electronic structure of antimony selenide (sb2se3) from gw calculations

Phys. Status Solidi B 248, No. 3, 700–705 (2011) / DOI 10.1002/pssb.201046225 p s sb

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basic solid state physics

Electronic structure of antimony
selenide (Sb2Se3) from GW calculations
Rajasekarakumar Vadapoo1,2, Sridevi Krishnan1,2, Hulusi Yilmaz1,2, and Carlos Marin*,1,2,3

1Department of Physics, University of Puerto Rico, San Juan, Puerto Rico 00931, USA2Institute for Functional Nanomaterials, University of Puerto Rico, San Juan, Puerto Rico 00931, USA3Department of General Engineering, University of Puerto Rico, Mayaguez, Puerto Rico 00681, USA

Received 4 May 2010, accepted 1 September 2010

Published online 5 October 2010

Keywords antimony selenide, density functional theory, density of states, Sb2Se3

*Corresponding author: e-mail [email protected], Phone: 1-787-764-0000 x 5846, Fax: 1-787-764-4063

Antimony selenide (Sb2Se3) has been proposed as an alternative

material for a wide range of applications; however, the

electronic structure of the Sb2Se3 lattice is not clearly known

yet. As a consequence, there are abundant contradictory

interpretations of experimental results leading to incoherent

determinations of its energy band gap and the type of optical

transitions. Moreover, Sb2Se3 is recently being synthesized in

different types of nanostructures; therefore, detailed knowledge

of the bulk electronic structure is necessary to evaluate

deviations due to confinement or surface effects. In this paper,

we study the electronic band structure of antimony selenide

using density functional theory (DFT) within the generalized

gradient approximation (GGA) with GW corrections. Our

calculations show that Sb2Se3 has an indirect energy band gap

of 1.21 eV; however, a direct transition only 0.01 eVhigher than

the band gap (1.22 eV) is also possible. The calculated density

of states agrees well with the experiments reporting photo-

emission spectra.

� 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Antimony selenide (Sb2Se3) has beeninvestigated for its optical and transport properties due to itshigh reflectance and anisotropic nature [1, 2]. It findsapplications as a thermoelectric, mostly alloyed with otherselenides and tellurides [3–5], and as pristine material formemory switching [6]. Currently, it is used for opticalcoatings in thermophotovoltaic [7] applications due to itshigh refractive index. It has also been proposed as a superiormedium for optical storage because amorphous Sb2Se3readily crystallizes with a slight increase in temperature [8].Very recently, it has been proposed as an alternative materialfor photovoltaic conversion [9]. In spite of the variousapplications proposed for Sb2Se3, very little is known of itselectronic structure; therefore, diverse and sometimescontradictory interpretations of experimental data arecommonly found in the literature. Sb2Se3 crystallizes in anorthorhombic structure and belongs to the space group Pbnm[10]. It has an anisotropic structure and also exhibitsanisotropic optical and electronic properties depending onthe crystalline direction when synthesized in bulk as well asin nanostructures.

The existing literature regarding the band gap of Sb2Se3includes experimental determinations from bulk single

crystals, crystalline thin films and nanostructures and sometheoretical derivations (see Table 1). There are contradictoryreports regarding the nature of the band gap (direct/indirect),as well as a significant range of values for its energy. Bandgaps from �1 to 1.82 eV for single crystals [11–15] havebeen reported. In the case of thin films, most of theexperimental band gap values have been obtained by Taucplot fitting of absorption measurements; the lowest energiesare found when the absorption fits better with indirecttransitions (1–1.2 eV) [16–19]. For experiments where thefitting is found better with direct transitions, the band-gapvalues reported are substantially larger (1.88–2.14 eV) [20,21]. Antimony selenide has recently been easily synthesizedin various types of nanostructures mostly by chemicalmethods. Recently, our group synthesized these nanostruc-tures by a physical vapour–liquid–solid (VLS) process [22]for the first time. Most of the reported energy band gaps ofthese nanostructures have also been calculated from Taucplot fitting of absorption measurements. However, for mostof these nanostructures the best fits are found for directtransitions, unlike the case of thin films (see Table 1). Also, averywide range of band gaps from1.13 to 1.49 eV [9, 23–29]has been determined. It should be noted that the effect due to


