported annealing of oxygen vacancies ?created by irradiation and identi?ed by EPR?in the range 530–630K.According to Table VI,this is consistent with

motion of V O2+.Indeed,we expect the2+charge state to be stable in the Li-doped hydrothermal ZnO crystals used in that study.Tuomisto et al.35identi?ed both V O and V Zn using positron annihilation spectroscopy in irradiated samples and observed them annealing out at temperatures between500 and600K,again consistent with our calculated barriers. Look et al.,111?nally,observed that a Zn-sublattice related acceptor anneals out starting at around300°C;this is in good agreement with our?nding for the zinc vacancy.

We note that our results support the fact that the observed radiation hardness of ZnO?Refs.20and111?can be attrib-uted to rapid defect annihilations that can take place already at temperatures around200K for the Zn sublattice and around400K for the oxygen sublattice.This property can be advantageous for electronic and photonic applications in high-radiation environments.

IV.SUMMARY

We have performed a detailed?rst-principles study of the electronic structure and diffusivity of all native point defects in ZnO.We have discussed a method to correct defect tran-sition levels and formation energies based on the LDA and LDA+U calculations.Contrary to the conventional wisdom, we?nd that isolated native point defects are unlikely to be the cause of the frequently observed unintentional n-type conductivity in ZnO.Our results show that oxygen vacancies are deep donors and have high formation energies in n-type samples;however,they can compensate p-type doping.Zinc interstitials are shallow donors,but have high formation en-ergies under n-type conditions;moreover,they are fast dif-fusers and hence unlikely to be stable as isolated point de-

fects.Zinc antisites are also shallow donors,but they have

high formation energies in n-type samples.Zinc antisites

show a large off-site displacement and induce a large local

lattice relaxation.

As an alternative explanation for the observed back-

ground n-type conductivity in ZnO,we suggest the uninten-

tional incorporation of donor impurities.Among the possible

impurities,hydrogen stands out as a likely candidate.101Re-

cently,we have shown that hydrogen can substitute on an

oxygen site and form a multicenter bond with the four

nearest-neighbor Zn atoms.112Substitutional hydrogen?H O?has a low formation energy,acts as a shallow donor,and can

explain the variation of conductivity with oxygen partial

pressure,consistent with a wide range of experimental

results.14,15,107,113,114

Zinc vacancies are deep acceptors and have low formation

energies under n-type conditions;they can therefore occur as

compensating defects in n-type samples.We suggest that

zinc vacancies are a possible source of the often-observed

green luminescence in ZnO.Oxygen interstitials have high

formation energies and are not expected to exist in signi?-

cant concentrations.They can exist as electrically inactive

split interstitials or as deep acceptors at the octahedral site in

n-type samples.In p-type samples,the neutral split intersti-tials are predicted to be more favorable.Oxygen antisites have the highest formation energies among the acceptor-type native point defects.They are deep acceptors and also show large off-site displacements,in which the oxygen atom bonds chemically to only one of the oxygen nearest neighbors.

The migration barriers of all the point defects are modest,

explaining why radiation damage can be annealed out at rela-

tively low temperatures?with some recovery already taking

place below room temperature?.Zinc interstitials diffuse

through the kick-out mechanism with a rather low migration

barrier of0.57eV,in agreement with experimental observa-

tions,and are responsible for the observed fast recovery of

the electrical properties in irradiated ZnO.The migration bar-

rier of oxygen interstitials in the octahedral con?guration ?relevant for n-type samples?is1.1eV,whereas zinc and oxygen vacancies diffuse with somewhat higher migration barriers of1.4and2.4eV,respectively.We note that these low migration barriers imply that most point defects will be highly mobile at the temperatures at which ZnO crystals and epilayers are commonly grown,indicating that such growth processes can be considered to be near equilibrium.Finally, our results provide a guide to more re?ned experiments to probe the in?uence of individual point defects on the elec-tronic properties of ZnO.

ACKNOWLEDGMENTS

We are grateful to G.D.Watkins,L.Halliburton,and D. Segev for valuable discussions.This work was supported by the NSF MRSEC Program under Grant No.DMR05-20415. It made use of the CNSI Computing Facility under NSF Grant No.CHE-0321368,and also of DataStar at the San Diego Super Computer Center.

