High-Performance Snse Thermoelectric Materials: Progress and Future Challenge

Accepted Manuscript

High-performance SnSe thermoelectric materials: Progress and future challenge

Zhi-Gang Chen, Xiaolei Shi, Li-Dong Zhao, Jin Zou

PII: S0079-6425(18)30051-3 DOI: https://doi.org/10.1016/j.pmatsci.2018.04.005 Reference: JPMS 513

To appear in: Progress in Materials Science

Received Date: 20 September 2017 Revised Date: 21 March 2018 Accepted Date: 24 April 2018

Please cite this article as: Chen, Z-G., Shi, X., Zhao, L-D., Zou, J., High-performance SnSe thermoelectric materials: Progress and future challenge, Progress in Materials Science (2018), doi: https://doi.org/10.1016/j.pmatsci. 2018.04.005

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Zhi-Gang Chena, b *#, Xiaolei Shia#, Li-Dong Zhaoc, and Jin Zou a, d,* aCentre For Future Materials, University of Southern Queensland, Springfield, QLD

4300, Australia bMaterials Engineering, The University of Queensland, St Lucia, QLD 4072, Australia cSchool of Materials Science and Engineering, Beihang University, Beijing 100191,

China dCentre for Microscopy and Microanalysis, The University of Queensland, St Lucia,

QLD 4072, Australia

#These authors contributed equally to this work.

Email address: [email protected]; [email protected];

Abstract

Thermoelectric materials offer an alternative opportunity to tackle the energy crisis and environmental problems by enabling the direct solid-state energy conversion. As a promising candidate with full potentials for the next generation thermoelectrics, tin selenide (SnSe) and its associated thermoelectric materials have been attracted extensive attentions due to their ultralow thermal conductivity and high electrical transport performance (power factor). To provide a thorough overview of recent advances in

SnSe-based thermoelectric materials that have been revealed as promising thermoelectric materials since 2014, here, we first focus on the inherent relationship between the structural characteristics and the supreme thermoelectric performance of

SnSe, including the thermodynamics, crystal structures, and electronic structures. The effects of phonon scattering, pressure or strain, and oxidation behavior on the thermoelectric performance of SnSe are discussed in detail. Besides, we summarize the current theoretical calculations to predict and understand the thermoelectric performance of SnSe, and provide a comprehensive summary on the current synthesis, characterization, and thermoelectric performance of both SnSe crystals and polycrystals, and their associated materials. In the end, we point out the controversies, challenges and strategies toward future enhancements of the SnSe thermoelectric materials.

Keywords

Thermoelectric materials, SnSe, electrical conductivity, Seebeck coefficient, thermal conductivity.

Contents

1. Introduction ...... 6 2. Structural characteristics of SnSe ...... 7 2.1 Thermodynamics ...... 7 2.1.1 Formulae and relevant enthalpies ...... 8 2.1.2 Sn-Se binary phase diagram ...... 9 2.1.3 Thermogravimetric analysis ...... 9 2.2 Crystal structure ...... 10

2.2.1 α-SnSe and β-SnSe ...... 10 2.2.2 Variation of parameters...... 11 2.3 Anharmonic bonding ...... 12 2.3.1 Harmonicity and anharmonicity ...... 12 2.3.2 Grüneisen parameter ...... 13 2.3.3 Lattice dynamics ...... 14 2.4 Phonon scattering effect ...... 15 2.4.1 Point defects ...... 15 2.4.2 Dislocations and grain boundaries ...... 16 2.4.3 Precipitates ...... 17 2.5 Influence of pressure ...... 18 2.5.1 Crystal structure variation ...... 18 2.5.2 Shear stress-strain relationship ...... 20 2.5.3 Mechanical properties ...... 21 2.6 Oxidation behavior ...... 22 3. Computational advances in SnSe ...... 24 3.1 Electronic structure ...... 24 3.1.1 Band structure and effective mass ...... 24 3.1.2 Density of states and Fermi energy ...... 25 3.2 Influence of the strain ...... 27 3.2.1 Band structure modification ...... 27 3.2.2 Thermopower optimization ...... 29 3.3 Energy band engineering ...... 30 3.3.1 n/p-type doping ...... 30 3.3.2 Carrier concentration tuning...... 31 3.4 Summary of calculation-based work ...... 32 3.4.1 Verification of experimental results ...... 32

3.4.2 Theoretical prediction ...... 33 3.4.3 Crystal design ...... 34 4. Single crystal SnSe ...... 36 4.1 Crystal growth ...... 36 4.1.1 Bridgman method ...... 36 4.1.2 Direct vapor transport method ...... 38 4.1.3 Temperature gradient growth method ...... 38 4.1.4 Hydro/solvothermal method ...... 39 4.2 Characterization ...... 40 4.2.1 Macro-sized crystal...... 40 4.2.2 Micro/nano-sized crystal ...... 42 4.3 Performance ...... 43 4.3.1 Strong anisotropy...... 43 4.3.2 Strength and drawback...... 44 4.4 Improvement ...... 45 4.4.1 p-type doping ...... 45 4.4.2 n-type doping ...... 46 4.5 Controversy on thermal conductivity ...... 47 5. Polycrystalline SnSe ...... 49 5.1 Fabrication ...... 49 5.1.1 Synthesis of product ...... 49 5.1.2 Sintering ...... 50 5.2 Feature ...... 51 5.2.1 Phase analysis ...... 51 5.2.2 Sinter-induced anisotropy ...... 52 5.2.3 Microscopic study ...... 53 5.3 Texturing ...... 54 5.3.1 Cold-pressing and hot-pressing ...... 55 5.3.2 Melting with SPS ...... 55 5.3.3 Solvothermal with SPS ...... 56 5.4 Doping and alloying ...... 58 5.4.1 Alkali ...... 58 5.4.2 I-B and II-B group metal ...... 59 5.4.3 Halogen ...... 61 5.4.4 IV-A and VI-A group ...... 62 5.5 Inclusions ...... 64

5.5.1 Solid solution and co-synthesis ...... 65 5.5.2 Coupled with doping and multiple inclusions ...... 66 6. Two-Dimensional SnSe ...... 67 6.1 Monolayer ...... 67 6.1.1 Lattice configuration ...... 67 6.1.2 Electronic structure ...... 69 6.1.3 Influence of strain ...... 70 6.1.4 Performance forecasting ...... 71 6.2 Recent advances ...... 73 6.2.1 Films ...... 73 6.2.2 Nanosheets ...... 75 6.2.3 Anisotropy behavior ...... 77 6.2.4 Organic/inorganic composites ...... 78 7. Conclusion, Challenge, and Strategy ...... 80 Acknowledgement ...... 82

1. Introduction

Thermoelectric materials, enabling the direct solid-state energy conversion between heat and electricity [1, 2], offer an alternative solution with full potentials for power generation and refrigeration [3-6]. In order to evaluate the thermoelectric efficiency, the figure of merit (ZT) is used and is defined as:

ZT = T = T, (1)

where S, σ, κ, κl, κe, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, lattice thermal conductivity, electronic thermal conductivity, and absolute temperature, respectively [7-9]. The power factor (S2σ) is associated with electrical transports [10]. As shown in Eq. (1), a relative high ZT requires a high S2σ and/or a low

κ [11, 12]. So far, significant progress has been made in enhancing ZT through increasing S2σ by resonant state doping [13-16], minority carrier blocking [17-20], band convergence [21-24], quantum confinement [25-28]; and/or reducing κ by nanostructuring [29-32], hierarchical architecturing [6, 33-35], and matrix with nanoprecipitates [36-39]. In general, one thermoelectric component contains an n-type and a p-type thermoelectric material, so that the developments of both n-type and p-type high-performance thermoelectric materials are necessary for the practical use of thermoelectric devices [40, 41]. Figures 1(a) and 1(b) present the major milestones achieved for ZT values as a function of T both for n-type [42-53] and p-type [6, 15, 54-

63] bulk thermoelectric materials, in which a remarkable high ZT of ~2.6 at 923 K found in the p-type single crystal SnSe (along the b-axis) was obtained as so-far the world record [61], as well as a relative high ZT of 2.2 at 773 K obtained from the n-type

Bi-doped single crystal SnSe (also along the b-axis) [52]. Such outstanding thermoelectric performances were derived from the ultralow κ observed from the high temperature SnSe phase at T > 973 K. Inspired by the ultralow κ and high electrical

6 performance (σ, S, and in turn S2σ), SnSe-based thermoelectric materials have attracted significant attention in recent years [64], and shortly became a globally focused research topic. Although SnSe single crystals have demonstrated outstanding thermoelectric property, they still have their own limitations for practical applications, mainly due to their poor mechanical properties, rigid-controlled crystal growth conditions, and high production cost for industrial scale-up [65]. For this reason, the development of high performance polycrystalline SnSe became a research focus, since there is a significant potential for enhancing the ZT values of polycrystalline SnSe materials through systematic optimization, such as texturing [66], doping [67], and alloying [64]. So far, the ZT values of polycrystalline SnSe materials have been improved from 0.5 to nearly

1.7 [68]. However, it should be noted that the thermoelectric performance of polycrystalline SnSe is still much lower than its single crystal counterpart due to its comparatively high κ and low σ [69]. Achieving an ultralow κ to be comparable to the single crystal counterpart has been a challenge and needs strategies. In this review, we aim to provide a thorough summary of current research on structural characteristics, theoretical calculations, syntheses, characterizations, and thermoelectric performance of both single-crystal and polycrystalline SnSe and its associated materials. On this basis, we also discuss the controversies, challenges and strategies toward future enhancements of the thermoelectric performance of SnSe-based materials.

2. Structural characteristics of SnSe

2.1 Thermodynamics

SnSe is an inorganic compound semiconductor [70], that has a Molar mass of 197.67 g mol-1, a theoretical density of 6.179 g cm-3 at room temperature [71], and a melting point of 1134 K [72, 73]. To obtain a stable phase of SnSe compound during the synthesis process, it is essential to understand the thermodynamic data of SnSe.

2.1.1 Formulae and relevant enthalpies

Sn can directly react with Se to form stable SnSe compounds. In a mass-spectrometric investigation of the vapor in equilibrium with solid SnSe, a number of reaction enthalpies were measured [74]. Taking the thermochemical data into account, the fundamental reaction formulae and relevant enthalpies between Sn, Se and SnSe can be summarized as follows [74, 75]:

o -1 Se (s) + Sn (s) → SnSe (s) ΔH 298, f (SnSe) = -21.5 ± 1.7 kcal mol ;

SnSe (s) → Sn (s) + Se (s) ΔH = 16.5 ± 2.0 kcal mol-1;

SnSe (g) → Sn (g) + Se (g) ΔH = 85.5 ± 2.0 kcal mol-1;

SnSe (g) → SnSe (s) ΔH = -52.4 ± 1.0 kcal mol-1;

Se (s) → Se (g) ΔH = 49.4 kcal mol-1; and

Sn (s) → Sn (g) ΔH = 72.0 ± 2.0 kcal mol-1.

These formulae are essential for exploring the nature of the atomic and molecular species composing the saturated vapor of SnSe. The total pressure of SnSe has been measured using classical techniques [75]. The evaporation was carried out below the

melting point (1134 K). For the dissociation energy of SnSe, (SnSe) = 4.54 eV [74].

Besides, the Gibbs formation energy of SnSe was determined by an electromotive force

(emf) measurement, in the temperature range from 435 to 485 K [76], and the value of

-1 = -95389 - 3.184 T J mol . The heat capacity (Cp) of SnSe in both temperature ranges from 373 to 1135 K and from 233 to 573 K was measured [61, 77], which is important to determine the stability of the SnSe compounds. Besides, the thermodynamic data can be used as the guidance for designing their fabrications, especially for the growth of SnSe crystals via the Bridgman method [61, 78-80] or solvothermal method [81-86].

2.1.2 Sn-Se binary phase diagram

The binary phase diagram is very useful to provide the thermodynamic information.

Figure 2(a) is the Sn-Se binary phase diagram [72, 87], in which two intermediate phases can be found as SnSe and SnSe2. In the Sn-SnSe region, a liquid miscibility gap, a monotectic reaction, and a eutectic reaction can be observed. Besides, eutectic reactions can also be found in the SnSe-SnSe2 and SnSe2-Se regions. The two eutectic

points, L1 (Sn) + SnSe and L2 SnSe2 + (Se), are very close to pure Sn and pure

Se, respectively. For the intermediate phase of SnSe, there are two stable SnSe phases, denoted as α-SnSe (low temperature) and β-SnSe (high temperature), respectively.

As an important and convenient synthesis method for fabricating SnSe, melting routes are widely used [65]. Generally, in order to obtain high pure and stable SnSe compounds, the melting route is to set T > 1134 K – the melting point [65, 66, 88-90].

To pursue a high density and stable structure in the sintering process of polycrystalline

SnSe, it is generally sintered at a high temperature ranging from 800 to 1105 K [91].

Therefore, the sintered products are often β-SnSe phase.

2.1.3 Thermogravimetric analysis

To investigate the thermal ability of SnSe, Figure 2(b) and 2(c) plots the temperature- dependent thermogravimetric analysis (TGA) and differential thermal analysis (DTA) curves of SnSe in the temperature range from 300 to 1273 K, performed in an inert nitrogen atmosphere [92]. The TGA curve shows a slight increase of weight when temperature reaches ~853 K and a peak at ~993 K due to the nitrogen adsorption on the surface during the analysis [92]. Such an adsorption is supported by an endothermic peak at ~993 K found in the DTA curve. Then a continuous loss of weight in TGA from

~993 to ~1133 K indicates a volatilization of Se [92]. This suggests that the volatilization of SnSe starts at the temperature much lower than its melting point. The

DTA curve shows a sharp exothermic peak accompanied by an endothermic peak, which can be attributed to a thermally induced phase transition of SnSe before melting at ~1133 K [92]. This information suggests that α-SnSe is much more stable than β-

SnSe and β-SnSe is easily to crack at high temperature [68]. There is no weight change seen in the TGA curve from 1133 K to 1273 K. However, in the DTA curve, there is an endothermic peak in this temperature range (at 1253 K), suggesting the formation of

Sn–N–Se phase which may be formed due to the incorporation of nitrogen into the sample. However, it is necessary to carry out X-ray diffraction studies at this temperature to confirm the presence of this Sn–N–Se phase.

The TGA and DTA of SnSe are important indicatives for the potential use of SnSe as a thermoelectric material in the device for the real application. Considering the instability of SnSe at high temperature, SnSe-based thermoelectric materials should be practically used for T < 1000 K.

2.2 Crystal structure

As mentioned above, SnSe has two stable phases: α-SnSe (T < ~800 K) and β-SnSe (T >

~800 K). These two phases possess a similar crystal structure (orthogonal), but different lattice parameters and space groups, as summarized in Table 1, where S.D. is the abbreviation of Strukturbericht designation [72, 87].

2.2.1 α-SnSe and β-SnSe

Low-temperature α-SnSe (T < ~800 K) has an orthogonal structure with lattice parameters of a = 11.37 Å, b = 4.19 Å, and c = 4.44 Å and a space group of Pnma

(#62). Figure 3(a) shows the atomic structure of α-SnSe in a unit cell, and Figures 3(b)-

3(d) show the projected crystal structure of α-SnSe viewed along the a-, b-, and c-axes, respectively. As can been seen, α-SnSe possesses a typical double-layered structure

[93], which shares the same structure with black phosphorus [94]. α-SnSe consists of

10 eight atoms in a unit cell [95]. The Sn and Se atoms are joined with strong heteropolar bonds to form the crystalline layers, consisting of two planes of zigzag Sn-Se type chains [95, 96]. Each Sn atom is bonded to three neighboring Se atoms and each Se atom is also bonded to three neighboring Sn atom. The adjacent layers are mainly bound to each other with a combination of van der Waals forces and a long-range electrostatic attractions [95, 97].

High temperature β-SnSe (~800 K < T < 1134 K) has an orthogonal structure with lattice parameters of a = 4.31 Å, b = 11.71 Å, and c = 4.42 Å and a space group of

Cmcm (#63) for [98]. Figure 4(a) shows the atomic structure of β-SnSe in a unit cell, and Figures 4(b)-4(d) show the projected crystal structure of β-SnSe viewed along the a-

, b-, and c-axes, respectively. Similar to α-SnSe, β-SnSe has a typical double-layered structure. Sn and Se atoms are joined with strong heteropolar bonds. Different from α-

SnSe, β-SnSe has a higher crystal symmetry. When cooling from β-SnSe to α-SnSe, a phase transition occurs at ~800 K, as well as a transformation of crystallographic axes.

2.2.2 Variation of parameters

To illustrate the change of atom position of Sn and Se during the phase transition,

Figures 5(a)-(b) show the variation of the atomic positional parameters (x and y) of Sn and Se atoms [71]. The y parameters are practically constant with temperature, whereas the x parameters change continuously with temperature and become equal to those of the β-SnSe phase. Therefore, the parameter x is identified as the primary order parameter [71]. Figure 5(c)-(d) shows the variation of the thermal parameters of the Sn and Se atoms with increasing the temperature [71]. At room temperature the components U11, U22 and U33 of the Sn and Se atoms are practically the same. When the temperature increase, the anisotropy in the thermal parameters becomes obvious. In the

11 case of the Sn atoms, the component U11 becomes much larger than U22 and U33. In the case of Se atoms, U11 and U22 becomes larger than U33.

Because of the change of crystallographic parameters and thermal parameters via phase transition, the α-SnSe phase expands its volume by ~2.5 % during cooling from β-SnSe.

Such a volume expansion is the main reason causing the breakage of silica tube and sample damage during crystal growth of SnSe [68].

2.3 Anharmonic bonding

As a property of lattice vibrations, anharmonicity affects the heat transportation in SnSe structure. The anharmonic bonding between Sn and Se is one of the most important features of the SnSe crystal structure, which is the key factor for the obtained ultralow κ of SnSe [99].

2.3.1 Harmonicity and anharmonicity

To illustrate the anharmonicity in the SnSe crystal structure, Figure 6(a) shows the relationship between harmonicity and anharmonicity [68, 100], where Ф(r), a0 and r are the potential energy, lattice parameter, and distance between two adjacent atoms, respectively. For harmonicity, during the transport of a phonon, if an atom is forced to deviate from its equilibrium position, the applied force is proportional to its displacement [100]. The proportionality of this relationship is referred as the spring constant (or stiffness) [100]. The harmonicity shows a balanced phonon transport [100].

On the other hand, anharmonicity represents that the applied force is no longer proportional to the displacement when an atom is under a force. As shown in Figure

6(a), the anharmonicity is the deviation from a linear relationship between the displacement and restoring force, showing an imbalanced phonon transport [101, 102].

High anharmonicity therefore results in enhanced phonon – phonon scattering and in turn reduces κl.

2.3.2 Grüneisen parameter

It should be noted that in real materials, all bonds are anharmonic, but the degree of anharmonicity varies from different materials [22, 100, 103-106]. To verify the strength of anharmonicity, the Grüneisen parameter (γ) is used, which can be described as follows [107]:

, (2) where β is the volume thermal expansion coefficient, B is the isothermal bulk modulus,

Vm is the molar volume, and Cv is the isochoric specific heat per mol, respectively. γ = 0 when the crystal is fully harmonic bonded, and large γ value represents a strong phonon scattering. For SnSe, the average γ values of SnSe along a-, b- and c-axes are 4.1, 2.1,

2.3, respectively [61]. As can be seen, the γ values along the three different axes are different, indicating that SnSe possesses strong anharmonicity, which is the key reason for giving rise to an ultralow of SnSe, especially along the a-axis [64, 102]. Besides, the large γ values of SnSe reflect the unique crystal structure. It was reported that by using the Grüneisen theory, first-principles calculations indicated that bulk SnSe possesses negative Possion’s ratio, similar to other two-dimensional (2D) systems, such as black phosphorus [108], 2D SnSe and phosphorene [109].

Figure 6(b) illustrates the resonant bonding of the highly distorted SnSe7 polyhedra

2+ caused by the long pair of Sn [68]. In the SnSe7 polyhedra, one Sn atom is surrounded by seven Se atoms, which exists unbalanced forces around the Sn atom caused by four long Sn-Se bonds and three short Sn-Se bonds. In this regard, SnSe possesses a soft lattice. Along b- and c-axes, the Sn-Se bond length cannot change directly if the mechanical stress was applied. Along the a-axis, the weaker bonding between SnSe layers can provide a good stress buffer, thus dissipating phonon transport laterally [100,

110]. Such a unique crystal structure may induce an ultralow κl along the a-axis. Other

13 studies showed that via heat capacity measurements, two characteristic vibrational energy scales in SnSe were revealed, which were corresponding to hard and soft substructures [111]. These distinct substructures derived from the strong bond divergence in SnSe, and the soft substructure was largely responsible for the thermal transport, which was consistent with the strong Umklapp scattering and low κ values observed in SnSe [111].

2.3.3 Lattice dynamics

To understand the lattice dynamics of SnSe, Figure 7(a) and 7(b) plot the phonon dispersion and density of states (DOS) of the optimized equilibrium α-SnSe and β-SnSe structures through a first-principles lattice-dynamics study, respectively [112]. As can be seen, compared to α-SnSe, β-SnSe displays a phonon softening and enhanced three- phonon scattering, leading to an anharmonic damping of the low-frequency modes and hence the thermal transport [112, 113]. Figure 7(c) compares the DOS curves for the equilibrium α-SnSe and β-SnSe structures. From which, an obvious red shift of the higher-frequency modes (with frequencies over 3 THz) is observed in β-SnSe with respect to α-SnSe [112]. To quantify this shift, Figure 7(d) plots the cumulative percentage of states under each curve as a function of frequency [112]. There are a similar number of states below 3 THz in both phases, but between 3~4 THz there are

~15 % more states in β-SnSe than in α-SnSe [112].

A combination of inelastic neutron scattering measurements and first-principles simulations was performed to illustrate that the strong anharmonicity of lattice dynamics results from a Jahn-Teller electronic instability, which is driven by the lattice distortion in SnSe [114]. The phonons in SnSe are strongly anisotropic, associated with a soft-mode lattice instability driven by the resonantly bonding Se p-states and stereochemically active Sn lone pair [115]. Comprehensive first-principles calculations

indicated that the remarkable anisotropy ( > > ) in the l is found in SnSe, which is mainly due to the anisotropic group velocity caused by the layered lattice structure [110]. The phonon relaxation times also indicate high anharmonicity in SnSe, accounting for the extremely low κl [116].

2.4 Phonon scattering effect

As discussed above, the ultralow κ of SnSe mainly derives from the layered crystal structure and strongly anharmonic bonding [117]. However, phonon scatterings also frequently occur at grain boundaries and lattice defects, such as point defects and dislocations [65, 81, 118, 119], especially in polycrystalline materials. Phonon scattering effects have been used as powerful tools to strengthen the scattering of phonons during transportation, in turn further reduce κl [31, 48, 120-124]. Figure 8 illustrates the main potential phonon scattering effects occurring in polycrystalline SnSe materials. In polycrystalline SnSe materials, potential phonon scattering sources include point defects, dislocations, precipitates, and grain boundaries [125].

2.4.1 Point defects

Point defects (include atom vacancies and substitutions) belong to atomic scale, dislocations and precipitates belong to nano scale, and grain boundaries belong to sub- micro scale [125]. Figure 9(a) shows a Sn vacancy in SnSe structure characterized by

STM [52], which illustrates that there are Sn vacancies exist in the SnSe structure, making the whole system presenting p-type [126].

To understand the phonon scattering effect by point defects, combined experimental measurements and computational modelling showed that the induced extended strain fields on point defects result in extra phonon scattering in SnSe-based thermoelectric materials [127]. The strength and extent of the induced strain fields depend strongly upon defect chemistry [127]. Besides, the existence of strain fields can obviously distort

15 the SnSe crystal structure and further enhance the anharmonicity [127]. By alloying with barium (Ba), the strain fields cause large shifts in the equilibrium positions of atoms, which is up to 0.5 Å [127]. Thus, introducing point defects was an effective method for the design and optimization of SnSe-based thermoelectric materials [110,

128, 129].

2.4.2 Dislocations and grain boundaries

Apart from the point defect scattering, dislocation and grain boundary scatterings also have obvious influence on reducing κ [125, 130, 131]. Figure 9 (b) shows a high resolution transmission electron microscopy (HRTEM) image of dislocations in SnSe, and Figure 9(c) shows the electron back-scattered diffraction (EBSD) result of polycrystalline SnSe to show grain boundaries and grains with different orientations

[84]. These dislocations and grain boundaries can induce extended strain fields and in turn result in strong phonon scatterings [125].

To compare the ability of scattering phonons between point defects, dislocations and grain boundaries, Figure 9(d) illustrates the full-spectrum phonon scattering by different sources [132]. The phonons cover a broad spectrum of frequency (f), and κl can be expressed as a sum of contributions from different frequencies [133, 134]:

κl = , (3) where κs(f) is the spectral lattice thermal conductivity [132], and can be described as:

, (4) where Cp(f) is the spectral heat capacity of phonons, v(f) is the phonon velocity, and (f) is the scattering time. It is well known that phonons in all crystalline materials are scattered by other phonons through Umklapp scattering [132], follow the relationship of

-1 2 2 U ~f . The Debye approximation for phonons has a relationship of Cp(f) ~f .

Combining this with the former one gives κs(f) = constant. This leaves a wide range of

16 phonon frequencies where all frequencies contribute to κ. Point defects scatter mostly

-1 4 high-frequency phonons ( P ~f ), and grain boundaries scatter mostly low-frequency

-1 0 phonons ( B ~f ) [132]. However, as shown in Figure 9(d), most of the remaining heat-carrying phonons have intermediate frequency around 0.63 THz. Taking

Bi0.5Sb1.5Te3 (bismuth antimony telluride) as an example, ~74 % of the heat is carried by 0.63 THz phonons [132]. These phonons avoid scattering from boundaries and point defects. However, the dislocations target to scatter the mid-frequency phonons with

-1 -1 3 both dependences of D ~f and D ~f , which is between those for point defect and boundary scattering [133, 134]. Thus, dislocations play a dominant role in phonon scattering effects. Because dislocations always distribute at grain boundaries [132], in order to increase the density of grain boundaries, nanostructuring has been widely used to realize a high-density of grain boundaries and dislocations [135-140]. Besides, liquid sintering has also been demonstrated to be useful for further increase the amount of dislocations embedded in grain boundaries [132].

