Introduction

Renewable energy production is becoming more popular due to worries about energy security, resource scarcity, and the environmental effects of burning fossil fuels. The development of renewable energy technologies has sparked a lot of research interest over the past few decades due to the conflict between the energy crisis and environmentally sustainable management [1]. Specifically, thermoelectric materials have drawn a great deal of interest because thermoelectric effects permit direct conversion of temperature difference into electric voltage and vice versa. One of the most significant solutions to the current energy problems is TE materials [2]. Thermoelectric has long been thought to be a promising and eco-friendly technology for resolving energy and environmental crises because it doesn’t produce dangerous emissions or has moving parts. High-performance thermoelectric materials are needed for large-scale applications to ensure a high heat-to-electricity conversion efficiency [3]. The dimensionless figure of merit ZT = S2T/ρκ governs the conversion efficiency of thermoelectric materials, where S, T, ρ, and κ are the Seebeck coefficient, absolute temperature, electrical resistivity, and thermal conductivity, respectively. Lattice (κL) and electronic (κe) thermal conductivities make up the total amount of thermal conductivity. Excellent thermoelectric materials must have a high S and low ρ, and κ [4] It is challenging to achieve high ZT values because the electrical transport and thermal properties are interconnected, it is impossible to enhance one property without affecting the other. Several attempts have been made to decouple and combine the individual TE properties in accordance with the underlying mechanisms with different strategies like do** [5], alloying [6], composites [7], nanostructuring [8,9,10], band engineering[11, 12], defect engineering [13,14,15,16], etc.

Regarding device applications, TE materials can be broadly divided into three groups: (1) Low-temperature TE materials whose working temperature lies between 300 and 500 K (Bi2Te3) [17,18,19], (2) Mid-temperature TE materials whose working temperature is between 500 and 900 K, and (3) High-temperature TE materials whose working temperature is about 900 K [20]. Group-IV–VI chalcogenides like PbSe [21,22,23,24], PbTe [25, 26] and PbS [27, 28] exhibit better thermoelectric efficiency in the mid-temperature range, but because they contain toxic Pb, this limits their commercial and domestic applicability. In view of this, tin makes a better replacement for lead. Tin selenide (SnSe) has been shown to be a suitable compound due to its abundance on earth and lack of toxicity. It also shows an intrinsically ultralow thermal conductivity [29].

Tin selenide (SnSe) is a layered chalcogenide material whose layers are linked together with a Sn–Se bonding and an IV–VI semiconductor [30]. At room temperature, SnSe crystallizes as a Pnma space group, layered orthorhombic structure along with lattice parameters of a = 11.501 Å, b = 4.153 Å, and c = 4.445 Å. The arrangement of the Sn, as well as Se atoms, is in double layers containing two zigzag planes and chains of Sn–Se on the x-axis. At a temperature of about 750 K, SnSe encounters a second-order displacive phase transition from an orthorhombic structure with Pnma space group to a higher-symmetry orthorhombic structure with Cmcm space group along with lattice parameters of a = 4.310 Å, b = 11.705 Å, and c = 4.318 Å [31], preserving bilayer stacking and allowing each Sn (or Se) atom to be coordinated to four neighboring Se (or Sn) atoms at the same distance over the y–z plane [32] and the bandgap (Eg) drops significantly from Pnma (0.61 eV) to Cmcm (0.39 eV) [33]. Thermoelectricity has recently made major advances, with extremely high ZT values of SnSe single crystals reaching a value of 2.6 at 923 K along the b-axis. SnSe single crystal’s high ZT is primarily caused by its extremely low lattice thermal conductivity, which was attributed to the high lattice anharmonicity [34]. Despite the exceptional thermoelectric properties that SnSe single crystals have shown, they still have their own practical application restrictions, primarily because of their weak mechanical qualities, rigidly controlled crystal growth conditions, and high cost of production for industrial scale-up. Due to the significant potential for improving the ZT values of polycrystalline SnSe materials through careful optimization, such as texturing [35, 36], do** [37, 38], and alloying [39, 40], the growth of high-performance efficient polycrystalline SnSe has become an area of study. Polycrystalline SnSe substances have increased ZT values from 0.5 to nearly 3.1 in p-type SnSe [41,42,43]. Additionally, n-type SnSe recently showed the highest ZT of 2.23 among all polycrystalline materials, including PbTe [44]. Yet, it should be observed that due to its comparably high thermal conductivity and low Seebeck coefficient, the thermoelectric performance of polycrystalline SnSe still needs optimization. Therefore, improving the thermoelectric efficiency of the polycrystalline samples is highly desired. However, in order to achieve this objective, a thorough understanding of the crystal’s electrical and thermal transport characteristics that are probably distinct from the properties of single crystals is required [45]. Adding Bi to the Sn site will optimize the carrier concentration and improve the electrical conductivity and Te to the Se site will reduce the total thermal conductivity. In this work, we carried out the synthesis and transport characteristics of p-type polycrystalline SnSe and doped SnSe samples, and this study includes a thorough analysis of the compounds’ structural, mechanical, and thermoelectric characteristics. The pure phase of the samples is confirmed by the Rietveld refinement analysis of the X-ray diffraction data. According to our research, Bi and Te do** significantly alter the electrical and thermal characteristics. 4% Bi-doped sample has significantly increased the power factor and ZT of the materials under study, and the enhancement of power factor and ZT in the samples after co-do** is studied. If certain challenges could be fixed, SnSe might be a promising thermoelectric material in the near future.