TABLE VI.Estimated annealing temperature T anneal for vacan-

cies and interstitials in ZnO based on transition state theory as de-

scribed in the text.

Defect E b?eV?T anneal?K?

Zn i2+0.57219

V Zn2? 1.40539

V O2+ 1.70655

V O0 2.36909

O i0?split?0.87335

O i2??oct? 1.14439

ANDERSON JANOTTI AND CHRIS G.V AN DE WALLE PHYSICAL REVIEW B76,165202?2007?

纳米氧化锌的部分特性

纳米氧化锌的部分特性 薛元凤051002231 摘要：纳米材料的物理化学性能与其颗粒的形状、尺寸有着密切的关系。因此，单分散纳米材料的制备及其与尺寸相关的性能研究成为近几年人们研究的热点之一。ZnO作为一种宽禁带半导体具有独特的性质，在纳米光电器件、光催化剂、橡胶、陶瓷及化妆品领域有着广阔的应用前景，随着对不同形状的纳米ZnO的制备及其相关的性能研究不断升温，对其应用方面的研究进展不断深入，单分散纳米ZnO材料已经引起了人们越来越广泛的关注。ZnO作为一种宽禁带，高激子结合能的氧化物半导体，以其优越的磁、光、电以及环境敏感等特性而广泛地应用于透明电子元件、UV 光发射器、压电器件、气敏元件以及传感器等领域。ZnO 本身晶格结 构特点决定了在众多的氧化物半导体中是一种晶粒形态最丰富的材料。本文主讲纳米氧化锌紫外屏蔽、光电催化、气敏、磁性等特性，及纳米氧化锌在生活中、工厂作业中的用途。 关键词：紫外屏蔽光电催化气敏导电性磁性 1 引言 随着纳米科学的发展，人类对自然的认识进入到一个新的层次。材料的新性质被逐渐发掘!认识，新的理论模型被提出"著名学者钱学森院士预言：“纳米左右和纳米以下的结构将是下一阶段科技发展的特点，会是一次技术革命，从而将是二十一世纪的又一次产业革命”。 纳米ZnO具有优异的光、电、磁性能，在当今一些材料研究热点领域表现活跃。与普通ZnO相比，纳米ZnO颗粒尺寸小，微观量子效应显著，展现出许多材料科学家渴望的优异性质，如压电性，荧光性，非迁移性，吸收和散射电磁波能力等。大量科研工作集中于纳米ZnO材料的制备、掺杂和应用等方面。制备均匀、稳定的纳米ZnO是首要任务，获得不同形貌的纳米结构，如纳米球、纳米棒、纳米线、纳米笼、纳米螺旋、纳米环等，将这些新颖的纳米结构材料所具有的独特性能，应用到光电、传导、传感，以及生化等领域，取得了可喜的成绩。世界各国相继大量投入，开发和利用纳米ZnO材料，使其在国防，电子，化工，冶金，航空，生物，医学和环境等方面具发挥更大的作用。 2简介 纳米氧化锌(ZnO)问世于20世纪80年代，其晶体结构为六方晶系P63mc空间群，纤锌矿结构，白色或浅黄色的晶体或粉末，无毒，无臭，系两性氧化物，不溶于水和乙醇，溶解于强酸和强碱，在空气中易吸收二氧化碳和水，尤其是活性氧化锌。

