1 Introduction

Thermoelectric generators (TEGs) have been the subject of many studies since TEGs provide increased efficiency. TEGs convert thermal energy into electrical energy directly or vice versa (Ref 1). Many researchers have investigated issues related to the efficiency of thermoelectric materials. The power factor (PF) is one of the variables indicating the performance of the TEGs, which is obtained from measurements of the Seebeck coefficient (S) and electrical resistivity (ρ). Mathematically, this can be written as

$${\text{PF}} = \frac{{S^{2} }}{\rho }$$
(1)

In addition, a variable to calculate performance that takes into account thermal conductivity (κ) is the figure of merit (zT). The equation is written as follows:

$$\mathrm{zT}=\left(\frac{{S}^{2}\sigma }{{\kappa }_{e}+ {\kappa }_{l}}T\right)$$
(2)

which is dimensionless (Ref 2). According to the equation, to obtain a large zT value, a high S, high σ, and low κ are needed. There are several techniques to increase the value of zT, one of which is forming nanopores in nanoplates. Nanoscale pores can reduce thermal conductivity but do not affect electrical conductivity (Ref 3, 4). The figure of merit equation shows that the thermal conductivity mechanism is influenced by two variables, the effect of charge carriers (κe) and phonons (κl). For materials that have high σ, the κ value is dominated by the contribution of electrons. Therefore, the zT value depends heavily on S. Wiedemann–Franz's law explains that the value of \({\kappa }_{e}\) can be calculated by knowing the σ value, the measurement temperature (T), and the Lorenz number (L) as shown in the following equation:

$$\kappa_{e} = L\sigma T$$
(3)

For free electrons, L is equal to \(2.44 \times 10^{ - 8} {\text{W}}\Omega {\text{K}}^{ - 2}\). Kim et al proposed a single parabolic band (SPB) model to calculate the L value, which depends on the value of S (Ref 5). Many thermoelectric materials are being explored for power generation applications, such as Sb2Te3 (Ref 6), Ag2Te (Ref 6), Bi2Te3 (Ref 7), PbTe (Ref 8, 9), GeTe (Ref 10,11,12), SnTe (Ref 13) and MnSi (Ref 14). However, Bi2Te3 is the most popular thermoelectric (TE) material, and it shows excellent performance at room temperature (Ref 15). Bi2Te3 has a rhombohedral unit cell with a space group of \(R\overline{3 }m\), where the unit cell is located in a hexagonal close-packed (HCP) structure. In a unit cell, there are two Bi and three Te atoms. The HCP structure consists of quintuple layers (Te2-Bi-Te1-Bi-Te2) in which van der Waals bonding exists between each layer. The Te2-Te2 bond is weak and is easy to cleave. The nature of the bonding between Bi and Te in the layer is ionic-covalent (Ref 16). At room temperature, the lattice parameters are a = b = 4.3866(2) Å and c = 30.4978(13) Å (Ref 17). Bi2Te3 has a narrow energy gap. The calculations carried out by Lawal et al. with and without spin-orbit coupling show that the energy gaps are 0.13 eV and 0.31 eV, respectively (Ref 18). There are several methods used to synthesize Bi2Te3-based materials, including hydrothermal (Ref 19), coprecipitation (Ref 20), solid-state reaction (Ref 21), and sol–gel (Ref 22) methods. However, the solid-state reaction is the simplest method to carry out. Several previous reports have shown that to improve the performance of thermoelectric properties, doping or compositing can be performed with other elements or compounds. Mg (Ref 23), Lu (Ref 24, 25), Dy (Ref 26), Ce (Ref 27), Tm (Ref 24), Se (Ref 28), Cu (Ref 29), Sn and CuI (Ref 7) doped or composited with CNTs can increase the S value and decrease the κ value of the material (Ref 30). Previously, research was carried out by Kartika et al. on the effect of Ti doping on the Bi2Te3 system. It was based on research conducted by Drašar et al., who performed Ti doping on Sb2Te3. Because Sb2Te3 has a similar structure, it is also possible to dope Ti into Bi2Te3. Interestingly, the hardness value tends to increase with the concentration of dopant compared to the pristine material (Ref 31, 32). In this research, Ti doping was carried out in the Bi2Te3 system particularly to study changes in the figure of merit (zT) as a result of doping, which has not been investigated in previous research.

