Litton C.W., . Reynolds D.C., Collins T.C. Zinc Oxide Materials for Electronic and Optoelectronic Device Applications

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energies of 115 and 164 meV would contribute to the measured p-type conduction. In 2004

Jeong et al.

[81]

reported on As-implanted bulk crystals and assigned a peak at 3.3589 eV

to an acceptor b ound exciton, and transitions at 3.3159 and 3.31859 eV to eA

and

DAP, respectively.

Results on phosphorous doping in ZnO came from Hwang et al.

[82]

They obtained

a bound exciton recombination at 3.355 eV, a free to bound transition at 3.31 eV, and

a DAP recombination at 3.241 eV, and deduced a binding energy of the P-acceptor in ZnO

of 127 meV in agreement with the results from Ye et al.

[83]

who obtained a value of

123 meV.

Figure 6.17 Temperature-dependent photoluminescence measurements in an undoped ZnO

epitaxial ﬁlm grown by vapor phase epitaxy. Reprinted from M. Schirra, et al., Stacking fault

related 3.31-eV luminescence at 130-meV acceptors in zinc oxide, Phys. Rev.B 77, 125215.

152 Spectral Identiﬁcation of Impurities and Native Defects in ZnO

Antimony doping was presented in the work of Xiu et al.

[84]

The luminescence line at

3.353 eV was assigned to neutral donor bound exciton recombination. Two emissions at

3.296 and 3.222 eV were attributed to eA

and DAP transitions, respectively. The acceptor

binding energy was calculated to be 140 meV.

In the work of Schirra et al.

[80]

the eA

transition is correlated with the structural data of

the ﬁlm as provided by electron microscopy. They concluded that the acceptors are located

in the basal plane stacking faults. Doping with group- V elements could lower the threshold

for stacking fault formation, where the stacking faults act as acceptor s. The observation

and identiﬁcation of the eA

transition at 3.31 eV is not necessarily an indication for

successful p-type doping of ZnO.

The high p-type carrier densities for ZnO:As, ZnO:Sb and ZnO:P require doping

concentrations of the order of 10

–10

3

. The solubility limits for dilute doping with

the group-V elements are not known. There is experimental evidence

[85]

that secondary

phases within the systems Zn-P-O and Zn-As-O form easily and limit the doping efﬁciency.

6.3 Magnetic Resonance Investigations

EPR spectroscopy has the ability to resolve hyperﬁne interactions of electrons or holes

related to doped atoms, impurities, or defects with their own nuclear core and/or the nuclei

of the constituting lattice atoms, e.g. Zn and O. This connection between the nuclear and the

electronic system allows on one hand an unambiguous identiﬁcation of species via the

isotopes and their abundances, and on the other hand statements on their electrical activity

and wave function distribution. This makes magnetic resonance spectroscopy a valuable tool

for the characterization of materials. The spectra are typically analyzed in the framework of

a Spin-Hamiltonian formalism which we brieﬂy introduce in the following:

[86]

H¼m



S 

g 

H þ

S 

A 

I ð6:1Þ

The ﬁrst term on the right-hand side of the equation describes the Zeeman interaction of

an electron characterized by its electron spin S with an external magnetic ﬁeld H via the g-

tensor, and the second term gives the hyperﬁne interaction (A-tensor) with the spin I of the

nuclei. For elect ronic centers with a single unpaired spin (S ¼

) in axial symmetry the

Hamiltonian is given by:

H¼m

½g

þ g

ðS

þ S

ÞþA

þ A

ðS

þ S

Þ ð6:2Þ

For S H

an additional ﬁne structure interaction has to be taken into consideration:

H¼

S 

D 

S ð6:3Þ

which in the principal axis system leads to

H¼DS



SSþ1ðÞ



þES

S



ð6:4Þ

where

I are the electron spin nuclear spin, respectively and their components S

A is the hyperﬁne interaction tensor and its components A

, A

g is

Magnetic Resonance Investigations 153

the g-tensor and its components g

, g

D is the ﬁne structure tensor and its

components, D is the axially symmetric part and E is the asymmetry parameter.

