Optical properties of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ layered mixed crystals $(0 \le x \le 1)$: Absorption edge and photoluminescence study at $T = 10\hbox { K}$

Abstract

Transmittance measurements of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ layered mixed crystals $(0 \le \, x \le 1)$ were performed in the 1.80–2.80 eV photon energy range at $T = 10 \hbox { K}$. Band-gap energies of the studied crystals were estimated by means of the derivative spectra of transmittance and photon energy dependence of absorption coefficient. The compositional dependence of direct band-gap energy at $T = 10\hbox { K}$ revealed that as sulphur (selenium) composition is increased (decreased) in the mixed crystals, the direct band-gap energy increases from 2.19 eV ($x = 0$) to 2.67 eV ($x = 1$). Photoluminescence spectra of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals were investigated in the photon energy region of 2.00–3.10 eV at $T = 10\hbox { K}$. The observed bands were assigned to the transitions of electrons from conduction band to the shallow acceptor levels in the band gap. The shift of the PL bands to higher energies with increasing sulphur content was revealed. In addition, the composition ratio of the mixed crystals was obtained from the energy-dispersive spectroscopy experiments.

1 Introduction

In recent years, semiconductors with layered structure have been widely explored in terms of the optic characteristics they exhibit [1, 2]. Structures of these types of semiconductors present anisotropy on account of different bonding of intra- and interlayers. Strong ionic–covalent bonding occurs within each layer packet while weak van der Waals bonding occurs between the packets. Thallium dichalcogenides with chemical formula $\hbox {TlBX}_{{2}}$ (where $\hbox {B} = \hbox {In}$ or Ga, $\hbox {X} = \hbox {S}$ or Se) are members of layered crystals and have been previously investigated with regard to optical, electrical and structural properties [3,4,5,6,7]. They can be good candidates for application in devices such as emission modulators, memory switching elements and nonlinear optical transducers [2]. Modification of the physical features of these crystals is possible and practicable due to the easy formation of mixed crystals on their own base.

The formation of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals exhibiting a continuum series with x varying between 0 and 1, and crystallising in two-dimensional layered structure, can be achieved from the composition of $\hbox {TlGaS}_{{2}}$ and $\hbox {TlGaSe}_{{2}}$. The variation of lattice parameters due to the influence of atom replacement, oscillator parameters and refractive index was accomplished and the results were reported in refs [8, 9]. The dependency of the band-gap energy on changing compositions of mixed crystals was studied at room temperature and it was shown that the energy band gap gradually alters from 1.97 to 2.45 eV [10]. Ellipsometry studies accomplished in the photon energy region of 1.2–6.2 eV resulted with the energies obtained due to interband transitions [11].

Fig. 1

Energy-dispersive spectroscopic analysis of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals.

Fig. 2

Transmission spectra of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals in the photon energy region 1.80–2.80 eV at $T = 10\hbox { K}$. Inset: Reflection spectra of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals.

Fig. 3

The first derivatives $\hbox {d}T/\hbox {d}(h\nu )$ of transmission spectra for $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals at $T = 10\hbox { K}$.

This study presents the results of transmission measurements at $T = 10\hbox { K}$ for various $x\,(0 \le x \le 1)$ in order to gain an insight to optical properties of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals. The band-gap energies for different compositions have been obtained from the transmittance spectra and the variations of band-gap energies by altering the amount of sulphur / selenide in the mixed crystals have been investigated. The crystals have been studied by virtue of photoluminescence (PL) measurements at $T = 10\hbox { K}$. This paper also gives information about the stoichiometric ratio of the constituted elements (Tl:Ga:Se:S) that are obtained from energy-dispersive spectroscopy.

2 Experimental details

Bridgman technique was used to grow $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ single crystals in our crystal growth laboratory (Middle East Technical University). The ingot was split into bulk crystals which possess mirror-like surfaces oriented perpendicular to the optical c-axis of the crystal. Thicknesses of the samples used for transmission experiments were in the range of $10{-}15\,\mu \hbox {m}$. Energy-dispersive spectroscopy measurements were performed to determine the stoichiometric proportion of the elements using scanning electron microscope having two equipments called ‘Noran System6 X-ray microanalysis system’ and ‘Semafore Digitizer’ which take part in the analysis of experimental data [12].

