Optoelectronic and thermoelectric properties of Sb₂S₃ under hydrostatic pressure for energy conversion

Antimony trisulfide (Sb₂S₃) is a V–VI semiconductor compound. It is a layered structure composed of [Sb₄S₆]_n atomic chains with van der Waals interaction.¹ Among the various metal-sulfides, Sb₂S₃ has attracted much interest first because of its characteristics such as low-cost, abundance in nature, non-toxicity, low melting point,^2–4 high absorption coefficient,⁵ sufficient bandgap, and other good optical^6,7 and thermoelectrical properties⁸ and second due to the wide range of applications in optoelectronics, microwave devices,⁹ switching,¹⁰ batteries,¹¹ and photovoltaic devices such as solar cells.¹² Annealed Sb₂S₃ thin films are promising materials for developing solar cell technologies.¹³ It has been shown that n-Sb₂S₃/p-Si heterojunction solar cells with improved photovoltaic properties have been fabricated through low-cost techniques.¹⁴ One density functional theory (DFT) calculation has proved that the two-step doping strategy using O-dopants and introducing other p-type dopants increases the efficiency of Sb₂S₃-based solar cells.¹⁵ 

Sb₂S₃ compounds have been fabricated by various techniques, such as chemical deposition and thermal evaporation.^14,16–20 Because of the size and the nature of the bandgap, the electronic band structure of Sb₂S₃ has remained controversial for decades. Theoretical and experimental studies have presented the direct and indirect bandgap of Sb₂S₃ in the range of 1.18–2.24 eV.¹⁵ Sb₂S₃ nanoribbons were successfully synthesized, and the optical absorption experiment revealed that Sb₂S₃ nanoribbons have a bandgap of about 1.15.²¹ 

The electrical and optical investigations have demonstrated that the indirect bandgap energy values of Sb₂S₃ thin film increase with increasing thickness²² and the presence of Ni-doped atoms decreases the bandgap.⁶ It has also been shown that Ni-doped-Sb₂S₃ leads to an increased optical absorption coefficient in the visible region, and it is introduced as a promising candidate for optoelectronic applications. It has been shown that the spin–orbit interaction has no effect on the electronic properties.⁷ Studies have shown that the thermoelectric (TE) performance of n-type Sb₂S₃ is better than that of the p-type and the optimal doping concentration is in the order of 10²¹ cm⁻³ for all temperatures.^8,23 Furthermore, it has become clear that the electronic properties are anisotropic and adding Be atoms to Sb₂S₃ decreases the Seebeck coefficient to 595 (−635) µV/K for p- (n-)type carriers at 300 K temperature. Bi₂S₃ is another layered semiconductor with a direct bandgap (E_g ≈ 1.3 eV), which is isostructural to Sb₂S₃ with an orthorhombic crystal structure. Bi₂S₃ has been proposed as a good thermoelectric (TE) material with a high Seebeck coefficient (about 500 µV/K) and low thermal conductivity (<1 W/mK). We have also found that optimizing the ball-milling process enhances the thermoelectric properties of polycrystalline Bi₂S₃.²⁴ The experimental investigation of the thermoelectric properties of (Bi_1-xSb_x)₂S₃ has also shown that for x = 0, the Seebeck coefficient is |s| = 180 µV/K and when increasing the concentration of Sb atoms to x = 0.6 and 0.8, the Seebeck coefficient becomes larger, about |s| = 230 and 460 µV/K.²⁵ 

Pressure tunes the bandgap and changes the optical properties, and it is able to balance the TE performance such as power factor and figure of merit.^24,26–28 The experimental and theoretical investigation shows that Sb₂S₃ has a stable structure at pressures up to 20 GPa and no first-order phase transition has been observed.^4,29–31

So far, numerous studies have been carried out on synthesis of the electronic, optic, and thermoelectric properties and the applications of Sb₂S₃.^14–20 To complete these known aspects, we have tried to investigate the electronic, optic, and thermoelectric of Sb₂S₃ under pressure. We also investigated the effect of different types and concentrations of doping (from 10¹⁸ to 10²¹ cm⁻³) and temperature (from 50 to 800 K) on thermoelectric properties. Our calculations show that applied pressure increases the high absorption of Sb₂S₃ in the extreme ultraviolet region. In addition, the bipolar effect is observable on the Seebeck coefficient curve at high pressures for the 10¹⁸ cm⁻³ doping concertation.

This paper is arranged as follows: The computational details are reviewed in Sec. II. In Sec. III, the obtained results, such as structural properties, band structures, electron density (Subsection III A), optical properties (Subsection III B), and thermoelectric results (Subsection III C), are discussed. Finally, a summary of the results is presented.

