First principles studies of the self trapped hole and the fluorine adsorption on the SrF2 (111) surface

Computational Materials Science 73 (2013) 9–14

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Computational Materials Science

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First principles studies of the self trapped hole and the fluorineadsorption on the SrF2(111) surface

0927-0256/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.commatsci.2013.02.009

⇑ Corresponding author. Tel.: +86 516 83591530.E-mail address: [email protected] (Z. Yi).

Ran Jia a,b, Zhijun Yi c,⇑, Chunsheng Liu b, Hongting Shi d, Hongxing Zhang a, Roberts I. Eglitis e

a Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, 130023 Changchun, PR Chinab Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germanyc Department of Physics, China University of Mining and Technology, 221116 Xuzhou, PR Chinad School of Science, Beijing Institute of Technology, 100081 Beijing, PR Chinae Institute of Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV1067, Latvia

a r t i c l e i n f o

Article history:Received 30 October 2012Received in revised form 5 February 2013Accepted 7 February 2013

Keywords:DFT-B3PWStrontium fluorideFluorine adsorptionH-centerElectronic structureSurface effectBand structure

a b s t r a c t

By using density functional theory (DFT) with hybrid exchange potentials, namely DFT-B3PW, the groundstates of self trapped hole and adsorbed fluorine atom on the strontium fluoride (111) surface are inves-tigated. The self trapped hole at an interstitial anion site is denoted by H-center. In both the H-center andfluorine adsorption cases, the strong relaxations due to the surface effects are observed. In the H-centercase, the unpaired electron distributes almost equally over two H-center atoms. This equivalent distribu-tion of the unpaired electron is totally different from that of the bulk H-center [J. Phys. Chem. A 114 (2010)8444]. The other case with an adsorbed fluorine atom lying outside the slab has a more polarized chargedistribution with respect to the H-center case. The surface effects and the polarizations of H centers canbe well explained with the calculated electric fields on the surfaces. A new b-hole band located 2.80 eVabove the top of valence band (VB) is observed in the case of fluorine adsorption, and a newb-hole band located 4.26 eV above the VB is also observed in the H-center case. Specifically, the b-holebands are primarily composed of pz-orbitals, which are localized on the defect points.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction applications of SrF2, it is important to clarify exactly the absorption

The strontium fluoride (SrF2) appears in nature as a mineralfluorite and is of special interest due to its wide use and high tech-nological potential. SrF2 is an ionic large-gap insulator with Fm3mstructure and has the lattice constant a = 5.799 Å in experiments[1]. Its direct band gap at the C point between the conduction band(CB) and valence band (VB) calculated from our previous study [2]also with B3PW method is 11.31 eV. The experimental value is11.25 eV [3]. In chip manufacturing, the new photolithographictechnology is based on 157 nm system. The whole class of thealkaline earth fluorides are important materials for the latest pho-tolithographic systems due to their high transparencies to deepultraviolet (UV) light and their isotropic optical properties. SrF2

can be used as laser-working-media, scintillation material,superionic conductor, etc. [4–8]. In scientific research, SrF2 is a con-venient model system for the studies of the magneto-opticalproperties of impurity paramagnetic ions [9]. The perfect singleSrF2 crystal is extremely transparent in the infrared and ultravioletspectral regions, but residual absorption, related to linearabsorption due to defects, can result in a degradation of opticalquality and lead to damage in high power applications. For further

mechanisms and the dynamics of intrinsic transient defectformation. In the last few decades, a number of experimental andtheoretical papers treated the varied defects and impurities inSrF2 crystals [10–19].

In this work, we focus on the ground states of the H-center andthe fluorine absorption on the SrF2(111) surface. An H-center isnamed for a hole trapped at an interstitial anion site. An H-centerin the SrF2 crystal has already been investigated experimentally inthe 70s of the last century by Beaumont et al. [20], Hayes [21]. Thewhole H center is neutral with respect to the lattice. Note thatanother common defect, namely Vk center, in the alkaline-earthfluorides is similar to the H center, but positively charged withrespect to the lattice. Although one can observe many phenomenadirectly by experiments, the understanding and interpretation forsuch phenomena are complex. Fortunately, with the improvementin computer power and the development of efficient algorithms forelectronic structure calculations, it is possible to perform suffi-ciently extensive ab initio simulations of surface adsorption pro-cesses with high accuracy.

