Dynamic carrier transports and low thermal conductivity in n -type layered InSe thermoelectrics

Semiconductor InSe with wide bandgap and layered crystal structure is expected to be a promising thermoelectric material, and its excellent plasticity brings great potential applications in ﬂexible and wearable thermoelectric devices. To advance its thermoelectric performance, this work systematically investigates the carrier and phonon transport properties in n -type InSe. It is found that InSe compound presents an exceptional dynamic carrier transport property due to the amphoteric indium (In + and In 3 + ), which contributes to favorable temperature-dependent increasing carrier concentration. More importantly, with S alloying in InSe, the carrier concentration can be further enhanced from ∼ 3.2 × 10 13 cm –3 in InSe to ∼ 4.8 × 10 15 cm –3 in InSe 0.97 S 0.03 at 300 K, because S ( χ P ∼ 2.58) with larger Pauling electronegativity than Se ( χ P ∼ 2.55) can induce more In 3 + state to increase carrier concentration in matrix. This boosted dynamic carrier transport property beneﬁts an obviously enhanced power factor. Additionally, InSe compound presents intrinsically low thermal conductivity ∼ 1.6 W m –1 K –1 at 300 K due to low-symmetry crystal structure and strong anharmonicity. This work indicates that the special dynamic carrier transport property and intrinsically low thermal conductivity in InSe make it as a worth-expecting thermoelectric material.


INTRODUCTION
Thermoelectric technology is considered as a promising conversion strategy between electricity and heat, and it has wide applications, such as waste-heat recovery, self-powered electronic device, radioisotope thermoelectric generator, thermoelectric refrigerator, etc. [1][2][3] The thermoelectric conversion efficiency is mainly determined by the performance in materials, which closely depends on its dimensionless figure of merit (ZT), ZT = S 2 σT/κ tot , where S, σ, κ tot , and T represent Seebeck coefficient, electrical conductivity, total thermal conductivity, and absolute temperature, respectively. [4][5][6] Obviously, high-performance thermoelectric materials require large absolute Seebeck coefficient, high electrical conductivity, and low thermal conductivity simultaneously. However, the thermoelectric performance is limited by these strongly coupled relationships between thermoelectric parameters. To develop high-performance thermoelectric materials, researchers can decouple these This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2021 The Authors. Aggregate published by John Wiley & Sons Australia, Ltd on behalf of South China University of Technology and AIE Institute thermoelectric parameters in a given material by using band structure engineering [7][8][9] and nanostructure designing, [10][11][12] or exploit new highly effective thermoelectric materials with intrinsic low conductivity and superior electrical transport properties. [13][14][15] Recently, indium selenide (InSe) has gained wide attention due to its exceptional plasticity as a semiconductor, making it promising to be applied in deformable or flexible electronics. 16,17 More importantly, InSe compound presents wide bandgap (E g ∼ 1.18 V) and low-symmetry layered crystal structure (space group: P6 3 /mmc), [18][19][20] which are completely consistent with the selection rules to seek highly effective thermoelectrics. 21 Therefore, semiconductor InSe is considered as a potential thermoelectric and might have promising applications in flexible and wearable thermoelectric devices. However, previous results found that InSe owns very low carrier concentration around ∼3.2 × 10 13 cm -3 at room temperature that largely restricts its thermoelectric performance. 22 26 are conducted to optimize the carrier concentration in InSe, but the increase of carrier concentration is limited. Noticeably, the theoretical calculation results indicate that a maximum ZT of ∼0.65 can be achieved at 800 K with optimal carrier concentration. 27 And an attractive ZT value of ∼0.46 has been successfully obtained in InSe monolayer at room temperature. 28 All these results above prove that InSe compound is a promising thermoelectric material and it is necessary to further optimize its electrical transport properties.
In this work, we find that n-type InSe shows a particular dynamic carrier transport property that the carrier concentration continuously increases with rising temperature at 300-723 K. This exceptional dynamic carrier concentration arises from amphoteric indium element, which causes mixed valence states In + and In 3+ in InSe. With increasing temperature, In + state will be thermally activated to release two free carriers into matrix by transmitting into In 3+ state. Thus, the Hall carrier concentration in n-type InSe increases by three orders of magnitude, from ∼3.2 × 10 13 cm -3 at 300 K to 6.2 × 10 16 cm -3 at 723 K. To further enhance the carrier concentration in n-type InSe, S element is introduced to alloy in InSe compound, which can induce more In 3+ state, namely more free electrons in matrix because S (χ P ∼ 2.58) owns larger Pauling electronegativity than Se (χ P ∼ 2.55). As a result, the Hall carrier concentration can obviously increase from ∼3.2 × 10 13 cm -3 in n-type InSe to ∼4.8 × 10 15 cm -3 in InSe 0.97 S 0.03 at 300 K, contributing to largely enhanced electrical transport properties. Furthermore, the sound velocity measurement uncloses that the lowsymmetry layered InSe compound exhibits comparably low Young's modulus (E ∼ 20.5 GPa) and high Grüneisen parameter (γ ∼ 2.28), and a minimum lattice thermal conductivity of ∼0.8 W m -1 K -1 at 723 K can be obtained. Finally, the ntype InSe obtains an obvious improvement in thermoelectric performance.

