Electronic structure and optical properties of RbPb2Br5

Electronic structure and optical properties of RbPb2Br5

Author’s Accepted Manuscript Electronic structure and optic al properties of RbPb2Br5 A.A. Lavrentyev, B.V. Gabrelian, V.T. Vu, N.M. Denysyuk, P.N. Sh...

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Author’s Accepted Manuscript Electronic structure and optic al properties of RbPb2Br5 A.A. Lavrentyev, B.V. Gabrelian, V.T. Vu, N.M. Denysyuk, P.N. Shkumat, A.Y. Tarasova, L.I. Isaenko, O.Y. Khyzhun www.elsevier.com/locate/jpcs

PII: DOI: Reference:

S0022-3697(15)30116-5 http://dx.doi.org/10.1016/j.jpcs.2015.12.003 PCS7687

To appear in: Journal of Physical and Chemistry of Solids Received date: 20 August 2015 Revised date: 3 November 2015 Accepted date: 5 December 2015 Cite this article as: A.A. Lavrentyev, B.V. Gabrelian, V.T. Vu, N.M. Denysyuk, P.N. Shkumat, A.Y. Tarasova, L.I. Isaenko and O.Y. Khyzhun, Electronic structure and optic al properties of RbPb2Br5, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2015.12.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Electronic structure and optical properties of RbPb 2Br5 A.A. Lavrentyev a, B.V. Gabrelian a, V.T. Vu a, N.M. Denysyuk b, P.N. Shkumat a, A.Y. Tarasova c, L.I. Isaenko c,d, O.Y. Khyzhun b a

Department of Electrical Engineering and Electronics, Don State Technical University, 1 Gagarin Square, 344010 Rostov-on-Don, Russian Federation b

Frantsevych Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, 3 Krzhyzhanivsky Street, UA-03142 Kyiv, Ukraine

c

Laboratory of Crystal Growth, Institute of Geology and Mineralogy, SB RAS, 630090 Novosibirsk, Russian Federation d

Laboratory of Semiconductor and Dielectric Materials, Novosibirsk State University, 630090 Novosibirsk, Russian Federation

Abstract. We report on density functional theory (DFT) calculations of the total and partial densities of states of rubidium dilead pentabromide, RbPb2Br5, employing the augmented plane wave +local orbitals (APW+lo) method as incorporated in the WIEN2k package. The calculations indicate that the Pb 6s and Br 4p states are the dominant contributors to the valence band: their main contributions are found to occur at the bottom and at the top of the band, respectively. Our calculations reveal that the bottom of the conduction band is formed predominantly from contributions of the unoccupied Pb 6p states. Data of total DOS derived in the present DFT calculations is found to be in agreement with the experimental X-ray photoelectron valence-band spectrum of this compound. The predominant contributions of the Br 4p states at the top of the valence band of rubidium dilead pentabromide are confirmed by comparison on a common energy scale of the X-ray emission band representing the energy distribution of the valence Br p states and the X-ray photoelectron valence-band spectrum of the RbPb2Br5 single crystal. Main optical characteristics of RbPb2Br5, such as dispersion of the absorption coefficient, real and imaginary parts of dielectric function, electron energy-loss spectrum, refractive index, extinction coefficient and optical reflectivity are explored for RbPb2Br5 by the DFT calculations. Keywords: A. semiconductors; A. optical materials; C. ab initio calculations; D. electronic structure; D. optical properties.

*Corresponding author: [email protected], Tel.: +38 044 390 11 23; Fax: +38 044 424 21 31

1.

Introduction. Rubidium dilead pentabromide, RbPb2Br5, belongs to a fascinating family of lead-containing halides