The hot probe method indicated that the crystals possess p-type conductivity. An Ar-ion laser (2.71 eV) was employed to excite the sample in order to carry out the PL experiment. Liquid nitrogen-cooled GaAs sensor detected the PL signal in the backscattering geometry. The signal was analysed using a Jobin–Yvon monochromator. Shimadzu 1201 model spectrometer was used for observing the transmittance spectra in the photon energy range of 1.80–2.80 eV. All the measurements were done at $T = 10\hbox { K}$ by placing the sample in a holder in the closed-cycle He gas cryostat (CTI-Cryogenics M-22). For the reflection experiments, we utilised the specular reflectance measurement attachment with $5^{\circ }$ incident angle. Technical reasons did not allow us a direct measurement of the reflectivity spectra at low temperatures. Therefore, we were able to register the reflectivity spectra of the studied samples only at room temperature. In order to calculate the absorption coefficient $\alpha$ at low temperatures, the spectral dependence of the room-temperature reflectivity was uniformly shifted in the energy according to the blue shift of the measured low-temperature transmission spectra.

3 Results and discussion

Figure 1 displays the EDS spectra of the investigated specimens of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals. The atomic composition ratios of the studied samples (Tl:Ga:S:Se) were found to be 25.4:25.2:49.4 ($x = 0$), 25.8:26.0:12.2:36.0 ($x = 0.25$), 25.7:25.9:24.1:24.3 ($x = 0.50$), 26.0:25.8:35.9:12.3 ($x = 0.75$) and 25.4:25.6:49.0 ($x = 1$). It is evident from figure 1 that intensity of the peak at 1.475 keV related to selenium decreases as the Se composition decreases in the $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ crystals.

Figure 2 displays the transmission spectra of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals in the photon energy range 1.80–2.80 eV at $T = 10\hbox { K}$. These spectra can be used to get the absorption edge of the crystal by employing different analyses methods. One of these methods, derivative spectrophotometry, has been an effective technique for three decades [13]. In the present paper, we have used the derivatives of transmittance curves to determine the band-gap energies. Figure 3 demonstrates the first derivatives of each spectrum for $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals. The photon energy dependence of $\hbox {d}T/\hbox {d}(h\nu )$ presents peaks at energies corresponding to band-gap energies. The obtained energy values of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ crystals from each spectrum are equal 2.19, 2.35, 2.47, 2.57 and 2.67 eV for compositions $x = 0, 0.25, 0.50, 0.75$ and 1, respectively. These values imply that band-gap energy shows a rising behaviour with increase of sulphur composition. This behaviour of band-gap energies is in agreement with the reported observation that band gap $E_{\mathrm{g}}$ increases with elevating concentration of the smaller anion [14]. It will be worthwhile to compare the determined energies with previously reported values. The direct band-gap energies of $\hbox {TlGaSe}_{{2}}$ and $\hbox {TlGaS}_{2}$ crystals at $T = 10\hbox { K}$ were reported previously as 2.184 and 2.664 eV, respectively [15,16,17]. These energy values show good consistency with those obtained from the derivative of transmittance spectra. Moreover, taking into account the type of band-gap energies reported in the referenced papers, $E_{\mathrm{g}}$ values achieved from our analyses can be strongly associated with direct transition structures.

Furthermore, the analysis of the dependence of absorption coefficient $\alpha$ on photon energy in the high absorption regions was carried out to obtain detailed information about the energy band gaps. The absorption coefficient $\alpha$ was calculated using the following relation [18]:

$$\begin{aligned} \alpha = \frac{1}{d} \ln \left\{ {\frac{( 1-R)^{2} + \left[ {( 1-R)^{4} + 4R^{2}T^{2}} \right] ^{ 1/2}}{2T} } \right\} , \end{aligned}$$

(1)

where d is the sample thickness.

The absorption coefficient $\alpha$ and photon energy h$\nu$ can be related by [18]

$$\begin{aligned} \alpha (h\nu )=A (h\nu -E_{\mathrm{g}} )^{\mathrm {p}}. \end{aligned}$$

In this equation, A is a constant that depends on the transition probability and p is an index that characterises the optical absorption process and it is theoretically equal to 2 and 1 / 2 for indirect and direct allowed transitions, respectively. From the analysis of the experimental data, it was revealed that the absorption coefficient $\alpha$ is proportional to ($h\nu -E_{\mathrm{g}})^{1/2 }$ (see figure 4). Using the extrapolations of the straight lines down to ($\alpha {h}\nu )^{2} = 0$, the values of the direct band-gap energies were determined for the $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals. These values are in good agreement with those established from the application of the first derivative of transmittance.