The SrF2(111) surface is highly stable in comparison with the(110) and (100) terminated surfaces [22,23]. An H-center is atwo (fluorine) atomic defect center in SrF2 crystal. One atom inthe H-center is called substitutional fluorine (H1 atom) which sub-stitutes a fluorine atom at the lattice point, and the other one is

10 R. Jia et al. / Computational Materials Science 73 (2013) 9–14

called interstitial fluorine (H2 atom) which locates at the intersti-tial site. H-centers can be formed by irradiating an alkaline earthfluoride crystals doped with heavier trivalent rare-earth ions(Re3+) with 50 kV X-rays at 4 K [20]. In undoped alkaline earth flu-orides one needs heavy irradiation with about 1 MeV electrons toproduce H centers at 77 K [21]. In addition, experiments haveshown that the hole is located on the H2 atom and that H2 atomas well as the nearest H1 atom give a [111] oriented molecularion [21,1]. Each SrF2(111) layer has three sublayers forming a fluo-rine–metal–fluorine (F–M–F) layer structure. We perform ourinvestigations for the surface H-center and fluorine adsorption ina slab system containing four layers with 3 � 3 supercells. Actually,there are 109 atoms in our simulation systems since an H-centerincludes two fluorine atoms. In fact, a fluorine adsorption at theSrF2(111) surface can also be treated as an H-center, since thecharge redistribution between the adsorbed fluorine atom andthe F anion on the surface leads to a self trapped hole on the ad-sorbed fluorine atom. Nevertheless, in order to make a distinctionwith the usual surface H-centers, we still call this case a fluorineadsorption. The geometry properties and electronic structures ofan surface H-center and a fluorine adsorption are presented in thiswork.

The paper is organized as follows: Section 2 introduces the cal-culational method and reports all required parameters in our sim-ulations. The main simulation results about the geometricalrelaxations and the electronic structures will be presented and dis-cussed in Section 3. A short summary can be found in the lastsection.

2. Calculation methods

It has been shown that the hybrid B3PW functional achievesremarkably accurate electronic and geometrical structures foralkaline earth fluorides [22,23,2,24], as well as for ABO3 perovsk-ites [25–27]. In our former works dealing with F and M centers,oxygen-vacancy dipoles and hydrogen impurities [22,23,2,24], reli-able band gaps for these defect systems have been obtained byusing the B3PW method. Therefore, the first-principles DFT-B3PW method is employed to investigate the surface H-centerand fluorine adsorption in this work. Here all numerical calcula-tions are performed using the CRYSTAL06 computer code [28].CRYSTAL06 employs the Gaussian-type functions (GTFs) localizedat atoms as the basis sets for an expansion of the crystalline orbi-tals. In order to employ the linear combination of atomic orbitals(LCAOs)-GFT method, it is desirable to use optimized basis sets(BSs). In our calculations for fluorine atoms, we apply the basisset named 7_311 which is developed by Nada et al. [29]. For Sratoms, the Hay–Wadt small-core effective core pseudopotential(ECP) is employed [30,26]. The small-core ECP replaces only innercore orbitals, the orbitals for subvalence electrons and for valenceelectrons are calculated self-consistently. The basis sets are trans-ferable, therefore, once some chemical constituents are deter-mined, they may be applied successfully in calculations for avariety of chemical substances.

