Improvement of thermoelectric properties and their correlations with electron effective mass in Cu1.98SxSe1−x

Sulphur doping effects on the crystal structures, thermoelectric properties, density-of-states, and effective mass in Cu1.98SxSe1−x were studied based on the electrical and thermal transport property measurements, and first-principles calculations. The X-ray diffraction patterns and Rietveld refinements indicate that room temperature Cu1.98SxSe1−x (x = 0, 0.02, 0.08, 0.16) and Cu1.98SxSe1−x (x = 0.8, 0.9, 1.0) have the same crystal structure as monoclinic-Cu2Se and orthorhombic-Cu2S, respectively. Sulphur doping can greatly enhance zT values when x is in the range of 0.8≤ × ≤1.0. Furthermore, all doped samples show stable thermoelectric compatibility factors over a broad temperature range from 700 to 1000 K, which could greatly benefit their practical applications. First-principles calculations indicate that both the electron density-of-sates and the effective mass for all the compounds exhibit non-monotonic sulphur doping dependence. It is concluded that the overall thermoelectric performance of the Cu1.98SxSe1−x system is mainly correlated with the electron effective mass and the density-of-states.

The dimensionless thermoelectric figure-of-merit (zT) is defined as zT = S 2 σT/κ = S 2 σT/(κ c + κ L ), where S, T, σ, κ, κ c , and κ L are the Seebeck coefficient, absolute temperature in Kelvin, electrical conductivity, total thermal conductivity, charge carrier thermal conductivity, and lattice thermal conductivity, respectively [1][2][3][4] . Enhanced zT values could be realized through adjusting the electronic structures and thermal conductivity by the doping approach [5][6][7][8][9] . It should be noted that zT is proportional to the square of S, indicating that improving S might be an easier way to get improved zT values, compared to regulating the other thermoelectric parameters such as σ and κ.
It is well known that σ and S can be estimated by the following formulas [10][11][12] , where n, μ, k B , h, and m * are the charge carrier density, carrier mobility, Boltzmann constant, Planck constant and effective mass of the carriers, respectively. Moreover, the effective mass (m*) and carrier mobility (μ) can be deduced from the electronic band structures and density-of-states (DOS) obtained from related first-principle calculations 13 . In this regard, S can be predicted through performing theoretical calculations on the electronic band structures and DOS, and the estimation of σ can also be roughly achieved with considering the average scattering time as a constant 14,15 . Therefore, it is highly desirable to gain insight into the electronic structures to get theoretical backup for the observed experimental phenomena.
Among all the state-of-the-art high temperature p-type thermoelectric materials, the copper-ion-liquid-like Cu 2−x Se and Cu 2−x S compounds show high thermoelectric performance, even though there still are some issues that need to be resolved before practical applications can be considered 16 . It has been reported that polycrystalline Cu 2−x Se and Cu 2−x S bulks can achieve the highest zT values of around 1.6 and 1.7 at 1000 K 17,18 , which have been further improved to 1.8 and 1.9 19,20 , respectively.
Additionally, it should be noted that the high-temperature β-Cu 2−x Se and α-Cu 2−x S have the same crystal structure, and both of them are superionic conductors. Besides the high crystal symmetry, these two systems also possess another important property, that of congruent melting, which means that highly dense samples can be easily fabricated by a facile melt-solidification technique.
The previous studies 20-22 on the electronic structures for Cu 2 Se and Cu 2 S compounds indicate that the copper deficiency makes both of them intrinsic p-type conductors owing to the contributions mainly from the Cu 3d-, Se 4p-, and S 3p-states near the Fermi level (E F ). These facts provide evidence that doping other elements into Cu or Se (S) sites could effectively alter their electronic structures, and consequently affect their electrical and thermal transport behaviour as well as their overall thermoelectric performance.
Generally, in order to obtain enhanced S and concurrent high σ as well as low κ values through the doping approach, the following factors should be considered when choosing dopants: (1) Dopants should have the same valence as the counterpart element, which will ensure the charge balance of the system and maintain the same crystal structure. (2) Dopants should have comparable radiuses to the counterpart element, which will result in little difference in the lattice parameters and provide good optimization of electrical and thermal transport properties.