The theoretical investigations of the crystal structure and optoelectronic and thermoelectric properties of Sb₂S₃ under hydrostatic pressure have been performed using the WIEN2k package and the full-potential linearized augmented plane wave method (FP-LAPW).³² The Generalized Gradient Approximation by Perdew–Burke–Ernzerhof (PBE-GGA) functional³³ is used to calculate the exchange-correlation potential for all the steps. The basis function is expanded to K_max × R_MT = 7.0, where K_max is the plane wave cut-off and R_MT is the smallest atomic muffin tin sphere radius in the unit cell. The magnitude of the largest vector in the Fourier expansion of charge density (G_max) is equal to 12 bohrs⁻¹. The number of k-points for the integration in the first Brillouin zone (BZ) is 100, 200, and 2000. The self-consistent calculations are converged when the variation in the total energy is less than 0.0001 Ry. The thermoelectric features are calculated via BoltzTraP,³⁴ which is supported by the WIEN2k package. The thermoelectric calculations are explained in detail in Subsection III C.

Under ambient conditions, the stable form of Sb₂S₃ at room temperature is the orthorhombic structure with a Pnma space group.^35,36 The primitive unit cell contains four molecules (Z = 4). Sb₂S₃ has two and three non-equivalent atomic positions for Sb [Sb (1) and Sb (2)] and S [S (1), S (2), and S (3)]. The experimental lattice parameters of Sb₂S₃ are a = 11.3045 Å, b = 3.8411 Å, c = 11.2386 Å, and α = β = γ = 90° at ambient pressure.³¹ The applied pressure changes these lattice parameters. We have extracted the values of these lattice parameters under pressure (up to 20.04 GPa) using the experimental results.³⁷ The optimized total energy of Sb₂S₃ in terms of (% c/a) with the experimental lattice parameters at different pressures was used to obtain the theoretical lattice parameters.

As shown in Fig. 1, the optimized and experimental lattice parameters decrease with increasing pressure. Indeed, we can observe a linear decrease up to 4.82 GPa and an increase at a pressure of 6.34 GPa; then there is another decrease. The optimized lattice parameters at different pressures are in good agreement with the experimental results.^37,38

Based on the optimized lattice parameters, we have investigated the band structures of Sb₂S₃ under different pressures. The band structure of Sb₂S₃ under pressures of 0.00, 3.29, 4.82, 6.34, 11.79, and 20.04 GPa is shown in Fig. 2.

The calculated bandgap of Sb₂S₃ is given in Table I. It is evident that from 0.00 to 4.82 GPa, the valence band maximum (VBM) and the conduction band minimum (CBM) are located at the Γ point (direct bandgap) while at pressures of 6.34–11.79 GPa, the VBM is shifted to between R and the Γ point.

At pressures more than 13.22 GPa, both VBM and CBM are shifted between R and the Γ point. With increasing pressure, the CBM also is moved to the lower energy, so the bandgap of Sb₂S₃ becomes small. The variations in the bandgap in terms of pressures are presented in Fig. 3.

Two discontinuities are observed: the first one is between the pressures of 4.82 and 6.34 GPa, and the second one is between the pressures of 11.79 and 13.22 GPa. These two discontinuities confirm the changes in the VBM and CBM under pressure and are in good agreement with previous observations.⁴ The calculated bandgap at ambient pressure is 1.44 eV, which is low compared to the experimental value (1.73 eV). However, the difference between the estimated bandgap and the experimentally obtained bandgap is 0.29 eV. This underestimation (between DFT and the experiment) can be seen in most of the DFT calculations, and it is due to the calculation of the exchange-correlation potential by the GGA.³⁹ 

Figure 4 shows the total and partial density of state (DOS) in terms of energy at ambient pressure. As can be observed, the total DOS confirms the semiconductor nature of Sb₂S₃ with a bandgap of 1.4 eV. The value of the bandgap at 0.00 GPa is in good agreement with other reported results.^4,40 In the partial DOS, the s orbitals of S and Sb atoms are considered important in the energy range from −14 to −11.7 eV and from −61 to −9 eV, respectively. At the energy of valence bands of −5 to 0 eV, the p orbitals of S (S-p) and Sb (Sb-p) atoms play a main role so that the contribution of S-p is more than that of Sb-p. This observation is reversed at the conduction energy levels, so the contribution of Sb-p becomes more than that of S-p.

Considering the DOS and large hybridization of S and Sb atoms at the valence and conduction electron energy levels, the Sb–S bond is a strong covalent bond.¹⁵ The variations in the total DOS under applied pressures near the Fermi level (at zero energy) are illustrated in Fig. 5. As seen with increasing pressure, the DOS of conduction electrons shifts to a lower energy while the variations in the valence electron DOS are negligible.