At this point it will be worthwhile to make some inferences about the results obtained after taking the previously published papers into consideration. The theoretical studies on the electronic band structure of $\hbox {TlGaSe}_{2}$ crystals have been accomplished using the pseudopotential method [19], the screened-exchange local density approximation [20] and the linear muffin-tin orbital method [21]. The calculations presented in three different papers predict the direct band-gaps energies as 2.1 eV [19], 1.85 eV [20] and 1.26 eV [21], respectively. The value predicted in the third paper is incomparably less than our experimentally determined energy band gap (2.19 eV), as well as that reported in [20] (2.11 eV). To our knowledge, there is only one paper in literature concerning the band structure of $\hbox {TlGaS}_{2}$ crystal [21]. Electronic band structure calculation of this crystal using the linear muffin-tin orbital method predicted the direct energy band gap as 1.70 eV. This value is significantly different from our experimentally determined value of 2.67 eV. The above-mentioned discrepancies make it impossible to figure out the meaning of the structures determined in the present study from the derivative spectra of transmittance and photon energy dependence of absorption coefficient in $\hbox {TlGaSe}_{{2}}$ and $\hbox {TlGaS}_{2}$ crystals.

Fig. 4

The dependence of $(\alpha {h}{\upnu })^{2}$ on photon energy for $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals at $T = 10\hbox { K}$.

Fig. 5

The dependencies of direct band-gap energies on the composition of $\hbox {TlGa}_{{x}}\hbox {In}_{1-x}\hbox {S}_{{2}}$, $\hbox {TlIn}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ and $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals at $T = 10\hbox { K}$.

Fig. 6

Photoluminescence spectra of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals in the photon energy region 2.00–3.10 eV at $T = 10\hbox { K}$.

Figure 5 presents the variations of direct $(E_{\mathrm{gd}})$ energy band gaps on composition of $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}\, (0 \le x \le 1)$ mixed crystals. As seen from this figure, the energy band gaps increase with the increasing sulphur atom content in the $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ mixed crystals. In addition, we also introduce in figure 5 the composition dependencies of the direct band-gap energies reported previously for isostructural mixed crystals $\hbox {TlIn}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ and $\hbox {TlGa}_{{x}}\hbox {In}_{1-x}\hbox {S}_{{2}}$ in which the anion and cation replacement respectively takes place [22]. It is seen from the figure that when bigger Se atoms are substituted with smaller sulphur atoms, the energy band gap increases $(\hbox {TlIn}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2})$, while the replacement of smaller atoms of gallium by bigger indium atoms causes a decrease in energy band gap $(\hbox {TlGa}_{{x}}\hbox {In}_{1-x}\hbox {S}_{2})$.

PL spectroscopy is one of the practical and reliable methods for defect characterisation and it gives information about the specific emission of the materials from the transitions between the energy levels in the band gap of the material. The PL spectra detected for $\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$ layered mixed crystals in the photon energy range between 2.00 and 3.10 eV at excitation density of $15.2 \hbox {W}/\hbox {cm}^{2}$ at $T = 10\hbox { K}$ are shown in figure 6. The emission bands with maxima at 2.16, 2.32, 2.44, 2.54 and 2.64 eV for $x = 0, 0.25, 0.50, 0.75$ and 1, respectively, can be seen from the spectra. As seen, these PL bands exhibit asymmetrical Gaussian line shape. The half-widths at low- and high-energy sides are 38 and 51, 146 and 152, 45 and 50, 92 and 97, 146 and 168 meV for $x = 0, 0.25, 0.50, 0.75$ and 1, respectively. The appearing PL bands were provisionally thought to be raised from the recombination of electrons from the conduction band with holes occupying the shallow acceptor levels having an energy of $E_{\mathrm{a}}\approx 30\hbox { meV}$. The energy level is ascribed to the formation of anion vacancies which can be raised due the possible stacking faults existing between the layers bonded with weak van der Waals forces [23].

4 Conclusion

Transmittance and photoluminescence measurements were performed on $\hbox {TlGa}(\hbox {S}_{{{x}}}\hbox {Se}_{1-{x}})_{2}$ crystals $(0 \le x \le 1)$ grown by Bridgman method in the 1.80–2.80 and 2.00–3.10 eV photon energy regions, respectively, for compositions of $x = 0, 0.25, 0.5, 0.75$ and 1.0 at $T = 10\hbox { K}$. Derivative analyses of transmittance curves and photon energy dependence of absorption coefficient of crystals demonstrated that band-gap energy increases from 2.19 eV ($x = 0$) to 2.67 eV ($x = 1$) when selenium is substituted by sulphur. The observed bands in PL spectra tentatively were attributed to the transition of electrons from conduction band to shallow acceptor levels. The shift of the PL bands to higher energies with rising sulphur content was revealed. Furthermore, the composition ratio of the mixed crystals was determined using the energy-dispersive spectroscopy.