Point Defects and Defect-Induced Optical Response in Ternary

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Point defects and defect-induced optical response in ternary LiInSe2 crystals: First-principles insight Yanlu Li, Xian Zhao, and Xiufeng Cheng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11044 • Publication Date (Web): 02 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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The Journal of Physical Chemistry

Point Defects and Defect-Induced Optical Response in Ternary LiInSe2 Crystals: First-Principles Insight Yanlu Li, Xian Zhao,* and Xiufeng Cheng State Key Lab of Crystal Materials, Shandong University, Jinan 250100, China

Abstract: Many experiments on LiInSe2 (LISe), a technologically important nonlinear optical crystal, suggest that nonstoichiometric defects play an important role in changing the crystal color and their optical applications in infrared and/or near visible regions. The exact defect species and structures remain unverified by either experiment or theory however. Thereby density functional theory (DFT) within (semi)local and hybrid exchange-correlation functional is employed to determine the dominant intrinsic point defects in LISe under various environments. It is found that the isolated point defects In antisite InLi2+ and Li vacancy VLi- are dominant in a Li-deficient environment, while the Li interstitial Lii+ turns to be energetically preferable in a Li-sufficient condition. Interstitial Ini3+ is regarded as an intermediate state to form InLi2+ (Ini3++VLi-→InLi2+) if Li-deficiency. In all possible charge-compensated defect complexes as well as Frenkel and Schottky defects, InLi2++2VLi- is the only possible complex configuration under Lideficiency according to the defect structures and formation energies. In particular, the clustering effect decreases the formation energies of all considered defects with respect to the dilute limit. The investigation of optical response gives further evidence that the intrinsic point defects are responsible for the crystal color change and optical absorption cutoff shift, and conversely, these phenomena could be helpful for recognizing the dominant defects in LISe crystals.

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INTRODUCTION Optically biaxial crystals are of great interest in several decades due to the possibility of thermally insensitive phase-matching directions. The interest to the AI-BIII-CVI2 ternary chalcogenides containing alkali metal Li is motivated in recent years by the successful growth of the orthorhombic LiInS2 (LIS) single crystal with sufficient size and quality for real applications in mid-infrared (IR) region.1-3 It exhibits remarkable properties, like smaller thermal expansion anisotropy that makes the crystals less stressed, larger band gap allowing the pumping at relatively short wavelengths without two-photon absorption, several times larger thermal conductivity that minimizes the thermal lensing effect, etc. compared with well-known compounds like AgGaS2, but with much smaller nonlinear coefficients involved in birefringent phase matching than those of AgGaS2 however.4 It is therefore of great importance and special interest to study its analogous LiInSe2 (LISe) since the substitution of S by Se is expected to improve the nonlinear susceptibility by 1.5~2 times and shift the transparency range to longer wavelengths5-9 on the premise of keeping other excellent properties. However, it is still difficult to obtain the large stoichiometric and homogeneous LISe crystals because of the changed melt composition during the growth process. It is unavoidable to incorporate intrinsic defects in the LISe lattice owing to the Li losses resulting largely from the high chemical reactivity of Li. Evidently, the crystal color and the cutoff of the absorption depends largely on the types of intrinsic point defects, forming during crystal growth as well as subsequent crystal cooling and related with a rather wide homogeneity range of LISe. These intrinsic point defects commonly act as carrier-compensation centers, and influence the optical transition by introducing optically active states in the band gap. They thus in many cases dominate the electronic and optical properties, which play a crucial role in the optical applications of LISe in infrared and near visible region. It remains challenging to study the defect chemistry and physics in the synthesized samples due to the limitation of both high quality crystal samples and the experimental measurement. For example, some experiments10-12 pointed out that the non-stoichiometric composition of LISe leads to the high optical absorption in the near infrared region. Attempts to determine the exact type of point defects gave some contradicting


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information however. Such absorption has been referred to the interstitial or substituent Se atoms by Ma et al.10 while the results by Ramasamy et al.11 indicated that it came from the Li vacancy, Se interstitial, and InLi antisite defects. Moreover, Isaenko et al.12 pointed out that in the case of point defects, it is possible to change their charge state and thus to affect the crystal color under proper illumination. Up to date the grown LISe crystals exhibit a variety of color casts from colorless to deep reddish to yellowish or greenish.9,1316

In Ref. 13, it is believed that the yellow LISe crystal has a lot of scattering centers,

whereas it is suggested in Ref. 14 that yellow LISe sample is the most stoichiometric. Therefore, it still requires speculation on the nature of the point defects in LISe. On the other hand, as an excellent mid-IR nonlinear optical crystal, it is also necessary to understand the effect of intrinsic point defects on the nonlinear optical parameters, such as the second-order nonlinear optical coefficient from the aspect of the practical application. A state-of-the-art first-principles approach based on density functional theory (DFT) offers an alternative method for avoiding the difficulty in the experimental methods. Calculations based on DFT can give a direct microscopic picture of the formation and ionization of individual defects and are hence highly complementary to experimental studies. Some theoretical works are already available for the structure, electronic, optical and vibrational properties of stoichiometric LISe crystals,17-21 but limited work has been done to real the fundamental factors associated with the intrinsic point defects. In this paper, we aim at answering the following issues concerning to the point defects in LISe: (1) What is the dominant type of intrinsic point defects? (2) Could the point defects change the color of crystals? (3) Which color corresponds to the stoichiometric crystal? (4) How do the point defects influence the linear and nonlinear optical properties? Therefore, the local defect configurations, their energetic stability, the type of charge compensation, as well as defect-induced electronic states and optical responses such as the frequency-dependent dielectric function and the second-order polarizability tensor of LISe have been examined by DFT, in order to provide a clear picture and new insights into the defect physics and chemistry of LISe.