Therefore, the increase in pressure decreases the bandgap, and it also predicts the redshift on the absorption spectrum. As mentioned before, an anomaly in the bandgap between pressures 4.82 and 6.34 GPa is observed, which is due to the change in its nature. The result points to the isostructural electronic phase transition.^4,37

The real part of the dielectric function shows the electrical polarization of the compound. The imaginary part, which is the sum of all inter-transitions between electronically occupied and unoccupied states, shows a loss.

The real part of the dielectric function at zero energy is called the static dielectric constant ε(0). The calculated static dielectric constants are given in Table I in the three directions. As shown in Table I, the static dielectric constant increases by increasing the pressure. The static dielectric constants at ambient pressure are 11.34, 16.32, and 15.39 in the x, y, and z directions, respectively. These values reach 13.6, 22.73, and 19.76 at 20.04 GPa. The calculated dielectric constants at ambient pressure are also in close agreement with those of the experiment.⁴³ 

The real part of the dielectric function is related to the dielectric polarization. As shown in Fig. 6, the calculated spectra show that there is a maximum value at an energy of 2 eV. It means that the light passing through the crystal with the energy in the visible range (1.75–3.11 eV) becomes strongly polarized, and this polarization increases with increasing the pressure, which leads to lattice compression. The lattice parameter in the y direction is smaller than that in the x and z directions. Hence, it can be concluded that the maximum dielectric constant and polarization exist in the y direction. The maximum polarization value in the y direction is 29.27, which reaches 33.14 by increasing the pressure.

The real dielectric function has negative values after energy values of 5, 3.12, and 3.52 eV in the x, y, and z directions, respectively. At these energy values, Sb₂S₃ behaves as a metal and reflects the electromagnetic wave completely.

The pressure moves the negative ε₁ to higher energy (5.92, 4.12, and 4.50 eV in the x, y, and z directions, respectively). Increasing the pressure widens the energy range for negative values of ε₁, and in this energy range, the real dielectric part always remains negative. This feature makes Sb₂S₃ suitable for supercooling and new photonic applications.^44,45

The peaks of the imaginary dielectric function imply transitions between the occupied valence bands and unoccupied conduction bands and present loss. For Sb₂S₃, energies of 3.41, 2.73, and 3.2 eV in the x, y, and z-directions, respectively, show the maximum peaks of the imaginary dielectric function, which indicates maximum loss. The applied pressure shifts the energy of maximum loss to higher energy in the x direction while decreasing the energy in the y and z directions.

By comparing the dielectric spectra in the three different directions, it can be seen that Sb₂S₃ has an anisotropic optical behavior. In fact, the difference in the charge density distribution along the different directions leads to different dielectric functions, resulting in anisotropic optical and photoelectric properties. The anisotropy in the dielectric function of Sb₂S₃ exhibits ferroelectric phase transition and piezoelectric behavior of this material at the nanoscale.⁴⁶ It is found that Sb₂S₃ as an anisotropic semiconductor with a wide optical response to the incident light can be used in polarized photodetection.⁴⁷ 

Figure 7 shows the absorption coefficients in terms of wavelength. The maximum absorption coefficient is the wavelength range of 100–125 nm and with increasing wavelength, the absorption decreases. As seen, the absorption coefficient of Sb₂S₃ is nonzero in the visible region, and it has a maximum value in the y direction.

Applying the pressure increases the absorption in the extreme ultraviolet region while at wavelengths of 250–300 nm, the pressure causes the absorption to decrease. Next, in the visible region, the pressure increases the absorption slowly. In conclusion, the high absorption of Sb₂S₃ is 180.56, 159.29, and 173.00 (10⁴ cm⁻¹), and the pressure increases them to values of 216.242, 195.81, and 192.48 (10⁴ cm⁻¹), respectively, in the wavelength range of 100–125 nm in the x, y, and z directions.

The refractive index is shown in Fig. 8. The static refractive indices are given in Table I. These values, under ambient pressure, are 3.37, 4.04, and 3.92 in the x, y, and z directions, which are in agreement with other studies.^5–7,22 As seen, the effect of applied pressure is the increase in static refractive indices. The maximum scattering of light is observed in the y direction with an energy of 2.2 eV. After energy values of 10, 9, and 10.5 eV in the x, y, and z directions, refractive values become less than 1, and the superluminal effect occurs.

