Enhancement of thermoelectric performance of n-type AgBi_1+xSe₂ via improvement of the carrier mobility by modulation doping

Abstract

High charge carrier mobility with low lattice thermal conductivity is one of the key factors for the design of a good thermoelectric material. Recent studies show that n-type Te-free AgBiSe₂ is promising compound for thermoelectric energy conversion due to intrinsically low lattice thermal conductivity. However, low charge carrier mobility in AgBiSe₂ is the constraint for enhancement of its power factor. In the present study, we use a chemical modification way to realize modulation doping in AgBiSe₂. The addition of 2–6 mol% excess Bi in AgBiSe₂ results in the formation of Bi-rich modulation-doped microstructures of topological semimetal, Bi₄Se₃ in AgBiSe₂ matrix. We show that due to facile carrier transport via semi-metallic Bi₄Se₃ microstructure results in overall improvement of carrier mobility without compromising Seebeck coefficient in AgBiSe₂ system, which in turn results in a remarkable improvement in the power factor (σS²) value. A highest σS² value of ~6.35 μW cm⁻¹ K⁻² at 800 K has been achieved in AgBiSe₂-3% Bi excess sample, which is higher than previously reported metal ion and halogen-doped AgBiSe₂.

Graphic abstract

1 Introduction

In the recent years, the energy and environment related concern intensified the research in the arena of efficient, cost-effective and pollution-free means of power generation. Thermoelectric materials are the all solid-state converters without any moving part, can directly and reversibly convert waste heat into electricity [1–4]. Over the last two decades, there has been an escalated interest in the field of thermoelectric materials research. The effectiveness of a thermoelectric material is governed by the thermoelectric figure of merit, zT = σS²T/κ, where σ is the electrical conductivity, S is the Seebeck coefficient, T is the temperature in Kelvin and κ is the thermal conductivity [1–4]. The fundamental challenge to design a promising thermoelectric material is intriguing due to conflicting thermoelectric parameters. To improve the thermoelectric properties, different concepts have been employed via improvement of the Seebeck coefficient or reduction of the thermal conductivity or by simultaneous tailoring of both the parameters. The Seebeck coefficient can be improved by the introduction of resonant levels in the electronic structure or by electronic band convergence [5,6]. On the other hand, κ_lat can be reduced by solid solution alloying, nanostructuring and all-scale hierarchical structuring [3,7,8]. The inorganic solids with intrinsically low κ_lat [9] due to rattling modes [10], soft phonon modes [11–13], resonant bonding [14] and high lattice anharmonicity [15] are realized recently to be promising candidates for the thermoelectric application.

Among the intrinsically low κ_lat compounds, the copper- and silver-based Te-free I–V–VI₂ (where I = Cu, Ag or an alkali metal; V = Sb, Bi; and VI = S, Se) chalcogenide semiconductors have shown promise for enhanced thermoelectric properties [16,17,18,19,20,21,22]. The multiple soft phonon modes and strong phonon–phonon interaction caused by large bonding anharmonicity due to repulsion between the ns² lone pair of group V elements and valence p orbital of chalcogenide is the origin of high thermal resistance for these compounds [16]. In recent years, several new Te-free materials from this class have been discovered as potential candidate thermoelectrics. In the p-type family, AgSbSe₂ and in n-type family, AgBiSe₂ have established to be the most promising candidates [17,20,21,23,24]. At room temperature, AgBiSe₂ crystallizes in a cento-symmetric cation-ordered hexagonal structure with space group P-3m1 and lattice parameter a = 4.194 Å, c = 19.65 Å [25]. It shows two structural transitions at higher temperature. The hexagonal (α) to rhombohedral (β) (space group R-3m, a = 7.022 Å) transition takes place at ~460 K (figure 1). During α–β transition, the cation sublattice remains ordered, but a slight atomic displacement and an elongation of the unit cell in the (001) direction of the hexagonal lattice take place. The ordered rhombohedral (β) to cation-disordered cubic (γ) (space group Fm-3m, a = 5.832 Å) phase transition takes place at ~580 K [25].

Figure 1

Temperature-dependent structural phase transitions in AgBiSe₂. The room-temperature hexagonal and the intermediate rhombohedral phases are cation-ordered structure. The high-temperature cubic phase is a cation-disordered structure.

