Thermoelectric Properties of Cu₂S Doped with P, As, Sb and Bi—Theoretical and Experimental Studies

Abstract

The aim of this work was to investigate the possibility of doping copper sulfide Cu₂S with selected fifth-group elements, potentially having a positive effect on the thermoelectric properties of the resulting materials. For the selected model structures, theoretical calculations and an analysis of the electronic structure and changes in the enthalpy of formation due to doping were performed using the WIEN2k package employing the Full-Potential Linearized Augmented Plane Wave (FP-LAPW) method within density functional theory (DFT) formalism. Polycrystalline materials with the nominal composition of Cu₃₂S₁₅X₁ (X = P, As, Sb, Bi) were synthesized in quartz ampoules, then sintered using the spark plasma sintering (SPS) technique and “SPS melting” method. The chemical and phase compositions of the obtained sinters were studied by X-Ray diffraction (XRD) and scanning electron microscopy (SEM). Additionally, investigations of thermoelectric properties, i.e., electrical conductivity, Seebeck coefficient and thermal conductivity in the temperature range 300–920 K, were performed. The results of this study indicate that only phosphorus is successfully incorporated into the Cu₂S structure.

1. Introduction

Cu₂S is a thermoelectric material and simultaneously superionic semiconductor with a very low thermal conductivity, resulting in high values of the ZT parameter [1,2,3], for which the concept of Phonon-Liquid Electron-Crystals (PLECs) described in [4] is applicable. The chalcocite Cu₂S can assume one of three stable structures: the monoclinic (γ) phase (T < 103 °C), space group P21/c; the hexagonal (β) phase (103 °C < T < 435 °C), space group P63/mmc; and the cubic (α) phase (T > 435 °C), space group Fm3m [5]. Historically, determining the precise atomic positions for copper has been challenging because copper atoms are statistically distributed across multiple sites, with their distribution depending on temperature (Figure 1). At higher temperatures in the cubic phase, copper atoms are very mobile and can “jump” at short time intervals between equivalent crystal lattice sites (the partially occupied Wyckoff position 8c—which is typical of an calcium antifluoride structure—as well as 192l and 4b [6]), and thus its structure can be viewed as a rigid sulfur lattice “filled” with “liquid” copper.

Undoped Cu₂S has an unsatisfying thermoelectric efficiency parameter ZT [7] (ZT_max = 0.68, T = 923 K [8], ZT_max = 0.32, T = 723 K [9], ZT_max = 0.58, T = 1000 K [10,11]); however, even a small deviation from the stoichiometry causes a significant increase in the ZT parameter, e.g., ZT_max = 1.9, T = 973 K for Cu_1.97S [12]. Another way of improving the thermoelectric properties of Cu₂S that has been used successfully in recent years is the formation of solid solutions with copper(I) selenides and tellurides. The improvements in thermoelectric properties with the addition of Se can be attributed to two main factors: (a) the increase in carrier concentrations and their effective mass m*, which results in a higher power factor PF = α²σ, i.e., the product of electrical conductivity σ and the square of the Seebeck coefficient α; and (b) a decrease in both the lattice component of thermal conductivity and total thermal conductivity. This allowed a ZT_max = 0.74, T = 723 K to be achieved for Cu₂S_1.9Se_0.1 [9]. An even more significant enhancement of the thermoelectric properties was achieved by alloying Cu₂S and Cu₂Te, which allowed the electrical conductivity to be increased by more than one order of magnitude with a simultaneous decrease in the Seebeck coefficient of about half, which, with a slight increase in thermal conductivity, made it possible to achieve ZT_max = 2.1, T = 1000 K for Cu₂S_0.52Te_0.48 [10] and ZT_max = 2.1, T = 1000 K for Cu₂S_0.94Te_0.06 [13]. However, such a substantial improvement in thermoelectric properties is suppressed by the formation of a mosaic nanostructure. The solid solution formation of Cu₂S, Cu₂Se and Cu₂Te did not give the expected further improvement in thermoelectric properties compared to Cu₂S_1-xTe_x, ZT_max = 1.5, T = 1000 K for Cu₂S_1/3Se_1/3Te_1/3 [14]; however, it allowed the thermoelectric properties to be better than in pure Cu₂S and in Cu₂S_1-xSe_x. There have also been attempts to improve Cu₂S transport properties by doping at the Cu sites. In the case of doping with Li, an improvement in thermoelectric properties was achieved with ZT_max = 0.84, T = 900 K for Cu_1.99Li_0.01S [15], due to an increase in electrical conductivity with a small decrease in Seebeck coefficient and a slight increase in thermal conductivity. In another study [16], the effects of Mn, Zn, Ga and Ge dopants on Cu_1.95X_0.03S systems was investigated. For all the above dopants, an increase in electrical conductivity was observed (the highest for Manganese and the lowest for Germanium), with a simultaneous decrease in the Seebeck coefficient. The doping also caused an increase in thermal conductivity, but for all dopants it was still possible to obtain an increased ZT parameter. The Mn-doped sample showed the best properties but was comparable to undoped Cu_1.98S (ZT_max = 0.91, T = 823 K). Despite all of the mentioned works, the number of studied dopants that could improve the thermoelectric properties of Cu₂S is still relatively small. In the best case, the improvement in thermoelectric properties was comparable to copper-deficient Cu₂S, so further studies devoted to transport property improvement via the respective doping methods are needed. Finding an effective dopant, besides improving the properties of pure Cu₂S, could also facilitate the further fine-tuning of Cu₂S-Cu₂Te alloys. As follows from the literature review, doping in a S sublattice has not been studied before, but as shown in studies conducted for Cu₂S-Cu₂Se and Cu₂S-Cu₂Te systems, the substitution of S atoms with other atoms is possible.

