Introduction

Waste heat accounts for roughly half of total energy generation. The harvested waste heat can be cost-effective converted into electricity using the thermoelectric generators. Thus, one of the main trends of the modern material science is development of highly efficient thermoelectric materials for waste heat recovery1,2. The energy conversion efficiency is quantified by a thermoelectric figure of merit ZT = S2σT/κ, where S, σ, T, and κ are the Seebeck coefficient value, electrical conductivity, temperature, and thermal conductivity, respectively. The efficient thermoelectric material should have high values for both Seebeck coefficient and electrical conductivity and low thermal conductivity values. The combination of the corresponding parameters allows one to consider the layered dichalcogenides MCrX2 (M = Cu, Ag; X = S, Se) as a promising functional materials for thermoelectric applications3,4,5,6,7,8,9. These compounds are formed by alternating metal and chalcogenide layers. The unstable dichalcogenide CrX2-layers are stabilized by metal atoms M, intercalated between the layers. The layered structure leads to the difference between their electron and phonon mean free paths and, thereby, the thermal conductivity decrease and the electrical conductivity increase. The chromium atoms in the dichalcogenide layers could be substituted with other transition metal atoms over a wide range of concentration without spatial group change9. The cationic substitution of MCrX2-matrix with heavy 3d- or 4f.-metal atoms allows one to decrease the thermal conductivity due to the phonon scattering increase. It was reported, that cationic substitution of the CuCrS2 layered dichalcogenide is an effective approach for improving the material physical properties4,7,9,11. In particular, the substitution of chromium with iron atoms at low-level doping concentration (x ≤ 0.03) results a significant increase of the Seebeck coefficient value in comparison with those for the initial CuCrS2-matrix9. Contrariwise, an increase of iron dopant concentration suppresses the thermoelectric properties of the cation substituted solid solutions due to the metal–insulator transition (MIT). Thus, the solid solutions low-level doping concentration are of special interest. The heavy lanthanide atoms could be used to increase the phonon scattering due to the increase of the nanoscale inhomogeneity that, thereby, decrease the material thermal conductivity1,2. The doping of CuCrS2-matrix with lanthanide ions leads to the Seebeck coefficient value increase11. Thus, the combination of the above mentioned approaches could be considered as a promising way to optimize the thermoelectric efficiency of CuCrS2-based solid solutions.

Note that ZT is determined mainly by the Seebeck coefficient value. Seebeck coefficient is complicated parameter determined by both the electron density of states (DOS) distribution and the carrier concentration and its mobility9,10:

$$\mathrm{S}=-\frac{{k}^{2}}{\mathrm{e}}\frac{1}{\mathrm{n}{\upmu }_{\mathrm{n}}+\mathrm{p}{\upmu }_{\mathrm{p}}}\left\{\left[2-\frac{{\mathrm{E}}_{\mathrm{F}}}{\mathrm{kT}}\right]\mathrm{n}{\upmu }_{\mathrm{n}}-\left[2-\frac{{\mathrm{E}}_{\mathrm{F}}+{\mathrm{E}}_{\mathrm{g}}}{\mathrm{kT}}\right]\mathrm{p}{\upmu }_{\mathrm{p}}\right\}=-\frac{\mathrm{k}}{\mathrm{e}}\left\{\frac{\left[2+\mathrm{ln}\left(\frac{\mathrm{Nc}}{\mathrm{n}}\right)\right]\mathrm{n}{\upmu }_{\mathrm{n}}-\left[2+\mathrm{ln}\left(\frac{\mathrm{Nv}}{\mathrm{p}}\right)\right]\mathrm{p}{\upmu }_{\mathrm{p}}}{\mathrm{n}{\upmu }_{\mathrm{n}}+\mathrm{p}{\upmu }_{\mathrm{p}}}\right\},$$
(1)

where k—the Boltzmann constant, e—the electron charge, n and p—the concentration of electrons and holes respectively, µn and µp—the mobility of the electrons and holes respectively, Eg—the band gap width, EF—the Fermi energy, Nc and Nv—effective DOS of the conduction and valence band respectively. According Eq. (1), one can conclude that the Seebeck coefficient of a p-type semiconductor is determined mainly by the valence band DOS as well as the Fermi level energy. The CuCrS2-based solid solutions are considered as p-type semiconductors3,4,5,6,9,11. Hence, the study of the electron density distribution in the valence band is of special interest.