2.4.3 Precipitates

It has been found that the formation of precipitates, especially the nanoprecipitates within the grains, can drastically decrease κl due to the phonon scatterings caused by these precipitates [8, 100, 125]. Figure 9(e) is a TEM image and shows a SnSe matrix with precipitates [67], and Figure 9(f) is a HRTEM image of a typical precipitate [67].

The precipitate has a coherent feature and a superstructure according to the fast Fourier transform (FFT) pattern (inset of Figure 9(f)). Another set of superlattice spots (marked by red circles) represents a zone-axis electron diffraction pattern, suggesting that the structure of the precipitate can be identified as Sn tetragonal phase [67].

-1 -1 An ultralow κl of only ~0.20 W m K at 773 K was obtained due to the nanoprecipitates obviously decreased l [67]. Other experiments [141] demonstrated

17 that rock-salt type SnSe nanoprecipitates coupled with mesoscale matrix grains can lead

-1 -1 to further κl reduction up to ~0.19 W m K at 850 K. However, it is important to produce appropriate precipitates with suitable size and/or amount during the fabrication, the misuse of precipitates may cause a decrease of electrical performance, as well as a weak mechanical property.

2.5 Influence of pressure

As one of the most important external conditions for the practical applications of thermoelectric materials, the induced external pressure during their services may distort the crystal lattice and in turn alters the thermoelectric performance [119, 142]. Besides, the study of shear stress as a function of strain under different shear directions is also important for the applications of SnSe thermoelectric materials.

2.5.1 Crystal structure variation

Figure 10(a) plots the temperature-pressure contour of electrical resistivity of SnSe, indicating the transition region from semiconductor to metallic or semi-metallic region under a pressure [143]. The crystal structure is distorted with increasing the pressure. To study the influence of pressure on SnSe crystal structures experimentally, the well- crystallized SnSe sample showed that a continuous transition from α-SnSe (Prototype:

GeS) to β’-SnSe (Prototype: TlI) at a high pressure of 10.5 GPa [144]. There were no indications of any discontinuities in the structural parameters as a function of pressure, suggesting that it was a second-order phase transition [144]. The β’-SnSe phase was closely related to β-SnSe (Prototype: CrB) at the ambient pressure [144]. Other studies show that for nanostructured SnSe, such phase transition derived from the change of crystallographic parameters during increasing the pressure, and the phase transition occurred between 5.6 and 8.2 GPa [145]. Beyond 8.2 GPa, no significant structural changes were observed, at least up to 18.0 GPa.

Figure 10(b) illustrates the projected crystal structures of α-SnSe along different axes in the unit cell at 5.6 and 8.2 GPa [145], in which the structure is stable at 5.6 GPa.

However, at 8.2 GPa, the projections along the b- and c-axes show similar atomic sequences arranged in a very distorted manner. Along the a-axis, the atoms tend to align along the (011) plane due to the above mentioned alignment [145]. Figure 10(c) shows the change in the fractional coordinates obtained from the Rietveld refinements with increasing the pressure [145]. Two regions of stability are found (before 4 GPa and after

8 GPa), and the shaded area represents the region of structural transition. Figure 10(d) illustrates the change of crystallographic parameters with increasing the pressure [145].

Other studies [143] showed that SnSe transforms from a semiconducting to semi metallic state under high pressure of 12.6 GPa, followed by a structural transition from orthorhombic to monoclinic. The average grain size of SnSe decreases when the pressure increases [143]. However, if the pressure continues to increase up to 58 GPa,

SnSe exhibits its superconductivity at 4.5 K, and shows a type of CsCl structure [146].

Compared with the condition at the normal pressure, induced high pressure can result in a phase transition from α-SnSe to β-SnSe, occurring at a much lower temperature.

Because β-SnSe possesses a much higher electrical performance and a much lower κ than α-SnSe [61], the application of pressure (or compressive strain) may enable SnSe to exhibit improved thermoelectric properties at temperatures lower than the ∼800 K, which is promising for the practical applications [147]. To verify the influence of pressure on the electrical performance of SnSe, theoretical calculations using density functional theory (DFT), ab-initio molecular dynamics (AIMD) and Boltzmann transport theory showed that the hydrostatic pressure can reduce the transformation temperature from α-SnSe to β-SnSe, which contributes to the enhancement in σ/τ and

S2 /τ of SnSe in the middle-temperature range [148], as shown in Figure 11(a-c) and (d- f). Here τ is the relaxation time [148].

In terms of κ, the change of crystal structure (and phase transition) influenced by induced high pressure can alter the anharmonicity to a great extent [148]. Calculations

[148] showed that at 0 GPa, the average γ values along the a-, b- and c-axes are 3.75,

1.9 and 2.6, respectively, indicating a strong anharmonicity. However, when the hydrostatic pressure increased to 4 GPa, the average γ values along the a-, b- and c-axes became to 1.70, 1.94 and 1.86, respectively, indicating the κ values along a- and c-axes both increase [148]. Such a larger decrease in the γ values along the inter-layer direction

(a-axis) could be related to the higher compressibility along a-axis due to the weak van der Waals force between layers [148]. Figure 11(g) shows the influence of the induced high pressure on , showed that the high pressure at high temperature can increase due to the compressed lattice. Other calculations also suggested that the induced pressure can significantly enhance the thermoelectric transport properties along all three directions, and makes SnSe efficient in the medium temperature ranges [142]. Even though, the κ values at 6 GPa are ~2 times larger than those at 0 GPa, benefited from the huge improvement of electrical performance, the estimated ZT values of p-type SnSe along the b- and c-axis can reach 2.5 and 1.7 at 6 GPa at 700 K, respectively, and the a- axis shows potential n-type behavior with a ZT value of 1.7 at 600 K [142].

2.5.2 Shear stress-strain relationship

In practical applications, it is important to choose appropriate pressure values and directions on SnSe thermoelectric materials to avoid the damage. To study the shear stress-strain relationships of SnSe at 0 K along various slip systems, Figure 11(h) plots the calculated shear stress as a function of strain under different shear directions [149].

The (100)/<010> and (100)/<001> systems show a similar modulus, and both are lower

20 than that of the (001)/<010> system, indicating the (100)/<010> and (100)/<001> systems are much weaker than the (001)/<010> system in resisting the external deformation [149]. Then the shear stress in both the (100)/<010> and (100)/<001> systems gradually increases until reaching the ideal strength. However, in the

(001)/<010> system, the shear stress suddenly drops to 0.76 GPa at a strain of 0.07, and then sharply increases to the point of maximum stress, indicating a significant structural rearrangement at that point. Beyond the maximum stress, the decreased shear stress represents a softening stage of SnSe before the failure. Finally, the shear stress suddenly drops to zero, indicating that the systems can no longer resist the external deformation, leading to the structural failure. Along the (100)/<001> system, a lowest shear strength of 0.59 GPa is obtained due to the weak van der Waals-like Se−Sn bond, suggesting that it is the likely plausible slip surface under pressure [149]. The maximum shear strength

(0.78 GPa) along the (100)/<010> slip system is slightly higher than the (001)/<010> system (0.59 GPa). The (001)/<010> slip system has a higher ideal strength of 2.81 GPa due to the much stronger covalent Se−Sn bond than the van der Waals-like Se−Sn bond in resisting shear deformation [149].

2.5.3 Mechanical properties

For polycrystalline SnSe, the mechanical properties, including compressive strength, bending strength, hardness, fracture toughness, fracture strength, and thermal shock resistance, all exhibits values that are comparable to those reported for other state-of- the-art thermoelectric materials. The compressive strength and bending strength of the as-synthesized polycrystalline SnSe were 74.7 MPa and 40.6 MPa [150], respectively.

The hardness values measured using Vickers indentation method [151] at a load of 0.98

N with a dwell time of 10 s was found to be 0.27 ± 0.05 GPa. Such a relatively low hardness value of SnSe was attributed to the brittle nature of SnSe. The fracture

1/2 toughness (KIC) was found to be 0.76 ± 0.05 MPa m , measured by SEM on the crack lengths of SnSe [90]. This value is comparable to the other commercial thermoelectric materials, such as PbTe [152] and Bi2Te3 [153]. The compatibility factor of the as- synthesized SnSe was found to be 0.68 at 773 K [90]. Because compatibility factor for any given material should be less than 2 to ensure a better power output, the value of

0.68 is also comparable to the other thermoelectric materials, such as Cu2Se [154] and half-hausler alloys [155]. The thermal shock resistance is another essential parameter during the actual operation of the device. The temperature gradient between the hot and cold ends of the thermoelectric device legs can lead to material failure due to the internal mechanical stress caused by the temperature gradients [156-158]. The thermal

-1 shock resistance parameter (RT) of SnSe was found to be ~252 ± 9 W m [90], which is much higher than those of most state-of-the-art thermoelectric materials [159].

Therefore, SnSe is a good candidate for the application in thermoelectric devices.

2.6 Oxidation behavior

During the synthesis process of SnSe, it is essential to avoid oxidation occurring on the surface of SnSe to secure a pure phase. Besides, for the applications of SnSe-based thermoelectric materials, it is also important to avoid oxidation due to the fact that the oxidized product may seriously affect the properties.

To determine the oxidation of SnSe, X-ray photoelectron spectroscopy (XPS), XRD and

DTA analyses have been used. At low temperatures (< 473 K), oxidation of SnSe took place on their surfaces [160]. With increasing the temperature in the range from 523 to

923 K, intermediate tin oxoselenides (presumably SnOSe or SnSeO2) form and subsequently converse to SnO2 [160]. Combined with analyses from XRD, optical microscopy, scanning electron microscopy (SEM) and energy dispersive spectrometry

(EDS), the oxide thickness has been observed more than 20 mm after oxidization at 873

K for 7 h [161]. Figure 12(a) shows the XRD pattern of SnSe surface oxidized under this condition [161], indicating that the surface contains SnO2 and SnSe2. In terms of the oxidation behavior at room temperature, a combination of aberration-corrected analytical TEM and EDS analysis show that a second thin amorphous layer can form underneath the outmost SnO2 oxide layer [162].

Figure 12(b) shows HRTEM image of the surface structure of oxidized SnSe [162], indicating that two different layers formed from the surface of SnSe after oxidation in air at room temperature for ~24 h. The outer surface layer marked as L1 has a width of

~2 nm, and an inner layer marked as L2 sandwiched between the L1 and the SnSe substrate has a width of ~4 nm. Figure 12(c) shows a FFT pattern of SnSe substrate

[162], indicating a typical SnSe crystalline. However, the FFT pattern of L1 and L2 indicates a typical amorphous structure [162], as shown in Figure 12(d). To study the composition of L1 and L2, EDS mapping was used. Figures 12(e-h) show the corresponding EDS mappings of Se, Sn, O, and mixture of Sn and Se, respectively

[162]. Clearly, the thin amorphous oxide layer (L1) was predominantly SnO2, and the second amorphous layer (L2) was Sn1-xSe alloy [162]. To illustrate the proposed formation mechanism of Sn1-xSe layer, Figure 12(i) shows the schematic free energy versus composition diagram of Sn and Se [162]. The equiatomic compound (SnSe) has a narrow homogeneity range, and its free energy rises rapidly when the chemical composition deviates away from the stoichiometric SnSe. During the oxidation process, the consumption of Sn from SnSe to form SnO2 drives the composition to be Se rich

[161]. With increasing the Se concentration, free energy elevated to a none-equilibrium state is higher than the amorphous phase in the Sn–Se alloy system (the dotted line).

This unstable phase can then collapse into the amorphous state, forming an amorphous

23 layer with an average composition Sn1-xSe [162], and decompose and eventually evolve into crystalline SnSe and SnSe2 if given sufficient kinetics [162].

The oxidation can seriously damage the thermoelectric performance of SnSe and result in a high κ, contributed by the oxidation products, mainly SnO2 [68]. Various experiments [163-166] showed that SnO2 possesses a much higher κ than SnSe (about

60 times of single SnSe). Because the ZT values of SnSe are much higher at high temperature, it is important that SnSe-based thermoelectric device should prevent to be used in air for long time, and needs to be used under vacuum or with a protective coating such as pure Si [161]. How to prevent the oxidation of SnSe during the synthesis, measurements, and applications needs urgent attention.

3. Computational advances in SnSe

3.1 Electronic structure

The electronic structures of SnSe-based materials, including the band structure and

DOS effective mass, are closely linked to their thermoelectric performance.

3.1.1 Band structure and effective mass

We first discuss the bandgap (Eg) of SnSe [61]. In 1990s, optical-absorption measurements found an optical bandgap value of 0.923 eV for α-SnSe [167]. With the rapid development of computational science and engineering, theoretical simulations such as first-principle calculations based on DFT are used to calculate the electronic band structure, as well as the bandgap [168-178]. Table 2 summarizes the recently reported data of the bandgap for SnSe and their calculation methods. As shown in Table

2, different groups reported different values of bandgap for α-SnSe and β-SnSe [179,

180]. The average bandgap of β-SnSe is only roughly half of that of α-SnSe, indicating there exists an obvious difference between α-SnSe and β-SnSe.

To compare the band structures of α-SnSe and β-SnSe, first-principle calculations based on DFT and many-body perturbation theory were used and results are shown in Figure

13(a) and 13(b) [181]. It is of interest to note that both of them have a very complex electronic structure with indirect bandgap. The calculated values are 0.83 eV for α-SnSe, and 0.46 eV for β-SnSe, respectively [179]. To illustrate the detailed parameters of these two band structures, Table 3 summarizes the Brillouin-zone positions, energies, and multiplicities of the band extrema of both α-SnSe and β-SnSe, where k1, k2, and k3 are the coordinates in the unit cell [181]. All energies are referenced to the valence band maximum (VBM) of each phase. For α-SnSe, the position of the VBM is at (0.00, 0.35,

0.00) along the Γ–Y direction of the first Brillouin zone, and a local valence-band maximum (VBM1) at (0.00, 0.42, 0.00) lies within 1 meV lower in energy than the

VBM. The conduction-band minimum (CBM) is located at (0.33, 0.00, 0.00) along the

Γ–X direction. For β-SnSe, both the VBM and CBM are located at (0.34, 0.50, 0.00) along the X–A direction. In addition, a VBM1 at (0.00, 0.20, 0.39) along the Γ –H direction and a local conduction-band minimum (CBM1) at (0.00, 0.54, 0.08) along the

X–H1 direction can be found. Both phases exhibit multiple local band extrema near their band edges that need to be considered when evaluating the thermoelectric properties for SnSe [181]. Besides, Table 3 lists the reported effective mass (m*) along different directions for both α-SnSe and β-SnSe [181]. Clearly, m*at each extremum is

* highly anisotropic: ma has a larger value along the a-axis than that of the in-plane (b-

* * axis (mb ) and c-axis (mc )). This is due to the two-dimensional nature of the SnSe structure, which favors electron transport within the atomic layers [181].

3.1.2 Density of states and Fermi energy

As a typical crystalline material, SnSe exhibits multiple extrema in its valence or conduction bands. The increase of the local DOS near the Fermi level can greatly

25 enhance S, and in turn enhance S2σ [68, 180, 181]. S can be expressed by the Mott equation [79, 182]:

(5)

with

(6) where kB is the Boltzmann constant, f(E) is the Fermi function, q is the carrier charge, n(E) is the carrier concentration, μ(E) is the carrier mobility, and g(E) is the DOS. Thus,

S depends on the energy derivative of the DOS. For a given n, it is well known that a high m* is beneficial for a high S. To study the contribution of each atom to the DOS in

SnSe, first-principles and semiclassical Boltzmann theory were used. Figure 13(c) and

13(d) show typical calculated DOS of α-SnSe and β-SnSe, respectively [180]. A finite gap between valence and conduction bands can be seen for both α-SnSe and β-SnSe, and the former one is 0.3 eV larger than the latter one. The valence band comprises of peaks at ~-7.5 eV and between 0 and -5 eV. The top of the valence band has major contributions from Se-p and Sn-s while the bottom of the conduction band arises from

Sn-p and Se-p states. Conduction band mainly comprises of Sn-p and Se-p states.

Meanwhile, it is obvious that the DOS of α-SnSe is higher than that of β-SnSe, indicating that α-SnSe has higher S than β-SnSe. The decrease of the DOS from α-SnSe to β-SnSe is mainly due to the decrease of Sn p-states and Se p-states, which is the main reason for S decrease in β-SnSe [180].

Figures 13(e) and 13(f) show the calculated Fermi energy [180] for α-SnSe and β-SnSe as a function of temperature with a hole concentration of 6×1017 cm-3. The Fermi energy lies within the bandgap for both phases at 300 K, with 0.1 eV above the VBM for α-

SnSe and 0.05 eV above the VBM for β-SnSe. With increasing the temperature, electrons are thermally excited from the valence band to the conduction band, and the

Fermi energy shifts towards the middle of the bandgap. The Fermi energy of β-SnSe stabilizes near the middle of the gap for temperatures above 700 K, indicating a comparable concentration of free electrons and holes and is consistent with the sign reversal of S at the high temperatures [61, 81, 180]. It is of interest to note that the experimental peak S value (marked as Smax) of SnSe single crystal is different from the calculated values [61]. The experimental Smax of SnSe single crystal is found between

500 K and 600 K (marked as T*) due to the bipolar transport [61], while the calculations showed that the onset of the bipolar transport should occur at a higher temperature (T* =

~700 K). This is because the calculations have not included the effect of the temperature on the calculated band structure, which decreases the bandgap with increasing the temperature and reduces the temperature onset of the bipolar transport [181].

3.2 Influence of the strain

As discussed in Section 2.4, strain can be induced by the point defects or dislocations in

SnSe materials. In addition, doping in SnSe can cause strain through the substitution of dopant atoms with different sizes.

3.2.1 Band structure modification

DFT calculations was used to study the influence of strain on electronic structure of

SnSe [183]. Figure 14(a) shows a typical electronic structure of the unstrained SnSe

[183] with an inset indicating the Brillouin zone of α-SnSe. The unstrained SnSe exhibits an indirect bandgap of 0.60 eV. As can be seen, three-fold degeneracy of p orbitals of both Sn and Se are lifted due to the orthorhombic structure [183]. The VBM is mainly of Se 4py state with small contribution from Se 4px state, while the CBM is dominated by 5px and 5pz states. The topmost valence band is quite dispersive along the

* Y–Γ and Z–Γ directions with the calculated hole effective mass (mh ), which is 0.16 me at the VBM, while it is flat along the Γ–X direction due to the layered structure [183].

The lowest conduction band along the Z–Γ direction is also dispersive around the CBM

* with the electron effective mass me = 0.137 me [183]. Compared to the CBM, conduction bands along the Γ–X direction are very dispersive, but located at rather higher energy. Therefore, it gives less effects to the thermoelectric properties in the unstrained SnSe [183].

To study the strain effect on band structure, the strains from -3% (compressive strain) to

+3 % (tensile strain) were applied in the bc-plane. Figure 14(b) and 14(c) show the band structures applied by -3 % and +3 % strains, respectively [183]. When strains were applied, the band structure and bandgap values were significantly affected, and the

CBM and VBM were also shifted with change in bandgap [183]. For +3 % strain, the

VBM occurs at (0.00 0.33 0.00), while for -3 % strain, it occurs at (0.00 0.43 0.00). The

-3 % strain shifts the VBM toward Y in Γ−Y, while the same orbital characters are retained regardless of -3 % or +3 % strains. Besides, the change in conduction band is quite different as these results from the level reversal between Sn px and pz orbitals. For the -3 % strain, the CBM occurs closer to Γ with dominant Sn px character, while for the

+3 % strain, it occurs close to Y with dominant Sn pz contribution. Meanwhile, for the

+3 % strain, many valleys in the CBM are pushed upward, while for the -3 % strain, those valleys moves downwards much closer to the VBM. As such, the strain on the bc- plane affects orbitals along the a-axis, which is well manifested with shifts of Sn px in conduction bands. However, the changes in valence states are not as dramatic as conduction bands [183]. Figure 14(d) shows volumes and bandgap values for different strains. It is obvious that tensile strains increase volumes and bandgaps, whereas compressive strains reduce both.

3.2.2 Thermopower optimization

S exhibits a strong dependence on the applied strain. Figure 15(a-c) show calculated effect of strain on S of SnSe in along a-, b- and c-axes [183]. All calculations are performed with n = 6×1017 cm-3. S anisotropy is well exhibited derived from the orthorhombic structure. It is of interest to note that the temperature of Smax (marked as

T*) increases from 525 K for 0 % strain to 700 K for +3 % strain, whereas T* reduces to

350 K for -3 % strain. The strain-dependent T* is attributed to the change of bandgap under the strain [183]. Strains can significantly affect the calculated S. For the -3 % strain, S changes significantly. Sb and Sc are strongly reduced compared to other cases.

The reduction of Sa is much more drastic, implying the system becoming n-type. The change of S at -3 % stems from the change in band structure. In lattices without strain or with the +3 % strain, the CBM occurs between Z and Γ, while for the -3 % strain, the

CBM appears nearly at Γ. Furthermore, due to the orbital reversal, conduction bands become highly dispersive for the -3 % strain. The reduction of S slows down by the applied +3 % strain at the high temperature, which means that applying appropriate strain can increase S at the high temperature. Compressive strain can make thermal excitation much easier, where the bipolar transport (a coexistence of n- and p-type carriers) can be realized [183].

As discussed above, doping with other elements may cause strain due to the substitution of dopant atoms with different atom size from Sn or Se atom. To investigate the lattice change caused by induced strain, Figure 15(d) shows that the unit cell volume varies with alloyed compositional species (S, Ge, Te, Sr, and Ba) with a solubility of >2 mol %

[127]. The unit cell volume for pure SnSe (black) is given for comparison. It demonstrates a linear dependence on the alloyed composition, following the classical

Vegard’s law [184]. Figure 15(e) shows the plots of κl as a function of temperature for

29 different dopants with 5 mol % doping amount [127]. It is clearly seen that the Debye–

Callaway model [185, 186] generates excellent fits for the temperature-dependent κl, indicating that the scattering physics is mainly determined by a combination of

Umklapp, boundary, and point defect scattering. Figure 15(f) shows the plots of κl with changing the doping amount of different dopants [127], which fits the Abeles model

[187]. With increasing the doping amount, the density of point defects increases, resulting in a decreased κl. Meanwhile, with increasing the atom size of dopant, κl decreases, indicating that the selection of heavy element is a suitable way to further decrease κl.

3.3 Energy band engineering

As discussed above, doping is one of effective routes to further decrease κ. In addition, the induced dopants can also produce new chemical or ionic bonding, which in turn alter the band structures and bandgaps of the materials [188], and improve the thermoelectric properties to a great extent [179].

3.3.1 n/p-type doping

To elucidate how dopants modify the band structure and thermoelectric properties of

SnSe, theoretical investigations based on the first-principles calculations and the

Boltzmann transport theory were used [189, 190]. Figure 16(a) and 16(b) show the calculated band structure of n-type Bi0.028Sn0.972Se (green solid line) and p-type

Ag0.028Sn0.972Se (blue solid line) at 300 K, and these compositions correspond to the n of

4.79×1020 cm-3 [188]. The entire bands are rigidly shifted along the y-axis, so that the chemical potential at 300 K is located at zero for each system. The band structure of the un-doped SnSe (red dashed line) [188] is also shown in both panels. Considerable changes in band structures have been observed around the CBM of Bi0.028Sn0.972Se and around the VBM of Ag0.028Sn0.972Se, respectively [188]. Besides, the bandgap slightly

30 narrows through the doping process. Other DFT calculations [79] showed the similar results. Figure 16(c) and 16(d) show the calculated band structures for undoped and 3 %

Na-doped α-SnSe using the super cell model, respectively [79]. From which, doping with 3 % Na can modify the band structure by shifting the Fermi level, as well as flattening the top of the valence band, which narrows the bandgap [79].

Figure 17(a) shows the DOS near the Fermi level [79], which is derived from the s- and p-orbitals of Sn and especially from the p-orbitals of Se. As can be seen, the contribution of the Na dopants to the DOS is almost negligible. Figure 17(b) shows the calculated DOS with different Na doping concentrations (namely 1 %, 2 %, 3 %, and

4 %), from which altered Fermi levels can be seen [79]. In particular, the Fermi level decreases with increasing the Na content, and the top of the VB remains at ~3.5 eV.

Figure 17(c) depicts this result by the red solid line [79], where the top bands refer to

VB1 or VB2 and the sub-bands refer to VB3 or VB4. The dopants change the profile of the original DOS by increasing the number of carrier pockets near the Fermi level.

Figure 17(d) shows the Fermi level shifts with increasing the temperature [79], deriving from n decrease during increasing the temperature.

3.3.2 Carrier concentration tuning

Doping can be used to effectively tune n, and in turn alter the electrical transport.

Equations (5-6) indicate that S depends on the energy derivative of the DOS (g(E)), as well as n or n(E) since n(E) = g(E)f(E). Both the calculations [181] and experiments [79] demonstrated that with increasing n, the onset of bipolar transport should occur at the higher temperatures, which is beneficial to enhance the thermoelectric performance at the higher temperature. However, Smax may decrease to some extent. More frequently used relationship between S and n can be described as [191-193]:

(7)

31 and

(8) where h is the Planck's constant. n can increase via doping of SnSe, resulting in an increase of σ [113]. Experiments demonstrated that by doping with Na, n increased from

~3×1017 cm-3 for undoped SnSe [61] to ~3.2×1019 cm-3 for 1 % Na-doped SnSe, and

~5.2×1019 cm-3 for 2 % Na-doped SnSe [79]. Although S of Na-doped SnSe is distinctly smaller than that of undoped SnSe, much higher σ leads to larger S2σ compared to the undoped SnSe [61, 79]. Thus, designing the suitable type and amount of dopant(s) plays a dominant role in further improving the thermoelectric performance of SnSe.

3.4 Summary of calculation-based work

Calculation materials science is essential for the verification of current experimental results, as well as the prediction of potential properties of materials and device performances. For this reason, extensive calculations have been performed in the SnSe materials system.

3.4.1 Verification of experimental results

Since SnSe has been reported as a promising thermoelectric system, many calculations were performed [90, 109, 110, 113, 117, 179-181, 188, 189, 194-200]. To verify the experimental results of single crystal SnSe [61], by using the equation of [188]:

(9)

where D( ) is DOS, n = 6×1017 cm-3 was obtained, from which the calculation successfully reproduced the experimental data [188]. Here the chemical potential μ is the parameter to adjust n. When choosing n = 3.3×1017 cm-3, the calculated electrical transport properties (such as σ and S) were all in good agreement with experimental results, and resulting in a very high ZT value of 2.1 at 923 K [113], which was a little lower than experimental value (ZT = 2.6 at 923 K) [61].