The aim of this work was to investigate the possibility of doping copper sulfide in an anionic sublattice with selected fifth-group elements, potentially having a positive effect on the thermoelectric properties of the resulting materials.

2. Materials and Methods

2.1. Computational Details

Ab initio calculations were performed using the WIEN2k package, which employs Full-Potential Linearized Augmented Plane Wave (FP-LAPW) approximation within density functional theory (DTF) formalism. All structures were fully relaxed and their internal parameters (unit cell parameters and atomic positions) were optimized with respect to the forces acting on atoms and the total energy of the system. PBESol generalized gradient approximation (GGA) was used as the exchange–correlation functional along with the convergence criteria of 10⁻⁵ Ry for energy, 5∙10⁻⁴ Ry/au for forces and 10⁻³ e for charge. To simulate Cu₃₂S₁₅X₁ (where X = P, As, Sb, Bi), 2 × 2 × 2 supercells were created as shown in Figure 2. The positions of the dopant atoms were identical for all structures.

The total energy of relaxed structures allows us to calculate the enthalpy of formation, H_F, which is defined as the energy difference between the total energy of a given structure and the sum of the total energies of the pure element structures in their thermodynamically most stable forms. For example, for Cu₃₂S₁₅As₁, we have:

$$H_F^{C{u}_{32}{S}_{15}A{s}_1}=E_{tot}^{C{u}_{32}{S}_{15}A{s}_1}-32·E_{tot}^{Cu}-15·E_{tot}^S-1·E_{tot}^{As}$$

(1)

where both H_F and E_tot are in eV/atom. The structures of pure elements were also optimized and relaxed. Since the enthalpy of formation is a sign of the stability of a structure, one should compare the enthalpy of doping, which is the difference in the enthalpy of the formation of undoped and doped Cu₂S.

WIEN2k also allows one to calculate the total and partial density of states (DOS) using the modified tetrahedron method [17]. However, because density functional theory is designed to describe ground state energies and one-electron eigenvalues are not suited to predicting one-electron excitations, the DFT calculations typically underestimate band gaps.