As for the Cu 2−x Se system, the doping approach, using such elements as Ag, Sb, Al, and Sn for the Cu sites 23-28 and Te and I for the Se sites 21,29 , has been chosen to modify its electronic structures and thermal conductivity up to now. The results illustrate, however, that only a small amount doping with one of these elements could lead to limited improvements to the thermoelectric performance in this system. Generally, the lighter atoms and heavier atoms should have opposite effects on the electronic and thermal transport properties. For the substitutions on Se sites, only the heavier atoms have been investigated so far, and no enhanced thermoelectric performance was observed except at the phase transition temperatures. Therefore, it is necessary to investigate the doping effects of lighter atoms, with a smaller atomic radius, to test whether or not the doping approach could be beneficial for the further enhancement of the overall thermoelectric performance of the Cu 2−x Se system.
In this work, we investigated sulphur doping effects on the thermoelectric properties of the Cu 2−x Se system based on the following considerations: (1) At high temperature, α-Cu 2 S has the same crystal structure as β-Cu 2 Se, and therefore, sulphur should be very easy to substitute into the lattice and replace Se. (2) S 2− has the same valence as Se 2− , which should result in good electron balance in this system. (3) The unit cell size should be reduced after S substitutes for Se, which will affect the migration of copper ions and lead to varied electrical and thermal transport behaviour.
It should be noted that, for practical applications of thermoelectric materials, besides the high zT values, the thermoelectric compatibility factor (s), derived as = + − · s zT S T 1 1 , is another important factor, which is crucial for the efficient operation of a high temperature thermoelectric device 12,[30][31][32][33] . The closer the s for two n-and p-type thermoelectric materials, the higher the combined efficiency that will be achieved when they are adjoining segments in one thermoelectric device. Little information on s, however, has been reported for the Cu 2−x Se or Cu 2−x S based thermoelectric materials. Hence, it is meaningful to calculate the s values for the sulphur doped Cu 2−x Se to gain sufficient information for their future practical applications.
Herein, the doping effects on the thermoelectric properties of highly dense Cu 1.98 S x Se 1−x polycrystalline bulks were investigated experimentally, in order to provide a full understanding of how the doping approach modifies the thermoelectric properties of the Cu 2−x Se system. We also conducted a systematic study on the sulphur doping effects on the electronic band structures and DOS for the Cu 15 S x Se 8−x compounds based on Density Functional Theory (DFT) calculations. The results indicate that the overall thermoelectric performance in Cu 1.98 S x Se 1−x is strongly dependent on the sulphur doping concentration, and it is mainly correlated with the electron effective mass and DOS.  23 ) when x ≤ 0.16. They then become composites of low temperature cubic structured Cu 1.8 Se and hexagonal structured Cu 2.001 S when x varies in the range from 0.2 to 0.7 (0.2 ≤ x ≤ 0.7). Finally, they become single-phase orthorhombic structured Cu 2 S (PDF: 23-961) when x is over 0.8.

Results and Discussion
Rietveld refinements were performed for all samples based on the obtained X-ray diffraction patterns and the deduced lattice parameters, and the R-factors are listed in Table S1 (Supplementary Information). The summarized phase diagram for the sulphur doping level dependence of the lattice parameters is also displayed in Fig. 2, revealing that the Cu 1.98 S x Se 1−x (x = 0.02, 0.08, 0.16) samples have slightly reduced lattice parameters in comparison with the Cu 1.98 Se sample, due to the smaller radius of sulphur compared to that of selenium. In the same way, the Cu 1.98 S 0.8 Se 0.2 and Cu 1.98 S 0.9 Se 0.1 samples have enlarged lattice parameters in contrast to the Cu 1.98 S sample, owing to the larger radius of selenium.
