New Insights into Intrinsic Point Defects in V2VI3 Thermoelectric Materials

Defects and defect engineering are at the core of many regimes of material research, including the field of thermoelectric study. The 60‐year history of V2VI3 thermoelectric materials is a prime example of how a class of semiconductor material, considered mature several times, can be rejuvenated by better understanding and manipulation of defects. This review aims to provide a systematic account of the underexplored intrinsic point defects in V2VI3 compounds, with regard to (i) their formation and control, and (ii) their interplay with other types of defects towards higher thermoelectric performance. We herein present a convincing case that intrinsic point defects can be actively controlled by extrinsic doping and also via compositional, mechanical, and thermal control at various stages of material synthesis. An up‐to‐date understanding of intrinsic point defects in V2VI3 compounds is summarized in a (χ, r)‐model and applied to elucidating the donor‐like effect. These new insights not only enable more innovative defect engineering in other thermoelectric materials but also, in a broad context, contribute to rational defect design in advanced functional materials at large.


Introduction
V 2 VI 3 compounds (V = Group V elements Sb and Bi, and VI = Group VI elements S, Se and Te) and their derivatives constitute an important class of semiconductor material in renewable energy and next generation information technology. For decades these compounds have been the benchmark thermoelectric (TE) materials. [ 1 ] Recently they became a focus in the study of bulk quantum topological insulators. [ 2 ] In this review we intend to address the fundamental yet underexplored role of intrinsic point defects in V 2 VI 3 compounds. While this gap of knowledge has led to ambiguities in the synthesis-structure-property REVIEW and the classic alloying (solid solution) approach by Ioffe et al. [ 28 ] dated back to 1950's. The outstanding TE performance and the wide range of composition in both p-type and n-type attained by alloying Bi 2 Te 3 with isostructural Sb 2 Te 3 or Bi 2 Se 3 showcases the effi cacy of defect engineering. [29][30][31] In addition, V 2 VI 3 compounds have been a test bed for novel material fabrication methods. [ 10 ] These methods, in turn, govern the type, amount, and topology of defects. The history of TE study of V 2 VI 3 compounds is a prime example of how a class of material can be rejuvenated by better understanding and manipulation of defects, ranging from 0D point defects, [ 32 ] 1D dislocations, [33][34][35] 2D grain boundaries, [ 36,37 ] to 3D nanoinclusions. [ 38 ] This review focuses on intrinsic point defects in V 2 VI 3 compounds.
Understanding the role of intrinsic point defects is a prerequisite for establishing the fundamental synthesis-structureproperty correlation in V 2 VI 3 semicoductors, however, it is challenging to correlate specifi c atomic level defects and macroscopic TE properties given the complex crystal structure, especially when heavily doped and/or in the presence of other types of defects. For example, the best commercial TE materials near room temperature are ternary p-type Bi 2x Sb x Te 3 and n-type Bi 2 Te 3x Se x . [ 27 ] The TE properties of these heavily extrinsically doped Bi 2 Te 3 are actually governed by intrinsic point defects , the causal chain follows: extrinsic point defects → intrinsic point defects → TE properties (cf. Section 3.1).
The signifi cance of intrinsic point defects in V 2 VI 3 compounds is justifi ed by a simple argument. The carrier concentration n is the material parameter of utmost importance in V 2 VI 3 compounds as the σ , α , and κ el depend closely on the value of n , intrinsic point defects are on a par with extrinsic point defects in the capacity of contributing charge carriers. Experimental and theoretical studies corroborated that the optimal carrier concentration n of V 2 VI 3 materials is on the order of 10 19 cm -3 [ 32,33,39 ] while intrinsic point defects alone can contribute 10 18 -10 20 cm -3 . [ 40 ] In a proof-of-principle study, we devised an intrinsic point defect engineering (IPDE) approach in n-type Bi 2 Te 2.3 Se 0.7 , which simultaneously optimized the PF , κ ph and zT . [ 32 ] The success of the IPDE approach is refl ected in the zT peak value of above 1.2 at 445 K and also high averaged zT values of 1.1 between 300 K and 500 K.
The signifi cance of intrinsic point defects is also confi rmed in other state-of-the-art TE materials. For example, vacancies modulate the carrier concentration n in Zintl compounds. [ 40 ] In Mg 2 Si 0.4 Sn 0.6x Sb x , [ 41 ] Sb doping at low ratios tunes the n while it facilitates the formation of Mg vacancies at high Sb doping ratios, Mg vacancies effectively scatter heat-carrying phonons; in addition, excess Mg in the starting material facilitates the formation of Mg interstitials that also alter the n . In ZrNiSnbased half-Heusler (HH) materials, the band gap is modulated by the content of Zr/Sn antisite defects. [ 42 ] The rest of the article is organized as follows. We discuss the creation and control of intrinisc point defects in V 2 VI 3 semiconductors in Section 2 and 3, respectively. As shown, intrinsic point defects can be created and manipulated compositionally, mechanically (via "the donor-like effect"), and thermally (via "the recovery effect"). We propose a simple ( χ , r )-model and discuss the donor-like effect. Section 4 and 5 are devoted to the impact of intrinsic point defects on the TE properties and how to engineer intrinsic point defects to tailor the material performance in different temperature ranges, respectively. In Section 6, we address the underheeded role of intrinsic point defects in nanostructuring and texturing process. Finally we conclude, in Section 7, with perspective remarks.

