This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 134.117.10.200

This content was downloaded on 05/06/2014 at 23:22

Please note that terms and conditions apply.

Hydrogen in oxides and nitrides: unexpected physics and impact on devices

View the table of contents for this issue, or go to the journal homepage for more

2010 IOP Conf. Ser.: Mater. Sci. Eng. 15 012001

(http://iopscience.iop.org/1757-899X/15/1/012001)

Home Search Collections Journals About Contact us My IOPscience

Hydrogen in oxides and nitrides: unexpected physics

and impact on devices

Chris G. Van de Walle and Anderson Janotti

Materials Department, University of California, Santa Barbara, CA 93106-5050, USA

E-mail: vandewalle@mrl.ucsb.edu

Abstract. Controlling the conductivity of wide-band-gap semiconductors is key to enablingapplications in electronics and optoelectronics. Many oxides exhibit unintentional n-typeconductivity, and oxygen vacancies have been widely discussed as the source of this conductivity.Based on first-principles investigations we have shown that this cannot be true in ZnO and SnO2.We suggest that the conductivity is due to unintentional incorporation of donor impurities, withhydrogen being a likely candidate. Both interstitial and substitutional hydrogen act as shallowdonors in a number of oxides. The atomic and electronic structures of these centers is discussed.

1. IntroductionTransparent conducting oxides (TCOs) provide metallic conductivity while absorbing little orno visible light [1, 2]; they are essential for devices such as solar cells, light-emitting diodes, andflat-panel displays. Recent efforts to enhance the performance of these oxides have highlightedthe fact that the causes and mechanisms of conduction are poorly understood. Controlling thisconductivity is also critical for achieving stable and reproducible ambipolar doping. Oxygenvacancies are widely discussed as the source of n-type conductivity, but our recent first-principlescalculations for ZnO [3, 4, 5, 6] and SnO2 [7] cast severe doubt on this hypothesis.

Instead, we point to the important role played by unintentional impurities. Most growthtechniques introduce impurities through the sources or as contaminants [8]; even in ultrahighvacuum, impurities such as hydrogen are present at high enough levels to incorporate in sizeableconcentrations in materials in which their solubility is high [9]. Hydrogen is indeed a particularlyinsidious impurity in this respect, since it is notoriously difficult to experimentally detect.

Based on our calculations we have suggested that hydrogen is a plausible cause ofunintentional doping in ZnO [9, 10, 11], a proposal now confirmed by numerous experimentalstudies [6]. Two forms of hydrogen can act as electrically active impurities: interstitial hydrogen,which prefers to attach to an oxygen host atom and diffuses relativily easily, and substitutionalhydrogen on an oxygen site, which is more stable and can alternatively be regarded as a complexconsisting of hydrogen and an oxygen vacancy. Both of these species act as shallow donors inZnO, SnO2 [7, 12], and In2O3 [13]. In addition, hydrogen has also been found to act as a shallowdonor in InN [15, 16].

In Sec. 2 we will briefly discuss the Methodology; Sec. 3 comments on some issues of notationand terminology, and Sec. 4 present an overview of key results for hydrogen in ZnO. Section 5concludes the paper.

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

c© 2010 IOP Publishing Ltd 1

2. MethodologyThe formation energy is a key quantity characterizing the properties of a defect or impurityin a solid. In the following, we will use the term “defect” to generically refer to both nativepoint defects and impurities. Defects that occur in low concentrations have a small or negligibleimpact on conductivity; only those whose concentration exceeds a threshold will have observableeffects. The concentration is determined by the formation energy through the expression:

c = Nsites exp (−Ef/kT ), (1)

where Ef is the formation energy, Nsites is the number of sites on which the defect can beincorporated, k is the Boltzmann constant, and T the temperature. We illustrate the definitionof the formation energy [17, 18] for a native point defect with the specific example of an oxygenvacancy in a 2+ charge state in ZnO:

Ef (V 2+O ) = Etot(V

2+O )− Etot(ZnO) + µO + 2EF . (2)