The geometry optimized primitive cells for the Cu 15 S x Se 8−x (x = 0, 1, 2, 4, 6, 8) compounds are displayed in Figure S2, and the lattice parameters for these compounds are summarized in Table S1 which exhibit the consistent variation trend as the obtained experimental results. The Cu 15  Since both Cu 2−x Se and Cu 2−x S are superionic conductors, and the migration of copper ions plays important roles on the system's electrical conductivity, the changed lattice parameters should lead to different electrical conductivity and Seebeck coefficient, which will, in turn, result in modified thermoelectric properties with different zT values. Thus, it is essential to discuss the sulphur doping effects on the thermoelectric properties of the Cu 2−x Se system, as well as the selenium doping effects on the thermoelectric properties of the Cu 2−x S system. Hence, we will focus on the thermoelectric properties of the single-phase Cu 1.98 S x Se 1−x (x = 0.02, 0.08, 0.16) and Cu 1.98 S x Se 1−x (x = 0.8, 0.9, 1.0) samples in the following part.  Figure 3a shows the temperature dependence of the electrical conductivity for the Cu 1.98 S x Se 1−x (x = 0, 0.02, 0.08, 0.16) bulks. It indicates that compared to Cu 1.98 Se, the Cu 1.98 S x Se 1−x (x = 0.02, 0.08, 0.16) samples have lower σ values over the whole measured temperature range, and the most obvious difference occurs at T = 420 K between 400 S · cm −1 for the Cu 1.98 S 0.08 Se 0.92 and 900 S · cm −1 for the Cu 1.98 Se. It should be pointed out that this difference becomes less obvious with increasing temperature because the high temperature phases are superionic conductors. Figure 3b displays the temperature dependence of the Seebeck coefficient for the Cu 1.98 S x Se 1−x (x = 0, 0.02, 0.08, 0.16) bulks. It reveals that the Cu 1.98 S x Se 1−x (x = 0.02, 0.08, 0.16) samples have larger S values than the Cu 1.98 Se. Specifically, among all the samples, the Cu 1.98 S 0.08 Se 0.92 has the highest S values, around 275 μ V · K −1 at T = 970 K, which is over 30% higher than that of the Cu 1.98 Se.   Figure 4 displays the temperature dependence of the electrical conductivity (a), Seebeck coefficient (b), total thermal conductivity (c), and dimensionless figure-of-merit (d) for the obtained Cu 1.98 S x Se 1−x (x = 0.8, 0.9, 1.0) bulks. The results indicate that, for the high temperature cubic structured Cu 2 S phase, the Cu 1.98 S x Se 1−x samples do not show a monotonic increase or decrease in their electrical conductivity compared to the Cu 1.98 S. The same trend is also observed for the temperature dependence of the Seebeck coefficient. Furthermore, the Cu 1.98 S 0.8 Se 0.2 sample has almost the same thermal conductivity as the Cu 1.98 S, while the Cu 1.98 S 0.9 Se 0.1 sample has much smaller thermal conductivity, with values around 0.5 W · m −1 · K −1 in the temperature range from 700 to 1000 K. This paradoxical result might be related to the characteristics of the superionic system and the larger radius as well as the heavier mass of selenium compared to sulphur. As aforementioned, the cubic structured Cu 2 S is a superionic conductor and it is the migration of copper ions that predominately determines its thermal conductivity. Therefore, the selenium doped samples should have higher thermal conductivity than the Cu 1.98 S, due to the enlarged lattice parameters evidenced from the refinements of the X-ray diffraction patterns. On the other hand, selenium is much heavier than sulphur, so the selenium doped samples should have lower thermal conductivity. As a result of these two opposite factors, the samples show the complicated and varying trend that is observed for the thermal conductivity.
The temperature dependence of the dimensionless figure-of-merit shown in Fig. 4d reveals that the selenium doping does not improve the overall thermoelectric performance of the Cu 1.98 S system, with the Cu 1.98 S having the highest zT values around 0.86 at 850 K among all the orthorhombic structured samples, even though certain thermoelectric parameter is enhanced. This observation is in good agreement with our previous reports on the tellurium and iodine doped Cu 2−x Se system 21 , which provides further evidence of the distinctiveness of superionic thermoelectric materials in comparison with the conventional thermoelectric materials.  which agrees very well with our previous theoretical and experimental discussions on sulphur (selenium) doping effects on the superionic Cu 2−x Se(S) system.
