1. Introduction

Transition-metal dichalcogenide ReS2 is a diamagnetic semiconductor that possesses an indirect gap in the near-infra-red (NIR) region of about 1.37 eV [1–2]. Layered ReS₂ are of considerable interest for various applications due to its optical, electrical and mechanical properties [3]. These applications include a sulfur-tolerant hydrogenation and hydrodesulfurization catalyst [4–5] and as a promising solar-cell material in the electrochemical cells [6–7]. Especially, ReS₂ crystallized in a distorted CdCl₂-type layer structure with triclinic symmetry. A clustering pattern of “diamond chains” consisting Re₄ parallelogram ions formed along the b-axis in ReS2 monolayer resulting in the crystal being optically biaxial. Optically biaxial behaviors of ReS2 were observed with the linearly polarized lights incident normal to the basal plane [E‖(001) and k⊥(001)]. The in-plane optical anisotropy of ReS2 with optical polarizations along b- and perpendicular to b-axis had ever been studied using polarization-dependent absorption and piezoreflectance (PzR) measurements [8–10]. The experimental results clearly indicated the near-band-edge transitions (i.e., band gap and excitons) in ReS₂ are polarization dependent. The absorption-edge anisotropy in the layer plane of ReS₂ renders the crystal possesses the potential capability to fabricate a polarization sensitive photodetector applied in multi-channel optical communication for detecting the various orientations of the linearly polarized lights [11–12]. Polarization dependence of the energy gaps of ReS₂ had ever been studied by polarized-transmission measurements with the polarization angles varied from E‖b (θ=0°) to E⊥b-axis (θ=90°) at 300 K [13]. The angular dependent relationship of the polarized gaps of ReS₂ was determined to be E_g(θ)=1.367-0.023·cos(2θ) eV [13]. The difference in minimum (θ=0°) and maximum (θ=90°) gaps of ReS₂ provides a potential capability of this layer material to be used as a polarized optical switch applied in polarized optical communication of NIR region.

ReS₂ usually crystallizes in distorted octahedral layer structure of triclinic symmetry (space group P 1) [14–15]. The lattice parameters of ReS₂ were determined to be a=6.450Å, b=6.390Å, c=6.403Å, α=105.49°, β=91.32°, and γ=119.03°, respectively [15]. Many research reports claimed the stabilized phase of ReS₂ is triclinic layer structure [3, 14–16], however, according to our recent work a new structural phase of this material was found after crystallization.

In this paper the structural change of ReS₂ is studied using temperature dependent PTR measurements in the temperature range between 25 and 300 K. ReS2 single crystals were grown by chemical vapor transport (CVT) method using Br₂ as a transport agent. Crystal morphologies of the as-grown crystals were found to possess two different kinds of the structural phases after crystallization. Observing in detail on the crystallized solids, the crystal phases can essentially be divided into the normal triclinic layer as well as the tetragonal structure. PTR experiments of the solids were carried out with optical polarizations along and perpendicular to the crystals’ b-axis for the layer and tetragonal crystals. According to the experimental observations, the occurrence of the structural change in ReS2 is mostly probable attributed to the atomic bonding deformation along b-axis, which is parallel to the Re4 parallelogram consisted diamond chains. Temperature dependences of the interband transition energies of the layered and tetragonal ReS₂ are analyzed by Varshni, O’Donnel and Chen, and Bose-Einstein type relations. The temperature dependences of the broadening function for the layered and tetragonal ReS₂ have also been interpreted in terms of a Bose-Einstein equation which contains the electron (exciton)-LO phonon coupling constant. The parameters that describe the temperature variations of the transition energies and broadening parameters for layered and tetragonal ReS2 are evaluated and discussed.