with the common formula APb2X5 (where A = K, Rb, Tl; X = Cl, Br) which, in recent years, have attracted significant attention from both scientific and technological viewpoints. The halides are found to be very promising low phonon energy materials for tunable middle infrared (mid-IR) and long-wavelength infrared (long-wave-IR) laser sources operating in compact devices with their potential application in free space communication, for remote sensing in the vibrational fingerprint region and in bio-chemical agents, thermal scene illumination, IR spectroscopy in clinical and diagnostic analysis, ultra-sensitive detection of drugs and explosives [1-9]. The above mentioned applications require moisture-insensitive materials, at ambient conditions, possessing high output power/energy. The RbPb2Br5 bromide is a promising candidate for the above applications. RbPb2Br5 single crystals are non-hygroscopic and readily incorporate rare-earth ions, in particular Nd3+ and Tb3+ [2,3,10]. Laser activity at 1.18, 1.07, and 0.97 m in a low phonon energy RbPb2Br5 host single crystal doped with Nd3+ was observed by Rademaker et al. [3]. Interestingly, when measuring the absorption spectra of Nd3+-doped RbPb2Br5 single crystals, Rademaker et al. [2] detected a strong dependence of absorption on polarization. Additionally, the absorption spectra measurements made in Ref. [2] revealed the importance of the RbPb2Br5 single crystal orientation for the pumping of the 4F5/2 +2H9/2 level at 0.81 m or the 4F7/2 level at 0.75 m in laser experiments. The RbPb2Br5 crystals were reported to exhibit comparatively high chemical stability, high resistance to corrosion and satisfactory thermal and mechanical properties [11-13]. The narrow phonon spectrum is characteristic of the RbPb2Br5 crystals [12] and they are transparent in the wide spectral range, namely from 0.3 to 30 m [13]. The RbPb2Br5 compound crystallizes in tetragonal symmetry (space group I4/mcm) with the unit cell parameters a = 8.4455 Ǻ and c = 14.5916 Ǻ [14] or a = 8.437 Ǻ and c = 14.572 Ǻ [15]. Fig. 1 presents the crystal structure of the RbPb2Br5 bromide. The RbPb2Br5 compound reveals no phase transitions up to the melting point [16]. It is worth mentioning that studies of RbPb2Br5 single crystal plates in polarized light, as performed in Ref. [16], have revealed that the RbPb2Br5 bromide is an optically uniaxial crystal possessing good extinction in cuts parallel to the optical axis in the temperature range of 77–600 K. Measurements of the fundamental absorption edges made at 80 and 300 K in Ref. [17] have indicated that the edge position for RbPb2Br5 depends on the polarization. In particular, the fundamental absorption edges for RbPb2Br5 at 80 and 300 K are found to be shifted toward higher energies by 0.03–0.05 eV in the case of E || c compared to those in the cases of E || a and E || b polarizations [17]. Furthermore, the band gap values, E g, measured for RbPb2Br5 at 300 K for E || c are determined to be 3.470.1 eV, while for of E || a and E || b polarizations Eg = 3.420.1 eV

[17]. The above Eg values are found to increase by about 0.19 eV as temperature of RbPb2Br5 decreased from 300 to 80 K [17]. To the best of our knowledge, complex studies of peculiarities of occupation of the electronic states associated with rubidium, lead and bromide atoms, constituting elements of the RbPb2Br5 compound, are absent. X-ray photoelectron spectroscopy (XPS) was employed recently in Refs. [17,18] to determine binding energies of core-level and valence electrons of RbPb2Br5 single crystals. In particular, the influence of middle-energy Ar+ bombardment on the valence-band and constituent element core-level XPS spectra of (001) surface of RbPb2Br5 was also investigated [17]. The XPS results [17] revealed low hygroscopicity of the RbPb2Br5(001) surface and its high stability with respect to Ar+ bombardment, and properties which are extremely important for handling this material as an efficient laser source operating at ambient conditions. In the present work, we use the ab initio band-structure augmented plane wave +local orbitals (APW+lo) method as implemented in the WIEN2k package [19] to calculate the peculiarities of the energy distribution of electronic states of different symmetries of atoms constituting the RbPb2Br5 compound. Based on these band-structure calculations, we also explore the optical properties of the RbPb2Br5 compound such as dispersion of the absorption coefficient, real and imaginary parts of dielectric function, electron energy-loss spectrum, refractive index, extinction coefficient and optical reflectivity. In order to verify data of the present theoretical band-structure calculations with respect to occupation of the Br 4p states in RbPb2Br5, we also use the X-ray emission spectroscopy (XES) method to record the XES Br K2 band which represents the energy distribution of the valence Br p states for the bromide under consideration. In the present work, we compare the above XES band on a common energy scale with the XPS valence-band spectrum reported for the RbPb2Br5 compound in Ref. [17].

2.