For the practical applications of thermoelectric materials, besides the high zT values that are needed, the thermoelectric compatibility factor, s, is another important factor that needs to be considered when designing an efficient thermoelectric generator 12,32,35 . The maximum efficiency of a thermoelectric generator will be decreased greatly if the compatibility factors for the segments of n-and p-type thermoelectric materials differ from each other by a factor larger than two. Therefore, in order to discover the best applicable temperature range and best matching material for a certain thermoelectric material, the calculation of s is quite essential. Figure 6 shows the temperature dependence of the thermoelectric compatibility factor for the Cu 1.98 S x Se 1−x (x = 0, 0.02, 0.08, 0.16, 0.8, 0.9, 1.0) bulks. It indicates that all the samples exhibit stable s values with small fluctuations over a large temperature range from 700 to 1000 K. In the measured temperature range, average s values of around 3.85, 2.92, 2.14, and 2.56 were achieved for the Cu 2 Se-phase Cu 1 For comparison purposes, the s values for some well-known n-type thermoelectric materials are also provided in Fig. 6. It indicates that polycrystalline SiGe, PbTe, La 2 Te 3 , and CoSb 3 bulks show s of around 1.37, 1.90, 2.14, and 2.31, respectively. It should be noted that these are very close to the s values of the Cu 1.98 S x Se 1−x (x = 0, 0.02, 0.08, 0.16, 0.8, 0.9, 1.0) bulks, with the differences less than a factor of 2 in the temperature range from 700 to 1000 K. Therefore, a relatively high efficiency could be gained from their coupled thermoelectric modules, which is gratifying for their future practical applications.
As aforementioned in the introduction part, the electrical conductivity and Seebeck coefficient is related to the charge carrier density, carrier mobility, and effective mass, which can be deduced from the calculated DOS and electronic band structures. Therefore, in order to fundamentally understand the strange sulphur doping effects on the thermoelectric properties of the Cu 1.98 S x Se 1−x system, it is much necessary to do some first-principles calculations on the system's electronic band structures and DOS.   , the selenium (sulphur) atoms form a face-centred cubic (fcc) sub-lattice, and the copper atoms occupy the tetrahedral interstitial positions. It should, however, be noted that β-Cu 2 Se and α-Cu 2 S have been reported to be superionic conductors, in which the copper ions behave like a liquid 17,19,[36][37][38] , and they are kinetically disordered throughout the whole structure. Figure 8 shows the calculated total and partial DOS for the Cu 15 S x Se 8−x (x = 1, 2, 4, 6) compounds. The sulphur doping level dependence of the total and partial DOS at E F for the Cu 15 S x Se 8−x (x = 0, 1, 2, 4, 6, 8) compounds is displayed in Fig. 9. The results indicate that the DOS at E F consists of the contributions from the Cu 3d-states, Se 4p-states, and S 3p-states of the Cu 15 S x Se 8−x compounds, with the Cu 3d-states predominately determining the total DOS at E F . In addition, the partial DOS for the S atoms obviously increases with increasing x, while the partial DOS for the Se atoms shows the opposite trend, decreasing with increasing x. The total DOS exhibits the same non-monotonic tendency as the partial DOS for the Cu atoms, further indicating that the DOS at E F for this system is mainly determined by the copper atoms rather than the S or Se atoms. In summary, the total DOS firstly increases slightly, then clearly decreases, with the Cu 15 S 6 Se 2 having the highest DOS among all the compounds, ~6.29856 states/eV/f.u.
The effective mass can be directly deduced from the calculated DOS based on some references 13,39 . Figure 10 shows the deduced effective mass for the Cu 15 S x Se 8−x (x = 0, 1, 2, 4, 6, 8) compounds. It indicates that, similar to the DOS, the sulphur doping also has a non-monotonic effect on the effective mass. It firstly has positive effects and gives the Cu 15 S 4 Se 4 its highest m * , with a value of ~1.151 m e . It then shows negative effects and results in decreased m * values as the sulphur doping level increases.