The Seebeck coefficient of CuCrS2-based solid solutions is significantly changed due to the reconfiguration of the electronic structure across the MIT. This fact allows one to conclude that the partial density of states (pDOS) localization character and, thereby, the integral charge distribution are the key aspects of the interpretation and prediction of the thermoelectric properties. However, the electronic structure features in the valence band of the lanthanide-doped CuCr0.99Ln0.01S2 (Ln = La, Ce) solid solutions has not been discussed yet. The X-ray photoelectron (XPS) and X-ray emission spectroscopy (XES) are the most effective experimental techniques to study the electronic structure12,13. The combination of these techniques allows one to investigate the atom oxidation state in the near-surface layers (XPS) and in the bulk (XES) of CuCr0.99Ln0.01S2 (Ln = La, Ce). The partial contributions in the electronic structure features in the valence band (VB) could be studied using the density functional theory (DFT) simulation of the experimental XPS VB spectra structure.

Methods

The powder samples CuCrS2 and CuCr0.99Ln0.01S2 (Ln = La, Ce) were synthesized from the initial metal oxides (CuO, Cr2O3, La2O3, CeO2) with purity of 99.99% using procedure described and reported previously in11. The current research was carried out using the samples from our previous work11. The synthesized samples were reported to be single-phase and isostructural to the initial CuCrS2-matrix11,13. The obtained crystal structure data agree well with the crystallographic data reported in14.

The XPS lines were measured using a SPECS spectrometer with a PHOIBOS-150 hemispherical analyzer. The sulfur (S2p), copper (Cu2p), lanthanides (Ln3d) lines and valance band spectra were recorded using AlKα radiation (E = 1486.6 eV). The chromium (Cr2p) lines were recorded using Mgα radiation (E = 1253.6 eV). The residual pressure in the spectrometer analysis chamber was < 1·10−9 Torr. The samples were fixed on a sample holder using a conductive double sided adhesive carbon tape and held at room temperature during the measurements. The XPS spectra processing (decomposition into individual components, measurement of XPS signal area and binding energies) was carried out after the background subtraction using CasaXPS 2.315. The experimental spectra were corrected with Shirley background approximation and fitted with the Gaussian–Lorentzian function. The binding energy scale was calibrated with the internal standard method using the C1s line (284.8 eV) for the carbon contained on the sample surface. The measurement accuracy of XPS binding energy was 0.2 eV.

The X-ray emission spectra (XES) of sulfur (SKα), chromium (CrKα) and copper (CuKα) were measured using Johann-type X-ray spectrometer with a cylindrically bent quartz \((10\overline{1}1)\) crystal-analyzer (X-ray tube voltage V = 24 kV, current I = 15 mA). The base pressure in the spectrometer analysis chamber was ~ 2.5·10−5 Torr. The samples on a double sided adhesive carbon tape were fixed on a secondary aluminum anode and held at a liquid nitrogen temperature during the measurements. The spectra were measured using a gas-flow argon-methane proportional counter. The measurement accuracy of the SKα1,2- and CrKα1,2-lines energy position was 0.05 eV, for the CuKα1,2-lines was 0.1 eV. The reference compounds Cu2S (99.99%), Cr2O3 (99.9%) and KSCN (≥ 99.0%) used are the commercial chemicals (Millipore Sigma, USA). The spectrometer resolution in the spectral region being studied was ~ 5·10−4. The XES spectra processing was carried out using XPSPeak fitting program16.

The partial density of states (pDOS) distribution in the valence band was calculated in BAND software package17 using the generalized gradient approximation (GGA), the standard Slater-type orbital basis set using three basis function per atomic orbital with one polarization function (TZP) and the Perdew-Burke-Ernzerhof exchange–correlation potential (PBESol-D). The crystallographic data for initial CuCrS2-matrix were taken from the Inorganic Crystal Structure Data base (ICSD)14. In the case of the lanthanide-doped CuCr1-xLnxS2 (Ln = La, Ce) solid solutions one of the three chromium atoms in the unit cell CuCrS2 was replaced by lanthanum or cerium atom (x≈0.33) and the geometry was optimized.