Etot(VqO) is the total energy of the supercell containing the (fully relaxed) defect, and Etot(ZnO)

is the total energy of the same supercell containing the ZnO perfect crystal. The Fermi energyEF is the chemical potential of electrons, i.e., the energy of the reservoir with which electronsare exchanged. The oxygen atom that is removed is placed in a reservoir, the energy of whichis the oxygen chemical potential µO. It is a variable, corresponding to the experimental notionthat ZnO can be grown under oxygen-rich or oxygen-poor conditions. However, µO is subjectto an upper bound equal to the energy of molecular O2. In equilibrium, the sum of µZn andµO corresponds to the energy of ZnO. An upper bound on µZn, set by the energy of bulk Zn,therefore leads to a lower bound on µO. The range over which the chemical potentials can varyis thus given by the enthalpy of formation of ZnO (exp.: -3.60 eV [19]).

Electrically active defects can occur in different charge states. For each position of the Fermilevel, one particular charge state has the lowest energy. The Fermi-level positions at which thelowest-energy charge state changes are called transition levels. Once the formation energies areknown, the transition levels immediately follow by taking energy differences:

ε(q/q′) = [Ef (Dq;EF = 0)− Ef (Dq′ ;EF = 0)]/(q′ − q), (3)

where Ef (Dq;EF = 0) is the formation energy of the defect D in the charge state q whenthe Fermi level is at the valence-band maximum (EF=0). When atomic relaxations are fullyincluded in the calculation of the formation energies for both charge states, a thermodynamictransition level is obtained. The experimental significance of this level is that for Fermi-levelpositions below ε(q/q′) charge state q is stable, while for Fermi-level positions above ε(q/q′),charge state q′ is stable. The transition levels should not to be confused with the Kohn-Shamstates that result from band-structure calculations for a single charge state. We also note that inoptical experiments (luminescence or absorption) the final state may not be completely relaxed,leading to different values for optical levels; for a discussion, see Ref. [18].

Equation (2) can be explicitly evaluated by performing density functional theory (DFT) [20]calculations. Introduction of a defect breaks the translational symmetry of the crystal; however,periodicity can be maintained by using a supercell geometry, in which the defect is placed in a cellthat is a multiple of the primitive unit cell of the crystal. This allows continued use of periodicityin the calculations, which is often exploited through the use of Fast Fourier Transforms, etc. Theuse of supercells also has the advantage that the underlying band structure of the host remainsproperly described. An alternative approach would be to use a large cluster with a defect atthe center. However, for computationally tractable sizes quantum confinement may significantlyaffect the host band structure. In addition, surface effects could interfere with the properties

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

2

of the defect. In practice, the supercell method has become the most widely used approach forstudying defects. Convergence as a function of supercell size should always be checked, to makesure that the quantities that are derived are representative of an isolated defect.

To make the calculations for large supercells computationally feasible, pseudopotential [21, 22]and projector-augmented-wave [23, 24] approaches have proven ideal. These are implementedin highly optimized codes such as the Vienna Ab initio Simulation Program (VASP) [25, 26, 27]

DFT calculations have traditionally used the local density approximation (LDA) [28] orgeneralized gradient approximation (GGA) [29, 30]. The use of DFT-LDA/GGA implies thatthe band gap is not properly described, and states within the band gap will therefore be affectedas well. If these states are occupied with electrons, the formation energy of the defect willtherefore also reflect these errors. Several approaches have been, or are being, developed toovercome these problems; currently the most promising one seems the use of hybrid functionals,which still fully fit within the DFT approach, but which are based on the inclusion of a smallfraction of non-local exchange in the Hamiltonian [31, 32, 33]. Several recent calculations haveillustrated the power of this approach [8, 12, 34]

3. Notation and terminologyAs already indicated in Eqs. (2) and (3), we denote charge states of defects with a superscriptthat reflects the actual charge on the defect, including its immediate vicinity. I.e., Dq indicatesthat defect D occurs with charge q. For a neutral defect, q=0. If one electron is removed, q=+1;if one electron is added, q=−1; etc. We believe this notation is more intuitive and more clearthan the historical Kroger-Vink notation [35], in which neutral charge states (0) are indicatedby a × superscript, negative charge states by a ′, and positive charge states by a •.

