Identification of 2H and 3R polytypes of MoS2 layered crystals using photoluminescence spectroscopy
S. Anghel, Yu. Chumakov, V. Kravtsov, A. Mitioglu, P.Plochocka, K. Sushkevich, G. Volodina, A. Colev, L. Kulyuk
FF I R S T D R A F T P L E A S E D O N O T D I S T R I B U T E Identification of 2H and 3R polytypes of MoS layered crystals usingphotoluminescence spectroscopy S. Anghel,
1, 2
Yu. Chumakov, V. Kravtsov, A. Mitioglu,
1, 3
P.Plochocka, K. Sushkevich, G. Volodina, A. Colev, and L. Kulyuk Institute of Applied Physics, Academiei Str. 5, Chisinau, MD-2028, Republic of Moldova Ruhr-Universitat Bochum, Anorganische Chemie III, D-44801 Bochum Germany ∗ LNCMI, CNRS-UJF-UPS-INSA, Grenoble and Toulouse, France State University of Moldova, Mateevici Str. 60, Chisinau, MD-2009, Republic of Moldova (Dated: November 17, 2014)The excitonic radiative recombination of intercalated Cl molecules for two different polytypes2H-MoS and 3R-MoS layered crystals are presented. The structure of the excitonic emission isunique and provides a robust experimental signature of crystal polytype investigated. This result isconfirmed by X-ray diffraction analysis and DFT electronic band structure calculations. Thus, thebound exciton emission provides a nondestructive fingerprint for the reliable identification of thepolytype of MoS layered crystals. I. INTRODUCTION
Transition metal dichalcogenides (TMDC) is an emerg-ing class of materials with an extremely wide spectrumof potential applications, ranging from optoelectronic de-vices, field effect transistors and solar cell convertors tomore mundane lubricants.
Single layers of TMDC werefirst obtained by mechanical exfoliation. Due to theirtruly 2D character single layer TMDC’s have attractedconsiderable attention as strong potential candidates forthe next generation of electronic devices. However, for fu-ture applications the quality of the atomically thin crys-tals is extremely important.In order to achieve the required high quality, the con-trol of the synthesis of single crystals is crucial. Amongthe different methods used to obtain single crystal, chem-ical vapor transport (CVT) method is widely used witha view to device fabrication. In this method, halogenmolecules are used as a transport agent.
When syn-thesizing MoS it is possible to obtain hexagonal (2H),as well as, rhombohedral (3R) polytype layered crys-tals which have quite different physical properties. Forexample, the 3R polytype of MoS , due to the non-centrosymmetric structure present in this form, exhibitsa valley polarization in photoluminescence emission evenfor a bulk crystal. To date the electronic properties of3R phase remain largely unexplored. Clearly, the de-velopment of an experimental probe to distinguish thepolytype “ in situ ” is essential, especially since traditionalRaman spectroscopy appears to be incapable of distin-guishing between the 3R or 2H crystal polytype.In this paper we show that the photoluminescencespectra of excitons bound to halogen molecules inthe van der Waals gap of the crystals provide a uniquefingerprint for the crystal polytype. X-ray analysis of thecrystal structure and density functional theory (DFT)calculations of electronic band structure of the layer typemodels of MoS have been performed to support our find-ings. II. SAMPLE CHARACTERIZATION
The synthetic 2H and 3R-MoS single crystals havebeen grown by the vapor transport method, using Mo andS as starting materials. The MoCl compound, which de-composes at high temperatures, was used as a source ofCl molecules for the CVT. The starting materials wereplaced in evacuated sealed quartz ampoules which wereslowly heated up to the synthesis temperature of 1150 ◦ Cfor two days and maintained under these conditions fortwo days more. Subsequently, the ampoules with thepolycrystalline material were placed in a two-zone tubefurnace. The temperature of the crystallization cham-ber was set at around 930 ◦ C in the region of the crystalsgrowth, according to references [13 and 14]. The twopolytypes were obtained by choosing a different temper-ature gradient and a different concentration of the trans-port agent, which seems to have an important influenceon the growth process. The ampoules were held insidethe furnaces for a period of up to 6 days, after which theywere slowly cooled to room temperature.The 2H- and 3R- polytypes were identified and struc-turally characterized by the single crystal X-ray method.The polymorphic purity of the as synthesized 2H- and3R-polytypes (bulk samples) was confirmed by com-paring the calculated and experimental X-ray powderdiffraction patterns. The X-ray diffraction data were ob-tained at room temperature using an