2 Experiment

Bi(2-x)TixTe3 with various dopant amounts (x = 0, 0.05, 0.1, and 0.15) was synthesized using a solid-state reaction method. The precursors used were Bi powder (95.5% purity, Polamet), Ti powder (≥ 98% purity, Merck), and Te powder (99.8% purity, Sigma–Aldrich). All precursors were mixed by grinding in an agate mortar for 1 hour according to the stoichiometry of the doping variants. The powders were compressed at 60 MPa on a 12-mm-diameter steel die. The pellets were buried in carbon powder in an alumina crucible with a lid to prevent oxidation during the heating process. Sintering was performed with the carbon burial method as described in previous research (Ref 26, 32, 33). Sintering was carried out at a temperature of 480 °C for 6 hours and a heating rate of 300 °C/h. The crystal structure was analyzed by powder x-ray diffraction (XRD, Bruker, D8 Advanced) and Bragg–Brentano diffraction at 40 kV and 40 mA with Cu-kα radiation at ~ 1.5406 Å. Measurements were conducted at room temperature in the range of 10-90° with a step size of 0.020°. First, the XRD data were analyzed qualitatively; that is, each peak was matched with databases from PDF 01-083-5983. Quantitative analysis was carried out using the Rietveld method with the GSAS-II program (Ref 34). Scanning electron microscopy (SEM, Jeol JSM-IT300) and energy-dispersive x-ray spectroscopy (EDS, Oxford Xmax 30) were used to observe the size and morphology of the particles and the ratio between constituent elements. The Seebeck coefficient (S) and resistivity (ρ) were measured using an LSR-4 (Linseis, Germany) in a helium atmosphere at a low pressure of 0.2 bar. Resistivity was measured using a four-point probe configuration with a distance between voltage probes of 6 mm. The applied current was 100 mA. All bulk samples were measured at a temperature range of 323-463 K at a temperature interval of 20 °C. The figure of merit (zT) could be directly determined using the Harman method on the same instrument. In principle, the Seebeck voltage is divided by the Ohmic voltage (Ref 35). Ni and Ni-Cr alloy wires were attached to the samples as voltage probes using a Hotspot TC Welder. The samples responded to the voltage of the applied current, which was 40 and 50 mA, and the acquisition times were 275 and 300 s, respectively. Hardness measurements were performed by using a Micro Vickers hardness tester in five different areas. The mass load was 25 gr, and the loading time was 10 s. The energy gap was characterized by using UV–Vis spectrophotometry (SPECORD 210 PLUS) in the wavelength range of 185-1100 nm. The corrosion rates were measured using a potentiodynamic corrosion tester in NaCl electrolyte solution with a mass fraction of 3% (Ref 36). The electronic structure of Bi2Te3 was calculated in Quantum Espresso version 6 using the density functional theory method (Ref 37, 38). The band structure, density of states, and partial density of states calculations of the relaxed structure of bismuth-telluride were performed using generalized gradient approximation (GGA) based on Perdew–Burke–Ernzerhof revised for solids (PBEsol) (Ref 39, 40). The partial density of states was applied to determine the density of states of each atom in the unit cell structure. The projected augmented wave (PAW) and ultrasoft pseudopotential were used without and with spin-orbit coupling, respectively, in the self-consistent field (SCF) calculation (Ref 41, 42).

