Improved electrical conductivity and power factor in Sn and Se co-doped melt-grown Bi₂Te₃ single crystal

The growth of (Bi_1−xSn_x)₂Te_2.7Se_0.3 single crystals have been carried out by melt growth technique. The precursor bismuth (Bi) (99.99%), tin (Sn) (99.9%), selenium (Se) (99.995%), and tellurium (Te) (99.99%) were weighed for 4 g in a stoichiometric ratio and ground in an agate mortar (open air-condition) for about 2 h. Ampoules (length of 200 mm and a diameter of 14 mm with 50 mm conical shape at the end) were sealed in a 10^–3 Torr vacuum. Residual argon gas was inserted in the ampoules at the pressure of 0.5 kg/cm³ to get an inert atmosphere. The ampoules were tied to a motor and suspended in the crystal puller “Nanotech 1200” temperature gradient with the help of Kanthal string. The crystal puller furnace is used to melt the mixture by prearranged thermal profile between 30 and 850 °C, with pulling rate of 2 mm per hour, at 600°C transition temperature. The ampoule holding the grown single crystal was then separated from the crystal puller unit. The grown crystals were isolated from the ampoule and cut into anticipated dimensions for characterization. The various stages involved in single crystal growth of (Bi_1−xSn_x)₂Te_2.7Se_0.3 and the thermal profile are shown in Fig. 1a and b.

Powder X-ray diffraction was utilized to know the purity, crystalline quality, and structure of finely powdered (Bi_1−xSn_x)₂Te_2.7Se_0.3 single crystals. The experiments were performed using the “Rigaku Ultima IV” diffractometer in the range of 20°–80° utilizing X-ray Cu Kα (1.54 Å) radiation. The crystalline perfection, symmetries, dislocations, and dopants influence on the inner plane structure of the single crystals were determined using high-resolution X-ray diffraction (HR-XRD) study. Good quality single crystals of dimension 3 mm × 4 mm × 1 mm were scanned by means of “D8 Brüker Diffractometer” (source: Cu Kα; 1D fast detector, Double crystal monochromator with global mirror). Using the “Carl Zeiss Sigma” field emission scanning electron microscope (FESEM), the surface morphological features of the single crystals were examined at the particle range of 1 μm with a magnification of 35 kX. (20 -120 μm range with an accelerating voltage of 30 kV with three detectors). To know the chemical composition of the grown single crystals, Energy dispersive X-ray analysis was carried out. The carrier concentration and mobility were determined at room temperature using the “Van der Pauw” technique, with the help of a Keithley 6220 m. Electrical resistivity, thermal conductivity, and Seebeck coefficient were measured in the temperature range of 10–400 K using a Physical Property Measurement System (PPMS, Quantum Design).

Figure 2 presents the XRD patterns of the (Bi_1−xSn_x)₂Te_2.7Se_0.3 samples in the 2θ range of 20–80°. The (015) peak is the most dominant one in all samples, representing a single orientation and good crystalline nature [18]. Rietveld refinement was performed using “EXPO 2014” [Fig. 3] to know the deviation of the observed XRD peak patterns from the theoretical ones, and the values are given in Table 1. Systematic broadening and splitting of the peaks from the pristine to the co-doped (Bi_0.98Sn_0.04)₂Te_2.7Se_0.3 crystals were observed at the angles 28°, 32°, 70°. These changes result from the sharing of single lattice points by the prevailing crystal face (Fig. 4) [19]. The two additional reflections noticed around the plane (015) are due to the unveiling of twining orientations [19, 20]. A systematic decrease in the crystallite size has been found with decreasing lattice parameters (Table 1), which is reported to be because of Sn atoms non–intercalation through Van der Waals interlayer [21]. The crystallite size is determined using the Williamson-Hall formula [16]. (Bi_1−xSn_x)₂Te_2.7Se_0.3 shows hexagonal crystal structure and R\(\overline{3}\) m space group with close-packed series of covalently bonded Te_(Se)–Bi_(Sn)–Te_(Se), when bismuth and tellurium are substituted by tin and selenium respectively in their sites [22]. The weak Van der Waals type of quintuple layers are formed by the interlayer forces [23]. The Bi₂Te₃ consists of an atomic layers sequence Te₍₁₎–Bi–Te₍₂₎–Bi–Te₍₁₎ (Bi₂Te₃). These layers are modified as Te₍₁₎–Bi–Se₍₂₎–Bi–Te₍₁₎ in Bi₂Te_2.7Se_0.3, and Se₍₁₎–Bi_(Sn)–Se₍₂₎–Bi_(Sn)–Se₍₁₎ due to doping. A small but adequate quantity of Te atoms are able to complete each quintuple layer because of continuous inclusion of Sn and Se in Bi₂Te₃ [24]. As a result, these layers are introduced with more and more stacking faults. The Bi–Te phase decreases with the Sn–Te, Sn–Se, and Bi–Se phases investigated using “Profex 3.14” and is presented in Table 2.