Experimental procedure

Materials and methodology

Polycrystalline SnSe and Sn1-xBixSe0.97Te0.03 (x = 0.00, 0.02, 0.04, 0.06) samples were synthesized via a solid-state reaction method in which the starting materials are Tin, Selenium, Tellurium (99.9%, Molychem, Mumbai, India), and Bismuth (99.999%, Otto Kemi, Maharashtra, India).

The above-mentioned materials were introduced in a suitable stoichiometric ratio (tabulated in Table 1) and mixed thoroughly in an agate mortar for a period of 2 h with an intense grinding process. Palletization of mixed fine powder was carried out under 5-ton compression pressure. Pellets with a volume of 10 × 2 × 5 mm3 were obtained. The pellets had been sintered at 400 °C for 24 h after being sealed in a quartz tube of 12 mm diameter under a vacuum of 10−4 torr. The furnace was then allowed to cool naturally to room temperature. The grinding process is repeated for the sintered pellets to enhance compound homogeneity. Palletization is repeated for the ground powder and sintered at 400 °C for 12 h. Finally, rectangular bulk samples are obtained for characterization. Figure 1 shows the sample synthesis process in detail.

Table 1 Stoichiometric proportion of precursors employed in the synthesis of SnSe and doped SnSe samples
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Figure 1
figure 1

Schematic representation of sample synthesis by solid state reaction method.

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Characterization techniques

Powder X-ray diffraction was performed using a Rigaku Ultima IV diffractometer with CuKα (1.540562 Å) radiation source and XRD patterns have been determined with a scan rate of 2°/min in the 2θ range 20°–80° with step size 0.02 to confirm the structure, purity, crystallinity, dominated phase, and compound formation of the synthesized samples. “EXPO 2014 software” was used for Rietveld refinement. By using a field emission scanning electron microscope (Carl Zeiss Sigma) with a range of particle sizes of 1 µm and a magnification of 40 kX, the surface morphological characteristics of the samples were examined. Energy dispersive Electron X-ray analysis (EDAX) was used to analyze the chemical makeup of grown samples using EVO MA18 and Oxford EDS (X-act). The hardness of every sample was determined with a Vickers microhardness tester (MMTX3/MMTX7 Matsuzawa CO. LTD.). The density of the synthesized samples is determined using the Archimedes principle along with the CONTECH CAS-234 density measurement system. Using a “Keithley meter 6220” and a magnetic field of 0.6 T and a current of 50 mA, the Van der Pauw technique was used to measure the carrier concentration and mobility at room temperature. ADVANCE RIKO ZEM-3 was used to measure both the Seebeck coefficient and high-temperature electrical resistivity simultaneously at temperatures between 300 and 670 K. Thermal diffusivity was measured using Linseis LFA 500 instrument in the temperature range 300–670 K. “Total thermal conductivity” (κ) was estimated using the following mathematical formula κ = DCPρ, where D-thermal diffusivity, CP-specific heat capacity, ρ-density, accordingly.