For polycrystalline SnSe, calculations based on the DFT and Boltzmann transport equations showed a reasonable agreement with the theoretically derived band gap and experimentally measured temperature-dependent and S [90]. These calculation results provide the evidence of the authenticity of experiment results.

3.4.2 Theoretical prediction

As discussed in Section 3.3, decoupling and S via tuning n through band engineering is a key strategy to improve ZT [48, 201]. Extensive experiments show that the highest

ZT can be approached for the single crystal SnSe along the b-axis when n can be optimized within the range of 1019 – 1020 cm-3 [79]. To predict the optimized n, calculations based on full-potential linearized augmented plane waves (FLAPW) method and the semiclassical Boltzmann theory were used [202, 203]. Figure 18 shows the calculated σ, S, S2σ, and ZT for both n-type and p-type SnSe at different n values at

770 K [204]. Figure 18(a) shows the plots of σ as a function of n, in which along the a- axis, n-type doping has much larger σ than that of p-type doping, but along the b-axis, σ of n-type doping is lower than that of p-type. Figure 18(b) suggests that along the different axes, S are roughly the same for both n-type and p-type doping. Therefore, S2σ of n-type doping are much greater than that of the p-type doping along the a-axis, and

S2σ of n-type doping are lower than that of the p-type doping along the b-axis, as shown in Figure 18(c). The maximum S2σ of n-type is nearly 10 times than that of p-type along the a-axis. In order to estimate ZT, the experimental κ values were selected [61]. Figure

18(d) shows that for p-type SnSe, the ZT value is increased to 2.2 along the b- axis compared with the experimental value of 1.5 at 750 K when n increased to 3.2×1019 cm-

3 [61]. Besides, the roughly estimated maximum ZT value is ~3.1 for n-type SnSe along the a-axis at 750 K, corresponding to n = 2.8×1019 cm-3. Although the estimated peak

ZT = ~3.1 for n-type SnSe may not be very accurate due to not directly deduce

33 relaxation time from experimental results [204], it does suggest the potential to further enhance the thermoelectric performance of SnSe.

The analysis of the doping effect by rigid-band approximation shows that the enhancement of the ZT value can be achieved by doping [188], particularly when n is in the range of 5×1019 – 5×1020 cm-3 for both p- and n-type doping. A maximum ZT of

~0.6 at 300 K and ~1.8 at 450 K can be predicted [188]. Calculations based on the semiclassical model incorporating nonparabolicity, the two-band Kane model, the Hall factor, and the Debye–Callaway model [113] demonstrated that at n = ~3×1019 cm-3, peak ZT values can be predicted to be ~0.5, ~1.5 and ~2.3 at temperatures of 300, 600 and 900 K, respectively. In fact, ZT = ~1.5 at 600 K can be very useful in some practical applications. Calculations based on DFT demonstrated that for p-type SnSe at 750 K, when n = ~6×1019 cm-3, peak ZT values can be predicted to be ~1.0, ~0.6 and ~0.5 along b-, c- and a-axes, respectively; while for n-type SnSe at 750 K, when n = ~4×1019 cm-3, peak ZT values can be predicted to be ~2.6, ~1.3 and ~1.0 along a-, c- and b-axes, respectively [110]. Calculations based on DFT with the full-potential linearized augmented plane-wave (LAPW) method also demonstrated that for p-type single crystal

SnSe at 675 K, the peak ZT values along a-, b- and c-axes were ~1.0, ~2.6 and ~1.7 at n of ~6.2×1019, ~3.6×1019 and ~4.1×1019 cm-3, respectively [196]. The highest ZT value of polycrystalline SnSe at the same temperature was predicted to be 1.86 for n = ~4.2×1019 cm-3 for p-type SnSe [196]. Therefore, tuning n is very important for securing high ZT, and it possesses full potential for both p-type and n-type doping for SnSe-based thermoelectric materials.

3.4.3 Crystal design

Apart from α-SnSe and β-SnSe, another cubic structured SnSe phase with a lattice parameter a0 = 11.9702 Å and space group of Fm3m (marked as π-SnSe) was also

34 identified under the condition of hydrothermally synthesized nanoparticles [141, 205].

Figure 19(a) shows the structure of π-SnSe with 64 atoms per unit cell [206]. Figure

19(b) shows the calculated band structure of π-SnSe using mBJ potential and

Boltzmann transport theory [206]. As can be seen, π-SnSe has a calculated bandgap of

0.97 eV. Figure 19(c) shows S, S2σ and ZT as a function of temperature for π-SnSe

[206]. π-SnSe exhibited high S values at low temperature, and the values decreased from 2292 to 444.3 μV K-1 with increasing the temperature from 200 to 900 K, resulting in a reduction in the ZT values [206]. It is noticeable that π-SnSe exhibits a higher value of ZT (~1.0) at relatively low temperature (200 K) when compared to the orthorhombic

SnSe [206]. Other computational calculations based on first-principles pseudopotential method showed that the bandgap of π-SnSe decreased from ~1.0 eV to ~0 eV when external hydrostatic pressure was applied and increased from 0 GPa to 40 GPa [207].

These results indicate that π-SnSe has a wide range of applications for pressure based thermoelectric materials.

Figure 19(d) shows a “star-like” SnSe nanotube with a cylindrical nanostructure, which was designed via first-principles simulations [208]. Figure 19(e) shows the calculated band structure of SnSe nanotube with a bandgap of 1.55 eV [208]. Figure 19(f) shows κl of SnSe nanotube compared with its single crystal counterpart [208], an ultralow κl of

0.18 W m-1 K-1 at 750 K was obtained. Besides, a large S of 900 μV K-1 for p-type nanotube and -700 μV K-1 for n-type nanotube were obtained both at 750 K. When doping level was tuned to around 1020 – 1021 cm-3, S2 of the p-type SnSe nanotube reached its maximum value of 235 μW cm-1 K-2, and an exceptional high ZT value of

3.5 – 4.6 under the optimal conditions can be calculated [208]. For SnSe nanoribbons

[209, 210], by using DFT coupled with semi-classical Boltzmann theory, a relatively high S of ~1720 μV K-1 and low κ of 0.2 W m-1 K-1 were calculated for the armchair

35 nanoribbon of 6 Å width [210]. Meanwhile, a large relaxation time of 55.57 fs and a

* small m of 0.11 me, both for carriers of holes, were obtained for the armchair nanoribbon of 47 Å width [210]. The simulation results showed that SnSe nanoribbons may provide thermoelectric performance that is similar to that of the monolayer and low-temperature bulk of SnSe.

4. Single crystal SnSe

4.1 Crystal growth

To date, there are four main methods to fabricate single crystal SnSe: Bridgman method

(including Bridgman-Stockbarger method) [211-213], direct vapor transport method

[214-216], temperature gradient growth method [52, 217, 218], and hydrothermal method (including solvothermal method) [219-222]. Table 4 summarizes the fabrication methods of single crystal SnSe reported in recent years, where the Bridgman method is abbreviated as B, the Bridgman-Stockbarger method as BS, the direct vapor transport method as DVT, the hydrothermal method as HT, solvothermal method as ST, and the temperature gradient growth method [223] as TGG. Within these fabrication methods,

HT and ST methods have been frequently applied for the fabrication of small-scaled single crystal SnSe, and these small crystals are often used as precursors for sintering bulk thermoelectric materials [81, 141, 224].

4.1.1 Bridgman method

Both the B method (including the BS method) and the DVT method have a similar pre- procedure to fabricate SnSe by melting [225-227] or solid-state reactions [228-230].

The precursors are high-purity Sn and Se powders or shots (or ingots) with a purity of >99.99 % to prevent impurity contaminations in the final fabricated products. For this reason, the transporting agents are needed [231]. There are mainly five steps for fabricating SnSe. First, the precursors and transporting agents are sealed under high

36 vacuum (from 10-4 ~10-7 Torr) in a quartz ampoule, then melted or solid state reacted in a furnace with an appropriate temperature and an appropriate heating speed. For the melting route, the targeted temperature can be set above the melting point of SnSe

(1134 K), while for solid-state reaction, the targeted temperature should be set just below the melting point. The heating speed should not be set too high to make sure that the Sn and Se are adequately reacted to form SnSe. When the furnace temperature reaches to the targeted temperature, keep this temperature for a long time (from 12 h to several days) to ensure a full reaction. When the reaction is fully proceeded, slowly cool the furnace to room temperature. The obtained ingots are crushed into powders and prepared for the single crystal growth. As discussed in Section 2.6, it should be note that the oxidization is better to be avoided during the fabrication of SnSe.

When using the B method (including the BS method), a seed SnSe crystal is first located at bottom, then the SnSe powders or ingot are heated above the melting point and slowly cooled down at the seed SnSe crystal. The single crystal SnSe grows on the seed along the same crystallographic orientation of the seed material. The growth process is always carried out in a vertical or horizontal geometry, which is called vertical Bridgman method and horizontal Bridgman method. The temperature controllers are needed to control the crystal growth process. There is some difference between the B method and advanced Stockbarger method [213]. Both methods need a moving crucible and a temperature gradient, but the Bridgman route uses the relatively uncontrolled gradient produced at the exit of the furnace; and the Stockbarger route applies a baffle (or shelf) to separate two coupled furnaces with temperatures above and below the freezing point. After the improvement by Stockbarger, the BS method possesses better control over the temperature gradient at the melt or crystal interface

[213].

4.1.2 Direct vapor transport method

In the DVT method [214-216], when the homogeneous polycrystalline SnSe powders are obtained from melting or solid-state reaction, the SnSe powders are then placed in a charged ampoule, and the ampoule is evacuated and sealed at a high vacuum of 10-3 Pa and placed in a dual zone horizontal furnace with a temperature gradient. The charge end (hot zone) is maintained at a higher temperature (such as 1063 K) and the tapered growth end (cold zone) at the lower temperature (such as 1013 – 943 K). The temperature is increased at a rate of 10 – 30 K per hour from room temperature (300 K).

When the targeted temperature is reached, the ampoule is left in the furnace for a long time (such as 240 h, much longer than the B method). After that, the cooling is carried out at a low rate (such as 5 K per hour) to room temperature. At last, the furnace is switched off and the ampoule is carefully taken out from the furnace. The ampoule is finally broken to obtain the single crystals.

It is obvious that single crystal SnSe need rigid conditions to grow. Besides, compared with the synthesis of polycrystalline SnSe materials, the efficiency of single crystal growth is low, and the cost is high. Further improvement of the growth technique of single crystals needs to be addressed.

4.1.3 Temperature gradient growth method

For TGG route, the temperature gradient plays a critical role in the growth of single crystal SnSe. Similar to B and DVT methods, high-purity Sn and Se powders were used as precursors for the crystal growth [52, 217, 218]. It was better to choose these precursors with particle sizes < 200 meshes to optimize the surface area, and thereby enhance the reaction kinetics [223]. Sn and Se powders were first loaded into thick wall quartz ampoules. Then, the ampoules were evacuated and sealed. Sometimes another quartz tube was sealed to protect the sample and ampoule. The powders in ampoule

38 were mixed and loaded into a vertical furnace. The temperature was slowly increased from room temperature to above the melting point of SnSe, and maintained at this temperature for an appropriate time (such as 10 h [52]). Finally, the temperature was slowly cooled at an appropriate rate to below the melting point of SnSe (such as 973 K

[52]), and then rapidly decreased to room temperature.

4.1.4 Hydro/solvothermal method

HT and ST syntheses [219-222] are also effective methods to obtain SnSe products, such as single crystal plates [81, 91, 232] and nanobelts [233]. In HT synthesis, single crystal SnSe is synthesized in hot water under high pressure. The apparatus for taking

HT synthesis is an autoclave (also called steel pressure vessel), in which a nutrient is supplied along with water. The autoclaves are put into an oven for chemical reactions under high temperature. With increasing the pressure and temperature, the water ions can rapidly increase. Under a high pressure (15 ~20 GPa) and high temperature, the density of water can reach 1.7 ~1.9 g cm-3. In this condition, water can be completely

- + dissociated into OH and H3O (behaving like a molten salt). Besides, the water viscosity decreases with increasing the temperature. In this situation, the mobility of ions and molecules is much higher than under normal condition. Many chemical reactions can be carried out in this environment. Meanwhile, during the chemical reaction, water is used as a solvent, and the dielectric constant is one of the very important properties of water. With increasing the temperature and pressure, the dielectric constant of water decreases [234]. Therefore, temperature plays a dominant role in the dielectric constant of water. In terms of ST synthesis, it is similar to the HT synthesis with the only difference of the solvent not being aqueous.

The merit of HT and ST methods is that it does not need very high synthetic temperature (normally below 500 K) [81, 118], but the synthesized products often have

39 a high quality, which can show identical information of crystal structure. In particular,

HT and ST methods can realize precise control of shape, size, and crystallinity of nanostructures by altering the experimental parameters, such as the reaction time, temperature, precursor type, solvent type, and surfactant type. In this respect, HT and

ST methods are useful to fabricate nanostructured products. In terms of the aqueous solution method [82, 235], it is similar to HT/ST methods. The difference is that for aqueous solution method, the boiling solution is always under normal pressure, and the reaction time is shorter than traditional HT/ST methods.

4.2 Characterization

The characterization of single crystal SnSe is important to determine the compositions of SnSe, as well as verify the quality of their crystal structures. Within these characterization methods, XRD is often used to determine the purity and structural features of the obtained products, and SEM, TEM and scanning tunneling microscope

(STM) [236] are frequently used to illustrate the morphological, structural and compositional characteristics of the obtained products.

4.2.1 Macro-sized crystal

For macroscopic SnSe single crystals, to verify the crystal plane of synthetized SnSe crystals, XRD was used [61, 216]. Figure 20(a) shows a typical α-SnSe cleavage plane of (400) [61], indicating that α-SnSe crystal is cleaved at the plane that is perpendicular to the a-axis. Figure 20(b) shows a typical EBSD image on a 1 mm2 surface of α-SnSe crystal [61], indicating homogeneous orientation within a large area of sample surface with relatively homogeneous orientation. Figure 20(c) shows a STM topographic image obtained from an in-situ cleaved (001) surface of SnSe [97], in which a layered structure can be seen. Figure 20(d) shows a HRTEM image of α-SnSe crystal. The bottom inset of Figure 20(d) is the corresponding selected area electron diffraction (SAED) pattern

40 taken along the zone-axis while the top inset is the line profile along the dotted line AB in the main panel, which shows the d spacing of (100) atomic planes [61]. All this information illustrates that such a single crystal is α-SnSe with a space group of

Pnma at room temperature. Figure 20(e) and 20(f) show the SAED patterns obtained from the same TEM specimen area at room temperature and 820 K [61], respectively.

As can be seen, at room temperature, α-SnSe with a zone-axis can be seen. When the temperature reached to 820 K, phase transformation took place and the resultant β-

SnSe crystal showed a zone-axis. Moreover, when the TEM specimen was cooled down to room temperature, the SAED patterns transfer again from Figure 20(f) to 20(e), indicating that the phase transition between α-SnSe and β-SnSe is reversible.

In terms of the doped SnSe single crystals, Figure 21(a) shows the XRD patterns of

SnSe single crystals doped with different amount of Na and Ag and their corresponding simulated diffraction patterns [61]. However, it is hard to see the peak deviation for the doped single crystal, which is controversial. Figure 21(b) shows a typical STM topographic image for SnSe on the b–c plane doped with Bi [52]. A few defects were found in the marked area by the black dashed circle and the inset HR-STM image. This distinctive feature is predicted to be originated by substitutional Bi atom occupying the

Sn-site [52]. Figure 21(c) shows a TEM image of Na-doped SnSe crystals with stacking faults (red arrows) and dislocations (green arrows) can be observed [78]. Figure 21(d) shows STEM image of the typical regions of the Na-doped SnSe crystals [78]. The high magnification annular bright field (ABF) image is inserted in Figure 21(d), indicating the two stacking faults. Other studies showed that using ABF-STEM, interstitial atoms can be observed in Sn0.985Na0.015Se single crystal [237], indicating that vast off- stoichiometric defects exist in single crystalline SnSe.

4.2.2 Micro/nano-sized crystal

Compared with macroscopic crystalline SnSe discussed above, to study the morphology of synthesized micro/nanoscopic crystals, XRD, SEM and TEM were all commonly used. Figure 22(a) shows the XRD patterns of SnSe crystals with different average size

(~30 and ~100 μm, respectively) [91]. All diffraction peaks for both type of crystals can be exclusively indexed as the orthorhombic structured α-SnSe with the lattice parameters of a = 11.37 Å, b = 4.19 Å, and c = 4.44 Å and space group of Pnma

(Standard Identification Card, JCPDS 48-1224) [91]. In Figure 22(a), (400) peak is the strongest peak, suggesting that these single crystals contain significant {100} surfaces.

The inserted optical images of crystals show features of metallic luster. Figure 22(b) shows the magnified XRD patterns of SnSe crystals. As can be seen, both type of crystals have peak deviation to some extent, indicating that the self-doping exists in the crystals [91]. The (111) peak for crystals with an average size of ~30 μm was much stronger than that of others with a larger average size, indicating that crystals with a larger average size possess much more {100} surfaces than their counterparts.

Figure 22(c) is the typical SEM image of SnSe single crystals with an average of ~30

μm and shows that the crystals have a plate-like morphology [91]. The inserted image in

Figure 22(c) is a zoom-in SEM image taken from a typical plate, from which the thickness of the plate can be estimated to be ~3 µm [91]. Figure 22(d) shows another

SEM image of the plate-like SnSe single crystals with a larger average size and a thickness of ~5 µm [91]. Figure 22(e) shows the plane information of one plate, indicating that the {100} planes are the preferred surfaces [91]. Figure 22(f) is a TEM image taken from a typical plate laid perpendicular to the electron beam [91]. Figures

22(g) and 22(h) are the corresponding HRTEM image and the SAED pattern taken

42 along the zone-axis of the plate [91], indicating typical orthorhombic structure of

α-SnSe.

4.3 Performance

Because of the anharmonic bonding of Sn and Se, the thermoelectric properties possess totally different values along different axes in single crystal SnSe [61]. Here, we summarize the main strength and drawback caused by anisotropic performance.

4.3.1 Strong anisotropy

Along the b-axis, a maximum ZT of ~2.6 was achieved at 923 K, derived from a high

S2σ (~8.5 μW cm-1 K-2) and a low κ (~0.35 W m-1 K-1) measured at the temperature [61].

It was found that an enhanced n (~7.3×1018 cm-3 at 773 K) derived from the thermal activation contributed to a high of ~72.9 S cm-1 and a high S of ~343.2 μV K-1 at 923

K, and the anharmonic bonding of Sn and Se along the b-axis contributed to a low κ of

-1 -1 -1 -1 ~0.35 W m K [61]. κl (~0.23 W m K ) occupied 65 % of κ at 923 K, indicating that

κ was dominated by lattice phonon transport along the b-axis [61]. Similarly, along the c-axis, a maximum ZT of ~2.3 was achieved at 923 K, derived from a high S2σ of ~6.6

μW cm-1 K-2 and a low κ of ~0.30 W m-1 K-1 measured at the temperature, both of which were lower than that measured along the b-axis [61]. However, along the a-axis, a maximum ZT of only ~0.8 was obtained at 923 K, derived from a low S2σ (~1.9 μW cm-

1 K-2) and a low κ (~0.23 W m-1 K-1) measured at the temperature, both of which were much lower than that measured along the b- and c-axes [61]. This is because along the a-axis, the SnSe layers arrayed along the a-axis composed by weak van der Waals force resulted in a much lower μ (~7.2 cm2 V-1 s-1 at 773 K), and in turn resulted in a much lower (~12.8 S cm-1 at 923 K) [61].

4.3.2 Strength and drawback

Although there are strong anisotropy for the thermoelectric properties of single crystal

SnSe, the properties still possess the same trend and show extraordinary performance at high temperature. Figure 23 shows the main thermoelectric properties (σ, S, S2σ, n, μ, κ,

κl, κl/κ and ZT) of SnSe single crystals along the a-, b- and c-axes discussed above [61].

For σ, as shown in Figure 23(a), from 300 to 525 K, an obvious decrease showed a metallic transport behavior of σ [61]. From 525 to 800 K, the σ value increased by the function of carriers thermal excitation, which started to show a thermally activated semiconducting behavior of σ [61, 238]. After that, the σ value slightly decreased again due to the phase transition from α-SnSe to β-SnSe. For S, as shown in Figure 23(b), the peak S values are found between 500 K and 600 K due to the bipolar transport occurs

[181]. Figure 23(c) shows the maximum value of S2σ along the b-, c- and a-axes were

10.1 µW cm-1 K-2, 7.7 µW cm-1 K-2 and 2.1 µW cm-1 K-2 at 850 K, respectively. Figure

23(f) demonstrates that κ decreased gradually before 800 K, then kept at a low value until 973 K, caused by the phase transition from α-SnSe to β-SnSe [61]. At room temperature, the κ values were measured as 0.46 W m-1 K-1, 0.70 W m-1 K-1 and 0.68 W m-1 K-1 along the a-, b- and c-axes, respectively, which are much lower than that of the other thermoelectric materials [3, 5, 239]. To calculate κl, κl = κ – κe = κ - LσT, where L is the Lorenz number [240], which was approximated to 1.5×10-8 W Ω K-2 in the case of non-degenerate semiconductors limited by phonon scattering, such as SnSe [241]. In fact, the theoretically calculated minimal κ are slightly larger than those from experimental measurements, which could possibly result from the value of the L

(1.5×10-8 W Ω K-2), which can vary in the range of 1–2.4 ×10-8 W Ω K-2 [61]. The ratio of κl to κ shown in Figure 23(h) is up to 65 %, indicating that that κ was dominated by lattice phonon transport (κl) [61].

Figure 23(i) illustrates ZT values of single crystal SnSe along the a-, b- and c-axes.

Although the ZT values are very high at high temperature, however, they were low before 800 K, indicating that the ZT value obtained from α-SnSe was much lower than that of β-SnSe. Considering that the mid-temperature (from 300 K to 700 K) is the most commonly used in practical applications, and the mechanical property of β-SnSe is much weaker than that of α-SnSe, α-SnSe should possess much better potential for practical application than β-SnSe. Thus, it is necessary to further improve the thermoelectric performance of α-SnSe.

4.4 Improvement

In order to further enhance the thermoelectric properties of α-SnSe, doping was used to realize p-type or n-type single crystals [78, 79]. For p-type doping, the dopants used include alkali metals (such as Na) [78, 79], and I-B group metals (such as Ag) [79, 242].

For n-type doping, the dopant used was V-A group metals (such as Bi [52]). Most of the dopants were used to substitute Sn positions to tune n.

4.4.1 p-type doping

For p-type doping, a maximum ZT of ~2.0 was achieved via doping with 3 % Na at 800

K along the b-axis [79]. Such significant thermoelectric performance derived from the obviously enhanced n values [79]. Experiments demonstrated that, with increasing the

Na content, n increased from ~3.2×1018 cm-3 [61] to ~2.1×1019 cm-3 doped with 1 % Na

[79] and ~2.7×1019 cm-3 doped with 2 % Na at 723 K [79], respectively. Although a high n resulted in a lower S value (~261.4 μV K-1) than that of undoped crystals (~437.0

μV K-1) at 773 K [61], a much higher (~212.1 S cm-1) [79]contributed to a much larger S2 (~14.5 μW cm-1 K-2) than that of single crystals at the same temperature [79].

After doping with 3 % Na, κ increased from 0.33 W m-1 K-1 [61] to 0.58 W m-1 K-1 [79] at 773 K. Other experiments also achieved a maximum ZT of ~2.0 at 773 K along the b-

45 axis in hole-doped SnSe via 1.5 % Na [78]. The significant thermoelectric performance also raised from high S2 (~14.2 μW cm-1 K-2), which came from high (~149.5 S cm-1) and strongly enhanced S (~307.8 μV K-1) at 773 K [78]. By angle-resolved photoemission spectroscopy, large hole effective masses were revealed in both undoped and hole-doped SnSe crystals [243], contributing to the high electrical transport performance.

For Ag-doped SnSe single crystals [79, 242], a maximum ZT of ~1.0 was obtained at

800 K along the b-axis via doping with 3 % Ag [79]. Compared with doping with 3 %

Na [79], a lower σ (~71.6 S cm-1) resulted in a lower S2σ (~7.86 μW cm-1 K-2) for doping with 3 % Ag, and a higher κ (~0.64 W m-1 K-1) was obtained at the same time [79].

Compared with Ag, the significant mass and size difference of Na and Sn atoms gave rise to a strong phonons scattering, and in turn contributed to a low κ [79].

4.4.2 n-type doping

For n-type doping, a maximum ZT of ~2.2 was achieved at 733 K along the b-axis via 6 %

Bi-doping with n of -2.7×1019 cm-3 [52, 244]. The excellent thermoelectric properties of n-type SnSe single crystals can be attributed to that (~61.5 S cm-1) is enhanced via the

Bi doping while maintaining a low κ (~0.29 W m-1 K-1) [52]. It demonstrated that both n- and p-types in a one-material system can be realized, and with both excellent performance.

Figure 24 plots the main thermoelectric properties ( , S, S2σ, κ and ZT) of SnSe single crystals before and after doping with different dopants along the b-axis [52, 78, 79]

(except doping with 3 % Ag [242] with pink line, which is along the a-axis). Theoretical calculations showed that a peak ZT of 2.57 can be obtained in p-type SnSe along the b- axis by optimizing n to ~3.6×1019 cm-3 [196]. Theoretical calculations indicated that heavy-light band overlapping near the valence band and a mixed ionic-covalent bonding

46 were the reasons for this extraordinary thermoelectric performance [196]. For n-type doping, theoretical calculations predicted that a peak ZT of ~3.1 can be obtained for n- type SnSe along the a-axis at 770 K at n of 2.8×1019 cm-3 [204]. Figure 24(f) shows the comparison of both average and peak ZT between doped and undoped single crystal

SnSe from 300 to 773 K. As can be seen, both Na-doped p-type single crystals and Bi- doped n-type single crystals have much higher average and peak ZT than those of their undoped counterparts in this temperature range. These results indicate that doping is a promising method to enhance the thermoelectric performance of α-SnSe, as well as a convenient way to realize n-type thermoelectric materials with a high thermoelectric performance.