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COMPUTATIONAL DETAILS The present calculations employ the Vienna ab initio Simulation Package (VASP)22,23 implementation of DFT in conjunction with the projector-augmented-wave (PAW) formalism.24 Thereby the Li 2s1, In 5s25p1, and Se 4s24p4 states are treated as valence electrons. The electronic wave functions are expanded in plane waves using an energy cutoff of 400 eV. The electron exchange and correlation (XC) within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) 25 functional is used to optimize the configurations and calculate the second-order polarizability tensor of LISe. The force convergence criterion for the structural relaxation is set to 0.01 eV/Å. All the other properties were performed by the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE).26,27 In this approach, the long-range exchange potential and the correlation potential are calculated with the PBE functional, while the short-range exchange potential is calculated by mixing a fraction of nonlocal Hartree-Fock exchange with PBE. The screening length and mixing parameter are fixed at 10 Å and 0.25 respectively. The Brillouin zones of the 128-atom orthorhombic supercells are sampled with 4×4×4 and 2×2×2 Monkhorst-Pack28 k-point mesh for PBE and HSE calculations respectively. We calculate the defect formation energy for the charge state q dependent on the Fermi level position according to29,30 = − + ∑ + + + ∆ +

(1)

where Etotal(Xq) is the total energy derived from a supercell with defect X, Etotal(bulk) is the total energy of the defect-free supercell, ni indicates the number of atoms of species i that have been added or removed upon defect creation, and µ i are the corresponding chemical potentials. EF is the Fermi level with respect to the bulk valence-band maximum (VBM) Ev, and ∆V is a correction term30 which aligns the reference potential in the defect supercell with that in the bulk. The defect charge-state transition level ε(q/q’) is defined as the Fermi level position below which the defect is stable in the charge state q, and above which it is stable in charge state q’.30,31 It is calculated as

ε (q / q′) =

E f (Diq ; EF = 0) − E f (Diq′ ; EF = 0) q′ − q


(2)

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The correction term Ecorr is used to correct the finite-size error that arises from the electrostatic interaction between charged defects in neighboring cell images due to the periodic boundary conditions. Several schemes have been proposed to correct such error, and the correction term suggested by Makov and Payne32 is adopted in this work. As the application of such a correction for the calculation of the defect formation energies indeed works well especially for the strongly localized charged defects,29,33,34 the electrostatic energy can be expressed in a multipole expansion,32,35 = +

!" #

+

$% &#' !"

+ ()*+

(3)

where E0 is the calculated total energy of the system, q is the total charge, Q is the quadrupole moment of the defect-induced charge, αM is the Madelung constant, and εs is the static bulk dielectric constant. The experimental value of the static dielectric constant 8.456 is used here. In this work, only corrections as given by the monopole are considered, and the quadrupole term is neglected as it is about one order of magnitude smaller than the Madelung energy for all investigated defects. Generally, the calculations showed good convergence at supercell sizes of 128 atoms after correction.

Figure 1. (Color online) Stability range of the chemical potentials (in eV) of the LISe constituents. The green shaded region CDE represents the thermodynamically allowed range of the chemical potentials. The yellow shaded region CFG indicates the chemical potentials exceed the LISe formation enthalpy under the In2Se3 reference state.



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The chemical potential µ i depend on the preparation conditions. The thermodynamic considerations restrict the accessible range of the µ i if one requires the LISe stability: Let us define ∆µ Li, ∆µ In, and ∆µ Se as differences from the respective bulk values of the chemical potential of Li, In, and Se. The stability of the ternary compound LISe against decomposition into its single components constraints the ∆µ i has to equal the LISe formation enthalpy, (4)

∆# + ∆,- + 2∆/0 = −∆1#,/0

The thermodynamically stable region is between the two extremes of LISe being in equilibrium with Li2Se and In2Se3, respectively.7,21 They are described by the relations # /0

2∆# + ∆/0 = −∆1

,- /0'

and 2∆,- + 3∆/0 = −∆1

(5) (6).