纳米氧化锌的奇妙颜色

纳米氧化锌的奇妙颜色 --作者冯铸（高级工程师，工程硕士宝鸡天鑫工业添加剂有限公司销售经理） 纳米级活性氧化锌有多种生产方式，而每种生产方式及各个生产方式的工艺差别的不同，使得最终产品的颜色不同，即呈现微黄色的程度不同。 一、物质颜色的由来 物质的颜色都是其反光的结果。白光是混合光，由各种色光按一定的比例混合而成。如果某物质在白光的环境中呈现黄色（比如纳米氧化锌），那是因为此物体吸收了部分或者全部的蓝色光。物质的颜色是由于其对不同波长的光具有选择性吸收作用而产生的。 不同颜色的光线具有不同的波长，而不同的物质会吸收不同波长的色光。物质也只能选择性的吸收那些能量相当于该物质分子振动能变化、转动能变化及电子运动能量变化的总和的辐射光。换句话说，即使是同一物质，若其内能处在不同的能级，其颜色也会不同。比如氧化锌，不论是普通形式的，还是纳米形式的，高温时颜色均很黄，温度降低时颜色变浅。原因在于在不同温度时，氧化锌的分子能及电子能的跃迁能量不同，因此，对各种色光的吸收不同。 二、粗颗粒的氧化锌与纳米氧化锌的结构区别，及由此导致的分子内能差异 粗颗粒的直接法或间接法氧化锌是离子晶体。通常来说，锌原子与氧原子以离子键形式存在。由于其颗粒较粗，每个颗粒中氧原子与锌原子的数量相当多，而且两种原子的数量是一样的（按分子式ZnO看，是1：1）。但对于纳米氧化锌，其颗粒相当细，使得颗粒表面的未成键的原子数目大增。也就是说，纳米氧化锌不能再看成具有无限多理想晶面的理想晶体，在其表面，会有无序的晶间结构及晶体缺陷存在。表面这些与中心部分不同的原子的存在，使得其具有很强的与其他物质反应的能力，也就是我们通常所说的活性。 研究表明：在纳米氧化锌中，至少存在三种状态的氧，他们是晶格氧（位于颗粒内部）、表面吸附氧及羟基氧（--OH），而且，颗粒中锌的数量大于氧的数量，不是1：1的状况。这一点与普通氧化锌完全不同。纳米氧化锌的表面存在氧空缺，有许多悬空键，易于与其他原子结合而发生反应，这也是纳米氧化锌在橡胶中、催化剂中作为活性剂应用的基本原理。 由于纳米氧化锌与普通氧化锌的上述不同。使得其颗粒中分子能及电子能的跃迁变化能级不同，因此，其颜色也不同。普通氧化锌是白色，而纳米氧化锌是微黄色。 三、纳米氧化锌随时间及环境湿度变化，其颜色的变化 对于纳米氧化锌，由于其颗粒表面存在吸附氧及羟基氧，而这两种氧的数量会随着时间的变化而发生变化，比如水分的吸附及空气中氧气的再吸附与剥离等。这两种氧的数量的变化，必然会引起颗粒中分子及电子能级的变化，对光的吸收也不相同，因此，纳米氧化锌的颜色变浅。 四、纳米氧化锌的颜色与纯度的关系 纯的纳米氧化锌，其颜色是纯微黄的，显得色泽很亮。 当纳米氧化锌含杂质，如铁、锰、铜、镉等到了一定程度，会使氧化锌的颜色在微黄色中带有土色的感觉，那是因为铁、锰、铜、镉等的氧化物均为有色物质，相互混合后，几种色光交混，显出土白色。而纳米氧化锌（或者活性氧化锌，轻质氧化锌）随着时间变化而发生的颜色变化，会被土色所掩盖，而使颜色显得变化极小；当纳米氧化锌中含杂质再高时，其颜色会变得很深，更无法观测到其颜色随时间变化的情况。 如前所述，物质的颜色是其对外界光线选择性的吸收引起的。因此，在我们比较氧化锌的颜色时，最好在户外光亮的地方观察比较确切。选择不同的环境做比较，会得到不同的比较结果，这也体现了光反射的趣味性。 五、关于纳米氧化锌颜色的另外一种解释 纳米氧化锌是经碱式碳酸锌煅烧而得。在此过程中，如果碱式碳酸锌未能完全分解，纳米氧化锌的颜色就会显得白一些，因为碱式碳酸锌为纯白色。此外，在南方与北方生产，或在潮湿的雨天与干燥的天气下生产，也会影响颜色。因为纳米氧化锌可与湿空气及二氧化碳反应生成碱式碳酸锌，发生了煅烧过程的逆反应。这种变化对产品质量的影响有多大，现在尚难断定，因为碱式碳酸锌本身也是具有催化作用的，适于在脱硫剂及橡胶行业使用；而在饲料行业，碱式碳酸锌具有与氧化锌同样的功能，它也是一种饲料添加剂，同时，在饲料行业，我们关心的问题主要是重金属的含量是否达到标准要求。