The reciprocal space integration is performed by sampling thetwo-dimensional Brillouin zone of the 109-atom supercell with6 � 6 Pack–Monkhorst net [31]. The thresholds N (i.e., the calcula-tion of integrals with an accuracy of 10�N) in our calculations werechosen as a compromise between the accuracy of calculations andthe necessary computational time for large supercells. They are 7,7, 7, 7 and 14 for the Coulomb overlap, the Coulomb penetration,the exchange overlap, the first-exchange pseudo-overlap and thesecond-exchange pseudo-overlap, respectively [32]. For the latticeconstant a of SrF2, we use the theoretical optimized value of5.845 Å from the Ref. [2].

In order to simulate the system with a surface H-center, webuild a 108-atom (111) slab including four F–Sr–F layers. Eachlayer unit cell is magnified up to a 3 � 3 2D supercell containing27 atoms. After the interstitial fluorine atom (i.e., the H2 atom inthe H-center or the adsorbed fluorine atom) is added, the atomicconfiguration of the surrounding atoms is re-optimized via asearch for the total energy minimum as a function of the atomicdisplacements from the regular lattice sites. Again, two fluorineatoms in an H-center are labeled as H1 and H2 in the present work,respectively. H1 denotes the substitutional fluorine atom and H2 isthe interstitial fluorine atom. The effective charges of the atomsand overlap populations between nearest neighbors are obtainedusing the standard Mulliken analysis.

3. Results and discussion

3.1. Geometrical properties

The H-center has two different arrangements in an arbitrary F–Sr–F layer, as shown in Fig. 1. The formation energy of an investi-gated defect system is computed by subtracting the total energy ofthe optimized 108-atom (111) perfect slab and the energy of anisolated fluorine atom from the total energy of the optimized109-atom (111) slab containing an corresponding defect, as shownin the following formula:

Eform ¼ Eðnþ1ÞH � Eð1ÞF � EðnÞperfect ð1Þ

where Eð1ÞF stands for the energy of an isolated fluorine atom. Eðnþ1ÞH

and EðnÞperfect represent the total energies of the slab with and withoutan H-center (or an adsorbed fluorine atom), respectively. Via theabove formula, the calculated adsorption energy is �0.55 eV. Thenegative Eform corresponds to stable adsorption. A trend of H-centers near the surface is observed in our simulation studies.According to our calculations, the fluorine adsorption and the firstarrangement of the H-center on the top layer are more stable thanother deeper-layer H-center systems. Furthermore, the energeti-cally favorable case in the research scope of this work is the fluorineadsorption. In other words, the total energy (or formation energy) ofthe adsorption system is the lowest. Therefore, we mainly focus onthe investigation of the fluorine adsorption and the first arrange-ment of the H-center on the top (111) layer. In the following dis-cuss, if there is no other particularly statement, H-center denotesthe first arrangement of the H-center on the top surface layer tosimplify our description.

The defect lengths of H-center (i.e., distance between H1 and H2atoms) in the CaF2, SrF2 and BaF2 bulk systems are consistent by1.98 Å [35,33]. The values of the adsorption and the H-center onSrF2(111) surface in the present work are 1.99 and 1.96 Å, respec-tively, thus being very close to the value in the bulk H-center sys-tem. There is only little surface effect on the surface cases. Theposition analysis shows that the surface H-center has a remarkableoutward relaxation towards the vacuum. The H1 atom in the sur-face H-center shifts outwards by 4.385% of a0 with respect to itsposition of the unrelaxed slab. Even though other F atoms in thetop sublayer of the surface move inwards like for the perfect alka-line-earth fluoride (111) surface case caused by the surface effect,the H2 atom locates above the lower fluorine sublayer of the toplayer. The H1 atom in the adsorption case moves inwards by0.536% of a0. Considering almost the complete H-center in thisadsorption case is outside of the surface, it is reasonable to con-sider reverse penetration as a possible explanation.

Fig. 1. A SrF2(111) layer constituted three sublayers, which are two fluorine sublayers (red spheres) and one strontium sublayer (green spheres), with an adsorbed fluorineatom (blue sphere) and two different arrangements of the surface H-centers. (For interpretation of the references to color in this figure legend, the reader is referred to theweb version of this article.)