The experimental XPS valence band spectra were compared with calculated data taking into account both the photoionization cross sections and atomic concentrations18. The calculated pDOS were broadened in order to take into account the AlKα-line width and the instrumental resolution using a Lorentz-type distortion function with half-width of 1 eV19.

The electrical resistivity temperature dependencies were measured in an atmosphere of helium at a pressure reduced to 5 Torr on the cylindrical compressed (~ 70 MPa) samples using two-probe resistance measurement technique. The samples were compressed in vacuum at 650 °C. The estimated sample density was ~ 4.1 g/cm3. The Thermodat-13K5 temperature controller was used for the temperature control and stabilization. The electrical resistivity was measured using digital multimeter Keysight 34461A.

Results and discussion

The XPS data allows one to determine the binding energy (BE) of individual core levels. The core level energy depends on the charge located on the constituent atoms. The charge redistribution affects the core level energy. Thus, XPS S(2p)-, Cr(2p)-, Cu(2p)- and La, Ce(3d)-core level were recorded to determine the atom oxidation state (Fig. 1).

Figure 1
figure 1

XPS lines of CuCrS2-matrix and lanthanide-doped solid solutions CuCr0.99Ln0.01S2 (Ln = La, Ce): (a) Cu(2p3/2)-, (b) Cr(2p3/2)-, (c) S(2p)- and Ln(3d5/2)-lines (d). Inset: Ce4d-region.

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Figure 1a shows the XPS Cu(2p3/2,1/2)-lines of CuCr0.99Ln0.01S2 (Ln = La, Ce) powder samples. The Cu(2p)-region exhibits two intense peaks corresponding to 2p3/2 and 2p1/2 levels (~ 932 and ~ 952 eV, respectively) and two groups of the satellite lines Sat (~ 943–946 and ~ 960–965 eV, respectively).

The satellite lines are characteristic for Cu2+ compounds and arising due to shake-up states corresponding to the p5d9 electronic configuration20. The Cu(2p3/2)- and Cu(2p1/2)-lines could be represented as a superposition of lines arising from the nonequivalent copper atoms (marked as I and II in Fig. 1) related to the different oxidation states21,22,23. The copper oxidation state analysis was carried out using the binding energy (BE) value of Cu(2p3/2)-lines (Table 1). The BE value of low energy I component (~ 932.5 eV) is typical for the compounds containing Cu+ (BE(Cu2S) ≈932.3 eV; BE(Cu2O) ≈932.4 eV; BE(CuCl) ≈932.3 eV)19,24,25. The BE of the high energy II component (~ 934.7 eV) is typical for Cu2+ compounds (BE(CuO) ≈933.7 eV; BE(CuCl2) ≈933.7 eV; BE(CuSO4) ≈935.4 eV)19,24,25. The high energy components II are assumed to include the defected near-surface layers22,26,27. These layers contain oxygen-contained compounds of Cu2+. This fact is additionally approved with data reported on the vanadium-doped CuCr1-xVxS2 solid solutions13,22,23.

Table 1 Binding energies values (eV) of the XPS Cu(2p3/2)-, Cr(2p3/2)-, S(2p3/2)-, La(3d5/2)- and Ce(3d5/2)-lines.
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The core-level X-ray emission spectroscopy (XES) as well as XPS could be sufficiently used to determine the effective atomic charges in molecules and solids. The main difference between these two experimental techniques is that in contrast to XPS, XES allows one to determine the atom oxidation state in the in the bulk. Thus, the combination of both XPS and XES allows one to obtain the total data on the atomic charges in CuCr0.99Ln0.01S2 (Ln = La, Ce).

The XES CuKα1,2-spectra for CuCrS2-matrix and lanthanide-doped CuCr0.99Ln0.01S2 (Ln = La, Ce) solid solutions are depicted in Fig. 2a. The CuKα-region exhibits two intense peaks corresponding to the 2p3/2,1/2 → 1 s transitions. The line-shape of the CuKα1,2-spectra does not significantly change after the cationic substitution. Note that additional oxidation forms of copper were not observed in the CuKα1,2-region. This fact indicates that Cu2+ forms arising in the Cu2p-region are contained only in the defected near-surface layers. The energy position of the CuKα1-line maximum for CuCr0.99Ln0.01S2 lies within the range of 8047.7–8047.8 eV (Table 2). The measured values are typical for Cu+ atoms and agree well with one for Cu2S reference compound containing monovalent copper atom. Thus, one can conclude that the copper atomic charge is preserved after cationic substitution of CuCrS2-matrix with Ce and La atoms.