Phys. Status Solidi B 248, No. 3 (2011) 701

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Table 1 Controversial reports of experimental and theoretical band gaps and nature of transitions of Sb2Se3.

direct/indirect/undetermined

bandgap (eV)

method comments

Bulk

direct [11] �1 from reflectivity minimum and the point ofmaximum slope of the absorption edge

single crystal

forbidden indirect [12] 1.11 from forbidden indirect Tauc plot fitting ofabsorption spectrum

single crystal

allowed indirect [13] 1.2 from allowed indirect Tauc plot fitting ofabsorption spectrum

single crystal

undetermined [14] 1.219 from microhardness measurement single crystalundetermined [15] 1.82 intersection point of the tangent of the

absorption edge with extended line of thediffuse reflectance at lower wavelength

single-crystalline tetragonal tubularstructure with width of 10–20mm,thickness of 5–10mm and length of5–10 mm

Crystalline thin films

allowed indirect [16] 1–1.2 from allowed indirect Tauc plot fitting ofabsorption spectrum

films deposited from differentchemical baths

allowed indirect [17] 1.1 by comparing allowed indirect and directTauc plots fittings of absorption spectrum

allowed indirect [18] 1.124–1.152 by comparing allowed indirect and directTauc plots fittings of absorption spectrum

depending on annealing temperature

allowed indirect [19] 1.13 from allowed indirect Tauc plot fitting ofabsorption spectrum

allowed direct [20] 1.88 from allowed direct Tauc plot fitting ofabsorption spectrum


Nanostructures


complex nanostructures


nanoribbons of thickness 20–60 nmand width 100–300 nm grown along[1–12]


nanorods of 100–200 nm diametergrown along [001]


tubes with diameter of 0.5–1mm andwall thickness of 100–200 nm grownalong [001]


spheres with diameter of 2–4 mm

allowed direct [26] 1.25, 1.33and 1.46

from allowed direct Tauc plot fitting ofabsorption spectrum

hollow nanospheres with wall thicknessin the range of 10–20 nm and the outerdiameter of 100–200 nm, 50–100 nmand 20–40 nm, respectively

undetermined [27] 1.29 reflectance–absorption edge nanowires of diameter �100 nmgrown along [001] in polyol method


nanowires of width 40–80 nmgrown along [001]

direct [29] 1.49 extrapolation of absorption edge. nanowires of diameter 30–80 nmgrown along [001] by solvo-thermalmethod

Calculations

indirect [30] 0.88 empirical LCAOundetermined [31] 1.14 DFT–LDA

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Figure 2 GGA calculated band structure and DOS of Sb2Se3.

quantum confinement is negligible, considering the sizes ofthese nanostructures. Nor the surface effects likely to beaffecting the band gap because the ratio of the atoms in thesurface to volume (completely coordinated) is clearlynegligible. Theoretical studies of the energy band gap forbulk Sb2Se3 have been conducted using the linear combi-nation of atomic orbital (LCAO) method and the localdensity approximation (LDA). The LCAO study reports anindirect band gap of 0.88 eV [30], whereas the LDA studyreports 1.14 eV of undetermined nature [31]. However, todate, the band structure of the Sb2Se3 lattice is not knownclearly, which might be part of the reason for the disparity inthe results reported so far and its interpretations. Here, wepresent density functional theory (DFT) calculations of thislattice using the generalized gradient approximation (GGA).Since it is well known that DFT calculations underestimatethe band gap for semiconductors and insulators, we haveused GW corrections for accurate results and take a closerlook at the possible transitions.

2 Structure Sb2Se3 has an orthorhombic crystalstructure with lattice parameters a¼ 11.62 A, b¼ 11.77 A,c¼ 3.962 A and belongs to the space group Pbnm [10]. Thecrystal structure (Fig. 1a) is anisotropic and consists of fourmolecular subunits of Sb2Se3 per unit cell and they exhibit avery clean cleavage plane along the a–c plane. A close lookat the pattern perpendicular to the b direction (Fig. 1b) willreveal the cleavage plane clearly. It can be seen that thestructure consists of strongly bound and infinitely long, one-dimensional (1D) ribbons of [A4B6]n units. These 1D ribbonscoordinate weakly between them, creating distinct layersalong the a direction. Figure 1c shows the first Brillouin zoneof Sb2Se3 with high-symmetry lines.

