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Dielectric function spectra and inter-band optical transitions in TlGaS2
Toshiyuki Kawabata a, YongGu Shim a,⁎, Kazuki Wakita b, Nazim Mamedov c
a Department of Physics and Electronics, Graduate School of Engineering, Osaka Prefecture University, Gakuen-cho 1-1, Nakaku, Sakai, Osaka 599-8531, Japanb Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino 275-0016, Japanc Department of Ellipsometry, Institute of Physics, Azerbaijan National Academy of Sciences, H. Javid Ave. 33, Baku AZ-1143, Azerbaijan
Please cite this article as: T. Kawabata, et alhttp://dx.doi.org/10.1016/j.tsf.2014.02.100
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Keywords:Dielectric function spectraOptical transitionsThallium compoundsElectronic band structure
TlGaS2 with a quasi-two-dimensional structure has been accessed by spectroscopic ellipsometry over the 1.5–6.0 eV spectral range. A uniaxial approach applicable to monoclinic TlGaS2 at room temperature has beenemployed for ellipsometric data treatment. Principal components of the dielectric function tensor have thenbeen retrieved. Inter-band optical transitions associated with the obtained dielectric function have been deter-mined by using standard critical point analysis. The transitions have been assigned within the electronic bandstructure obtained for TlGaS2 from calculations based on density functional theory.
The ternary thallium chalcogenide compounds such as TlGaS2, TlInS2and TlGaSe2 have a quasi-two-dimensional layered monoclinic struc-ture and exhibit incommensurate (IC) phase transitions at low temper-ature [1–4]. IC phasemay have a peculiar electronic spectrum caused byspatial modulation at the nanoscale [5] and optical properties of thematerials with IC phase attract much attention [6–8]. Irregular behaviorof the absorption edge as well as optical anisotropy with temperaturehas been reported for TlInS2 [9,10]. Interesting memory effects havebeen observed in photoluminescence of TlGaS2 in the course ofthermo-cycling between low and room temperature phases [11].
Although optical properties of TlGaS2 have been studied quite exten-sively [12–15], optical constants have been determined only in a regionbelow energy gap [16]. Dielectric function and corresponding inter-band optical transitions above the energy gap of TlGaS2 still remainuninvestigated.
Here we report the dielectric function spectra of TlGaS2 for lightpolarization, E⊥c* and E//c* (c*: direction normal to the layer plane, E:electrical vector) at room temperature in the 1.5–6.0 eV photon energyrange. The critical points (CPs) for inter-band optical transitions havebeen determined from the second derivative spectra of the retrieveddielectric function.Obtained results are discussedusingdensity functionaltheory (DFT)-based electronic band structure calculated for TlGaS2.
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2. Experimental details and analysis
The samples studied in thisworkwere obtained frombulky ingots ofsingle crystalline TlGaS2 grown by Bridgman method. The TlGaS2 has aquasi-two dimensional crystal structure [17]. Generally, TlGaS2 is a bi-axial material with C62h space group of symmetry at room temperature.However, light figure studies [18] have shown that at normal ambientbiaxial anisotropy, birefringence in (001)-plane is vanishingly smalland the angle between two optical axes is quite negligible. Therefore,within accuracy of our ellipsometric measurements we can treatTlGaS2 as a uniaxial material with optic axis c* normal to the layers [9].
Ellipsometric measurements were performed with the aid of aphase-modulated spectroscopic ellipsometer (HORIBA Jobin-Yvon,UVISEL-TK9017TK) at an incident angle of 65° in the energy range of1.5–6.0 eV. The measurements were carried out on the (001) and(100) surfaces of bulky TlGaS2. The clean and perfect (001) surfaceswere obtained from the bulky ingot by cleaving. The (100) surfaceswere obtained after cutting the ingot with a wire saw and mechanicalpolishing with 0.1 μm alumina suspension.
In treating ellipsometric data we used a conventional ellipsometricapproach [19] to obtain E//c* and E⊥c* components of complex dielectricfunctions of optically anisotropic TlGaS2.
Fig. 1(a) shows a configuration of the ellipsometric measurementson (001) surfaces. Since for such a configuration the influence of E//c*component has little effect on the measured psi and delta, the obtaineddielectric function can be regarded with a good accuracy as E⊥c* com-ponent of the dielectric function tensor [20]. On the other hand,ellipsometric parameters obtained in another configuration that isshown in Fig. 1(b) aremainly determined by E//c* component of the di-electric function since the plane of incidence is parallel to the optic axis
nd inter-band optical transitions in TlGaS2, Thin Solid Films (2014),
Fig. 1. Optical configurations for ellipsometric measurements in E⊥c* (a) and E//c*(b). Solid arrows indicate directions of propagation for incident and reflected lightbeams in the plane of incidence. Dashed arrows indicate the position of optic axis c*.