氧化锌纳米材料简介

目录 摘要 (1) 1.ZnO材料简介 (1) 2.ZnO材料的制备 (1) 2.1 ZnO晶体材料的制备 (1) 2.2 ZnO纳米材料的制备 (2) 3. ZnO材料的应用 (3) 3.1 ZnO晶体材料的应用 (3) 3.2 ZnO纳米材料的应用 (5) 4.结论 (7) 参考文献 (9)

氧化锌材料的研究进展 摘要介绍了氧化锌（ZnO）材料的性质，简单综述一下近几年ZnO周期性晶体材料和ZnO纳米材料的新进展。 关键词：ZnO；晶体材料；纳米材料 1.ZnO材料简介 氧化锌材料是一种优秀的半导体材料。难溶于水，可溶于酸和强碱。作为一种常用的化学添加剂，ZnO广泛地应用于塑料、硅酸盐制品、合成橡胶、润滑油、油漆涂料、药膏、粘合剂、食品、电池、阻燃剂等产品的制作中。ZnO的能带隙和激子束缚能较大，透明度高，有优异的常温发光性能，在半导体领域的液晶显示器、薄膜晶体管、发光二极管等产品中均有应用。此外，微颗粒的氧化锌作为一种纳米材料也开始在相关领域发挥作用。纳米ZnO粒径介于1-100nm之间，是一种面向21世纪的新型高功能精细无机产品，表现出许多特殊的性质，如非迁移性、荧光性、压电性、吸收和散射紫外线能力等，利用其在光、电、磁、敏感等方面的奇妙性能，可制造气体传感器、荧光体、变阻器、紫外线遮蔽材料、图像记录材料、压电材料、压敏电阻、高效催化剂、磁性材料和塑料薄膜等[1–5]。下面我们简单综述一下，近几年ZnO周期性晶体材料和ZnO纳米材料的新进展。 2.ZnO材料的制备 2.1 ZnO晶体材料的制备 生长大面积、高质量的ZnO晶体材料对于材料科学和器件应用都具有重要意义。尽管蓝宝石一向被用作ZnO薄膜生长的衬底，但它们之间存在较大的晶格失配，从而导致ZnO外延层的位错密度较高，这会导致器件性能退化。由于同质外延潜在的优势，高质量大尺寸的ZnO晶体材料会有利于紫外及蓝光发射器件的制作。由于具有完整的晶格匹配，ZnO同质外延在许多方面具有很大的潜力：能够实现无应变、没有高缺陷的衬底-层界面、低的缺陷密度、容易控制材料的极性等。除了用于同质外延，ZnO晶体

重点高中生物必修三第三章第一节植物生长素的发现教案

重点高中生物必修三第三章第一节植物生长素的发现教案

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植物生长素的发现 一、教学目标 1.知识目标 （1）直到生长素的发现过程。 （2）领会生长素发现过程中相关的实验现象和结论。 2.能力目标 （1）通过探究实验的参与，培养学生动手能力，提高实验技能。 （2）通过教学使学生能初步运用所学知识进行分析的问题：通过对生长素的生理作用及特点的理解，灵活地应用于生活实际，解决生产实践中的问题。 （3）培养学生学会透过生命现象把握生命本质，运用生长素作用原理分析解决农业生产实际问题的能力。 （4）通过学生查阅有关资料，培养学生收集、处理资料和信息的能力以及知识的迁移和重组能力。 3.情感、态度及价值观目标 通过探究性学习活动，培养学生执著的探索精神，实事求是的科学态度、严谨的科研作风、团结协作的精神，提高学生的科学素质。 二、教学重点难点 重点： 生长素发现、向光性的原因。 难点： 1.生长素的产生、运输和分布。 2.科学实验设计的严谨性分析。 三、课时安排 1课时。 四、教学过程 导入新课 师：同学们好！首先，先告诉大家一个不幸的消息，前些天我们社区发生了一起跳楼事件。 生：是什么？

