Thermodynamic Stability and Vacancy Defect Formation Energies in

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Thermodynamic Stability and Vacancy Defect Formation Energies in SrHfO Syed Muhammad Alay-e-Abbas, Safdar Nazir, Naveed Ahmed Noor, Nasir Amin, and Ali Shaukat J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp506263g • Publication Date (Web): 05 Aug 2014 Downloaded from http://pubs.acs.org on August 16, 2014

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The Journal of Physical Chemistry

Thermodynamic Stability and Vacancy Defect Formation Energies in SrHfO3 S. M. Alay-e-Abbas a, b, S. Nazir a, N. A. Noor c, N. Amin b and A. Shaukat a,* a

Department of Physics, University of Sargodha, 40100 Sargodha, Pakistan

b

Department of Physics, GC University Faisalabad, Allama Iqbal Road, 38000 Faisalabad, Pakistan

c

Department of Physics, University of the Punjab, Quaid-e-Azam Campus, 54590 Lahore, Pakistan

*

Corresponding authors (A.Shaukat) Email: [email protected], Telephone: +92-48-9230914

Abstract Density functional theory based ab-initio calculations are used to investigate the thermodynamic stability, defect formation energies and electronic properties of isolated neutral and charged vacancies in SrHfO3 under various chemical environments. We find that cation defects lead the system into holedoped state, while oxygen vacancies yield defect levels near the conduction band minimum. The partial and full Schottky defect reaction energies and mixed electron hole conduction behavior of SrHfO3 is also evaluated. Furthermore, various cases for neutral oxygen vacancy clustering are examined for tuning the electrical properties of oxygen deficient SrHfO3. We show that ordered oxygen vacancies in HfO layers are energetically favorable and induces metallicity in this system which emerges due to charge transfer between vacancy site and the hafnium dangling bond. ---------------------------------------------------------------------------------------------------------------------------Keywords: Perovskite; Vacancies; Defect formation energies; Electronic density of states;

1 ACS Paragon Plus Environment


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1- Introduction The recent advances in research efforts focused on perovskite oxides with general formula ABO3 can be attributed to the availability of wide variety of functionalities in these compounds, which are achievable in their pristine, nanoscopic and defective forms

1–4

. Particularly, the alkaline-earth metal

hafnates compounds, such as SrHfO3 (SHO), have become the focus of research interest due to their practical utilization in various optical and electronic devices large band gap (6.1 - 6.5 eV)

8 – 10

5–6

. For instance, the high-permittivity 7,

and the epitaxial deposition of < 1 nm thick layers on Si (100) has

earned SHO an important candidature for future metal-oxide-semiconductor field-effect transistor technology

10 – 11

. Although SHO is optically inactive due to its large band gap, recent studies on

nanoparticles and thin films of strontium hafnate have brought forth exciting functionalities of this material which include visible photoluminescence

12

and UV excitation

13

due to vacancy defects and

dopant, respectively. Defect and vacancy clustering in perovskite oxides can be controlled during synthesis by varying the epitaxial and tensile strain 14 – 15. Consequently, extra free charge carriers are generated which lead to opto-electronic responses that are distinct from the pristine material. For example, experimentally observed oxygen vacancy clustering and ordering in insulating perovskite oxides have long been known to be responsible for high-temperature superconductivity 16. Moreover, the loss of stoichiometry and crystal symmetry resulting from the presence of oxygen vacancies can be exploited for improving ionic conductivity of bulk perovskites which is of importance for devices such as oxygen sensors, solid oxide fuel cells and conducting membranes 3, 17. First-principles electronic structure calculations provide a route for efficiently probing, analyzing and understanding novel behavior resulting from the incorporation of vacancy defects

18

, however,

earlier experimental and theoretical studies for SHO have mostly been restricted to structural and


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electronic characterization


6, 9, 10, 12 - 13

. To the best of our knowledge, no account of intrinsic defects in

strontium hafnate are available in the literature. In this paper, we present density functional theory (DFT) based ab-initio calculations for evaluating the thermodynamic stability, defect formation energetics and electronic properties of cation and oxygen vacancies in SHO. Section 2 contains the computational methods and structural details. Results and discussions are described in section 3, while conclusions are presented in section 4.