Formation of Intrinsic Point Defects in V 2 VI 3 Binary Compounds
The V 2 VI 3 binary compounds grown from stoichiometric melts tend to have Group V element excess because Group VI element often precipitates as a secondary phase (mainly Te) [ 43,44 ] or is volatile (mainly S or Se). [ 32 ] Satterthwaite et al. reported that the as-grown Bi 2 Te 3 ingot is p-type when the actual Te content is less than 62.8 at% (namely, Te-defi cient), and the hole concentration n h rapidly decreases with Te excess; at the other end, the ingot exhibits n-type ( Figure 1 a). [ 45 ] These less intuitive observations can be explained by intrinsic point defects. Harman et al. proposed that the dominant intrinsic point defects in the asgrown Bi 2 Te 3 ingot are negatively charged antisite defects Bi Te ′ on the Te-defi cient side and positively charged antisite defects i Te Bi on the Te-rich side. [ 46 ] This scenario is supported by the results of packing density measurements and the density values calculated for various defect models (Figure 1 b). [ 47 ] The presence of antisite defects in Bi 2 Te 3 thin fi lm is confi rmed by high precision chemical analysis. [ 48 ] In the same vein, the dominant intrinsic point defects in p-type Sb 2 Te 3 are Sb Te ′ , [ 49,50 ] while ii V Se are the dominant point defects in n-type Bi 2 Se 3 . [51][52][53] Horak et al. pointed out that Bi Se ′ coexists with ii V Se in n-type Bi 2 Se 3 . [ 53 ] The predominance of these intrinsic point defects has been confi rmed by fi rst-principles calculations. [54][55][56][57][58][59][60] Table 1 lists the type and the concentration of dominant intrinsic point defects in Sb 2 Te 3 , Bi 2 Te 3 , and Bi 2 Se 3 . [ 58 ] In addition to intrinsic point defects, Bi excess (Te defi ciency) may create extended defects such as the seven-layer-lamella defect Bi 3 Te′ 4 with the sequence Te 1 -Bi-Te 2 -Bi-Te 2 -Bi-Te 1 . The presence of Bi 3 Te′ 4 is confi rmed by high resolution electron microscopy measurements in bulk crystals, [ 61,62 ] fi lms, [ 63 ] and nanowires of Bi 2 Te 3 . [ 64 ] First-principles calculations suggest that the low formation energy of the nearest neighbor X Bi-Te1 (i.e., the exchange of a Bi atom with a Te 1 atom in the same supercell) facilitates the formation of Bi 3 Te′ 4 . [ 56 ] Furthermore, Horak et al. proposed that Bi Te ′ and Bi 3 Te′ 4 are favored at low and high Bi excess, respectively. [ 65 ]

Manipulation of Intrinsic Point Defects
In Section 3, we address how to implement intrinsic point defects in V 2 VI 3 compounds, following the order of pre-synthesis control (Section 3.1), in-synthesis control (Section 3.2), and post-synthesis control (Section 3.3 and Section 3.4). Alternatively, these controls can be categorized into compositional/ chemical control (Section 3.1 and 3.2), mechanical control (Section 3.3), and thermal control (Section 3.4).