Figure 9 presents the excitation coefficient of Sb₂S₃ in terms of energy that determine the light loss inside the compound, and the peaks correspond to the transition between the occupied and unoccupied electron bands. The extinction peaks in the x, y and z directions in the energy range of 3–4 eV decrease with increasing pressure.

Another optical property of Sb₂S₃ is reflectivity, which is shown in Fig. 10. Our results present that the reflectivity of Sb₂S₃ in the visible region (gray area) is from 37% to 57% and it increased slightly with pressure.

It was also found that Sb₂S₃ has maximum reflectivity of about 60% at an energy of 3.90 eV (ultraviolet region) in the z direction and under ambient pressure. Above energies of 5 eV, a reflectivity increase can be observed with increasing pressure. Our results under ambient pressure are in good agreement with those of other studies.^6,22

Plasmon energies can be determined with the energy of remarkable peaks, as illustrated in Fig. 11. Under ambient pressure, the Eloss peaks are located at energies of 18.97, 19.44, and 19.35 eV in the x, y, and z directions, respectively. Our results show that the pressure shifts these peaks to higher energy and causes the loss intensity to increase. The plasmon energies are 21.29, 21.15, and 20.80 eV at 20.04 GPa.

To the best of the researchers’ knowledge, the thermoelectric properties of Sb₂S₃, under hydrostatic pressure, have not been investigated yet. The results are obtained for different doping levels of 1 × 10¹⁸, 1 × 10¹⁹, 1 × 10²⁰, and 1 × 10²¹ per cm⁻³, from 50 to 800 K temperatures, and under applied different pressures from 0 to 20.4 GPa. A dense k-mesh of 22 000 k-points has been used to calculate the transport properties.

First, the temperature dependence of the Seebeck coefficient under applied pressures at different doping levels has been investigated. To simplify, Fig. 12 shows the temperature dependence of the Seebeck coefficient under selected applied pressures (0.00, 7.58, 13.22, and 20.04 GPa) and doping levels of 10¹⁸ and 10²¹ per cm⁻³. The positive (negative) values of the Seebeck coefficient indicate the p- (n-)type carriers in the Sb₂S₃ compound. With respect to vertical axes, it is clear that the increasing the doping concentrations leads to a reduction in the Seebeck coefficient.

The Seebeck coefficients increase with increasing temperature except for the pressure range of 13.22–20.04 GPa at a doping level of 10¹⁸ cm⁻³ and at 20.04 GPa at a doping level of 10¹⁹ cm⁻³. Indeed, the Seebeck coefficients increase with increasing temperature, and then there is a remarkable decrease. In other words, the bipolar effect occurs at high pressures and low doping concentrations. The bipolar effect that commonly occurs in narrow bandgap semiconductors indicates the effect of both carrier types on electrical transport.^48–51 The result of the bipolar effect is the increase in thermal conductivity in comparison to the case where a type of carrier plays a role in transport.

It was found that the applied pressure generally decreases the Seebeck coefficient at different doping concentrations. In the temperature range of 50–250 K and at a doping level of 10²¹ cm⁻³, the Seebeck coefficient of n-type carriers first decreases with increasing pressure up to 4 GPa and then increases. At ambient pressure and a temperature of 300 K, the Seebeck coefficient is 612.6 (−536.09), 414.67 (−338.27), 221.20 (−146.73), and 86.82 (−32.13) µV/K for p- (n-)type carriers at doping levels from 10¹⁸ to 10²¹ cm⁻³, respectively. These values are comparable with the experimental values of Sb₂S₃ thin film⁵² and other compounds similar to stibnite, such as Sb₂Se₃ (about 580 µV/K with a direct bandgap of 1.43 eV),⁵³ Bi₂Se₃ (−100 µV/K topological insulator),^54,55 In₂S₃ (200–400 µV/K with an indirect bandgap of about 1.04 eV),⁵² and Bi₂S₃ (about 500 µV/K with a direct bandgap of 1.3 eV).²⁴ 

Figure 13 shows the variations in electrical conductivity with temperature and pressure at different doping levels. In most curves at different doping levels, the variation in electrical conductivity is approximately flat, which means that the conductivity is independent of temperature at ambient pressure.

The electrical conductivity decreases slowly because of the temperature at high pressure, except that the increase in temperature leads to an exponential increase in the conductivity at a low doping level of 10¹⁸ cm⁻³. As mentioned before, the bipolar effect results in the increase in electrical conductivity at 10¹⁸ cm⁻³ doping concentration, and increasing doping concentration increases the electrical conductivity. For all pressures, n-type doping of Sb₂S₃ has greater electronic conductivity than p-type doping. The values of p- (n-)type electrical conductivity at 0.00 GPa and 300 K are 2.21 × 10¹⁶ (6.23 × 10¹⁶), 2.20 × 10¹⁷ (6.22 × 10¹⁷), 2.12 × 10¹⁸ (6.07 × 10¹⁸), and 1.63 × 10¹⁹ (3.96 × 10¹⁹) for 10¹⁸ to 10²¹ cm⁻³, respectively.