Table 2 Energy position of X-ray copper, chromium and sulfur Kα1,2-emission lines maximum (eV).
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The XPS Cr(2p3/2,1/2)-lines are depicted in Fig. 1b. The Cr(2p)-region exhibits two intense 2p3/2 and 2p1/2 spin doublet components (~ 575 and ~ 584 eV, respectively). The main 2p3/2-line could be presented as a superposition of two components (I and II) related to the different oxidation states. The BE of the low energy I component (~ 574.7 eV) for Cr(2p3/2)-line is typical for the compounds containing Cr3+ (BE(Cr2S3) ≈575.2 eV; BE(CuCrSe2) ≈574.7 eV; BE(CuCr2Se4) ≈574.5 eV)19,24,25.

The high energy components II (~ 576.6 eV) could be related to the oxygen-containing compounds of Cr3+ on the powder surface (BE(Cr2O3) ≈576.5 eV; BE(CuCrO2) ≈576.0 eV)19,24,25,28. It should be noted that the measured BE values of Cr(2p3/2) are in good agreement with previously reported XPS data for CuCrS2-matrix5,21,22,23,29. Figure 2b plots the XES CrKα1,2-region of CuCrS2-matrix and lanthanide-substituted solid solutions CuCr0.99Ln0.01S2 (Ln = La, Ce). The energy position of chromium Kα1-maxima lies within the range of 5414.90–5414.98 eV (Table 2). Taking into account the measurement accuracy, the CrKα1-maxima energy position values correlate with one for Cr2O3 reference compound and typical for Cr3+13. The absence of the significant chemical shifts of Cr(2p)- and CrKα-lines indicates that cationic substitution does not significantly affect the chromium atomic charge. The CrKα-line shape fact indicates the absence of the additional chromium oxidation states. Note, that 2p to 1 s core level electron transition, corresponding to XES Kα-lines, occurs in the Coulomb field created by surrounding atoms of the system. Thus, the position of the XES line depends only on the electron density localized on the investigated atom. The potential from the chemical surrounding does not affect the XES lines energy position. Hence, the additional components arising in Cr(2p)-region from the Cr3+ oxidation forms could not be resolved in CrKα-region 13.

Figure 2
figure 2

XES Kα1,2-spectra of CuCrS2-matrix and CuCr0.99Ln0.01S2 (Ln = La, Ce) solid solutions: (a) CuKα1,2-, (b) CrKα1,2- and (c) SKα1,2-spectra.

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Figure 1c plots the XPS S(2p3/2,1/2)-lines of CuCrS2-matrix and lanthanide-substituted solid solutions. Table 1 lists the experimental BE values of S(2p3/2)-lines. The S(2p)-line is a superposition of two components (S(2p1/2) and S(2p3/2)) arising from the spin–orbit coupling of S2p core-level. The experimental S(2p)-region presents a superposition of lines arising from the several nonequivalent groups containing different types of sulfur atoms (denoted as I, II and III in Fig. 1c).

The first group (I) includes the sulfur atoms in the composition of the CuCrS2-matrix and lanthanide-doped solid solutions (Table 1). The energy position of S(2p3/2)-line (BE ~ 161.5 eV) corresponds to S2− oxidation state and is typical for the transition metal sulfides (BE(CuFeS2) ≈161.5 eV; BE(Cu2S) ≈161.8 eV)19,24,25. The second group of S(2p)-lines (II) with BE ~ 163 eV is assumed to include the elemental sulfur (BE ≈ 163.5 eV) on the powder surface. The presence of the “surface” elemental sulfur is typical for the natural and synthesized sulfide materials26. The last group of S(2p)-lines (III) with BE ~ 168.2 eV is assumed to include the oxygen-containing compounds of sulfur on the powder surface (BE(CuSO4) ≈169.6 eV; BE(C12H8SO2) ≈168.2 eV, BE ((NH4)2SO4) ≈168.3 eV; BE(SO(CH3O)2) ≈168.4 eV)19,24,25.