2. Experimental details

ReS₂ single crystals were grown by chemical vapor transport method using Br₂ as a transport agent. Prior to the crystal growth, quartz tubes containing Br₂ and the elements (Re: 99.95% pure, S: 99.999%) were evacuated and sealed. The quartz tube was placed in a three-zone furnace and the charge prereacted for 24 h at 800 °C with the growth zone at 1000 °C, preventing the transport of the product. The furnace was then equilibrated to give a constant temperature across the reaction tube and was programmed over 24 h to produce the temperature gradient at which single crystal growth takes place. Temperature gradient for the growth was set as 1050 °C→990 °C with the heat slope of -3°C/cm for two quartz ampoules. The growth time was about 20 days. After the growth, a lot of layer-type crystals as well as a little tetragonal-like solid are simultaneously found inside the quartz tube. The as-grown layered ReS2 formed thin, silver-colored, graphite-like, hexagonal-shaped platelets up to 2 cm² in area and 100 µm in thickness, while the tetragonal crystals possessed a size of less than 1.8×0.7×0.7 mm³. Electron probe microanalysis (EPMA) of the tetragonal ReS₂ shows a little chalcogen deficiency and slight bromine incorporation (Re : S : Br≅0.33 : 0.63 : 0.04) inside the crystals. In comparison with the bromine free character of the layered ReS₂, the structural transformation of ReS₂ from triclinic layer to tetragonal perhaps closely correlated to the incorporation of the bromine atoms inside the crystals.

For PTR experiments, a 150 W tungsten-halogen lamp filtered by a PTI 0.35 m monochromator provided the monochromatic light. The reflected light of the sample was detected by an EG&G type HUV-2000B silicon photodiode and the signal was recorded from an EG&G model 7265 dual phase lock-in amplifier. A pair of OPTOSIGMA near-infrared-dichroic-sheet polarizers with the measured range of 760–2000 nm was employed in the PTR measurements of the layer-type crystals whereas a pair of visible-dichroic-sheet polarizers was utilized for the tetragonal ReS₂. For thermal modulation measurements, a glass substrate was acted as a heat sink. The glass substrate was evaporated with a winding path of aluminum tracks as the heating element and the shape of the aluminum path was formation by a cooper mask [17]. The heating path consists of two wide tracks at the end sections and one narrow track lies in between them. The narrow track in the middle section of the Al path is designed to act as a heat generation source when the electrical current passes through the heater. The function of the wide tracks at the end sections of the path is the auxiliary of heat dissipation when the electrical power is off. The layered and tetragonal samples were closely attached on the narrow track of the Al path by silicone grease. Thermal modulations of the samples were achieved by indirect heating method of supplying the current pulses to the Al heating path periodically. Heated pulses of low frequency and long duty cycle are more efficient in the periodic thermal perturbation of the crystals [17]. A 4 Hz square wave with the duty cycle of 50% is employed in the TR experiment. The measurements were done in the temperature range between 25 and 300 K with a temperature stability of about 0.5 K or better. A closed-cycle cryogenic refrigerator equipped a digital thermometer controller was utilized to facilitate the temperature dependent measurements.

3. Results and discussion

The crystal morphologies of the as-grown ReS₂ with the hexagonal-layer and tetragonal-shape solids are demonstrated in Fig. 1. The photograph of the layered ReS₂ is in 20× magnifications and the SEM (scanning electron microscope) picture of the tetragonal-type crystal is in 35× magnifications. Layer-type crystals essentially belong to the hexagonal structure with a sandwich stacking type. For layered ReS₂, the metal atoms in the Re monolayer slip off their regular octahedral sites forming in the Re₄ units which coupling into one-dimensional clustering pattern of “diamond chains” in the metal monosheet. This consequence results in the distortion of the crystal lattice, which comprising a triclinic unit cell with the lattice parameters being a≠b≠c and α≠β≠γ (See Fig.1). For tetragonal ReS₂, the lattice constants of the a- and c-axes are shown to be equal. The lattice parameters of the tetragonal unit cell are a=c≠b and α=β=γ=90°. The b-axis is the longest principal edge of the tetragonal ReS₂ illustrated in Fig. 1.

 

Fig. 1. The crystal morphologies of the as-grown layer-type and tetragonal ReS₂ single crystals. The structural unit cells for both triclinic layer and tetragonal structure are included for comparison.

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Fig. 2. Polarized thermoreflectance spectra of (a) layer-type ReS₂ [denoted as ReS₂(L)] and (b) tetragonal ReS₂ [denoted as ReS2(T)] at 25K. The dashed lines are the experimental results and the solid curves are least-square fits to a derivative Lorentzian line-shape function which yield transition energies indicated by arrows.

