Results and discussion 1. Background

Raman spectra of bulk 2H-TS2(T = Mo or W) have been studied extensively both experimentally and theoretically[18–21]. 2H-TS₂ belongs to theD⁴_6hspace group. It has 12 modes of lattice vibrations at the point in the hexagonal Brillouin zone[18,20]. There are four first-order Raman-active modes in 2H-TS₂, corresponding to symmetries (the corresponding Raman shifts are in parentheses for MoS2and WS2, respectively): E1g(286 and 306 cm⁻¹),E¹_2g(383 and 356 cm⁻¹), A1g(408 and 421 cm⁻¹) andE_2g² (32 and 27 cm⁻¹) [19,21]. These modes have Raman polarization dependent tensors of the form[22]

In back-scattering experiments on a basal plane, i.e., on the sur-face perpendicular to the c-axis, the E1gmode is forbidden whereas A_1gand E_2gones are allowed[18,20]. Also, theE²_2gmode, so-called the “rigid-layer” mode is expected in the region with very low-wavenumber value[20,23].

3.2. Raman spectra of 2H-MoS2and 2H-WS2

Fig. 1 depicts the Raman spectra of 2H-MoS₂ and 2H-WS₂ samples in the range from 200 to 1000 cm⁻¹ obtained with the incident laser light polarized perpendicular to the c-axis. The spec-tra reveal the first-order Raman signals as well as the second-order Raman (SOR) processes due to a coupling of phonons with non-zero momenta. Two prominent first-order Raman-active modes for 2H-TS₂(T = Mo or W) single crystals designated asE¹_2gand A_1gare positioned in the range between 300 and 450 cm⁻¹. These modes are due to vibration of atoms within an S–T–S layer (seeFig. 2).

For WS2, we can observe a splitting of the Raman signal at around 355 cm⁻¹into two peaks at 352 and 356 cm⁻¹. Comparing the peak positions with the previous reports[19,21], the peak located at

Fig. 1. Raman spectra of (a) 2H-MoS2and (b) 2H-WS2layered crystals in the range between 200 and 1000 cm⁻¹, showing the prominentE¹_2gand A1gmodes as well the second-order bands.

356 cm⁻¹is tentatively assigned as the first-orderE¹_2gmode while the peak at 352 cm⁻¹is attributed to the SOR band due to the 2LA(K) overtone and will be discussed later. The other SOR bands can be assigned as combinations of sum or difference of bands involving phonons at the K point coupled to the LA(K) mode[24]. The ener-gies and relative intensities of the observed peaks for both 2H-MoS2

and 2H-WS₂spectra corresponded well to the earlier reported well-known Raman modes[18–21].

3.3. Raman spectra of Mo1−xWxS2layered mixed crystals

To accurately determine the position ofE₂¹_gand A_1gmodes as well as the SOR band located in the vicinity ofE¹_2g of the tung-sten containing samples, polarization dependent measurements in the back-scattering configuration had been carried out. The widely used Porto Notation method[25]for the designation of the crystal and polarization directions was utilized in this work. The [1 0 0], [0 1 0] and [0 0 1] crystallographic axes are being denoted by the letters X, Y and Z, respectively. The notationZ(XX) ¯Z means the direc-tion of incident radiadirec-tion is along Z, the first and second terms in the bracket denotes the polarization of the incident and scattered light, respectively, and ¯Z represents the direction of scattered light. For Z(XX) ¯Z configuration, the analyzer placed just in front of the charge coupled device (CCD) camera was set to have polarization axis parallel to the polarization of the incident linearly polarized laser beam. A fine adjustment in the orientation of the [1 0 0] crystallo-graphic axis of the sample to the E vector of the incident linearly polarized laser beam was made by the maximizing the intensity of the A_1gmode. TheZ(XY) ¯Z configuration was obtained simply by placing the half-wavelength plate directly between analyzer and CCD.

Fig. 2. Displacement of atoms for the Raman-activeE¹_2gand A1gmodes in TS2(T = Mo or W) layered crystals of the 2H polytypes.

942 D.O. Dumcenco et al. / Journal of Alloys and Compounds 506 (2010) 940–943

Fig. 3. Polarized Raman spectra of (a) MoS2, (b) WS2, (c) Mo0.1W0.9S2and (d) Mo0.3W0.7S2layered mixed crystals in the range from 250 to 450 cm⁻¹withZ(XX) ¯Z andZ(XY) ¯Z configurations. The dotted vertical lines show the position of the main peaks designating as I, II, III and IV. The insets in (b)–(d) show the lineshape fits in the vicinity ofE¹_2gmode.