Method of calculations Calculations of the electronic structure of RbPb2Br5 are made in the present work employing density

functional theory (DFT) within the first-principles APW+lo method as implemented in the WIEN2k package [19]. The method has proven to be one of the most accurate methods for the computation of the electronic structure of solids [20-24]. In our calculations, we use the full potential depending on the orbital momentum inside and outside the atomic spheres. The unit cell parameters and positions of the constituent atoms of RbPb2Br5 (Table 1) are chosen as determined for this compound in Ref. [14]. The

MT Rmin k max parameter, where

MT denotes the smallest muffin-tin (MT) sphere radius and k max determines the value of the largest k vector Rmin

in the plane wave expansion, is taken to be 7.0 (the charge density is Fourier expanded up to the value Gmax = 12 (a.u.)-1). The valence wavefunctions inside the MT spheres in the potential decomposition are expanded up to

lmax = 10, while outside the MT spheres up to lmax = 4. The MT sphere radii of atoms in our calculations are assumed to be 2.5 a.u. for Rb, Pb, and Br atoms (1 a.u. = 0.529177 Å). The basis function consists of the atomic orbitals of Rb, Pb, and Br as listed in Table 2. In the present DFT band-structure calculations of RbPb2Br5, total number of semi-core and valence electrons (in addition to core electrons) per unit cell is equal to 576. For calculations of the exchange-correlation potential, generalized gradient approximation (GGA) proposed by Perdew, Burke and Ernzerhof (PBE) [25] and modified Becke-Johnson (MBJ) potential [26] are used. Additionally, the calculations are also made using the PBE+U and MBJ+U models [27,28]. The tetrahedron method [29] is used for integration through the Brillouin zone (BZ). In the present work, the BZ sampling is made by using 1000 k-points within the irreducible wedge of the zone. The iteration process has been verified taking into account changes in the integral charge difference q

   n   n1 dr , where  n1 (r ) and  n (r )

are input and output charge density, respectively. The calculations have been interrupted in the case of

q  0.0001 . It is worth indicating that complex dielectric function the electron energy band structure of solids. Dielectric function

    1    i 2     

is directly related to

is the most important characteristic when

calculating the optical response of materials with respect to electromagnetic interference. It is known that dielectric function should include inter-band and intra-band transitions. Nevertheless, intra-band transitions are important only for metals [30]. Inter-band transitions can be divided into direct and indirect band transitions. The phonon contribution included in the indirect inter-band transitions is ignored in the present calculations, and the direct transition zone between the occupied and unoccupied states is taken into account. In order to calculate frequency-dependent dielectric function

   , we need to know the exact energy eigenvalues and electronic

wave functions [31]. The crystal structure of the compound under study allows only two main diagonal non-zero components of dielectric tensor of the second rank: components of dielectric tensor

 2  

 xx  

and

 zz  

along the

a

and

c

axes. The above

are necessary for complete description of the linear optical

susceptibility of a uniaxial crystal and they can be derived using the expression [32]:

 2ij   

4 2e2    kn pi kn  kn p j kn  Vm2 2 nn '



 f kn 1  f kn   Ekn  Ekn   where



(1)

m and e stand for mass and charge of electron, respectively,  is the angular frequency of

electromagnetic radiation, V is the unit cell volume, p in the bracket-notation corresponds to the momentum

kn is the wave function of the crystal with the crystal momentum (wave vector) k , and  is spin

operator,

corresponding to energy eigenvalue,

Ekn . Fermi distribution function, f kn , makes a certain count of transitions

from the occupied to unoccupied state. The term



 Ekn  Ekn  

 indicates a condition for conservation

of total energy, resulting in the summation of the combined density of states. Spectral peaks in the absorbing part of dielectric function determine the allowed electric-dipole transitions between the valence and conduction bands. To identify the fine-structure peculiarities, we compare the optical matrix element values. Observed fine structures correspond to the transitions possessing big values of optical dipole matrix elements of the transitions. Real part of dielectric function 1   is extracted from imaginary part of dielectric function

 2  

taking into account Kramers-Kronig’s relation [33]:

1    1 

2



  2    d  2 2     0



P

(2)

where P is the principal value of the integral. The optical properties such as the absorption coefficient coefficient

   , refractive

index n   , extinction

k   , optical reflectivity coefficient R   and electron energy-loss spectrum L   are derived

from 1   and

 2  

using the following equations [30,34,35]:

2 k ij   ,     c ij

nij   

12 1  ij 2 2  , ij ij               1 2 1  2 

(4)

k ij   

12 1  ij 2 2  , ij ij               1 2 1  2 

(5)

(nij  1)2  k ij 2 Rij    ij  (n  1)2  k ij 2

 

L     Im  ij

3.