Xcalibur E diffrac-tometer. The data were collected and processed using theprogram CrysAlisPro and were corrected for the Lorentzand polarization effects and absorption . The structurewas refined by the full matrix least squares method on F with anisotropic displacement parameters using theprogram SHELXL. The unit cell parameters for 2H-MoS are a = b =3.1625(1)˚A, c =12.300(1)˚A and for 3R-MoS a = b =3.1607(7)˚A, c =18.344(9)˚A, and the corre-sponding atomic coordinates are listed in Table I. Theseparameters are in good agreement with those reportedin reference [17] which allows us to conclude that theintercalation with Cl molecules does not change the pa- a r X i v : . [ c ond - m a t . m t r l - s c i ] N ov X y Z U eq Mo 1/3 2/3 0.25 6(1)S 1/3 2/3 6228(1) 7(1)3R-MoS X y Z U eq Mo 0 0 0 12(1)S1 0 0 2490(3) 11(1)S2 0 0 4189(3) 9(1)TABLE I. Atomic coordinates 10 and equivalent isotropicdisplacement parameters (˚A × ). U eq is defined as onethird of the trace of the orthogonalized U ij tensor. rameters of the crystal structure. III. PHOTOLUMINESCENCEMEASUREMENTS
The PL spectra, recorded using a standard lock-intechnique, were excited by the second harmonic emissionof a cw-operating YAG: Nd ( λ = 532nm). The sampleswere placed in a closed cycle cryostat operating in thetemperature range 10 − c -axis).Representative PL spectra measured on the 3R and2H polytypes of MoS single crystals at T = 25K arepresented in Fig. 1. The emission spectra of 2H and 3Rpolytypes are marked by red solid and blue broken linesrespectively. Each spectrum exhibits several sharp lines.The two strong lines in the energy range 1 . − .
19 eVcorrespond to the two zero-phonon excitonic lines. Welabel them B and C following our previous notation. The lower energy part of the spectrum is dominated bytheir phonon replicas where ph ph ph =23.9meV, E ph =28meV,and E ph =32.1meV. To the best of our knowledge this isthe first observation of halogen bound exciton emissionin the case of the 3R-polytype. Fig. 2 shows an expandedview of PL spectra of the two polytypes measured at dif-ferent temperatures. Although, the structure of the spec-trum for both polytypes is clearly similar, the emissionthe same excitonic complexes appears at significantly dif-ferent energies. For example, the 3R emission occurs atan energy 3.5 meV (for B exciton) and 6 meV (for C exci-ton) lower than for 2H emission. The resulting energeticseparation of the excitonic lines is 10.3 meV for the 3Rcrystal and only 7.6 meV for the 2H crystal. Thus, thesize of the splitting provides a unique fingerprint for eachpolytype which also has the advantage that it does not FIG. 1. (color online) Luminescent spectra at low temper-ature of Cl intercalated 2H (blue broken line) and 3R (redsolid line) MoS single crystals. depend on the absolute calibration of the spectrometer.Fig. 2(a),(b) also shows that the 2H and 3R emissionevolves in a qualitatively similar manner with tempera-ture. For both polytypes the emission of exciton C gainsin intensity with respect to the emission from exciton B .Quantitatively there are some differences. In contrastto 3R for which the exciton B emission dominates atall temperatures, in the 2H polytype the intensity ratiobetween B and C excitonic lines changes in favor of exci-ton C with increasing temperature. For both polytypes,increasing the temperature above 60K leads to a rapidquenching of all PL emission. Such a of the excitonicspectral lines in the case of 2H-MoS :Cl crystals can beunderstood in terms of non-radiative transitions (phononemission) which dominate over radiative recombination(photon emission) at higher temperatures. A com-mon characteristic of the emission spectra for the bothpolytypes is that the excitonic region, very prominentat low temperatures, is accompanied by strong phononreplicas: C ph - C ph and B ph - B ph (see Fig. 2(a),(b)).The energies of the phonon replica emission are in goodagreement with previous studies, where they were in-terpreted as local phonon modes induced by the centerat the origin of the exciton related luminescence. FIG. 2. (color online) PL spectra at different temperatures of (a) 2H-MoS and (b) 3R-MoS polytypes measured at differenttemperatures. The dashed vertical lines are a guide to the eye indicating the position of the weak C excitonic lines at 10K(which are nevertheless clearly visible in the T = 35 K spectra). IV. MODEL DESCRIPTION
In order to explain the difference between 2H and 3Rpolytypes, we propose a model which describes the inter-calation of halogen molecules in the two polytypes. Asthe X-ray single crystal study did not reveal any essen-tial changes in the unit cell parameters in both studiedpolytypes, we have assumed the Cl molecule is presentin a relatively low concentration. In other words, weconsider that the halogen molecules disturb the crystallattice only locally. The intercalation of a considerablequantity of molecules should lead to a larger interlayerdistance, compared to that in the pure phase; indeed suchan increase of the inter-layers separation upon intercala-tion has been observed. Due to the lack of struc-tural information concerning the position of the chlorinemolecule, the DFT band structure calculations were car-ried out for the surfaces of 2H-MoS and 3R-MoS crys-tals. The