Theoretical details

The DFT calculations were performed using the Quantum Espresso (QE) software, notably utilizing the plane-wave self-consistent field (PWscf) method [46]. The computations employed the LDA approximation for all calculations. Calculations were conducted for (a) SnSe in its pure form and (b) SnSe doped with Bi and Te. A k-mesh with dimensions of 5 × 5 × 4 was employed in the first Brillouin zone [47]. The relaxation stage of both pure and deficient structures occurs after the energy convergence reaches 5 × 10−6 eV and persists until the force’s pier atom decrease to 0.05 eV. We have integrated the Quantum Espresso package with the BoltzTraP code to compute the thermoelectric characteristics. We employed the Boltzmann Transport Equation (BTE) approach for these calculations.

Result and discussion

Powder X-ray diffraction

The prepared samples were subjected to X-ray diffraction study at a rate of 2°/min in the range of 20°–80°. Figure 2a demonstrates the powder XRD patterns acquired for pristine and doped samples. Powder X-ray diffraction studies of the synthesized samples reveal that all the materials are polycrystalline in nature. As Bi/Te is added to the Sn and Se sites, the XRD peak patterns shift to the lower angle 2θ side, as shown in Fig. 2b. This finding suggests that dopant atoms are incorporated into the SnSe lattice. The Rietveld refinement is used to fit the XRD patterns (Fig. 3) using “EXPO 2014” [48]. All the diffraction peaks were found to match with the jcpds data (48-1224) without secondary phases within the detection range. The occurrence of a single phase in all the prepared samples is verified by the absence of an additional peak within the XRD measurement limit, indicating that the desired samples are formed. In all the samples, the peak corresponding to the plane (400) was found to have the highest oriented phase. All the samples belong to the low-temperature SnSe phase with an Orthorhombic crystal system and Pnma space group. The high-intensity peak of (400) is slightly shifted to a lower angle as the dopant concentration of the sample increased, owing to the enlargement of the lattice parameters and increase in crystallite size are tabulated in Table 2, which are well in agreement with the early reports [34]. Peak shift as in the XRD spectrum has been noticed as a result of the dopants’ ionic radii slightly varying from Sn’s, which causes strain in the matrix [29]. Here the ionic radius of Bi is 230 pm and Sn’s ionic radius is about 225 pm, which indicates that there is a difference of 5 pm in the ionic radii, due to this there is a tensile stress in the compounds. The highest intense peak at (400) denotes the sample’s preferred growth orientation. The Rp (Profile factor), RWP (Weighted Profile factor), Rep (Expected Profile factor), χ2 (Goodness of fit) values, lattice parameters, cell volume, and density are reported in Table 2.

Figure 2
figure 2

a Powder XRD pattern. b Shift in XRD pattern of (i) SnSe (ii) Sn0.98Bi0.02Se0.97Te0.03 (iii) Sn0.96Bi0.04Se0.97Te0.03 iv) Sn0.94Bi0.06Se0.97Te0.03 samples and c Cell volume and strain of Sn1-xBixSe0.97Te0.03 (0 ≤ x ≤ 0.06) samples.

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Figure 3
figure 3

Rietveld refinement XRD plots of a SnSe. b Sn0.98Bi0.02Se0.97Te0.03. c Sn0.96Bi0.04Se0.97Te0.03. d Sn0.94Bi0.06Se0.97Te0.03 samples.

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Table 2 Powder XRD data analysis of pristine and doped SnSe polycrystalline samples
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We adopted different methods, including the Scherrer, and Williamson–Hall, to determine the crystallite size (D) and strain (ε). The Scherrer equation is provided as follows and is based on the prepared sample’s average crystallite size, D [49].

$$D = \frac{0.9\lambda }{{\beta {\text{Cos}}\theta }}$$
(1)

\(\beta\)-FWHM \(\lambda\)-wavelength of X-ray, \(\theta -\)Braggs diffraction angle. According to Eq. (1), the average crystallite size is predicted to lie between 30 and 51 nm tabulated in Table 2. The crystallite size and strain have been found using the Williamson–Hall formula [50],

$$\beta \text{cos}\theta =\left(\frac{0.9\lambda }{D}\right)+4\varepsilon \text{sin}\theta$$
(2)