Experimental

(3)

1

ij



1ij  iij2  1

2

1ij  iij2  1

 2ij   1ij     2ij   2

2

,

(6)

,

(7)

Information regarding the energy distribution of the Br 4p states in RbPb2Br5 can be obtained from measurements of the X-ray emission Br K2 (K  MII,III transition) band. In the present work, the mentioned band has been recorded using the high-quality RbPb2Br5(001) surface of the single crystal synthesized in Ref. [17]. The technique used to measure the XES Br K2 band of RbPb2Br5 was similar to that described in detail in Ref. [36]. Briefly, we have used a Johann-type DRS-2M spectrograph equipped with an X-ray BHV-7 tube (gold anode). The above band has been recorded in the second order of reflection (a quartz crystal with the (0001) reflecting plane is used as a dispersion element). The spectrograph energy resolution is estimated to be about 0.3 eV in the energy region corresponding to the position of the measuring XES Br K2 band. Operation conditions of the X-ray BHV-7 tube have been chosen as following: accelerating voltage, Ua = 45.0 kV; anode current, Ia = 72.5 mA.

4.

Results and discussion The results of the APW+lo band-structure calculations of the RbPb2Br5 total DOS using the PBE,

PBE+U, and MBJ+U approximations are plotted in Fig. 2. The XPS valence-band spectrum of this compound, as measured at room temperature in Ref. [17], is also presented in Fig. 2 for comparison. It should be mentioned that the curve of total DOS of RbPb2Br5 calculated using PBE approximation [25] reveals significant underestimation of the energy position of the partial Pb d and Rb p densities of states, which are found to be shifted by about 2.0 eV towards the Fermi energy in comparison with the energy positions of the features G and D, respectively, of the XPS valence-band spectrum of the compound under consideration (see Fig. 2). The main reason of this discrepancy is the absence of consideration of strongly correlated electrons in PBE approximation [25]. The PBE+U model [27,28] overcomes this problem. In the PBE+U model [27,28], the correction parameter U is added only for strongly correlated electrons and the U value is often considered as an adjustable parameter to match the experimental data. In the present APW+lo calculations, the value U = 0.43 Ry was used for Pb d and Rb p electrons (this value is a fitting parameter to experimental data as suggested for ternary halides [37,38]). The curves shown in Fig. 2 reveal that the use of PBE+U approximation in our calculations causes the partial Pb d and Rb p densities of states to shift away from the Fermi energy, resulting in better agreement of the theoretical results with the experimental data. However, the bandgap values, Eg, calculated employing PBE approximation [25] are known to be underestimated in semiconductors and insulators [26,39,40]. As a result, the present APW+lo band-structure calculations of RbPb2Br5 performed within PBE approximation [25] give Eg = 2.920 eV, the value which is somewhat underestimated in comparison with the bandgap data measured experimentally for this compound at ambient conditions in Ref. [17]. The use of PBE+U approximation [27,28]

in our APW+lo calculations increases slightly bandgap value of RbPb2Br5 up to 2.937 eV. Nevertheless, when the MBJ+U potential [26] is used in the calculations, we have obtained Eg = 3.415 eV, and the value almost coincides with that measured experimentally for the RbPb2Br5 compound in Ref. [17]. Further, due to the fact that Pb is considered to be a heavy element [41], in our APW+lo band-structure calculations with MBJ+U potential [26] spin-orbit coupling (SOC) [42-44] has been taken also into account (we shall refer these calculations to MBJ+U+SO). SOC application in the first-principles electronic structure calculations for the compounds based on heavy elements (e.g., U, Np, Pu, Am, Th, etc.) have revealed changes in many parameters such as elastic modulus, chemisorption energy of light atoms on surfaces of heavy atoms, magnetic moments, degree of localization of 5f states, etc. [45-47]. In our MBJ+U+SO calculations of the RbPb2Br5 compound, SOC has been also used for Rb 4p electrons. From Fig. 2, it is apparent that energy positions of the main features of the curve of total DOS of RbPb2Br5 calculated within MBJ+U+SO resemble those derived for this compound within MBJ+U potential [26] and PBE+U approximation [27,28]. Nevertheless, the MBJ+U+SO calculations give the best correspondence of the theoretical total DOS curve of RbPb2Br5 to the experimental XPS valenceband spectrum of the compound. In the present MBJ+U+SO calculations, the value of spin-orbital splitting for Pb 5d5/2,3/2 electrons is determined to be 2.5 eV that correlates well with the experimental data for this splitting [17]. The results of the APW+lo calculations (adopting MBJ+U+SO approximation) of total and main partial densities of states of RbPb2Br5 are plotted in Fig. 3 together with the XPS valence-band spectrum. While detailed total and partial densities of states associated with Rb, Pb and Br atoms in the bromide are presented in Fig. 4. It is obvious that the main part of the valence band of RbPb 2Br5 consists of two rather broad non-separating subbands marked as A and B in Fig. 4 and a somewhat narrow sub-band C. The bottom of the sub-band B is separated from the top of the sub-band C by a gap of about 2.8 eV. The curves of partial densities of states of atoms constituting RbPb2Br5 reveal that the Br 4p and Pb 6s states are principal contributors to the valence band and they contribute predominantly at its top (sub-bands A and B) and its bottom (sub-band C), respectively (cf. Figs. 3 and 4). The Pb 6s and Pb 6p states are among other significant contributors to the sub-bands A and B, respectively, while the sub-band C of the valence band of RbPb2Br5 is formed also by smaller Br 4p states contribution. In addition, the present APW+lo calculations indicate that below the bottom of the valence band (sub-band C, which is dominated by contributions of the Pb 6s states as mentioned above) the Rb 4p states form two narrow sub-bands (marked as D and E in Fig. 3), while the Br 4s states form the sub-band F positioned just below the sub-band E. Finally, the present APW+lo calculations reveal that the fine-structure features G and H of the XPS valence-band spectrum of RbPb2Br5 are formed due to contributions of the Pb 5d 5/2 and Pb 5d3/2 electrons, respectively. It should be mentioned that the Br 4p states are hybridized in comparatively high degree