Fig. 2. Real and imaginary parts of pseudo-dielectric function of TlGaS2; (a)—bεN(001)(E⊥c* configuration), (b)—bεN(100) (E//c* configuration).
Fig. 3. Second-derivative spectra of pseudo-dielectric function of TlGaS2, togetherwith theresults of the fitting within SCP model; (a)—E⊥c* configuration, (b)—E//c* configuration.The vertical arrows indicate energies of the obtained CPs.
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c* during ellipsometric measurements. Hereafter, we call configurationsin Fig. 1(a) and (b) as E⊥c* and E//c* configurations, respectively.
We treated ellipsometric data in both configurationswithin ambient/substratemodel. The results obtained in this case are commonly referredto as pseudo-dielectric function. As shown long ago by Aspnes [20], apseudo-dielectric function obtained at large angles of incidence is accu-rate enough to performcritical point analysis. Therefore, we believe thatin our case the quality of the obtained CP data has also been ensured.
The calculations of electronic band structure of the room temperaturephase (normal phase) of TlGaS2 have been performed within DFT in thegeneralized gradient approximation using scalar relativistic implemen-tation of the linearized augmented plane wave method by WIEN2kprogram code [21,22].
3. Results and discussions
In this report, we use bεN(001) and bεN(100) notations for pseudo-dielectric function retrieved from ellipsometric measurements in E⊥c*and E//c* configurations, respectively. The obtained complex compo-nents of the pseudo-dielectric function spectra are shown in Fig. 2.The spectral features of the components in Fig. 2(a) and (b) are differ-ent, indicating a strong anisotropy of optical transitions in TlGaS2. Fringestructures around 2.0 eV in Fig. 2(a) resulted from interference causedby backside reflection in the sample. At the same time a weak structureat around 2.5 eV is probably caused by indirect band gap transitions.
In order to obtainmore information on inter-bandoptical transitionsin TlGaS2 we have analyzed the second derivative spectra of thebεN(001) and bεN(100), using the standard-CP (SCP) model [23]. Thesespectra are shown in Fig. 3, togetherwith the results of the fittingwithinSCPmodel. In Fig. 3(a) and (b) we have used Evj and Epj notations for CPenergies indicated by arrows. Subscripts vj and pj, where j (j=1, 2…) isCP's number indicate each CP in E⊥c* and E//c* configurations, respec-tively. The energies of the CPs, together with the type of each CP andelectronic states involved in each inter-band transition are given inTable 1.
Please cite this article as: T. Kawabata, et al., Dielectric function spectra and inter-band optical transitions in TlGaS2, Thin Solid Films (2014),http://dx.doi.org/10.1016/j.tsf.2014.02.100
Table 1CP energies and types, together with nature of optical transitions for each CP as deter-mined from SCP analysis of second derivative of pseudo-dielectric function in E⊥c* andE//c* configurations. Notations of CPs are the same as in Figs. 3, 4 and 5.
Configurations(polarization)
CPs Type CP energy(eV)
Main atomic orbitals ofelectronic states relatedto the optical transitions
E⊥c* Ev1 2D M0 3.11 Tl 6s + S 3p → Tl 6p + S 3pEv2 2D M2 3.29 S 3p → Tl 6p + S 3pEv3 2D M0 3.53 Tl 6s + S 3p → Tl 6p + S 3pEv4 2D M2 3.73 Tl 6s + S 3p → Tl 6p + S 3pEv5 2D M1 4.16 Tl 6s + S 3p → Tl 6p + S 3pEv6 2D M2 4.33 Tl 6s + S 3p → Tl 6p + S 3pEv7 2D M2 4.81 Tl 6s + S 3p → Tl 6p + S 3pEv8 2D M1 5.31 Ga 4p + S 3p → Tl 6p + Ga 4s
+ S 3pEv9 2D M2 5.67 Ga 4p + S 3p → Ga 4s + S 3p
E//c* Ep1 2D M0 2.96 Tl 6s + S 3p → Tl 6s + Ga 4s+ S 3s + S 3p
Ep2 2D M0 3.39 S 3p → Tl 6p + S 3pEp3 2D M1 3.77 S 3p → Tl 6p + S 3pEp4 2D M0 4.12 S 3p → Tl 6pEp5 2D M1 4.33 S 3p → Tl 6p + Ga 4s + S 3pEp6 2D M0 4.79 S 3p → Tl 6pEp7 2D M2 5.10 S 3p → Tl 6p + S 3pEp8 2D M0 5.51 S 3p → Tl 6p + S 3p
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In Fig. 4 we have shown the calculated electronic band structure ofTlGaS2. According to the obtained band structure, TlGaS2 is a semicon-ductor with the valence band top at Γ point and conduction band bot-tom on Γ–Y line of the Brillouin zone (BZ). This is consistent with theexperimental studies [12–15] indicating an indirect nature of bandgap transitions in this material. However, transition energy isunderestimated by 0.5–0.6 eV that can be related to the internal defi-ciency of DFT- based calculations which usually underestimate energygap, fairly well reproducing the other important features of thematerial's band structure. Therefore, we have made a scissor shift by0.56 eV to obtainmore realistic joint density-of-states for inter-bandop-tical transitions between valence and conduction band states. We havethen used Monkhorst–Pack special point technique [24] for integrationover the BZ to obtain the imaginary part of the dielectric function. Thereal part of the dielectric function has been obtained from the imaginarypart by Kramers–Kronig transformation.