3 Results and Discussion

Figure 1(a) shows the powder XRD pattern of Bi(2-x)TixTe3 for a range of doping levels. The main phase of Bi2Te3 is formed, while there are peaks of the impurity phase of Bi2TeO5 (COD 4319514), which is marked with a star. The presence of Bi2TeO5 might be caused by oxidation during the sintering process, in which the particles on the Bi2Te3 surface absorb oxygen (Ref 43). Ti substitutes for sites with Bi due to their similarity in oxidation number and ionic radii. It can be seen from the highest peak in the XRD data, as shown in Fig. 1(b), that increasing the Ti doping concentration causes a shift in the peak (10-5) toward a higher angle. According to Bragg's law, the shift is due to a reduction in the size of the lattice volume because the ionic radius of Ti4+ is smaller than that of Bi3+, at 0.745 Å and 1.17 Å, respectively (Ref 44, 45). The peak shift is not linear at the highest doping level. The shift in the peak toward a lower angle at doping level x = 0.15 potentially occurs because not all Ti atoms can occupy the atomic positions of Bi. This analysis is based on the results reported by Kartika et al., who mixed Ti with a Bi2Te3 compound and showed a shift in the peak toward a lower angle as a function of increasing Ti concentration (Ref 32). Based on the results of this research shown in Table 1, the lattice volume decreased as a function of doping but not for the highest doping level. The increasing cell volume at the x = 0.15 doping level is hypothesized to be due to the presence of independent Ti. An increase in the volume of Bi2Te3 cells was also reported by Kulsi et al. when it was composited with RGO (Ref 46). Nonlinear changes at high doping concentrations also apply to local structures, distances, and angle bonding. Crystallite size and lattice strain can be analyzed by using the Williamson-Hall model.

$$\beta \cos \theta = \frac{K\lambda }{D} + \varepsilon (4\sin \theta )$$
(4)

where β is the FWHM (full width at half maximum), K is the form factor, λ is the wavelength of Cu-kα radiation, and D is the crystallite size (Ref 47, 48).

Fig. 1
figure 1

(a) XRD pattern of several samples of Bi(2-x)TixTe3 in doped variants (x = 0.0, 0.05, 0.1, 0.15). The main phase was defined by a rhombohedral crystal structure with a space group of R \(\overline{3 }\) m (PDF 01-083-5983), while for the impurity phase, an orthorhombic crystal structure with a space group of Abm2 (COD 4319514) was used. (b) Peak shift (10-5) at 2θ = 27.5-28° as influenced by Ti doping. (c) Crystal structure of Bi1.95Ti0.05Te3

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Table 1 Lattice parameters, phase fraction, cell volume, local structure (distance and angle of bonding), atomic position of Bi, Te, and Ti as a result of refinement using the rhombohedral crystal with a space group of R \(\stackrel{\mathrm{-}}{3}\) m as well as crystallite size and lattice strain obtained from analysis using the Williamson-Hall model on all samples as influenced by Ti doping
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Figure 2(a-e) gives some information about the surface morphology and EDS measurement results of Bi(2-X)TiXTe3 samples. Grain boundaries are shown on the order of µm. The experimental results of all samples show that the ratio between Te and Bi is slightly below that from theoretical calculations. Therefore, it can be concluded that Te is deficient in all samples. EDS also exhibited the elemental spectrum of oxygen, which confirmed that the XRD pattern indicated a peak for the Bi2TeO5 phase. Ti was detected only in the sample with the highest doping level, while in the other doping variations, it was not. This absence might occur because the doping amount was very small. As shown in Fig. 2(e), Bi and Te are homogeneously distributed, while Ti tends to agglomerate. Ti is probably a residual element that cannot be substituted into Bi sites so it is present in the interstitial spaces in the crystal structure of Bi2Te3. Figure 3(a-g) shows some of the results of the thermoelectric property measurements of all samples with Ti doping. Each quantity was measured several times to obtain the standard deviation value.