Compositional Control in Cation-Rich V 2 VI 3 Compounds
As mentioned in Section 2, V 2 VI 3 binary compounds synthesized from stoichiometric starting composition tend to be cation rich. There is an important correlation between the conduction type and the carrier concentration of intrinsic point defects and the electronegativity χ and covalent radius r of cations and anions. [ 2,32,[66][67][68][69][70][71] We hereafter call this correlation the (χ, r)-mechanism or the (χ, r)-model. As shown in Figure 2 a, the smaller the difference in χ and r between the cation and the anion the easier for antisite defects to form. At the other end, increasing the difference in χ and r between the cation and the anion will favor the formation of anion vacancies. We present the χ , r of constituent elements in binary V 2 VI 3 compounds in Table 2 .
The formation energy of antisite defect E AS can be enumerated in ascending order as: Figure 1. a) Room temperature carrier concentration of Bi 2 Te 3 ingots as a function of Te content. [ 45 ] b) Room temperature mass density of Bi 2 Te 3 ingots as a function of Te content. [ 47 ] Meanwhile, the formation energy of anion vacancies E V is listed in descending order as: ) and that of the carrier concentration in cation-rich V 2 VI 3 single crystals and zone-melted ingots. [ 32 ] For example, the difference in E AS explains why Sb 2 Te 3 exhibits a strong p-type characteristic whereas Bi 2 Te 3 is weakly p-type in light of inequality (1). Inequality (2) can explain the strong n-type characteristic of Bi 2 Se 3 in terms of the low E V .
The formation energy of Bi Te ′ in cation-rich binary Bi 2 Te 3 can be calculated by the following formula derived from statistical thermodynamics: [ 47 ] ln 1 where k b is the Boltzmann constant, T m the melting point, BiTe ′ n the number of Bi Te ′ per cm 3 , and Te N the number of available Te sites per cm 3 , respectively. The typical value of E AS is 0.35 eV, 0.50 eV, 0.64 eV for binary Sb 2 Te 3 , Bi 2 Te 3 , and Bi 2 Se 3 , respectively. [ 47,49,50,53 ] These values are confi rmed by fi rst-principles calculations (Figure 2 b). Generally, cation antisite defects and anion vacancies are energetically more favorable than anion antisite defects and cation vacancies under the cationrich condition. [ 58 ] The ( χ , r )-model can be extended to ternary and quaternary V 2 VI 3 materials. In general, substituting more electronegative or smaller atoms of the same valence on the cation site tends to drive the material towards hole-like (p-type) conduction, while substituting more electronegative or smaller atoms of the same valence on the anion site tends to drive the system towards electron-like (n-type) conduction. For instance, increasing Sb content in p-type Bi 2x Sb x Te 3 reduces the E AS , thereby increasing the hole concentration n h owing to a smaller difference in χ and r between Sb and Te than the counterpart between Bi and Te ( Figure 3 a). [ 29,50,72 ] Similarly, substituting Te by Se in Bi 2 Te 3 increases the E AS and supresses the E V , resulting in a n-type conduction. [ 32 ]  Se ′ ), a p-type to n-type crossover occurs (Figure 3 b). [ 32,73 ] Notably, S substitution on the Se-site quickly shifts the p-n crossover point down to x = 0.13. [ 68,74,75 ] Doping n-type Bi 2 Se 3 with Sb [ 76 ] or doping p-type Sb 2 Te 3 with Se [77][78][79] rapidly diminish the carrier concentration (Figure 3 c). Teramoto et al. found that y 0 , the y value at which the p-n transition occurs, increases with the x value in the Sb x Bi 2x Te 3y Se y quaternary system (Figure 3 d). [ 80 ] An important implication of these results is that intrinsic point defects can be actively tuned by isoelectron extrinsic dopants . The best commercial room temperature TE materials p-type Bi 2x Sb x Te 3 and n-type Bi 2 Te 3x Se x alloys are good examples. These results also serve as a caveat when we try to derive the causal chain in data analysis: implementing isoelectron extrinsic dopants leads to the formation of intrisinsic point defects, then the latter govern the observed conduction type and the magnitude of carrier concentration.
Comparing to the case of isoelectron extrinsic doping , the interplay between intrinsic point defects and heteroelectron extrinsic dopants is more complex. Nonetheless, it is known  The calculated formation energies of intrinsic point defect considering spin-orbit interactions in the cation-rich case. [ 58 ] V C , A C , V A , and C A represent cation vacancies, anion antisite defects, anion vacancies, and cation antisite defects, respectively. that heteroelectron dopants such as Li, [ 81 ] Ag, [ 82,83 ] Cu, [ 84 ] Pb, [85][86][87] Sn, [ 88 ] I, [ 89 ] Mn, [ 90 ] Ge, [ 91 ] affect the formation of intrinsic point defects. For example, Te loss can be suppressed by adding a small amount of Cu to increase the formation energy of ii V Te [ 92 ] Indium (In) doping is a manifestation of the signifi cance of intrinsic point defects in the presence of heteroelectron extrinsic dopants. Doping by indium modulates the formation energy of intrinsic point defects and thus alters the carrier concentration, shifting the optimal operation regime from room temperature to higher temperature. [ 93,94 ] Indium (5s 2 5p 1 ) occupying the Sb (5s 2 5p 3 )-site is expected to form a negatively charged substitutional point defect and thus increases the hole concentration n h ( i In In 2h Sb → ′′ + ). However, Figure 4 a shows the opposite: indium substitution moderately decreases the n h in Sb 2x In x Te 3 , [ 94 ] in contrast to iodine doping [ 95 ] and Ti doping. [ 96 ] To explain this counter-intuitive observation, Horakproposed that incorporation of indium into Sb 2 Te 3 creates charge neutral point defects In Sb × , accompanied by a In(5s 5p ) In (5s 5p ) 2 1 Sb 0 3 → x electronic transition. [ 71 ] In this scenario, the substitution of Sb by In does not directly alter the n h , rather, it raises the E AS due to the greater difference in χ between In and Te than that between Sb and Te, thereby reducing the n h . A similar scenario has been proposed for Tl, [ 97 ] Bi, [ 50 ] or Se [ 77 ] -doped Sb 2 Te 3 . The relative reduction of n h due to the doping on the Te-site is enumerated in descending order as: Tl > In > Se > Bi. [ 94 ] To elucidate the effect of indium doping on the n h , the E AS of Sb Te ′ is estimated by the following relation: [ 94 ] ( )e x p k where N AS is the concentration of antisite, C Sb the Sb concentration, C In the In concentration, k b the Boltzmann constant, T m the melting point (assuming a linear relationship between T m (Sb 2 Te 3 ) = 902 K and T m (In 2 Te 3 ) = 940 K), respectively.
35 eV is the activation energy of Sb Te ′ in undoped Sb 2 Te 3 , [ 49 ] and Δ E the activation energy increment of Sb Te ′ due to indium doping. As shown in Figure 4 b, the Δ E rapidly increases with increasing indium content, a refl ection of the fact that the formation energy of Sb Te ′ in indiumdoped Sb 2 Te 3 is higher than that of undoped one. [ 94 ]