Although pristine AgBiSe₂ exhibits low thermal conductivity, its thermoelectric performance is poor due to low electrical transport [20]. The thermoelectric property of AgBiSe₂ has been improved by regulating carrier concentration, using electron doping strategy in host cationic or anionic site. For instance, solid solution alloying of higher valent cation (Nb, In or Ge) in the Ag site, optimizes the n-type carrier concentration and leads to enhancements of zT [20,26,27]. The doping of monovalent halide ion (Cl⁻/Br⁻/I⁻) on the divalent selenium (Se²⁻) site can act as an n-type dopant in AgBiSe₂ and results in the significant improvement in thermoelectric properties [21]. Furthermore, the effect of Ag vacancy defect and tellurium substitution on the transport property of AgBiSe₂ has been investigated [28,29]. However, low carrier mobility for pristine AgBiSe₂ (~67 cm² V⁻¹ s⁻¹) and doped samples still restrict to improve the electrical transport properties.

Generally, in heavily doped semiconductors, the high population of free carriers leads to a diminution of carrier mobility due to increased carrier–carrier scattering and ionized impurity scattering [1]. Recently, the concept of three-dimensional (3D) modulation doping (MD) has been introduced to improve the carrier mobility in thermoelectric materials [1,22,30]. Usually, modulation-doped samples are a physical mixture of two-phase composites made of undoped and heavily doped counterparts. The undoped counterpart has low carrier concentration, but high carrier mobilities, whereas the doped counterpart has high carrier concentrations, but low carrier mobilities. In a heavily doped semiconductor, the high population of free carriers can spill over throughout the matrix. However, in a modulation-doped sample, one can force the charge carriers to spill over from the modulation-doped region into the surrounding host matrix. Therefore, the ionized atoms remain spatially separated within the modulation-doped region. Consequently, the ionized impurity scattering rate can be decreased in modulation-doped sample and an overall improvement of carrier mobility can be achieved [22,30–32]. Historically, this technique was first implemented in two-dimensional electron gas (2DEG) thin film devices for improving the carrier mobility and thus, the electrical conductivity [33]. In thermoelectrics, using modulation doping, enhanced power factor was achieved in Si_1−xGe_x composites by mechanically mixing the doped and undoped Si_1−xGe_x nanograins [32]. The concept of modulation doping is successfully applied to BiCuSeO [30], BiAgSeS [22] and half-Heusler TiNiSn [33]. All these reports encouraged us to investigate the MD approach in intrinsically low thermal conductivity AgBiSe₂ system where electronic transport can be improved by enhancing the carrier mobility.

Herein, we report a large enhancement of power factor in AgBiSe₂ by enhancing carrier mobility by modulation doping. The present modulation doping is quite different from the conventional approach. In our study, we have used 2–6 mol% excess Bi as a modulation dopant in AgBiSe₂ to improve the carrier transport. We demonstrate a chemical modification way to realize modulation doping in AgBiSe₂ by embedding bismuth-rich microstructure in AgBiSe₂ matrix through matrix encapsulation technique. We have chosen Bi for two reasons. Firstly, Bi is an n-type semimetal with a small Fermi surface (low carrier effective mass), long carrier mean free path and extremely high electron mobility (~10⁴ cm² V⁻¹ s⁻¹ at 300 K) [34]. Secondly, Bi is a constitute element of AgBiSe₂ and therefore, it ruled out the aliovalent doping in the parent AgBiSe₂ phase and minimizes the possibility of ionized impurity scattering process. The diffusion of electrons from AgBiSe₂ matrix to Bi-rich semi-metallic precipitate results in an overall enhancement of carrier mobility in AgBiSe₂-x% Bi (x = 2–6 mol%) system. We show that the addition of small fraction of Bi in AgBiSe₂ results in a large effect on the microstructure and transport properties of AgBiSe₂. PXRD and microstructure analysis reveals that AgBiSe₂-x% Bi samples are not single phase, but rather forms a microstructure composed of well dispersed Bi-rich nano/micro-inclusion of topological semimetal, Bi₄Se₃ [35,36] in the matrix of AgBiSe₂. Electrical transport measurement shows that the MD approach enhances the carrier mobility and hence, electrical conductivity in AgBiSe₂ which results in a remarkable improvement in the power factor (σS²) value over wide temperatures. A maximum power factor value of ~6.35 μW cm⁻¹ K⁻² at 800 K was measured in AgBiSe₂-3% Bi, which is higher than the metal ion and halogen-doped AgBiSe₂ system.