3 Methods First-principles calculations based onDFT within the GGA [32] and the LDA as implemented inthe Vienna ab initio simulation package (VASP) wereemployed. The wavefunctions were expanded using a planewave basis set up to a kinetic energy cut-off of 300 eV. The

Figure 1 (online colour at: www.pss-b.com) (a) Orthorhombic unitrepresent Se atoms). (b) [001] directional view of the crystal struct(c) Brillouin zone of Sb2Se3 with the high-symmetry lines.


projector augmented wave (PAW) [33, 34] method wasemployed in the calculations. For the Brillouin zoneintegration, Monkhorst–Pack grids of 6� 6� 18 were used.The total energy converged within 0.1meV. A fine grid of20 k-points was used for band-structure calculations alongthe high-symmetry lines (Fig. 1c). The quasiparticle GWcalculations were carried out by performing a single-shotG0W0 calculation as implemented in VASP [35–38]. GWcalculations were performed on top of the PBE ground state.TheGWcalculationswere carried out using a total number of150 bands. The Monkhorst–Pack grids of 3� 3� 9 wereused.

4 Results and discussion4.1 Band structure The band gap and nature of

transport are related to the energy and position ink-space of the valence-band maximum (VBM) and conduc-tion band-minimum (CBM). So, it is of interest to analyse theelectronic structure in detail. Figure 2 shows the bandstructure and corresponding density of states (DOS) ofantimony selenide (Sb2Se3) calculated by the GGA. A closer

cell of Sb2Se3 (pink spheres represent Sb atoms and cyan spheresure showing the cleavage plane perpendicular to the b direction.

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Table 2 Possible transitions from the VBM to the CBM in different regions by LDA, GGA and GW.

band gap, Eg (eV) direct gap (eV) indirect gap (eV)

at G [G–X] [U–Y] [Y–S] [G–X] [U–S] [Y–S]

LDA 0.79 1.10 0.82 1.14 0.96 0.81 0.90 0.91GGA 0.88 1.15 0.91 1.22 1.04 0.90 0.98 0.99GW 1.21 1.35 1.22 1.54 1.42 1.21 1.37 1.38

look at the VBM and the CBM shows that Sb2Se3 is anindirect band gap material with the band gap of 0.88 eVwith the VBM in the region U–Y and the CBM in the regionG–X.

Direct gaps of 1.15 eV atG and 0.91, 1.22 and 1.04 eV arefound in the regions G–X, U–Y and Y–S, respectively. Also,indirect gaps of 0.90, 0.98 and 0.99 eV are found in theregions G–X, U–S and Y–S, respectively. It is important tonote that the energy difference between the absolute bandgap (Eg) and the indirect gap in the region G–X is only0.02 eV and also the difference between the energies of thedirect and indirect gaps in this region is only 0.01 eV. It isclear that the structure of the material leads to many possibletransitions due to the peculiar existence of many VBMswithin a very close energy range. The LDA band structurealso showed a similar behaviour and the band gap was foundto be 0.79 eV, which is much lower than the previouslyreported LDA band gap of 1.14 eV [31]. Probably, that couldbe the gap at the gamma point, which is comparable to ourvalue (see Table 2).

In order to achieve accurate energy band gap values ofSb2Se3, we have carried out the GW calculations. Figure 3shows the GW corrected band structure of Sb2Se3 with thecorresponding DOS. The results show that Sb2Se3 is indeedan indirect band gap semiconductor with energy band gap of1.21 eV.

Figure 4 takes a closer look comparing the GW bandstructure with that of GGA. GGA results show that the

Figure 3 GW calculated band structure and DOS of Sb2Se3.

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indirect transition of lowest energy takes place from theVBM inU–Y to theCBM inG–X, whereas theGWlocates theindirect transition of lowest energy from the VBM to theCBM, both in G–X, which requires a small momentumexchange compared to GGA.

Figure 5 depicts the details of the GW calculatedelectronic structure of Sb2Se3 to display the transitionsbetween VBMs and CBMs. It shows possible directtransitions with gaps of 1.35 eV at G, 1.22, 1.54 and1.42 eV at the regions G–X, U–Y and Y–S, respectively.The indirect transition of lowest energy is in the G–X regionwith a value of 1.21 eV and a moderate requirement ofmomentum exchange. Also, with a requirement of only anextra energy of 0.01 eV, there is a possibility of a directtransition. Indirect transitions with larger momentumexchange could occur with energy of 1.22 eV from theVBM inU–Y to the CBM in G–X and with energy of 1.23 eVfrom theVBM inY–S to theCBM inG–X. Indirect transitionsrequiring higher energies of 1.37 and 1.38 eV as well aslarger momentum exchange are found in U–S and Y–S,respectively.