\(\beta\)-FWHM \(\lambda\)-wavelength of X-ray, \(\varepsilon -lattice \,strain\), D-crystallite size, \(\theta -\)Braggs diffraction angle. βCosθ in the y-axis versus 4Sinθ in the x-axis has been plotted, and the line (y = mx + c) has been fitted to the data. Figure 4a–d shows the fitted graphs and the data from the experiments. The strain value is calculated from the line’s slope (ε = m), and the crystallite size is calculated from the line’s intercept (D = kλ /c). Table 2 contains the results for crystallite size (D) and strain (\(\varepsilon\)). The typical crystallite size produced by the WH technique varies between 44–63 nm. Impurities, or dopants, can act as point defects, which can increase the lattice strain when it is added to polycrystalline materials. These defects may result in lattice strains, which raise the overall stress in the sample. Dopants can also alter the lattice parameters, adding to the strain. Since the dopant atoms in this condition, whose radii are larger than the host atoms, i.e., Bi atomic radii are larger than Sn, they may cause lattice expansion, which will increase the lattice strain. Additionally, the dopants may cluster within the crystal lattice, which could result in additional stresses and strains. Here the addition of dopants like Bi creates strain in the samples. As shown in Fig. 2c, there is an incremental rise in cell volume and strain with increasing dopant concentration. The crystallite size rises with increasing dopant concentration, and this is a result of the crystal’s extensible nature.

Figure 4
figure 4

WH plots of a SnSe. b Sn0.98Bi0.02Se0.97Te0.03. c Sn0.96Bi0.04Se0.97Te0.03. d Sn0.94Bi0.06Se0.97Te0.03 samples.

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Crystal structure of SnSe and doped SnSe samples

The crystal structures of pure and doped SnSe are shown in Fig. 5. Here, spheres with gray color represent the Sn atom, Se atoms, are in green color, and dopant atoms are shown in red-and blue-colored spheres representing Bi and Te, respectively. Lattice optimization has also been done for structural stability for pure and doped SnSe. The crystal structures of each have been optimized before the calculations of electronic and thermal-electric properties.

Figure 5
figure 5

Crystal structure of a pure and b doped SnSe samples.

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Mechanical hardness

In order to determine the suitability of a crystalline surface for any specific utilization, it is crucial to consider the mechanical properties of a grown crystal [51]. Improving the mechanical properties is critical for the usage of such materials in thermoelectric systems [52]. The hardness for the prepared samples is assessed using a Vicker’s hardness tester with a diamond microindenter at a load of 100 g force and a dwell time of 15 s. Figure 6 illustrates the hardness of Sn1-xBixSe0.97Te0.03 (0 ≤ x ≤ 0.06) samples in relation to dopant concentration. The estimated hardness of the pure sample, SnSe, is 0.42(\(\pm \hspace{0.17em}\)10%) GPa and this is in line with the previous research reports [53]. The results show that the addition of dopants significantly increases hardness. The sample with x = 0.06 depicts a high value of hardness of about 0.72(\(\pm \hspace{0.17em}\)10%) GPa. An increase in dopant concentration could increase the microhardness of the SnSe matrix by filling up the intergranular space as well as strengthening the material. The maximum elastic interaction energy between the dislocation and dopant atom, along with the increase in microhardness, can also be used to explain the phenomenon. The elastic interaction parameter (ξ), which is given by [54],

Figure 6
figure 6

Vicker’s hardness varies with dopant concentration for Sn1-xBixSe0.97Te0.03 (0 ≤ x ≤ 0.06) compounds.

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$$\xi =\frac{{r}_{1}-{r}_{0}}{{r}_{0}}$$
(3)

where the covalent radius of the substituted atom, denoted by r0, is 1.3 Å (Sn radii), and the dopant atom, denoted by r1, is 1.48 Å (Bi radii). The elastic interaction parameter (ξ) has a direct relationship with the hardness. Sn is replaced by Bi, which results in a positive value for (0.06), showing that the elastic interactions between atoms have increased the hardness. The improved mechanical properties associated with the synthesized materials, especially for small devices, are advantageous for the manufacturing of TE modules [55].

Field emission scanning electron microscopy (FESEM)