with the Pb 6s and Pb 6p states over the energy regions corresponding to the sub-bands A and B of the valence band of RbPb2Br5, respectively. As a result of such hybridization of the above-mentioned electronic states, there exists a significant contribution of the covalent component to the chemical bonding of the RbPb2Br5 compound in addition to the ionic component. With respect to the occupation of the conduction band of RbPb2Br5, its bottom is dominated by contributions of the unoccupied Pb 6s states (cf. Figs. 3 and 4). Somewhat smaller contributions of the unoccupied Br 4p states at the bottom of the conduction band are also characteristic of the electronic structure of RbPb2Br5. It is worth mentioning that contributions of the electronic states associated with Rb atoms are rather minor within the valence band and conduction band regions of the RbPb2Br5 compound, as the present first-principles calculations reveal (see Figs. 3 and 4). It should be mentioned that in a series of complex multicomponent Rb-bearing oxides the contributions of the electronic states of Rb in the valence band region are also expected to be very small [48-54]. Regarding the RbPb2Br5 valence band occupation, data of the APW+lo band-structure calculations are confirmed by comparison on a common energy scale of the X-ray emission Br K2 band and the XPS valenceband spectrum of the bromide, as shown in Fig. 5. The technique of matching the above X-ray photoelectron and emission spectra of the RbPb2Br5 compound on a common energy scale is similar to that described in Ref. [55] and it is generally applied in experimental studies of solids adopting XPS and XES methods [56,57]. It is worth mentioning that zeros of energy of the XES Br K2 band and the XPS valence-band spectrum of the RbPb2Br5 compound presented in Fig. 5 correspond to the position of the Fermi level of the PHOIBOS 150 hemispherical energy analyzer of the UHV-Analysis-System. The experimental results plotted in Fig. 5 reveal that the main contributions of the Br 4p states occur in the upper portion of the valence band of RbPb2Br5 (fine-structure peculiarities A and B of the XPS valence-band spectrum), being in agreement with the results of the APW+lo calculations. Regrettably, available facilities do not allow investigating experimentally peculiarities of the energy distribution of the Pb 6s and Pb 6p states, which are other significant contributors to the valence-band region of the RbPb2Br5 compound, as revealed by the present APW+lo band-structure calculations. However, taking into account the theoretical data presented in Figs. 2–4, one can assume that the peculiarity C of the XPS valenceband spectrum of RbPb2Br5 (Fig. 5) is formed mainly due to contributions of the Pb 6s states. It is worth mentioning that divalent lead ion, Pb(II), has long been associated with a chemically inert 6s 2 lone pair filling an orbital created due to hybridization of the 6s and 6p orbitals in solid state materials [58-61]. Furthermore, the chemically inert Pb(II) 6s2 pair of electrons are considered to be stereochemically active, leading to formation of distorted crystal structures [59]. The DFT calculations of the PbO and PbS compounds in both the rocksalt and litharge structures have demonstrated [59] that the asymmetric electron density formed by Pb(II) ions is due to the interaction of the antibonding combination of Pb 6s and O(S) p states with unfilled Pb