It is helpful to recall that the hyperﬁne interaction A can be split into an isotropic part (a)

and an anisotropic fraction (b):

a ¼ 1=3ðA

þA

Þ; b ¼ 1=2ðA

aÞð6:5Þ

The isotropic part which is a measure of the spin density on the position of the nucleus

(Fermi contact term)is given by:

a ¼ 16p=3m

ð6:6Þ

and the anisotropic part which is due to dipole–dipole interactions is given by:

b ¼ 4=5m

3

ið6:7Þ

We will use these equations to show that Na

is a deep acceptor rather than a shallow

one (see below).

To structure the magnetic resonance data on ZnO we have organized the rest of this

section as follows: we start with the results on shallow donors, than describe deep center

properties, especially the oxygen vacancy, and ﬁnally present the results on acceptors.

Table 6.1 summarizes the data on the individual centers.

6.3.1 Shallow Donors

In ZnO shallow donors are characterized by a single line spectrum at a ﬁeld position

corresponding to a g-value of g 1.96. In ZnO single crystals the resonance is slightly

anisotropic due to the wurzite symmetry. The deviation of the shallow donor g-value from

the free electron value of g ¼2.0023 is in ﬁrst order a result of the admixture of valence

band states (p-type) to the s-type conduction band.

[87–89]

In most cases the EPR linewidth of shallow donors varies between 1 G and 10 G, which

depends on the concentration of the shallow donors and the details of the measurement

conditions. A hyperﬁne interaction is rarely resolved, thus direct information on the

chemical nature of the donors cannot be given. The reason is that the donor ele ctron is in

an effective mass-like state with a Bohr radius of about 1.5 nm, thus it is distributed over

many lattice sites. Consequently the electron density on the nucleus of the donor atom is

low, typically less than a percent compared with the atomic values, thus the hyperﬁne

interaction is often smaller than the instrumental resolution in the EPR experiment.

Two fortunate cases have been found where the hyperﬁne interaction was large enough to

be resolved. In the case of the In-donors a 10 line spectrum was observed reﬂecting the I ¼9/

2 nuclear spin of the

115

In isotope (95% abundance)

[26,90]

and Ga-donors gave a four line

spectrum due to the nuclear spin I ¼3/2.

[26,91]

For the third common group-III donor in ZnO,

namely Al, the enhanced resolution of the ENDOR had to be used to resolve the inter-

action.

[92]

Experiments of the same kind were successful to identify H as a shallow donor.

[24]

To act as a shallow donor in semiconductors is quite unusual behavior for H. We just recall

here the passivating properties of H on dangling bonds in amorphous Si.

[93,94]

However,

meanwhile also complex centres were observed in which H plays a role as a passivating

154 Spectral Identiﬁcation of Impurities and Native Defects in ZnO

Table 6.1 Spin Hamilton parameters (spin state, g-values, hyperﬁne interactions) and defect assignments

Spin g-values Hyperﬁne interaction Fine structure Defect assignment Reference

S ¼

¼1.955 Not observed Shallow donor [87]

¼1.953

S ¼

¼1.957 Not observed Shallow donor [88]

¼1.956

S ¼

g ¼1.956 Not observed Shallow halogen donors [88]

S ¼

¼1.957 A(

115

In) ¼36.6 G Shallow In donor [26,90]

¼1.956 A(

Ga) ¼4.2 G Shallow Ga donor [26]

Ga,

Ga) ¼6.7 G Shallow Ga donor [91]

Shallow Ga donor [89]

S ¼

g ¼1.9595 A(

Al) ¼1.45 MHz Shallow Al donor [92]

S ¼

¼1.9569 A(

H)¼1.4 MHz Shallow H donor [24]

¼1.9552

S ¼1/2 g

¼1.9605 Shallow Zn interstitial [97]

¼1.9595

S ¼

¼1.9945 Axial center: Oxygen vacancy, F

þa

[101]

¼1.9960 A

¼57.34 MHz [99,100]

¼42.3 MHz [102,103]

Nonaxial center:

¼76.6 MHz

¼75.9 MHz

¼94.8 MHz

(continued )

Magnetic Resonance Investigations 155

Table 6.1 (Continued)

