Electron, phonon and thermoelectric properties of Cu7PS6 crystal calculated at DFT level

The promising class of the environment-friendly thermoelectrics is the copper-based argyrodite-type ion-conducting crystals exhibiting just extraordinary low thermal conductivity below the glass limit associated with the molten copper sublattice leading to a softening of phonon modes. To explain why the argyrodite structure containing copper ions favors the low thermal conductivity, we have utilized the ab initio calculations of the electron, phonon, and thermoelectric properties of Cu7PS6 crystal in the framework of the density functional and Boltzmann transport theories. To obtain the reliable thermoelectric properties of Cu7PS6, we take into account the dependence of the electron effective mass m* on the redundant carrier concentration n. We propose to use the Burstein–Moss effect for the calculation of the electron effective mass m* of a semiconductor. We have found the strong nonlinear character of copper atom vibrations in Cu7PS6 which exceeds substantially the similar values for phosphorous and sulfur atoms. The large vibration nonlinearity of the copper atoms found in Cu7PS6 explains the diffusion-like heat transfer and the relatively low coefficient of the lattice thermal conductivity (κ = 0.7 W/(m K)), which is favorable to achieve the large thermoelectric figure of merit.

www.nature.com/scientificreports/ or leads to amorphization. This amorphization causes the coefficient of thermal conductivity lowering and as a consequence increases the thermoelectric figure of merit. On the other hand, the copper ion diffusion in the crystal creates in fact the copper vacancies, which lead to the appearance of the electron donor states in the band structure. In turn, these electron states may increase electric conductivity, which also improves the material's thermoelectric characteristics. Thus, one may expect the increased ion-and electron-conducting properties among the representatives of Cu 7 P(Se 1−x S x ) 6 , which may induce advanced thermoelectric and solid electrolyte properties. That is why the theoretical study of the electron and phonon properties of Cu 7 PS 6 and Cu 7 PSe 6 crystals and their solid solutions Cu 7 P(Se 1−x S x ) 6 is a promising task, solving of which may deliver more information on how to improve the solid electrolyte and thermoelectric properties of materials by appropriate selection of the chemical composition. The most important electronic characteristics of a crystal for their thermoelectric and photovoltaic applications are the bandgap E g , the effective electron mass m * , the carrier relaxation time τ, Seebeck coefficient α, and the coefficients of electric (σ) and thermal (κ) conductivities 8 . The ability to determine these characteristics for certain material compositions by using the theoretical methods is promising for the prediction of the main thermoelectric and photovoltaic characteristics (without having them synthesize) and evaluation of their possible practical applications. In the present study, we develop consistent and complex methods to determine the mentioned above material constants by calculations within the density functional and Boltzmann transport theories. To illustrate the effectiveness of our approach, the proposed methods have been employed for Cu 7 PS 6 crystal and the obtained results have been compared with experimental data. We intentionally have chosen this crystal out of other contents of Cu 7 P(Se 1−x S x ) 6 solid solutions, because, Cu 7 PS 6 possesses the relatively large energy gap, E g ≈ 2 eV, among other representatives of the group Cu 7 P(Se 1−x S x ) 6 , that is suitable for the study of the influence the extrinsic carriers on the electronic and thermoelectric properties of Cu 7 P(Se 1−x S x ) 6 solid solutions. Further, having good consistency of our calculations with the available experimental data for Cu 7 PS 6 , in the next stage of our work, we intend to extend our calculations to a wide group of the argyrodite-type solid solutions to determine the chemical composition-structure-properties relations useful for finding the most effective thermoelectric material among this group.