师：据家属说是有一盆盆栽自己掉下了楼，没有任何人触碰。大家想，植物好好的为什么会直接掉下楼去呢？这个问题相信大家都还比较难回答，现在老师给大家一点点提示——植物生长素。至于什么是生长素，怎么发现的生长素，便是我们这一节课将要研究的问题。 板书：植物生长素的发现及其作用 推进新课 师：观察下列现象，说明问题。 课件展示： ①放在窗台上的花盆中的植物，朝向光照的地方生长； ②向日葵幼嫩的花盘会随着太阳转； ③玉米胚芽鞘会弯向单侧光方向生长； ④向日葵、玉米胚芽鞘受到均匀光照时的生长状况。 师：看了这些资料，大家对“跳楼事件”肯定会有一定的看法了，先把这件事情放在一边，老师先问大家一个问题，就是从这几个资料中，大家可以找到什么共同点？ 生：植物体会弯向光源方向生长。 师：那么，为什么植物会向光生长呢？谁给的刺激呢？ 生：光照。 师：方向怎样？ 生：单侧光照下，才表现向光弯曲生长现象。 师：对，非常好，在生物学中我们把这种植物向光源方向生长的现象叫做植物的向光性。那么，同学们还知不知道其他类似的现象呢？大家先看这么一个资料。 课件展示： 展示植物根的向地性。 生：植物体受到单一方向外界刺激而引起的定向运动叫向性运动。 师：体验下列现象是否是向性运动？找学生代表从不同方向刺激含羞草叶片，叶片闭合。请同学们思考回答：含羞草叶片受到刺激，产生闭合现象，是否是向性运动？为什么？ 生：不是，因为不管从什么方向刺激，都引起闭合。不是单一方向刺激引起的定向运动。 师：答得好。 师：请同学们讨论植物还有哪些向性运动的例子？学生讨论，老师简单总结：向性运动：单一，定向。 师：同学们了解清楚了向性运动，下面我们来探讨植物为什么会产生向性运动？

植物生长素的作用机理

植物生长素的作用机理 陶喜斌 2014310218 种子科学与工程

摘要；经过多位科学家的研究，发现了与植物生长有关的重要激素——生长素。生长素在植物芽的生长，根的生长，果实的生长，种子休眠等方面有重要作用。那么，生长素是如何发挥这这些作用? 1;什么是生长素 生长素(auxin)是一类含有一个不饱和芳香族环和一个乙酸侧链的内源激素，英文简称IAA，国际通用，是吲哚乙酸(IAA；。4-氯-IAA、5-羟-IAA、萘乙酸(NAA)、吲哚丁酸等为类生长素。1872年波兰园艺学家谢连斯基对根尖控制根伸长区生长作了研究~后来达尔文父子对草的胚芽鞘向光性进行了研究。1928年温特证实了胚芽的尖端确实产生了某种物质，能够控制胚芽生长。1934年， 凯格等人从一些植物中分离出了这种物质并命名它为吲哚乙酸，因而习惯上常把吲哚乙酸作为生长素的同义词。 2;植物生长素的生理作用 生长素有多方面的生理效应，这与其浓度有关。低浓度时可以促进生长，高浓度时则会抑制生长，甚至使植物死亡，这种抑制作用与其能否诱导乙烯的形成有关。生长素的生理效应表现在两个层次上。 在细胞水平上，生长素可刺激形成层细胞分裂~刺激枝的细胞伸长、抑制根细胞生长~促进木质部、韧皮部细胞分化，促进插条发根、调节愈伤组织的形态建成。 在器官和整株水平上，生长素从幼苗到果实成熟都起作用。生长素控制幼苗中胚轴伸长的可逆性红光抑制~当吲哚乙酸转移至枝条下侧即产生枝条的向地性~当吲哚乙酸转移至枝条的背光侧即产生枝条的向光性~吲哚乙酸造成顶端 优势~延缓叶片衰老~施于叶片的生长素抑制脱落，而施于离层近轴端的生长素促进脱落~生长素促进开花，诱导单性果实的发育，延迟果实成熟。 生长素对生长的促进作用主要是促进细胞的生长，特别是细胞的伸长。植物感受光刺激的部位是在茎的尖端，但弯曲的部位是在尖端的下面一段，这是因为尖端的下面一段细胞正在生长伸长，是对生长素最敏感的时期，所以生长素对其生长的影响最大。趋于衰老的组织生长素是不起作用的。生长素能够促进果实的发育和扦插的枝条生根的原因是；生长素能够改变植物体内的营养物质分配，在生长素分布较丰富的部分，得到的营养物质就多，形成分配中心。生长素能够诱 导无籽番茄的形成就是因为用生长素处理没有受粉的番茄花蕾后，番茄花蕾的子房就成了营养物质的分配中心，叶片进行光合作用制造的养料就源源不断地运到子房中，子房就发育了。 生长素在植物体作用很多，具体有；1.顶端优势 2.细胞核分裂、细胞纵向伸长、细胞横向伸长3.叶片扩大4.插枝发根5.愈伤组织6.抑制块根7.气孔开放8.延长休眠9.抗寒 3;生长素的作用机理 3.1生长素作用机理的解释 激素作用的机理有各种解释，可以归纳为二； 一、是认为激素作用于核酸代谢，可能是在DNA转录水平上。它使某些基因活化，形成一些新的mRNA、新的蛋白质(主要是酶；，进而影响细胞内的新陈代谢，引起生长发育的变化。 二、则认为激素作用于细胞膜，即质膜首先受激素的影响，发生一系列膜结构与功能的变化，使许多依附在一定的细胞器或质膜上的酶或酶原发生相应