It was found that the thermal conductivity increases with increasing temperature, doping level, and pressure (Fig. 14) while at a doping level of 10¹⁸ cm⁻³, the increase in thermal conductivity at high temperature and high pressure is exponential.

The figure of merit (ZT) in terms of temperature for the p- (n-)type carriers at doping levels of 10¹⁸ and 10²¹ under selected pressures is shown in Fig. 15. As seen, the value of ZT at the same temperature decreases with increasing doping levels, and the increasing temperature leads to continuously increasing ZT at the high doping level. Appling pressure at all doping levels also decreases ZT.

At a doping level of 10¹⁸ cm⁻³, ZT increases up to 100 K, then it remains constant, and finally, at high temperature (about 800 K), it undergoes a decrease. The increase in pressure higher than 13.22 GPa reduces ZT at temperatures of 700, 550, and 500 K. The bipolar effect occurs at temperatures lower than 800 K for high pressures while it occurs at high temperatures (higher than 800 K) at ambient pressure.

An interesting point is that at doping levels of 10¹⁸ and 10¹⁹ cm⁻³, the high value of ZT is independent of temperature and pressure in an interval of temperature. With increasing pressure, this interval of temperature becomes smaller than before. The values of p- (n-)type carrier ZT are 0.95 (0.92), and 0.90 (0.85) at 10¹⁸ and 10¹⁹ cm⁻³, respectively. As an applicable point, at these interval temperatures, the uncontrolled and unwanted laboratory conditions such as environmental pressure do not affect the thermoelectric performance of Sb₂S₃.

In the present study, the optoelectronic and thermoelectric properties of Sb₂S₃ were studied using DFT based on the FP-LAPW and the PBE-GGA functional as the exchange-correlation potential using the WIEN2k package. The results demonstrated that increasing the pressure from 0.00 to 20.4 GPa changes the calculated bandgap from 1.44 to 0.84 eV. Between pressures of 4.82–6.3 GPa, there was a discontinuity due to the isostructural electronic phase transition. Hence, we can tune the bandgap state (direct vs indirect) and gap energy using the applied pressure.

The results also illustrated that pressure increases the maximum polarization inside the compound. A large absorption coefficient in the order of 10⁴ cm⁻¹ is one of the most interesting properties of Sb₂S₃. Applying pressure results in a red shift of the optical absorption edge and increases the absorption coefficient. By applying pressure, the maximum reflectivity is about 60% at an energy of 3.90 eV (ultraviolet region), and the intensity of reflectivity is increased at high energy (energy >5 eV). The applied pressure also increases the static dielectric constant and static refractive index.

Under ambient conditions and at a doping level of 10¹⁸ cm⁻³, the obtained Seebeck coefficient was 612.6 (−536.09) µV/K, for p- (n-)type carriers. These values are comparable with the experimental values of Sb₂S₃ and other compounds similar to stibnite. By increasing the doping concentration and pressure, the Seebeck coefficients decrease. It was found that the bipolar effect occurs at low doping concentrations and high pressure. The variation in electrical conductivity is approximately independent of temperature at ambient pressure. At high pressure and 10¹⁸ cm⁻³ doping concentration, the bipolar effect leads to the increase in electrical conductivity. It was found that the values of electrical conductivity for n-type doping carriers were greater than those of the p-type doping carriers. The results also show that the thermal conductivity increases with increasing temperature, doping level, and pressure. The maximum value of ZT is 0.95 (0.92) for p- (n-)type carriers at 10¹⁸ cm⁻³ and under ambient conditions. As an interesting point, it was found that the high value of ZT is independent of temperature and pressure at doping levels of 10¹⁸ and 10¹⁹ cm⁻³ and in the mid-range of temperature.

The authors are grateful to P. Blaha (Vienna University of Technology, Austria) for his technical assistance in using the WIEN2k code.

The authors have no conflicts to disclose.

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by M.A., H.A.R.A., and E.G.Ö. The first draft of the manuscript was written by M.A., and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Maliheh Azadparvar: Conceptualization (equal); Software (equal); Writing – original draft (equal). H. A. Rahnamaye Aliabad: Conceptualization (equal); Supervision (equal); Writing – original draft (equal). Evren Görkem Özdemir: Conceptualization (equal); Investigation (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.