4.5 Controversy on thermal conductivity

Table 5 summarizes the measured density (ρ) by using Archimedes’ method and estimated ρ of SnSe single crystal along different axes if the original articles have not provided, in which ρ was estimated using the relation [61]:

(9) where D is the thermal diffusivity, and Cp is the specific heat capacity at constant pressure. Experimentally, measured D, Cp, and κ can be used to determine ρ. For the reported undoped SnSe single crystal [61], the calculated ρ was only ~5.45 g cm-3 along the three axes, which was much lower than the theoretical value (6.18 g cm-3), indicating a very low relative density (~88 %). In this respect, the observed ultralow κ values may not be intrinsic for fully dense single-crystalline SnSe (chemical ratio is

SnSe = 1:1) [245]. However, considered that the SnSe single crystal has a strong anisotropy and weak mechanical properties which lead to facile cleavage, the crystal can easily be damaged during cutting, handling and measurements, and in turn result in a high uncertainty between 15 % and 20 % for the measured κ [61]. In this respect, the

47 calculated low ρ is reasonable. At the same time, experiments based on a vertical-

Bridgman-grown single crystal SnSe [246] with a high density (ρ = 6.10 ± 0.05 g cm-3) showed that the intrinsic κ of single crystal SnSe is likely significantly higher than that of the reported undoped SnSe single crystals with a density of ~88 % [61]. The single crystal SnSe with a relative density of 99 % showed that the κ values along the a-, b-, and c-axes were 1.2, 2.3, and 1.7 W m-1 K-1 at 300 K, respectively [246], which were higher than the values of 0.46, 0.70 and 0.67 along the a-, b-, and c-axes [61]. These results were consistent with early studies performed on single crystal SnSe (1.9 W m-1

K-1 at 300 K perpendicular to the c-axis) [247]. Besides, the single crystal SnSe with a relative density of 99 % demonstrated that the values along the a-, b-, and c-axes were all ~1.0 W m-1K-1 at 700 K [246], which were higher than the reported results of ~0.24,

0.34 and 0.31 along the a-, b-, and c- axes, respectively [61]. In this respect, the reported single crystal with a low calculated ρ should be at least “SnSe crystal”.

For doped single crystal SnSe, the measured/calculated ρ values are also listed in Table

5. Compared with the case of undoped single crystal, the 3 % Na-doped single crystal possessed a calculated ρ value of ~6.25 g cm-3, close to the theoretical value (6.18 g cm-

3) [79], which can be treated as within the uncertainty of measured results [79].

Similarly, the 1.5 % Na-doped single crystal possessed calculated ρ values of ~6.43,

~5.89 and ~5.99 g cm-3 along the a-, b-, and c-axes at ~773 K, respectively [78], which derived from the κ uncertainty (~12 %) comprised uncertainties of 5 % for the measured

-3 D, 5 % for the measured Cp, and 2 % for the measured ρ (~6.0 g cm ). Although there exist controversies on the intrinsic κ values of single crystal SnSe, it should be noted that SnSe-based thermoelectric material is still a promising candidate with full potentials for further improving the thermoelectric performance.

5. Polycrystalline SnSe

Although SnSe single crystals have demonstrated excellent thermoelectric performance due to their ultralow κ along the b- and c-axes [61], they suffered from the poor mechanical properties, rigid crystal growth conditions, and high cost of their production.

Also, the techniques used for growing single crystals are limited for industrial scale-up

[65]. For this reason, SnSe single crystals may be difficult to be employed in large-scale practical thermoelectric devices. To overcome this challenge, polycrystalline SnSe has become a research topic, and has been preliminarily applied into the thermoelectric modules [248].

5.1 Fabrication

Texturing and doping have been the two key approaches used for improving thermoelectric performance of polycrystalline SnSe, from which their ZT values have been improved from ~0.4 to ~1.7, although such ZT values are still lower than their single crystal counterparts, mainly due to their relatively high κ and low σ [65, 66, 81,

88, 89, 118, 119, 249-252]. Table 6 summarizes the synthesis methods with relevant parameters for producing polycrystalline SnSe materials.

5.1.1 Synthesis of product

As shown in Table 6, the melting [225-227] or solid-state reaction [228-230] routes are the two most commonly used methods, especially for the melting route. The principles and main procedures of the melting and solid-state reaction routes have been discussed in Section 4.1. For the arc-melting route [88, 253], it is different from the traditional melting route, because the heats for arc-melting are provided through an electric arc

[254]. The precursors are directly exposed to the electric arc, and the current in the furnace terminals passes through the charged precursors. In this regard, the arc-melting has a much higher heating speed than the traditional melting.

When the melting or solid-state reaction were finished, sometimes the annealing, keeping for several days and then cooling down to room temperature [249, 250], followed at the temperature below the melting point of SnSe to change the ductility and hardness of the obtained SnSe [255]. Moreover, the annealing can lead to re-alignment of crystalline domains and in turn result in the increase in S and [250].

Mechanical alloying [256] is a solid-state powder processing technique. By blending

SnSe powder precursors in a high-energy ball mill, it is powerful to produce a homogeneous SnSe product. During mechanical alloying, the precursors were milled on a planetary ball mill at an appropriate speed for an appropriate time [257] by using a stainless steel vessel filled with a mixed atmosphere such as Ar and H2 gases.

Sometimes, mechanical alloying was also treated as a step after melting [258-260].

Experiment showed anisotropy in the grains can be achieved by ball milling for 1 minute [258].

5.1.2 Sintering

In order to obtain bulk SnSe materials, the synthesized SnSe products should be ground into powders and then sintered, to realize a polycrystalline structure with high density and a good mechanical property. Because the polycrystalline SnSe fabricated via cold- pressing route has demonstrated a poor thermoelectric performance [250], while hot- pressing and SPS have been demonstrated as the two most commonly used sintering methods to fabricate polycrystalline SnSe bulk materials. Traditional hot-pressing is a low-strain-rate powder metallurgy process taken under high pressure, commonly used to produce brittle and hard materials [261]. For SnSe, hot-pressing can sinter SnSe powder compactly at a high temperature and a high pressure (up to 600 MPa) [252, 262].

In terms of the SPS technique, it has played a dominant role in the sintering of powder compacts with high density at lower sintering temperature compared to conventional

50 sintering techniques such as hot or cold pressing [263]. It is different from the traditional hot-pressing for that the heat generation is internal during SPS process, and the heat is provided by external heating elements during hot-pressing. For SnSe, SPS can achieve a very high heating and cooling rate (up to 1000 K min-1), resulting in a very fast sintering process (within several minutes) [150]. SPS has the great potential of densifying SnSe powders with high density and orientation. After sintering, annealing treatment can be used to re-alignment the crystal crystalline domains of SnSe pellets

[250].

5.2 Feature

The characterization of polycrystalline SnSe is important to confirm the composition of

SnSe for both synthesized products (such as powders) and sintered bulks. Within these characterization methods, XRD and XPS are used to analyze the purity and binding structures of SnSe products, and XRD is also used to verify the anisotropy of sintered bulks. SEM and TEM are frequently used to characterize the morphology and structural information of polycrystalline SnSe.

5.2.1 Phase analysis

Figure 25(a) shows a typical XRD pattern obtained from SnSe synthesized via solid- state reaction [90]. All the peaks can be indexed to the orthorhombic phase of α-SnSe with a strong (400) diffraction peak. The average crystallite size of the as-synthesized

SnSe was determined to be ~42 nm using Williamson–Hall method [90]. Apart from

XRD, XPS can also be used to analyze the phase of SnSe [81, 264-266]. Figure 25(b) shows a partial high resolution XPS spectrum of SnSe synthesized via solvothermal route [81], indicating the existence of one valence state for Sn and Se. The peaks of Sn

3d3/2 and Sn 3d5/2 were singlet and no accessorial binding energy peaks can be found,

51 indicating the divalent characteristic of Sn ions, and a binding energy peak of Se 3d was also observed at 53.7 eV, suggesting Se2+ [81].

To determine the compositional ratio of Sn and Se in the materials, EDS [267-269] and high-resolution electron probe micro-analysis (EPMA) [81, 91, 128, 257] are commonly used. Figure 25(c) shows a typical EDS spot analysis of SnSe synthesized by microwave-assisted solvothermal route, the atomic ratio of Sn and Se was roughly 1:1.

To exam the existence and dispersion of dopants, EDS mapping is also frequently used.

Figure 25(d) shows an EDS mapping of Ag in Ag-alloyed SnSe and the observed contrast indicates the successful alloying of Ag [268] and that Ag is segregated in some regions of few microns. To obtain more exact stoichiometry of the as-synthesized SnSe products, EPMA is widely used. A typical result is shown in Sn0.98Se, which provide the stoichiometric ratios of Sn:Se = 49.5:50.5 ± 0.4 for self-doped SnSe [91].

5.2.2 Sinter-induced anisotropy

Because SnSe has a typical layered structure, anisotropy in the sintered polycrystalline

SnSe materials is widely existed [66]. To verify the anisotropy, XRD and SEM are used.

Figure 26(a) is the typical XRD patterns at the direction perpendicular to the sintering pressure (marked as ⊥) and parallel to the sintering pressure (marked as //) for the sintered polycrystalline SnSe [91], respectively. As can be seen, the pellet cut along the

⊥ direction shows a strong (400) peak, similar to the XRD pattern taken from plates

(refer to Figure 22(a)) [91]. In contrast, the pellet cut along the // direction shows a weak (400) peak, but a strong (111) peak, indicating a strong anisotropy in the sintered

SnSe pellets. Figures 26(b) is the typical SEM images of the polished pellet surface cut along the ⊥ direction [91], indicating that the flat surface is without observable flaw.

Figures 26(c) and 26(d) are the typical SEM images of pellets fractured along ⊥ and // directions to the SPS pressure [91] respectively, from which distinct fracture features

52 confirm that the sintered pellets have a preferred orientation. Figure 26(e) is a HRTEM image taken from the pellet and the inserted SAED pattern taken along the zone- axis of the pellet, indicating the typical orthorhombic structure of SnSe.

5.2.3 Microscopic study

Figure 27(a-c) shows the high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of polycrystalline SnSe viewed along the a-, b- [270], and c-axis [270] with overlays showing Sn atoms in red and Se atoms in blue , respectively. The dashed rectangle indicates the projected unit cell. Figure 27(d) shows an atomic-scale EDS mapping from zone axis of [270], confirming the arrangement of Sn and Se atoms. For the case of sintered bulks with nanoprecipitates, Figure 27(e) shows an EBSD phase map of SnSe with grains identified as cubic rock-salt phase in red and orthorhombic α-phases in blue [141], and

Figure 27(f) shows a TEM image of SnSe with rock-salt phase with an inserted SAED pattern detected on the grain [141], indicating the existence of rock-salt phase of SnSe nanoprecipitates as second phase. Experimental and theoretical studies have shown that cubic rock-salt SnSe has an almost negligible energy difference from α-phase [271, 272].

Possible transition from α-SnSe to cubic SnSe phase will occur due to a strong correlation between the lattice constants of isostructural and chemically analogous cubic phase and α-phase. Recent studies showed that the cubic rock-salt SnSe can be induced by microstructure control [273].

TEM is a powerful tool to determine the nature of crystal defects. Figure 27(g) is a

HRTEM image taken from a sintered SnSe pellet [119], and shows nanosized grains with disordered atomic planes with dislocations (marked by dashed circle) and lattice curvatures (marked by dashed line) [119]. For doping with other elements (such as Na

[274] and Ag [268]), Figure 27(h) shows a HRTEM image of Ag-doped SnSe [275],

53 from which a dark area was observed to be predicted to be amorphous. In terms of incorporating with other compounds (such as SnTe), Figure 27(i) shows a TEM image of the boundary of two phases for SnSe and SnTe [276]. Besides, TEM is also useful to characterized nanoprecipitates [67, 141], as discussed in Section 2.4.

5.3 Texturing

As mentioned in Section 5.1, polycrystalline SnSe has become a research topic due to their better mechanical properties, easier synthesis, and lower cost than single crystal

SnSe [65]. However, most of ZT values of polycrystalline SnSe are much lower than that of single crystals due to the low , low S and high κ [65]. To enhance S, arc-melting method was used to fabricate SnSe without sintering, realizing a high S of ~660 μV K-1 at 395 K, as well as an ultralow κ of 0.1~ 0.2 W m-1 K-1 at the same temperature [88].

However, a low n of 7.95×1015 cm-3 resulted in a low of ~0.16 S cm-1 at 395 K [88], which in turn resulted in a low S2 , as well as a low ZT. SnSe nanocrystals synthesized via the solvothermal route shows a n of ~1 ×1019 cm-3 [118]. However, after sintering, a low S of ~160 μV K-1, as well as a high κ of ~1.4 W m-1 K-1 were obtained at 300 K, resulting in a low ZT. Therefore, it is still a challenge to decoupling , S, S2σ, and κ to realize high ZT for undoped polycrystalline SnSe.

As discussed in Section 4.3, single crystal SnSe has a peak ZT value of ~2.6 along the b- axis [61]. In Section 5.2, the sintered polycrystalline SnSe shows high anisotropy [66].

Extensive experiments [65, 66, 91, 249] showed that the anisotropy became stronger when texturing was applied in the undoped polycrystalline SnSe, leading to a better thermoelectric performance measured along the ⊥ direction than that measured along the // direction. This is because that along the ⊥ direction, most of the grains were arrayed along the b- or c-axes [65, 66, 91, 249], resulting in higher and higher S2σ.

5.3.1 Cold-pressing and hot-pressing

It has been found that the thermoelectric performances obtained from different texturing methods are different. For the cold-pressing route, thermal annealing can influence both the microstructure and the thermoelectric properties via re-alignment of crystalline domains [250], which has increased both S and σ. However, it was hard to achieve high

ZT via cold-pressing due to the high electrical resistivity [250], which derived from low

σ [250]. Combined cold-pressing with annealing [250], a maximum ZT of ~ 0.1 was achieved, which was still very low.

In the case of hot-pressing, through the combination of traditional melting, a highly textured polycrystalline SnSe ingot was obtained, and a maximum ZT of 1.1 was obtained caused by a obtained high of ~61.9 S cm-1 and a high S of ~366.3 μV K-1, and resulting in a high S2σ of ~8.3 μW cm-1 K-2 at 873 K [66]. However, κ (~0.66 W m-1

K-1) was very high in this case [66]. Strong anisotropy was found in the sintered ingot due to the high-pressure and long-time sintering process. For the case of fusion method combined with ball milling route [252], SnSe nanoparticles were sintered into ingot via hot-pressing, and the effect of hot-pressing temperatures on the thermoelectric properties was explored. Due to the n optimization, the peak ZT value reached 0.73 for samples hot-pressed at 673 and 723 K, indicating that the thermoelectric performance can be significantly improved by hot-pressing.

5.3.2 Melting with SPS

Although hot-pressing can secure a good quality of sintered bulks, the long-time sintering by hot-pressing can be time-consuming, as shown in Table 6. To solve this problem, SPS was chosen. For SPS, the heat generation is internal during the sintering process, and a high heating or cooling rate can be realized, contributing to a high density at a low sinter temperature. As a result, the SPS process is fast, often within a

55 few minutes, to both increase the efficiency of sintering and prevent the growth of grains. Thus, SPS has been widely used in recent studies based on polycrystalline SnSe thermoelectric materials, and the thermoelectric performances were comparable to the hot-pressing one (ZT = ~1.0).

For the traditional melting and SPS route [65], anisotropic transport properties were observed, and a peak ZT of ~0.5 was obtained due to the moderate S2σ (~4.0 μW cm-1 K-

2) at 823 K [65]. This value was still higher than that via the combination of the cold- pressing and annealing route [250]. However, (~0.63 W m-1 K-1) was relatively high

[65], which need further optimization. When combining the melting, annealing, and

SPS route [249], a pure phase with preferred orientation along the -axis was obtained, resulting in strong anisotropic thermoelectric properties. Although a low κ (~0.4 W m-1

K-1 at 790 K) [249] was obtained via annealing, the low n of 1.1×1017 cm-3 resulted in a low σ of ~18.7 S cm-1 and a low S2σ of ~2.7 μW cm-1 K-2 at 790 K, thus a low peak ZT of ~0.5 was obtained at 790 K. By combining the zone-melting with SPS route [89], highly textured structures and strong anisotropic thermoelectric performance were obtained with a peak ZT of ~1.0 along the // direction. This derived from a high σ of

~49.9 S cm-1, a high S of ~408 μV K-1 and a very high κ of ~0.7 W m-1 K-1 at 873 K [89].

5.3.3 Solvothermal with SPS

For traditional synthesis routes such as melting and mechanical alloying, it was a challenge to achieve high anisotropy in sintered SnSe bulks due to the random orientated synthesized products before sintering. In order to achieve a high anisotropy in the synthesized products, hydro- or solvothermal methods were used. Because the synthesized products via these routes are micro/nano-sized single crystals, the products should possess strong anisotropy just like macro-sized single crystals. During the

56 sintering process, these micro/nano-sized single crystals can be sintered together with a very high anisotropy.

In the case of combining solvo-thermal with SPS route [81], the pure phase SnSe single crystals with a preferred orientation along the (100) surfaces can be obtained, with an average size of less than 5 μm. This led to a high anisotropy of the corresponding bulks, in which σ was greatly improved in the entire temperature range because of the increased n up to ~1×1019 cm-3 [81]. An enhanced S2σ was obtained and κ was lower than 1 W m-1 K-1 [81]. As a result, higher ZT were achieved in a relatively wide mid- temperature range, which reached 0.44 at 522 K and 0.5 at 573 K [81]. These averaged

ZT values are higher than these reported averaged ZT values for single crystals [61]. To further increase the anisotropy and improve n, through combining the solvo-thermal with SPS route [91], a very high peak ZT of ~1.36 at 823 K was achieved [91]. The synthesized SnSe crystals (Sn0.98Se) have a preferred orientation along (100) surfaces with a much larger average size of >100 μm [91]. As a result, the anisotropy of synthesized products is much stronger. In addition, Sn vacancies of the synthesized

19 -3 SnSe crystals (Sn0.98Se) resulted in a large enhanced n of ~1.5 ×10 cm at 823 K, which in turn led to a high of ~72.4 S cm-1, a high S of ~309.9 μV K-1 and a low κ of

~0.42 W m-1 K-1 at 823 K [91]. Consequently, a very high peak ZT of ~1.36 was achieved [91]. Alternatively, Se vacancies can lead to n-type polycrystalline SnSe1-x, but the thermoelectric performance was quite low [86].

Figure 28 summarizes the recent obtained temperature-dependent thermoelectric properties (σ, S, S2σ, κ, and ZT) for undoped polycrystalline SnSe prepared by different texturing routes discussed above. All properties were measured along the ⊥ direction.

As can be seen, all textured un-doped polycrystalline SnSe presented p-type thermoelectric properties. Figure 28(f) presents the comparison of peak and average ZT

57 values of the obtained polycrystalline SnSe fabricated by different techniques, in which a peak ZT = 1.36 and an average ZT = 0.68 were achieved through the combination of the solvo-thermal with SPS route [91], both represent the highest values. Table 7 summarizes the comparisons of thermoelectric performance for undoped polycrystalline

SnSe until now. As can be seen, most of the ZT values are low than 1.5, indicating that new methodologies are highly needed to be developed.

5.4 Doping and alloying

In order to decouple σ, S, S2σ, and κ to realize a high ZT value for polycrystalline SnSe, doping is a useful method to tune n [119, 128, 258, 267-269, 274, 277-279] via controlling vacancies [280]. Besides, doping can also transfer the polycrystalline SnSe from p-type to n-type [259, 281, 282]. For p-type doping, the dopants used include alkali metals (Li [283], Na [258, 270, 274, 283-286], and K [67, 270, 283]), II-A group alkali earth metals (Ca [127], Sr [127], Ba [127]), I-B group metals (Cu [127, 269, 287],

Ag [268, 275-277, 288]), II-B group metals (Zn) [127, 262], III-A group metals (Al

[269], In [269, 279], Tl [278]), IV-A group elements (Ge [127, 289-291], Pb [269, 286]),

VI-A group metalloid (Te) [128, 232, 267], and lanthanides (Sm [292] and LaCl3

[293]). For n-type doping, the dopants include halogens (Cl [235, 281], Br [294], and I

[259]), V-A group metals (Bi) [281]. Sometimes multiple dopants were used, such as p- type Sn0.99Na0.01Se0.84Te0.16 [128] and n-type Sn0.74Pb0.20Ti0.06Se [295]. Most of the dopants were used to substitute Sn sites to tune n, while Te was used to substitute Se sites [128, 267].

5.4.1 Alkali

Because each alkali (such as Li, Na and K) atom has 1 valence electron, and in SnSe, each Sn atom has 2 valence electrons, alkali metals are used to achieve p-type doping.

Considering the alkali metals possess high activity, it is a challenge to dope them into

SnSe via solution routes such as hydro- or solvothermal method. Thus, melting routes are frequently used to realize alkali metal doping.

Practically, Na-doping is the most frequently used for alkali doping. As shown in Table

6, n was increased to ~2.7×1019 cm-3 in 2 at. % Na-doped SnSe samples prepared by melting and hot-pressing [258]. Along the // direction, a peak ZT of ~0.8 was achieved via doped with 1.5 % Na due to the obtained low κ of ~0.33 W m-1 K-1 at 773 K [258].

Such a low κ value derived from the induced point defects. For K-doping, K0.01Sn0.99Se polycrystals were prepared by combining mechanical alloying and SPS [67]. The maximum S2σ was enhanced significantly from ~2.8 μW cm-1 K-2 for undoped SnSe to

~3.5 μW cm-1 K-2 for K-doped SnSe [67]. The absence of Sn oxides at grain boundaries and nanoprecipitates contributed to an ultralow κ of ~0.24 W m-1 K-1, resulting in a peak

ZT of ~1.1 via doping with 1 % K at 773 K along the ⊥ direction [67]. In the case of Na and K co-doping [270], the energy offsets of multiple valence bands in SnSe were decreased via Na-doping and further reduced by (Na, K) co-doping, resulting in an

2 -1 -2 enhancement in S and an increase in S σ to 4.92 μW cm K . In this case, κl of polycrystalline SnSe was decreased by the introduction of effective phonon scattering centres such as point defects and anti-phase boundaries, which decreased to as low as

0.29 W m-1 K-1 at 773 K [270]. Thus, a high peak ZT of 1.2 was obtained for 1 % (Na, K) co-doped SnSe [270]. In another Li-doped case, S2σ of ~4 μW cm-1 K-2, κ of ~0.7 W m-1

K-1 and peak ZT of ~0.5 were obtained at 800 K through combining melting and SPS

[283].

5.4.2 I-B and II-B group metal

Similar to alkali metals, I-B group metals (such as Cu and Ag) have 1 valence electron in each atom, so that I-B group metals are also good candidates to realize the improvement of thermoelectric performance by p-type doping. Different from alkali

59 metals, I-B group metals such as Cu have been demonstrated to be able to dope into

SnSe system via solution routes [296]. Thus, there are more choices for the doping of I-

B group metals during synthesis process. Besides, other metals such as II-B group metals (Zn) were used to realize the p-type doping.

For the case of Cu doping, by employing conventional fusion method followed by SPS,

2 % Cu doped SnSe showed an enhanced peak ZT of ~0.7 ± 0.02 at 773 K [269]. This enhancement primarily derived from the presence of Cu2Se second phase associated with intrinsic SnSe nanostructures. A high n of 1.84×1020 cm-3 was achieved via Cu- doping, contributing a moderate σ of ~20 S cm-1 and a moderate S of ~250 μV K-1 at

773 K [269]. However, κ was very low (~0.3 W m-1 K-1 at 773 K) [269], thus a good peak ZT was achieved. In another case of doping with Cu, Sn1-xCuxSe (x = 0 – 0.03) was obtained by combining melting with high pressure (6.0 GPa) sintering, in which

2 -1 -2 maximum S σ and ZT values were 3.78 μW cm K and 0.79 for Sn0.97Cu0.03Se at 823

K, and the obtained κ was relatively low (~0.4 W m-1 K-1) (HPS) [287].

For the case of Ag doping, by employing conventional melting method followed by SPS

[277], a peak ZT of 0.74 was achieved via doping with 1 % Ag at 823 K [277], in which the doped Ag can tune n to a high value of 1.9×1019 cm-3 at room temperature, resulting in a high S2 of ~6.0 μW cm-1 K-2 at 823 K. For another case of Ag doping, undoped

SnSe polycrystals with novel nanolaminar structures have been fabricated via conventional solid-state reaction at high temperature [275]. The phase transition contributes to the enhancement of n and phonon scattering above 600 K, and the nanolaminar polycrystals significantly improved the performance via promoting μ and simultaneously strengthening the phonon scattering [275]. 1.5 % Ag-doped nanolaminar

2 -1 -2 SnSe polycrystals realized in a high S of ~6.0 μW cm K , an extremely low κl of

0.23 W m-1 K-1, and a high peak ZT of 1.3 at 773 K [275].

For the case of doping with II-B group metals (such as Zn) [262], through combining traditional melting with hot-pressing route, the obtained Zn0.01Sn0.99Se polycrystals showed a peak ZT of ~0.96 at 823 K [262]. Zn dopants can decouple and S to achieve a high S2 of ~8.0 μW cm-1 K-2 via tuning n to an appropriate value of ~4.5×1018 cm-3.

5.4.3 Halogen

Because the valence state of halogens (such as Cl, Br and I) is -1 in most compounds, and Se in SnSe always present -2, halogens are good candidates to tune n for p-type doping, as well as realize the n-type doping. Considering halogens possess high reactivity, similar to the alkali metals, they are difficult to be doped into SnSe via solution routes such as hydro- or solvo-thermal method. Thus, melting routes are frequently used to realize halogen doping.

For realizing p-type Cl-doping, solid-state reaction was used to fabricate SnSe0.985Cl0.015

2 polycrystals using precursors of Sn, Se and SnCl2 [275]. From which, a high S of ~4.5

μW cm-1 K-2 and a low κ of ~0.23 W m-1 K-1 were achieved, leading to a high peak ZT of 1.1 at 773 K [275]. On the other hand, n-type Cl doping can be realized from the aqueous solution method for the facile synthesis of Cl-doped SnSe nanoparticles [235].

After sintering by hot-pressing, a low σ of ~4 S cm-1 and a moderate S of ~-300 μV K-1 were obtained, resulting in a low S2σ of ~0.02 μW cm-1 K-2 at 540 K. Although such thermoelectric performances are low, this study provided a simple, rapid, and low-cost method to fabricate n-type SnSe thermoelectric materials. In the case of n-type BaCl3- doping, SnSe0.95-BiCl3 compounds were synthesized through melting with SPS, in which a peak ZT of ~0.7 was obtained via doping with 0.4 % BiCl3 at 793 K [281]. In

2 -1 -2 this case, doped BiCl3 can decouple σ and S to achieve a high S σ of ~5.0 μW cm K .