Fig. 2
figure 2

Scanning electron microscopy with a magnification of 10,000× and the ratio between Bi and Te as a result of energy-dispersive x-ray spectroscopy for (a) Bi2Te3, (b) Bi1.95Ti0.05Te3, (c) Bi1.9 Ti0.1Te3, (d) Bi1.85Ti0.15Te3, (e) mapping of each constituent element of Bi1.85Ti0.15Te3

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Fig. 3
figure 3

Temperature dependence of transport measurements for the thermoelectric properties of Bi(2-x)TixTe3 with various amounts of dopant (x = 0, 0.05, 0.1, 0.15) (a) resistivity, ρ, (b) Seebeck coefficient, S, (c) power factor, PF, (d) figure of merit, zT, (e) total thermal conductivity, \({\kappa }_{\mathrm{tot}}\), (f) lattice thermal conductivity \({(\kappa }_{\mathrm{l}})\), and (g) electronic thermal conductivity \({\kappa }_{\mathrm{e}}\)

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Figure 3(a) shows that the resistivity increases with increasing temperature, according to which all the samples exhibit metallic behavior. Undoped samples displayed a different trend, especially at temperatures of ~ 445 K. The decrease in the ρ value when a sample is heated indicates the semiconductor state (Ref 49). The ρ value of Bi2Te3 is affected by the direction of crystal orientation. In the a-b direction, the plane is more conductive than that perpendicular to the cleavage plane (c-direction) (Ref 16). Increasing Ti doping causes an increase in the ρ value. It can be concluded from the theory proposed by Drašar et al for the Sb2Te3 system that if the Ti atom completely substitutes for Bi sites, electron donors are formed, which causes a decrease in the concentration of charge carriers (n) (Ref 31). This is due to the difference in oxidation numbers between Bi and Ti. The defect notation can be written as follows: \({\text{2Ti}}\mathop{\longrightarrow}\limits^{{{\text{Bi}}_{{2}} {\text{Te}}_{{3}} }}{\text{2Ti}}^{ \cdot } {\text{Bi}}\). A decrease in the concentration of n causes an increase in the ρ value (Ref 2) as in the following equation:

$$\rho = \frac{1}{ne\mu }$$
(5)

Another possible reason is that the addition of Ti also reduces the mobility (μ) of charge carriers. The ρ value of the undoped sample obtained in this study is greater than that in a previous report (Ref 30). This is due to the presence of an impurity phase consisting of Bi2TeO5, which is an insulator (Ref 43, 50).

Figure 3(b) shows the absolute Seebeck coefficient (S) as a function of temperature (T). The S value of all samples increases as a function of increasing temperature, which corresponds to the following equation:

$$S = \frac{{8\pi^{2} k_{B}^{2} }}{{3eh^{2} }}m^{*} T\left( {\frac{\pi }{3n}} \right)^{\frac{2}{3}} (1 + R)$$
(6)

where \({k}_{\mathrm{B}}\) is the Boltzmann constant, h is the Planck constant, \({m}^{*}\) is the effective mass of the charge carriers, n is the carrier concentration, T is the absolute temperature, and R is the scattering function (Ref 51). The S value was negative, indicating that the majority of charge carriers were electrons. The undoped sample has the greatest absolute S and tends to decrease with the addition of Ti. At a temperature of ~ 323 K, the S value of the undoped sample is ~ 200 μV/K. The absolute coefficient Seebeck obtained is greater than that reported in the research conducted by Cao et al. and Wu et al. but slightly smaller than that reported by Chen et al. (Ref 25, 27, 52). Figure 3(c) shows the value of the power factor (PF) resulting from the square of the absolute S divided by ρ. Bi2Te3 has the greatest PF value at all measurement points compared to the other samples. This is because the absolute S contributes more than ρ.

The measurement of zT, which is a dimensionless quantity, is carried out using the Harman method, as shown in Fig. 3(d). The largest zT value is observed for the undoped sample at a temperature of approximately 327 K, which is ~ 0.46 and decreases with increasing temperature. This value is similar to that in previous research, which is 0.41 at a temperature of 323 K (Ref 26). Ti doping causes a drastic decrease in zT and a shift in the highest value toward a high temperature. Doping of x = 0.05, 0.1, and 0.15 showed the best results of 0.28 (368 K), 0.26 (387 K), and 0.24 (406 K), respectively.