Another aspect of the Kroger-Vink approach is that the physics of defects is invariablyexpressed as a function of explicit reactions that involve pairs of defects, e.g., Frenkel pairs. Inprinciple, our formation-energy formalism is entirely equivalent to this defect-reaction approach,but with the important advantage that defects (and their energetics) can be studied individually,and that the dependence of their formation energy (and hence concentration) on Fermi leveland atomic abundances can be explicitly examined. Thermodynamics is also more cleanlyseparated from kinetics in this fashion. Formation energies of individual defects are plotted asa function of Fermi level position. Since these defects can also affect the Fermi level position, aself-consistent analysis involving all relevant defects and impurities can be performed, invokingoverall charge neutrality, in order to determine the defect concentrations and Fermi-level positionin the material as a function of growth or annealing conditions [17].

Finally, we note that different communities seem to have different designations forconfigurations of hydrogen within a solid. What we call “interstitial hydrogen” in this paper isoften referred to in the oxide literature as an “OH−” ion. Interstitial hydrogen in many oxidesprefers the positive charge state, which we label as H+

i . Since this species is attracted to theoxygen anion in the system, an O-H bond tends to form. I.e., the atomic structure of interstitialH+

i is such that it sits close to an oxygen atom. Since in oxides the anion is often considered tooccur as an O2− ion, the complex with hydrogen then leads to the concept of an OH− ion beingpresent.

4. Hydrogen in ZnOZnO is a technologically important multifunctional material, widely used in varistors,piezoelectric transducers, phosphors, pigments, and as a catalyst. In most of the currentapplications, high crystalline quality and low concentration of impurities and defects are notessential requirements. ZnO often exhibits high levels of unintentional n-type conductivity, withcarrier densities of up to 1017 cm−3 [36, 37]. The cause of the unintentional n-type conductivityhas been heavily debated. In recent years, ZnO has become considered for novel applications: its

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

3

wide and direct band gap of 3.4 eV, large exciton binding energy of 60 meV, and the availabilityof large single crystals make ZnO a promising material for optoelectronic devices [6]. Controllingthe electrical conductivity of ZnO is an essential step towards its utilization as a semiconductorin photonic and electronic devices.

The unintentional n-type conductivity in ZnO has long been attributed to oxygen vacancies[35]. This hypothesis was based on the assumption that oxygen vacancies are shallow donors,and exist in appreciable concentrations in n-type samples. Circumstantial evidence was providedby the observation that the n-type conductivity varies inversely with the oxygen partial pressurein growth or annealing environments. It has recently been established that oxygen vacanciesare very unlikely to be the cause of unintentional n-type conductivity in ZnO. They are verydeep donors, with an ionization energy of ∼1 eV; in addition, they have high formation energiesin n-type ZnO, resulting in negligible concentrations under equilibrium conditions [6]. Thesecalculated properties agree well with careful electron paramagnetic resonance experiments onirradiated samples [3, 38].

About 10 years ago we showed, based on first-principles calculations, that interstitial hydrogenbehaves as a shallow donor in ZnO [10]. This was surprising, because hydrogen typically actsas a passivating agent in semiconductors, reducing the electrical conductivity rather than beinga source of doping. The theoretical prediction was quickly confirmed in numerous experiments(summarized in Ref. [6]). However, interstitial hydrogen is highly mobile [39, 40] and thus canbe removed from ZnO by annealing at relatively modest temperatures (∼150 ◦C). There areclear experimental indications, however, that hydrogen also exists as a more thermally stabledonor that persists upon annealing [41, 42] at temperatures up to ∼500 ◦C. We have explainedthis additional hydrogen-related donor species in terms of substititutional hydrogen in ZnO,i.e., a hydrogen atom occupying the position of an oxygen atom in the ZnO lattice [11]. Thissubstitutional hydrogen species is more stable than interstitial hydrogen in ZnO, with a diffusionbarrier consistent with the observed reduction in hydrogen activity above ∼500 ◦C [41, 42]. Itsformation energy, and hence the solubility of substitutional hydrogen, is consistent with observedconcentrations, and because of its location on an oxygen site it can also explain the observeddependence of unintentional n-type conductivity on the oxygen partial pressure in the growthor annealing environments.