It is important to note that the VBMs inU–Y and Y–S areonly 0.01 and 0.02 eV lower than the VBM in G–X.Therefore, at room temperature (kBT¼ 0.025 eV) VBMs at

Figure 4 (online colour at: www.pss-b.com) Close-up view of theVBM and the CBM, showing the region of possible transitions andthebands involved, in theGGAandGWcalculations. Inset shows thecorresponding band structure for thewhole range of high-symmetrylines in the Brillouin zone.


704 R. Vadapoo et al.: Electronic structure of antimony selenide from GW calculationsp

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Figure 5 (online colour at: www.pss-b.com) Nature of possibleoptical transitions betweenVBMandCBMand the energy involved,fromGWband structure. The indirect transitions are noted as italicsin blue.

Figure 6 ComparisonofGWcalculatedDOSofSb2Se3 and exper-imentally reported photoemission peaks with error bars.

Table 3 Comparison of GW calculated DOS and DOS maximaderived from photoemission measurements with the accuracy of0.2 eV for bulk Sb2Se3 [2].

DOS maximafrom photoemissionmeasurements (eV)

major peaks ofcorrespondingGW DOS (eV)

valence band �3.3 �3.22�2.6 �2.50�1.6 �1.60�0.8 �0.63

conduction band 6.4 6.457.2 7.177.8 7.828.5 8.429.3 9.3

G–X, U–Y and Y–S all might be comparable sources ofcarriers. As mentioned earlier, the lowest direct (1.22 eV)and lowest indirect (1.21 eV) transitions differ only by0.01 eV. Moreover, indirect transitions involving a largemomentum exchange of 1.22 eV can also occur. This diverseand complex nature of the optical transitions of Sb2Se3 couldpossibly be the reason behind the wide variety of Taucfittings and the source of incoherency of reported energyband gaps. The GW corrected energy band gap is close toseveral of the experimentally reported values. The peculiarband structure might explain why similar values are found inexperiments where some better fit to direct transitions andsome to indirect ones.

4.2 Density of states Here, we correlate the GWcalculated DOS to the DOS maxima derived from photo-emission measurements reported for antimony selenide byHurych et al. [2] (Fig. 6). It is evident that it matches wellwith our GW DOS from Fig. 6 and Table 3. From thephotoemission measurements [2], they have proposed avalley at about 2 eV below the valence-band maxima. TheGW DOS also shows a valley (V1) at about 1.82 eV belowthe VBM, which agrees well with our results considering thefact that the accuracy of their results is 0.2 eV. They haveconcluded that the primary contribution to the upper part ofthe valence band separated by the valley V1 is from theselenium lone p-pair electrons. These are the electrons thatparticipate in the optical transitions of energy ranging fromthe band gap (hn¼ 1.21 eV) to�hn¼ 3 eV. Also, our resultsshow that the seleniump-states have a dominant contributionin that energy region. Also, they have suggested that thebonding states are at about 6 eV below the VBM; in our case,the GWDOS shows them at 6.56 eV below the VBM. To ourknowledge, there have not been any experimental reports forthe DOS maxima in the lower conduction region up to 6 eVfrom the VBM for crystalline Sb2Se3.


5 Conclusion We have calculated the band structureof Sb2Se3 with GGA and have applied accurate correctionsusing the GW approximation. GW calculations showed thatit is an indirect band gap semiconductor with an energy bandgap of 1.21 eV. However, a direct transition is possible at anenergy of 1.22 eV. The calculations reveal that Sb2Se3 haspeculiar and complex optical transitions due to the existenceofmultiple valence-bandmaxima at very close energies. Thecalculated DOS matches well with the experimentallyreported photoemission studies.

Acknowledgements Computations were performedutilizing the High Performance Computing facility (HPCf) at

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UPRandTeraGrid resources. This researchwas supported in part bythe National Science Foundation through TeraGrid resourcesprovided by the National Center for Supercomputing Applications(NCSA).

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electronic structure of antimony selenide (sb2se3) from gw calculations

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