Synthesis Environment Control
We in Section 3.2 discuss the control of intrinsic point defects in the case of off-stoichiometric starting materials. We hereafter call this mechanism "synthesis environment control". Under a cation-rich growth condition, ii V Se , Bi Te ′ , and Sb Te ′ are responsible for the native n-, p-, and p-type conduction in Bi 2 Se 3 , Bi 2 Te 3 ,   [ 29,50,72 ] b) Room temperature carrier concentration of unidirectionally grown n-type Bi 2 Te 3x (Se/S) x as a function of Se or S content. [ 29,73,74 ] c) Room temperature carrier concentration of unidirectionally grown p-type Sb 2 Te 3x Se 3 and p-type Bi 2x Sb x Se 3 as a function of Se content and Sb content, respectively. [ 76,77 ] d) The y 0 value (the Sb content at which the p-n transition occurs) of unidirectionally grown Bi 2y Sb y Te 3x Se x as a function of Se content x . [ 80 ] and Sb 2 Te 3 ingots, respectively. Under an anion-rich condition, i Se Bi , i Te Bi , and V Sb ′′′ are responsible for the native n-type, n-type, and p-type conduction in Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 ingots, respectively. [ 58,98 ] In the zone-melted (ZM) p-type Bi 0.5 Sb 1.5 Te 3 ingots, it is found that the formation of antisite defects can be suppressed by adding extra Te (>60 at%) to the melts because the E AS is higher under a Te-rich condition ( Figure 5 a). [ 27,43 ] Meanwhile, excess Bi (>40 at%) in Bi 2 Te 3 and Bi 2 Se 3 facilitates the formation of Bi Te ′ and Bi Se ′ . Horak et al. pointed out that the p-type ZM B 2+ x Te 3 and n-type ZM B 2+ x Se 3 ingots show an increase of the n h and a decrease of n e because of the increase of Bi Te ′ and Bi Se ′ concentration with increasing x , respectively. [ 65 ] Controlling intrinsic point defects in V 2 VI 3 compounds now has an impact beyond the fi eld of TE material research. Bi 2 Te 2 Se becomes the subject of crystal growth research owing to its topological insulator properties. [ 2,29,32 ] In the study of 3D topological insulators a grand challenge is to minimize the bulk electrical conduction to help discern the surface electrical conduction. However, stoichiometric Bi 2 Te 2 Se grown by a modifi ed Bridgman method is metal-like, with a n e on the order of 10 19 cm -3 . To suppress the bulk electrical conduction, Jia et al. fabricated highly bulk resistive Bi 2+ x Te 2− x Se samples under a slightly Bi-rich condition in which the Bi excess introduces Bi Te ′ (Figure 5 b). [ 99 ] In another study of topological insulator, Jiang et al. fabricated high-quality Sb 2 Te 3 fi lms by molecular beam epitaxy and observed the intrinsic point defects by in situ scanning tunneling microscopy and spectroscopy. They found that in a strong Te-rich environment V Sb ′′′ is the defect with lowest formation energy while Sb Te ′ becomes the lowest energy defect in a less Te-rich environment. [ 100 ]