Crystal structure and electronic band structure in InSe
The crystal structure of InSe is illustrated in Figure 1A-C. It is crystalized in hexagonal system with a space group of P6 3 /mmc, and presents a low-symmetry layered crystal structure along c axis. The adjacent layers are connected by weak van der Waals forces, [18][19][20] which results in strong anharmonicity and intrinsically low lattice thermal conductivity in InSe, as discussed below. The XRD patterns of InSe in Figure 1D are indexed into pure phase with the lattice parameters of a = b = 4.004 Å and c = 16.682 Å, which is consistent with the theoretical value of a = b = 4.005 Å and c = 16.640 Å. 29 In Figure 1E, the optical absorption measurement shows a large bandgap (E g ) of ∼1.18 eV in InSe compound. Noticeably, these intrinsic characters of wide bandgap, low-symmetry and layered crystal structure in InSe are well consistent with the rules to select new highly effective thermoelectric materials. 21 Therefore, the thermoelectric performance in InSe is worthy to being systematically investigated. Figure 2A presents the electronic band structure of InSe obtained by density functional theory (DFT) calculation. The theoretical calculation shows that InSe is a direct bandgap semiconductor with a large bandgap (E g = ∼0.73 eV). It is worthy to note that the theoretical bandgap is calculated at 0 K without considering the effect of temperature, which is smaller than the optical measured result (E g ∼ 1.18 eV) at room temperature. InSe can be regarded as multiple band model with band offsets of ∼0.4 and ∼0.3 eV in conduction band and valence band, respectively. Notably, the conduction band owns much sharper shape than valence band, which is consistent with the density of states (DOS) in Figure 2B. Different band shapes in conduction and valence bands can lead to a lower carrier effective mass in n-type InSe than its p-type counterpart. Relatively low carrier effective mass in n-type InSe is capable to achieve high carrier mobility and electrical conductivity, while high Seebeck coefficient can be obtained in p-type InSe due to large carrier effective mass. The DFT calculation unveils a favorable electronic band structure in InSe, and signifies potential thermoelectric performance in both n-type and p-type InSe.