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Shown in Fig. 2 are the PTR spectra of (a) layer-type ReS₂ [denoted as ReS₂(L)] and (b) tetragonal ReS₂ [denoted as ReS2(T)] at 25K. The dashed lines are the experimental results and the solid curves are least-square fits to a functional form appropriate for the interband transitions expressed as a Lorentzian line-shape function of the form [18–19]

where A_i and ϕ_i are the amplitude and phase of the line shape, and E_i and Γ_i are the energy and broadening parameter of the interband transitions for layered and tetragonal ReS₂. The transition energies of ${\mathrm{E}}_1^{\text{ex}}$ and ${\mathrm{E}}_2^{\text{ex}}$ for ReS₂ (L) and E_d1 and E_d2 for ReS₂ (T) in Fig. 2 can be analyzed by fitting the PTR spectra to Eq. (1) that obtained transition energies are indicated with arrows. The polarization dependence of the transition energies of ${\mathrm{E}}_1^{\text{ex}}$ and ${\mathrm{E}}_2^{\text{ex}}$ for ReS₂ (L) clearly indicated that ${\mathrm{E}}_1^{\text{ex}}$ transition is present in E‖b polarization while the ${\mathrm{E}}_2^{\text{ex}}$ feature only appears in the E⊥b polarization. The transition features E_d1 and E_d2 for ReS₂ (T) also present the same polarization-dependent character with respect to the optical polarizations along and perpendicular to the tetragonal crystal’s b-axis. This result lends an experimental evidence that the structural change of ReS₂ formed from the triclinic layer to tetragonal structure is mostly probable attributed to the atomic bonding deformation along b-axis, which is parallel to the Re₄ parallelogram consisted diamond chains. Recently published results claimed a ReS₂ nanotube could be formed by wrapping around the rhenium-sulfide sheets on an original ReO_x material or a carbon nanotube [20–21]. Perhaps the similar concept could be utilized to account for the formation of the tetragonal-shape crystal by wrapping around the ReS2 monolayer along b-axis of the Re₄ clustering chains.

As shown in Fig. 2, the transition energies of E_d1 and E_d2 are much higher (~0.17eV) than those of the ${\mathrm{E}}_{\text{ex}}^1$ and ${\mathrm{E}}_2^{\text{ex}}$ at 25 K. The high energy blue-shift behavior for ReS₂(T) provides experimental evidence that the structural change of ReS₂ is coming from the alteration of the crystal symmetry in lattice rather than any kinds of the doping effects occurred in the crystals with the same structure. The broader line features of the E_d1 and E_d2 transitions for ReS₂(T) also indicated the crystalline quality of layer-type ReS₂ is still better than the new-type tetragonal crystals.

 

Fig. 3. Temperature-dependent PTR spectra of (a) ReS₂ (L) and (b) ReS2 (T) with E‖b and E⊥b polarizations at various temperatures between 25 and 300 K. The dashed lines and solid curves are respectively the experimental PTR spectra of E‖b and E⊥b polarizations while the hollow-circle lines are least-square fits to Eq. (1).

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Displayed in Fig. 3 are the temperature-dependent PTR spectra of (a) ReS₂ (L) and (b) ReS₂ (T) with E‖b and E⊥b polarizations at various temperatures between 25 and 300 K. The dashed lines and solid curves are respectively the experimental PTR spectra of E‖b and E⊥b polarizations while the hollow-circle lines are least-square fits to Eq. (1). As the general semiconducting behavior, the values of the transition energies for both layer-type and tetragonal ReS₂ lowed when the temperature is raised from 25 to 300 K. The broadening parameters of the transition features for both layer and tetragonal crystals also show the broader line-shape character at the higher temperatures. The temperature variations of the transition energies for ReS₂(T) [see Fig. 3(b)] show the temperature insensitive behavior at low temperatures from 25 to 180K. The temperature insensitive property of the interband transitions for ReS₂(T) may cause by the bonding type that determining the transition origins of the E_d1 and E_d2. From the experimental observations of the polarization and temperature dependences of the E_d1 and E_d2, we can infer that the E_d1 and E_d2 transitions should be different, and which are originated from the largely metal Re-Re bonds in the tetragonal ReS₂.