studied surfaces were modeled by three molec-ular layers of polytypes that are without and with inter-calation of Cl molecules (model I and II respectively).For model I, three layers and corresponding atomic coor-dinates were taken from the structure of bulk crystals. Inmodel II we assume that Cl molecules are intercalatedin the van der Waals gap only between two layers andmove them apart while the other interlayer gap remains unchanged.Possible positions of Cl molecules intercalated be-tween MoS layers were chosen on the basis of the bulkcrystal structure analysis using PLATON tools. Thecrystal packing of the layers revealed two types of in-terstitial cavities in the interlayer of the van der Waalsgap. These cavities are similar in both polytypes andare formed by six or four surrounding sulphur atoms andhave the shapes of a trigonal antiprism and a trigonalpyramid, respectively. The coordinates of correspond-ing centroids of these cavities are 0, 0, 0.5 and 2/3, 1/3,0.561 in 2H-polytype and 2/3, 1/3, 0.167 and 1/3, 2/3,0.208 in 3R-polytype. The shortest distance between thecentroids of two such nearest cavities, which share a com-mon face (three common sulpha atoms) equals 1.97˚A inboth polytypes. On the other hand a search of the Cam-bridge Structural Database (version 5.34) and Inor-ganic Crystal Structure Database revealed that Cl - Cldistances in a chlorine molecule are between 1.96 and1.98˚A and that the shortest Cl - S inter molecular con-tacts in the crystal are in the range 3.29-3.31˚A. Thus,the centroids of conjugate cavities are complementary tothe chlorine molecule and this position obviously mini-mizes the necessary split of the interlayer of the van derWaals gap to adopt chlorine molecule taking into accountthe van der Waals size of these molecules and minimalpossible Cl - S intermolecular distance. FIG. 3. (color online) (a), (b) Mutual arrangement of twoneibouring layers in the structure of 2H- (a) and 3R- (b) poly-types and position of Cl molecule between these layers. Viewapproximately along c crystallographic axis. Mo, S and Clatoms are shown as spheres of arbitrary radii of cyan, yellowand green color, respectively. To place Cl molecules in the desired positions, thegap between two MoS layers in model II was extendedto provide the required Cl - S intermolecular distance.The separation between the planes of sulpha atoms fromtwo neighboring MoS layers was increased up to 6.083and 6.279˚A for the 2H- and 3R- polytypes, respectively,compared with the corresponding separation of 3.021and 2.997˚A in the bulky crystals and in model I. Al-though the chlorine molecule has a similar nearest neigh-bor surrounding, the further environment in polytypesdiffers due to unlike mutual arrangement of MoS layers(Fig. 3(a), (b)). Even such small differences in halogenpositions may affect the radiative properties of excitonsbound to the halogen molecules, leading to distinct emis-sion spectra.Self-consistent ground-state calculations were per-formed with the ABINIT code to obtain the de-tailed electronic structures. Electronic calculations wereperformed in the generalized gradient approximationwith the Perdew-Burke-Ernzerhof exchange-correlationenergy functional. Orbitals are expanded in plane waves up to a cut-offof 25 Hartrees. The pseudo potentials used in our work were generated from the pseudo potentials of Troullier-Martins. The slab-model approach was used to con-struct the surface-induced bulk alignment of the crystals.In a slab model the super cell with the dimensions 3 a × b along the layers and parameter along c axis, which corre-sponds to three layers, were selected and repeated by useof periodic boundary conditions. When used with peri-odic basis functions (e.g., plane waves), the repetition isperformed in three dimensions and a vacuum layer withthe thickness of 10˚A is introduced to isolate the slabs.Thus, the super cell always includes three MoS layers forboth 2H and 3R polytypes in models I and II. Only onechlorine molecule was introduced per super cell to modelthe low concentration. The 3 a × b dimension along thelayer was chosen to perform calculations in reasonablecomputation time with available recourses. V. DISCUSSION
For bulk MoS , the electronic states near the Fermilevel are dominated by Mo 4 d and S 3 p levels. Specifi-cally, the conduction band states at the K point on theBrillouin zone, are primarily composed of strongly local-ized d orbitals at Mo atom sites. At the K point, the oc-cupied part of the d band has dominant d xy − d x − y char-acter whereas the unoccupied portion is dominated by d z character. They have minimal interlayer coupling sinceMo atoms are located in the middle of the S-Mo-S unitcell. The valence band maximum (VBM) is located atthe Γ point while the conduction band minimum (CBM)is located about halfway between Γ and K points; the gapis thus indirect having a value of 1.28 eV. On the otherhand, states near the Γ point originate from a linear com-bination