First-Principles Insights into the Structural and Physical Properties of AgSbS₂

1 Introduction

AgSbS2 is a ternary p-type semiconductor inorganic photovoltaic material belonging to the I-V-VI2 group. Its unique layered structure endows optoelectronic devices with excellent absorption performance [1,2]. Abundant, environmentally friendly and non-toxic, AgSbS2 holds great potential for enhancing visible light absorption and improving the photoelectric conversion efficiency of photovoltaic devices [3]. AgSbS2 exhibits outstanding photoelectric properties. Firstly, making it suitable for solar cell fabrication [4]. Moreover, the bandgap can be adjusted through elemental doping and selenization to optimize the performance of thin films and corresponding devices. Secondly, AgSbS2 has a high absorption coefficient, enabling it to absorb a large amount of sunlight in thin absorption layers, thereby reducing device fabrication costs, improving material utilization, and promoting commercialization [5]. As early as 1995, Ibrahim’s research group [6] conducted preliminary studies on AgSbS2, preparing AgSbS2 thin films and investigating the structure, and physical properties of AgSbS2 thin films. Choi et al. studied the surface ligand interactions of AgSbS2 quantum dots synthesized with 1-dodecanethiol used as a stabilizer [7]. Recently, Dutkova et al. have successfully synthesized a ternary AgSbS2 semiconductor through a one-step mechanical chemical synthesis method using elemental silver, antimony and sulfur as raw materials, after grinding [8]. In addition, Oubakalla et al. reported the fabrication of a novel AgSbS2 electrode via electrodeposition onto fluorine-doped tin oxide (FTO) substrates and systematically compared its supercapacitive performance in lithium-containing aqueous versus organic electrolytes [9]. Mohanty et al. report the preparation and systematic investigation of structural, optical, and compositional properties of Ag25−xS35Se40Sbx (x = 0, 5, 10, 15, 20 at%) quaternary chalcogenide thin films [10]. On the theoretical side, Hosni et al. [11] conducted a detailed study on the electronic properties of AgSbS2 based on density functional theory calculations. Although experiments and some theories have been conducted on AgSbS2, the optical and thermodynamic properties of the system have not been reported. This paper has conducted a detailed study on the optical and thermodynamic properties of the material, hoping that our research can provide some assistance for experimental studies.

2 Computational Methods

Geometric optimization calculations were performed in the CASTEP code [12,13,14,15]. For the geometric structure optimization of AgSbS2, the ultrasoft pseudopotential was selected, the GGA-PBE exchange-correlation energy was adopted [16,17], and the cutoff energy was set to 400 eV. After comprehensive consideration, the k-point grid was set to 5 × 5 × 5. The valence electron configurations of the atoms were chosen as follows: Ag: 4d105s1, Sb: 5s25p3, and S: 3s23p4.

3 Results and Discussion

3.1 Structural Optimization

AgSbS2 belong to the pyrargyrite type, crystallizing in the monoclinic system with a point group of 2/m and a space group of C2/c (Fig. 1). A crystal model was constructed, with lattice constants set to a = 12.72 Å, b = 4.27 Å, and c = 13.19 Å [18]. In the crystal, the model contains 32 atoms, Ag atoms occupy 4e and 4b Wyckoff positions, whereas Sb and S occupy 8f Wyckoff position. The structural parameters of AgSbS2 are listed in Table 1. The optimized result we obtained is consistent with the other values [18,19], indicating that our calculation is reliable.

Figure 1: Unit cell of AgSbS₂.

3.2 Electronic Structure

Fig. 2 shows the energy band structure of AgSbS2, with a band gap (Eg) of 1.456 eV. From the energy band diagram, the valence band maximum (VBM) and the conduction band minimum (CBM) are not on the same line, indicating that AgSbS2 is a direct bandgap semiconductor.

Figure 2: Band structure of AgSbS₂.

Fig. 3 presents the density of states of AgSbS2 obtained using the GGA method. Analysis of the data in Fig. 3 reveals the detailed characteristics of the valence band structure of AgSbS2, which exhibits a distinct layered distribution consisting of three band components. The lower valence band shows a significant peak in the electron density of states at a photon energy of −12.1 eV, indicating that S-3s and Sb-5p contribute to the total density of states in the energy range of −14.2 eV to −11.2 eV, with hybridization of the Sb-5s orbital, resulting in obvious electron localization. The middle valence band has a distribution peak at −8.75 eV, indicating that Sb-5s and S-3p dominate in the range of −9.45 eV to −6.88 eV, with a small contribution from the S-3s orbital, further enhancing electron localization. The upper valence band spans the energy −5.63 eV to 0 eV, with two peaks at −2.91 eV and −0.756 eV. The former is formed by the combined action of the Ag-4d, S-3p, and Sb-5p, accompanied by the participation of a small amount of the Sb-5s orbital; the latter is formed by the combined action of the S-3p and Sb-5p orbitals, with hybridization of the Ag-4d and Sb-5s. As shown in Fig. 3, the VBM is mainly composed of S-3p and Ag-4d, while the CBM mainly relies on the Sb-5p orbital, with a small contribution from the Ag-4d orbital.