0 1 2 3Fermi level (eV)

-1

0

1

2

3

4

5

Fo

rma

tio

n e

ne

rgy (

eV

)

O-poor

ε(2+/0)

+

OV0

OH+i

H

OV

2+

6

8

0 1 2 3Fermi level (eV)

-1

0

1

2

3

4

5

O-rich

ε(2+/0)

+

OV0

OH+

iH

OV

2+6

8

(a) (b)Figure 1. Formation energy asa function of Fermi-level positionfor substitutional hydrogen HO,interstitial hydrogen Hi, and theoxygen vacancy VO in ZnO. Resultsfor (a) oxygen-poor and (b) oxygen-rich conditions are shown. Thezero of Fermi level corresponds tothe valence-band maximum. Theslope of these segments indicatesthe charge state. The kink in theformation-energy curve of VO atEF = 2.4 eV indicates the ε(+2/0)transition level.

In Figure 1 we plot the calculated formation energies of substitutional hydrogen HO,interstitial hydrogen Hi, and oxygen vacancy VO in ZnO. The oxygen vacancy is a deep donorwith the ε(+2/0) ionization level at ∼1 eV below the conduction-band minimum. For Fermi-level positions below ε(+2/0), the oxygen vacancy is stable in the +2 charge state, and for

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

4

Fermi level positions above ε(+2/0), oxygen vacancy is stable in the neutral charge state. It isa negative-U center, where the + charge state is not stable for any Fermi level position, andexhibits large local relaxations [3].

Interstitial hydrogen strongly bonds to oxygen, by breaking a Zn-O bond. It can occupydifferent positions in the ZnO lattice: bond-center and antibonding sites next to oxygen, parallelto the c axis or forming an angle of about 112◦ with the c axis. In all these configurations,interstitial hydrogen results in effective-mass shallow donor levels, and they have similarformation energies, within less than 0.2 eV. We find that the bond-center configuration with anO-H distance of 1.05 A gives the lowest formation energy.

Substitutional hydrogen HO, on the other hand, bonds equally to all four nearest-neighborzinc atoms and also results in an effective-mass shallow donor. Its formation energy is only ∼0.1eV higher than that of interstitial hydrogen in oxygen-poor conditions. The electronic structureand bonding properties of HO were discussed in Ref. [11].

5. Concluding remarksWe have presented evidence that hydrogen activates the oxygen vacancy in ZnO. Hydrogencombines with an oxygen vacancy into a stable substitutional effective-mass n-type dopant inZnO. Our finding is quite unexpected and has important technological implications. First,shallow substitutional dopants for a given elemental or compound semiconductor most oftenbelong either to the column on the left (p-type) or on the right (n-type) side (in the PeriodicTable of Elements) of the element being substituted. This “empirical” rule is justified by theneed to minimize the valence mismatch between the dopant and the host atom that is beingreplaced. In the case of substitutional hydrogen HO in ZnO, this rule is clearly not obeyed,and the fact that HO results in a shallow donor level is, at least, counterintuitive. Second,since hydrogen is present in almost all growth environments, it constitutes a likely unintentionaldonor. We emphasize that hydrogen is by no means the only shallow donor impurity thatcan be unintentionally incorporated; however, since is it ubiquitous, generally hard to detectexperimentally, and not usually considered as a potential donor, special attention should bedevoted to its potential effects on the electronic properties.

AcknowledgmentsThis work was supported by the NSF MRSEC Program under award No. DMR05-20415and by Saint-Gobain Research. Collaborations with Sukit Limpijumnong, John Lyons, JorgNeugebauer, Pakpoom Reunchan, Matthias Scheffler, Abhishek Singh, Joel Varley, and JustinWeber are gratefully acknowledged.