2 Experimental

Ingots (~7 g) of pristine AgBiSe₂ and AgBi_1+xSe₂ (x = 2–6 mol%) were synthesized by melting reaction of stoichiometric amounts of high-purity elemental silver (Ag, 99.9999%, metal basis, Alfa Aesar), elemental bismuth (Bi, 99.9999%, metal basis, Alfa Aesar) and elemental selenium (Se, 99.999%, metal basis, Alfa Aesar), taken in quartz tubes which were sealed under high vacuum (~10⁻⁵ Torr). The sealed tubes were slowly heated up to 723 K in 12 h, then heated up to 1123 K in 4 h, soaked for 10 h, and eventually slow-cooled to room temperature over a period of 12 h. For transport property measurements, the samples were cut using a low-speed diamond saw and polished using a polisher. Density of the samples was found to be ~97% of the theoretical value of pristine AgBiSe₂. Powder X-ray diffraction patterns (PXRD) for finely powder samples were recorded using a CuKα (λ = 1.5406 Å) radiation source on a Bruker D8 diffractometer. The room temperature carrier concentration of the samples was determined by Hall coefficient measurement system using a home-build measurements system. FESEM images were derived using NOVA NANO SEM 600 (FEI, Germany) operated at 15 kV. Electrical conductivity and Seebeck coefficients were measured concurrently under a helium atmosphere from room temperature to ~823 K on a ULVAC RIKO ZEM-3 instrument system. The sample for the measurement is parallelepiped with dimensions of ~2 × 2 × 8 mm³. The longer direction matches the direction in which the thermal conductivity was measured. Heating and cooling cycles gave repeatable electrical properties for a given sample. Electrical and thermal transports are measured in the same direction. The thermal diffusivity (D) was measured by laser flash method (Netzsch LFA-457) from room temperature to ~823 K. It was performed on carbon-coated disc samples of 8 mm in diameter and 2 mm thickness under an N₂ atmosphere. Temperature-dependent heat capacity, C_p, was derived using the standard sample (pyroceram) in LFA-457. Cowan model with pulse correction was used to analyse the thermal diffusivity data. The total thermal conductivity, κ_total, was estimated using the formula: κ_total= DC_pρ, where ρ is the density.

3 Results and discussion

The crystalline ingots of AgBiSe₂ and AgBiSe₂-x% Bi (x = 2–6 mol%) were synthesized by elemental melting reaction in vacuum-sealed quartz tubes followed by slow cooling. Figure 2a shows PXRD pattern of pristine and AgBiSe₂-x% Bi samples. The pattern for pristine sample could be indexed based on hexagonal AgBiSe₂. The XRD patterns for Bi excess samples show additional reflections of the second phase of topological semimetal, Bi₄Se₃ (* marked in the plot). The intensity of the additional peaks increases with the rise in bismuth concentration which implies the increase in secondary phase of Bi₄Se₃ in the sample. Supplementary figure S1 shows that * peaks can be indexed to Bi₄Se₃ in 6% Bi-excess sample.

Figure 2

(a) Room temperature powder XRD pattern of pristine AgBiSe₂-x% Bi (x = 0–6 mol%) samples. * marks indicate extra reflection due to the second phase of Bi₄Se₃. (b) Backscattered FESEM image of the cleaved surface of AgBiSe₂-3% Bi sample, the Bi-rich precipitates with bright contrast is circled with black dotted line. (c) EDAX elemental line scan along the matrix and precipitate.

To confirm these extra reflections of secondary phase of Bi₄Se₃ in PXRD data, we have carried out backscattered electron imaging (BSE) during FESEM and energy dispersive X-ray spectroscopy (EDAX) to understand the microstructure in AgBiSe₂-x% Bi (x = 2–6 mol%). The BSE–FESEM image of 3% Bi modulation-doped sample is presented in figure 2b and c. The micrograph clearly shows two distinct regions with dark and bright contrasts. The elements with the higher atomic number has greater probability for elastic collision and looks brighter in BSE image. Thus, the region with bright contrast is related with heavier elements of the sample which is Bi₄Se₃ precipitates in the present case and EDAX analysis in supplementary figure S2b, confirms that the precipitates are Bi-rich phases, Bi₄Se₃. The darker contrast regions correspond to the matrix in supplementary figure S2a. To further evaluate the composition of the matrix and the precipitate, we have performed elemental line scanning which shows Bi-rich precipitate, while the matrix is close to the composition of AgBiSe₂. Thus, the microstructure analysis further confirms the presence of Bi-rich secondary phase of Bi₄Se₃ in the AgBiSe₂ sample.