Fig. 4. Electronic band structure of TlGaS2. The main inter-band optical transitions areindicated by the vertical arrows. Solid and dashed arrows show transitions allowed inE⊥c* and E//c*, respectively.
Please cite this article as: T. Kawabata, et al., Dielectric function spectra ahttp://dx.doi.org/10.1016/j.tsf.2014.02.100
In Fig. 5 the calculated real and imaginary parts of bεN(001) andbεN(100) (solid curves) are shown together with corresponding experi-mental data (dashed curves). The energies of the calculated CPs are in-dicated by vertical arrows in Fig. 5. A fair agreement between calculatedand experimental data is observed in Fig. 5(a) related to E⊥c* configura-tion,while in Fig. 5(b) related to E//c* configuration the correspondencebetween calculations and experiments is worse. The experimentalstructures in Fig. 5(b) are smeared as compared to calculated ones,which are by fare due to the surface roughness and/or residual overlayerthat is hardly unavoidable in the case of (100) surface. Nevertheless, it isyet possible to find qualitative correspondence between the calculatedCPs and experimental spectral features such as a shoulder structurearound 3.0 eV and a peak structure around 4.0–5.0 eV.
The CP energies obtained from SCP analysis from the experimentalresults were compared with the calculated band structure. By takinginto account k-dependentmomentum–matrix element [24], we carriedout individual calculations of imaginary part of the dielectric functionspectra for each band combination around the band gap of TlGaS2 andmanaged to find from the absolute value and peak energy the band-combinations and k-points whichmostly contribute to the optical tran-sitions forming the obtained dielectric function spectra. As a result, theexperimentally obtained CPs listed in Table 1 were assigned to the opti-cal transitions given by vertical arrows in Fig. 4. As seen from Fig. 4,dielectric function spectra of TlGaS2 are predominately formed byinter-band optical transitions between the valence and conductionband states lying on Γ–Y and T–Z lines.
4. Conclusions
We have studied the dielectric function spectra and related opticaltransitions for layered TlGaS2 compound. The bεN(001) and bεN(100)components of the pseudo-dielectric function have been obtained by
Fig. 5. Real and imaginary parts of calculated dielectric function of TlGaS2; (a)—E⊥c*,(b)—E//c*. Vertical arrows indicate CP energies, broken curves represent pseudo-dielectric function in E⊥c* and E//c* configurations.
nd inter-band optical transitions in TlGaS2, Thin Solid Films (2014),
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means of spectroscopic ellipsometry at room temperature in the photonenergy range of 1.5 to 6.0 eV. The energies of inter-band optical transi-tions have then been determined by the SCP analysis. The valence andconduction band states involved in the observed optical transitionshave been assigned according to the calculated DFT-based electronicband structure. It is likely that the GW-correction to our electronicband structure obtained from local density approximation is necessaryto better reproduce energy gap and all optical transitions in TlGaS2. Atthe same time, more effort shall be made for the preparation of high-grade (100) surfaces with optical quality in order to get more reliablebεN(100) component of dielectric function of TlGaS2.
Acknowledgment
This work was supported by JSPS scientific research GrantNo. 24560381, Faculty Innovation fellowship support grant in GraduateSchool of Engineering, Osaka Prefecture University, and by Science Devel-opment Foundation under the President of the Republic of Azerbaijan—
Grant Nos. EİF-2010-1(1)-40/01 and EİF-2012-2(6)-39/01/1.
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