The surface morphology images of doped and pristine SnSe samples are depicted in Fig. 7. The microstructural investigations of the samples illustrate the formation of tightly packed grains. SnSe is a layered chalcogenide material [33] and the layered structure is confirmed through FESEM images (arrows in the image show the layered structure). The grains in the pure sample are widely dispersed [56], it has been realized as the do** in the SnSe matrix increases, the porosity decreases. The insertion of a do** element into the sample and volatilization of selenium due to high vapor pressure during the sintering process might be the cause for the emergence of white patches on the sample surface. The selenium vaporization leads to leaving a few minor scattered voids here and there in the matrix of the samples [45]. The selenium's high vapor pressure heightens the surface’s negative gradient of selenium precipitates. All the doped samples show less porosity, indicating that the doped samples are dense and have tightly packed grains. Increased grain boundaries in a material due to high grain density can restrict the movement of charge carriers (electrons or holes) and this increases the scattering. This might lead to an increase in the material’s Seebeck coefficient [57]. The specific gravity method is utilized to figure out the density of the synthesized samples, and the results are depicted in Table 2. There is a slight variation in the density of doped samples as compared to pristine because the pristine sample is slightly porous as compared to doped samples. The study confirms that after adding the dopants the density of the material is increased slightly from 5.83 to 6.05 g/cm3 because the atomic mass of Bi and Te is more than Sn and Se when we mix Bi and Te to SnSe, we are adding a heavier element to the compound, which will increase the overall average atomic mass of the material. This increase in atomic mass contributes to the increase in density, but there is a very slight difference in theoretical and observed density (Table 2) because of the volatilization of Se in the samples and the obtained density results match with the previously published data [58]. The microstructural changes are a consequence of solid-state diffusion [50]. In addition, some cracks and voids can be found in bulk materials. Furthermore, because of the strengthened carriers’ scattering, the carrier mobility may be reduced. As a result, it seems that the cracks and voids will affect the electrical properties of SnSe and doped SnSe polycrystals [59].

Figure 7
figure 7

FESEM images of a SnSe. b Sn0.98Bi0.02Se0.97Te0.03. c Sn0.96Bi0.04Se0.97Te0.03. d Sn0.94Bi0.06Se0.97Te0.03 samples.

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Energy dispersive X-ray analysis (EDAX)

EDAX was used to verify the elemental composition of synthesized SnSe polycrystal samples. Figure 8 shows the EDAX images of pristine and doped SnSe samples. The elemental distribution map confirms the composition and presence of tin and selenium in the pristine SnSe (Fig. 8a) and it proves that pure SnSe has a 1:1 stoichiometry, which means that the amount of Sn and Se atoms in its crystal structure is comparable. It is found that dopants like Bi/Te are present along with Sn and Se in doped SnSe (Fig. 8b,c,d) and are uniformly distributed throughout the samples. As depicted in Table 3, the experimentally determined atomic percentages of the compounds are closely matched with the predicted atomic percentage. Figure 9 shows the color map** of SnSe and doped SnSe. It shows the uniform distribution of elements throughout the matrix of the compound.

Figure 8
figure 8

EDAX images of a SnSe. b Sn0.98Bi0.02Se0.97Te0.03. c Sn0.96Bi0.04Se0.97Te0.03. d Sn0.94Bi0.06Se0.97Te0.03 samples.

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Table 3 Elemental composition of Sn1-xBixSe0.97Te0.03
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Figure 9
figure 9

Elemental map** of a SnSe. b Sn0.98Bi0.02Se0.97Te0.03. c Sn0.96Bi0.04Se0.97Te0.03. d Sn0.94Bi0.06Se0.97Te0.03 samples.

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Electrical properties

Hall measurement

At room temperature, Hall effect measurements were conducted on each sample to figure out the carrier concentration, carrier type, and mobility as functions of dopant (Bi, Te) concentration. Table 4 presents the measured Hall data. The pure SnSe sample exhibits p-type semiconductor behavior, according to the positive sign of the carrier concentration and doped samples exhibit n-type semiconducting behavior, according to the negative sign of the carrier concentration at room temperature. The Hall measurement data match with the Seebeck coefficient information at room temperature. Figure 10 displays the relationship between dopant content, carrier concentration, and mobility. Mobility is decreased as a result of increased carrier scattering. It has been noted that carrier concentration and mobility exhibit opposite trends [57]. The carrier concentration can be defined by the following formula [60],

$$n = \frac{\sigma }{\mu e}$$
(4)
Table 4 Carrier concentration, mobility, activation energy, and σo values of Sn1-xBixSe0.97Te0.03 samples
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Figure 10
figure 10

Graph of mobility and carrier concentration as an effect of Bi do** content at room temperature (300 K).