Mechanical Control: Deformation and the Donor-like Effect
In addition to compositional control (Section 3.1) and synthesis environment control (Section 3.2), mechanical control via postsynthesis deformation is another approach. [101][102][103][104][105][106][107][108] It is well known that the p-type Bi 2 Te 3 ingots can be inverted to n-type   [ 94 ] b) Indium content dependence of formation energy of Sb Te ′ in Sb 2x In x Te 3 single crystals. [ 94 ] Reproduced with permission. [ 94 ] Copyright 2015, Elsevier. single crystals as a function of excess Te content. [ 43 ] b) Carrier concentration measured at T = 10 K of Bi 2+ x Te 2− x Se with x = 0, 0.015, 0.02, 0.04, and 0.06 at different positions in the crystal boule ("0" marks the end of the crystal boule). [ 99 ] simply by pressing, [ 109 ] and the pressed n-type material can be re-inverted to p-type via sintering at suffi ciently high temperatures. [ 110 ] Heavy plastic deformation of Bi 2 Te 3 ingots produces non-basal slips and ii V Te , changing the conduction type from p-type to n-type, and simultaneously enhancing the electrical conductivity ( Figure 6 a). [ 101 ] Ionescu et al. suggested that non-basal slip produces 3 Bi to 2 Te vacancy-interstitial pairs during heavy deformation processing. [ 111 ] In presence of Bi vacancies, Bi atoms diffuse from Te sites back to their original sublattice sites, extra Te vacancies and excess electrons are thus produced. This important mechanism is called " the donor-like effect ", expressed as: where V Bi ′′′ and ii V Te are the Bi and Te vacancies, Bi Te ′ the antisite defects, and e′ the excess electrons, respectively. Similar formulae like (5) hold for V Sb ′′′ , Sb Te ′ , ii V Se , and Bi Se ′ . The donor-like effect is a delicate multiple-stage n-type doping mechanism involving multiple intrinsic point defects. The study of donor-like effect is warranted because grinding, ball milling, hot/cold deformation, and hot pressing processes have been extensively used for various purposes in TE research. The past decade has witnessed great strides toward understanding and untilizing the donor-like effect in V 2 VI 3 compounds.
Experimentally, the impact of donor-like effect is refl ected in the large difference in α , which is inversely correlated to the n , between (Bi,Sb) 2 (Te,Se) 3 single crystal and hot pressed (HP) sample (Figure 6 b). [ 103 ] The (Bi,Sb) 2 (Te,Se) 3 single crystal shows a p-type conduction for all compositions of Bi 2x Sb x Te 3 and a p-n transition at Bi 2 Te 2.1 Se 0.9 , in contrast, the HP sample exhibits a p-n transition at Bi 0.66 Sb 1.34 Te 3 and a n-type conduction for all compositions of Bi 2 Te 3x Se x . The donor-like effect can explain these observations. Importantly, hot deformation (HD) processes promote the donor-like effect. [ 2,32,33,66,67,112 ] Different from the strong donor-like effect created by heavy deformation such as grinding, ball milling (BM), and extrusion, HD produces weaker donor-like effect due to milder deformation.
More severe deformation produces fi ner powders and a greater decrease in the n h in p-type Bi 2x Sb x Te 3 [ 113 ] and a larger increase in the n e in n-type Bi 2 Te 3− x Se x . [ 114 ] Shin et al. deformed the p-type Bi 0.5 Sb 1.5 Te 3 ingot by cold pressing at 700 MPa from one to eleven times using the tool steel mold. [ 115 ] They showed that the α increases with the increasing number of times of cold pressing, which correlates with a stronger donor-like effect. Similarly, increasing the number of times of HD [ 33,67 ] or prolonging the BM time [ 105,106 ] facilitates the donor-like effect and hence increased the n e in n-type Bi 2 Te 3− x Se x (Figure 6 c and 6 d). The donor-like effect gets marginal above a certain level of deformation.

Thermal Control via the Recovery Effect
The recovery effect can be regarded as a post-deformation thermal relaxation process, which basically counters the donor-like www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600004   Figure 6. a) Room temperature Seebeck coeffi cient of extruded Bi 2 Te 3 ingot as a function of annealing time at different annealing temperatures. [ 101 ] b) Room temperature Seebeck coeffi cient of (Bi,Sb) 2 (Te,Se) 3 single crystals and HP alloys as a function of Se and Sb doping ratios. [ 103 ] c) Room temperature carrier concentration of Bi 2 Te 3x Se x alloys as a function of the number of times of hot deformation. [ 33,67 ] d) Room temperature carrier concentration of Bi 2 Te 3x Se x alloys as a function of ball milling time. [ 105,106 ] effect regarding the carrier concentration change. The microscopic picture of the recovery effect posits that anion vacancies are annihilated by dislocation climb and array formation upon annealing. As expected, the recovery effect has a strong dependence on the annealing temperature (Figure 6 a). [ 101 ] Low-temperature annealing only slightly mitigates the donorlike effect and thus slightly reduces the n e . As a result, the σ is reduced while the α is somewhat enhanced. At the other end, when the deformed samples are annealed at high temperatures for a long time, the donor-like effect can be nearly removed, as a result, the electrical properties revert slowly back to the original ones. Studies also showed that raising HP or SPS temperatures also mitigates the donor-like effect (i.e., ii V Te or ii V Se ) due to the recovery effect. [ 32,[116][117][118] It should be pointed out that the HD and annealing temperatrue are substantially higher than the operation temperature of V 2 VI 3 TE materials so the thermal stability of as formed intrinsic point defects is not an issue in operation. This has been confi rmed by our repetitive test measurements.

Role of Intrinsic Point Defect towards Higher zT
In Section 4 we address how intrinsic point defects generally impact the TE properties σ , α and κ , which sets the stage for elucidating intrinsic point defect engineering in Section 5.

Optimizing Electron Band Structure
Optimizing electron band structure involves two basic tasks: (i) tuning the band fi lling to attain an optimal carrier concentration n ; and (ii) enhancing the electron density of states (DOS) near the Fermi level E F to increase the α . While implementing extrinsic point defects by doping remains the mainstream methodology to optimize the value of n , we recently showed that intrinsic point defects alone can attain an optimal n value ≈ 5 × 10 19 cm -3 in both p-and n-type V 2 VI 3 materials. [ 32 ] To enhance the DOS near E F , theoretical calculations by Hashibon et al. showed that the E F is shifted into the valence band by Bi Te ′ , and into the conduction band by i Te Bi , [ 56 ] forming resonant (defect) states. [ 21 ] On the other hand, the band structure tuning by intrinsic point defects In V 2 VI 3 compounds will strongly interplay with composition optimization, which results in the change in band gap. The discussion on this topic is specially presented in Section 5.2.