of Mo d z orbitals and the S p z orbitals and arefairly delocalized and have an antibonding nature. Theyhave strong interlayer coupling and their energies dependsensitively on the layer thickness. As a consequence, in-creasing the separation between consecutive MoS layersleads to weaker layer-layer interaction and lowers the en-ergy of the antibonding states which causes the VBMto shifts downwards. Thus, in the limit of widely sepa-rated planes, i.e., monolayer MoS , the material becomesa direct gap semiconductor with a gap of about 1.9eVat 300K. Moreover, the stacking effect on the inter-layer bonding was confirmed by the low energy diffrac-tion study of MoS single crystals, which shows that theinter-plane distance between the Mo and S atomic planeswithin the topmost layer shrink about 5% compared toits bulk value. To resume, the electronic states at the Γpoint are strongly affected by the long-range interlayerCoulombic interactions. In our case, halogen moleculesintercalated within MoS layers should influence the in-terlayer interaction especially at the Γ point. It shouldbe not forgotten that the intercalation of any moleculesbetween the layers leads to an enlargement of the adja-cent layers, as was revealed in earlier publications. This interaction is more pronounced in the case of onlyfew MoS layers as was suggested in. This assumption is confirmed by our theoretical cal-culations of the electronic structure of the two poly-types with and without halogen intercalation, presentedin Fig. 4. The model I has an indirect band gap struc-ture, VBM being located at the Γ point while the CBMis located about halfway between Γ and K points. Thevalues of indirect gaps are equal to 1.119 and 1.113 eV for2H and 3R polytypes (Fig. 4 (a),(b)); the values for thegap of both polytypes are less than experimental ones butit is known that the density functional methodology un-derestimates the band gaps of semiconductors comparedto the experimental results (in our calculations, whichare not presented here, the E g for these bulk materi-als were equal to 1.062 and 1.019eV respectively, whichare also underestimated compared to experimental val-ues). A similar band gap narrowing in 3R polytype, incomparison to that of 2H, was also observed in siliconcarbide. Moreover, it was found for two single stacked sheets ofMoS that when the inter-sheet separation is greater than4.5˚A, the band gap reaches the value found for a singlesheet, as the inter-sheet interaction vanishes. For bothpolytypes in our first model the number of layers is thesame but the interlayer distances and stacking sequencesare different. Within the stacking sequences ABAB for2H-MoS and ABCABC for 3R-MoS the distances be-tween the planes of sulphur atoms of neighboring S-Mo-Slayers and distances between the planes of sulpha atomswithin the same layer are 3.021, 2.997 and 3.129, 3.117˚A,respectively. Moreover, in 3R-MoS polytype the S-Mo-S layers are significantly shifted relatively each other incomparison with 2H-MoS one (Fig. 3). Thus the struc-tural features of these polytypes affect the long-range,interlayer Coulombic interactions which led to a differ-ence in values of the band gaps.In the second model for two polytypes the Cl inter-calation creates energy levels in the band gap near theconduction band edge which consist of 2 p antibondingstates of Cl atoms while the valence bands are comprisedof d -electron orbitals of Mo atoms. Moreover, halogen in-tercalation completely changes the local band structureand the distribution of energy states over the Brillouinzone: both polytypes have now direct band gap transi-tion at the Γ point with 1.323 and 1.246 eV values, for2H and 3R polytypes, respectively (Fig. 4 (c),(d)). Thevalues of halogen levels within the band gap of 2H and3R polytypes are equal to 1.148 and 1.112 eV, respec-tively. The intercalation of Cl molecule has led to widen-ing of the band gaps compared to the band structure ofthe polytypes investigated in model I. The difference inthe values of the given halogen levels is related to differ-ent positions of Cl molecules between the layers wherethey have different spatial surrounding. For 2H-MoS ,only one Cl atom in the molecule has a contact (4.32˚A)with Mo atom (Fig. 3(a)) that is less than above the in-dicted threshold (4.5˚A) when band gap does not dependon inter-layer separation. In contrast for 3R polytype, the Cl atoms in the molecule have both contacts with themetals and they are less than in 2H polytype and equal to4.279 and 4.316˚A, respectively (Fig. 3(b)). Since in Cl molecule the electrons are shared (not transferred), thereare no existing ions that are positive or negative charges,which leads to the creation of full outer shells of chlorineatoms. This means that the repulsive forces hinder inter-layer coupling when Cl and Mo atoms are brought closerto each other, leading to a widening of the band gaps ofthe polytypes. In turn, that leads to a greater splittingof the antibonding states