The results of polarization dependent Raman spectra of several Mo1−xWxS2mixed crystals in the wavenumber range between 250 and 450 cm⁻¹ are shown inFig. 3. The intensity of Raman lines inZ(XX) ¯Z and Z(XY) ¯Z configurations differ appreciably showing the strong polarization dependence of the first-order Raman-active modes. In this wavenumber range, for 2H-MoS2 single crystal (Fig. 3(a)), the peak denoted by I corresponds to A_1g mode is detected forZ(XX) ¯Z configuration and quenched almost completely for that ofZ(XY) ¯Z configuration. The lower lying peak denoted by II is associated toE₂¹_g mode and is observed both forZ(XX) ¯Z and Z(XY) ¯Z polarization configurations. Furthermore, the mea-sured intensities of peak II for bothZ(XX) ¯Z and Z(XY) ¯Z polarization revealed very similar value. The obtained results together with the strong polarization dependence agree well with the selection rules ofE¹_2gand A1gmodes as given by the Raman scattering tensors˛ [22]. For the 2H-WS₂sample (seeFig. 3(b)), a similar polarization behavior for higher wavenumber peak I is observed and assigned to be the A_1g mode. The lower lying structure is determined to be composed of two peaks positioning at 356 cm⁻¹(designated as III) and 352 cm⁻¹(designated as IV) in theZ(XX) ¯Z configuration.

A clear resolution of this structure can be seen in the unpolarized Raman spectrum of 2H-WS₂as depicted in Fig. 1(b) and for the Z(XY) ¯Z configuration in the polarized spectra (Fig. 3(b)). The rela-tive intensities for peak III–IV in theZ(XY) ¯Z configuration is larger than that of theZ(XX) ¯Z configuration. This observation agrees with that reported by Sekine et al.[20]. Hence, the peak at 356 cm⁻¹ is assigned to be theE¹_2g mode, while the peak at 352 cm⁻¹ is attributed to be a second-order band. For the mixed Mo_1−xWxS₂ samples, the assignment of peaks I and II can be facilitated by com-paring their locations and polarization dependence with that of the binary end crystals while the relation of the relative intensities of

Fig. 4. Raman spectra of Mo_1−xWxS2layered mixed crystals in the range between 250 and 450 cm⁻¹. The dotted lines guided by eyes show position dependence of the peaks with W compositions x.

peaks III and IV in the polarized Raman spectra has been utilized for the assignment (Fig. 3(c) and (d)).

Fig. 4represents the Raman spectra of Mo_1−xWxS₂in the range from 250 to 450 cm⁻¹. As shown inFig. 4, in the order from top to bottom, the value of the tungsten composition x increases from 0 to 1 with a composition step size x = 0.1 according to the stoichiometry of the constituent elements W and Mo. With W composition increasing, peak I moves to higher wavenumber. In contrast, as x value increases, peak II shifts to lower wavenumber with a reduction of peak intensity. Also with increasing of the tung-sten composition, on the lower wavenumber side of Raman spectra of Mo_1−xWxS2, two additional peaks III and IV appear. Both of them demonstrate blue shift and become the dominant peaks at higher x values. It is noted that an alloy disorder-related peak[26] posi-tioned in between peaks II and III is also observed for the mixed ternary Mo_1−xWxS₂samples.

The dependence of the wavenumbers of the Raman-active modes on the composition of Mo1−xWxS2 layered mixed crystals are depicted inFig. 5. For the A_1gmode, a one-mode behavior is the most typical, while for theE¹_2gmode, a two-mode behavior is observed. These experimental results can be explained satisfacto-rily on the basis of the atomic displacements for each mode; for A_1g mode only sulfur atoms vibrate and this give rise to a one-mode type behavior for the mixed crystals. ForE¹_2g mode metal atoms also vibrate as well as sulfur atoms (seeFig. 2). The atomic weight of tungsten atom is 1.92 times larger than that of molybdenum one, and this mass difference most probably causes the two-mode type behavior ofE¹_2gmode. These behaviors of the composition depen-dences are often seen in the Raman spectra of the solid solutions in which no ordered distribution of the constituent atoms exist [27,28].