Figure 3: Density of states of AgSbS₂.

3.3 Elastic Properties

Elastic constants (Cij) characterize a crystal’s resistance to elastic deformation, reflect interatomic bond stiffness and lattice mechanical stability, and serve as the basis for calculating bulk modulus, shear modulus and other mechanical parameters, as well as for judging mechanical anisotropy and structural stability. The data in Table 2 indicates that for the monoclinic structure, AgSbS2 possess thirteen independent elastic constants (Cij). To assess its mechanical stability, the Cij values of AgSbS2 were determined according to Ref. [20]. The results (Table 2) fulfilled all necessary stability criteria, confirming that the material is mechanically stable.

In Table 3, the bulk modulus B and shear modulus G of AgSbS2 gradually increases with increasing pressure. The Poisson’s ratio v can determine the material’s resistance to shear deformation; typically, a Poisson’s ratio between −1 and 0.5 indicates relative stability against shear deformation. The Poisson’s ratio of AgSbS2 ranges from 0.2 to 0.4, indicating that the higher the pressure, the better the plasticity. The ductility of a material is represented by B/G. Pugh’s B/G criterion [21] is a widely used method to evaluate material ductility: A material is deemed ductile if the B/G ratio surpasses 1.75; otherwise, it exhibits brittle behavior. As shown in the table, the B/G value of AgSbS2 is much greater than 1.75, confirming that the crystal has excellent ductility and is suitable for mechanical processing. This ductility provides strong support for the application of AgSbS2 in precision manufacturing.

3.4 Optical Properties

The optical properties of the crystal are determined by the dielectric function ε(ω) given by ε(ω) = ε1(ω) + iε2(ω). The imaginary part of ε2(ω) depends on the joint density of states and the momentum matrix elements. The real part ε1(ω) was obtained from ε2(ω) by the Kramers-Kronig relations [22,23]: ε1(ω)=ε∞+2πp∫0∞ω′ε2(ω′)ω′2−ω2dω′(2) ε2(ω)=−2ωπp∫0∞ε2(ω′)−ε∞ω′2−ω2dω′(3) ε∞: High-frequency dielectric constant, ω: Angular frequency of incident light, ω′: Integral variable (angular frequency), P: Cauchy principal value integral (avoiding integral singularities and ensuring integral convergence).

Fig. 4 shows the evolution law of the dielectric function. The static dielectric constant ε1(0) of the material is 8.25. Notably, the imaginary part ε2 exhibits a steep increase in the low-energy region, reaching a peak of 12.15 when the photon energy is 3.67 eV, followed by an attenuation in the higher energy region, gradually approaching zero after the energy reaches 10.39 eV. The variation curve of the real part ε1 rises to a maximum of 12.15 at 2.15 eV, then drops sharply to the negative region of −5.03 at 6.0 eV, and then gradually recovers to a gentle upward trend.

Figure 4: Dielectric function of AgSbS₂.

As can be seen from Fig. 5, the static refractive index n0 of AgSbS2 is 2.87. In the low-energy regime, the refractive index n rises monotonically with photon energy, attains a maximum value of 3.57 at 2.41 eV, and subsequently declines steeply as the photon energy further increases. It is worth noting that the peak distribution of the extinction coefficient k is plotted in Fig. 4, and its overall variation trend is similar to that of the imaginary part ε2. In contrast, the extinction coefficient k peaks at 2.37 when the photon energy is 4.67 eV.

Figure 5: Refractive index and extinction coefficient of AgSbS₂.

Fig. 6 shows the calculated absorption coefficient α. When the photon energy < 0.67 eV, α is almost zero. When the photon energy is greater than 0.67 eV, α increases sharply, reaching a maximum absorption peak of 2.11 × 105 cm−1 at approximately 6.62 eV, and then decreases with increasing energy, eventually approaching zero.

Figure 6: Absorption coefficient of AgSbS₂.

Fig. 7 shows the reflectivity calculation results. The static reflectivity R(0) of AgSbS2 material is 0.23. Notably, as the photon energy rises to 9.33 eV, the reflectivity peaks at 84%, which is the maximum value in the entire energy range.

Figure 7: Reflectivity of AgSbS₂.

Fig. 8 shows the calculated conductivity. In the energy range of 0 eV~0.77 eV, the real part of the conductivity is zero. This phenomenon is due to the bandgap of AgSbS2 being 1.456 eV; electrons with photon energy lower than this cannot be endowed with sufficient energy to achieve transition. As the photon energy rises to 4.14 eV, the real part reaches a maximum of 5.73 (fs)−1. Finally, with the increase of photon energy, the real part of the conductivity continues to decrease and gradually approaches zero.

Figure 8: Conductivity of AgSbS₂.

Fig. 9 shows the calculated loss function. There is a resonance peak; when the photon energy is 12.17 eV, the energy loss of AgSbS2 reaches a maximum, and then drops sharply to zero.