The XES SKα1,2-spectra are unresolved spin-doublets (Fig. 2c). The measured SKα1-line energy position values correspond to divalent sulfur and correlates with one for KSCN reference compound containing S2− (Table 2). The SKα1,2-line shape and the energy position allow one to conclude that additional groups of sulfur atoms are localized in the near-surface layers. Thus, the absence of the significant chemical shifts of the S(2p)- and SKα-lines allow one to conclude that cationic substitution of CuCrS2-matrix with lanthanide atoms does not significantly affect the sulfur atoms oxidation state.

The XPS lines of lanthanides (La and Ce) are presented in Fig. 1d. The BE values of Ln(3d5/2)-lines are listed in Table 1. The Ln(3d)-region exhibits the main peak (I) accompanied with a satellite line (II) arising due to the multi-electron processes (multiplet structure)30. The La(3d5/2)-line is unresolved peak with structure typical for La3+ (two components with the similar intensity)24. The obtained La(3d5/2) BE value equal to ~ 835.4 eV corresponds to La3+ (BE (La2O3) ≈835 eV)24,25.

The multiplet splitting (MS) between the main and the satellite lines in the Ln(3d)-spectra allows one to identify the Ln oxidation state. The measured MS value of La(3d5/2)-line is equal to 3.2 eV. The typical MS value for La3+ compounds lies within the range of ~ 3.5–4.6 eV25. Thus, one can conclude that lanthanum atoms in the composition of CuCr0.99La0.01S2 are trivalent. In contrast to the lanthanum, the cerium could exhibit a few stable oxidation forms (Ce3+ or Ce4+). It should be noted that as it was reported previously for vanadium-doped solid solutions CuCr1-xVxS2 (x < 0.15), the vanadium atoms were found to be in V4+ oxidation state13. Hence, the cerium oxidation state is of special interest. The Ce(3d5/2)-line has a structure similar as those for La(3d5/2)-line. The BE values corresponding to the different oxidation forms of the cerium atoms lies almost in the same energy region. For instance, the BE value for Ce4+ (BE(Ce4+) ≈882–882.7 eV) is slightly higher than for Ce3+ (BE(Ce3+) ≈880–881.5 eV)24,25,31,32. The measured BE value of Ce(3d5/2)-line for cerium-doped solid solution CuCr0.99Ce0.01S2 is equal to ~ 882.1 eV. At the same time, the MS values for Ce4+ and Ce3+ are reported to have more significant difference (MS(Ce4+) ~ 6.3 eV; MS(Ce3+) ~ 4.5 eV)24,25,31,32. Allowing for this, the Ce(3d5/2)-line multiplet structure analysis could provide more reliable information on the cerium oxidation state. The measured MS value for CuCr0.99Ce0.01S2 is equal to ~ 4.2 eV. Thus, taking into account the preservation of the Cu, Cr and S atomic charges discussed above, one can conclude that Cr3+ is substituted by Ce3+. This fact was additionally approved by the BE value of ~ 112 eV for Ce(4d)-spectra, typical for Ce3+ oxidation state33,34.

Thus, both XPS and XES spectra analysis have shown that doping of CuCrS2-matrix with lanthanides does not significantly change the atomic charges of the matrix elements. The chromium and lanthanide atoms in the composition of CuCr0.99Ln0.01S2 (Ln = La, Ce) were found to be in trivalent oxidation state. The cationic substitution does not affect the copper and sulfur atoms oxidation state. The copper atoms oxidation state remains monovalent (Cu+), the sulfur—divalent (S2−). The results obtained are well agreed to the previously reported copper, chromium and sulfur XANES investigation data11. Note that the high sensitivity of the XPS spectroscopy allowed one first time study the lanthanide atoms oxidation state in CuCr0.99Ln0.01S2 (Ln = La, Ce).