HR-XRD investigation for the (015) plane, azimuthal (ϕ), and scan of the rocking curve for (0015) plane is carried out on 3 mm × 4 mm × 1 mm cleaved surface of single crystals. Figure 5 shows the θ–2θ measurement of scan for the crystals in between 10° and 80° measured at 2° per minute scan rate. It is observed that the most significant peak in the Bi₂Te₃, Bi₂Te_2.7Se_0.3, and (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 samples are due to the (006) plane in the ‘c’ direction, which corresponds to the desired and dominant phase in these samples. In (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3 crystal, on the other hand, the most significant peak is due to the (0015) plane [25]. Various crystallographic orientations show somewhat different dynamics in the release of deposited energy due to a few random nucleation or growth. This significantly impacts selecting the process parameters, particularly the growth temperature and time required for achieving the desired properties at the final stage [26]. The sharpness of the peak due to the (0015) plane shows the high degree of crystallinity of the single crystals containing low angle grain boundaries [27‐29]. Figure 6 shows the inner (015) θ–2θ scan for the between 20° and 80° measured at the rate of 2° per minute. It is established that crystal growth has been taken along the (015) plane and all individual sample demonstrates dual intense sharp peaks at angles of about 27° and 55°, which specifies the equivalent parallel planes of the crystals. The crystallite size values and strain of lattice are presented in Table 3.

The ϕ scan for our crystals is performed in the range of − 180° to 180° at the rate of 2° per minute for the plane (015). Figure 7 exhibits three peaks corresponding to the symmetry of the threefold (015) plane, representing in-plane orientation in the crystal. The intensity differences among pristine and doped samples are due to the variation in the population of domains [29, 30]. Peak intensity discrepancies of the crystals in few regions result from a disorder of in-plane orientation and the slight deviation between tilt angle and normal direction. Since the interval between the two peaks is 120°, it is inferred that the crystals possess a hexagonal structure.

To know the perfection of the single crystals, a rocking curve scan has been carried out for (0015) plane in the 2θ between 16° to 28° at the rate of 2° per minute, and the results are shown in Fig. 8. Lorentzian non-linear fitting of the curve has been used to validate the rocking curves of entire samples, where the theoretical curves are found to match quite well with the experimental curves. Lorentzian fitting factor (R²) values and FWHM (β) are provided in Table 3. The crystals Bi₂Te₃ and (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3 have sharp and fine peaks without any amorphous behaviors, whereas the crystals Bi₂Te_2.7Se_0.3 and (Bi_0.04Sn_0.02)₂Te_2.7Se_0.3 have shown slight splitting of the peak. This is attributed to the occurrence of the low angle grain boundary with crystal domains misorientation [31‐33]. The Sn and Se doping in (Bi_0.98Sn_0.02)₂Se_2.7Te_0.3 and (Bi_0.96Sn_0.04)₂Se_2.7Te_0.3 are predictable to produce point defects and mosaic orientation in the crystals [34‐36]. The minor tilt angles generated through super-stoichiometric nature with ions Bi_(Sn) is the reason behind the rocking curve \(\omega\) shift of individual crystal.

The characteristic surface morphological features of (Bi_1−xSn_x)₂Te_2.7Se_0.3 samples are shown in Fig. 9, where the pristine Bi₂Te₃ shows homogeneous interfaces without any low angle grain boundary and porosity (Fig. 9a). The crystals Bi₂Te_2.7Se_0.3 (Fig. 9b) shows tiny boundaries of tilt, which are ascribed to rise in the densities of dislocation and are determined by the relations [37]

where b_s is screw dislocation constant (45 nm), and b_e is edge dislocation constant (2.17 nm), and ω is the full width at half maximum intensity of rocking curve. It is observed that there are few black domains found on the surface of single crystal (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3. This is due to the interface created by the micro precipitate formed due to Se and Te particles throughout the melt growth process (Fig. 9c). As Se is inserted into Bi₂Te₃ matrix_, unrestrained melt mixture in ampoule is seen due to peritectic reactions [38]. However, due to Se evaporation, few micro precipitates and microdots are observed in the (Bi_0.96Sn_0.04)Te_2.7Se_0.3 sample [39]. Moreover, some small white patches of coarse grains are observed in the (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 crystal because of the thermal and mechanical fluctuations in the crystal melting process (Fig. 9c) [40‐43].