Figure 9: Energy loss function of AgSbS₂.

3.5 Thermal Properties

We obtained the total energy E and volume V of the primitive cell through energy calculations, and fitted E-V curve according to the Murnaghan equation [24], as shown in Fig. 10. The thermal properties of AgSbS2 under high pressure and high temperature, we have used the quasi-harmonic Debye model as implemented in the Gibbs code [25].

Figure 10: Relationship between E and V.

Fig. 11 shows the relationship between B and T under P = 0: when T < 100 K, the value of B is basically stable; when T > 100 K, B decreases linearly with increasing temperature.

Figure 11: Variation of B with T at P = 0.

Fig. 12 presents the variation curves of B with P in the range of 0~15 GPa when T is 0 K, 500 K, and 1000 K: under isothermal conditions, B increases with increasing pressure; under isobaric conditions, B decreases with increasing temperature. Increasing pressure or decreasing temperature can produce similar changes in the bulk modulus of the material.

Figure 12: Variation of B with P at different temperatures.

Table 4 shows the Entropy S, Grüneisen parameter γ, and Debye temperature θ obtained under different temperatures and pressures. At the same pressure, S and γ increase with increasing temperature T, and decrease with increasing temperature; at the same temperature, θ increases with increasing pressure P, while S and γ decrease with increasing pressure. When the pressure increases, the decline in S occurs more rapidly at lower temperatures than at higher ones, moreover, the rate of rise in θ accelerates at elevated temperatures compared to that observed at lower temperatures, and the decrease rate of γ at high temperatures is faster. Overall, the γ value ranges from 1.6 to 2.3, indicating that AgSbS2 has moderate thermal expansion. As the P rises from 0 GPa to 15 GPa, the entropy S decreases by 43.85%, the Debye temperature θ increases by 37.73%, and the Grüneisen constant γ decreases by 28.67%, at 100 K, the entropy S decreases by 19.52%, the Debye temperature θ increases by 38.73%, and the Grüneisen constant γ decreases by 29.07% at 400 K, the entropy S decreases by 15.25%, the Debye temperature θ increases by 39.86%, and the Grüneisen constant γ decreases by 29.69% at 700 K, the entropy S decreases by 13.47%, the Debye temperature θ increases by 41.07%, and the Grüneisen constant γ decreases by 30.17% at 1000 K, respectively.

Fig. 13 illustrates how the heat capacity CV varies with T. At the same pressure, as the temperature changes from low to high, CV gradually increases. In the low-temperature region (0~200 K), CV shows a strong increasing trend, which is because acoustic phonons mainly contribute to the heat capacity at low temperatures. With increasing temperature, the growth rate of isochoric specific heat accelerates, which is due to the gradual excitation of optical phonons and their increasing contribution to the CV. With the continuous increase of temperature T and pressure P, the CV gradually stabilizes, approaching the Dulong-Petit limit value.

Figure 13: Variation of C_V with T under different pressures.

Fig. 14 shows the relationship between α and T. Over the T interval from 0 K to 1000 K, the thermal expansion coefficient gradually increases with increasing temperature. In T < 300 K, the α is small; with increasing temperature, α increases significantly, which is because the atomic vibration intensifies and the average distance between atoms increases, leading to the expansion of the unit cell volume. Beyond 300 K, the parameter α exhibits a gradual linear rise. Notably, the increase in pressure will weaken the rate of change of α with temperature, especially in the high-temperature region, where α is almost unaffected by temperature fluctuations.

Figure 14: Variation of α with T under different pressures.

Fig. 15 shows the relationship between α and P. The curves under various temperature conditions all show that α decreases with increasing pressure P. At P > 15 GPa, the α value at high temperatures approaches and stabilizes, indicating that under high temperature and high pressure, α is basically unaffected by temperature T and pressure P. The increase in pressure causes the lattice to deform, shortening the equilibrium distance between atoms and prompting them to move into more repulsive regions of the interatomic potential energy curve. This makes the potential energy well more robust, inhibiting its inherent asymmetry (which is the fundamental cause of thermal expansion), and limiting the amplitude of atomic thermal vibrations during heating. Overall, these effects weaken the overall increase in average atomic spacing, thereby reducing the phenomenon of thermal expansion.

Figure 15: Variation of α with P at different temperatures.

4 Conclusions

Based on first-principles calculations, this study systematically investigates the physical properties of monoclinic AgSbS2. The optimized structural parameters are consistent with previous theoretical values. Electronic structure analysis reveals a direct bandgap of 1.456 eV, and the density of states indicates that the valence and conduction bands mainly originate from the hybridisation of Ag-4d, S-3s, and Sb-5p states. From the calculated elastic constants Cj, key mechanical parameters (B, G, E and ν) are derived. The B/G ratio exceeds 1.75, confirming that AgSbS2 is an excellent ductile material. The optical properties are also calculated and analysed. Finally, the pressure and temperature dependencies of the heat capacity, entropy, Grüneisen parameter, thermal expansion coefficient, and Debye temperature are systematically obtained.