Except Cl, Br and I were also used as n-type dopants. PbBr2-doped polycrystalline SnSe has been synthesized using the combination of melting with hot-pressing and has an

61 improved n of 1.86×1019 cm-3 [294]. Consequently, an increased σ of 40 ± 2 S cm-1 and a high S2σ of ~4.8 μW cm-1 K-2 were achieved at 713 K [294]. Since κ of ~0.7 W m-1 K-1 was relatively high, a moderate peak ZT of 0.54 ± 0.1 was obtained at 793 K along the

⊥ direction. By using melting and hot pressing, n-type I-doped SnSe polycrystals can be obtained [259]. The 3 % I doped SnSe has a peak ZT of ~1.0 due to the obtained high

S2σ of ~3.9 μW cm-1 K-2 and a low κ of ~0.3 W m-1 K-1) at 773 K [259].

5.4.4 IV-A and VI-A group

Sn belongs to the IV-A group, and Se belongs to the VI-A group, so that IV-A group elements (such as Ge and Pb) can substitute Sn atoms, and VI-A group elements (such as S and Te) can substitute Se atoms during the doping. These dopants can induce point defects, leading to further improvement of the thermoelectric performance of SnSe.

For example, Ge-doped nanostructured SnSe has been prepared by an arc-melting method [289]. This Ge-doped nanostructured SnSe shows a semiconductor behavior with resistivity values higher than that of the pure SnSe compound, because Ge does not donate carriers [289]. However, S has been improved significantly and reaches to a value of 1000 μV K-1 with a low Ge-doping level [289]. Due to a high density of point defects caused by Ge-doping, the obtained κ was extremely low to be ~0.1 W m-1 K-1 at

385 K. For another case of Ge-doping, polycrystalline Sn1-xGexSe were fabricated using a solid solution route [290]. The doping of Ge has a mild effect on the reduction (~0.5

-1 -1 2 W m K at 800 K for Sn0.92Ge0.08Se), while S σ was significantly deteriorated (1.87

-1 -2 μW cm K at 823 K for the Sn0.92Ge0.08Se), leading to a peak ZT of 0.6 for

Sn0.96Ge0.04Se at 823 K. On the contrast, in the other Ge-doped case [291], it was found that Ge is not a suitable dopant because the peak ZT of Sn0.97Ge0.03Se was only 0.15 at

773 K although a decreased κ of ~0.25 W m-1 K-1 at 773 K was observed.

In terms of VI-A group doping, Te has been widely used. For an example, SnSe0.98Te0.02 has been fabricated by a simple and rapid high pressure and high temperature (HPHT) method [119]. By narrowing the bandgap of SnSe to 0.746 eV, a moderate S of ~330 μV

K-1, as well as a maximum S2 of ~1 μW cm-1 K-2 were obtained at 3 GPa. For other case of n-type Te-doping, SnSe0.9375Te0.0625 bulks were fabricated by melting method

[267]. The bandgap of SnSe reduced from 0.643 to 0.608 eV after Te-doping [267], but a low of ~3.5 S cm-1 and a moderate S of ~-270 μV K-1 led to a low S2 of ~0.7 μW cm-1 K-2 at 673 K. Recently, a facile microwave-assisted solvo-thermal method has been used to fabricate large-scale SnSe1-xTex nanoplates [232]. After sintering via SPS, both peak ZT of 1.1 at 800 K and an average ZT of 0.56 from 300 to 800 K were achieved in

-1 -1 the p-type SnSe0.9Te0.1 pellet. The reduced κ of ~0.52 W m K at 800 K was attributed to the enhanced phonon scattering by point defects, and the enhanced S2 of ~6.8 μW cm-1 K-2 was caused by the secured high preferential orientation and the increased n of

1×1019 cm-3 [232].

To summarize, Figure 29(a-e) shows the main temperature-dependent thermoelectric properties (σ, S, S2σ, κ, and ZT) for undoped [65] and doped with 1.5 % Ag [275], 1 %

(Na, K) [270], 1 % Te [232], 1 % Ge [290], 1 % Zn [262], 0.4 % BiCl3 [281] and 3 % I

[259] polycrystalline SnSe, and the more detailed thermoelectric performances of doped polycrystalline SnSe are summarized in Table 8. As can be seen, most of the dopants can enhance σ in a wide temperature range by tuning n, resulting an improvement in S2σ.

It should be noted that compared with undoped polycrystalline SnSe, most of the dopants can further decrease κ in a wide temperature range (between 323 K and 773 K).

In fact, the induced dopants can achieve large quantities of point defects and/or nanoprecipitates, which cause strain fields around substituted Sn or Se atoms and/or nanoprecipitates. In this respect, phonon scattering effects can be strengthened, leading

63 to decreasing κl [61]. Figure 29(f) presents a comparison of peak and average ZTs for polycrystalline SnSe doped with different dopants, and shows that a peak ZT of 0.98 and an average ZT of 0.49 via doped with 1 % K [67] both represent the highest values.

These results indicate that doping is a promising method to enhance the thermoelectric performance of polycrystalline SnSe, as well as a convenient way to realize n-type thermoelectric materials with a high thermoelectric performance for polycrystalline

SnSe.

5.5 Inclusions

The introduction of appropriate inclusions in polycrystalline SnSe can achieve a high peak ZT in SnSe system [84, 276]. Many different types of inclusion, such as second phase (SnSe2 [84] and Se nanowires [297]), nanoprecipitates (rock-salt-type SnSe [141] and Sn oxides [67]), simple substance (carbon black nanoinclusions [298]), compounds

(SnS [129, 299], 2D-MoSe2 [300]) and compounds (SiC [259] and PbTe [301]) have been developed in SnSe. Sometimes multiple inclusions, such as (MoS2 + graphene) also developed [85]. In some case, both dopant and inclusion were induced at the same time, such as p-type SnTe/Ag0.005Sn0.995Se composites which was SnSe doped with 0.5 %

Ag and incorporated with 0.5 mol % SnTe [276]; Ag0.01Sn0.99Se1−xSx compounds which was SnSe doped with 1 % Ag and incorporated with SnS [302]; and n-type

(Sn0.9Se0.87I0.03)(SnS)0.1 which was 90 % SnSe doped with 3 % I and alloyed with 10 %

SnS [257]. SnSe can also be treated as inclusion in other thermoelectric materials systems, such as (Cu2Se)0.97(SnSe)0.03 [303], and (PbSe)0.9(SnSe)0.1 [257].

It is difficult to compare the thermoelectric performance of inclusion/SnSe composites because the induced inclusions show different mechanism. In this respect, we only briefly summarize some typical cases here.

5.5.1 Solid solution and co-synthesis

Due to the extremely low κ, solid solution, such as SnS–SnSe [129], PbSe–SnSe [284] and SnTe–SnSe [304] system, shows a potential way to optimize thermoelectric performance [129]. SnS shows analogous band structure and electrical properties with

SnSe, making SnSe to be a good candidate to form solid solution such as SnS–SnSe system. In SnSe–SnS solid-solution, a low κ of ~0.3 W m-1 K-1, a high S of ~600 μV K-1, and a peak ZT of 0.82 was achieved for SnS0.2Se0.8 at 823 K via melting route [129].

Besides, the solid solution system also exhibited anisotropic thermoelectric performance along the // and ⊥ directions [129]. Other case showed that by mechanical alloying followed by SPS, SnS1-xSex solid solutions also exhibited anisotropic thermoelectric performance [299]. The κ decreased with increasing the Se content and fell to 0.36 W

-1 -1 2 m K at 823 K for the composition SnS0.5Se0.5 [299]. The optimized S of ~3.7 μW cm-1 K-2 and the reduced κ of ~0.5 W m-1 K-1 resulted in a peak ZT value of 0.64 at 823

K for SnS0.2Se0.8 along the // direction [299]. Except for the SnSe–SnS solid-solution system, single-phase SnSe–PbSe solid-solution (Sn1-xPbxSe) was obtained via alloying

-1 -1 [284]. κl was reduced from 1.4 to 0.85 W m K by 12 at. % PbSe alloying, derived from the strain and mass fluctuations [284]. Interestingly, S and n were nearly unchanged by Pb substitution, indicating a constant m* and an undisrupted VBM [284].

Except for solid-solution, the SnSe–PbSe system can be achieved via hydro-thermal route [84]. During hydro-thermal synthesis process, SnSe and PbSe were synthesized together at the same synthesis conditions [84]. A maximum ZT of ~1.7 was achieved for

1 % PbSe/SnSe composites [84] due to a high S2σ of ~8.9 μW cm-1 K-2, as well as a low

κ of ~0.25 W m-1 K-1 at 873 K [84]. Such high S2 is derived from the induced PbSe phase and such low κ is attributed to the enhanced phonon scattering at all-scale hierarchical architectures (from the nanoscale precipitates to mesoscale grains) [84].

5.5.2 Coupled with doping and multiple inclusions

To improve the thermoelectric performance of SnSe, both dopant and inclusion are induced in SnSe system and multiple inclusions have been developed [84, 276, 305,

306]. For the case of inducing both Ag as dopant and SnTe as inclusion, a peak ZT of

1.6 with a high of ~112.3 S cm-1 and a high S2σ of ~11 μW cm-1 K-2 at 875 K was achieved for 0.5 mol % SnTe/Ag0.005Sn0.995Se composites [276]. In Ag0.005Sn0.995Se fabricated via solution method [276], the 0.5 % doped Ag resulted in n of ~3.99×1018 cm-3 at room temperature [276], and the induced 0.5 mol % SnTe resulted in enhanced

2 -1 -2 -1 -1 S σ of ~11 μW cm K and reduced l of ~0.4 W m K [276] at 875 K. Furthermore, these polycrystalline composites have high peak ZT (> 1) from 800 to 900 K and good experimental repeatability [276]. For the SnSe-PbSe solid-solution with Na as dopant

[84], a maximum ZT of ~0.7 was achieved for Sn0.88Pb0.12Se–1 % Na [276] due to a high n of ~6.5×1019 cm-3 adjusted via the doping of Na and relative a low κ of ~0.5 W m-1 K-1 derived from the solid-solution.

For the case of multiple inclusions, by rapid induction melting followed by rapid hot- pressing, a peak ZT of 0.98 and a low κ of ~0.39 W m-1 K-1 were achieved at 810 K for

3.2 wt % MoS2/graphene/SnSe composites [85]. Such low κ derived from the induced layered MoS2 + graphene composites [85]. For the case of inducing 2D-materials

(MoSe2) [300], by the solid solution method followed by SPS, introducing 2D-MoSe2 into SnSe matrix achieved a high n of ~2×1019 cm-3 without distinctly deteriorating κ

[300], leading to a peak ZT of 0.5 at 773 K [300].

To summarize, Figure 30(a-e) plots temperature-dependent thermoelectric properties (σ,

2 S, S σ, κ, and ZT) for pure SnSe [65], (SnSe)0.8(SnS)0.2 [129], 0.5 mol % SnTe +

Ag0.005Sn0.995Se composites [276], 1 % PbSe + SnSe composites [84], 3.2 wt %

MoS2/graphene + SnSe composites [85], and 1.5 % MoSe2 + SnSe composites [300]

66 discussed above. Figure 30(f) also presents a comparison of the peak and average ZTs for polycrystalline SnSe incorporating with different inclusions, and shows that a peak

ZT of 1.72 presents the highest value via incorporating with 1 % PbSe [84], and an average ZT = 0.62 presents the highest value via incorporating with 0.5 % mol SnTe and doped with 0.5 % Ag [276]. Table 9 also summarizes the thermoelectric performance of polycrystalline SnSe incorporated with different inclusions in more detail.

6. Two-Dimensional SnSe

The initial investigations on two-dimensional (2D) thermoelectric materials [307, 308] predicted that the quantum confinement effect of electronic carriers in low-dimensional materials can enhance S2σ [307, 308]. In Section 6, we discuss the structural characteristics of monolayer SnSe in detail, and summarize the recent advances in 2D

SnSe-based thermoelectric materials, such as thin film, nanosheets, and organic/inorganic composites.

6.1 Monolayer

As discussed above, SnSe is a layered structure [309-311] with a narrow bandgap [197].

A monolayer of SnSe sheet exhibits low formation energy (about 200 meV per atom) due to the interlayer weak van der Waals force and strong covalent bonds within the layer [312]. It should be easy to extract a monolayer SnSe sheet from its bulk material without any substrates [130]. In addition, monolayer SnSe has a large negative

Poisson’s ratio of ~0.17, which may act as a 2D auxetic material [313]. In this respect,

SnSe has full potential to present a high ZT value for a single-layered SnSe sheet [314].

6.1.1 Lattice configuration

Figure 31(a) illustrates an optimized configuration of monolayer SnSe [130], and shows a highly puckered honeycomb structure [130, 315], which is similar to graphene [316].

Monolayer SnSe possesses Pm21n symmetry with an orthogonal lattice [130], which is a

67 lower symmetry than that of its bulk counterpart due to the lack of an inversion symmetry [130]. The zigzag (marked as b) and the armchair (marked as c) axes are denoted in Figure 31(a). The calculated lattice parameters are 4.307 Å and 4.362 Å respectively along the b- and c-axes [130]. Figure 31(b) shows a side view of this configuration. Other results show that the lattice parameters are 4.29 Å and 4.46 Å respectively along the b- and c-axes [317], which is similar to the results above.

The difference of lattice parameters between b and c may be responsible for the strong anisotropic properties [313], similar to phosphorene [100, 318, 319]. The region in

Figure 31(a) characterized by the dashed chart is the primitive unit cell of monolayer

SnSe, which contains two Sn atoms and two Se atoms [130]. Calculations based on

DFT show that monolayer SnSe is dynamically stable [320], and calculations based on

AIMD simulations show that monolayer SnSe is thermally stable in a wide temperature range from 300 to 900 K [130].

Figure 31(c) shows 2D charge density of monolayer SnSe [313] illustrated in the bc plane crossing all Sn atoms. The red and blue colors depict the high and low charge density, respectively. The unit of charge density is e bohr-3. The electron density exhibits an obvious symmetry along the b- and c-axes, confirming that the electrons move in square-like potential [313]. The electron density around Se atoms is obviously higher than that of Sn atoms, indicating that electrons transfer from Sn to Se atoms. It may be owing to the large difference of electronegativity of Se and Sn atoms, implying that the Sn-Se bond may be a polar covalent bond with a strong polarity. Besides, a high electron density is found between the nonbonding neighboring Sn and Se atoms, revealing that strong nonbonding interactions exist between them, which are weaker than the Sn-Se bond but are still much stronger than common van der Waals interaction.

6.1.2 Electronic structure

The electronic band structures of monolayer SnSe are different from their bulk counterparts [321]. Figure 31(d) shows the calculated the electronic band structure of the monolayer SnSe [130] based on Perdew–Burke–Ernzerhof (PBE) functional within generalized gradient approximation (GGA) [322] (blue dashed line) and the Heyd–

Scuseria–Ernzerhof (HSE06) functional [323] (red solid line), and the corresponding

DOS [130]. The VBM is located on the Γ–Y path, while there exists two energetically nearly degenerate CBMs, one is on the Γ–Y path, and the other is on the Γ–X path. Both

VB and CB have a typical characteristic of pudding mold [241, 324, 325], which consists of a dispersive portion with some corrugations and a highly dispersive flat portion, resulting in multiple Fermi surfaces and in turn contributing to a high S and σ

[130].

For the bandgap, calculations based on the GGA–PBE functional suggests that the monolayer SnSe is a quasi-direct-bandgap semiconductor with a bandgap of 0.914 eV

[130], which is larger than that of the bulk SnSe (0.83 eV for α-SnSe and 0.46 eV for β-

SnSe) [179] due to the weak interaction between the layers. Meanwhile, calculations based on the HSE06 functional with 25 % Fock exchange [130] predicted a more accurate bandgap of 1.28 eV for monolayer SnSe, much larger than that calculated using PBE functional [130]. Such a large bandgap of monolayer SnSe can effectively suppress the bipolar conduction at high temperature, which may improve its thermoelectric performance [130, 326]. By using first-principles DFT calculations, the band structure and bandgap of a few layer SnSe (such as bilayer SnSe) were also calculated and showed that the interactions between layer play a major role in the direct- indirect bandgap transition [327]. Table 10 summarizes the bandgap data of 2D SnSe and related calculation methods, which showing similar values.

6.1.3 Influence of strain

To understand the impact of strain on the band structure of 2D-SnSe, Figure 32(a) and

32(b) show the band structures calculated by mBJ method under uniaxial strain from -

10 % to 10 % along the b- and c-axes [313]. The VBMs (VX and VY) are indicated by small filled circles and squares, and the CBMs (CX and CY) are indicated by small unfilled circles and squares, respectively. From the theoretical simulations, with increasing the compressive strain along the c-axis, CX moves down and VY moves up, resulting in a shrinking indirect bandgap. With increasing the tensile strain along the c- axis, CX moves up and VY moves down, while VX and CY are nearly stable, resulting in a nearly intact indirect bandgap. With increasing the compressive strain along the b-axis,

CX moves up and VY moves down, while VX and CY are nearly stable, resulting in a nearly intact indirect bandgap. With increasing the tensile strain along the b-axis, CX moves down and VY moves up, resulting in a shrinking indirect bandgap.

Figure 32(c) and 32(d) show the energies of CY, CX, VY, and VX as a function of strain along the b- and c-axes [313]. The compressive strain along the b-axis affects the same way as the tensile strain along the c-axis, and vice versa. Here, VX is always stable whenever the compressive and tensile strains are applied along the b- or c-axes. CY acts similarly when the tensile strain along the c-axis or the compressive strain along the b- axis is applied. VY and CX are always sensitive and have nearly linear response to any strain, showing an anisotropic response of electronic structures to the strain [313]. In

Figure 32(c) and 32(d), the colored areas marked by II and V correspond to the direct bandgap, while I, III, IV and VI represent the indirect bandgap. A strain-induced direct - indirect bandgap transition can be observed. It is clear that a low strain can give rise to diverse electronic structures, which makes 2D-SnSe an excellent 2D semiconductor material for the strain band engineering [328, 329].

6.1.4 Performance forecasting

Similar to bulk (3D) SnSe thermoelectric materials, modelling is essential for predicting thermoelectric performance for 2D-SnSe sheets. Figure 33(a-c) show the calculated S, σ,

2 and S σ as a function of chemical potential (μe) along different directions at different temperatures [130], in which the calculations were based on BTE using the BoltzTraP code [130]. Figure 33(a) shows that S varies dramatically with μe, indicating that an optimal n is beneficial to achieve efficient thermoelectric performance. S decreases rapidly with increasing the temperature due to a bipolar conduction effect or the excitation of carriers with both positive and negative charges, suggesting an increasing inverse Hall coefficient [130]. The peak S for n-type monolayer SnSe were - 2150 μV

K-1 along the b-axis and - 2080 μV K-1 along the c-axis at room temperature [130], and the peak S for p-type monolayer SnSe were 2160 μV K-1 along the b-axis and 2200 μV

K-1 along the c-axis at room temperature [130], respectively. These enhanced S nearly four times when compared with that of the bulk SnSe [61]. Such remarkable enhancement of S can be ascribed to the quantum confinement effect which induces sharp DOS peaks near the Fermi energy [130]. Figure 33(b) shows that is less sensitive to temperature [130]. With increasing μe, increases drastically. Simulations based on extensive ab-initio calculations show a very high hole mobility (10000 cm2 V-1 s-1) for monolayer SnSe [313]. Consequently, as shown in Figure 33(c), S2σ of monolayer SnSe (~250 μW cm-1 K-2 along the b-axis and ~275 μW cm-1 K-2 along the c- axis at 700 K) [130] were much larger than that of bulk SnSe materials [61]. Other calculations based on DFT combined with Boltzmann transport theory showed that for

2 -1 -1 SnSe monolayer, along the c-axis , the carrier mobility μx was 1035.84 cm V s , 621.5 cm2 V-1 s-1, and 443.93 cm2 V-1 s-1 at 300 K, 500 K, and 700 K, respectively, and the

* effective mass m x was 0.15 me [317]; along the b-axis, the carrier mobility μy was

965.23 cm2 V-1 s-1, 579.13 cm2 V-1 s-1, and 413.6 cm2 V-1 s-1 at 300 K, 500 K, and 700 K,

* respectively, and the effective mass m y was 0.16 me, which was close to that of along the c-axis [317]. The calculated peak S was 1750 μV K-1 at 300 K [317].

For the calculations of thermal transport properties of monolayer SnSe, Figure 33(d) shows that e exhibits trends similar to σ due to the relationship of κe = LσT, where L was approximated to 1.5×10-8 W Ω K-2 in the case of non-degenerate semiconductors limited by phonon scattering [241]. Figure 33(e) shows the temperature dependence of

-1 axial κl, which is satisfied with the relationship of κl ∝ T , indicating that anharmonic phonon–phonon interactions are dominant in the phonon scattering [330]. The

-1 -1 -1 -1 calculated κl was ~2.5 W m K along the b-axis [130] and ~2.02 W m K along the c- axis at room temperature [130]. Extensive ab-initio calculations showed that SnSe

-1 -1 monolayer possessed an ultralow κl (< 3 W m K at 300 K), making it probably the most heat-insulating and flexible material in known 2D atomic materials [313]. The low intrinsic κ is a combined consequence of the heavy constituent elements and the low atomic coordination [130]. The calculated average γ values along the b- and c-axis were

1.65 and 2.03, respectively [130]. However, it should be noticed that the κl calculated for a monolayer SnSe [130] was much higher than that of the bulk counterpart [61, 65].

This is because the real bulk SnSe has many other scattering sources, such as boundary, defect, and impurity, while monolayer SnSe loses the distorted SnSe7 polyhedra structure [61], weakening the anharmonicity. Figure 33(f) shows the ZT value of monolayer SnSe as a function of μe at different temperatures [130]. At 700 K, the peak

ZT values of 2.47 at μe = -0.62 eV and 2.76 at μe = 0.575 eV along the b-axis [130], and the peak ZT values of 2.51 at μe = -0.63 eV and 3.27 at μe = 0.54 eV along the c-axis were predicted [130]. The calculated ultrahigh peak ZT values indicated a great potential for monolayer SnSe as a 2D high performance thermoelectric material [130].

6.2 Recent advances

Until now, it has been successfully fabricated macro-sized 2D-SnSe materials (such as

SnSe film), however its application is still a challenge in the thermoelectric device. For micro/nano-sized 2D-SnSe materials (such as SnSe nanosheets [331-334]), both the fabrication technique and the application are under exploration. This section will discuss the recent advances in the fabrications and applications of 2D-SnSe materials.

6.2.1 Films

For fabricating SnSe films, the synthetic methods are relatively mature, including atomic layer deposition (ALD) [335], brush plating technique [336], simple bath deposition [337-339], thermal evaporation method [340-346], solution method [347,

348], hot wall epitaxy technique [349-351], flash evaporation method [352, 353], vacuum deposition technique [309, 354-357], chemical deposition technique [358], pulsed laser deposition (PLD) [359-366], spray pyrolysis technique [367], and electrodeposition technique [368-372]. Most of the fabricated films are orthorhombic α-

SnSe while rock-salt structure (111) SnSe film was also grown with molecular beam epitaxy (MBE) technique on Bi2Se3 surface [273]. Figure 34(a) reveals XRD patterns of a bare SrTiO3 (STO) substrate, a 5 quintuple-layer (QL) Bi2Se3 film on STO substrate and a 16 nm SnSe film grown on Bi2Se3 film on STO [273]. Figure 34(b) shows the

STM image of a 7 nm SnSe film (60 nm × 60 nm) [273]. The inset shows the line profile along the black line. The STM-measured step height, well consistent with the peak, corresponds to a spacing d = 3.37 Å shown in Figure 34(a). Figure 34(c) shows the cross-section HRTEM image of a 16 nm SnSe film grown on 5 QL Bi2Se3 film

[273]. The SnSe film shows an obvious bilayer structure with the lattice constants along the and directions being 4.19 Å and 3.37 Å, respectively [273].

Figure 35(a) shows the XRD patterns taken from SnSe thin films deposited at a normal angle and at an 80° glancing angle [359]. For the thin film grown at a normal angle, the strong diffraction peaks of (200), (400) and (800) indicate that SnSe films were preferentially grown along the a-axis during the depositing process. For the thin film grown with a glancing angle, (200) and (800) diffraction peaks are not present, suggesting that the growth direction and orientation is not preferred. Figure 35(b) and

35(c) shows the cross sectional SEM images of film deposited at normal angle and glancing angles [359], respectively. It is clear that the film deposited at a normal angle possesses large grains, while the film grown at a glancing angle shows a nanopillar structure rather than a continuous film on the substrate, and the nanopillars are grown with a relatively high density. The thickness of SnSe thin film grown with the normal angle can be estimated as ~730 nm , while it is ~300 nm for its counterpart [359].

In terms of the property measurements (such as S, , and ), the Harman transient method [373-375] and the time-domain thermos-reflectance (TDTR) method [376-378] were widely used. To study the thermoelectric performance of SnSe films deposited at different angles, Figure 35(d-g) show σ, S, S2σ and out-of-plane κ [359]. It suggested that the film deposited at a glancing angle possesses much better σ, S, and S2σ than that deposited at normal angle with the entire temperature, as well as lower κ before 300 K.

A high S of 498.5 μV K-1 and a high S2σ of 18.5 μW cm-1 K-2 [359] were achieved. The results reveal that the glancing angle deposition can greatly reduce the grain size of the thin film and significantly enhance S and S2σ. The enhanced thermoelectric property can be attributed to the potential barrier scattering at grain boundaries owing to the reduced grain size and increased grain boundaries in the film [359].

Other studies showed that p-type SnSe thin films possess good thermoelectric performance at low temperature [357]. Figure 36(a) shows Raman spectrum of the SnSe

-1 thin film [357]. The peak at 108 cm corresponds to B3g vibration mode and the peaks

-1 at 130 and 150 cm both correspond to Ag vibration mode, which all belong to α-SnSe

[379]. Figure 36(b-f) show temperature-dependent thermoelectric properties for thin

SnSe film [357]. At 42 K, SnSe thin film exhibited an ultrahigh S of ~7863 μV K-1, as well as a good S2σ of ~7.2 μW cm-1 K-2, resulting in a high ZT of ~1.2 [357]. The ultrahigh S observed below 84 K should derive from the effect of phonon drag on charge carriers, which results from the interaction of phonons with mobile carriers and both the electrons and phonons contribute to the remarkable rise in S [357, 380]. These results showed that SnSe thin film can be considered as an ideal material for low temperature thermoelectric applications. For n-type SnSe thin film [381, 382], a new cross-plane thermoelectric measurement was conducted and applied on the measurement of (SnSe)x(TiSe2)x (x =1, 3, 4, 5) [381], the cross-plane S decreased from -

31 to -2.5 μV K-1 with x decreased from 5 to 1 [381]. SnSe films prepared by spray pyrolysis technique [367] also showed a low thermoelectric performance. More studies are undertaking to further improve the properties of n-type SnSe thin films.