Reduced Lattice Thermal Conductivity
Compared to the closely inter-dependent σ , α , κ el , the κ ph is the only TE property that can be tuned fairly independently. To date, the basic strategy to reduce the κ ph is to introduce more and diverse phonon scattering centers because heat-carrying phonons have a wide distribution in energy (frequency) and momentum (wavelength). Intrinsic point defects are effective phonon scatters above room temperature because the average wavelength of heat-carrying phonons gets shorter at elevated temperatures. Termentzidis et al. studied the effects of vacancies and antisite defects on the κ ph by non-equilibrium molecular dynamics simulations (NEMD). [ 119 ] The reduction of κ ph is >60% for 5 % [V Bi ′′′ ] and > 70% for 4 % [ ii V Te ] in Bi 2 Te 3 ( Figure 7 a). In contrast, the reduction in κ ph is about 20% regardless of the concentration of Bi Te ′ or Te • Bi (Figure 7 b). These results are understandable in that the vacancies possess larger mass difference and larger strain fl uctuation than the antisite defects, thus more effectively scattering heat-carrying phonons.
Grain boundaries provide us with another effective phonon scattering mechanism. At fi rst glance, grain boundaries are irrelevant to intrinsic point defects. However, the routine powder metallurgy methods used to refi ne grain size often involve deformation processes that create vacancies (c.f. Section 3.3). [ 32,120 ] The specifi c contribution of vacancies to the reduction of κ ph is often unaccounted or mistakenly attributed to grain boundaries. He et al. recently studied the relation between point defects, grain boundaries, and the reduction κ ph in Bi 2 Te 3 nanocrystals by means of thermal conductivity, electron microscopy, and positron annihilation measurements. [ 120 ] It is instructive to note that the κ ph of Bi 2 Te 3 nanocrystals increases with an increasing annealing temperature but the grain size barely changes upon annealing (Figure 7 c). Positron annihilation lifetime measurements indicated a gradual reduction of vacancy concentration upon annealing (Figure 7 d).
Hence the reduction of κ ph in Bi 2 Te 3 nanocrystals is due to phonon scattering by vacancies rather than grain boundaries.

Intrinsic Point Defect Engineering
In this section, we discuss how to engineer intrinsic point defect to optimize the material's TE performance in different temperature ranges. In view of the donor-like effect and the recovery effect, it is imperative to compare the behavior of single crystal, ZM ingot, HP and HD sample in relation to their synthesis and deformation conditions. All the HP samples are prepared from ballmilled powder, if not otherwise noted.

Reassessment of Optimal Compositions
V 2 VI 3 -based compounds are often subject to powder metallurgy processes such as BM, HP, and HD etc. The donor-like effect (cf. Section 3.3) and the recovery effect (cf. Section 3.4) thus make the optimal composition of n-and p-type HP and HD V 2 VI 3 materials different from that of a single crystal or a ZM ingot.