Spin g-values Hyperﬁne interaction Fine structure Defect assignment Reference

Axial at room temperature: P-center in ref. [131] [132]

S ¼

¼2.0038 Zinc-vacancy related [131]

¼2.018 Di- or trivacancy centers

[133]

¼2.0191 [102,103]

¼2.0149

¼2.0134

S ¼

¼2.0038 Zinc-vacancy related

[131]

¼2.0018

¼2.0217

S ¼1 g

¼2.0095 |D| ¼1465 MHz Zinc-vacancy related

[131]

¼2.0141 |E| ¼58 MHz [133]

¼2.019 [102,103]

S ¼

Axial center: Axial center: Hole on an oxygen atom adjacent to

a Li atom; deep Li acceptor

[88]

¼2.0028 A

¼0.22 G [114]

¼2.0253 A

¼1.81 G [115]

Nonaxial center: Nonaxial center:

¼2.004 A

¼0.29 G

¼2.0254 A

¼1.8 G

¼2.0223 A

¼1.8 G

156 Spectral Identiﬁcation of Impurities and Native Defects in ZnO

S ¼

Axial center: Axial center: Hole on an oxygen atom adjacent to

a Na atom; deep Na acceptor

[116]

¼2.0024 A

¼2.89 G

¼2.0298 A

¼1.58 G

Nonaxial center: Nonaxial center:

¼2.0032 A

¼4.15 G

¼2.0302 A

¼1.42 G

¼2.0241 A

¼1.61 G

S ¼

¼1.9953 A

¼81.3 MHz Deep nitrogen acceptor [108]

¼1.9633 A

¼9.5 MHz [91,127]

S ¼

¼2.0036 A

¼9.8 MHz N



acceptor [127,128]

¼1.9935 A

¼20.1 MHz

S ¼1 g

¼1.971 D ¼0.763 GHz None [108]

¼2.0224 [106]

¼1.984

¼2.025 D ¼260 10

4

1

Oxygen vacancy; F-center [106]

S ¼

¼2.020 (Zn

N



) [129]

¼2.006

After e



or n

irradiation.

Magnetic Resonance Investigations 157

defect (see below). While the understanding of hydrogen and the group-III donors in ZnO

has greatly developed over recent years much less is known about the halogen donors.

Not only the extrinsic donors may contribute to the n-type conductivity of nominally

undoped ZnO, but also intrinsic defects are often of great importance and relevance.

Very often the exact stoichiometry of the ZnO samples is not known, and defects

accommodating nonstoichiometry such as the donor Zn interstitials and oxygen vacancies

have to be considered with equal importance. In order to study the role of intrinsic defects

Gorelkinskii and Watkins

[95]

and Vlasenko and Watkins

[96,97]

used optically detected

magnetic resonance (ODMR) in combination with low-temperature, high-energy electron

irradiation to create and possibly identify the relevant defects. By choosing the appropriate

electron energy they created and characterized the primary radiation defects and were able

to show convincingly that Zn interstitial atoms are shallow donors. Due to the low

abundance of Zn with nuclear spin (5%) hyperﬁne interactions were not observed, but

the g-value for the Zn interstitials is clearly that of a shallow donor. The oxygen vacancy

turned out to be a deep level defe ct. Son et al. als o performed ODMR experiments on high

energy electron irradiated samples – this time at room temperature – and discovered

similar defects but with different thermal stabilities.

[98]

6.3.2 Deep Level Defects

By the 1970s the paramagnetic charge state of the oxygen vacancy was observed by

EPR.

[99–103]

Very recently the deep level behavior was conﬁrmed, and the V

level

position was determined to be about 0.9 eV above the valence band.

[104]

This diverges

somewhat from theoretical calculations which locate the level closer to the conduction

band.

[105]

Also the negative correlation energy predicted for the oxygen vacancy demands

an experimental conﬁrmation. Another open question is the relationship of the oxygen

vacancy to the “green” luminescence band in ZnO. At least three models are under

discussion: (i) it is related to the presence of Cu impurities

[91]

– a less likely model – the

pronounced phonon structured luminescence band can easily be distinguished; (ii) a

shallow donor (D

) to oxygen vacancy (V

) recombination;

[96,104]

and (iii) it originates

from an internal triplet recombination of the neutral oxygen vacancy (S ¼1), similar to

color center emissions in ionic crystals.