The value of total thermal conductivity (κ) was obtained based on calculations with measured zT, absolute S, and ρ values. As shown in Fig. 3(e), Ti doping causes a decrease in the κ value, which is the same result reported by Drašar et al for single-crystal Sb2Te3 (Ref 31). Figure 3(f) and (g) illustrates that the contribution of lattice thermal conductivity (\(\kappa_{l}\)\(\text{)}\) was greater than the factor of charge carriers (\({\kappa }_{e}\)) in Bi2Te3. A similar result was reported by Byun et al., who found that the thermal conductivity of the lattice (\({\kappa }_{l}\)) increases as a function of temperature (Ref 23). The \(\kappa_{e}\) value shows a different trend for pristine and Ti-doped samples.

The band structure and partial density of states (PDOS) of Bi2Te3 without SOC calculation are shown in Fig. 4(a). The calculated direct band gap is approximately 0.37 eV in Γ momentum space. Meanwhile, the calculation with SOC is shown in Fig. 4(b), where the indirect band gap is approximately 0.14 eV between Γ and M momentum space. This value is similar to several previous reports of 0.154 eV (Ref 53) and 0.13 eV (Ref 18). The calculation of the PDOS with SOC showed that the state of the Te atom dominated in the valence band and passed the Fermi level, which indicated that Bi2Te3 is metallic. The energy gap of Bi(2−x)TixTe3 was measured using UV–Vis spectrophotometry. The data are displayed for the wavelength region in which the sample absorbs light. The absorption data obtained are plotted in (αd)2 as a function of \(E = \frac{hc}{{e\lambda }}\) The intercept of the slope on the X-axis is the energy gap (Eg) value.

Fig. 4
figure 4

Band structure and partial density of states (PDOS) of undoped (Bi2Te3) (a) without SOC and (b) with SOC

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Figure 5(a-d) shows that the Eg value tends to increase with increasing Ti doping. These results are certainly consistent with the ρ data, which increase with Ti doping. According to the experimental results, all materials have high Eg, with values ranging from 3.07 to 3.9 eV, because the nanoscale crystallite size increases dislocation density (Ref 54, 55, 56) and Ti doping in Bi(2−x)TixTe3 compounds increases the difference in electronegativity between Ti4+ and Bi3+ as cations with Te2- as anions (Ref 57, 58).

Fig. 5
figure 5

Band gap energy as a result of UV–Vis spectrophotometry measurements of (a) Bi2Te3, (b) Bi1.95Ti0.05Te3, (c) Bi1.9 Ti0.1Te3, and (d) Bi1.85Ti0.15Te3

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Figure 6(a) shows the results of hardness measurements, which were conducted several times in 5 different areas. The sample hardness value increases as a function of dopant concentration, from 27.14-31.4 VHN. The hardness value is similar to that reported by Kartika et al for the undoped sample, while for the doped sample, it is quite different (Ref 32). This is due to the difference in the calculation method for Ti doping. The corrosion rate of Bi(2-x)TixTe3 was characterized by using a potentiodynamic technique in a 3 wt.% NaCl solution. The inserted graph in Fig. 6(b) shows that Ti doping reduces the corrosion rate of Bi2Te3. This is because titanium has excellent chemical stability (Ref 59). Table 2 shows the figure of merit (zT) of our samples in this study and earlier publications (Ref 19, 26, 60,61,62,63).

Fig. 6
figure 6

(a) The hardness measurement results of bulk Bi(2-x)TixTe3 with different amounts of Ti doping and (b) the corrosion rate of Bi(2-x)TixTe3 as a result of potentiodynamic measurements

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Table 2 Figure of merit (zT) of some samples in this research and previous reports
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4 Conclusions

We successfully synthesized Bi(2−x)TixTe3 with various doping concentrations (x = 0, 0.05, 0.1, and 0.15) using a solid-state reaction and carbon burial sintering method. The powder x-ray diffraction pattern of all samples revealed the presence of Bi2TeO5 impurities, with the greatest amount at x = 0.05, which was 5.2%. The highest figure of merit (zT) was found in the undoped sample, which was 0.46 at 327 K, and tended to decrease with increasing doping concentration. The energy gap for Bi2Te3 was 3.07 eV and widened with increasing Ti doping. Ti doping caused an increase in hardness and reduced the corrosion rate.