EDAX has been carried out to determine the chemical composition of the crystals, and the images are shown in Fig. 10. The pristine Bi₂Te₃ is found to contain bismuth and tellurium (Fig. 10a), whereas the Bi₂Te_2.7Se_0.3 is found to contain selenium along with the bismuth and tellurium (Fig. 10b). Figure 10c, d establish the occurrence of tin in the (Bi_1−xSn_x)₂Te_2.7Se_0.3 samples. The expected/nominal composition matches well with the measured elemental composition of the studied crystals, as shown in Table 4. The EDAX results confirm that the atomic percentage of Sn in crystal (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3 and (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 are 0.97% and 1.74%, respectively. On the other hand, the atomic percentage of Se in Bi₂Te_2.7Se_0.3, (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3 and (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 are 10.31%, 10.82% and 12.46%, respectively.

The temperature dependence of electrical resistivity ρ(T) of the (Bi_1−xSn_x)₂Te_2.7Se_0.3 samples is presented in Fig. 11 between 10 and 395 K. Overall, and the ρ(T) values decrease systematically from the pristine to the co-doped samples. The pristine Bi₂Te₃ has the highest electrical resistivity with quasi degenerate semiconducting behavior. Initially, there is an enhancement in the value of electrical resistivity with a rise in temperature from 10 to 250 K due to the low mobility of the opposing charges around another donor atom, which causes direct cation-cation interaction of homopolar Bi–Bi bonds [44]. The electrons fail to conduct significantly unless the temperature is raised sufficiently (above 250 K). With sufficient energy supply beyond 250 K, the negative charge mingles with extra electrons of all the donor atoms, leading to the usual semiconducting behavior at higher temperatures. The Te_Bi formed in the lattice due to the vaporization of Te increases the concentration of Te vacancies [V_Te] [45, 46].

Additionally, point defects are created by introducing Se in the Te sites in Bi₂Te_2.7Se_0.3, and antisite defects of Bi on Te_(Se) sites are also formed [47]. The substituted Se atom in the anion sublattice of Te sites generates anion vacancies. The added dopant Sn (0.02, 0.04) exists in the form of Sn_Bi. As a result, there is an increase in the antisite defect of Sn_Bi on Te_Se. Sn easily replaces Bi with the polar bond because of the electronegativity difference between them [48]. The electrical transport properties of polycrystalline samples are governed by more grain boundaries. As a result, the uniform heat flow and the movement of electrons/holes through a sample consisting of randomly oriented polycrystalline grains is difficult. Whereas, the single crystals are having few grain boundaries, divide both the electrical and thermal conductivities along the two equivalent principal directions [49]. On the other side, the carrier concentration of the samples are modified by the donor-like effect produced by heavy deformation, where \({V}_{Bi}^{{\prime}{\prime}{\prime}}\), \({V}_{Te}^{..}\) are the vacancies of Bi_(Sn) and Te_(Se), respectively. Another positively charged anion vacancy \({V}_{Se}^{..}\) induces more negative carrier in the lattice which changes the electrical properties drastically [50]. This leads to the reduction of electrical resistivity by 3.3 times for (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 in comparison with the pristine sample at 395 K. Antisite defect equation is provided by

Mott’s variable range hopping (VRH) model (Fig. 12) is utilized to study conduction in hopping near Fermi-level in localized states at low temperatures (10–40 K). The electrons in a preliminary localized state get sufficient thermal energy to hop to the closest localized state [51]. When the internal microscopic disorder is high, tunneling of electrons between the nearest sites is also energetically unfavorable [52]. The electrical resistivity in the VRH model is expressed as

where T₀ is the characteristic temperature and ρ₀ is the pre-exponential factor. The characteristic temperature is given bywhere N(E_F) is the density of state at the Fermi level, k_B is the Boltzmann constant, and α is average localization length (19 nm⁻¹), calculated using the relation

Table 5 presents the calculation results of density of state (DOS) N(E_F) values, calculated using Eq. 5 (Fig. 13).