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When n-type dopant Bi is added to p-type SnSe, the electrons produced by the dopants lead to a change in carrier type from hole to electron and a decrease in carrier concentration from ( + )1.55 × 1016 cm−3 to (−)0.562 × 1016 cm−3. This results in the un-doped SnSe becoming n-type Sn0.98Bi0.02Se0.97Te0.03 with 2% Bi dopant concentration. Following that, as the concentration of Bi do** rises, the carrier type continues to be electron and the carrier concentration keeps rising to (−)4.7 × 1016 cm−3 in a 6% Bi-doped sample. As the concentration of Bi dopants increases, the carrier's Hall mobility first rises because there is less carrier scattering because of the neutralization effect between n-type Bi dopants and p-type defects, and then falls because there is increasing carrier scattering [52]. Figure 11b shows the bar chart representation of electrical conductivity. By observing Fig. 11b we can conclude that the pristine and 4% Bi-doped samples have high electrical conductivity of about 295  and 236 Sm−1 at 667 K, respectively. This study indicates that the thermal activation model, commonly referred to as the Arrhenius law, governs the electrical transport mechanism. The conductivity deviation with temperature (Arrhenius law) is given as [63],

$$\sigma = \sigma_{{\text{o}}} \exp \left( {\frac{{ - E_{{\text{a}}} }}{{k_{{\text{B}}} T}}} \right)$$
(5)
Figure 11
figure 11

a Electrical conductivity graph of SnSe and doped SnSe polycrystalline samples in relation to temperature. b Bar chart representation of electrical conductivity as a function of dopant concentration at 660 K.

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In this case, σo stands for a conductivity pre-exponential aspect, Ea is for the activation energy, kB is for Boltzmann’s constant, and T is the temperature in kelvin. Ea and σo can be determined from Fig. 12a–d and are tabulated in Table 4. With an increase in Bi content, the computed value for Eo rose from 0.209 to 0.283 eV, with the notable exception of the 4% Bi-doped sample.

Figure 12
figure 12

SnSe and doped SnSe samples’ electrical resistivity were fitted with a thermal activation model.

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Seebeck coefficient

The Seebeck coefficient (S) for SnSe and doped SnSe polycrystals are depicted in Fig. 13a, the measurements were done in the 300–670 K range. Seebeck coefficient(S) can be obtained using the Pisarenko relations as follows [60],

$$S = \frac{{8\pi^{2} k_{{\text{B}}}^{2} }}{{3eh^{2} }}m^{*} T\left( {\frac{\pi }{3n}} \right)^{2/3}$$
(6)
Figure 13
figure 13

a Seebeck coefficient graph. b Power factor graph of SnSe and doped SnSe polycrystalline samples as a function of temperature.

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Positive Seebeck coefficients were found in the un-doped sample that displays the p-type behavior of the sample across the entire temperature range, here the dominance of positive charge carriers in the conduction mechanism was observed; whereas, negative Seebeck coefficients were identified in the Bi-doped samples. There is a p to n-type transition in the SnSe sample was observed after Bi do** [64]. The magnitude of the Seebeck coefficient in SnSe and Bi-doped samples declines with temperature. Therefore, consistent results from our evaluations of Seebeck coefficients and Hall effects indicate that Bi do** of SnSe induces electron carriers [65]. These p-to-n-type transitions in our samples are connected with the bipolar conducting mechanism. The vacancies of Sn served as acceptors and produced holes in the valence band; while, the added Bi offered electrons to move from the valence band to the conduction band. The donor impurities become activated as the temperature rises, and n-type conduction takes over, negative S is attained as a result. When the temperature rises above a certain threshold, the valence band electrons have enough thermal energy to move up to the acceptor levels, where they produce holes. Positive S is attained when the hole takes over as the primary charge carrier [66]. With an increase in dopant content, the values of the Seebeck coefficient decline. Notably, there is a visible improvement between the Seebeck coefficients for Sn0.96Bi0.04Se0.97Te0.03 and SnSe. Sn0.96Bi0.04Se0.97Te0.03 reaches its foremost value of 422 µV/K−1 at 576 K. The Seebeck coefficients, however, declined as the Bi content increased. According to this finding, Bi-doped samples with x = 0.06 have lower Seebeck coefficient values than un-doped SnSe and those with x = 0.02 and 0.04 doped samples, respectively. By observing Fig. 13a, we can conclude that the Seebeck coefficient is maximum for x = 0.04 doped sample. As a result of the influence of bipolar conduction at high temperatures, carrier–phonon scattering, and carrier–carrier scattering led to a decrease in the Seebeck coefficient in Sn1-xBixSe0.97Te0.03 (0 ≤ x ≤ 0.06) samples.