The near-surface layers of the sample studied were found to contain additional oxidation forms of copper (Cu2+) and sulfur (S0, S4+, S6+). The presence of the additional copper oxidation form (Cu2+) indicates that the surface layers contain the additional scattering centers. These centers are assumed to increase the electrical resistance component related to the carrier scattering on the material “magnetic structure". The grain boundary magnetic scattering is one of the significant aspects in the interpretation of the colossal magnetic resistance (CMR) origin35. Thus, the electronic density distribution study of CuCrS2 and CuCr0.99Ln0.01S2 allows one to expect the promising CMR values due to the presence of the Cu2+ oxidation states on the powder surface. It should be noted that the presence of the additional oxidation forms of sulfur and copper atoms in the composition of the oxygen-containing compounds on the powder surface should significantly affect the thermoelectric properties. The oxygen-containing compounds typically have band gaps on the order of 2 to 4 eV. For instance, CuO and CuSO4 have band gaps of ~ 1.5 and ~ 4 eV, respectively36,37. Thus, their presence on the powder surface could increase the Seebeck coefficient value of CuCrS2-based solid solutions. This conclusion correlates with the fact that the Seebeck coefficient value for CuCrS2-matrix crystal samples were reported to be two times lower than one for ceramic and compacted powder samples5,9.

The physical properties of chemical compounds are determined by the electronic structure features. The data on the electron density and partial orbital contributions in the band structure could be studied using the combination of both experimental and theoretical approaches. Thus, the current study involves the DFT calculation of the partial density of states (pDOS) and the experimental XPS valence band (VB) investigation.

The pDOS of CuCrS2-matrix and lanthanide-doped CuCr1-xLnxS2 (Ln = La, Ce) solid solutions are presented in Fig. 3a–c. The electronic structure of CuCrS2-matrix is shown in Fig. 3a. The main chromium and copper d-states contributions are located near the valence band top at − 1 and − 2.5 eV below the Fermi level, respectively. The sulfur p-states contribution is mostly localized at − 4 eV. The conduction band bottom structure is dominated by the chromium d-states. The sulfur p-states and mixed copper p-, d-, s-states have a smaller contribution to the conduction band bottom structure. According to the data obtained, the undoped copper-chromium disulfide is a semiconductor with a band gap of ~ 0.29 eV (inset in Fig. 3a). The calculated pDOS distribution character is in good agreement with both experimental and calculated data reported in4,38.

Figure 3
figure 3

Theoretical total and partial DOS (a–c) for CuCrS2 and CuCr0.99Ln0.01S2 (Ln = La, Ce). Comparison of the experimental valence band (VB) spectra (green line) with theoretical DOS simulations (d–f) showing raw DOS simulations (black line); simulated DOS mathematically broadened for better consistency with the experimental VB (blue line); DOS scaled to the photoionization cross-sections of respective levels (red lines); DOS scaled to the photoionization cross-sections of respective levels; scaled and broadened DOS (magenta line).

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The cationic substitution of CuCrS2-matrix does not significantly affect the partial DOS distributions of the Cu, Cr and S matrix elements (Fig. 3b,c). Since the lanthanum has empty 4f.-shell the lanthanum states contribution in the valence band structure is dominated by d-states. The main contribution of the lanthanum occupied d-states is localized at ~  − 4 eV in the valence band. The lanthanum unoccupied f-states main contribution is localized in the conduction band at ~ 3 eV.

Since the presence of electron in 4f.-orbital, the main occupied cerium f-states contributions in CuCr1-xCexS2 are localized in the valence band top at ~  − 0.2 eV. The unoccupied cerium f-states are shifted to the conduction band bottom and localized at ~ 1 eV.

The lanthanide-doped CuCr1-xLnxS2 solid solutions conduction band bottom structure is dominated by the lanthanide f-states. The presence of the lanthanide states causes the metal–insulator transition (MIT) and the band gap vanishing (insets in Fig. 3b,c).