The model of small polaron hopping (SPH) is applied for analyzing electrical resistivity data in the range 140–250 K, using the expression [53]where E_A is the activation energy. The plot of ln(ρ/T) versus 1/T shown in Fig. 14 suggests that thermally triggered small polarons are accountable for conduction in hopping at higher temperature region in the (Bi_1−xSn_x)₂Te_2.7Se_0.3 system [53]. Small polaron formation occurs more readily in disorder sites of the materials [54]. The impurity atom Sn overlaps on Bi sites, creates a defect state, and stays in the vicinity of the top of the valence band. These defect states absorb additional electrons or holes without shifting the Fermi energy too much. The activation energy of each of the samples is given in Table 5.

Figure 15 shows the temperature dependence of the Seebeck coefficient of the present samples in the range 10–395 K. It is observed that all the grown crystals exhibit n-type semiconducting behavior due to antisite disorder Te_Se–Bi_Sn and Te–Bi for the doped and pristine single crystal samples correspondingly. The magnitude of the Seebeck coefficient increases as the temperature increases from 10 K due to the generation of Bi_Te defects. Sn exists in Bi₂Te_2.7Se_0.3 in the polar form of Sn_Bi bond. Bi–(Sn)–Te² by Bi–(Sn)–Se² are replaced by these polar bonds leading to the increase of antisite defects [55, 56]. Seebeck coefficient value starts to saturate and decrease beyond 200 K due to the initiation of thermally excited holes, which neutralizes electrons with the formation of polar bonds in the pristine and co-doped samples [57]. It is observed that there is a decrease in the grain size as the number of grain boundaries subsequently increases. They act as a barrier and allow high energy charge carriers and restrict low energy charge carrier. Hence the average energy of charge carriers is increased, leading to enhancement in the Seebeck coefficient of polycrystalline (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 samples in our previous report. Whereas in single crystal (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3, there are only few grain boundaries, the added Sn atom is assumed to occupy the lattice sites of Bi. It is noticed that the electrons occupy the extended states of band. An active donor defect Sn_Bi creates the distortion in the lattice structure. This gives rise to the degenerate behavior of electron concentrations in single crystal (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3. The immediate formation of an intermediate band acting as balancing center of electrons and holes, which leads to limited excitement of carrier concentration [48, 58]. This indicates that the added Sn has a significant impact on the carrier concentration throughout the temperature range. The dopant Sn is capable of suppressing the bond between Bi_Te and Bi_Se due to its higher electronegativity. The unusual decrease of the Seebeck coefficient values from pristine to the doped single crystal samples is because of formation of electronically active intrinsic disorder.

To understand the charge transport mechanism properly, hall voltage measurements were performed, which established the n-type semiconducting behavior of samples and provided experimentally measured value charge carrier concentration. The theoretical carrier concentration, on the other side, was estimated using [59]

n is the carrier concentration, m* is the effective mass of an electron, and e is the charge of an electron. Both theoretical and experimental carrier concentration values were predicted to be of identical order (10²⁵ m⁻³). The theoretical mobility value was determined using

Table 6 presents values of experimental and theoretical carrier concentrations, mobility, and scattering factor. The production of \({V}_{Te}^{..}\) and \({V}_{Se}^{..}\) (Te and Se vacancies) could be the reason behind the random variation in values \({\mu }_{Th}\). Electrons having different effective masses carry different quantities of current under various conditions of doping. Hence, the time of relaxation and nature of scattering of electrons varies with changes in doping levels. With the assistance of experimental carrier mobility, weighted mobility (μ_w) were determined utilizing [60]

Due to the high concentration of ionized impurities, including acceptors and donors, antisite defects are produced on Te(Se) atoms by Bi(Sn) in (Bi_1−xSn)_xTe_2.7Se_0.3 layered crystals. Moreover, there are excess negative charges in the nearby sites and many vacant sites, making the single crystal exhibit n-type semiconducting behavior. The effective mass is determined by employing Eq. (8) and presented in Table 6. The Fermi energy (E_F) of compounds is determined utilizing

When the electronically active element Sn is doped in the Bi₂Te₃ single crystals, they create active intrinsic donor or accepter type defects. This shifts the Fermi-level in the vicinity of the density of states results in an uneven variation of the population with respect to temperature and doping [61]. Generation of antisite defects of Bi_Sn on the Te_Se site leads to super stoichiometry, which encourages lattice scattering [62]. The lattice of crystal comprises antisite defects of negatively charged sites of Bi(Sn)_Se and Bi(Sn)_Te vacancies of positively charged in tellurium sublattice \({V}_{Te}^{..}\) and \({V}_{Se}^{..}\). The concentration of \({V}_{Te}^{..}\) and \({V}_{Se}^{..}\) surpasses the number of antisite defects. Hence Fermi energy has not shown any specific variation of trend as a function of composition in current compounds. The scattering factor (\(\gamma )\) was calculated using [63]

Fermi-energy and values of theoretical and experimental scattering factors are presented in Table 6.