These requirements are visualized in Figure 1. Within the triangle ABC the stiochiometric sum of ∆µ Li, ∆µ In, and ∆µ Se yields the LISe formation enthalpy, i.e., Eq. (4). Equation (5) defines the region within the triangle CDE, while the region enclosed between point A, B, C, F, G satisfies Eq. (6). The presence of dotted triangle CFG indicates that the Li-poor extreme satisfied Eq. (6) exceeds the LISe single components constraints Eq. (4). In other words, the Li-deficient condition (In2Se3 reference state) is the dominate growth atmosphere with less possibility to generate the second-phase as relative to the Li-sufficient condition (Li2Se reference state). Therefore, the green shaded region CDE satisfied Eqs. (4) to (6) indicates the LISe stability range, and values of the chemical potentials outside this region lead to the precipitation of other phases. Thereby, in the following calculations, the chemical potentials of Li, In and Se are taken according to Figure 1 as -2.74, -5.14, -5.93 eV for Li2Se reference state, and -5.95, -2.95, -5.42 eV for In2Se3 reference state respectively. A different choice of the reference state will modify the relative stability of the investigated defects. Strictly speaking, the Gibbs free energy has to be used to determine the chemical potentials instead of the Helmholtz enthalpy in Eqs. (4) to (6). However, it is customary to replace Gibbs free energy with the Helmholtz enthalpy, as the entropic terms are expected to be small and of the same order of magnitude for all the investigated systems.36,37 Neglecting the entropy term will thus not qualitatively change our conclusions.


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The cohesive energy of the complex X1X2…Xn, i.e., the energy necessary to separate it into single defects X1, X2, …, Xn, is obtained from the formation energies

45 … - 7 = 45 … - 7 − ∑-5 - 8

(7)

where q = q1 + q2 + … + qn. A negative cohesive energy corresponds to a stable complex. Based on the relaxed defect configurations, dielectric function ε(ω) as well as second

harmonic generation (SHG) 9:; ?@ ω spectra were calculated for the stoichiometric material as well as for the stable single point defects and defect complex models. The calculations were carried out within DFT-GGA as the HSE approach of SHG spectra is too computer-consuming for defect calculations. We can see from Figure 9 that in the calculated energy range, the point defects narrow the spectra signatures and enhance the SHG signal strength by 0.2 eV mostly. In our previous study, also for a Li-containing system, LiNbO3,36 we found that the hybrid



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functional blueshifted the spectra by about 0.8 eV and overall lowered the spectra intensity, which illustrated close values to the experimental data. Assuming that the hybrid DFT has the similar effect on the SHG spectra of LISe, the calculated spectra data seemingly agree well with measured value.10 However, due to the difficulties of estimating the degree that hybrid DFT lowers the spectra in current system, we fail to evident the point defects from the SHG spectra. As the defects change the SHG signal strength to a quite small extent, further improvement of applying hybrid DFT or other advanced modeling method to SHG spectra calculations is needed for obtaining more accurate calculation results. Furthermore, more experimental data covering a larger energy window rather than a single frequency are required for recognizing point defects and the conclusive experiment-theory comparison.

Figure 9. (Color online) Calculated 24 χ(2)(ω) tensor components for bulk LISe as well as the most stable single defects and defect complex in comparison with experimental data. The calculations here are performed within DFT-GGA.


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CONCLUSION In conclusion, the structure and stability of point defects in LISe, as well as their influence on the linear and nonlinear optical susceptibilities, have been investigated using (semi)local and hybrid DFT. The application of hybrid potential drastically decreases the band-gap problem of LISe, leading to a band-gap opening of 1.02 eV with respect to the value calculated by the (semi)local electron XC functional. It is found that In antisite InLi2+ and Li vacancy VLi- are energetically favorable for values of the electron chemical potential in the major part of band gap associated with Li-deficiency, which therefore supports the experimental observations from the component and the spectra measurements. In Li-sufficient condition, the interstitial Li with +1 charge state is predicted to be the most stable in the whole range of energy range however, with negative defect formation energy. On the other hand, by investigating the formation energies of all possible Frenkel, Schottky, and 2+

charge-compensated non-stoichiometric defect -

complexes, we found that InLi +2VLi defect complex is considered as the most possible in the crystal, in which the two VLi- locate at the nearest-next-neighboring sites of InLi2+ in- and out-plane respectively, forming zigzag-type configuration. The single defects and defect complex all redshift the optical absorption cutoff accompanied by reducing the absorption peak strength of LISe. It is interesting that single defect InLi2+ and defect complex InLi2+ +2VLi- all cause the absorption edge redshift by 0.7 eV which is quantitative similar as the energy difference (0.76 eV) between the yellow and red color crystals. We therefore deduce the point defects InLi2+ and VLi- as well as their chargecompensated complex are the dominant defects in LISe samples, and at least partially accounts for the crystal color change. On the other hand, our calculated 24 component of SHG tensors agree well with the experimental data, and the agreement is expected to be improved if include the hybrid XC functional.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]



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Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS We gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant No. 51172127), and the Fundamental Research Funds of Shandong University (Grant No. 2015TB008).

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xxxxxx. Figure S1 Comparison of optical absorption calculated by DFT-GGA and hybrid functional HSE for LISe containing various point defects and defect complex, as well as the defect-free one.

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Abstract graphic


Point Defects and Defect-Induced Optical Response in Ternary

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