6p states. The results by Walsh and Watson [59] are found to be in contrast to the traditional lone pair theory. In the case of RbPb2Br5, as the present DFT calculations reveal, the basic Pb polyhedral are unaffected by the above mentioned potential effect. From the DFT results plotted in Fig. 4, it is apparent that Pb atoms in the RbPb2Br5 structure do not undergo sp-like hybridization that could lead to some dielectric dipole arising from a 6s2 lone electron pair that would be oriented in some direction caused by this kind of hybridization. The results of the MBJ+U+SO calculations of the main optical parameters, such as the absorption coefficient

   ,

dielectric functions

1  

and

 2   ,

refractive index

n   , extinction coefficient

k   , optical reflectivity coefficient R   and electron energy-loss spectrum L   of RbPb2Br5, are depicted in Figs. 6-11. It should be indicated that main contributions to the optical spectra arise due to transitions from the top of the valence band to the bottom of the conduction band. From Fig. 6, one can see that the optical absorption edge, i.e. the first critical point, appears in the RbPb2Br5 compound at about 3.0 eV due to transition from the occupied valence Br p, Pb s and Pb p states to the unoccupied Pb p and Br p states. It is worth mentioning that the band gap value derived in our APW+lo calculations employing MBJ+U+SO potential equals 3.124 eV and is in excellent agreement with the experimental E g value of RbPb2Br5 measured for this compound at 300 K, namely Eg = 3.470.1 eV for E || c polarization and Eg = 3.420.1 eV for of E || a and E || b polarizations [17]. DFT band-structure calculations are known to underestimate energy gaps in semiconductors and insulators as it has been already mentioned above. Accordingly, due to the fact that the calculated optical properties are known to be very sensitive to the inter-band energy distances, in calculations of the optical parameters a scissors corrected value of E g is usually used. In the present work, we have made calculations of the optical properties of the RbPb2Br5 compound adopting the theoretically derived E g value (3.124 eV) and scissors correction of 0.35 eV using the technique reported in detail elsewhere [62]; the mentioned scissors value is derived as a difference between the calculated and experimentally measured energy gaps of the bromide crystal. In the both sets of calculations we have obtained almost identical results. Therefore, in the present work we report results of calculations of the optical properties that were derived adopting the theoretically obtained Eg value for RbPb2Br5. The calculation results plotted in Fig. 6 indicate that the absorption coefficient increases rapidly for photon energy higher than 3 eV. From this figure, it is obvious that the region of strong absorption extending from 3 eV to about 27 eV is characteristic of the RbPb2Br5 compound. The mentioned energy region consists of spectral peaks arising due to electronic transitions. Changes in the peak intensities vs. energy within the absorption region indicate that the RbPb2Br5 compound is a promising material for its application in optoelectronic devices. Fig. 7a presents results of calculations of real part of complex dielectric function 1  

of RbPb2Br5. From the figure, one can see that values of statistical dielectric constants at zero frequency are following: 1

xx

 0  = 8.032 and 1zz  0  = 7.442. As can be seen from Fig. 7a, calculated real part of dielectric

function 1   of RbPb2Br5 reveals four well resolved peaks, namely A(~4.5 eV), B(~5.5 eV), C(~9.5 eV) and D(~11 eV). Energy positions of the mentioned peaks, as comparison of Figs. 7a and 7b reveals, correspond well to those of the similar peaks on imaginary part of dielectric function

 2   of the RbPb2Br5 compound that was

calculated for photon energies ranging from 0 to 27 eV. Taking into account the data of calculations of total and partial densities of states plotted in Figs. 3 and 4, one can state that the peaks A at ~ 4.5 eV and B at ~ 5.5 eV on the

 2   curve

originate due to electronic transitions from the valence Br p states to the unoccupied Br s

states in the conduction band, while the peak C at ~ 9.5 eV on the

 2   curve is due to transitions from the

valence Pb s states to the unoccupied Pb p states, which are positioned at the bottom of the conduction band the RbPb2Br5 compound. Further, the peak D at ~ 11 eV on the

 2   curve can be attributed to transitions from

the valence Pb s states to the unoccupied Br p states. As can be seen from Fig. 7a, the calculated real part of dielectric function

1  

decreases starting from about 9 eV to about 12–13 eV, and, then, it increases with

increasing photon energy up to about 27 eV. In contrast, the calculated imaginary part of dielectric function