According to Equations 1-4 and previous discussions on σ, S, n and μ, we know that both σ and S are linked to the m * and the DOS. Specifically, σ is proportional to the carrier density (n) and inversely proportional to m * .
S, however, is proportional to m * and ( ) n 1 2/3 . Therefore, based on the obtained information on the DOS and m * , we can anticipate the variation trends for the values of S. σ values can also be roughly estimated with disregarding the average scattering time. Hence, we can predict that the cubic structured sulphur doped Cu 2−x Se compounds should exhibit non-monotonic variation in σ and S with increasing sulphur concentration according to the calculated DOS and m * using the DFT method.
It should be pointed out that, for the monoclinic structured Cu 2 Se phased Cu 1.98 S x Se 1−x samples, the observed sulphur doping level dependence of the electrical conductivity and the Seebeck coefficient is in good agreement with the theoretical predictions. The DOS is enhanced as the sulphur doping level increases, while the effective mass is reduced as the doping level increases. Additionally, σ and S are proportional to ⁎ n m and m * , respectively. Therefore, enhanced electrical conductivity and reduced Seebeck coefficient can be obtained when the contribution from the DOS is stronger than that from m * . When the contribution of the effective mass is stronger, decreased electrical conductivity and increased Seebeck coefficient will be achieved.
In summary, the Cu 1.98 S x Se 1−x compounds have the same crystal structure as monoclinic structured Cu 2 Se when x ≤ 0.16, become composites of cubic structured Cu 1.8 Se and hexagonal structured Cu 2.001 S when 0.2 ≤ x ≤ 0.7, and finally have the same crystal structure as orthorhombic structured Cu 2 S when 0.8 ≤ x ≤ 1.0. The overall thermoelectric performance of the Cu 1.98 S x Se 1−x compounds is mainly correlated with the electron effective mass and the density of states, with the zT values first increasing and then decreasing. Additionally, all the samples show stable thermoelectric compatibility factors over a broad temperature range from 700 to 1000 K, which could greatly benefit their practical applications. DFT calculations indicate that sulphur doping   were pressed into pellets and sealed in evacuated quartz tubes, then heated to 873 K for 1-5 hours with a heating rate of 5 K/min, followed by a furnace cooling to room temperature. Finally, the as-sintered pellets were used in a melt-solidification approach to achieve highly dense polycrystalline bulks, which has been described in detail in our previous work 19,21 . The obtained polycrystalline bulks were then shaped into round disks and rectangular bulks for electrical conductivity and thermal diffusivity measurements, respectively.
Measurements. X-ray diffraction (XRD) patterns were collected on a GBC MMA system using Cu Kα radiation. The electrical conductivity and Seebeck coefficient were measured simultaneously in a helium atmosphere from 300 to 973 K using an RZ2001i system. The thermal diffusivity (D) was measured by the laser flash method (LINSEIS LFA 1000), and the specific heat (C p ) was determined by differential scanning calorimetry (NETZSCH DSC 204F1). The sample density (dd) was determined by the sample mass divided by volume, and the thermal conductivity (κ) was calculated according to κ = D × C p × dd.
Calculations. The calculations of electronic band structures, and total and partial DOS were performed based on the DFT method, implemented by the CASTEP package 40 with the generalized gradient approximation (GGA) 41 . The calculations were parameterized by the Perdew-Burke-Ernzerhof (PBE) 42 and ultra-soft pseudo-potentials. The plane wave cut-off energy was set at 400 eV. For Cu 2 Se and Cu 2 S, a primitive cell with the Brillouin zone path of Γ XWLΓ K (Fig. S1 in Electronic Supplementary Information) was employed for the band structure calculations. For the Cu 15 S x Se 8−x (x = 0, 1, 2, 4, 6, 8), geometry optimizations were performed on a 2 × 2 × 2 supercell, with one copper atom deleted, of the Cu 2 Se primitive cell. Then, the Brillouin zone path of ΓXWLΓK and a k-point set of 15 × 15 × 15 for the supercell were used to calculate the electronic band structures, and the total and partial DOS, respectively.