R. Jia et al. / Computational Materials Science 73 (2013) 9–14 11

3.2. Electronic properties

Table 1 presents the effective charges and spins of the H1 andH2 atoms in both adsorption and H-center systems. The H1 andH2 charges in SrF2 bulk [33] are �0.621 and �0.339e, respectively.According to our previous calculations, the total charge of the H-center is not distributed equally between two fluorine atoms ofan H-center, and the hole is mainly located on the H2 atom (i.e.,the interstitial fluorine). However, for the surface H-center, theeffective charges of H1 and H2 are vrey close, the hole is equallylocated on the H1 and H2 atoms. Due to the surface effect, the totalcharge of the surface H-center (�0.973e) is less than that of thebulk H-center [33] (�0.985e) by 0.012e, and the electrons belong-ing to the fluorine atoms near the surface tend to move inwards[2]. The charge difference between the surface and the bulk H1atoms is 0.137e, thus being more pronounced than that of the othersurface atoms, that implicates a stronger surface effect on the H-center. The first derivatives of the electrostatic potential of thefluorine adsorption and the surface H-center in z-direction areshown in the middle panel of Figs. 2 and 3. In fact, they are thez-components of the inverse electric field strength (�Ez). The dis-tribution of the electric field at the perfect fluorine site in vacuumis changed just a bit through the influence of its defect neighbor.This electric field points from internal to external of the surface.As we know, an electron moves always along the opposite direc-tion of the electric field. Obviously, the electrons on the H-centershould move inwards, i.e., the electrons should move from theH1 atom to the H2 atom. This just explains why the charge distri-bution of the surface H-center is more balanced than in the othercase. The electronic field on the defect position is changed strongly,and the field strength is increased. Further analysis of the effectivecharges demonstrates that this electron transfer is mainly causedby the pz-electrons in the outer orbital shells. For the H-centersin the deeper layers, the charge distributions between two fluorineatoms are similar to the bulk H-center case.

For the adsorption case, the electron distribution between H1(fluorine at the substitution site) and H2 (adsorbed fluorine) inthe surface H-center is even more unbalanced than within the bulkH-center system. Whereas the total charge at the adsorption site(�0.969e) is very close to the value of the surface H-center(�0.973e), being also smaller than the bulk H-center charge. Noticethat the top atom at the adsorption site is the H2 atom instead of

Table 1The defect length (i.e., the distance between the H1 and H2 atoms) on the SrF2(1 11) surfacethe H1 atoms are labeled as Z% a (a percentage of the lattice constant: 5.845 Å). DQ labeQF = �0.954e) [2]. Spin labels present the spin difference of the electrons (i.e., na–nb) in un

H1

Defect length (Å) Z% a0 Q (e)

Adsorption 1.99 �0.536 �0.763H-center 1.96 +4.385 �0.529

H1, which differs from the adsorption case, and there is no othercharged atom in the vacuum influencing on the H2 atom. Thepolarization of the electron distribution of the fluorine adsorptioncan also be explained by the fact that some electrons belonging tothe H1 atom move outwards to the H2 atom in the vacuum due tothe electric field in the surface region. This causes a strong polar-ized H-center. Also the change of the surface electric field at theadsorption position reduces the surface effect since the effectivecharge on the H2 atom is still smaller than the perfect surfacefluorine.

The localizations of the unpaired electron at the H-centers areclearly shown via the spin density maps in Figs. 2 and 3. In the sur-face H-center system, the spin polarization of the neighbor atomsalmost disappear and the spin densities on the H1 and H2 atomsare similar. Statistically, the unpaired electron is equally locatedon the fluorine atoms of the surface H-center. However, the spindensity map for the fluorine adsorption system is different anddemonstrates a more distinct spin polarization on the H2 atom.Additionally, the spin density of the H-center looks like a spin-dle-shaped pattern, which indicates that the unpaired electronmainly consists of p-orbitals. Further analysis of the direction ofspindle axis (z-direction) indicates that the projected pz-orbitalsform the hole. As mentioned before, the total charge of the surfaceH-center is less than that of the bulk H-center. However, the totalspins (+0.999e and +0.996e for the fluorine adsorption and the sur-face H-center, respectively) are by around 1.53% and 1.83% largerthan the bulk H-center spin (+0.981e) [33], implicating a strongspin polarization.