Results and discussion
Electron band structure and related thermoelectric properties of Cu 7 PS 6 . The value of the energy gap E g = 0.83 eV obtained using the ordinary DFT approach (Fig. 2a) is more than twice smaller than the experimental one, E g = 2.02 eV 9,10 . The thermoelectric properties of Cu 7 PS 6 calculated using the energy gaps E g = 0.83 eV and E g = 2.02 eV have been found to be almost the same for different temperatures in the range T < 500 K, and therefore may be related to the extrinsic electrons in Cu 7 PS 6 . The mentioned above underestimation of the calculated energy gap E g may be corrected using for example the DFT + U approach 11,12 , Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) 13 , or modified Becke-Johnson exchange potential with L(S)DA correlation 14,15 . We used the HSE06 functional and the modified Becke-Johnson exchange potential (mBJ) and have obtained the calculated energy gap E g close to the experimental one, E g = 2.02 eV 9,10 .
The thermoelectric properties of the heavy degenerated wide energy gap semiconductors are determined mainly by the extrinsic charge carrier concentration in the conduction (n-type carriers) or valence (p-type carriers) bands and the energy gap value E g = 2.0 eV of Cu 7 PS 6 , should not influence substantially these properties at the temperatures not much higher than the ambient one. Taking the later remark into account, we present the thermoelectric properties of Cu 7 PS 6 calculated by the BoltzTrap2 code 16,17 using the results of the ordinary DFT band structure calculations performed by VASP code [18][19][20][21][22][23] with opt-B86b exchange-and-correlation functional 24 and PAW-PBE pseudopotentials 23 and applying the scissor factor s = 2.0 corresponding to the energy gap E g = 2.0 eV 9,10 .  www.nature.com/scientificreports/ The highest valence bands of the crystal Cu 7 PS 6 in the range 0 to − 3.0 eV are relatively flat (Fig. 2a). The highest valence band dispersion is observed at the points Γ and R of the Brillouin zone (Fig. 2a). The bottom conduction bands, located in the energy range of 0.83-5 eV, are characterized by the relatively large electron wave vector dispersion of energy E(k) in comparison to the top valence bands. This means that the electron effective masses m * = ħ 2 /(d 2 E/dk 2 ), as one of the main characteristics of semiconductors, for the bottom conduction bands are substantially smaller than the similar values for the top valence bands.
In view of the electric and thermoelectric properties of a material, the most significant energy ranges of the corresponding band structure are those neighboring to the energy gap E g . The top valence and bottom conduction bands of the crystal in the range -3 to 3 eV are formed mainly by the d-electrons of copper and p-electrons of sulfur (Fig. 2b). This mainly is caused by the highest relative content of copper and sulfur atoms in Cu 7 PS 6 . The smallest PDOS of phosphorous is explained by the smaller it's content in the formula unit Cu 7 PS 6 . The band structure is characterized by the relatively high hybridization of electronic states in the energy ranges close to the energy gap E g , which manifests itself in the similar PDOS maxima in the range of the top valence and bottom conduction bands (Fig. 2b). Thus the bonding electrons of the most numerous atoms copper and sulfur form mainly the electronic states, which may be relevant to the electron conductivity of Cu 7 PS 6 .