 2  

decreases almost monotonously starting from about 10.5–12 eV and goes to about zero in the above

mentioned energy region. The L   function of RbPb2Br5 presented in Fig. 8 increases monotonously starting from about 3 eV and reveals a sharp maximum at ~7.5 eV following by further monotonous increasing up to about 19 eV, resulting in appearance of three oscillation peaks at ~19, 21.5 and 23 eV and, then, the function again increases up to its maximum at about 26.5 eV. One can assume that the maxima positioned at about 19, 21.5 and 23 eV on the curve of electron energy-loss spectrum

L  

of fast-moving electrons correspond to plasma frequencies

of the RbPb2Br5 compound. As can be seen from Fig. 8, anisotropy of the L   function for the different components of the tensor (xx, zz) is quite minor at energies ranging from about 3 eV to about 27 eV. Fig. 9 presents the calculated curve of refractive index

n   of the RbPb2Br5 compound. It is obvious

that that refractive index of the RbPb2Br5 compound at low energies is inversely proportional to the width of the band gap. Calculated refractive indices at zero frequency are close to

n xx  0  =2.834 and n zz  0  =2.728. As

Fig. 9 displays, maximum values of refractive index

n   of RbPb2Br5 are positioned in the energy range of

3–7 eV with several small peaks appearing at some specific energy, and, then, the

n   curve goes to zero at

high energies. Energy positions of the maxima on the n   curve are found to be at about 4.5, 5.5, 9.5 and 10– 11 eV that correspond well to energy positions of the maxima of real and imaginary parts of dielectric function,

1  

and  2   , respectively, of the RbPb2Br5 compound (Figs. 7a and 7b). The origin of the peaks

detected in our calculations of refractive index n   of the RbPb2Br5 compound (Fig. 9) is due to the interband electronic transitions mentioned above. The

n   curve tends to zero at energies ranging from about 13

eV to about 27 eV. Fig. 10 shows the relationship between the calculated extinction coefficient k   of the RbPb2Br5 compound and photon energy. The

k   spectrum follows closely to the  2   spectrum, as comparison of

Figs. 7b and 10 reveals. The small deviation of the

k   and  2   curves from each other can be explained

by the fact that the mBJ+U+SO generalization is not justified for mediums possessing some absorption coefficient. Maximum values of the

k   curve are positioned within energy regions 4–7 and 10–14 eV, with

several fine-structure peculiarities in each case. Two nonzero components of the optical reflectivity coefficient R   of the RbPb2Br5 compound reveal 22.88% and 21.49% which correspond to reflections at 0 eV (Fig. 11). Energy positions of the maxima presented on the

R   curve, namely ~4.5 and ~ 5.5–6.0 eV, coincide with those of the maxima A and B

observed on the curve of imaginary part of dielectric function Further, optical reflectivity coefficient

 2   of

the RbPb2Br5 compound (Fig. 7b).

R   of the RbPb2Br5 compound reveals a sharp minimum at energies

of about 8 eV. Its energy position corresponds well to that of the minimum observed on the curve of imaginary part of dielectric function

 2   (Fig. 7b). As can be seen from Fig. 11, for energies ranging from about 9 eV

to about 18 eV small peaks in the form of humps are evident on the 23 eV sharp minima are observed on the maxima of electron energy-loss spectrum plasma frequencies.

R   curve. At energies of ~19, 21.5 and

R   curve. Their energy positions correspond to those of the

L  

of fast-moving electrons (Fig. 8) that can be attributed to

5.

Conclusions Electronic structure of rubidium dilead pentabromide, RbPb2Br5, has been studied in the present work

from both experimental and theoretical viewpoints. Based on density functional theory, ab initio band-structure calculations have been performed using the APW+lo method, as incorporated in the WIEN2k package, in order to elucidate total and partial densities of states of atoms constituting the RbPb2Br5 compound. The present calculations reveal that the principal contributors to the valence band of the RbPb2Br5 compound are the Pb 6s and Br 4p states contributing mainly at the bottom and at the top of the band, respectively. With respect to the occupation of the conduction band, our band-structure calculations indicate that its bottom is formed predominantly from the unoccupied Pb 6p states. Regarding the peculiarities of the occupation of the valence band of RbPb2Br5 by the Br 4p states, results of the present APW+lo band structure calculations are confirmed experimentally by comparison of the X-ray emission Br K2 band and the XPS valence-band spectrum of the studied compound provided that a common energy scale is used. The present calculations indicate that the absorption coefficient