2.2. Experimental Details

Cu (99.9% Alfa Aesar, Kandel, Germany), S (99.999%, Alfa Aesar, Kandel, Germany), P (98.9%, Alfa Aesar, Kandel, Germany) and As powders (99%, Alfa Aesar, Kandel, Germany) and Bi and Sb ingots (99.5 and 99.99%, Alfa Aesar, Kandel, Germany) were used for the synthesis. A series of samples with the nominal composition Cu₃₂S₁₅X₁ (X = P, As, Sb, Bi) and Cu₃₂S_16-xP_x (x = 0, 0.15, 0.25 and 1) were prepared by a direct two-step synthesis (I stage: T₁ = 380 °C, t₁ = 24 h, II stage: T₂ = 900 °C, t₂ = 18 h) from the above-mentioned elements in quartz ampoules, and sealed under a vacuum using a rocking furnace, similar to our previous works [8,18]. After each synthesis step, the obtained ingots were ground in an agate mortar. Next, the powders were densified in the SPS apparatus with an AC current, which does not cause the migration of copper ions, in contrast to the DC current, which causes the degradation of Cu₂S, as shown in our previous work [18] (T = 500 °C, p = 65 MPa, t = 5 min, vacuum atmosphere p = 1∙10⁻² mbar). Since the boiling point of phosphorus is 431 °C [19], the sintering of samples with phosphorus was carried out in a protective argon atmosphere (p = 1.4∙10³ mbar) to limit the possible release of unreacted phosphorus from the samples. Additionally, a modified SPS technique, which we named “SPS melting”, was employed. This method involves placing a special graphite container with powder in a graphite die, allowing for the melting and simultaneous densification of the synthesized samples (T = 1250 °C, t = 2 min). The density ρ of the samples was determined by Archimedes’ hydrostatic method and was higher than 99% of the theoretical density for the undoped samples. The obtained samples were characterized using the X-Ray powder diffraction method (XRD) (X-Ray Diffractometer Panalytical Empyrean, CuKα, λ = 1.5418 Å) and scanning electron microscopy (SEM) (FEI Nova NanoSEM 200 FEI Europe Company Scanning Electron Microscope equipped with an EDAX detector). The uniformity of the Seebeck coefficient of the samples was examined by a scanning thermoelectric microprobe (STM) at room temperature (tested area size 2 × 2 mm, 0.1 mm step) [20,21]. The thermoelectric properties were measured within the temperature range of 300 to 923 K using custom-made apparatus. Electrical conductivity σ was measured using alternating polarity DC current by the four-probe technique. During the measurements of the Seebeck coefficient α, a slight temperature gradient was applied (ΔT < 4 K). The thermal diffusivity a was measured and the specific heat C_p was determined by the laser flash method (LFA) (Laser Flash Apparatus LFA 427) in the temperature range 300–923 K. The thermal conductivity λ was calculated by λ = a∙C_p∙ρ [22,23]. The thermoelectric figure of merit ZT parameter was assessed from the relationship ZT = α²σλ⁻¹T [23,24,25,26].

3. Results and Discussion

3.1. Electronic Structure and Enthalpy of Doping

The first thing worth noting is that in all cases the valence bands close to the maximum have a predominant Cu character, while the conduction bands exhibit a more mixed character originating from both Cu and S states. For the undoped Cu₂S, our calculations predict a metallic character without any band gap for the reasons explained in the theoretical details (Figure 3). In the case of doped structures, a shift in Fermi level toward lower energies can be seen, resulting in a non-zero density of states at the E_F, indicating p-type semiconducting (Figure 4).

The negative values of enthalpy of doping means that the given structure is more favorable energetically than pure Cu₂S (

Table 1. Enthalpy of doping for Cu₃₂S₁₅X₁ (X = P, As, Sb, Bi).

Model Structure	Enthalpy of Doping ∆H [eV/atom]
Cu32S15P1	−0.00682
Cu32S15As1	0.00722
Cu32S15Sb1	0.02018
Cu32S15Bi1	−0.21230

). It is, however, worth noting that in practice they might not necessarily form a real, doped material, since one cannot exclude the possibility that dopant atoms will energetically prefer to form other phases (sulfides, arsenides, bismuthinides and so on); nevertheless, predicting this is far beyond the scope of this work.

3.2. Structural and Microstructural Analysis

The XRD patterns of the synthesized powders as well as the sintered samples show that the materials obtained consist mostly of Cu₂S with a monoclinic structure of chalcocite, a stable form of copper sulfide at room temperature. The appearance of secondary phases of copper, copper phosphides, antimonides and arsenides, and bismuth can also be observed for all samples (Figure 5), but they represent the vast minority of material. This means that not all of the dopant has been integrated into the structure and the dopant content has exceeded the solubility limit for each of the elements used. However, the accurate determination of the precipitate content is difficult due to a large number of Cu₂S-derived reflections overlapping with the peak positions of the analyzed phases. The largest changes in the diffractogram appearance are observed for phosphorus doping. The intensities of the reflections undergo the greatest changes and the half-width of the reflections appear to be slightly enlarged. The main impurity observed is Cu₃P, which is a typical phase in the Cu-P system [27]. For As doping, mainly Cu₃As impurity peaks are observed in agreement with the phase diagram of the Cu-As system [28].