Thermal conductivity

The thermal conductivity (κ) of the material above room temperature can be calculated using the relation, κ = ρCPD, where D [m2 s−1] is the thermal diffusivity, ρ [g cm−3] is the density and the specific heat capacity Cp [J g−1 K−1]. The relationship between thermal conductivity and thermal diffusivity is derived from a linear nonequilibrium thermodynamic heat equation [67]. Using the Dulong–Petit model, the specific heat capacity (Cp) was calculated as Cp = 3nR/M, where n-number of atoms in a formula unit, R-universal gas constant, and M-molecular mass [68] and the thermal diffusivity plots are shown in Fig. 14a. The “total thermal conductivity” (κtot) of SnSe and doped SnSe polycrystals was assessed between 300 and 670 K to figure out the ZT value. The total thermal conductivity was explained by the following formula [69]:

$$\kappa_{{{\text{tot}}}} = \kappa_{{\text{e}}} + \kappa_{{\text{l}}}$$
(7)
Figure 14
figure 14

a Thermal diffusivity. b Total thermal conductivity. c Electronic thermal conductivity. d Lattice thermal conductivity. e Dimensionless figure of merit (ZT) graph of SnSe and doped SnSe polycrystals as a function of temperature.

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where κe is the electronic and κl phonon components of thermal conductivity, respectively [34]. Figure 14b reflects the temperature-related total thermal conductivity(κtot) of SnSe and doped SnSe polycrystals. The lowest thermal conductivity was found in 6% Bi-doped sample due to enhanced phonon scattering at that temperature. The κtot value of SnSe is ~ 0.36 W/mK and for 6% Bi-doped sample is about 0.275 W/mK at 670 K, which is 1.3 times lower than pristine sample. This implies that the incorporation of heavy Bi atoms into the SnSe lattice contributes to the decrease in thermal conductivity. Therefore, the difference in mass between the heavier Bi atoms and Sn intensifies the anharmonic phonon vibrations, which lowers the thermal conductivity [52]. As seen in Fig. 14c, the electronic component of the total thermal conductivity is subtracted to determine the lattice thermal conductivity (κl). The electronic thermal conductivity as shown in Fig. 14d was assessed by employing the “Wiedemann–Franz law” [70],

$$\kappa_{{\text{e}}} = L\sigma T$$
(8)

where L is the Lorentz number, σ is the electrical conductivity, and T is the temperature. It can be noted that the lattice phonons significantly contribute to κtot in semiconductors. Therefore, the effect of electron carriers on κtot in our samples is very small, so lattice thermal conductivity contributed more to total thermal conductivity than electronic “thermal conductivity”[65]. So, κtot’s main source was speculated to be κl. The additional phonon scattering from grain boundaries in polycrystalline samples should result in lower thermal conductivity.

Power factor (PF) and figure of merit (ZT)

For thermoelectric materials, the power factor of the substance is directly related to its power output. The power factor is deemed more crucial than the figure of merit for real-world applications, according to recent arguments. In contrast to the traditional method of reducing the lattice thermal conductivity, raising PF was therefore proposed as an alternate tactic to increase efficiency along with output power generation [71]. Seebeck coefficient (S) and electrical conductivity (σ) are used for figuring out the power factor (PF), which is expressed as S2σ [72]. Figure 13b depicts the thermoelectric power factor (PF) with respect to the temperature of SnSe and doped SnSe polycrystals. Because of the minimal Seebeck coefficient, modest PF values were achieved in p-type SnSe and heavily Bi-doped samples. We noticed an increase in PF with temperatures up to 550 K in all the samples and then a decrement in the PF was found. The significant improvement in the power factor for the 4% Bi-doped sample is attributed to high electrical conductivity and high Seebeck coefficient and was found to be ~ 25µ W/mK2. The PF of Sn0.96Bi0.04Se0.97Te0.03 sample is 2.0 times higher than pristine SnSe. Diverging PF values were observed at low and high temperatures; while, closer PF values were found in the room temperature range. After 450 K there is an increase in the PF value of the samples, again after 550 K there is a huge decrement in the PF value was observed. These results confirmed that Bi and Te do** can enhance the sample’s power factor, with suitable do** concentration tuning.