of Cl atoms in 3R-MoS , caus-ing the lowering of the impurity levels in this polytypein comparison with 2H polytype. The band gap widen-ing for both polytypes in model II in comparison withmodel I may be related to a long-range Coulombic inter-action of chlorine molecules with the adjacent layers. Forband structure calculation, molecules intercalated withinMoS layers increase the distance between the two layers.In order to understand the effect of halogen intercalationon the band structure transformation we calculated theenergy bands for model II with increased distances butwithout Cl (not presented here). The obtained valuesare equal to 1.319 and 1.248 eV for 2H and 3R polytypesrespectively. These values are very similar to direct bandgap transition at the Γ point in model II for 2H, 3R-MoS which means that the intercalation of chlorine moleculeshave increased the distances between the adjacent layerswhich in turns have led to the local band gap widening.Theoretical calculations have confirmed that the dif-ference in halogen molecules positions in two polytypesshould result in different PL spectra separated by a smallamount of energy which, indeed, is observed experimen-tally. The temperature rise of the C peak in the lumines-cent spectra to the detriment of the B peak for 2H poly-type occurs because the level responsible for the C emis-sion peak has a radiative lifetime much shorter than the B level. In the case of 3R polytype, despite a smaller(in comparison with 3R polytype) distance between the B and C excitonic levels (7.5meV instead of 10.3meV),the temperature increase of the C -line relative intensity isunimportant. This indicates that the radiative lifetimesof these levels are not significantly different, and the rel-ative intensity of lines B and C is determined mainlyby their population (Boltzmann distribution). However,this approach should be confirmed experimentally by ki-netic (time resolved) measurements, which will be thesubject of a future publication. VI. CONCLUSION
To summarize, the synthetic MoS single crystals weregrown by means of the CVT method using Cl moleculesas a transport agent. 2H-MoS and 3R-MoS polytypeswere identified and structurally characterized using X-raydiffraction to determine its structure under intercalationof Cl molecules. The absence of any changes of the unitcell parameters in both polytypes investigated indicates FIG. 4. (color online) Calculated electronic band structures of two models containing three layers of MoS . Band structures of2H (a) and 3R (b) polytypes of MoS where layers are fixed at bulk positions. Electronic band structure of halogen intercalated2H (c) and 3R (d) polytypes of MoS . The orange line in (c) and (d) correspond to the halogen level within the band gap.The coordinates of k points in the Brillouin Zones in studied super cells are following: Γ: (0,0,0), M: (1/2,0,0), K: (1/3,1/3,0).The red arrows indicate the minimum energy value. The horizontal dashed lines indicate the valence band maximum. that the concentration of Cl molecules in the crystals isrelatively low. Therefore, it was assumed that halogenmolecules disturb the crystal lattice only locally becausetheir intercalation in large concentration would have ledto a larger interlayer distance in comparison to that inthe pure phase. PL related to the excitons bound tothe halogen molecules was investigated for the as grown2H-MoS and 3R-MoS polytypes. It was shown thatthere is an evident difference between the low tempera-ture luminescence spectra of the investigated polytypes:Notably the excitonic splitting is significantly differentproviding a robust signature of the polytype under in-vestigation. The observed spectral shift and dissimilarbehavior of the spectra as a function of temperature areexplained as consequence of slightly different positions ofhalogen molecules in the interstitial space of the studiedpolytypes, which leads to a different interaction of thebound excitons with the local crystal field. To interpretthe obtained experimental results the DFT band struc-ture calculations were performed for three molecular lay- ers of 2H-MoS and 3R-MoS polytypes without (modelI) and with (model II) intercalation of Cl molecules. Formodel II, the structural features of these polytypes wereshown to affect the long-range interlayer Coulombic in-teractions, which led to a difference in values of the bandgaps in 2H-MoS and 3R-MoS due to slightly differentpositions of halogen molecules in the interstitial space ofthese polytypes. The DFT band structure calculationsfor model II are in accordance with the spectroscopic ex-periments, i.e., that the halogen bounded excitonic spec-tra of 2H polytype are shifted to higher energies com-pared to those of 3R polytype. It was also shown thatthe halogen intercalation completely changes the localband structure and distribution of energy states over theBrillouin zone of both polytypes. ACKNOWLEDGMENTS
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