The temperature dependence of thermal conductivity of grown single crystals in the temperature between 10 and 395 K is revealed in Fig. 16. All crystals exhibit a sharp enhancement of thermal conductivity with increasing temperature between 10 and 50 K because of restraining the mean phonons free path length through low angle grain boundaries by specular reflection [64]. The highest and lowest thermal conductivity values were observed in single crystal (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 and Bi₂Te₃ samples, respectively, between 50 and 360 K. The co-doped extrinsic regime is preferred by low vacancy energy formation. The small bandgap in the material hinders thermal conductivity towards room temperature by forming bipolar conduction. Hence there is a crossing over of total thermal conductivity value of (Bi_0.96Sn_0.04)₂Te_2.7Se_0.3 by (Bi_0.98Sn_0.02)₂Te_2.7Se_0.3 [65].

The contribution of electronic heat transport κ_e is determined by Wiedemann–Franz law (\({\kappa }_{e}=\frac{{L}_{0}T}{\rho }\)) where L₀ is temperature-dependent Lorentz number and is determined utilizing [60] (Fig. 17).

The lattice component of thermal conductivity (Fig. 18) (\({\kappa }_{l}\)) is calculated by subtracting electronic thermal conductivity [Fig. 19] from total thermal conductivity (κ). Values of \({\kappa }_{l}\) Change as 1/T above 50 K in doped compounds due to greater possibility of Umklapp process. The significant concentration of doping in Bi₂Te₃ results in charge transfer, phonon Umklapp scattering, and point defect scattering. It is observed that the main contribution to measure \(\kappa (T)\) initiates from phononic components rather than charge carriers.

The experimental values of thermal conductivities imply that some minor additional holes are created due to the doping of Sn. Because of the effect of differences in mass and lattice constants among the dopants Sn and Se over Bi and Te, there is an expectation of a probable disorder by the intercalation of Sn and Te/Se [66]. Thus, modification of distortion could deteriorate the phonon scattering and enhance thermal conductivity with respect to doping concentration [67]. As (Bi_1−xSn_x)₂Te_2.7Se_0.3 shows semiconducting behavior of n-type, heat flow is monodirectional, only because of free electron density [68]. The present reported thermal conductivity of single crystal Bi₂Te₃ shows a decrease in thermal conductivity (0.6 W/mK) in comparison to our previously reported polycrystal Bi₂Te₃ (3.0 W/mK) at 300 K [16] due to the peierls distortion [69]. In polycrystalline Bi₂Te₃, a charge density wave system encourages strong electron–phonon coupling which weakens the effect of the Peierls distortion on the mechanism of lattice thermal conductivity. As a result of decrease in an harmonicity of polycrystalline samples leading to higher lattice thermal conductivity than the single crystals. The low lattice thermal conductivity in single crystal Bi₂Te₃ originate from the quantum confinement effect and the charge density wave induced by Periels distortion. It has been revealed that materials form resonant bonding like Bi-Te in pristine Bi₂Te₃ single crystal. Usually the single crystal chalchogenides have long-ranged interactions in hexagonal structure. This leads to the strong an-harmonic scattering with different phonon mean-free path results in low value of lattice thermal conductivity [70]. As the anisotropic transport property is exhibited by polycrystalline samples, phonon scattering dominates in the disordered lattice.

Figure 20 displays the temperature-dependent power factor (PF = S²/ρ) of present single crystals. Because of the significant variation in Seebeck coefficient and electrical resistivity, it was observed that the PF value of (Bi_0.96Sn_0.02)₂Te_2.7Se_0.3 (390 μW/mK²) is 1.1 times greater than that of pristine (330 μW/mK²). The variation of thermoelectric figure of merit for (Bi_1−xSn_x)₂Te_2.7Se_0.3 is shown in Fig. 21. The highest ZT value of 0.34 is observed for Bi₂Te₃. Though there is a systematic decrease in electrical resistivity of single crystal series (Bi_1−xSn_x)₂Te_2.7Se_0.3, due to the significant variation in Seebeck coefficient and thermal conductivity, the ZT value has been decreased for co-doped samples. The values of ZT of some standard reported compounds are given in Table 7.