The mixed crystals cannot have an ideal periodic lattice. As the composition of W increases, the disorder effect increases in the lay-ered mixed crystals Mo_1−xWxS₂, and the intensities of the modes related to 2H-MoS2 decreases, while 2H-WS2 associated modes increases. This finite periodicity in the mixed crystals relaxes the q = 0 Raman selection rule, thus leading to the broadening and

D.O. Dumcenco et al. / Journal of Alloys and Compounds 506 (2010) 940–943 943

Fig. 5. The variation of peaks I, II, III and IV as a function of W composition x of Mo_1−xWxS2layered mixed crystals.

asymmetry of the Raman lineshape. Symmetric phonon line of the A_1gmode for pure 2H-MoS₂(Fig. 6(a)) and 2H-WS₂(Fig. 6(c)) become asymmetric for Mo_1−xWxS₂mixed crystals (Fig. 6(b)). The low-wavenumber side half-width (low) is larger than the high-wavenumber side half-width (high). The ratiolow/highshows maximum at x = 0.5. This indicates that the mixed crystal disor-der effect is the main source for the Raman lineshape change as a function of composition. At this point, it is worth noting that

Fig. 6. Lineshape analysis of Raman spectra of A1gmode for (a) MoS2, (b) Mo0.5W0.5S2

and (c) WS2layered crystals. The inset in (c) represents the W composition depen-dence of linewidth broadening of A1gmode for the Mo1−xWxS2 layered mixed crystals.

similar broadening and asymmetry of the phonon lines have been previously observed in TlGaxIn_1−xS₂ layered mixed crystals[29].

The inset ofFig. 6(c) shows the composional dependence of the full width at half maximum (FWHM) for A_1gmode. It is noticed that FWHM values of the corresponding modes for MoS₂layered crystals were found to be higher than those for WS2 crystals. In addition, as expected, the FWHM dependence has maximum at x = 0.5, which corresponds maximum substitutional disorder in the mixed crystals.

4. Summary

The Raman spectra for Mo_1−xWxS₂layered mixed crystals were investigated for a wide range of the composition with 0≤ x ≤ 1. The peaks of the two dominant first-order Raman-active modes, A1g

andE₂¹_g, and several second-order bands have been observed in the range of 200–1000 cm⁻¹. The peaks corresponding to A_1gmode show one-mode type behavior while the peaks ofE₂¹_gmode demon-strate two-mode type behavior for the entire series. These results are explained on the basis of the atomic displacements for each mode. For A_1gmode only sulfur atoms vibrate and this give rise to a one-mode type behavior for the mixed crystals. While forE_2g¹ mode, metal atoms also vibrate as well as sulfur atoms. The mass differ-ence of the vibrating Mo and W cations causes the two-mode type behavior ofE2¹gmode. The largest FWHM value and asymmetry of A_1gmode at x = 0.5 are due to crystal disorder.

Acknowledgements

The authors would like to acknowledge the financial supports by the National Science Council of Taiwan under Grant Nos. NSC 97-2112-M-011-001-MY3 and 98-2811-M-011-003.

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Journal of Alloys and Compounds 506 (2010) 46–50

Contents lists available atScienceDirect

Journal of Alloys and Compounds

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j a l l c o m

Temperature-dependent study of the band-edge excitonic transitions of Cu ₂ ZnSiS ₄ single crystals by polarization-dependent piezoreflectance

S. Levcenco

, D. Dumcenco

, Y.S. Huang

, E. Arushanov

, V. Tezlevan

, K.K. Tiong

, C.H. Du

aDepartment of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan

bInstitute of Applied Physics, Academy of Sciences of Moldova, Chisinau, MD 2028, Republic of Moldova

cDepartment of Electrical Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

dDepartment of Physics, Tamkang University, Tamsui 251, Taiwan

a r t i c l e i n f o

The temperature dependence of the band-edge excitonic transitions of Cu2ZnSiS4single crystals were characterized by using polarization-dependent piezoreflectance (PzR) in the temperature range of 10–300 K. The PzR measurements were carried out on the as-grown basal plane with the normal along [2 1 0] and the c axis parallel to the long edge of the crystal platelet. The PzR spectra revealed polarization-dependentE^ex_⊥ andE^ex_|| features for E⊥c and E||c polarization, respectively. Both E_⊥^exandE^ex_|| features are associated with the interband excitonic transitions at point and can be explained by crystal-field splitting of valence band. From a detailed lineshape fit to the PzR spectra, the temperature dependence of the transition energies and broadening parameters of the band-edge excitons were determined accu-rately. The temperature dependence of near band-edge excitonic transition energies were analyzed using Varshni and Bose–Einstein expressions. The temperature dependence of the broadening parameter of excitonic features also has been studied in terms of a Bose–Einstein equation that contains the electron (exciton)–longitudinal optical phonon-coupling constant. The parameters that describe the temperature variation of the excitonic transition energies and broadening parameters were evaluated and discussed.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, ternary chalcopyrites and quaternary chalco-genides have been studied to observe their semiconducting and optical properties. Cu2ZnSiS4 is an indirect semiconductor [1]

which belongs to the family of Cu-based quaternary chalcogenide compounds, Cu₂–II–IV–VI₄, crystallizing in the wurtz–stannite structure with space group Pmn21[2–4].The structure of Cu2ZnSiS4

consists of alternating cation layers of mixed Zn and Si atoms which are separated by layers of Cu atoms. It is therefore derived from an ordering of the cations of the wurtzite cell. In this compound every sulfur atom has four nearest neighbor cation atoms (two copper atoms, one zinc, and a silicon atom) at the corners of the surround-ing tetrahedron[2–4]. The material is of interest for its nonlinear optical properties[5,6]and potential for application in the field of energy, environment and optoelectronics[7,8]. Despite its inter-esting optical properties and possible applications, up-to-date, the

∗ Corresponding author. Tel.: +886 2 27376385; fax: +886 2 27376424.