[106]

New aspects in the discussion of the

properties of the oxygen vacancies came recently from the theoretical calculations.

[107]

Their calculations predict that oxygen vacancies have high formation energies in n-type

material, hence have negligible abundance, and play no role in the optical recombinations

in ZnO. They further predict that Zn vacancies are the most abundant intrinsic defects and

recombinations in the green spectral range are caused by Zn vacancies and associates.

They assigned the spin triplet (S ¼1) recombination investigated in the work of Leiter

et al.,

[106]

Carlos et al.

[108]

and Vlasenko and Watkins

[109]

to a pair defect consisting of a

singly negatively charged Zn vacancy (S ¼1/2) and a neut ral shallow donor (S ¼1/2)

which by exchange interaction couple to a S ¼1 state (EM

þV



! EM

þV

2

While such a possibility cannot be ruled out, it is in conﬂict with the available

experimental data and arguments are given in the following.

In the model of Leiter et al.

[106]

the S ¼1 signal originates from the two-electron state of

the oxygen vacancy (V

). In its neutral charge state two electrons are paired with

antiparallel spins, a singlet ground state. Photo-excitation does not involve band states

but occurs as an internal atomic excitation into a singlet excited state. From there

158 Spectral Identiﬁcation of Impurities and Native Defects in ZnO

inter-system crossing occurs to the emitting states, a spin- and orbital-triplet state. Here the

radiative recombination into the singlet ground state takes place (“green emission”). In an

atomic model this is a

Pto

S type recombination, the band states of ZnO are not

involved. For a comparison see the results on the two-electron centres in CaO (color

centers).

[110–112]

The parameters of the S ¼1 center are g

¼1.984, g

¼2.025, and the ﬁne structure

splitting constant is D ¼þ0.78 GHz [see Table 6.1 and Equation (6.3)].

Janotti and Van de Walle

[107]

suggest as a model an exchange coupled pair consisting

of a singly negatively charged Zn vacancy (S ¼1/2) and an effective mass type donor

(S ¼1/2) for the recombinatio n. Coupling the two spins to a total S ¼1 system and

assuming the ﬁne structure splitting D to be zero, we expect the g-value of this center to

be:

[113]

pair

¼ðg

þg

donor

Þ=2 ð6:8Þ

Shallow donors have g-values of g

¼1.957 and g

¼1.955 and the g-values for V



are g

¼2.0024 and g

¼2.0193, thus the g-values should be g

¼1.979 and g

¼1.987.

Such g-values are typical for the centers observed by Vlasenko and Watkins

[109]

but they

are considerably different from the experimental values of g

¼1.971 and g

¼2.022 (see

Table 6.1). Vlasenko and Watkins

[109]

indeed observed several Zn vacancy related centers

which show an effective mass donor to Zn vacancy acceptor type of recombination

(EM

þV



! EM

þV

2

), however, none of these had this particular g- and D-value.

Furthermore, the trigonal symmetry of V



should show up in the angular dependence of the

magnetic resonance signals.

The S ¼1 center detected in the green band has a positive ﬁne structure or zero ﬁeld

splitting D. The D of spin-exchange coupled pairs is mediated by the dipole–d ipole

interaction D

and is negative.

[112]

¼ðm

=4pÞð3g

=2r

Þð6:9Þ

where g

and g

are the g-values of the two spin s and r is the distance between the spins.

For anion vacancies the zero ﬁeld splitting became positive because there are two

contributions to D ¼D

þD

, the dipole–dipole interaction as given in Equation (6.3)

and D

is the spin-orbit interaction in the triplet states which are not spin-only states but

have angular momentum.

[112]

In the ODMR experiments Leiter et al.