n-type Ternary Bi 2 Te 3 -x Se x
In light of the ( χ , r )-mechanism (cf. Section 2), and the greater difference in χ and r between Bi and Se than that between Bi and Te (cf. Table 2 ), substituting Te by Se in Bi 2 Te 3 single crystal increases the E AS and decreases the E V, resulting in a p-type conduction. A p-n crossover occurs when the electrons contributed by anion vacancies ( ii V Te and ii V Se ) outnumber the holes created by antisite defects (Bi Te ′ and Bi Se ′ ) ( Figure 8 a). Unidirectionally grown Bi 2 Te 3x Se x ZM ingots have optimal compositions at REVIEW ( [ 29,73 ] Electron doping by halide inhibits the p-n crossover and attains an optimal electron concentration n e ≈ 5 × 10 19 cm -3 . [ 32,33 ] Notably, inhibiting the p-n crossover can be achieved by the donor-like effect. [ 101,103 ] Figure 8 a shows that the donor-like effect gives rise to a high n e value, all the HP and HD samples are n-type conductive, especially at the traditional optimal compositions x = 0.15-0.3. [ 32 ] Figure 8 showcases the effects of compositional, mechanical, and thermal control of intrinsic point defects in n-type ternary Bi 2 Te 3x Se x . As shown in Figure 8 a, the n e value of the HD and HP sample fi rstly decreases and then increases with increasing Se content x . We fi rst look at the HP sample. Increasing Se content in the synthesis stage suppresses the formation of antisite defects. Because the intensity of donor-like effect is directly correlated with the concentration of antisite defects (Equation ( 5) ), a reduced concentration of antisite defects leads to the reduced n e , which is the case at x < 1. The optimal composition for n-type polycrystals is shifted to x = 0.7-1.0 with a n e ≈ 5-7 × 10 19 cm -3 (Figure 8 a). [ 32 ] To understand the change of slope of n e at x >1 in the HP sample, one has to take into account the volatility of Se. The Se loss tends to be more severe at higher x , resulting in a higher concentration of antisite defects and thereby increasing the n e .
We may understand the behavior of the HD sample in a similar way, the only extra consideration is the recovery effect (cf. Section 3.4). Figure 8 a shows that the HD sample has a n e value consistently lower than the HP sample at x < 1.0, above which it is the opposite. We thus infer that nearly all antisite defects participate in the donor-like effect (cf. Equation ( 5) ) in the HD sample at x < 1.0, the recovery effect sets in and mitigates the donor-like effect, leading to a lower value of n e . [ 32,104 ] At high Se contents ( x > 1.0), however, there is a higher concentration of antisite defects due to the Se loss. As such, a portion of antisite defects participates in the donor-like effect during the BM process, the remainder of antisite defects participate in the donor-like effect during the HD process (Figure 8 a). [ 32 ] The stronger donor-like effect gives rises to a higher n e value (>6 × 10 19 cm -3 ) than in the HP sample. Such a n e value is favorable for a high PF but too high for a good zT .
Intrinsic point defects impact the κ ph as well. Both antisite defects and vacancies reduce the κ ph , but the impact of vacancies is much greater because of the larger mass and size differences. [ 119 ] The deformation-induced vacancies V Bi ′′′ and ii V Te (or ii V Se ) in the HD sample strongly scatter the heat-carrying phonons and effectively reduce the κ ph . The high-density lattice defects such as the lattice distortions and dislocations generated during the HD process also contribute to the reduction of κ ph . [32][33][34] Our recent work showcases the effi cacy of intrinsic point defect engineering via tuning the Se content and the HD condition. The HD Bi 2 Te 2.3 Se 0.7 sample attains a zT ≈ 1.0 at 500 K (Figure 8 b). In contrast to the ZM ingot with an optimal www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600004   Figure 7. Calculated lattice thermal conductivity for defected bulk Bi 2 Te 3 obtained from NEMD for a system size of 8 × 8 × 4 cells as a function of the a) vacancy defect percentage, and b) antisite defect percentage. [ 119 ] c) Temperature dependent lattice thermal conductivity of Bi 2 Te 3 nanocrystals annealed at different temperatures (The inset presents the grain size of Bi 2 Te 3 nanocrystals annealed at different temperatures). d) Variations of positron lifetime τ 1 , τ 2 , intensity I 2 , and average lifetime τ av as a function of annealing temperature. [ 120 ] composition x = 0.15-0.3, [ 29,73 ] the optimal composition of the HD sample is shifted to a signifi cantly higher Se content x = 0.7 due to strong donor-like effect. [ 32 ] Notably, repetitive HD process further improves the zT of Bi 2 Te 2.3 Se 0.7 . Due to the recovery effect, the reduction of n e leads to remarkable improvement in α with increasing number of times of HD. Meanwhile, the κ ph is reduced owing to the deformation-induced multiple-scale defects. Consequently, a zT ≈ 1.2 at 445 K and an average zT av ≈ 1.1 between 300-500 K were achieved in n-type Bi 2 Te 2.3 Se 0.7 hot deformed for three times (HD3), a 20% improvement over the sample hot deformed once (HD1). [ 32 ]

p-type Ternary Bi 2 -x Sb x Te 3
Intrinsic point defect engineering in p-type Bi 2x Sb x Te 3 follows the same principle, as the underlying mechanisms are basically the same as in n-type Bi 2 Te 3x Se x . Increasing the Sb content in p-type Bi 2− x Sb x Te 3 reduces E AS and thereby rapidly increases the n h because of the smaller difference in χ and r between Sb and Te than that between Bi and Te ( Figure 9 a). Compared to single crystalline Bi 0.5 Sb 1.5 Te 3 , [ 50 ] the donor-like defect in the BM sample partially compensates the holes and causes the reduction of n h at all Sb contents (Figure 9 a). [ 102 ] For example, the n h value of the BM sample with x = 1.7 is nearly equal to that of single crystal with x = 1.5. [ 32 ] Notably, the HD process can further reduce the n h at x < 1.7, while the impact of HD on the n h is insignifi cant at x > 1.7 (Figure 9 a). [ 32,121 ] We infer that at high Sb contents ( x > 1.7) the deformation induced V Sb ′′′ (or V Bi ′′′ ) and ii V Te are depleted during the BM process, thus the donor-like effect is less pronounced.
Compared to a value of zT ≈1 near room temperature in the Bi 0.5 Sb 1.5 Te 3 ZM ingot, [ 29,72 ] the HD Bi 0.3 Sb 1.7 Te 3 shows a higher zT value ≈ 1.3 at 380 K (Figure 9 b). [ 32 ] Our result is consistent www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600004   Figure 8. a) Room temperature carrier concentration of the undoped single crystals, [ 29,73 ] HP and HD polycrystalline [ 32 ] Bi 2 Te 3x Se x samples. The arrows are to help visualize the trend of carrier concentration variation upon BM and HD processing. b) Se content dependences of zT of the ZM, [ 39 ] HP and HD [ 32 ] Bi 2 Te 3x Se x samples. All thermoelectric properties are measured along the in-plane direction. Reproduced with permission. [ 32 ] Figure 9. a) Room temperature carrier concentration of the undoped single crystals, [ 50 ] HP and HD polycrystalline [ 32 ] Bi 2x Sb x Te 3 samples. The arrows are to help visualize the variation trend of carrier concentration upon BM and HD processing. b) Sb content dependence of zT values for the ZM, HP, and HD Bi 2x Sb x Te 3 samples. [ 32 ] Reproduced with permission. [ 32 ] with the recent work by Li et al., [ 122 ] in which they reported a high zT for the mechanical alloyed (MA) Bi 0.3 Sb 1.7 Te 3 . Notably, there is a signifi cant improvement in the average zT av over the temperature range studied, and the average zT av between 300 K and 480 K for the hot deformed Bi 0.3 Sb 1.7 Te 3 sample is 1.2. These results demonstrate again that the signifi cance of donor-like effect and the effi cacy of intrinsic point defect engineering.