E-mail address:[email protected](Y.S. Huang).

1Permanent address: Institute of Applied Physics, Academy of Science of Moldova, 5, Academiei str., MD-2028, Chisinau, Republic of Moldova.

theoretical and experimental understanding of the basic properties of Cu2ZnSiS4is still relatively incomplete[1,9], due to the difficulty of preparing high quality single crystals.

In this paper, we report a detailed study of the temperature dependence of the band-edge excitonic transitions of Cu2ZnSiS4

single crystals by using polarization-dependent piezoreflectance (PzR) in the temperature range between 10 and 300 K. High quality single crystals of CuZnSiS4were grown by chemical vapor trans-port using iodine as the transtrans-port agent. PzR has been proven to be useful in the investigation and characterization of semiconductors [10–12]. The derivative nature of PzR spectra suppresses uninter-esting background effects and greatly enhances the precision in the determination of transition energies. The shaper lineshape as compared to the conventional optical techniques have enabled us to achieve a greater resolution and hence to detect weaker fea-tures. The PzR measurements were carried out on the as-grown basal plane with the normal along [2 1 0] and the axis c parallel to the long edge of the crystal platelet. The PzR spectra revealed polarization-dependentE_⊥^exandE_||^exfeatures for E⊥c and E||c polar-ization, respectively. From a detailed lineshape fit, the temperature dependence of the energies and broadening parameters of the excitonic transitions near direct band-edge were determined accu-rately. The parameters that describe the temperature variation of

0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.jallcom.2010.07.027

S. Levcenco et al. / Journal of Alloys and Compounds 506 (2010) 46–50 47

Fig. 1. A schematic arrangement of the polarization-dependent PzR measurements.

the excitonic transition energies and broadening parameter were evaluated and discussed.

2. Experimental

Single crystals of Cu2ZnSiS4were grown by vapor transport of stoichiometric amounts of the elements with 5 mg iodine/cm³as the transport agent. Optimum crystal growth was achieved with the charge zone maintained at 850^◦C and the growth zone at 800^◦C. The transport process was carried out for a period of 14 days.

Single crystals Cu2ZnSiS4formed thin, greenish, blade shape up to 10 mm× 1.5 mm in area and 300␮m in thickness. The orientation of the basal plane was determined by comparing back-reflection Laue pattern with computer generated Laue plots.

With the X-ray beam normal to the basal plane, the Laue pattern displayed a twofold asymmetry pattern. Analyzing the symmetry of Laue pattern confirms the formation of orthorhombic structure and reveals that the normal of the basal plane is [2 1 0]

and the long edge of the crystal platelet is parallel to c axis. The full width at half maximum (FWHM) of the rocking curve ( scan) in the vicinity of (2 1 0) normal peak was determined to be∼0.007^◦. The small value of FWHM indicates that high quality single crystals of CuZnSiS4were grown.

Fig. 1depicts the schematic arrangement of the polarization-dependent PzR measurements with polarization configurations of E⊥c and E||c performed on the as-grown basal plane with the normal along [2 1 0] and c parallel to the long edge of the crystal platelet. A 150 W xenon arc lamp filtered by a 0.25 m grating monochro-mator provided the monochromatic light. Model PRH 8020 CASIX Rochon prisms were employed for polarization-dependent measurements. A model 3378 Hama-matsu photomultiplier tube was used to detect the transmitted or reflected signals.

The PzR measurements were achieved by gluing the thin (∼100 ␮m) single-crystal specimens on a 0.15 cm thick lead zirconate titanate piezoelectric transducer driven by a 300Vrmssinusoidal wave at 200 Hz. The DC output of the reflected signal was maintained constant by a servomechanism of a variable neutral density filter. A dual-phase lock-in amplifier was used to measure the detected signals. The entire data acquisition procedure has been performed under computer control. Multiple scans over a given photon energy range was programmed until a desired signal-to-noise level has been obtained. For temperature-dependent measurements, a closed-cycle cryogenic refrigerator equipped with a digital thermometer controller was used for the low temperature measurements with a temperature stability of 0.5 K or better.