Dynamic carrier transport property in InSe
InSe is a sister compound of In 2 Se 3 , and the difference between these two compounds is that indium element presents valence fluctuation (In + and In 3+ ) in InSe, while In 2 Se 3 contains full In 3+ valence state. 30,31 To shed light on the effect of amphoteric indium, the carrier transport properties between InSe and In 2 Se 3 are compared in Figure 3. All these carrier transport properties compared here are from in-plane direction, because InSe and In 2 Se 3 possess layered crystal structure and high anisotropy. It is shown that both InSe and In 2 Se 3 exhibit intrinsic n-type transport behaviors. Differently, In 2 Se 3 exhibits a much higher electrical conductivity and lower Seebeck coefficient than InSe, shown in Figure 3A,B, because of its large carrier concentration around 1.9 × 10 17 cm -3 in In 2 Se 3 and low carrier concentration around 3.2 × 10 13 cm -3 in InSe at room temperature. The different carrier concentrations in these two compounds F I G U R E 4 Phase analysis of InSe 1−x S x (x = 0, 0.01, 0.03, 0.05): (A) powder XRD patterns, and (B) calculated lattice parameters as a function of S-alloying concentration leads to great discrepancy in power factor, and In 2 Se 3 shows higher power factor than InSe in the whole temperature range, as shown in Figure 3C. Notably, the turning point at around 470 K in electrical transport properties of In 2 Se 3 originates from its phase transition from α-In 2 Se 3 to β-In 2 Se 3 . Additionally, the temperature-dependent Hall measurement in Figure 3D proves that In 2 Se 3 has orders magnitude higher carrier concentration than that in InSe in the entire temperature range, which might arise from more In 3+ valence state in In 2 Se 3 . More importantly, the Hall measurement uncloses that InSe has a dynamic carrier transport property and the carrier concentration continuously increases with rising temperature, from 3.2 × 10 13 cm -3 at 300 K to 6.2 × 10 16 cm -3 at 723 K. This particularly dynamic carrier concentration in InSe is attributed to the amphoteric indium (In + and In 3+ ), which has been observed in In-doped PbTe. 32,33 With thermal activation, the In + state in InSe will transmit into In 3+ state and simultaneously release two free carriers into matrix, thus causing increasing temperature-dependent carrier concentration in the entire temperature range. This dynamic carrier transport property in InSe motivates us to enhance its carrier concentration by manipulating valence state of indium. Compared with the electronegativity of Se atom (χ P ∼ 2.55), S atom possesses a larger electronegativity of χ P ∼ 2.58, indicating that S atom is more capable to attract electrons and can induce more In 3+ state in InSe. Therefore, S alloying is conducted in InSe, and the carrier concentration in InSe 0.97 S 0.03 is significantly enhanced as expected (shown in Figure 3D). Compared with the carrier concentration in InSe, InSe 0.97 S 0.03 obtains an obvious enhancement in the whole temperature range, and the maximum carrier concentration increases from ∼6.2 × 10 16 cm -3 in InSe to ∼1.0 × 10 17 cm -3 in InSn 0.97 S 0.03 at 723 K. This boosted dynamic carrier concentration is expected to further optimize its thermoelectric properties in InSe matrix.

Electrical transport properties in S-alloyed InSe
A series of S-alloyed InSe samples (InSe 1−x S x , x = 0, 0.01, 0.03, 0.05) are prepared and their phases are first identified by X-ray diffraction (XRD). From the XRD patterns in Figure 4A, all the S-alloyed samples can be indexed into single phase with hexagonal structure (P6 3 /mmc). The calculated lattice parameter in Figure 4B shows a decreasing tendency with increasing S content along a and c axes, proving that S can fully alloy in InSe within 0.05 S content. Figure 5 presents the electrical transport properties of InSe 1−x S x (x = 0, 0.01, 0.03, 0.05). The electrical conductivity in S-alloyed sample obtains an obvious enhancement, especially in InSe 0.97 S 0.03 sample as shown in Figure 5A. The Seebeck coefficient in S-alloyed InSe is still negative value, indicating an electron-dominated n-type transport property in Figure 5B. Correspondingly, the absolute value of Seebeck coefficient in S-alloyed InSe decreases, which arises from the enhanced carrier concentration, as shown in Figure 5C. The room-temperature carrier concentration is largely improved after S alloying, from 3.2 × 10 13 cm -3 in InSe to 2.7 × 10 16 cm -3 in InSe 0.99 S 0.01 , and then slightly decreases to 2.8 × 10 15 cm -3 in InSe 0.95 S 0.05 . The improved carrier concentration in S-alloyed InSe is originated from the large electronegativity of S that can attract two electrons from In + state and then release more free carriers into matrix, as discussed above. Notably, large electronegativity in S atoms is doubleedged sword, which will inversely capture the free carrier with high S content and finally suppress the carrier concentration with increasing S alloying content in InSe 1−x S x samples. Therefore, it is of great importance to optimize the S content in order to enhance its carrier concentration in InSe. As shown in Figure 5C, InSe exhibits very low carrier mobility, ∼1.9 cm 2 V -1 s -1 at room temperature, and the carrier mobility in S-alloyed InSe continuously decreases due to its enhanced carrier concentration. As a result, the power factor achieves an improvement due to increased concentration in S-alloyed InSe, from ∼0.4 μW -1 cm -1 K -2 in InSe to ∼0.6 μW -1 cm -1 K -2 in InSe 0.97 S 0.03 .