纳米氧化锌的研究进展

学号：201140600113 纳米氧化锌的制备方法综述 姓名：范丽娜 学号： 201140600113 年级： 2011级 院系：应用化学系 专业：化学类

纳米氧化锌的制备方法综述 姓名：范丽娜学号： 201140600113 内容摘要:介绍了纳米氧化锌的应用前景及国内外的研究现状,对制 备纳米氧化锌的化学沉淀法、溶胶凝胶法、微乳液法、水热合成法、 化学气相法的基本原理、影响因素、产物粒径大小,操作过程等进行 了详细的分析讨论;提出了每种创造工艺的优缺点,指出其未来的研 究方向是生产具有新性能、粒径更小、大小均一、形貌均可调控、生 产成本低廉的纳米氧化锌。同时也有纳米氧化锌应用前景的研究。 Describes the application of zinc oxide prospects and research status, on the preparation of ZnO chemical precipitation, sol-gel method, microemulsion, hydrothermal synthesis method, chemical vapor of the basic principles, factors, product particle size, operating procedure, carried out a detailed analysis and discussion; presents the advantages and disadvantages of each creation process, pointing out its future research direction is the production of new properties, particle size is smaller, uniform size, morphology can be regulated, production cost of zinc oxide. There is also promising research ZnO. 关键字：纳米氧化锌制备方法影响研究展望 正文：纳米氧化锌是一种多功能性的新型无机材料，其颗粒大小约在1～100纳米。由于晶粒的细微化，其表面电子结构和晶体结构发生 变化，产生了宏观物体所不具有的表面效应、体积效应、量子尺寸效 应和宏观隧道效应以及高透明度、高分散性等特点。近年来发现它在

生长素的发现(含详解)

生长素的发现 一、单选题 1.选取某种植物生长状况相同的四组枝条进行如图处理，其中甲、乙、丙切去顶芽， 丁保留顶芽．将切下的乙顶芽放回原位置，将切下的丙顶芽放置在琼脂块上一段时间后将琼脂块置于原顶芽位置．四组枝条均给予相同的单侧光照．下列叙述正确的是（） A. 最先发育为侧枝的是侧芽1和4 B. 乙组枝条在单侧光下表现为直立生长 C. 丙组枝条在单侧光下背光侧生长素多于向光侧 D. 若此实验在黑暗中进行，实验现象不变的是甲和丙 解析：A、最先发育成侧枝的是侧芽1，因为无顶芽，侧芽的生长素浓度降低，促进侧芽发育，A错误； B、乙组枝条向光弯曲生长，单侧光引起生长素分布不均，背光一侧多，生长素极性向 下端运输，使背光一侧生长快，植物表现出弯向光源生长，B错误； C、感光部位是顶芽，则单侧光刺激对琼脂块中生长素的分布没有影响，丙植株直立生 长，C错误； D、甲、丙均无尖端，所以生长素的分布与单侧光刺激无关，因而照光和不照光对其实 验结果无影响，D正确． 故选：D． 2.下图所示条件下，一段时间后，燕麦胚芽鞘生长状况一致的是 A. ③④ B. ①③ C. ②④ D. ①④ 解析：①垂直光照，燕麦胚芽鞘直立生长；②燕麦胚芽鞘尖端下部右侧放 上琼脂片，生长素可透过琼脂片，左侧光照，将向左弯曲生长；③燕麦胚 芽鞘尖端放上琼脂块，没有生长素，燕麦胚芽鞘不生长，也不弯曲；④燕 麦胚芽鞘尖端下部放上云母片，生长素无法透过云母片，燕麦胚芽鞘不生 长，也不弯曲。综上所述，A正确，BCD错误。故选A。 3.下面是生长素发现过程中的部分实验示意图，根据图中信息判断，下列说法正确的 是