The effective masses of electrons m * e and holes m * h are essential parameters characterizing the mobility of electric charges in semiconductors and substantially influence the thermoelectric and photoelectric properties 25 . The effective masses of electrons and holes in Cu 7 PS 6 have been calculated by utilizing the Effective Mass Calculator 26 and by using the Burstein-Moss effect. In the latter case, the excess charge carriers (electrons or holes), associated with doping of semiconductors, cause the increase of energy gap 27,28 . The energy gap increase ΔE g , caused by the excess electrons, is equal to the Fermi energy change ΔE F = ΔE g depending on the carrier concentration n and the effective electron mass m ⁎ in the conduction band, where h is Planck's constant. The energy gap increase ΔE g may be caused by the excess or lack of electrons in the crystal unit cell. On the basis of the measured or calculated value ΔE g = ΔE F and using the relation (1) one can calculate the effective electron or hole masses, m * e or m * h , corresponding to the ranges of conduction (c) or valence (v) bands. In the present study, the energy gap increase ΔE g = ΔE F , caused by the excess electron concentration n, was simulated computationally and taken as the Fermi energy shift ΔE F = E F − E cbm , where E F is the Fermi energy of the n-type semiconductors studied and E cbm is the energy of the conduction band corresponding to the bottom conduction one of the nominal crystal. Similarly, in the case of the hole conductivity, the value of ΔE F was taken as the Fermi energy shift ΔE F = E F − E vbm , where E vbm is the energy of the valence band corresponding to the top  Table 1). For both, electron and hole excess carriers, the averaged increase of the absolute value of the effective carrier mass |m e * | and |m h * | takes place in the range 1.4 × 10 20 -1.7 × 10 22 cm −3 of the excess carrier concentration. This result is generally in agreement with the view of the conduction bands of Cu 7 PS 6 , where the decrease of the band dispersion d 2 E/dk 2 is clear visible at an increase of energy (Fig. 2a), which corresponds to the increase of the electron effective mass m * (there is no such clear change of the band dispersion d 2 E/dk 2 in the range of the top group of valence bands (Fig. 2a).
The analysis of the electron/hole effective mass of Cu 7 PS 6 presented above indicates that the effective mass of the conduction electrons is much smaller than the similar value for the holes. Thus, one may expect the corresponding differences in the physical values of Cu 7 PS 6 depending on the effective electron mass.
Several thermoelectric properties of Cu 7 PS 6 were calculated in the framework of DFT using the VASP and BoltzTraP2 codes. One of the main thermoelectric parameters is the Seebeck coefficient (α), which is proportional to the charge carrier effective mass m * , temperature T, and the inverse charge carrier density n −2/329 , Here, k B is Boltzmann's constant, e is the electron charge, h is Planck's constant. Thus, a large Seebeck coefficient is expected in material possessing large effective mass and small carrier concentration. Having calculated the Seebeck coefficient of Cu 7 PS 6 by applying the VASP and BoltzTraP2 codes (Fig. 3), one has the possibility to calculate the effective mass m * from the relation (2) (solid lines in Fig. 3b). Thus calculated effective mass m * is comparable with that obtained by the method utilizing the Burstein-Moss effect in the limited ranges of the In the inset, the effective mass m * , obtained on the basis of the relation (3), where the values μ and τ were calculated using AMSET code 30  www.nature.com/scientificreports/ carrier concentration, 1 × 10 19 -3 × 10 21 cm −3 for electrons and 1 × 10 20 -3 × 10 21 cm −3 for holes (Fig. 3b). For smaller concentrations (n < 1 × 10 19 cm −3 for electrons and n < 1 × 10 20 cm −3 for holes), the decrease to zero of the absolute value of the carrier effective mass |m * | is observed (solid lines in Fig. 3b). This result is not reasonable because it does not agree with the limited electron and hole effective masses, |m e * | ≈ 0.6 m e and |m h * | ≈ 6 m e , expected on the basis of the bottom conduction and top valence band energy dispersions d 2 E/dk 2 of Cu 7 PS 6 at Γ-point of BZ (Fig. 2a). That is why the effective mass m * , calculated using the Burstein-Moss effect, may be utilized for the proper calculations of the carrier mobility μ, relaxation time τ, and electric conductivity σ. Afterward, the power factor PF and the figure of merit ZT, as the main thermoelectric values, may be calculated using the BoltzTrap2 code. In the present study, the thermoelectric properties of Cu 7 PS 6 were calculated using the new AMSET code 30 , which uses also the BoltzTrap2 one.
According to the relation of the effective masses |m h * | >|m e * | mentioned above (Fig. 3b), the absolute value of the Seebeck coefficient α is larger for the p-type carriers of Cu 7 PS 6 , in comparison to the n-type one (Fig. 4a). The decrease of the Seebeck coefficient |α| is observed when the carrier concentration n increases. For every carrier concentration n the absolute value of Seebeck coefficient |α| increases with the increase in temperature (Fig. 4a). These features are in agreement with the relation (2).