The temperature-dependent dimensionless figure of merit, ZT for SnSe, and doped SnSe polycrystal samples are depicted in Fig. 14e. The power factor and thermal conductivity values can be employed to figure out the thermoelectric figure-of-merit, ZT. The 4% Bi-doped sample has a maximum ZT value of 0.055 at 670 K, which is an enhancement over that of the SnSe sample 0.016. Due to a reduction in total thermal conductivity in the higher temperature range because of phonon scattering and increased PF value highest ZT was attained. The ZT value of Bi-doped sample is 3.43 times higher than the pristine SnSe. This result shows that the Co-do** of Bi/Te in the SnSe matrix will enhance the thermoelectric properties of the SnSe sample.

Theoretical calculations on electronic and thermal properties using DFT

To see the electronic band gap of pure and doped SnSe, DFT calculations were used to get the density of states, and it is clearly observed that in the case of pure SnSe electronic bandgap is 0.86 eV. After the introduction of dopant Bi at the Sn site and Te at the Se site, an additional state arises in between the conduction band and valance band, as a result, the electronic bandgap is reduced from 0.86 to 0.52 eV (see Fig. 15a, b). Hence, introducing do** on SnSe will also tune the electronic bandgap, due to which electrical and mechanical properties are also modified [73, 74].

Figure 15
figure 15

Density of states of a pure and b Bi & Te doped SnSe and c Seebeck coefficient of SnSe and doped SnSe samples.

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In order to validate the experimental findings, we conducted theoretical calculations on the thermal conductivity of SnSe doped with both Bi and Te using the Boltzmann Transport Equation (BTE) approach for these calculations. We have determined the Seebeck coefficient as shown in Fig. 15c, and the thermal conductivity of both pure and doped SnSe using several approximations such as PBE, LDA, and HSE (see Table 5). It is noteworthy that our theoretical results closely align with the experimental data, indicating a significant correlation between the two. Sn0.98Bi0.02Se0.97Te0.03 and Sn0.94Bi0.06Se0.97Te0.03 exhibit the highest thermal conductivity, while for other samples it is less. The specific heat capacity for pure and doped SnSe has been determined and presented in Table 5. Furthermore, to confirm experimentally observed variations in power factor (PF) and electronic thermal conductivity we have also simulated, and the observed values are closely matched. Figure 16 shows observed simulated values of (a) power factor and (b) Electronic thermal conductivity of pure and doped SnSe.

Table 5 Calculated thermal conductivity and specific heat capacity of SnSe
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Figure 16
figure 16

Theoretically observed values of a Power factor. b Electronic thermal conductivity of pure and doped SnSe.

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Conclusion

Solid-state reaction technology has been used to grow Sn1-xBixSe0.97Te0.03 polycrystals. XRD was done to evaluate structural parameters. Electronic and structural stabilities are also confirmed by DFT calculations. Vicker’s hardness test facilitated us to verify that the samples’ mechanical strength and hardness increase with do** concentration increases. Our examination of the electrical resistivity details demonstrates that the samples’ semiconducting properties are within the examined temperature range. The switch of the temperature-dependent Seebeck coefficient from p-type SnSe to n-type in Bi-doped SnSe samples suggests that the materials’ charge carrier properties variation. In the case of doped samples, electrons will dominate, but in pristine samples, p-type behavior was observed all over the temperature range with the hole having a majority charge carrier. The co-doped Sn0.96Bi0.04Se0.97Te0.03 sample displayed a significant increment in electrical conductivity and an enhanced Seebeck coefficient, which led to the power factor enhancement of approximately 2.0 times in contrast to the pristine sample. A larger contribution from lattice thermal conductivity contribution when compared to electronic thermal conductivity is observed in total thermal conductivity in all the samples. The total thermal conductivity of the 6% Bi-doped sample is 1.3 times lower than the pristine SnSe sample. The 4% Bi-doped sample has a maximum ZT value of 0.055 at 670 K, which is an enhancement over that of the SnSe sample 0.016. Due to a reduction in total thermal conductivity and increased PF value highest ZT was attained. The ZT value of the 4% Bi-doped sample is 3.43 times higher than the pristine SnSe. Using the Boltzmann transport equation from DFT approximations electric properties, Seebeck coefficient, specific heat calculations, thermal conductivity, and power factor have been done. Having combined experimental and theoretical analysis our findings are well matched. More optimization in this series of compounds is necessary to achieve higher efficiency, as the optimized Sn1-xBixSe1-yTey polycrystals may be employed as a thermoelectric module for converting heat into electrical energy for use in electrical vehicles, and power generation applications.