Thermal transport properties and ZT value in S-alloyed InSe
To investigate the intrinsic thermal transport properties in InSe, this work conducted ultrasonic pulse echo measurements. With the measured sound velocity, series elastic properties can be calculated, including Poisson ratio (ν p ), Young's modulus (E), shear modulus (G), and Grüneisen parameter (γ). 34 Generally, low Young's modulus, low shear modulus, and large Grüneisen parameter are the indicators of low thermal conductivity. [34][35][36] The relationships between sound ( where ν a , ν p , and ρ are average sound velocity, Poisson ratio, and density of samples, respectively. The Debye temperature (θ D ) is estimated as follows: 36 where h, k B , N, and V are the Plank constant, Boltzmann constant, number of atoms in a unit cell, and volume of a unit cell, respectively. All the calculated elastic parameters are listed in Table 1 and compared with typical mid-temperature thermoelectric materials, PbTe and PbSe. 37  Note: Room-temperature lattice thermal conductivity (κ L ), sample density (ρ), and sound velocity (ν l and ν s ) of InSe are obtained by experimental measurement; elastic parameters are calculated by Equations (1)- (5), and Debye temperature is estimated by Equation (6). The data of PbQ (Q = Se, Te) are based on previous reports. 37 stress. The values of the calculated Young's modulus and shear modulus of InSe are ∼20.5 GPa and ∼7.5 GPa, which are lower than those of PbSe (E ∼ 65.9 GPa and G ∼ 25.6 GPa) and PbTe (E ∼ 53.7 GPa and G ∼ 20.9 GPa). Because Young's modulus and shear modulus are related to the interatomic bonding strength, the low modulus implies a weak van der Waals force between layers in InSe. As known, Grüneisen parameter (γ) is a reflection of lattice vibration anharmonicity. 38 The Grüneisen parameter of InSe is ∼2.28, which is much larger than PbSe (∼1.65) and PbTe (∼1.45), indicating that InSe processes a strong anharmonicity in crystal lattice. The Debye temperature can be evaluated by using average sound velocity, and InSe has a lower Debye temperature of ∼128 K compared with PbSe ∼191 K and PbTe ∼163 K. These evaluated elastic parameters clearly reveal the intrinsic thermal transport property in InSe and contribute to a comparably low lattice thermal conductivity of ∼1.6 W m -1 K -1 at room temperature.
To discuss the possibilities of further reducing the thermal conductivity, the phonon mean free path (MFP) of InSe is evaluated with the following expression: 34,39,40 where C V is the heat capacity at constant volume, which can be replaced by C V = ρC P (ρ represents sample density and C P represents the heat capacity at constant pressure), l is the phonon MFP. The MFP of InSe calculated by Equation (7) is 26.49 Å, which is much larger than the lattice parameters in the unit cell (a = b = 4.004 Å and c = 16.682 Å). Thus, the lattice thermal conductivity of InSe could be further suppressed by nanostructure engineering. Using the interatomic distance as the minimum phonon MFP, the minimum lattice thermal conductivity (κ lat,min ) can be expressed as follows according to Cahill's model: 39,41,42 lat,min = 1 2 where V is the volume of per atom in the unit cell. Value of the minimum κ lat estimated by Equation (8) is ∼0.3 W m -1 K -1 . The evaluated minimum lattice thermal conductivity in InSe is much lower than the measured room temperature value of ∼1.6 W m -1 K -1 , suggesting that there is large space to further reduce its thermal conductivity. Figure 6 presents the thermal transport properties and final ZT values. The thermal diffusivity, the heat capacity, Lorentz constant, and electronic thermal conductivity are showed in Figures 6A, 6B, 6C, and 6D, respectively. The temperaturedependent thermal conductivities of InSe 1−x S x (x = 0, 0.01, 0.03, 0.05) samples are showed in Figure 6E. The total thermal conductivity is close to lattice thermal conductivity in S-alloyed InSe because its negligible electronic thermal conductivity (κ ele ) shown in Figure 6D caused by poor electrical conductivity, following the equation κ ele = LσT. With the increasing S content, the κ lat decrease is obviously ascribed to more point defects scattering caused by S substitution. The minimum lattice thermal conductivity in S-alloyed InSe can be achieved at ∼0.6 W m -1 K -1 in InSe 0.95 S 0.05 at 723 K. Finally, combining the suppressed lattice thermal conductivity and optimized power factor above, the ZT value obtains a distinct improvement, as shown in Figure 6F.