We have found that the value of scattering rate SR ([SR] = s −1 ) of electric carriers (electrons and holes) in Cu 7 PS 6 is determined mainly by the polar optical phonon scattering. The mechanism of the ionized impurity scattering prevails only for the heavy doped Cu 7 PS 6 (n ≥ 10 21 cm −3 ). The scattering rate related to the acoustic deformation potential is found to be two orders of magnitude smaller than that related to the polar optical phonon mechanism. Thus the carrier scattering mechanisms associated with the acoustic deformation potential, polar optical phonons, and ionized impurities were taken into account at the properties calculations using AMSET code. One of these calculated properties is the carrier mobility μ, calculated for the different electron (n) and hole (p) carrier concentrations n and temperatures (Fig. 4b). As was expected for the extrinsic semiconductor, the carrier mobility decreases with increasing the carrier concentration and temperature.
Having calculated by the AMSET code the mobility μ, and the scattering rate, SR = τ −1 , one can obtain the effective mass m * on the basis of the known relation, where e is the electron charge. Such calculated effective mass m * as a function of the carrier concentration n, corresponding to the temperature 300 K, is presented in the inset of Fig. 3b. This dependence m * (n) is in satisfactory agreement with that obtained by using the Burstein-Moss effect (Fig. 3b). Thus, in Cu 7 PS 6 , the hole effective mass m h * is about one order of magnitude larger than the electron effective mass m e * . The monotonous increase of specific conductivity σ with an increase of carrier concentration n is expected in the whole range of the concentration n for both types of charge carriers (Fig. 5a). Here, the n-type conductivity of Cu 7 PS 6 is at least one order of magnitude larger than the p-type one. A similar monotonous increase takes Figure 4. Dependences of (a) Seebeck coefficient α and (b) mobility μ on carrier concentration n for Cu 7 PS 6 at the temperatures 200 K, 300 K, 400 K, 500 K, and 600 K for electron (n) and hole (p) types carriers. www.nature.com/scientificreports/ place for the concentration dependences of the power factor PF (PF = α 2 σ) up to n ≈ 10 20 cm −3 (Fig. 5b). The clear extremum-like concentration dependences in the range 10 20 -10 22 cm −3 of the power factor PF for different temperatures take place for the p-type carriers (Fig. 5b). The large drop of the power factor for the n-type carriers at n = 10 21 cm −3 and the extremum-like concentration dependences PF(n) are caused by the very small Seebeck coefficient α in the range 10 20 -10 22 cm −3 (Fig. 4a). Also, the opposite characters of the temperature dependences PF(T) for the n-type carries are observed in the concentration range n < 3 × 10 18 cm −3 and n > 3 × 10 18 cm −3 (Fig. 5b). For metals and extrinsic semiconductors, the temperature dependence of the specific resistivity ρ(T) (ρ = σ −1 ) may be fitted by the relationship, where ρ 0 is the resistivity at the temperature T 0 and p is the power index depending on the features of the carrier scattering 31 . The power indices p calculated for two carrier concentrations n (10 14 and 10 21 cm −3 ) in two temperature regions (200-240 K and 540-600 K) for the n-and p-type Cu 7 PS 6 are presented in Table 1. Here worth reminding that the power index p = 1 corresponds to the linear temperature dependence of resistivity in the ideal pure metal, when the power index p = 0 means no temperature dependence of resistivity. More strong temperature dependence of the specific resistivity ρ(T) of Cu 7 PS 6 is observed for the p-type conductivity in comparison with the n-type one (Table 1).