In figure 3, we present temperature-dependent electronic transport properties of AgBiSe₂-x% Bi (x = 0–6 mol%). Pristine AgBiSe₂ exhibits a σ value of ~63 S cm⁻¹ at room temperature (figure 3a, inset). The temperature-dependent, σ in the hexagonal phase maintains nearly constant value upto ~460 K. In the rhombohedral phase (temperature window of 460–580 K), the system exhibits metallic behaviour with σ drops from ~52 S cm⁻¹ at 460 K to ~16 S cm⁻¹ at 580 K. In the cubic phase (above ~585 K), the σ value increases to ~24 S cm⁻¹ at 708 K. The σ value for Bi-modulation-doped samples is considerably higher than the pristine sample, which shows an increasing trend with rise in Bi concentration (figure 3a). The modulation-doped samples show a similar metal to semiconductor type transition during rhombohedral to cubic phase transformation like in pristine AgBiSe₂, which is also observed in metal ion and halogen-doped samples of AgBiSe₂ [20,21,26,27]. Typically, for AgBiSe₂-3% Bi sample, the σ value changes from ~380 S cm⁻¹ at room temperature to ~435 S cm⁻¹ at 800 K.

Figure 3

Temperature-dependent (a) electrical conductivity (σ) and (b) Seebeck coefficient (S) of AgBiSe₂-x% Bi (x = 0–6 mol%) samples. The inset in (a) shows zoomed data for pristine AgBiSe₂.

To get better insights for the improvement of the electrical conductivity value, we have measured carrier concentration of the selected samples. The negative value of Hall coefficient (R_H), at ambient temperature for pristine and AgBiSe₂-x% Bi (x = 0–6 mol%) samples indicates n-type conduction in the system. We have estimated the carrier concentration (n) and carrier mobility (μ) from the formula: n = 1/eR_H, and μ = σ/ne, respectively, where e is the electronic charge. The electrical conductivity (σ) is related to n through the carrier mobility (µ) through the following expression:

$$ \sigma = ne\mu , $$

(1)

µ relies on the additional conditions shown in equation (2)

$$ \mu = \frac{e\tau}{{m^{*} }}, $$

(2)

where τ is the relaxation time and m* the carrier’s effective mass. Notably, in the halogen- and cation-doped AgBiSe₂, the improvement in the carrier transport primarily due to the rise of carrier concentration. The Bi incorporation results in a slight increase in carrier concentration, while the carrier mobility increases dramatically compared to pristine sample (table 1). Typically, for AgBiSe₂-3% Bi, μ shows a value of ~248 cm² V⁻¹ s⁻¹, which is much higher than previously reported cation- and anion-doped AgBiSe₂ samples ranging from ~22 to ~63 cm² V⁻¹ s⁻¹ with similar carrier concentration [20,21], indicating that modulation doping suppresses the ionized impurity scattering. In addition, the diffusion of electrons to Bi₄Se₃ precipitate, where carrier mobility is higher than AgBiSe₂ matrix results in an overall improvement of μ in the system.

Table 1 Room temperature carrier concentration (n), electrical conductivity (σ), carrier mobility (µ) and effective mass (m*) of AgBiSe₂-x% Bi (x= 0–6 mol%) samples.

Temperature-dependent Seebeck coefficient (S) of AgBiSe₂ and Bi modulation-doped samples has been presented in figure 3b. Typically, AgBiSe₂-3% Bi sample shows an S value of −82.5 μV K⁻¹ at room temperature which reaches a value of −100 μV K⁻¹ at 460 K within the hexagonal phase. After the hexagonal to rhombohedral phase-transition, the Seebeck coefficient shows an increasing trend and reaches a value of the maximum value of −160 μV K⁻¹ at 560 K. In the cubic phase, the S value decreases and reaches −120 μV K⁻¹ at 800 K. Although the trend of S in the present case of Bi-excess is similar to the metal ion and halogen-doped AgBiSe₂, the value of S is lower in the measured temperature range. To understand this, we have calculated carrier effective mass (m*) assuming single parabolic band model with acoustic phonon scattering (r = −1/2). The details of equation for the calculation can be found in electronis supporting information. We have observed a large decrease of m* compare to pristine sample (table 1). Besides, the m* value ranging from 0.18 to 0.20 is much smaller than halogen-doped samples with m* ranging from 0.46 to 0.59 [21]. Thus, lower S value in the present case is due to a combined effect of decreased m* and increase in the carrier concentration (n), as given by Mott equation, where S is directly proportional to the m* (S ~ m*) and inversely proportional to n (S ~ n^−2/3) [2]. We would also like to mention that low carrier effective mass (m*) in the modulation-doped samples assists to increase overall carrier mobility (supplementary equation (S2)) which improve the σ in the present case.