A. 实验一证明胚芽鞘尖端产生了某种刺激 B. 鲍森·詹森的实验二证明胚芽鞘尖端产生的刺激可以通过琼脂片传递给下部 C. 实验三证明胚芽鞘弯曲生长与光照无关 D. 实验四证明造成胚芽鞘弯曲的刺激是一种化学物质 解析：A.实验一自变量为尖端是否感光，尖端感光向光弯曲生长，否则直立生长，说明感受单侧光刺激的是胚芽鞘尖端，A错误； B.实验二中，无尖端的胚芽鞘不生长，尖端与下部隔断的胚芽鞘可以生长，说明胚芽鞘尖端产生的影响可以透过琼脂片传递给下部，B正确； C.实验三中，尖端产生的刺激在其下部分布不均匀，使得胚芽鞘弯向对侧生长，说明胚芽鞘的弯曲生长是尖端产生的刺激在其下部分布不均匀造成的，C错误； D.实验四中，可以证明造成胚芽鞘弯曲的原因是尖端产生了一种化学物质在其下部分布不均匀造成的，另外缺少空白对照，D错误。 故选B。 4.如图甲、乙、丙、丁为胚芽鞘的系列实验,下列有关实验现象和分析的叙述不合理的 是 A. 图丙中胚芽鞘Y的生长现象是向光弯曲 B. 图乙琼脂块中生长素的含量左多右少,主要是生长素在胚芽鞘尖端横向运输的结果 C. 图甲中的胚芽鞘向光生长 D. 图丁胚芽鞘向右弯曲,是生长素在其下端分布不均匀的结果 解析：A.实验丙中胚芽鞘Y不生长，原因是生长素只能由植物的形态学上端运输到形态学下端，A错误； B.图乙琼脂块中生长素的含量左多右少，主要是受到单侧光照使生长素横向运输的结果，B正确； C.图甲中的胚芽鞘受到单侧光照，向光生长，C正确； D.图丁胚芽鞘向右弯曲，是生长素在其下端分布不均匀的结果，D正确。 故选A。 5.如下图所示，a、b、c、d四个琼脂块中，a、c含生长素，下列不生长的胚芽鞘是 A. ① B. ② C. ③ D. ④

生长素的作用机理

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高中生物生长素的生理作用 教材分析 新课标 人教版 必修3精编版

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1928 温特（荷兰） 1934 郭葛（荷兰） 讲述科学家的生平简介和研究成果。 从1880年至1954年，前后经过五十四年的研究，最终发现了生长素。一项科学发明、科学发现需要几年、几十年乃至几代人的艰辛努力，这就需要我们不仅理解科学家的科学方法、实验过程，理解科学家的逻辑思维特点。更要有科学家的探索精神，有持之以恒、坚忍不拔的毅力 现在，让我们一起来探索！ 三、实验教学流程： 科学家做了大量实验，从其中经典的实验设计，可以看出科学思维的巧妙性。 （多媒体）生长素的发现 实验关键步骤 向光性现象——向光性研究——感光部位研究——研究性实验设计实验一观察在黑暗、单侧光下胚芽鞘的生长情况 1、（多媒体）呈现Flash动画： a、大小和形态相同的两个暗室 b、暗室内有大小和形态相同的完整胚芽鞘 c、暗室壁上有大小、形态和位置相同的两个孔 2、教师对实验关键点讲解并设问： 将两孔一个打开，另一个关闭，给以单侧光照射，请大家预测可能发 生的现象。 学生小组讨论发表见解 3、观察现象：小孔打开的暗室中，胚芽鞘发生了弯向光源生长的现象。 小孔关闭的暗室中，胚芽鞘直立生长。 验证推测，引起植物朝向光源生长的外界刺激是单侧光 4、结果分析：胚芽鞘具有向光生长的特性 （讲解）上述实验中用了研究问题的常用方法——对照实验，对照实验通常只能有一个变量，如果实验结果不同，就说明是由这一变量引起（学生分析）实验装置中的单一变量：单侧光