To obtain the thermoelectric figure of merit ZT of material, Figure 5. Dependences of (a) electric conductivity σ and (b) power factor PF on carrier concentration n for Cu 7 PS 6 at the temperatures 200 K, 300 K, 400 K, 500 K, and 600 K for electron (n) and hole (p) types carriers. www.nature.com/scientificreports/ one has to know the coefficient of thermal conductivity κ. The later value is a sum of the corresponding electron and lattice (phonon) components, κ = κ e + κ ph . The coefficient of electron thermal conductivity κ e of Cu 7 PS 6 is determined on the basis of the corresponding specific electric conductivity σ using the Wiedemann-Franz Law, where L is the Lorenz number, equal to 2.45 × 10 -8 W Ohm K −2 , T is temperature. The calculated thermal conductivity κ e does not exceed the values κ e = 2 × 10 -3 Wm −1 K −1 for electron carriers and κ e = 2 × 10 -4 Wm −1 K −1 for holes even for the relatively high carrier concentration n = 10 20 cm −3 (Fig. 6a).
To obtain the thermoelectric figure of merit ZT of Cu 7 PS 6 one has to have the total coefficient of thermal conductivity κ = κ e + κ ph . Thus, estimation of the coefficient of lattice thermal conductivity κ ph is necessary to obtain the reliable value of the total coefficient of thermal conductivity κ and finally the figure of merit ZT.
Lattice-based thermal conductivity of Cu 7 PS 6 . Two models of thermal conductivity in solids have been used to estimate the coefficient of the lattice thermal conductivity of Cu 7 PS 6 . The first one is phonon-based and the second one is diffusion-based 32 . The phonon-based model is implemented in the Phono3py code 33 and is usually applied to the crystalline solids of the high and moderate coefficient of thermal conductivity. In turn, the diffusion-based model of Allen and Feldman 34-36 is applied more successfully to the amorphous or polycrystalline materials possessing a relatively small coefficient of thermal conductivity 32 . The Cu 7 PS 6 crystal is close to the latter type of materials due to the weak bonding of copper atoms in the structure, similar to that found in Cu 7 PSe 6 4 .
In the phonon based model, the coefficient of thermal conductivity is calculated by the principle relation, where c is the specific heat, v g is the phonon group velocity, and τ is the phonon relaxation time. In the diffusionbased model, the maximum thermal conductivity is calculated by the relation, κ e = Lσ T, www.nature.com/scientificreports/ where n is the density of atoms, ω avg is the averaged oscillator frequency, k B is Boltzmann constant 32 . In the present study, the averaged oscillator frequency ω avg of Cu 7 PS 6 has been obtained from the calculated vibration density of states obtained by using the lattice and molecular dynamics ( Supplementary Figs. 1, 2). The dispersion of phonon bands was calculated using the VASP and Phonopy 37 codes and the results are presented in Fig. 7a. From the phonon dispersion, we notice that there exist soft phonon optical modes with frequency decreasing near the BZ center, as highlighted in red in Fig. 7a. A similar feature of the phonon dispersion was observed in Ref. 38 . It was commented that such optical phonon softening induces strong phonon anharmonicity 39,40 . The optical phonon softening detected (Fig. 7a) is in agreement with the anharmonicity of the copper atoms in Cu 7 PS 6 observed in the molecular dynamics ( Supplementary Fig. 1b). Small negative frequencies in the vicinity of Γ-point (Fig. 7a) show the structural instability of Cu 7 PS 6 , which may be associated with the increased mobility of the copper atoms. This feature implies the low lattice thermal conductivity of Cu 7 PS 6 . It should be mentioned that the presence of these negative frequencies is independent of the atoms displacements amplitude A in the range 0.015-0.1 Å, the phonon q-mesh density (12 × 12 × 12 and 24 × 24 × 24), or the electron k-mesh density (2 × 2 × 2, 4 × 4 × 4, and 6 × 6 × 6).