2- Computational method and structural details All calculations have been performed by using the full-potential linear-augmented-plane-wave plus local orbitals (FP-LAPW+lo) method, which is implemented in WIEN2k code

19

. The exchange-

correlation energies have been approximated using the generalized gradient approximation (GGA). Non-overlapping muffin-tin spheres of radii (RMT) 2.5 . ., 1.98 . .and 1.75 . .for Sr, Hf and O, respectively, have been chosen within which the wave functions, charge density, and potential are expanded in spherical harmonics. In these calculations, spin-orbit coupling (SOC) is neglected because our test results reveal that the inclusion of SOC has negligible influence on the electronic properties of pristine and defective SHO. Moreover, we also confirmed that the difference in calculated total energies resulting from the inclusion of SOC can be separated in purely atomic contributions

20

and,

therefore, do not change enthalpy of formation values presented in Table 1. To ensure uniformity in total energy calculations for SHO bulk unit cell and the supercell (SC) structures for defect calculations, = 7.0⁄ . . (where Ro = 1.75. .) is used for the plane wave cutoff and = 10 and = 18. .are used for the angular momentum and the charge density expansion, respectively. Self-consistent calculations are iteratively carried out and the energy convergence up to 10-4 has been confirmed. All the SC structures were fully relaxed by allowing for the minimization of atomic forces to a value less than 2 ⁄ . .. For 2 × 2 × 2SC structure containing isolated



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neutral and charged cation and oxygen vacancies a 6 × 6 × 6 k-mesh has been selected which was then compared with calculations performed using a higher k-mesh and was found sufficient for energy convergence and force minimization. Experimentally, both orthorhombic (space group # 62, ) and cubic phases (space group # 221, 3¯) of SHO have been reported with lattice parameters

!"# $%# =

4.087 Å 21 and #

$%# =

4.099 Å 13, respectively. Since a2 × 2 × 2cubic SC (equivalent to a√2 × 1 × √2SC of orthorhombic SHO) conveniently encompasses an orthorhombically distorted perovskite unit cell, no differences prevail between the defect formation energies of pseudo-cubic and orthorhombic modification of ABO3 22 - 23

. For the SC structures discussed in this work, the lattice parameter of SHO (see Table 1) has been

optimized with a 12 × 12 × 12k-mesh and for the subsequent calculations involving pristine as well as defective SHO a 40-atom SC (Sr8Hf8O24) has been derived from the optimized cubic unit cell. The isolated neutral and fully charged vacancies in SHO have been incorporated by removing one Sr, Hf, or O atom from the pristine SC resulting in off-stoichiometric materials having compositions Sr7Hf8O24, Sr8Hf7O24 or Sr8Hf8O23, respectively. For neutral as well as fully charged states of vacancies, these SCs 2-

4-

/()* , (,/ (,- and (/ /(/2+ , correspond to 12.5 %, 12.5 % and 4.167 % vacancy concentrations of ()*

respectively. In order to study the effects of ordered oxygen vacancies in SHO, we extend the calculations for (/ by clustering oxygen vacancies in the21212SC. To achieve this, 8.333 % and 16.667 % O vacancy concentrations are considered. The 8.333 % oxygen vacancy concentration is realized by either removing two O atoms in the (110) plane of21212SC ((2/ ) or by removing two third-nearest-neighbor O atoms in SrO ((2/,)* ) and HfO ((2/,,- ) layer along the [001] direction of the 21212SC. The higher oxygen vacancy clustering (16.667 %) in the21212SC is achieved by removing four O atoms from SrO ((4/,)* ) and HfO ((4/,,- ) layers. In case of(2/,)* and (2/,,- the oxygen vacancies are repeated in both 4 ACS Paragon Plus Environment

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[100] and [001] directions such that one perfect SrO or HfO layer is present between two O-deficient SrO or HfO layers. On the other hand, the O-deficient SrO or HfO layers appear after one perfect layer only in the [001] direction for the case of (4/,)* and(4/,,- . It is worth pointing out here that the introduction of ordered oxygen vacancies in ABO3 perovskite oxides yields a spontaneous polarization in a non-centrosymmetric structure for which a continuum model polarization correction must be included 24. Since correcting the spurious electrostatic self-interactions with background charges due to periodicity and finite size of SC structures is an area of ongoing research work 25, we restrict ourselves to clustering of neutral O vacancies. The size effects have been minimized by using uniform values of × , and for SC assuming various crystallographic symmetries on introducing isolated and ordered vacancies in pristine SC. Moreover, the k-mesh for SCs have been scaled by dividing the 12 × 12 × 12k-mesh with the corresponding ratio of SCs' and bulk unit cell's lattice parameters.