3.3. Band structure and density of states

In order to understand the impact of a self trapped hole on thesurface on the optical properties of SrF2 crystal, the band structuresof the fluorine adsorption and the surface H-center on the SrF2(111)surface are studied in this section. The exhibition of an opticalabsorption for SrF2 with H-centers is about 4.03 eV [20]. Our calcu-lated results for the defect levels, displayed in Fig. 4, allow us to ex-plain qualitatively this experimental observed optical absorption. Inthe one-electron approximation scheme, the experimental ob-served optical absorption could be due to an electron transfer fromthe H-center ground state, to the empty band atzb-spin induced by the hole localized on the H-center (see Fig. 4).

, the effective charges (Q (e)) and spins on the H1 and H2 atoms. Atomic relaxations ofls the change in the effective charge compared to perfect SrF2 crystal (QSr = +1.909e,it (e).

H2

DQ (e) Spin (e) Q (e) DQ (e) Spin (e)

+0.191 +0.232 �0.206 +0.748 +0.767+0.425 +0.464 �0.444 +0.510 +0.532

Fig. 2. Electrostatic potential (upper), its first derivative in z-direction (middle) andspin density (lower) contours in the YZ-plane of the SrF2(111) surface with aadsorbed fluorine atom from side view. The electrostatic potential map is plottedfrom �0.10 a.u. to 0.50 a.u. with a linear spacing of 0.02 a.u. And its first derivativein z-direction is mapped between �0.20 a.u. and 0.05 a.u. with a linear spacing of0.01 a.u. The spin density map shows the contours from �0.1e/bohr3 to +0.7e/bohr3

with a linear spacing of 0.025e/bohr3.

Fig. 3. Electrostatic potential (upper), its first derivative in z-direction (middle) andspin density (lower) contours in the YZ-plane of the SrF2(111) surface with thesurface H-center from side view. The mapping parameters are same as Fig. 2.

12 R. Jia et al. / Computational Materials Science 73 (2013) 9–14

According to our previous work [33], the correspondingcalculated value is 3.01 eV for the SrF2 bulk H-center system, whichis reasonable, however, it is underestimated with respect to

the experimental result. The recent scheme based on theBethe–Salpeter equation in many body perturbation theory give a

much better description of certain excited state properties aspointed out in our previous work [2,34]. For the H-center system,as discussed above, there is an unpaired electron localized on theH-center. The presence of the unpaired electron is also revealedby the band structure of the defective system as shown in Fig. 4.The a-defect band lies in the gap, but very closes to the top of VB.The empty level induced by a hole localized on the H-center appears

Fig. 4. Calculated B3PW band structures for the 109-atom supercell modeling thefluorine adsorption (upper panel) and the H-center (lower panel) on the SrF2(111)surface. a and b denote the up- and down-spin bands, respectively. Fermi energy isshifted to 0 eV.

R. Jia et al. / Computational Materials Science 73 (2013) 9–14 13

in the b-spin band structure above the VB. Due to the selection rules,the electron transition from the a-occupied band to the b-unoccu-pied band is forbidden. Therefore, the optical absorption could beexplained by an electron transfer from the b-VB top to the b-emptylevel, induced by a hole localized on the H-center.

The optical band gaps of the adsorption case and the surfaceH-center system can be found in Table 2. The calculated band gapsat the C point for both cases are less than that of the bulk H-centersystem (11.19 eV) [33], and this is similar to the phenomenon ofthe surface effect narrowing the band gap of perfect SrF2 crystal[2]. The b-defect level for the fluorine adsorption system is4.26 eV above the VB, magnified by 1.25 eV (approx 41.5%) with re-spect to the band gap of the bulk H-center system. For the surfaceH-center, the defect level is higher than the top of VB by 2.80 eV,which is less than the corresponding values for the bulk H-centersystem by 0.21 eV. Moreover, it is less than the gap in the adsorp-tion case by 1.46 eV (in other words, around 52.1%). Whereas theband gap in the fluorine adsorption system almost does notchange, and this indicates a marked hole-level movement towardsCB. In the fluorine adsorption system, the hole is located on the

Table 2Direct optical band gaps (eV) (C ? C) for the fluorine adsorption and surfaceH-center systems on the SrF2(111) surface.