The SEM observations combined with energy-dispersive X-Ray spectroscopy (EDS) analysis allow the determination, within the sensitivity of the EDS method, of the solubility of dopants in the material grains and the observation of precipitates in the obtained samples. All the samples have high density and there is no visible porosity (ρ > 99% of the theoretical density for undoped Cu₂S), which is clearly visible in the sample fractures (Figure 6). All the obtained sinters are homogeneous and consist predominantly of a phase with a composition corresponding to Cu₂S; however, minor precipitates of impurities are visible in each of the samples.

For the As-doped sample, a larger number of precipitates can be observed (Figure 7 and Figure 8). Most of these precipitates have a composition corresponding to Cu₃As, which agrees with the XRD observations. Linear compositional analysis through the areas containing precipitates shows that there is hardly any sulfur in these precipitates, and the boundary between Cu₃As and Cu₂S is sharp and no enrichment of Cu₂S with arsenic is observed near this boundary. The elemental distribution maps show that As is primarily accumulated in the precipitates. At the same time, point analysis did not show (within the sensitivity of the EDS method) any presence of As in the material grains.

In the case of Sb doping, SEM images show the presence of a large number of precipitates (Figure 9 and Figure 10). Composition analysis showed that most of these precipitates correspond to the Cu₃Sb phase, and a minority are Cu₂Sb. Chemical composition maps show that antimony is contained almost exclusively in the precipitates. A linear EDS analysis of the composition confirms these observations, showing that antimony is present exclusively in the precipitates, in which in turn sulfur is absent. A more detailed EDS point analysis of the composition showed that the Sb content in the Cu₂S phase is close to zero and much smaller than the uncertainty of the measurement method.

For bismuth-doped Cu₂S samples, the SEM observations also showed many impurity precipitates (Figure 11 and Figure 12). EDS compositional analysis shows that these are mostly bismuth precipitates. EDS linear analysis through the region containing bismuth precipitate showed that these precipitates were devoid of sulfur or copper. Careful EDS spot analysis in the Cu₂S grains showed (within the sensitivity of this method) no Bi presence.

The elemental distribution maps for Cu₃₂S₁₅P₁ are shown in Figure 13 and Figure 14. In the case of Cu₂S doped with phosphorus, precipitates rich in phosphorus and copper are visible, which is consistent with the XRD results.

Simultaneously, EDS point analysis in the material grains indicated a phosphorus content of 0.5–0.7 at.%, which is lower than the assumed nominal composition, i.e., about 2%. This is likely due to the formation of Cu₃P, but this does not exclude the partial incorporation of P into the Cu₂S structure. For this reason, phosphorus doping was considered the most promising, and additionally, samples with lower phosphorus content than in the initial one, i.e., x = 0.15 and 0.25 (for Cu₃₂S_16-xP_x) were synthesized. Then, the materials were densified by the SPS method and the structural and thermoelectric properties examined.

The XRD results obtained for the Cu₃₂S_16-xP_x (x = 0–1) samples show that in each case, the dominant phase is the monoclinic Cu₂S, and only in the sample with phosphorus content corresponding to x = 1 are the reflections originating from the Cu₃P (Figure 15a,b) phase clearly visible. Based on the XRD results, the lattice parameters were determined using the Rietveld method, and in the case of P-doped samples, the cell volume was smaller compared to undoped Cu₂S, which may indicate the successful phosphorus incorporation into the Cu₂S structure. The densities of the samples for x = 0.15 and x = 0.25 are very similar, and equal to ρ = 5.67 ± 0.01 g∙cm⁻³ and ρ = 5.68 ± 0.01 g∙cm⁻³, respectively, and simultaneously lower compared to undoped Cu₂S (ρ = 5.74 ± 0.01 g∙cm⁻³). On the other hand, for the x = 1 sample, the measured density is higher than for undoped copper sulfide (ρ = 5.77 ± 0.01 g∙cm⁻³), which is likely the result of the presence of the Cu₃P phase (with a theoretical density of 7.37 g∙cm⁻³).