The temperature-dependent power factor (σS²) for all the samples, estimated from measured σ and S have been shown in figure 4a. The Bi modulation-doped samples show large improvement in σS² than the pristine sample. Typically, the AgBiSe₂-3% Bi sample shows a σS² of ~2.6 μW cm⁻¹ K⁻² at room temperature which reaches a maximum value of ~6.35 μW cm⁻¹ K⁻² at 800 K. Indeed, the maximum σS² value obtained in the present ingot samples is higher than that of the halogen- and metal ion-doped AgBiSe₂ ranging from ~2.0 to ~5.45 μW cm⁻¹ K⁻² (figure 4b) [20,21,26,29].

Figure 4

(a) Temperature-dependent power factor of (σS²) AgBiSe₂-x% Bi (x = 0–6 mol%) samples and (b) comparison of power factors of the halogen- and metal ion-doped AgBiSe₂ samples.

Figure 5a represent temperature-dependent total thermal conductivity, κ_total, of all the samples. κ_total has been estimated using the formula, κ_total= DC_pρ, where D is the thermal diffusivity, C_p is specific heat and ρ is density of the sample (supplementary figure S3). All the doped samples show an increasing trend of κ_total over the measurement temperature. Typically, for AgBiSe₂-3% Bi sample, a κ_total of ~0.95 W m⁻¹ K⁻¹ has been measured at room temperature, which decreases to a minimum value of ~0.67 W m⁻¹ K⁻¹ in the rhombohedral at 570 K. With further increase in temperature in the cubic phase, the κ_total initially show an increasing trend and then reaches to a value of ~0.93 W m⁻¹ K⁻¹ at 823 K. For higher concentration modulation-doped samples, AgBiSe₂-x% Bi (x = 4–6 mol%) in the cubic phase, the κ_total shows increasing trend. To understand this, we have extracted the contribution of lattice thermal conductivity (κ_lat) and electronic thermal conductivity (κ_el) (supplementary figure S4b) to the κ_total (figure 5b) using Wiedemann–Franz law: κ_el = LσT, where L is the Lorenz number (supplementary figure S4a). L has been calculated using single parabolic band model, which can be found elsewhere [17]. The analysis indicates a large contribution from the κ_el at higher temperature results in such an observation. We also observed a small increase in κ_lat value in the modulation-doped sample compared to the pristine AgBiSe₂. Generally, in I–V–VI₂ family of compounds, the phononic contribution towards κ_total is already to a minimum value as the mean free path of the phonons is in the range of interatomic distance. Thus, the possibility of scattering of smaller mean free path phonons by the micrometer size precipitate can be ruled out here. We therefore, attribute that the increase in κ_lat might be associated with the additional contribution of κ_lat from the microstructure phase of Bi₄Se₃ which probably has higher thermal conductivity.

Figure 5

Temperature-dependent (a) total thermal conductivity (κ_total) and (b) lattice thermal conductivity (κ_lat) of AgBiSe₂-x% Bi (x = 0–6 mol%) samples.

The estimated temperature-dependent thermoelectric figure of merit, zT from the electrical and thermal transport data for all the samples has been given in figure 6. The estimation includes ~10% error from the different measurement. The modulation-doped samples show higher zT value compared to pristine sample. The improvement in the zT value is due to large enhancement of electrical conductivity and power factor value due to improved carrier mobility of the sample. A highest zT value of ~0.53 at 800 K has been achieved for AgBiSe₂-3% Bi sample.

Figure 6

Temperature-dependent thermoelectric figure of merit (zT) of AgBiSe₂-x% Bi (x = 0–6 mol%) samples. 10% error bar has been shown in zT estimation.

4 Conclusions

In summary, our study shows that modulation doping is an effective way to improve carrier mobility in AgBiSe₂. We have shown that addition of small amount of Bi in AgBiSe₂ results in a large effect on the microstructure and transport properties of AgBiSe₂. The suppression of the ionized impurity scattering and injection of charge carrier to the precipitate of topological semimetal, Bi₄Se₃ from the AgBiSe₂ matrix result in the large improvement of carrier mobility. As a consequence, we have observed an increase in thermoelectric power factor and zT in AgBiSe₂. In general, low carrier mobility in I–V–VI₂ class of materials is constraint for the improvement of power factor. Our study demonstrates that use of heterogeneous modulation doping approach could be an effective strategy for improvement of carrier transport in I–V–VI₂ class of compounds.