6.2.2 Nanosheets

Nanosheets generally possess thicknesses of multiple Sn-Se monolayers and each monolayer has a thickness of 5.75 Å [383]. For SnSe nanosheets with fewer layers

(such as bilayer [384]), historically, the phase-controlled synthesis is a challenge [348].

In 2013, a single-crystalline SnSe nanosheet with four-atomic thickness was synthesized for the first time [385]. In 2014, a phase-controlled method was employed to synthesize

SnSe nanosheets [348]. Since then, significant progress has been made in fabricating

SnSe nanosheets and exploring their thermoelectric applications.

By a two-step synthesis method, synthesized first by Chemical vapour deposition (CVD)

[386-388] method and subsequently followed by a nitrogen etching technique, both

75 multi-layered nanosheets and monolayer SnSe were obtained on the SiO2/Si substrate

[334]. Figure 37(a) shows the AFM image and inserted SEM image of rectangular shaped SnSe nanosheets with lateral dimensions of about 30 μm × 50 μm, as well as a thickness of 54.9 nm, and Figure 37(b) shows the corresponding images of a SnSe monolayer with a thickness of 6.8 Å (tested by AFM), which is close to the theoretical value [334]. Figure 37(c) shows a HR-TEM image of monolayer SnSe with inserted

SAED pattern [334], indicating that the obtained monolayer has a typical orthorhombic structure of α-SnSe.

In terms of the electrical transport properties, electrical devices using individual rectangular shaped SnSe nanosheet were fabricated on a 300 nm SiO2/Si substrate, and the 50 nm Au and 50/10 nm Ag/Au contact electrodes were used [334]. Figure 37(d) show transport characteristic curves of the devices at Vds = 1 V for the SnSe/Ag and

SnSe/Au contacts, respectively; and insets show the corresponding optical images of the devices [334]. Both of them exhibited p-doped ambipolar characteristics. The hole field- effect mobility at room temperature was estimated as ~0.11 and 0.16 cm2 V-1 s-1 for Ag- contacted and Au-contacted transistors, respectively; which are comparable to some

2 -1 -1 other 2D-thermoelectric materials such as ultrathin SnSe2 nanosheets (~0.6 cm V s )

[389] and multilayer GaTe nanosheets (~0.1 cm2 V-1 s-1) [390]. Figure 37(e-f) show the output characteristic curves of the devices made by the SnSe/Ag and SnSe/Au contacts at different Vg values, respectively [334]. The linear increase of the drain current (Id) with drain voltage (Vds) suggests an excellent ohmic contact at the source and drain electrode. These linear output curves also indicate the high electronic quality of the samples, and the device resistance of the nanosheets is estimated as ~15 MΩ [334].

Except for the electrical transport properties, the study of temperature-dependent Raman spectroscopy behavior shows that SnSe nanosheets have a high susceptibility to

76 temperature [386], as well as obvious anharmonic phonon properties [386]. Calculations based on first-principle DFT showed that the bandgap monotonically increased with the reduction of the nanosheet thickness [384], which indicated full potentials for use in thermoelectric applications. For other cases of the thermoelectric performance, SnSe nanosheets were obtained from a bulk SnSe ingot by pulverization, Li-intercalation, and exfoliation processes [391-394] in 2016, and a peak ZT of 0.32 was obtained from this

SnSe nanosheets [391]. Similar, SnSe1-xSx nanosheets are prepared from bulk by hydrothermal Li intercalation and subsequent exfoliation [331, 392-395]. The scattering of phonons at a number of atomic disorders and nanosized boundaries derived from the substitution of S atoms into SnSe and contributed to an effective reduction of κ and an improved peak ZT of 0.12 at 310 K [331]. The thermoelectric performance of 2D nanostructured SnSe still needs further improvement in their synthesis, characterization and thermoelectric performance.

6.2.3 Anisotropy behavior

In terms of the polarized Raman response and electrical transport studies, Figure 38(a) shows a measured optical image of a measured nanosheet, in which the crystallographic axes (y represents b-axis and z represents c-axis), the incident light polarization direction, and the angle θ between the incident light are indicated [387]. Figure 38(b) and 38(c) show the typical polarized Raman spectra of a SnSe nanosheet with different sample rotation angles excited using a 633 nm laser under parallel-polarization configuration and cross-polarization configuration [387], respectively. The polarized

Raman spectra exhibit an angular dependence that reveals the anomalous anisotropic

1 light−matter interaction of the crystal [387]. Because only four Raman modes (Ag , B3g,

2 3 Ag , and Ag modes) can be resolved in this case [387], Figure 38(d) shows the side views of the atomic displacements of these four modes, in which the two rows in the

77 figure represent two adjacent layers [387]. The calculated frequencies provided in parentheses are in good agreement with the experimental values [387]. Figure 38(e) shows the optical image of a typical SnSe nanosheet with 12 electrodes spaced at 30° apart [387], and Figure 38(f) shows the polar plot of the angle-resolved conductivity

[387]. The angle-dependent conductivity shows strong anisotropy, with a maximum conductivity along the zigzag direction and a secondary maximum conductivity along the armchair direction.

Other studies also demonstrated that SnSe nanosheets have obvious anisotropic electrical transport properties [383, 388]. A large anisotropic ratio of carrier mobility μx

/μy of ~5.8 between the b- and c-axes was obtained, which was a record high value reported for 2D anisotropic materials [383].

6.2.4 Organic/inorganic composites

Organic polymer thermoelectric materials, such as polypyrrole [396, 397], polythiophene [391, 398], and polyaniline [399, 400], are promising candidates due to their relatively high σ and intrinsically low κ. Among them, poly (3, 4- ethylenedioxythiophene):poly (styrenesulfonate) (PEDOT:PSS) is the most promising polythiophene-based material, which possesses remarkable high σ [401-404]. However, when compared with inorganic materials, the performance of PEDOT:PSS is restricted by relatively low S2σ deriving from low S [405]. To overcome these issues, inorganic fillers with high S, such as Bi2Te3 [406, 407] and PbTe [408], has been added into the system to improve S of conducting polymer-based thermoelectric materials, resulting in a kind of inorganic/organic composites. Among these inorganic candidates, SnSe possesses relative high S, high and very low κ, which is a good candidate for the role of a composite material.

To illustrate, Figure 39(a) shows a schematic representation of the overall fabrication procedure for various SnSe/PEDOT:PSS composites [332]. SnSe nanosheets were obtained from the SnSe ingot after Li-intercalation and following exfoliation [392, 393,

409], and then evenly distributed in the PEDOT:PSS matrix and affected the intrinsic conduction of the composites. In addition, the polar solvent treatment [410-412] applied to the prepared SnSe/PEDOT:PSS composites can further improve the thermoelectric performance [332]. Figure 39(b-d) show the thermoelectric properties (σ, S, S2σ and κ) as a function of the percentage of SnSe nanosheets for SnSe/PEDOT:PSS composite films [332]. With increasing the SnSe nanosheet content, although decreases to some extent, the S of SnSe/PEDOT:PSS composites increase significantly, leading to a high

S2σ at high SnSe content. σ and S can also be modeled as series-and parallel-connected composites in the simple case of a filler/matrix binary system [413, 414]. Meanwhile, κ also increased from ~0.22 W m-1 K-1 to 0.6 W m-1 K-1 [332]. To further enhance the thermoelectric performance of SnSe/PEDOT:PSS composites, various proportions of organic solvent (DMSO) were mixed with the different amounts of SnSe nanosheets dispersed PEDOT:PSS solutions. Figure 39(e-g) show thermoelectric properties (σ, S,

S2σ and κ) as a function of the DMSO content for varied SnSe/PEDOT:PSS composites

[332]. After the DMSO treatment, the SnSe/PEDOT:PSS composites exhibited a significant σ enhancement without considerable reduction of the S values. In addition, the composites with large amounts of PEDOT:PSS exhibited enhanced σ values, which mainly derived from the morphological changes of PEDOT:PSS in the composite structure occurring upon addition of the polar solvents [415]. As a result, S2σ of DMSO- treated composite films were considerably higher than that of the composite film without solvent treatment [332]. The 5 vol. % DMSO-treated SnSe_20/PEDOT:PSS

79 composite film had the maximum S2σ of ~3.86 μW cm-1 K-2, which is ~257 times higher than that of the pristine PEDOT:PSS film (~0.015 μW cm-1 K-2) [332].

7. Conclusion, Challenge, and Strategy

Compared with other traditional thermoelectric materials, SnSe-based thermoelectric materials are highly promising. SnSe consists of light elements and has a very small and simple unit cell, which is against the established rules for searching a promising thermoelectric material [64]. The record high ZT of ~2.6 at 923 K for single crystals along the b-axis [61] was achieved without optimizing the n, resulting in a moderate S2σ of 8.5 μW cm-1 K-2 at 923 K [61]. An ultralow κ of only ~0.35 W m-1 K-1 at 923 K is attributed to the strong anharmonicity of chemical bonds in this SnSe layered compound

[61]. Thus, the finding of SnSe was a real breakthrough in the thermoelectric community and has the guidance to exploring and designing high-efficiency thermoelectric materials with low κ.

In terms of SnSe single crystals, suffered from the poor mechanical properties, rigid crystal growth conditions, and high cost of their production, single crystals are difficult to be synthesized with a large scale and a high success rate [65], it is still restriction for the development of high-performance single crystals and their practical application.

Besides, further investigations are necessary to solve the controversies on whether the ultralow κ values reported of SnSe single crystals [61] are intrinsic and their high- temperature thermoelectric property after phase transition. Furthermore, when doping is applied in single crystal SnSe, the inappropriate type and/or amount of dopant may cause a failure of the growth of big single crystals, which is still a big problem for the accurate thermoelectric evaluations. As for polycrystalline SnSe, it is hard to achieve a very strong anisotropy like single crystal because the SnSe powders (grains) are hard to array orderly along the uni-axis by sintering, leading to a much lower S2σ than that of

80 the single crystals. The effect of doping on polycrystalline SnSe is limited because it is still a challenge to optimizing n to achieve a maximized ZT as indicated by theoretical calculation. Last but not least, the mechanism of inducing inclusions to further improve the thermoelectric performance of polycrystalline SnSe is far to fully understand.

In this respect, we point out potential strategies to dealing with the challenges for further improving the thermoelectric performance of SnSe-based thermoelectric materials and summarize in the compass-like diagram of Figure 40. Because SnSe single crystals possess the highest ZT along b-axis, optimization of fabrication process is highly needed for the growth of single crystal with repeatable and trustable quality. In particular, it is urgently to find new facile methodology to fabricate high-quality SnSe single crystal for the assembly of thermoelectric devices and their evaluations, which will expand the real application of SnSe. For polycrystalline SnSe, there are mainly three routes to further increase its thermoelectric performance. For the texturing, it is better to synthesize the polycrystalline SnSe with both large scale and high crystallinity along b- or c-axis for realization of high anisotropy. Facile solve-thermal method has been demonstrated to possess the ability to large-scale fabrication of SnSe plates with their lateral dimension of up to hundreds µm along b- or c-axis and controllable thickness from several nm to tens of nm [91]. After advanced sintering process, a very strong anisotropy can be achieved in the products fabricated by solve-thermal method, leading to a good thermoelectric performance. Therefore, it is high potential to expanding the fabrication research on solve-thermal method. Using nanostructuring to tune grain size of polycrystalline SnSe will help to control the density of grain boundary and crystal defects, contributing to strengthening the phonon scattering and further reducing κ. Both anion and cation doping/or alloying are suitable to optimizing n and band structures and in turn enhance their thermoelectric properties.

In particular, four strategies will be highlighted here for the future development of

SnSe. The first strategy is the combination of band engineering and texturing to maximize the anisotropy and S2σ with optimized n [277]. Second strategy is the combination of band engineering and single crystal growth. Both p-type [78] and n-type

[52] doping have showed the potentials to improving the thermoelectric performance of single crystals. This is an important way to further improve the thermoelectric performance of α-SnSe, as well as realizing n-type doping with a high thermoelectric performance. Third strategy is the combination of nanostructuring and texturing.

Nanograins possess the same axis (along b- and c-axis) via ideal texturing process, κ along these axes will have ultralow values, which may be even lower than that of single crystals due to the addition of phonon scattering effects occurring at grain boundaries and crystal defects. In this respect, a very high ZT can be predicted. Fourth strategy is the combination of nanostructuring and single crystal growth. Crystal defects such as point defects can be induced into the single crystals to further reduce the κ by strengthening the phonon scattering effect. Thus, an ideal SnSe-based thermoelectric material should be described as polycrystalline SnSe composed by nanograins with single-crystal-like anisotropy and optimized n.

Acknowledgement

The authors are thankful to Min Hong, Yichao Zou, Lina Cheng, Guang Han, Weidi Liu,

Yuan Wang, Raza Moshwan for their respective valuable experimental contributions and constructive discussion. This work was financially supported by the Australian

Research Council. ZGC thanks the USQ Start-up Grant and Strategic Research Projects.

The Australian Microscopy & Microanalysis Research Facility is acknowledged for providing characterization facilities.

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Magnetothermoelectric Effect in Two-Dimensional Tin Selenide. J Phys-Condens

Mat 2018;30:055301.

[429] Parenteau M, Carlone C. Influence of temperature and pressure on the electronic

transitions in SnS and SnSe semiconductors. Phys Rev B 1990;41:5227-34.

128

Single crystal SnSe doped with 6% Bi a Half-Heuslers Ti Zr Hf NiSn 2.0 0.5 0.25 0.25 Mg Si Sn 2 0.5 0.5 Single crystal In Se 1.5 4 2.35 Skutterudites Ba0.08La0.05Yb0.04Co4Sb12

Clathrates Ba9Ga16Ge30 ZT 1.0 Si80Ge20

Bi2Te2.7Se0.3

0.5 La3Te3.35Sb0.65

(PbTe)0.84(PbSe)0.07(PbS)0.07 Zintls Mg Sb Bi Te 0.0 3 1.48 0.48 0.04

Mg2Sn0.75Ge0.25 400 600 800 1000 1200

T (K)

Single crystal SnSe b 2.5 Skutterudites DD0.59Fe2.7Co1.3Sb11.8Sn0.2 PbTe-PbS (12 %)

2.0 Ge0.89Sb0.1In0.01Te BiSbTe 1.5 PbTe-SrTe (4 %) Half-Heuslers FeNb Ti Sb

ZT 0.8 0.2

1.0 -Zn4Sb3

NaxCoO2- 0.5 Zintls Yb14MnSb11 TAGS Ge Ag Sb □ Te 0.0 0.53 0.13 0.27 0.07 Cu2Se/CuInSe2 with 1 mol % In 400 600 800 1000 1200

T (K) Fig. 1 Temperature-dependent ZT values for some typical classes of (a) n-type [42-53] and (b) p-type [6, 15, 54-63] bulk thermoelectric materials.

129

b 105 c 0.03 ) 100 -1 0.00 95

K mg K -0.03 (

90 -SnSe -SnSe -0.06 85 -SnSe -SnSe

Weight(%) 80 -0.09 TGA curve DTA curve

75 Difference -0.12 T T 300 450 600 750 900 10501200 300 450 600 750 900 10501200

T (K) T (K) Fig. 2 (a) Sn-Se binary phase diagram [72, 87], reproduced and revised with permission,

Publishing.

Fig. 3 (a) Unit cell of α-SnSe and crystal structure along (b) a-axis, (c) b-axis, and (d) c- axis.

131

Fig. 4 (a) Unit cell of β-SnSe and crystal structure along (b) a-axis, (c) b-axis, and (d) c- axis.

132

0.15 a Sn b 0.87 Se 0.12 0.84 -SnSe

y 0.09

-SnSe y

, ,

-SnSe x

x x 0.06 0.51 -SnSe y 0.03 x 0.48 y 0.00 0.45 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

c 0.09 -SnSe d 0.06 -SnSe U11 U11 Sn Se U22

U22 )

) U 2 2 0.06 33 0.04 U

o o 33

(

ij U U 0.03 0.02 -SnSe -SnSe 0.00 0.00 300 400 500 600 700 800 900 300 400 500 600 700 800 900

T (K) T (K) Fig. 5 Temperature-dependent positional parameters x (green line) and y (red line) of (a)

Sn and (b) Se atoms, and temperature-dependent thermal parameters of (c) Sn and (d)

133

Fig. 6 (a) Schematic diagrams of harmonicity and anharmonicity and (b) resonant bonding in SnSe. Here Ф(r), a0 and r are the potential energy, lattice parameter, and distance between two adjacent atoms, respectively. Reproduced with permission [68].

134

c d 100 1.0 -SnSe -SnSe -SnSe -SnSe 80 0.8 60

0.6

0.4 Cumulative % Area % Cumulative RealtiveDoS Phonon 0.2 20

0.0 0 -2 0 2 4 6 -2 0 2 4 6 Frequency (THz) Frequency (THz) Fig. 7 Phonon dispersions and density of states (DOS) of the optimized equilibrium (a)

α-SnSe and (b) β-SnSe, (c) comparison of the DOS curves, and (d) cumulative percentage of states under each curve as a function of frequency [112].

135

Fig. 8 Schematic diagrams of phonon scattering effects occur in SnSe.

136

d 0.25 Umklapp (U)

Grain Boundary (B) + )

-1 0.20 Point Defect (P)

K -1 0.15

Dislocation (D) pW sm pW

( 0.10

)

f (

s U  0.05 U + B + P U + B + P + D 0.00 0.0 0.3 0.6 0.9 1.2 1.5 1.8 Frequency (THz)

Fig. 9 (a) One point defect in SnSe characterized by STM, reproduced with permission

Advancement of Science, (e) low magnification and (f) HRTEM images of SnSe matrix with precipitates along , inset figures in panels (e) and (f) are the FFT images in the matrix and precipitates, respectively. Reproduced with permission [67], Copyright

2016, John Wiley and Sons.

137

c d 11.5 a 0.8 b 11.0 c 0.6 o xSe

(A) 10.5

zSn 0.4

zSe a, b, b, a, c

xSn 4.0 0.2

Fractional coordinates Fractional 3.5 0 3 6 9 12 15 18 0 2 4 6 8 10 12 14 16 18 Pressure (GPa) Pressure (GPa) Fig. 10 (a) Temperature-pressure contour plot of resistivity, reproduced with permission

[143], Copyright 2016, Royal Society of Chemistry, (b) ball-and-stick models of SnSe at 5.6 and 8.2 GPa in three perpendicular projections (the yellow spheres represent Se atoms and the grey spheres represent Sn atoms), (c) pressure-dependent fractional atomic coordinates, and (d) pressure-dependent crystallographic parameters [145].

138

a 100 b 800 c 5 a-axis ) a-axis

b-axis 700 -1 b-axis )

S 4 -1

10 c-axis 600 -2 c-axis

)

-1 -1 500 -SnSe -SnSe -1

0 GPa 3 S m S

V K V a-axis

400



( W cm W

b-axis 2 10 S 300 μ -SnSe 

( c-axis -SnSe



/ 0.1 200

 10 1 -SnSe (

-SnSe 100 0 GPa 0 GPa

 /



0.01 0 2 0

300 450 600 750 900 300 450 600 750 900 S 300 450 600 750 900 T (K) T (K) T (K)

100 e 800 5

f ) d a-axis a-axis

a-axis -1

700 b-axis S

) b-axis b-axis 4 -2

-1 10 600 c-axis c-axis

s K

c-axis )

-1 

-SnSe -1 -1

500 3 4 GPa

S m S

V K V

400

4 GPa 

( W cm W

-SnSe 2

μ S 10 300

( -SnSe

4 GPa 10  -SnSe / 0.1 200

-SnSe -SnSe 10

 1 (

100

 / 0.01 0  0

300 450 600 750 900 300 450 600 750 900 2 300 450 600 750 900 S T (K) T (K) T (K) g h 0.35 3.0 a-axis b-axis 2.5 ) 0.30 -1 c-axis K 2.0 -1 0 GPa 0.25 (100)/<010>

1.5

(100)/<001> W m W ( 0.20 (001)/<010>

a-axis 1.0

min min l  0.15 b-axis

Shear Stress (GPa) Stress Shear 0.5 c-axis 0.10 4 GPa 0.0 200 250 300 350 400 450 500 0.0 0.1 0.2 0.3 0.4 T (K) Shear Strain Fig. 11 Temperature-dependent electrical transport properties (a) σ/τ, (b) S, (c) S2σ/τ at 0

GPa and (d) σ/τ, (e) S, (f) S2σ/τ at 4 GPa, (g) temperature-dependent κ at both 0 GPa and

4 GPa [183], and (h) calculated shear stress as a function of strain under different shear directions. Here τ is the relaxation time. Reproduced with permission [149]. Copyright

2017, ACS Publications.

139

a-SnxSey

Free Energy Free

SnSe2 SnSe 0 20 40 60 80 100 Sn Atomic Percent of Se Se

Fig. 12 (a) XRD pattern of SnSe surface oxidized at 873 K for 7 hours, reproduced with permission [161], Copyright 2016, Elsevier Publishing, (b) Cs-corrected HRTEM image of the surface structure of oxidized single crystal SnSe, the FFT patterns corresponding to (c) the yellow boxed region and (d) the blue boxed region. EDS mappings of (e) Se,

(f) Sn, (g) O, and (h) mixture of Sn and Se, and (i) schematic free energy versus

140 composition diagram to illustrate the proposed formation mechanism of α-Sn1-xSe layer.

141

e f 0.8 0.4 0.6 -SnSe -SnSe

0.4

0.2

0.0 Fermi Energy (eV) Energy Fermi Fermi Energy (eV) Energy Fermi 0.0

300 450 600 750 900 300 450 600 750 900 T (K) T (K) Fig. 13 Calculated SnSe electronic band structures of (a) α-SnSe and (b) β-SnSe, reproduced with permission [181], Copyright 2015, AIP Publishing, the total and partial

Springer Nature, and the temperature-dependent Fermi energy of (e) α-SnSe and (f) β-

SnSe [181].

142

) 0.8

d 3

o A 240 (

0.6

230 Volume Volume

220 0.4

210 Strain (%) (eV) gap Energy 0.2 200 -3 -2 -1 0 1 2 3

Fig. 14 (a) Band structures of the unstrained SnSe. Inset: Brillouin zone of the orthorhombic SnSe with labels of high symmetry k points, Colors represent p orbitals, the electronic band structure of SnSe in (b) -3 % compressive strain and (c) +3 % tensile strain, (d) dependence of volume and bandgap with different strain level from -3 % to

+3 % [183].

143

a 600 b 600 c 600

400 400 400

)

-1 -1

-1 200 200 200

μV K μV

μV K μV (

0 0 % -3 % ( 0 0

(

-3 % 0 % -3 %

0 %

c b

a 1 % -2 % S S 1 % -2 % 1 % -2 % S -200 -200 -200 2 % -1 % 2 % -1 % 2 % -1 % 3 % 3 % 3 % -400 -400 -400 300 400 500 600 700 300 400 500 600 700 300 400 500 600 700 T (K) T (K) T (K)

1.6 1.6 d215 S e S Ge f Te Sr ) Ge

3 1.4 1.4 )

o 214 Ba )

A -1

Te -1

( K

1.2 No dopant K 1.2 -1

213 -1

Reference SnSe

212 1.0 1.0 S

W m W W m W

( Ge

(

l Te 211 Sr  0.8  0.8 Ba Sr

Cell Volume Volume Cell Ba 210 0.6 0.6 0.00 0.02 0.04 0.06 0.08 0.10 300 350 400 450 500 550 0.00 0.02 0.04 0.06 0.08 0.10 Nominal Composition (X) T (K) Nominal Composition (X)

Fig. 15 Effects of strain on S along (a) a-axis, (b) b-axis, and (c) c-axis [183], (d) cell volume varying with alloy composition, (e) κl with the temperature for 5 mol % dopant amount, and (f) κl with different alloyed dopants (S, Ge, Te, Sr, Ba). Reproduced with permission [143], Copyright 2016, Royal Society of Chemistry.

144

Fig. 16 Calculated band structures of (a) n-type Bi0.028Sn0.972Se (green solid line) and (b) p-type Ag0.028Sn0.972Se (blue solid line) by super cell model, in which the band structure of the un-doped SnSe (red dashed line) is also shown. Reproduced with permission

[188]. Copyright 2015, Royal Society of Chemistry. Calculated band structures of (c) undoped and (d) 3 % Na-doped α-SnSe by super cell model. Reproduced with permission [79]. Copyright 2015, Royal Society of Chemistry.

145

c 3.8 Forbidden zone d 3.8 Forbidden zone

Top bands 3.6 3.6 Top bands EC EC E 3.4 3.4 sub

E Energy (eV) Energy

sub (eV) Energy DoS increase DoS 3.2 3.2 Sub-bands increase DoS Sub-bands 0 1 2 3 4 300 400 500 600 700 800 Doping concentration (%) T (K)

Fig. 17 Calculated (a) partial DOS for 3 % Na-doped α-SnSe, (b) total DOS of Sn1- xNaxSe (x = 0, 0.01, 0.02, 0.03, 0.04), and Fermi level as a function of the doping concentration (c) and the temperature (d). Reproduced with permission [79]. Copyright

2015, Royal Society of Chemistry.

146

600 a 10 a-axis, p-type b a-axis, p-type b-axis, p-type 400 b-axis, p-type a-axis, n-type

) 8 )

-1 b-axis, n-type 200 -1 6

V K V

S cm S



( 4

4 -200

10 ( 2 -400  a-axis, n-type b-axis, n-type 0 -600 19 20 21 19 20 21 10 10 10 10 10 10 -3 -3 n (cm ) n (cm )

c 25 a-axis, p-type d a-axis, p-type 4 b-axis, p-type

) b-axis, p-type

-2 a-axis, n-type a-axis, n-type K 20 b-axis, n-type b-axis, n-type -1 3

ZT 2 μW cm μW

( 10



2 1

S 5

0 19 20 21 0 19 20 21 10 10 10 10 10 10 -3 -3 n (cm ) n (cm ) Fig. 18 Calculated n-dependent σ, (b) S, (c) S2σ, and (d) ZT at 750 K. Reproduced with permission [204]. Copyright 2015, Elsevier Publishing.