 

Fig. 4. Temperature dependence of the transition energies of layered and tetragonal ReS2 with representative error bars. The dashed curves are least-squares fits to Eq. (2), the solid lines are least-squares fits to Eq. (3) and the hollow-square curves are least-squares fits to Eq. (4).

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The polarized transition energies of ${\mathrm{E}}_1^{\text{ex}}$ and ${\mathrm{E}}_2^{\text{ex}}$ for ReS₂(L) and E_d1 and E_d2 for ReS₂(T) as a function of temperature are plotted in Fig. 4. Representative error bars are shown. The dashed curves are least-squares fits to a Varshni semiempirical relationship [22]

which yields fitting parameters are listed in Table 1. The parameter E_i (0) of Eq. (2) is the transition energy at absolute zero and α and β are constants. The constant α is related to the electron-phonon interaction and β is closely related to the Debye temperature [22]. The fitting is poor at low temperatures because Eq. (2) predicts a quadratic temperature dependence for transition energy, whereas our experimental results indicate that the energy values are almost temperature independent at low temperatures. The data which describing the temperature dependence of the transition energies for ReS₂ have also been fitted to an empirical expression proposed by O’Donnel and Chen [23],

where ${\mathrm{E}}_{\mathrm{i}}^{\text{oc}}$ (0) is the transition energy at zero temperature, S is a dimensionless coupling constant related to the strength of electron-phonon interaction, and <ħΩ> is an average phonon energy. The excellent fits obtained are shown as solid lines in Fig. 4. They are statistically better than the Varshni fits at low temperaures. The obtained values of ${\mathrm{E}}_{\mathrm{i}}^{\text{oc}}$ (0), S and <ħΩ> together with those of the Varshni fits are listed in Table 1. The values of fitting parameters for the temperature dependence of the indirect gap [2] of layered ReS₂ are included for comparison. The values of Debye temperature related constant β for E_d1 and E_d2 in ReS₂(T) are much larger than those of the ${\mathrm{E}}_1^{\text{ex}}$ and ${\mathrm{E}}_2^{\text{ex}}$ in ReS₂(L). The larger value of β in Eq. (2) indicates the temperature variations of the transition energies in tetragonal ReS₂ are nearly invariant, especially in the low temperature region (<180K) observed in Fig. 4. This analysis matches well with the experimental observations of the PTR spectra found in Fig. 3(b).

Table 1. Values of fitting parameters of Varshni equation and an expression proposed by O’Donnel & Chen which describe the temperature dependence of the transition energies for layer-type and tetragonal ReS₂ by PTR measurements. The values of fitting parameters for the temperature dependence of the indirect gap of layered ReS₂ are included for comparison.

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The temperature dependence of the interband transition energies can also be fitted (hollow-square lines) by an expression containing the Bose-Einstein occupation factor for phonon [24–25]:

where i=1 or 2, E_iB is the energy value at 0 K, a_iB represents the strength of average electron (exciton)-phonon interaction and Θ_iB corresponds to the average phonon temperature. The fitted values of E_iB, a_iB and Θ_iB for the layer-type and tetragonal ReS₂ are given in Table 2, and the corresponding values for CdSe [26], GaAs [27], and InP [28] are listed for comparison. The temperature variations of the interband transition energies are dominated by the lattice constant vibrations and the interactions with relevant acoustic and optical phonons. From Table 2 the obtained values of the electron-phonon interaction strength aB and average phonon temperature Θ_B for ReS₂(T) are statistically larger than the layered ReS₂ and the other II–VI and III–V compounds. This result is in good agreements with the higher value of the Debye temperature related constant β for ReS₂(T) found in Table 1.