References[1] Gordon R G 2000 Bulletin of the Mater. Res. Soc. 25 52[2] Hosono H 2007 Thin Solid Films 515 6000[3] Janotti A and Van de Walle C G 2005 Appl. Phys. Lett. 87 122102[4] Janotti A and Van de Walle C G 2006 J. Cryst. Growth 287, 58[5] Janotti A and Van de Walle C G 2007 Phys. Rev. B 75 165202[6] Janotti A and Van de Walle C G 2009 Re. Prog. Phys. 72 126501[7] Singh A K, Janotti A, Scheffler M and Van de Walle C G 2008 Phys. Rev. Lett. 101 055502[8] Lyons J L, Janotti A and Van de Walle C G Phys. Rev. B 80 205113[9] Van de Walle C G 2003 Phys. Status Solidi B 235 89[10] Van de Walle C G 2000 Phys. Rev. Lett. 85, 1012[11] Janotti A and Van de Walle CG 2007 Nature Mater. 6, 44[12] Varley J B, Janotti A, Singh A K and Van de Walle C G 2009 Phys Rev. B 79 245206[13] Limpijumnong S, Reunchan P, Janotti A and Van de Walle C G 2009 Phys. Rev. B 80 193202[14] Van de Walle C G, Lyons J L and Janotti A 2010 Phys. Status Solidi A 207 1024[15] Limpijumnong S and Van De Walle C G 2001 Phys. Status Solidi B 228 303

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

5

[16] Janotti A and Van de Walle C G 2008 Appl. Phys. Lett. 92 032104[17] Van de Walle C G, Laks D B, Neumark G F and Pantelides S T 1993 Phys. Rev. B 47 9425[18] Van de Walle C G and Neugebauer J 2004 J. Appl. Phys. 95 3851[19] Dean JA 1992 Lange’s Handbook of Chemistry, 14th ed. (McGraw–Hill, Inc., New York)[20] Hohenberg P and Kohn W 1964 Phys. Rev. 136 B864[21] Vanderbilt D 1990 Phys. Rev. B 41 7892[22] Kresse G and Hafner J 1994 J. Phys. Cond. Mat. 6 8245[23] Blochl P E 1994 Phys. Rev. B 50 17953[24] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758[25] Kresse G and Hafner J 1993 Phys. Rev. B 47 558[26] Kresse G and Furthmuller 1996 Phys. Rev. B 54 11169[27] Kresse G and Furthmuller 1996 Comput. Mat. Sci. 6 15[28] Kohn W and Sham L J 1965 Phys. Rev. 140 A1133[29] Perdew J P and Wang Y 1991 Phys. Rev. Lett. 66 508[30] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865[31] Muscat J, Wander A and Harrison N M 2001 Chem. Phys. Lett. 342 397[32] Heyd J, Peralta J E, Scuseria G E and Martin R L 2005 J. Chem. Phys. 123 174101[33] Franchini C, Podloucky R, Paier J, Marsman M and Kresse G 2007 Phys. Rev. B 75 195128[34] Janotti A, Varley J B, Rinke P, Umezawa N, Kresse G and Van de Walle CG 2010 Phys. Rev. B 81 085212[35] Kroger F A 1974 The Chemistry of Imperfect Crystals (Amsterdam: North Holland Publishing Co.)[36] Look D C, Reynolds D C, Sizelove J R, Jones R L, Litton C W, Cantwell G and Harsch W C 1998 Solid

State Commun. 105 399[37] Look D C 2001 Mater. Sci. Eng. B 80 383[38] Vlasenko L S and Watkins G D 2005 Phys. Rev. B 71 125210[39] Thomas D G and Lander J J 1956 J. Chem. Phys. 25 1136[40] Wardle M G, Goss J P and Briddon P R 2006 Phys. Rev. Lett. 96 205504[41] Jokela S J and McCluskey M D 2005 Phys. Rev. B 72 113201[42] Shi G A, Stavola M, Pearton S J, Thieme M, Lavrov E V and Weber J 2005 Phys. Rev. B 72 195211

11th Europhysical Conference on Defects in Insulating Materials (EURODIM 2010) IOP PublishingIOP Conf. Series: Materials Science and Engineering 15 (2010) 012001 doi:10.1088/1757-899X/15/1/012001

6