[106]

were in the fortunate situation to observe the

level anticrossing (LAC) in the circular polarization of the emission (Figure 6.18). The

LAC allows an unambiguous determination of the sign of D. The intensity of the circular

polarization of the emission is measured as the difference of the left- and right-circular

polarized emission components:

DIðB; TÞ¼I

s

I

s þ

ð6:10Þ

In case of a positive zero ﬁeld splitting D the |0H sub-state is located below the |1H

sub-states of the S ¼1 triplet. With increasing magnetic ﬁeld B the MCPE intensity

increases due to partial thermalization in the sub-states. At the ﬁeld position of LAC the

level mixing of the |1H radiative state and the more populated nonradiative |0H results

in an increase of the s



emission, i.e. a positive signal DI. For a negative D the opposite

holds, the intensity of the MCPE would decrease.

Magnetic Resonance Investigations 159

A typical situation in many ZnO samples is that the emission in the visible spectral range

is a superposition of various recombinations. A broad vibronic coupled band with almost no

structure is the consequence. Therefore it was of importance to investigate the spectral

dependence of the LAC signal and the ODMR resonances responsible for our S ¼1 center

(see Figure 6.19). The dependence of the ODMR (LAC) signals on the emission wavelength

reproduces the photoluminescence spectrum (see Figure 6.19), thus the recombination band

centered at 2.45 eV is caused by this particular spin triplet recombination.

This does not mean that other recombinations and hence other defects cannot participate

in the emission in the visible spectral range but for the samples used by Carlos et al.,

[108]

Leiter et al.

[106]

and Vlasenko and Watkins

[109]

the broad unstructured green luminescence

band was caused by a defect with a S ¼1 conﬁguration in the excited state. However, the

relationship between the “green” emission and the oxygen vacancies is still under discus-

sion. Rather more settled is the identiﬁcation of the oxygen vacancy in its paramagnetic

single ionized charge state.

[99–103]

Further experiments are needed to get solid information

on the neutral charge state and if possible also on the 2þ charge state. Furthermore, the

predicted negative correlation energy for the oxygen vacancy needs conﬁrmation.

[105,107]

Figure 6.18 Observation of the level-anti-crossing in the magnetic circular polarized emission

(MCPE) of the S ¼1 center in ZnO. The insets show the magnetic resonance as signal decrease

and increase, and a schematic model of the zero-ﬁeld splitting of the S ¼1 states. Reprinted

with permission from F.H. Leiter, Thesis, Gieben, 2002

160 Spectral Identiﬁcation of Impurities and Native Defects in ZnO

6.3.3 Extrinsic Acceptors: Li, Na and N

For the group-I elements it is well established that they introduce deep acceptor states.

With binding energies of 800 meV (Li) and 600 meV (Na) they compensate the back-

ground shallow donors and produce high resistive material.

[114–116]

For “shallow” effective

mass like acceptors in ZnO one would expect in an atomic limit g-values around g 1(a

hole localized in a p-orbital) whi ch is clearly not the case for the deep Li and Na centers

(see Table 6.1).

The hyperﬁne constants of the centers can be interpreted in a linear combination of

atomic orbitals (LCAO) approach where one assumes that the electron wavefunction is

made up from Na 3s and 3p orbitals:

Y ¼ aYð3sÞþbYð3pÞð6:11Þ

þb

¼h

G 1 allows for admixtures of non-sodium orbitals for example from

surrounding oxygen atoms. The term b

reveals the hybridization of the investigated

atom which is also reﬂected in the bond angle w. Using the relationship:

[117]

tanðwÞ¼½2ð1 þb

Þ

1=2

ð6:12Þ

and the measured angle w we can estimate the term to be 4.7 times more p-like than in an

ideal sp

hybrid.

Inserting the measured values of a and b and the wavefunction values of the free atoms

given by Morton and Preston

[118]

one ﬁnds a

¼0.12, b

¼0.59, and h

¼0.71 for the

nonaxial Na centers. For the axial Na centers the values become: a

¼0.11, b

¼0.29, and

¼0.4. The h

value shows different admixtures of oxygen states for the axial type and

Figure 6.19 (a) Photoluminescence spectrum and (b) ODMR excitation spectrum of the S ¼1

defect in ZnO. Reprinted with permission from F.H. Leiter, Thesis, Gieben, 2002

Magnetic Resonance Investigations 161