The experimental XPS valence band (VB) spectra are plotted in Fig. 3d–f (green lines). The simulated DOS (black lines in Fig. 3d–f) were mathematically broadened for better consistency with the experimental VB (blue lines). However, the line shape of broadened DOS (marked with “br.” in Fig. 3d–f) overestimates the intensity of the low energy shoulder feature in comparison with those for VB. Note that the photoionization cross section value (σph) for the copper 3d-sates is greater in comparison with those for sulfur 3p- and chromium 3d-states. Hence, the simulated DOS were scaled taking into account the σph of respective levels (denoted as DOS × σph in Fig. 3d–f, red lines). Thus, the better consistency of simulated DOS with experimental VB was observed for the scaled and broadened DOS (magenta line). The experimental VB structure of CuCrS2-matrix is mainly determined by the contribution of the copper states localized at ~  − 2.5 eV (Fig. 3d). The simulated and experimental VB for CuCr0.99Ln0.01S2 (Fig. 3e,f) have a structure character similar to those for CuCrS2-matrix (Fig. 3d). The data on the partial density of states and the band structure features are of special interest for thermoelectric compounds. As it was mentioned above, in the terms of the band theory the Seebeck coefficient of the semiconductors could be described as a function of DOS and carrier concentration (see Eq. (1) )10.

The isovalent substitution character discussed above allows one to conclude that the cationic substitution of CuCrS2-matrix with La or Ce does not emerge the additional charge carriers. Thus, according to the Eq. (1) the Seebeck coefficient of the lanthanide-doped CuCr0.99Ln0.01S2 (Ln = La, Ce) solid solutions is dominated by the DOS distribution character. This fact is in good agreement with an increase of the Seebeck coefficient value for CuCr1-xLnxS2 in comparison with those for CuCrS2-matrix11. The replacing of the occupied chromium 3d-states by the unoccupied lanthanum 4f.-states causes the electronic density decrease in the valence band region. Thus, the Seebeck coefficient value in CuCr0.99Ln0.01S2 increases in comparison with those for initial matrix. The lower Seebeck coefficient values for the cerium-doped solid solution is due to the presence of the electron in the Ce 4f.-orbital and the localization of the occupied cerium f-states in the valence band top.

The described electronic structure features affect the electrical resistivity of the compounds studied (Fig. 4). The lanthanum-doped CuCr0.99La0.01S2 solid solution exhibits the highest electrical resistivity values in comparison with those for CuCr0.99Ce0.01S2 and CuCrS2-matrix. Thus, the increase of the Seebeck coefficient value is accompanied with the electrical resistivity increase. Note that the DFT calculation was carried out for the model compounds CuCr1-xLnxS2 at high lanthanide concentrations (x≈0.33). The reported data on the electrophysical properties of CuCrS2-based solid solutions indicates that the high doping concentration (x ≥ 0.2) causes the MIT9,39. The MIT results the band-gap vanishing due to the presence of the additional states near the Fermi-level. Thus, the band-gap vanishing is accompanied by the electrical resistivity decreasing. In case of the CuCr0.99Ln0.01S2 the electrical resistivity decrease was not observed due to the low-doping concentration of lanthanide atoms. However, the DOS calculation for concentration of 0.33 allow one to predict the MIT in case of high doping level.

Figure 4
figure 4

Temperature dependence of electrical resistivity for CuCrS2 and CuCr0.99Ln0.01S2 (Ln = La, Ce).

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Conclusion

The electronic density and the atom oxidation state comprehensive study was carried out using experimental (XPS and XES) techniques and DFT calculations. It was shown that cationic substitution does not significantly affect the atomic charges and the partial DOS distribution character on the matrix elements (Cu, Cr, S). The experimental valence band spectra structure of CuCrS2-matrix and CuCr0.99Ln0.01S2 (Ln = La, Ce) is mainly determined by the occupied copper d-states contribution. The contribution of the lanthanide-states in the valence band structure is lower in comparison with those for the matrix elements. The major contributions of the lanthanum and cerium electronic states were found to be localized near the conduction band bottom. It was shown that the partial DOS distribution character determines the Seebeck coefficient value increase of CuCr1-xLnxS2 in comparison with those for CuCrS2-matrix. The lanthanum-doped CuCr0.99La0.01S2 solid solution exhibits the highest electrical resistivity values. The lanthanide and chromium atoms were found to be in the trivalent state, while the copper atoms in the monovalent state. The sulfur atoms in the composition of CuCrS2-matrix and the lanthanide-doped solid solutions were found to be in the divalent state. The near-surface layers contain the additional oxidation forms of the sulfur (S0, S4+, S6+) and the copper (Cu2+) atoms.