The coefficient of lattice thermal conductivity κ ph (1) of Cu 7 PS 6 was calculated using VASP and Phono3py 33 codes (Fig. 7b). In accordance with the expectation, we have obtained the extremely small value of the coefficient of the lattice thermal conductivity of Cu 7 PS 6 , κ ph (1) = 0.05 Wm −1 K −1 at the temperature 300 K (Fig. 7b). For the calculations, the default displacement amplitude of atoms A = 0.03 Å was used. We have checked the convergence of the calculated coefficient κ ph (1) in relation to the inverse lattice q-mesh size and the cutoff distance of the interatomic interaction. The convergence test in relation to the influence of the q-mesh size on the κ ph (1) coefficient, presented in Fig. 7b, confirms the validity of the calculated κ ph (1) coefficient for Cu 7 PS 6 . Also, when the cutoff distance R cutoff changes from 3 Å to the nonlimited value in the unit cell box 9.6 × 9.6 × 9.6 Å 3 the coefficient κ ph (1) changes in the range of 8% of the mean κ ph (1) value, but this dependence was found to be not monotonous. Using the same version of the Phono3py code (v.2.0.0) the calculated coefficient of the lattice thermal conductivity of silicon crystal has been found to be close to the reference value κ ph (1) = 130 Wm −1 K −1 (Fig. 7b). This may be regarded as the confirmation of the correctness of the calculations using the applied Phono3py version. On the other hand, we are aware that the extremely small value of the coefficient κ ph (1) = 0.05 Wm −1 K −1 may partly be a result of the negative acoustic frequency ν and negative derivative dν/dk close to the Γ-point (Fig. 7a), which may decrease the acoustic velocity in the crystal.
The electron part of the thermal conductivity κ e of the extrinsic Cu 7 PS 6 ( Fig. 6a) is much smaller than the lattice one κ ph (1) of the nominal crystal (Fig. 7b). Taking into account the relation κ ph (1) > > κ e , the values κ ph (1) were used for the calculation of the thermoelectric figure of merit ZT presented in Fig. 6b. According to these estimations, the value ZT of the extrinsic Cu 7 PS 6 may be of practical interest (ZT > 0.1) for the heavy doped n-type Cu 7 PS 6 of the electrons concentration n ≥ 10 18 cm −3 and the holes concentration n ≥ 10 19 cm −3 . (2) = 0.7 W/(m K) is one order of magnitude larger than the similar value κ ph (1) = 0.05 W/(m K) obtained by utilizing Phono3py code (Fig. 7b). Both above mentioned calculated values of the lattice thermal conductivity κ ph (1) = 0.05 W/(m K) and κ ph (2) = 0.7 W/(m K) of Cu 7 PS 6 at the temperature 300 K may in principle be acceptable because they correspond to the figure of merit ZT calculated for different carrier concentration and temperatures (Fig. 6b). It is hard to compare the calculated here the thermoelectric figure of merit ZT of the extrinsic Cu 7 PS 6 and the corresponding experimental results 41 because the latter ones relate to the mixed type of electric conductivity covering the activation-like and scattering-like mechanisms.

Methods of calculations
A study of the electronic properties of Cu 7 PS 6 crystals was performed in the framework of the density functional theory (DFT) using the VASP code [18][19][20][21][22][23] and PAW pseudopotentials 23 . In view of the relatively large conventional unit cell of the crystal (a = b = c = 9.59 Å, space group no. 198), the dispersion interactions (van der Waals) have been taken into account in the form of the opt-B86b functional 24 .
Before the production calculations of the crystal studied, the total energy convergence tests were performed in relation to the cutoff energy of plane waves (E cutoff ) and the k-points grid used. Finally, the cutoff energy E cutoff = 390 eV and the k-points grids from 6 × 6 × 6 to 10 × 10 × 10 of the reciprocal lattice have been used, depending on the type of the calculation task.