Gaps Adsorption H-center

a b a b

VB ? H – 4.26 – 2.80VB ? CB 10.95 10.95 10.94 10.95

adsorbed fluorine atom, which is outside the surface. Therefore,the surface effect on this hole is more pronounced than the otherone inside the surface.

The densities of states (DOSs) are also calculated. The total andprojected DOS of the fluorine adsorption system and the surface H-center on the SrF2(111) surface are displayed in Fig. 5. The H1 andH2 p-orbitals form the b-hole band in the bulk H-center systems,and the H2 makes the major contribution [33].

Unlike the SrF2 bulk, the projected p-orbitals in px-, py- andpz-directions of the hole on the surface are not equivalent for theformation of b-hole band. According to the DOS calculations forthe fluorine surface adsorption and the surface H-center systems,the b-hole band mainly consists of pz-orbitals of the holes, as wecan see in Fig. 5. As discussed above, the spin patterns in Figs. 2and 3 look like spindles with a z-axis direction (vertical to the sur-face), which corresponds to a typical p-shape electron cloud. OurDOS calculations are in agreement with the previous spin densitydiscussion. In Fig. 5, the H1 peak is much smaller than the H2 peakfor the fluorine adsorption, however, the H1 peak is similar to theH2 peak in the surface H-center case, also being in agreement withthe earlier statements about the locations of the holes in the fluo-rine adsorption and the surface H-center systems, respectively.

4. Conclusions

By using the first-principles approach within the hybrid DFT-B3PW scheme, the fluorine adsorption and surface H-center onthe SrF2(111) surface have been calculated. Several surface H-cen-

Fig. 5. The total and projected DOS for the fluorine adsorption (upper panel) andthe H-center (lower panel) on the SrF2(111) surface. a and b denote the up- anddown-spin states, respectively. Fermi energy is shifted to 0 eV.

14 R. Jia et al. / Computational Materials Science 73 (2013) 9–14

ter configurations and one fluorine adsorption are studied. we findthat the adsorption case and the first arrangement of the surface H-center represent the energetically favorable configurations for thesimulated surface systems, suggesting a trend of the H-centerslocations, which are close to the surface. The surface effect onthe defect length is not pronounced. According to our calculations,the hole in the adsorption system is mainly localized on the ad-sorbed fluorine. That is in agreement with the result of the bulkH-center. Whereas for the surface H-center with first arrangement,the effective charges of the H1 and H2 atoms are very close. Thisphenomenon can be explained with the help of the electrostaticpotential and its first derivative. The spin density study shows thatan unpaired electron with a spindle-shaped electron cloud, impli-cates a pz unpaired electron, localized around the defects.

The band structures of our investigated systems indicate thatthere is a defect level in each case induced by the self trapped holein the gap between VB and CB in the b-spin band map, however, inthe a-spin band structure, the defect level is very close to the top ofVB. According to our calculations, the b-hole bands located 4.26 eVand 2.80 eV above the top of VB for the fluorine adsorption and thesurface H-center, respectively. This gap in the fluorine adsorptionsystem is much larger than the corresponding value in the bulkH-center case.

The analysis of the DOS calculations clearly reveals that theb-hole band is primarily composed of pz-orbitals localized on theholes, as a result of the broken symmetry of p-orbitals, thus beingin agreement with the previous spin discussion. The DOS investiga-tions dealing with other atoms suggest that the disappearingdefect levels in the a-band gap results from the occupied a-defectlevel also consisting mainly of the fluorine p-orbitals.

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