The experimental values of Γ(T) [half width at half maximum (HWHM)] of the interband transitions as obtained from the lineshape fits for ReS₂(L) and ReS₂(T) are displayed in Fig. 5. Representative error bars are shown. As the temperature is raised, the linewidths for both ReS₂(L) and ReS₂(T) slowly increase from its zero-temperature value because of acoustical phonon scattering. Above about 77K the LO phonon contribution becomes important and eventually dominates the linewidth broadening of the crystals. The temperature dependence of the linewidth broadening of the semiconductors can be expressed as [24–25]

Table 2. Values of the Bose-Einstein type fitting parameters which describe the temperature dependence of the transition energies and band gaps of ReS₂(L), ReS₂(T), CdSe, GaAs, and InP.

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where i=1 or 2, the Γ_i0 parameter represents the broadening invoked from temperature independent mechanisms, such as impurity, dislocation, electron interaction and Auger processes, whereas Γ_iLO is caused by the electron (exciton)-LO phonon (Fröhlich) interaction. The quantity Γ_iLO represents the strength of the electron (exciton)-LO phonon coupling while Θ_iLO is the LO phonon temperature [24–25]. The solid curves in Fig. 5 are least-squares fits to Eq. (5), which made it possible to evaluate the values of Γ_i0, Γ_iLO and Θ_iLO for the interband transitions of ReS₂(L) and ReS₂(T). The obtained values of these quantities are list in Table 3 together with the numbers for CdSe [26], GaAs[29], and InP [30]. The value of Γ₀ for the interband transitions of E_d1 and E_d2 in tetragonal ReS₂ are much larger than those of the other single crystals of ReS₂(L), CdSe, GaAs, and InP. This result shows the crystalline quality of the layered ReS₂ is still better than the new-type tetragonal crystal. The worse quality of the tetragonal ReS₂ maybe coming from the higher defect densities and a little bromine containment involved inside the crystals. Perhaps the structural phase of the triclinic layer is still the most stabilized phase formed in the synthetic ReS₂ after crystallization. However, our PTR results of the layered and tetragonal ReS₂ just provide the useful information for further studies of the energy-band and atomic-bonding transformations inside the rhenium sulfide solids.

 

Fig. 5. Temperature dependent spectral linewidths of the interband transitions ${\mathrm{E}}_1^{\text{ex}}$, ${\mathrm{E}}_2^{\text{ex}}$, E_d1, and E_d2 for ReS₂ (L) and ReS₂ (T). Representative error bars are shown. The full curves are least-squares fits to Eq. (5).

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Table 3. Values of the parameters that describe the temperature dependence of the broadening function of the transition energies and band gaps of ReS₂(L), ReS₂(T), CdSe, GaAs, and InP.

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4. Conclusions

In conclusion, the tetragonal-type ReS₂ single crystals were, for the first time, grown by the CVT method using Br₂ as a transport agent. EPMA analysis shows slight bromine incorporation inside the crystal. Optical property of the structural change in ReS₂ is studied using temperature dependent PTR measurements in the temperature range between 25 and 300 K. PTR experiments were implemented with optical polarizations along and perpendicular to the crystals’ b-axis for both layer-type and tetragonal ReS₂. The PTR spectra of the tetragonal and layered ReS₂ present the same polarization dependent character with optical polarizations along and perpendicular to the crystals’ b-axis. This observation lends experimental evidence that the structural change in ReS₂ is mostly probable attributed to the atomic bonding deformation along b-axis, which is parallel to the Re₄ parallelogram consisted diamond chains. Energy red-shift behavior of the tetragonal ReS₂ reveals temperature insensitive at low temperatures from 25 to 180K. The transition origins of the E_d1 and E_d2 in ReS₂(T) are mostly probable originated from the largely Re-Re bonds. Temperature variations of the interband transition energies were analyzed by Varshni, O’Donnel and Chen, and Bose-Einstein type relations. The temperature dependence of the broadening function has also been interpreted in terms of a Bose-Einstein equation which contains the electron (exciton)-LO phonon coupling constant. The larger value of Γ₀ for tetragonal-type ReS₂ indicates the crystalline quality of the layered ReS₂ is much better than the new-type tetragonal solids. The worse quality of the tetragonal ReS2 may come from the higher defect densities and a little bromine containment involved inside the crystals.