CONCLUSION
In this work, the dynamic carrier transport property and intrinsic low lattice thermal conductivity in InSe are systematically investigated. Its particularly increasing temperaturedependent carrier concentration arises from the amphoteric indium in InSe, and this dynamic carrier transport property can be boosted by introducing S alloying due to large electronegativity. The intrinsic low lattice thermal conductivity in InSe is related to its low-symmetry layered crystal structure and strong anharmonicity of lattice vibration, which is unclosed by sound velocity. This work suggests that InSe might be a promising thermoelectric material and its properties can be further enhanced with well-optimized carrier concentration. Some potential approaches to further improve the carrier concentration in n-type InSe include halogen doping (Cl, Br, or I) in Se site, high-valent cation doping (Ti, V, or Ni) in In site, and interstitial atoms doping (Cu or Ag). Furthermore, excellent thermoelectric performance is expected to be achieved in InSe crystal owning to high carrier mobility, as realized in SnSe and SnSe crystals. Last but not least, this interesting dynamic carrier engineering proved in InSe can be regarded as a promising strategy to be extended to other thermoelectric systems.

EXPERIMENTAL SECTION
The samples in this work with nominal composition of InSe 1−x S x (x = 0, 0.01, 0.03, 0.05) were synthesized by the melting reaction. Stoichiometric amounts of In (purity, 99.99%), Se (purity, 99.99%), and S (purity, 99.99%) powders were weighed and mixed in a vacuum-sealed quartz tube, heated to 1023 K in 12 h, kept at 1023 K for 10 h, and followed by furnace cooling to room temperature. The obtained ingots were ground into powders using an agate mortar and then densified by spark plasma sintering (SPS) at 773 K for 5 min under 50 MPa, resulting in polycrystalline samples with ϕ 12.7 × 12 mm dimensions.
The phase of sample was characterized by X-ray diffraction (D/MAX2200pc) with Cu Kα radiation (λ = 0.15418 nm). The samples obtained by SPS were cut and polished into 3 × 3 × 8 mm bulks for measurements of Seebeck coefficient and electrical resistivity using Cryoall CTA measurement system at 300-723 K in the helium atmosphere. The carrier concentration (n H ) was calculated by n H = 1/(e⋅R H ), where e denotes electron charge and R H denotes the Hall coefficient measured by Lake Shore 8400 series. The thermal conductivity of the samples was determined by κ tot = DρC p . Thermal diffusivities (D) was measured by Netzsch LFA457 at 300-723 K using the pieces cut and polished into 8 × 8 × 1.2 mm. The density (ρ) of samples was obtained by the ratio of mass to volume, and specific heat capacity (C p ) was estimated using the Debye model with room-temperature value of 0.25 J g -1 K -1 . The optical bandgap was obtained by Shimadzu UV-3600 Plus UV-VIS NIR spectrophotometer. The sound velocity of InSe was measured by ultrasonic pulse echo measurements at room temperature, and a series of mechanical parameters were calculated. The above measurements were conducted in a direction parallel to the pressure to obtain more excellent thermoelectric properties of polycrystal samples.

C O N F L I C T O F I N T E R E S T
The authors declare that there is no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.