3.3. Thermoelectric Properties

The studies carried out using a scanning thermoelectric microprobe (STM) showed that all samples have a unimodal distribution of the Seebeck coefficient (Figure 16), with a clearly visible difference between the mean values and standard deviations of the samples for x = 0–0.25 and x = 1, which appears to be related to the presence of an additional Cu₃P phase, which has a very low Seebeck coefficient at room temperature (α = 11.2 μV∙K⁻¹ for the Cu₃P polycrystalline thin films [29], α = 9,85 μV∙K⁻¹ theoretically calculated [30]). Samples in the range of x = 0–0.25 exhibit a narrow distribution of the Seebeck coefficient, with standard deviations equal to α_σ = 13 μV∙K⁻¹ for x = 0, α_σ = 12 μV∙K⁻¹ for x = 0.15 and α_σ = 8 μV∙K⁻¹ for x = 0.25. This indicates the high homogeneity of these materials. The mean values of the Seebeck coefficient obtained in STM measurements were qualitatively consistent with the measurements of this parameter for bulk samples at room temperature (Figure 17).

The results of the measurements of the Seebeck coefficient as a function of temperature for P-doped Cu₂S samples are presented in Figure 17a. The positive values of the Seebeck coefficient for all samples indicate that the obtained materials are p-type semiconductors. In the case of samples for x = 0.15 and x = 0.25, the character of the Seebeck coefficient course is similar to that of undoped Cu₂S, while in the cubic phase region (T > 710 K), which is particularly interesting from the perspective of thermoelectric properties, samples in the range of x = 0–0.25 exhibit very similar values. However, for the sample with x = 1, the Seebeck coefficient values are significantly lower compared to the undoped sample over the entire tested temperature range. The electrical conductivity (Figure 17b) for samples with x = 0.15 and x = 0.25, like the Seebeck coefficient, has values similar to those of undoped Cu₂S, while the x = 1 sample shows significantly higher values, especially in the high-temperature cubic phase region. The course of thermal conductivity values (Figure 17c) for samples doped with phosphorus is consistent with the results of the Seebeck coefficient and electrical conductivity; the samples with x = 0.15 and x = 0.25 show similar values to those of the undoped sample, while the x = 1 sample has significantly higher thermal conductivity values across the entire tested temperature range. The clear differences in the thermoelectric properties of the sample with x = 1 compared to the samples with a lower nominal amount of phosphorus dopant seem to be an effect of the presence of the Cu₃P phase, which is the result of significantly exceeding the solubility limit of P dopant in Cu₂S. The thermoelectric efficiency parameter ZT determined from the transport property measurements is highest for the undoped Cu₂S sample (ZT_max = 0.63, T = 923 K), which is slightly higher than that of the x = 0.15 sample (ZT_max = 0.6, T = 923 K). It is also noteworthy that the average ZT value for the high-temperature cubic phase is greater for the x = 0.15 sample compared to the x = 0 sample (Figure 17d).

4. Conclusions

High-temperature synthesis and material densification employing the SPS of copper(I) sulfide doped with fifth-group elements, with the general formula Cu₃₂S₁₅X₁ (X = P, As, Sb, Bi) and Cu₃₂S_16-xP_x (x = 0, 0.15, 0.25 and 1), were carried out in this study. All obtained materials had the dominant monoclinic phase typical for copper(I) sulfide. The chemical composition of the obtained samples was examined by point and line analysis using SEM (scanning electron microscopy). Within the sensitivity limits of the method, the solubility of Sb, Bi and As dopants in the Cu₂S structure was not confirmed. The low solubility of P was indicated; however, despite its observed slight presence in the material grains, it was also found in the precipitates, forming compounds with copper. Only in the case of phosphorus was a small amount in the material grains detected, which indicates its solubility in the Cu₂S structure. The theoretical analysis of the electronic structure showed that Cu₂S doped with phosphorus should be a p-type semiconductor, which was confirmed by the experimental results of the Seebeck coefficient measurements. The phosphorus dopants were successfully introduced into the Cu₂S structure for x = 0.15 and x = 0.25, and have similar thermoelectric properties compared to the undoped material, with the average values of the ZT parameter for the sample with x = 0.15 being higher than for the undoped Cu₂S for the high-temperature cubic phase.