  

of RbPb2Br5 increases rapidly for photon energy above 3 eV, and the region of

strong absorption extends from 3 eV to about 27 eV. The peak intensity changes vs. energy within the absorption region allow the conclusion that RbPb2Br5 is a promising material for its application in optoelectronic devices. The calculated real part of dielectric function 1   of the RbPb2Br5 compound decreases starting from about 9 eV to about 12–13 eV, and it increases at higher photon energy up to about 27 eV. In contrast, in the above mentioned energy region, the calculated imaginary part of dielectric function

 2  

of RbPb2Br5 decreases

almost monotonously starting from about 10.5–12 eV and goes to about zero at higher energies. The calculations indicate that the maxima positioned at about 19, 21.5 and 23 eV on the curve of electron energy-loss spectrum

L  

of fast-moving electrons correspond to plasma frequencies of the RbPb2Br5 compound. Further,

anisotropy of the L   function for the different components of the tensor (xx, zz) of RbPb2Br5 is quite minor at energies 3–27 eV. Two nonzero components of the optical reflectivity coefficient

R   of RbPb2Br5 reveal

values of 22.88% and 21.49%. At energies of ~19, 21.5 and 23 eV the sharp minima on the

R   curve the

RbPb2Br5 compound are observed. Their energy positions correspond to those of the maxima on the spectrum of fast-moving electrons that can be attributed to plasma frequencies.

L  

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Table 1. Atomic parameters for RbPb2Br5 used in the present APW+lo calculations (space group I4/mcm, a=8.4455 Å, c=14.5916 Å [14]). Wyckoff Atom

x

y

z

position Rb

4a

0

0

0.250

Pb

8h

0.158

0.658

0

Br1

4b

0

0

0

Br2

16l

0.163

0.663

0.365

Table 2. Atomic orbitals used in the present APW+lo calculations of the electronic structure of RbPb2Br5. Atom

Core electrons

Semi-core

Valence

Number of electrons

electrons

electrons

involved

in

the

APW+lo calculations Rb

1s22s22p63s23p6

3d104s24p6

5s1

19

Pb

1s22s22p63s23p63d104s24p64d104f145s2

5p65d10

6s26p2

20

Br

1s22s22p63s23p6

3d10

4s24p5

17

Figure captions Figure 1. Crystal structure of RbPb2Br5: Rb – purple circles, Pb – gray circles, Br – brown circles. Figure 2. Comparison on a common energy scale of curves of total DOS calculated for RbPb2Br5 with PBE, PBE+U, MBJ+U and MBJ+U+SO approximations and the XPS valence-band spectrum of this compound measured in Ref. [17]. Figure 3. Total DOS and main partial densities of RbPb2Br5 (calculated with MBJ+U+SO) matched on a common energy scale with the XPS valence-band spectrum measured for this compound in Ref. [17]. Figure 4. Partial densities of states of (a) Rb, (b) Pb and (c) Br atoms calculated for the RbPb2Br5 compound. Figure 5. Comparison on a common energy scale of (1) the X-ray emission Br K2 band and (2) the XPS valence-band spectrum [17] of the RbPb2Br5 compound.

Figure 6. Absorption coefficient

  

of RbPb2Br5 (calculated with MBJ+U+SO).

Figure 7. (a) Real part of dielectric function

1  

and (b) imaginary part of dielectric function

RbPb2Br5 (calculated with MBJ+U+SO). Figure 8. Electron energy-loss spectrum Figure 9. Refractive index

n  

Figure 10. Extinction coefficient Figure 11. Optical reflectivity

L  

of RbPb2Br5 (calculated with MBJ+U+SO).

of RbPb2Br5 (calculated with MBJ+U+SO).

k  

R  

of RbPb2Br5 (calculated with MBJ+U+SO).

of RbPb2Br5 (calculated with MBJ+U+SO).

 2  

of

Figure 1

Figure 2

Figure 3

Figure 4a

Figure 4b

Figure 4c

Figure 5

Figure 6

Figure 7a

Figure 7b

Figure 8

Figure 9

Figure 10

Figure 11

Highlights ► DFT calculations of total and partial densities of states of RbPb 2Br5 are reported ► Pb 6s and Br 4p states are the dominant contributors to the valence band ► The conduction band is formed mainly from contributions of unoccupied Pb 6p states ► Electronic structure of RbPb2Br5 is studied by XPS and XES methods► Main optical characteristics of RbPb2Br5 are calculated Graphical Abstract