147

)

2400 s 60 1.00

c -2

K 50 0.98 -1

2000 40 0.96

W m W

10 30 0.94 )

-1 20 0.92

×10 ( 1600

 10 0.90

2 S V K V 0 0.88

300 600 900 

( 1200 T (K)

S S 800 S2 ZT 400 300 600 900 T (K)

f 2.0 single crystal, b-axis single crystal, c-axis 1.6 single crystal, a-axis

) nanotube

-1 K

-1 1.2

W m W 0.8

(

l  0.4

300 400 500 600 700 800 T (K)

Fig. 19 (a) Schematic crystal structure of π-SnSe and its atomic position having 64 atoms per unit cell, (b) electronic band structures of π-SnSe along Ʃ using mBJ potential,

Copyright 2017, Elsevier Publishing, (d) top view of a SnSe nanotube, (e) Electronic band structures of the SnSe nanotube, and (f) Temperature-dependent κl of the SnSe nanotube compared with that of single crystal SnSe. Reproduced with permission [208].

148

(d) HRTEM image with bottom inset SAED pattern and top inset line profile along the dotted line AB in the main panel showing the d spacing of (100), SAED patterns obtained at room temperature (e) and 820 K (f). Reproduced with permission [61].

149

Publishing Group, low-magnification image of the typical regions of the Na doped SnSe in (c) TEM model and (d) STEM model with inserted inset high magnification ABF image, the red vertical arrows indicate contrast of stacking faults and the green horizontal arrows indicate full/partial edge dislocations. Reproduced with permission

150

20 25 30 35 40 45 50 55 60 65 70 30.0 30.5 31.0 31.5 32.0 0.99 size: ~ 30 m size: ~ 100m 0.99

a0.66 b0.66

0.33 0.33

0.00 0.00 (400) 0.99 0.99

0.66 0.66

(400)

(a.u.)

0.33 0.33(a.u.)

(111) (800)

(111) ~ 100 m 0.00 0.00 0.99 0.99

0.66 0.66

(400)

0.33 (400)

(800) 0.33 (111)

(111) ~ 30 m Intensity 0.00 0.00Intensity 0.99 0.99

0.66 PDF#48-1224 0.66 PDF#48-1224

(111)

0.33 0.33

(111) Peak deviation (400) 0.00 0.00 (400) 20 25 30 35 40 45 50 55 60 65 70 30.0 30.5 31.0 31.5 32.0 2 theta (degree) 2 theta (degree)

Fig. 22 (a) XRD patterns of SnSe single crystals (blue line for crystals with an average size of ~30 μm and orange line for crystals with an average size of ~100 μm) with inserted optical images, (b) magnified XRD patterns of SnSe single crystals to see the peak deviation, SEM image of SnSe single crystals with inserted SEM image shows a typical plate for (c) crystals with an average size of ~30 μm and (d) crystals with an average size of ~100 μm, (e) description of planes for one SnSe single crystal plate, (f)

TEM image of a typical SnSe single crystal plate, (g) corresponding HRTEM image and

151

c 12 a 90 a-axis b 600 a-axis b-axis ) b-axis 550 -2 9 K c-axis

) c-axis

-1

) -1

60 -1 500 α-SnSe β-SnSe

β-SnSe K V 450 α-SnSe β-SnSe

α-SnSe cm W

S cm S

(



(



30 (  400 a-axis 3 S  b-axis 2 350 S 0 c-axis 0 300 300 450 600 750 900 300 450 600 750 900 300 450 600 750 900 T (K) T (K) T (K)

d a-axis e250 a-axis f 1.0 a-axis b-axis b-axis b-axis )

19 -1 10 ) 200 c-axis c-axis

c-axis -1 0.8

)

-1 -3

-1 150 α-SnSe β-SnSe V

0.6

(

W m W

100 (

n 1018

cm  (

0.4  50

0 0.2 1017 300 400 500 600 700 800 300 400 500 600 700 800 300 450 600 750 900 T (K) T (K) T (K)

i g 1.0 a-axis h 1.0 2.5 a-axis b-axis b-axis ) 2.0 -1 0.8 c-axis c-axis

K 0.9

-1 1.5 β-SnSe 

α-SnSe / α-SnSe β-SnSe

0.6 ZT  0.8

W m W 1.0

(

l  0.4 a-axis 0.5 0.7 b-axis 0.2 c-axis 0.0 0.6 300 450 600 750 900 300 400 500 600 700 800 300 450 600 750 900 T (K) T (K) T (K) Fig. 23 Temperature-dependent thermoelectric properties for single crystal SnSe: (a) σ,

2 (b) S, (c) S σ, (d) n, (e) μ, (f) , (g) l, (h) l/ and (i) ZT along different axes. The phase transformation is pointed out by orange dash line. Reproduced with permission [61].

152

600 a1500 Pure b 3 % Na

1200 3 % Ag 300

)

) -1 1.5 % Na -1 900

6 % Bi 0 Pure 3 % Na V K V

3 % Ag  S cm S

( 3 % Ag 1.5 % Na

( 600

S 6 % Bi 3 % Ag  -300 300

0 -600 300 400 500 600 700 800 300 400 500 600 700 800 T (K) T (K) Pure 3 % Na c 50 d 2.5 Pure

) 3 % Ag 1.5 % Na 3 % Na -2

6 % Bi 3 % Ag )

K 40 2.0 3 % Ag

-1 -1

K 1.5 % Na 30 -1 1.5 6 % Bi

3 % Ag

W cm W

W m W 

20 (

( 1.0

  2 10

S 0.5

0 0.0 300 400 500 600 700 800 300 400 500 600 700 800 T (K) T (K) e 3.0 Pure 3 % Na f 3.0 Average 3 % Ag 1.5 % Na Peak 2.5 6 % Bi 3 % Ag 2.5 2.07 2.06 2.0 2.0 1.94

1.52 1.55 ZT 1.5 ZT 1.5 1.12 1.02 1.0 1.0 0.96 0.55 0.43 0.44 0.5 0.5 0.3 0.0 0.0 300 400 500 600 700 800 Pure 3 % 3 % 1.5 % 6 % 3 % Na Ag Na Bi Ag T (K) Fig. 24 Temperature-dependent thermoelectric properties for pure SnSe [61],

Sn0.97Na0.03Se [79], Sn0.97Ag0.03Se [79], Sn0.985Na0.015Se [78], 6 % Bi-doped SnSe [52],

2 and Sn0.97Ag0.03Se [242]: (a) , (b) S, (c) S , (d) and (e) ZT. (f) Comparison of both average and peak ZT between different materials from 323 to 773 K.

153

a (400) SnSe Se b 3d Sn Se 3d 5/2 3d

3/2

(111) Sn 3d (110) (212) (020) (800)

(201) Intensity (a.u.) Intensity(a.u.)

10 20 30 40 50 60 70 80 50 55 60 490 500 2 theta (degree) Binding Energy (eV) c 500 Se At% 400 Sn 50.1 Sn

300 Se 49.9

200

100

Intensity(a.u.) Sn Sn Se Se 0 0 5 10 15 20 keV

Fig. 25 (a) XRD pattern of SnSe powders via solid-state reaction [90], (b) XPS spectrums of SnSe synthesized by solve-thermal route [266], (c) EDS spot spectrum of pure SnSe synthesized by microwave-assisted solve-thermal route, and (d) EDS mapping image of 1 % Ag alloyed SnSe alloys. Reproduced with permission [268].

154

0.99 a X-Ray P

0.66

(400)

0.33 Surface⊥pressure (111)

0.00

0.99 P

(a.u.)

0.66 X-Ray

(111)

0.33 Surface∥ pressure (400)

0.00

Intensity 0.99

0.66

(111)

PDF#48-1224 (400) 0.33

0.00 20 25 30 35 40 45 50 55 60 65 70 2 theta (degree)

Fig. 26 (a) XRD patterns of sintered SnSe pellets measured along both the ⊥ (red line) and // (green line) direction, (b) SEM image of the surface of pellets polished along the

⊥ directions, SEM images of pellets fractured from (c) the ⊥ directions and (d) the // directions, (e) HRTEM image of pellets. Reproduced with permission [91]. Copyright

2018, Elsevier Publishing.

155

Fig. 27 (a) High resolution HAADF-STEM images of SnSe viewed along (a) a , (b) b , and (c) c with overlays showing Sn atoms in red and Se atoms in blue, (d) atomic-scale EDS mapping from zone axis , reproduced with permission [270],

Copyright 2017, ACS Publications, (e) EBSD phase map of SnSe with grains identified as Fm3m cubic rock-salt phase in red and Pnma orthorhombic phases in blue, (f) TEM image showing rock-salt structured SnSe with inserted SAED pattern measured on the grain, reproduced with permission [141], Copyright 2017, RSC Publishing, (g) HRTEM images of sintered SnSe pellet, reproduced with permission [119], Copyright 2016,

Elsevier Publishing, (h) HRTEM images of stripes with inserted corresponding inverse fast Fourier transform (IFFT) images of the dashed red rectangles, reproduced with

157

a 160 M + HP b 800 M + HP M + A + SPS 140 M + A + SPS SS + SPS ZM + SPS

SS + SPS 700 M + SPS CP + A )

) 120

ZM + SPS -1 -1 600

100 M + SPS V K V

500

80 CP + A



S cm S

(

60 400  S 40 300 20 0 200 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

c 12 M + HP M + A + SPS M + HP d 1.6 ) SS + SPS ZM + SPS M + A + SPS

-2 10

M + SPS CP + A ) SS + SPS

K -1 -1 ZM + SPS 8 K 1.2

-1 M + SPS

6 CP + A

W cm W W m W

 0.8

(

  2 S 2 0.4 0 300 400 500 600 700 800 900 300 400 500 600 700 800 900

T (K) T (K) e 1.4 M + HP f 1.4 1.36 Average M + A + SPS Peak 1.2 1.2 1.1 SS + SPS 1.04 1.0 ZM + SPS 1.0 M + SPS 0.8 0.8 0.68

CP + A

ZT ZT 0.6 0.6 0.53 0.44 0.4 0.4 0.25 0.25 0.19 0.2 0.2 0.13 0.16 0.06 0.0 0.0 M+A 300 400 500 600 700 800 900 M SS ZM M CP + + + + + + T (K) HP SPS SPS SPS SPS A Fig. 28 Temperature-dependent thermoelectric properties for pure polycrystalline SnSe prepared by melting + hot-pressing [66], melting + annealing + SPS [249], solve- thermal + SPS [91], zone melting (ZM) + SPS [89], melting + SPS [65], and cold- pressing + annealing [250]: (a) , (b) S, (c) S2 , (d) and (e) ZT. (f) Comparison of both average and peak ZT of different materials from 323 K to 873 K.

158

a 140 No doping 1.5 % Ag b 900 No doping 1 % Na, K 1 % Na, K 1 % Te 1 % Ge 0.4 % BiCl 120 3

1 % Ge 1 % Zn 600 ) 100 3 % I )

0.4 % BiCl3

-1 -1

80 300

V K V 1.5 % Ag 1 % Te

60 

S cm S

(

0 1 % Zn 3 % I

 40 S 20 -300 0 -600 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

c 12 No doping 1.5 % Ag d 2.0 No doping 1.5 % Ag

) 1 % Na, K 1 % Te 1 % Na, K 1 % Te

-2 10

1 % Ge 1 % Zn ) 1.6 1 % Ge 1 % Zn

K -1 -1 0.4 % BiCl 3 % I 0.4 % BiCl 3 % I

8 3 K 3

-1 1.2

W cm W

W m W



( (

4 0.8   2 2 S 0.4 0 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

e 1.6 No doping 1.5 % Ag f 1.3 Average 1.4 1 % Na, K 1 % Te 1.2 1.2 1.1 Peak 1.2 1 % Ge 1 % Zn 0.96 1.0 0.9 0.84

0.4 % BiCl3

0.8 ZT ZT 3 % I 0.61 0.6 0.6 0.55 0.57 0.6 0.530.5 0.4 0.2 0.3 0.26 0.16 0.15 0.19 0.18 0.0 0.0 300 400 500 600 700 800 900 Pure Ag Na, K Te Ge Zn BiCl3 I 1.5 % 1 % 3 % T (K) 1 %1 % 1 %0.4 % Fig. 29 Temperature-dependent thermoelectric properties for pure [65] and doped with

1.5 % Ag [275], 1 % (Na, K) [270], 1 % Te [232], 1 % Ge [290], 1 % Zn [262], 0.4 %

2 BiCl3 [281] and 3 % I [259] polycrystalline SnSe: (a) , (b) S, (c) S , (d) and (e) ZT.

(f) Comparison of both average and peak ZT of different materials from 323 K to 873 K.

159

a 150 Pure + SnS b900 Pure + SnS + SnTe/Ag + PbSe + SnTe/Ag + PbSe 120 + MoS /graphene 750

2 + MoS2/graphene

)

) -1 + MoSe2 -1 + MoSe

90 600 2

V K V

 S cm S

60 (

(

450

 S 30 300 0 150 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

c 14 Pure + SnS Pure + SnS d 1.6 ) + SnTe/Ag + PbSe + SnTe/Ag + PbSe

-2 12

) + MoS /graphene

K + MoS /graphene 2

2 -1 -1 10

K 1.2 + MoSe + MoSe2

2 -1

W cm W 0.8

6 m W



(



 4 2

S 0.4 2 0 300 400 500 600 700 800 900 300 400 500 600 700 800 900 T (K) T (K)

e 1.8 Pure f 1.8 1.71 1.72 + SnS Average 1.5 1.5 + SnTe/Ag Peak 1.2 + PbSe 1.2 1.01

+ MoS2/graphene

0.9 ZT 0.9 ZT + MoSe2 0.62 0.62 0.5 0.6 0.53 0.46 0.6 0.47 0.3 0.3 0.16 0.17 0.13

0.0 0.0 + + + + + 300 400 500 600 700 800 900 Pure SnS SnTe PbSe MoS2 MoS2 T (K) Ag graphene Fig. 30 Temperature-dependent thermoelectric properties for pure SnSe [65],

(SnSe)0.8(SnS)0.2 [129], 0.5 mol % SnTe + Ag0.005Sn0.995Se composites [276], 1 % PbSe

+ SnSe composites [84], 3.2 wt % MoS2/graphene + SnSe composites [85], and 1.5 %

2 MoSe2 + SnSe composites [300]: (a) , (b) S, (c) S , (d) and (e) ZT. (f) Comparison of both average and peak ZT of different materials from 323 to 873 K.

160

Fig. 31 (a) Top view and (b) side view of optimized atomic configuration of monolayer

SnSe, reproduced with permission [130], Copyright 2015, RSC Publishing, (c) two- dimensional charge density of SnSe in the bc plane crossing all Sn atoms, the unit of charge density is e bohr-3, reproduced with permission [313], Copyright 2016, Nature

Publishing Group, and (d) electronic band structures of monolayer SnSe based on PBE

(blue dashed line) and HSE (red solid line) functional and the corresponding DOS [130].

161

Fig. 32 Calculated band structures by mBJ method under uniaxial strain from -10 % to

10 % along (a) c- and (b) b-axis, the CBM and VBM are marked by CY, CX and VY, VX, respectively. The energies of CY, CX, VY, and VX as a function of strain in the (c) c- and

Publishing Group.

162

16 700 K, b a 2 b 700 K, b 500 K, b 500 K, b

300 K, b )

) 12 300 K, b -1 1 700 K, c -1 700 K, c 500 K, c 500 K, c

300 K, c 300 K, c S m S

8 μV K μV

(

-1

 4 S -2 0 -2 -1 0 1 2 -2 -1 0 1 2

e(eV) e(eV)

c 30 700 K, b d 700 K, b

500 K, b 75 500 K, b )

2 25 300 K, b 300 K, b ) K 60 700 K, c

700 K, c -1 -1

20 500 K, c K 500 K, c

300 K, c -1 45 300 K, c

mW m mW

W m W (

( 30

10  e

2 

S 5 15

0 0 -2 -1 0 1 2 -2 -1 0 1 2

e(eV) e(eV)

e 2.7 b f 700 K, b 500 K, b 4 300 K, b 700 K, c

2.4 c 500 K, c 300 K, c )

-1 2.1 3 3.27 K

-1 1.8

1.5 ZT

W m W

(

l  1.2 1 0.9 0 300 400 500 600 700 -2 -1 0 1 2  (eV) T (K) e

2 Fig. 33 Calculated chemical potential-dependent (a) S, (b) , (c) S and (d) e at different temperature, (e) calculated temperature-dependent l and (f) calculated chemical potential-dependent ZT at different temperature. Reproduced with permission

163

Fig. 34 (a) XRD patterns of a bare STO substrate, a 5 QL Bi2Se3 film on STO substrate and a 16 nm SnSe film grown on Bi2Se3 film on STO, (b) STM image of a 7 nm SnSe film (60 nm × 60 nm), the inset shows the line profile along the black line, (c) Cross- section HRTEM image of a 16 nm SnSe film grown on 5 QL Bi2Se3 film. Reproduced with permission [273]. Copyright 2015, John Wiley and Sons.

164

d Normal angle

300 80° glacing angle )

-1 200

S cm S 100

(

 0

300 350 400 450 500 550 T (K)

e 600 Normal angle f 24 Normal angle g 0.20 Normal angle

80° glacing angle ) 80° glacing angle 80° glacing angle

500 -2 20 K

) 0.18

-1 )

400 16 -1 K

-1 0.16

V/K 300



W cm W

(

200  (

W m W 0.14

S 8

(  100 2 4  S 0.12 0 0 0.10 350 400 450 500 550 300 350 400 450 500 550 200 225 250 275 300 325 T (K) T (K) T (K) Fig. 35 (a) XRD patterns of the thin film deposited at a normal angle and an 80° glancing angle with Ts = 603 K, cross sectional SEM images of films deposited at (b) normal angle and (c) glancing angle at Ts = 603 K, and temperature-dependent thermoelectric properties for thin SnSe film deposited at different angles: (a) , (b) S, (c)

165

-1 a 108 cm Raman spectrum c 8000 500 b 0.15  S -1

130 cm 6000 )

) 0.14

400 -1 -1 150 cm-1

4000

V K V

0.13 

300 cm S

(

 0.12 S 2000 Intensity(a.u.) 200 0.11 0 50 100 150 200 250 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Raman shift (cm-1) T (K) T (K)

7 2 d S  e 4.5  f ZT

) 1.2 -2

6 ) -1

K 4.0 -1 5 K -1 0.8

4 3.5

W m W

3 m W -4 0.4 -2 3.0

10 2

(

 1 2.5 2  0.0 S 0 2.0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0 50 100 150 200 250 300 T (K) T (K) T (K)

Fig. 36 (a) Raman spectrum of the SnSe thin film [357], and temperature-dependent thermoelectric properties for thin SnSe film: (b) , (c) S, (d) S2 , (e) and (f) ZT.

166

d 110 SnSe/Ag contact SnSe/Au contact e 150 -50 V f 20 -80 V 15 100 100 50 V 10 80 V

90 50 5 (nA) 0 0

(nA)

I I 70 -50 I -5 -10 60 -100 SnSe/Ag contact -15

50 SnSe/Au contact -150 -20 -80 -40 0 40 80 -2 -1 0 1 2 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 V (V) V (V) V (V) g ds ds Fig. 37 AFM image and inserted SEM image of (a) SnSe nanosheet with a thickness of

54.9 nm and (b) monolayer with a thickness of 6.8 Å, (c) HRTEM image of the monolayer with inserted SAED pattern, (d) Transport characteristic curves of the devices at Vds = 1 V for the SnSe/Ag and SnSe/Au contacts, respectively, insets show the corresponding optical images of the devices, and output characteristic curves of the devices with the (e) SnSe/Ag and (f) SnSe/Au contacts at different Vg values, respectively. Reproduced with permission [334]. Copyright 2017, IOP Publishing.

167

1 2 ⊥ Ag A // b g c 1 B3g B 3 Ag 2 3g Ag o Ag o 180 180 o 150o 150 o 120o 120

90o 90 o 60o 60

30o 30o Intensity(a.u.) Intensity(a.u.) 0o 0o

40 80 120 160 200 40 80 120 160 200 -1 -1 Raman shift (cm ) Raman shift (cm )

Fig. 38 (a) Optical image of a measured SnSe nanosheet. Typical polarized Raman spectra of a nanosheet with different sample rotation angles excited using a 633 nm laser under (b) parallel-polarization configuration and (c) cross-polarization configuration, (d) side views of the atomic displacements of the four modes measured in the 50 − 200 cm-1 range, the two rows in the figure represent two adjacent layers. The calculated frequencies provided in parentheses are in good agreement with the experimental values. (e) Optical image of a typical nanosheet with 12 electrodes spaced at 30° apart, and (f) the polar plot of the angle-resolved conductivity. Reproduced with permission [387]. Copyright 2016, RSC Publishing.

168

b 20 SnSe/PEDOT:PSS c 600 SnSe/PEDOT:PSS d Parallel-connected model Parallel-connected model   18 ) 200 S  0.6

Series-connected model 500 Series-connected model -2

)

-1

) )

16 -1

K -1 -1 400

14 -1

V K V

300 m W 100 0.4



S cm S

W m W

(

12 (

S    200 

10 S 100 8 0 0.2 6 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Weight Fraction of SnSe Weight Fraction of SnSe Weight Fraction of SnSe e1000 SnSe_0 SnSe_10 f g 500 SnSe_0 SnSe_10 SnSe_20 SnSe_30 600 SnSe_20 SnSe_30

800 SnSe_50 ) SnSe_50 SnSe_100

-2 400 )

) SnSe_100

K -1 -1 SnSe_0 SnSe_10 600 400 SnSe_20 SnSe_30 -1 300

V K V SnSe_50 SnSe_100



S cm S

(

W m W

(

400  200 S  ( 200   100 200 S 0 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Solvent content (vol.%) Solvent content (vol.%) Solvent content (vol.%) Fig. 39 (a) Schematic diagram of the overall fabrication procedure for

SnSe/PEDOT:PSS composite film, and thermoelectric properties as a function of the

SnSe nanosheet content for SnSe/PEDOT:PSS composite films: (b) σ, (c) S, (d) S2σ and

κ, and thermoelectric properties as a function of the solvent (DMSO) content for varied

SnSe/PEDOT:PSS composites: (e) σ, (f) S, and (g) S2σ. Reproduced with permission

169

Fig. 40 Compass-like illustration of the ZT enhancement strategies for SnSe-based thermoelectric materials.

170

Table 1 Crystal structure data of SnSe system [72, 87].

Phase Composition, Pearson Space S. D. Lattice Prototype % Se symbol group Parameters (Å) α-SnSe 50 oP8 Pnma B16 a = 11.37, b = GeS 4.19, c = 4.44

β-SnSe 50 oC8 Cmcm Bf a = 4.31, b = CrB 11.71, c = 4.32

169

Table 2 A summary of bandgap data of SnSe and calculation methods.

Structure (Calculated) (Calculation) Method Year Ref. Bandgap (eV) α-SnSe, 0.61, 0.39 First-principles density 2014 [61] β-SnSe functional theory α-SnSe, 0.829, 0.464 Density functional and many-body 2015 [181] β-SnSe perturbation theory α-SnSe, 0.86, 0.355 Full-potential Korringa-Kohn- 2015 [179] β-SnSe Rostoker α-SnSe 0.44 First-principles density 2015 [188] functional theory α-SnSe 0.60 First-principles density 2015 [79] functional theory α-SnSe 0.643 First-principles density 2012 [267] functional theory α-SnSe 0.63 First-principles density 2017 [197] functional theory α-SnSe 0.93 First-principles density 2017 [384] functional theory α-SnSe 0.65 First-principles density 2017 [317] functional theory with Vienna Ab Initio Simulation Package α-SnSe 0.78 Ab initio many-body perturbation 2015 [110] theory α-SnSe 0.86 Vienna Ab Initio Simulation Package 2015 [117] α-SnSe 0.60 Vienna Ab Initio Simulation Package 2015 [183] α-SnSe 0.80 Vienna Ab Initio Simulation Package 2016 [90] α-SnSe 0.935 Full-potential linearized augmented 2015 [204] plane waves α-SnSe 0.69 Full-potential linearized augmented 2015 [194] plane waves α-SnSe - Full-potential linearized augmented 2015 [177] plane waves α-SnSe 0.923 Optical-absorption measurements 1981 [167] α-SnSe 0.86 mBJ method 2015 [196]

170

Table 3 A summary of calculated values of the positions, energies of the conduction and valence band extrema, and effective masses along the a, b, and c-axes [181].

* * * Multiplicity (k1, k2, k3) E ma mb mc

(eV) (me) (me) (me) α-SnSe, VBM 2 (0.00, 0.35, 0.000 0.74 0.31 0.16 0.00) α-SnSe, 2 (0.00, 0.42, 0.000 0.90 0.12 0.15 VBM1 0.00) α-SnSe, CBM 2 (0.33, 0.00, 0.829 2.40 0.11 0.15 0.00) β-SnSe, VBM 2 (0.34, 0.50, 0.000 0.34 0.04 0.09 0.00) β-SnSe, 2 (0.00, 0.20, -0.031 0.77 0.12 0.05 VBM1 0.39) β-SnSe, CBM 2 (0.34, 0.50, 0.464 3.07 0.04 0.10 0.00) β-SnSe, 2 (0.00, 0.54, 0.534 0.06 0.82 1.52 CBM1 0.08)

171

Table 4 A comprehensive summary on the synthesis of single crystal SnSe. Here the

Bridgman method is abbreviated as B, the Bridgman-Stockbarger method as BS, the

direct vapor transport method as DVT, the hydro-thermal method as HT, solve-thermal

method as ST, and the temperature gradient growth method as TGG.