3- Results and discussion 3.1- Thermodynamic stability Chemical potential is an important parameter for defining the thermodynamic stability diagram, which controls the formation energies of vacancy defects in solids

26

. The individual chemical potential of

isolated atoms (5 ) is generally less than the atomic chemical potential of the same species in their "6%!⁄7

stable elemental form. Therefore, if5 = 5

"6%!⁄7

+85 (where5

denotes the chemical

potential of the standard reference state equivalent to the cohesive energy per atom

27

) then

85)* , 85,- , 85/ ⩽ 0. This also requires 85 to be varied in order to maintain stability of compound such that the sum of the varying chemical potential of all atoms is equal the enthalpy of formation of SHO, )*,-/;

85)* + 85,- + 385/ = 8:-

… (1)



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For

85,- + 285/ ⩽ 8:-

… (3)

The calculated enthalpy of formation without the zero point energy correction for the relevant compounds is presented in Table 1 which have been obtained from, )*CDD

− @A > ... (4)

,-EDF

− 2 2 @A > … (5)

8:-)*/ ≈ @A)*/ − @A ,-/>

8:-

)*,-/;

8:,-/>

where@A)*/ , @A ,-EDF

@A

)*,-/;

and@A

,-/>

≈ @A

)*,-/;

≈ @A

− @A

/

2

,-/>

− @A)*/ − @A

/

/

− 3 @A > … (6) 2

)*CDD

are the minimum total energies of the bulk unit cells. Here,@A

and

are the minimum total energies of structurally optimized face centered cubic (fcc) strontium and /

hexagonal close packed (hcp) hafnium, respectively.@A > represents the minimum total energy of an O2 dimer which has been computed by placing two O atoms at a distance of 1.210 Å in artificial periodic conditions inside a cubic unit cell of edge 15 Å and relaxing the dimer using only the Γ point for ksampling 30. The calculated cohesive energies (computed as the difference of total energy of elemental solid at optimized lattice parameter and atomic energy of the same element in a 15 Å fcc unit cell) and enthalpy of formation values which are important for formation energy calculations show good agreement with experimental data presented in Table 1. In accordance with the criteria for stable production of oxide perovskites from their binary oxides

29

)*,-/;

, the calculated modulus of8:)*,-/;

larger than the sum of enthalpy of formation values of HfO2 and SrO (i.e. |8:|8:-)*/ |).


,-/>

| > |8:-

is

|+

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Table 1. Comparison of calculated properties with experimental data. ao, bo and co: lattice parameters (Å); r0: O2 dimer bond length (Å); Ec: cohesive energies (eV/atom); ∆Hf: enthalpy of formations (eV/formula unit). Experiment

Calculated

Srfcc (space group # 225, G3¯) ao Ec

6.040 31 –1.720 32

6.027 –1.589

Hfhcp (space group # 194, 6H ⁄I) ao co Ec

3.198 33 5.061 33 –6.440 32

3.197 5.053 –6.772

SrO (space group # 225, G3¯) ao ∆Hf

5.160 34 –6.136 35

5.198 –5.982

O2 (dimer) r0 Ec

1.21 32 –2.601 32

1.225 –4.523

HfO2 (space group # 14, 2 I) ao bo co ∆Hf

5.117 36 5.175 36 5.292 36 –11.864 37

5.136 5.197 5.324 –11.269

SrHfO3 (space group # 221, 3¯) ao ∆Hf

4.099 13 –18.811 38

4.155 –18.984

From the calculated enthalpy of formation values listed in Table 1, we have obtained the thermodynamic stability diagram shown in Figure 1, where equilibrium of SHO is maintained without any secondary phases for the

Thermodynamic Stability and Vacancy Defect Formation Energies in

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