The thermoelectric properties of Cu 7 PS 6 were calculated using the recently published AMSET code 30 developed on the basis of VASP and BoltzTraP2 16,17 . The BoltzTraP2 code is based on the semi-classical Boltzmann transport theory 42 with the density of electron states (DOS) only as input. Therefore, before the calculations of thermoelectric properties using AMSET and BoltzTraP2 codes, the DFT calculations of the electronic band structure were performed using the VASP code. Apart from the calculation of the Seebeck coefficient α, electric conductivity per relaxation time σ/τ and electron thermal conductivity per relaxation time κ e /τ, performed using the BoltzTrap2, the calculation of the electron/hole scattering factor may be realized by using the AMSET code (Ab initio Scattering and Transport). In the AMSET code, different models of the electron/hole scattering are implemented (e.g. acoustic deformation potential, polar optical phonon scattering, and ionized impurity), which permits to obtain of the reliable values of the carrier relaxation time in the material studied. Due to this, the more reliable thermoelectric values necessary to compare with the corresponding experimental ones may be obtained.
The dispersion of the phonon bands of Cu 7 PS 6 crystal was calculated using the Phonopy code 37 . The coefficient of lattice thermal conductivity κ ph (1) of Cu 7 PS 6 was calculated using the VASP and Phono3py codes 33 . To obtain the reasonable value of κ ph coefficient one generally should not use a small unit cell 33 . Due to the relatively large unit cell dimensions of Cu 7 PS 6 crystal (a = b = c = 9.6 Å) and the number of atoms (N a = 56) the supercell 1 × 1 × 1 has been used for the corresponding calculations. At the cubic symmetry P2 1 3 of Cu 7 PS 6 , the number of the VASP structure files (and corresponding runs of the SCF electron calculations), necessary for the calculation of the FORCES_FC3 file for the Phono3py calculations, is equal to 9436. This indicates that the use of larger supercells, e.g. 2 × 2 × 2, together with the dense k-point grid for this purpose may not be acceptable because of the huge amount of the necessary computational resources.
To obtain better insight into the phonon-associated effects in Cu 7 PS 6 crystal the molecular dynamics calculations have been performed using the VASP code at different temperatures in the range of 20-800 K. The results of MD obtained were elaborated using the nMoldyn 3.0 code 43 . www.nature.com/scientificreports/

Conclusions
The Burstein-Moss effect is shown to be successfully utilized for the calculation of the electron effective mass dependence on the electric carrier concentration of the extrinsic type in Cu 7 PS 6 crystal. An increase of the absolute value of the electron effective mass in Cu 7 PS 6 with an increase of the electrons and holes concentration in the range n > 3 × 10 20 cm −3 has been detected, which should be taken into account in the calculation of the thermoelectric properties depending on the electric carriers mobility. The polar optical phonon scattering of the electric carriers is the predominant one in Cu 7 PS 6 . The mechanism of the ionized impurity scattering prevails only for the heavy doped Cu 7 PS 6 (n ≥ 10 21 cm −3 ). The weak chemical bonding of copper atoms in Cu 7 PS 6 leads to the extremely small coefficient of the lattice thermal conductivity κ ph (1) ≈ 0.05 Wm −1 K −1 obtained from the calculated phonon lifetime using the Phono3py code. The relatively high temperature stimulated mobility of the copper atoms in comparison to the phosphorous and sulfur ones found in Cu 7 PS 6 crystal justifies the applying of the diffusion-based model of thermal conductivity. In the framework of this model, the calculated coefficient of lattice thermal conductivity of Cu 7 PS 6 , κ ph (1) ≈ 0.7 Wm −1 K −1 , is close to the experimental one κ exp ≈ 0.2-0.3 Wm −1 K −1 . For the heavy doped Cu 7 PS 6 of the carrier concentration about 1 × 10 19 -1 × 10 21 cm −3 , the calculated values of the thermoelectric figure of merit are comparable with the corresponding experimental ones obtained for the mixed type of electric conductivity covering the activation-like and scattering-like mechanisms.