氧化锌介绍

制备途径 自然界的红锌矿中存在氧化锌，但纯度不高。工业生产中使用的氧化锌通常以燃烧锌或焙烧闪锌矿的方式取得。全球氧化锌的年产量在1000万吨左右，[1]有以下几种生产方法。间接法 间接法的原材料是经过冶炼得到的金属锌锭或锌渣。锌在石墨坩埚内于1000 °C的高温下转换为锌蒸汽，随后被鼓入的空气氧化生成氧化锌，并在冷却管后收集得氧化锌颗粒。间接法是于1844年由法国科学家勒克莱尔（LeClaire）推广的，因此又称为法国法。间接法生产氧化锌的工艺技术简单，成本受原料的影响较大。间接法生产的氧化锌颗粒直径在0.1-10微米左右，纯度在99.5%-99.7%之间。按总产量计算，间接法是生产氧化锌最主要的方法。间接法生产的氧化锌可用于橡胶、压敏电阻、油漆等产业。锌锭或锌渣的重金属含量直接影响产物的重金属杂质含量，重金属含量低的产品，还可用于家畜饲料、药品、医疗保健等产业。 直接法 直接法以各种含锌矿物或杂物为原料。氧化锌在与焦炭加热反应时，被还原成金属锌被蒸汽，同时再被空气中的氧气氧化为氧化锌，以除去大部分杂质。直接法获得的氧化锌颗粒粗，产品纯度在75%-95%之间，一般用于要求较低的橡胶、陶瓷行业。 湿化学法 湿化学法大体可分为两类：酸法与氨法。二者分别使用酸或碱与原料反应，而后制备碳酸锌或氢氧化锌沉淀。经过过滤、洗涤、烘干和800°C的煅烧后，最终得到粒径在1~100纳米的高纯度轻质氧化锌。酸法通常是将含锌原料与硫酸反应，得到含有重金属离子的非纯净的硫酸锌溶液。然后经过氧化除杂、还原除杂，以及多次沉淀，除去大量的铁、锰、铜、铅、镉、砷等离子，得到纯净的硫酸锌溶液。将此溶液与纯碱中和，得到固体的碱式碳酸锌。碱式碳酸锌经洗涤、烘干及煅烧，得到轻质氧化锌。酸法生产的产品质量较高。氨法通常是用氨水及碳铵与含锌原料反应，得到锌氨络合物，然后除杂，得到合格的锌氨络合溶液，然后经过蒸氨，使锌氨络合物转换为碱式碳酸锌。最后经烘干、煅烧而得到轻质氧化锌。氨法的成本相对较低。 水热合成法 水热合成法是指在密闭的反应器（高压釜）中，通过将反应体系水溶液加热至临界温度，从而产生高压环境并进行无机合成的一种生产方法。该方法获得的氧化锌晶粒半径小，且结晶完好。将水热法与模板技术相结合，则能获得不同形态、不同尺寸的纳米氧化锌粉体。该方法目前还仅停留在试验阶段，尚存在工艺设备复杂、成本较高的问题，但也被认为是一种很有产业化潜力的方法。 喷雾热分解法 喷雾热解法是将金属盐溶液以雾状喷入高温气氛中，通过溶剂的蒸发及随后的金属盐热分解，直接获得纳米氧化物粉体；或者是将溶液喷入高温气氛中干燥，然后经热处理形成粉体的生产方法。该法制备的纳米粉体纯度高，分散性好，粒径分布均匀，化学活性好，并且工艺操作简单，易于控制，设备造价低廉，是最具产业化潜力的纳米级别氧化锌粉体的制备方法之一。 编辑本段应用领域 橡胶制造 工业生产的氧化锌有50%流向橡胶工业。氧化锌和硬脂酸作为橡胶硫化的重要反应物，是橡胶制造的原料之一。氧化锌和硬脂酸的混合加强了橡胶的硬化度。氧化锌也是汽车轮胎的重要添加剂。除了硫化作用，氧化锌能大大提高橡胶的热传导性能，从而有助于轮胎的散热，保证行车安全。氧化锌添加剂同时也阻止了霉菌生物或紫外线对橡胶的侵蚀。主

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