Product Precursors Atmosphere Pressure Temperature Heating Keeping Crystal Year Ref. (Torr) (K) Time Time Growth (hours) (hours) Method

-4 Sn0.985Na0.015Se 99.999 % vacuum 10 1223 10 6 B 2015 [78] Sn, Se and Na SnSe 99.999 % vacuum 10-4 1223 10 6 B 2014 [61] Sn and Se SnSe ------B 1992 [416] SnSe ------B 1989 [417] SnSe ------B 1986 [418] SnSe 99.999 % vacuum - 1223 - 20 Modified 2017 [246] Sn and Se B - Sn1-xRxSe (R = - argon ~3.7×10 1273 12 10 Modified 2015 [79] Na, Ag) 6 B SnSe 99.999 % vacuum - 1223 - 20 Modified 2015 [115] Sn and Se B -4 Sn0.985Na0.015Se 99.999 % vacuum ~10 1223 10 6 Vertical B 2017 [237] Sn, Se and Na - Sn0.97Ag0.03Se - vacuum ~7.5×10 1183 - 20 Horizontal 2017 [242] 6 B SnSe - vacuum ~7.5×10- 1223 ~0.8 - Horizontal 2017 [419] 6 B SnSe 99.999 % vacuum 10-5 1183 - 24 BS 2009 [420] Sn and Se SnSe 99.99 % vacuum 5×10-5 1234 - 48 BS 1989 [80] Sn and Se SnSe 99.99 % vacuum 10-5 1073 ~13 72 DVT 2009 [216] Sn and Se SnSe 99.99 % vacuum ~7.5×10- 1053 - 170 DVT 2007 [92] Sn and Se 6 SnSe ------DVT 2000 [231] SnSe 99.99 % vacuum 10-5 1053 ~75 168 DVT 1994 [215] Sn and Se

172

SnSe ------DVT 1981 [167] SnSe - vacuum 10-6 1173 - 4 DVT 1977 [421] SnSe 99.95 % EDTA - 453 - 168 ST 2000 [224] Se and

SnCl2 -4 Sn1-xBixSe 99.999 % vacuum 10 1203 90 10 TGG 2016 [52] Sn, Se and Bi SnSe1-xSx - vacuum - - - - TGG 2017 [217] -4 SnSe1-xSx 99.8 % vacuum <10 1233 - 33.3 TGG 2017 [218] Sn, 99.9 % Se and 99 % S

173

Table 5 Comparison of calculated/measured ρ and κ for SnSe crystals along different

-3 directions reported in the literature (ρth = 6.18 g cm ). The measured ρ is labelled with *.

Product axis 휅 at D at Cp at ρ at 휅 at D at Cp at ~773 Ref. ~323 K ~323 K ~323 K ~323 K ~773 K ~773 K K (J g-1 K- (W m-1 (mm2 s-1) (J g-1 K- (g cm-3) (W m-1 K- (mm2 s- 1) K-1) 1) 1) 1) Pure a ~0.45 ~0.33 ~0.252 - ~0.23 ~0.16 ~0.259 [61] Pure b ~0.68 ~0.49 ~0.252 - ~0.33 ~0.23 ~0.259 [61] Pure c ~0.65 ~0.47 ~0.252 - ~0.28 ~0.20 ~0.259 [61] 3 % Na b ~1.70 ~1.08 ~0.252 - ~0.58 ~0.34 ~0.259 [79] 3 % Ag b ~1.92 ~1.21 ~0.252 - ~0.64 ~0.40 ~0.259 [79] 1.5 % Na a ~0.62 ~0.40 ~0.250 6.0* ~0.27 ~0.16 ~0.265 [78] 1.5 % Na b ~1.55 ~1.00 ~0.250 6.0* ~0.54 ~0.35 ~0.265 [78] 1.5 % Na c ~1.29 ~0.82 ~0.250 6.0* ~0.40 ~0.25 ~0.265 [78] 6 % Bi a ~0.46 ~0.30 ~0.252 - ~0.18 ~0.12 ~0.259 [52] 6 % Bi b ~0.82 ~0.53 ~0.252 - ~0.27 ~0.17 ~0.259 [52] 6 % Bi c ~0.73 ~0.47 ~0.252 - ~0.24 ~0.15 ~0.259 [52] 3 % Ag a ~2.05 - ~0.252 6.178* ~0.61 - ~0.259 [242 ]

174

Table 6 A comprehensive summary on the synthesis of polycrystalline SnSe. Here, for

the synthetic methods of SnSe, melting method is abbreviated as M, arc-melting method

is abbreviated as AM, annealing is abbreviated as A, mechanical alloying is abbreviated

as MA, solid-state reaction is abbreviated as SSR, combustion method is abbreviated as

CM, and aqueous solution is abbreviated as AS; For the sintering methods, spark plasma

sintering is abbreviated as SPS, hot-pressing is abbreviated as HP, cold-pressing is

abbreviated as CP, and open die pressing is abbreviated as ODP.

Product Type Dopant Synthetic Synthetic Synthetic Synthetic Sintering Sinter Sinter Sinter Year Ref. or Method Pressure Temperature Time Method Pressure Temperat Time Mixture (Torr) (K) (hour) (MPa) ure (K) (min) SnSe p - M - 1223 24 SPS 50 698, 708 7 2014 [65] SnSe p - AM ------2015 [88] SnSe p - M 10-5 1173 18 HP 60 773 20 2016 [66] SnSe p - M 10-4 1193 2 HP, SPS 55 753 5 2016 [89] SnSe p - SSR 10-5 773 96 SPS 60 773 2 2016 [90] SnSe p - M - 1200 12 SPS 60 830-850 - 2015 [249] SnSe p - HT - 453 12 SPS 45 673 15 2015 [118] SnSe p - ST - 393, 413, 12 SPS 50 773 5 2016 [81] 433 SnSe p - AS - - 2 HP 60 773 20 2016 [82] SnSe p - M ~7.5×10-6 1223 24 HP 600 723 60 2017 [252] SnSe p - - - - - ODP - - - 2017 [251] SnSe p - AM ------2017 [422]

Sn0.98Se p - ST - 503 36 SPS 60 850 5 2018 [91] SnSe - - ST, A ------2005 [83] SnSe p - ST - 473 24 HP 50 923 10 2017 [233] min SnSe p - HT - 423-443 6-12 CP + HP 2 tons 853 - 2017 [423] SnSe p - - - - - CP, A - - - 2016 [250] SnSe p - MA - - 20 SPS 30, 60, 823 5-10 2017 [424] 80, 100, 120 SnSe P - CM - - < 1 SPS 50 773 5 2018 [150] -6 Sn1- p Na M < 10 1223 12 SPS - 746 20 2016 [161]

xNaxSe -5 Sn1- p Na M 7.5×10 1253 24 SPS 50 873 5 2016 [274]

xNaxSe -4 Sn1- p Na M ~3×10 1173-1223 6 HP 50 873 7 2016 [258]

xNaxSe

Sn1- p Na - - - - SPS 40 873 5 2017 [425]

xNaxSe

Sn1- p Na High - 1123 0.5 + 1 SPS 70 823 10 2017 [285]

xNaxSe pressure

Sn1- p NaCl SSR - 1073 10 min Rapid HP 50 ~823 5 2017 [426]

xNaxSeClx -4 NaySn1−xP p Na, Pb M ~10 1223 12 SPS 50 ~783 5 2017 [286]

bxSe

175

SnSe1- p Te SSR - 1023 1 HP 80 - 120 2012 [267]

xTex

SnSe1- p Te MA (450 - - 15 SPS 50 793 5 2015 [128]

xTex rpm)

SnSe1- p Te Microwav - 503 6 SPS 40 873 5 2017 [232]

xTex e-ST -5 AgxSn1- p Ag M, A 7.5×10 1253 24 SPS 50 873 5 2016 [277]

xSe

AgxSn1- p Ag M, A - 1200 12 HP 36 800 10 2014 [268]

xSe

AgxSn1- p Ag ST - 413 15 SPS 50 500 5 2017 [288]

xSe -6 Sn1-xTlxSe p Tl M ~7.5×10 1223 6 HP 70 673 60 2016 [278] SnSe p Al, Pb, A - 773 ~72 SPS 60 773 ~10 2016 [269] In, Cu

Sn1- p Cu M - 1203 2 HP 6000 1073 3 2017 [287]

xCuxSe

Sn1- p Cu HT - 403 36 SPS 50 693 7 2018 [296]

xCuxSe -5 SnSe1-xInx p In M ≤ 10 1223 48 HP 70 850 60 2016 [279]

Sn1- p Ge AM ------2016 [289]

xGexSe -5 Sn1- p Ge ZM ~7.5×10 1223 2 HP 60 753 20 2017 [290]

xGexSe

Sn1- p Ge M - 1203 2 - - - - 2017 [291]

xGexSe

KxSn1-xSe p K MA (425 - - 5, 8, 12 SPS 50 773 5 2016 [67] rpm) SnSe p Li, Na, M 10-4 1223 8 SPS - 873 5 2016 [283] K

NaxKySn1- p Na, K MA (425 - - 5 SPS 50 773 5 2017 [270]

x-ySe rpm) -6 ZnxSn1- p Zn M ~7.5×10 1223 24 HP 600 673 60 2016 [262]

xSe -3 Sn1-xSe p SnSe2 M, A 10 1223 24 SPS 50 708 6 2017 [427]

Ag0.015Sn0 p Ag M - 1273 10, 8 - - - - 2017 [275]

.985Se

Sn1- p Sm M - 1203 2 Rapid HP 6000 1073 3 2017 [292]

xSmxSe SnSe p LaCl3 MA (425 - - 8 SPS 50 773 5 2018 [293] rpm)

SnSe0.985 p SnCl2 M - 1273 10, 8 - - - - 2017 [275]

Cl0.015

(Cu2Se)1- p β-Cu2Se M - 1403 10 SPS 50 923 5 2015 [303]

x(SnSe)x -4 SnS1-xSex p SnS M, A 10 1223 20 SPS 50 903 7 2015 [129] SnSe-SnS p SnS MA (450 - - 15 SPS 50 903 7 2017 [299] rpm)

Sn1- p PbSe HT - 403 36 SPS 50 693 7 2016 [84]

xPbxSe

(Sn1- p Na, M, A - 1223 10 SPS 50 873 5 2017 [284]

xPbx)0.99N PbSe

a0.01Se -6 SnTe/Ag0. p SnTe, M ~7.5×10 1223 24 SPS 20 673 20 2016 [276]

005Sn0.995S Ag

176

e composite s SnSe/C p carbon M - 1223 10, 24 HP 600 673 60 2016 [298] composite black s SnSe/PbT p PbTe M ~7.5×10-6 1223 10, 24 HP 600 673 ~96 2016 [301] e composite s SiC/SnSe p SiC M - 1223 10 HP 50 823 10 2016 [260] composite ceramic s s SnSe/Mo p MoS2/ SSR, HT - ~1073 1/6 HP 50 ~823 5 2017 [85]

S2/ graphen graphene e composite s -7 SnSe/Mo p MoSe2 M ~7.5×10 1223 24 SPS 50 773 5 2017 [300]

Se2 composite s

Ag0.01Sn0. p Ag, SnS M, A - 1273 24 HP 50 773 30 2017 [302]

99Se1−xSx

Na0.015Sn0 p Na, M, A - 1253 24 SPS 50 753 5 2018 [305]

.985Se/CN carbon Ts nanotub composite es s SnSe p Se MA (150 - 453 1 HP 50 823 10 2018 [297] nanowir rpm), HT es

SnS0.2Se0. p Ag MA (450 - - 12 SPS 50 813, 833 6 2018 [306]

8 rpm) and 853

SnSe1−x n - ST - 453 24 - - - - 2016 [86] - SnSe1-x n - M ~3.75×10 1273 20 HP 60 923 60 2018 [282] 6 SnSe n Cl AS - - 2 HP ~60 773 20 2017 [235] -6 SnSe0.95- n BiCl3 M ~7.5×10 1193 1 SPS 55 753 8 2016 [281]

BiCl3 -5 SnSe0.95- n PbBr2 M ~7.5×10 1193 1 HP 60 753 30 2017 [294]

PbBr2

SnSe1-xSx n SnS, I M - 1193 6 HP 50 873 7 2016 [259]

Pb1- n PbSe MA (450 - - 24 SPS 50 873 5 2015 [257]

xSnxSe rpm)

Sn1- n Ti, Pb MA (450 - - 6 SPS 50 773 5 2017 [295]

xTixSe, rpm)

Sn0.94- xPbxTi0.06 Se -3 Sn1-xXxSe - Ca, Sr, M, A 10 1273 18 HP 100 798 45 2015 [127] Ba, Cu, Zn, Ge

177

Table 7 A comprehensive summary on the thermoelectric performance of undoped

polycrystalline SnSe. The marked (r) in n column means the n values were tested at room

temperature.

Produ Type Direction Synthetic ZT T (K) 𝜎 S S2σ κ ρ n Year Ref. ct Method (S cm-1) (μV K-1) (μW cm-1 (W m-1 (g cm-3) cm-3 K-2) K-1) SnSe p ⊥ M + SPS ~0.5 823 ~31.6 ~355.7 ~4.0 ~0.63 5.93 - 2014 [65] SnSe p - AM - 395 - ~660 - 0.1~0.2 - 7.95×1015 2015 [88] (r) SnSe p - ST + SPS - 300 - ~160 - ~1.4 ~5.99 ~1 ×1019 2015 [118] SnSe p ⊥ M + A + ~0.5 790 ~18.7 ~379.8 ~2.7 ~0.40 5.92 1.1×1017 2015 [249] SPS (r) SnSe p - M + SPS - 850 ~66.0 ~300 ~6.0 - 6.13 - 2016 [90] SnSe p ⊥ M + HP 1.1 873 ~61.9 ~366.3 ~8.3 ~0.66 6.05 4.0×1017 2016 [66] (r) SnSe p ⊥ M + SPS ~1.0 873 ~49.9 ~408.0 ~8.3 ~0.70 6.03 5.25×1017 2016 [89] (r) SnSe p ⊥ ST + SPS ~0.6 773 ~28.7 ~339.8 ~3.3 ~0.44 5.87 1.02×1019 2016 [81] (r) SnSe p ⊥ CP + A ~0.1 772 ~15.3 ~279.8 ~1.2 ~0.75 - 2016 [250] SnSe p ⊥ M + HP 0.73 800 ~64.3 ~322.7 ~6.7 ~0.73 - 5.57×1016 2017 [252] SnSe p ⊥ HT + CP 0.54 550 ~13.9 360 ~1.8 ~0.18 - ~2.5×1018 2017 [423] + HP (r) SnSe p ⊥ MA + ~0.7 873 ~43.2 ~292.8 3.7 ~0.45 6.14 4.18×1017 2017 [424] SPS 1 (r) SnSe p - AM - 625 - 1050 - - - - 2017 [422] SnSe p ⊥ ST + HP ~0.8 803 ~16.7 ~346.0 ~2.0 ~0.2 - ~1.75×101 2017 [233] 3 9 SnSe p ⊥ CM + SPS 0.5 773 ~25.0 ~368.8 ~3.4 ~0.53 ~5.99 3.4×1017 2018 [150] (r) 19 Sn0.98 p ⊥ ST + SPS 1.36 823 72.4 309.9 6.9 0.42 6.09 1.48×10 2018 [91] Se SnSe1 n ⊥ ST - 400 ~0.4 ~-130.0 ~0.007 ~0.24 - 2016 [86] −x

SnSe0. n // M + HP 0.07 773 ~4.5 ~-364.3 ~0.6 ~0.47 6.05 - 2018 [282]

178

Table 8 A comprehensive summary on the thermoelectric performance of doped

polycrystalline SnSe. The marked (r) in n column means the n values were tested at room

temperature.

Product Typ Direction Synthetic ZT T 𝜎 S (μV K- S2σ κ n ρ Year Ref. e Method (K) (S cm-1) 1) (μW cm-1 (W m-1 cm-3 (g cm-3) K-2) K-1) 18 Ag0.01Sn0.99 p // M + A + 0.6 750 ~45.9 ~344.1 ~5.4 ~0.68 ~3.5×10 ~5.93 2014 [268] Se HP (r) Sn0.99Na0.01 p ⊥ MA + 0.72 773 ~67.4 ~275.0 ~5.1 ~0.50 - - 2015 [128] Se0.84Te0.16 SPS 19 Na0.01Sn0.99 p ⊥ M + SPS 0.75 823 ~49.6 ~311.1 4.8 ~0.53 1.0×10 ~5.99 2016 [274] Se (r) 19 Na0.015Sn0.98 p // M + MA ~0.8 773 ~37.9 ~298.8 ~3.4 ~0.33 ~2.1×10 5.81 2016 [258]

5Se + HP (r) 19 Na0.01Sn0.99 p ⊥ M + SPS ~0.8 800 ~81.2 ~267.2 ~5.8 ~0.50 ~1.5×10 - 2016 [283] Se 19 Na0.02Sn0.98 p ⊥ High 0.87 798 ~56.4 ~288.8 4.7 0.4 3.08×10 ~5.62- 2017 [285] Se pressure + (r) 5.81 SPS 19 Na0.005 p ⊥ MA + 1.2 773 ~34.9 ~374.7 ~4.9 0.32 ~7.2×10 5.71 2017 [270] K0.005Sn0.99 SPS (r) Se 1 Na0.005Sn0.99 p ⊥ SSR + HP 0.84 810 ~79.2 ~228.6 ~4.1 ~0.39 ~3.95×10 ~5.93 2017 [426] 9 5SeCl0.005 (r) 19 Na0.01(Sn0.96 p ⊥ M + SPS ~1.2 773 ~89.4 ~269.7 ~6.5 ~0.45 ~2.8×10 - 2017 [286] Pb0.04)0.99Se 19 Ag0.01Sn0.99 p ⊥ M + A + 0.74 823 ~54.8 ~330.9 6.0 ~0.66 1.9×10 ~5.99 2016 [277] Se SPS (r) 18 Ag0.03Sn0.97 p ⊥ ST + SPS 0.8 850 ~90.3 ~266.2 ~6.4 ~0.68 9×10 (r) >5.56 2017 [288] Se Sn0.995Tl0.005 p ⊥ M + HP 0.6 725 ~68.9 ~300.0 ~6.2 ~0.75 - ~5.99 2016 [278] Se 20 Sn0.98Cu0.02 p - M + A + 0.7 773 ~42.4 ~238.6 ~2.4 0.27 1.84×10 ~6.12 2016 [269] Se SPS (r) 17 Sn0.97Cu0.03 p - M + HP 0.79 823 ~35.0 ~325.1 ~3.7 ~0.39 1.57×10 6.16 2017 [287] Se (r)

Sn0.99Cu0.01 p - HT + SPS 1.2 873 ~35.2 ~310.6 ~3.4 0.2 - - 2018 [296] Se 17 Sn0.99In0.01S p // M + HP 0.2 823 ~6.53 ~350.0 ~0.8 ~0.36 ~2.9×10 ~5.87 2015 [279] e (r)

Sn0.9Ge0.1Se p - M - 400 - ~843.2 - ~0.39 - - 2016 [289] 17 Sn0.96Ge0.04 p ⊥ ZM + HP 0.6 823 35.6 ~378.5 5.1 ~0.7 3.36×10 >5.81 2017 [290] Se (r) 18 K0.01Sn0.99S p ⊥ MA + ~1.1 773 ~18.6 ~421.4 ~3.3 ~0.24 9.2×10 - 2016 [67] e SPS (r) 18 Zn0.01Sn0.99 p ⊥ M + HP 0.96 873 ~74.1 ~328.5 8.0 ~0.73 ~4.5×10 - 2016 [262] Se 19 Na0.01Sn0.99 p ⊥ M + A + 0.85 800 ~100.4 ~271.5 ~7.4 ~0.50 ~6.5×10 5.94 2017 [284] Se SPS (r) 18 Ag0.015Sn0.98 p - M 1.3 773 ~44.7 ~344.0 ~5.2 ~0.30 ~8×10 5.87 2017 [275]

5Se (r)

179

17 SnSe0.985Cl0 p - M 1.1 773 ~25.5 ~399.3 ~4.1 ~0.30 ~1×10 5.87 2017 [275]

.015 (r) 19 Sn0.97Na0.03 p ⊥ SPS 0.82 773 ~65.1 ~280.2 ~5.1 ~0.50 ~2.2×10 ~5.93 2017 [425] Se 19 SnSe0.9Te0.1 p ⊥ ST + SPS 1.1 800 ~57.4 ~322.8 ~6.0 ~0.44 ~1×10 ~5.87 2017 [232] (r) 1 Sn0.97Sm0.03 p - M + HP 0.55 823 ~33.6 ~250.0 ~2.1 ~0.32 ~1.27×10 - 2017 [292] Se 7 (r) SnSe-1.0 wt p ⊥ MA + 0.55 750 ~15.6 ~350.6 ~1.9 ~0.27 1.53×1016 ~5.93 2018 [293] % LaCl3 SPS (r) 17 SnSe0.9375Te n ⊥ M + HP - 673 ~3.63 ~-276.2 ~0.3 - -2.1×10 ~5.87 2012 [267] 0.0625 (r) 19 SnSe0.95- n ⊥ M + SPS 0.7 793 ~28.9 ~-414.0 ~5.0 ~0.60 -1.07×10 - 2016 [281] 0.4% BiCl3 (r) 19 SnSe0.95- n ⊥ M + HP 0.54 793 ~36.0 ~-360.0 ~4.7 ~0.72 -1.86×10 5.99 2017 [294] 3% PbBr2 (r) 16 SnSe0.87S0.1I n // M + MA ~1.0 773 ~10.0 ~-624.5 ~3.9 ~0.30 -3.8×10 5.75 2016 [259]

0.03 + HP (r) SnSe-Cl n ⊥ HT + HP - 540 ~9.0 ~-264.8 ~0.6 - -6.43×1018 ~5.87 2017 [235] (0.6%) (r) 16 Sn0.74Pb0.20 n ⊥ MA + 0.4 773 ~14.8 -450 3.0 ~0.58 2.47×10 2017 [295] Ti0.06Se SPS (r)

180

Table 9 A comprehensive summary on the thermoelectric performance of polycrystalline

SnSe incorporated with other compounds. The marked (r) in n column means the n values

were tested at room temperature.

Product Type Direct Synthetic ZT T σ S S2σ κ n ρ Year Ref. ion Method (K) (S cm-1) (μV K-1) (μW cm-1 (W m-1 cm-3 (g cm-3) K-2) K-1) 20 (Cu2Se)0.97( p - M + SPS 1.41 823 ~302.4 ~199.2 12.0 ~0.70 9.93×10 ~6.61 2015 [303]

SnSe)0.03 (r) 17 (SnS)0.2(Sn p // M + A + 0.82 823 ~13.8 ~466.9 3.0 ~0.30 ~3.0×10 ~5.93 2015 [129] Se)0.8 SPS (r) 0.5 mol % p // M + SPS 1.6 875 ~112.3 ~313.0 ~11.0 0.5 3.99×1018 ~6.07 2016 [276]

SnTe/Ag0.00 (r)

5Sn0.995Se composites 1 % p // HT + SPS ~1.7 873 ~74.8 ~344.9 ~8.9 ~0.55 6.1×1018 (r) - 2016 [84] PbSe/SnSe composites Sn oxide p ⊥ MA + ~1.1 773 ~18.6 ~421.4 ~3.3 ~0.24 9.2×1018 (r) - 2016 [67] nanoprecip SPS itates/K0.01S

n0.99Se 17 (SnS)0.2(Sn p // MA + 0.64 823 ~26.3 ~332.1 ~2.9 ~0.38 2.1×10 (r) 5.45 2017 [299]

Se)0.8 SPS 3.2 wt % p ⊥ M + HP 0.98 810 ~70.5 ~258.2 ~4.7 ~0.39 2.49×1019 ~5.93 2017 [85] MoS2/grap (r) hene/SnSe composites 1.5 % p ⊥ M + SPS 0.5 773 ~21.8 ~428.3 ~4.0 ~0.64 ~2×1019 - 2017 [300] MoSe2/SnS e composites rock-salt- p // HT + SPS 1.3 850 ~48.6 ~288.5 ~4.0 ~0.26 5.6×1018 (r) - 2017 [141] type nanoprecip itates/SnSe SnSe2/Sn0.98 p ⊥ M + A + 0.61 848 ~48.3 ~308.6 ~4.6 ~0.64 - ~5.99 2017 [84] Se SPS 18 Ag0.01Sn0.99 p // M + A + 1.67 823 ~25 296.4 ~2.2 0.11 7.6×10 (r) - 2017 [302]

Se0.85S0.15 HP 2.5 vol % p ⊥ M + HP 1.21 903 ~100.2 ~310.0 9.6 ~0.72 >1.8×1019 ~5.81- 2016 [298] SnSe/C 6.06 composites 1.5 vol % p ⊥ M + HP 1.26 880 ~94.7 ~301.2 9.2 ~0.64 ~1.94×1019 - 2016 [301] SnSe/PbTe composites 19 Na0.015Sn0.98 p ⊥ M + A + ~0.9 773 ~55.6 ~299.2 ~5.0 ~0.4 ~4×10 (r) ~6.06 2018 [305] 5Se/CNTs SPS 6 composites 19 Sn0.995Ag0.00 p ⊥ MA + ~1.1 823 ~53.4 ~315.1 ~5.3 ~0.4 ~2×10 5.78, 2018 [306] 5S0.2Se0.8 SPS 5.68, 5.56

181

SiC/SnSe n - M + MA 0.12 300 ~7.3 -581 ~2.5 ~0.6 -5.77×1018 - 2016 [260] composites + HP 5 19 (PbSe)0.9(S n - MA + 1.0 773 ~491.1 ~-183.3 ~16.5 ~1.2 -3.5×10 ~7.61 2015 [257]

nSe)0.1 SPS 16 (Sn0.9Se0.87I n // M + MA ~1.0 773 ~16.0 ~-500.0 ~4.0 ~0.36 -3.8×10 (r) 5.75 2016 [259]

0.03)(SnS)0.1 + HP

182

Table 10 A summary of bandgap data of 2D-SnSe and calculation methods.

Composition Structure (Calculated) (Calculation) Method Year Ref. Bandgap (eV) SnSe Sheet 0.88 First principles Density 2017 [428] Functional Theory SnSe monolayer 1.45 mBJ method 2016 [313] SnSe monolayer 1.28 Vienna Ab Initio 2015 [130] Simulation Package SnSe monolayer 0.898 Optical-absorption 1990 [429] ~1.238 measurements SnSe monolayer 1.79 First principles Density 2017 [384] Functional Theory SnSe monolayer 0.99 First principles Density 2017 [317] Functional Theory with Vienna Ab Initio Simulation Package SnSe bilayer 0.64, 0.91, First principles Density 2017 [327] 0.82, 0.72 Functional Theory SnSe multilayer 0.86 First principles Density 2017 [383] Functional Theory SnSe 7-layer 1.35 First principles Density 2017 [384] Functional Theory SnSe 15-layer 1.13 First principles Density 2017 [384] Functional Theory SnSe film 1.2 Optical-absorption 2017 [357] measurements

Sn1-xCaxSe film ~1.0 (x < Optical-absorption 2017 [366] 0.5) measurements

183