Tailoring Intrinsic Point Defects for Applications in Different Temperature Ranges
In this Section, we discuss how to engineer intrinsic point defects to tailor the material performance [ 33,66,94,123 ] in different temperature regimes.

Room Temperature Refrigeration
The best commercial TE materials for refrigeration near room temperature are ZM n-type Bi 2 Te 3x Se x ( x = 0.15-0.3) and ZM p-type Bi 0.5 Sb 1.5 Te 3 ingots. We showed that hot deforming ZM ingots without intermediate BM process (namely, direct HD) is an effective way to enhance TE performance near room temperature. [ 33,112 ] The donor-like effect introduced by direct HD is weaker than that with intermediate BM process because of less deformation and a stronger recovery effect. [ 2,32,33,66,67 ] The carrier concentration slightly increases (decreases) for the n-type ZM Bi 2 Te 2.79 Se 0.21 (p-type ZM Bi 0.5 Sb 1.5 Te 3 ) sample upon direct HD, a high α value is thus retained ( Figure 10 a,b). [ 33,112 ] In contrast, the n e of the n-type HP Bi 2 Te 2.79 Se 0.21 sample is nearly tripled and the n h of the p-type HP Bi 0.5 Sb 1.5 Te 3 sample is reduced nearly by half due to a stronger donor-like effect introduced by HP. [ 33 ] www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600004 Figure 10. Room temperature carrier concentration and carrier mobility of a) n-type Bi 2 Te 2.79 Se 0.21 alloys, [ 33 ] and b) p-type Bi 0.5 Sb 1.5 Te 3 alloys. [ 112 ] Temperature dependent lattice thermal conductivity of c) n-type Bi 2 Te 2.79 Se 0.21 alloys, [ 33 ] and d) p-type Bi 0.5 Sb 1.5 Te 3 alloys. [ 112 ] Temperature dependence of zT of e) n-type Bi 2 Te 2.79 Se 0.21 alloys, [ 33 ] and f) p-type Bi 0.5 Sb 1.5 Te 3 alloys. [ 112 ] a,c,e) Reproduced with permission. [ 33 ] b,d,f) Reproduced with permission. [ 112 ] Copyright 2013, The Royal Society of Chemistry.
Compared with the n-and p-type ZM ingots, all ZM-HD samples exhibit somewhat lower carrier mobility µ , due to the weakened texture and increased grain boundary density. [ 33,112 ] As expected, the fi ne-grained HP sample (subject to BM) exhibits the lowest µ . The HD sample shows moderately degraded µ compared with the HP sample owing to largely retained textures and coarse grain sizes. Importantly, the weak donor-like effect, which leads to an increase of σ in n-type sample and an increase of α in p-type sample, offsets the adverse effect of µ degradation on the PF . [ 33,112 ] Since the electrical properties of the n-type sample tend to be more sensitive to the texture and the carrier concentration variation than the p-type sample, [ 33,124,125 ] HD is recommended for the n-type sample.
Concerning the κ ph , direct HD introduces multi-scale microstructures, including micro scale grains and reduced texture, nanoscale distorted regions, and atomic scale line and point defects. [ 33,112 ] These multi-scale scattering centers can effectively scatter heat-carrying phonons with a wide wavelength range and thus effectively suppress the κ ph (Figure 10 c,d). [ 33,112 ] As a result, the maximum zT reaches ≈1.2 at 357 K and ≈1.3 near room temperature for n-type ZM-HD2 Bi 2 Te 2.79 Se 0.21 (HD2 denotes that the sample is hot deformed twice) and p-type ZM-HD Bi 0.5 Sb 1.5 Te 3 , respectively (Figure 10 e,f). In comparison, the HP samples (subject to BM) show a lower zT than the ZM ones owing to a larger PF degradation than the reduction of κ ph . [ 33,112 ]

Low-Temperature Power Generation
The abundant low to mid-temperature (below 500 K) waste heat from industry sectors and automobile exhaust warrants the development of higher performance TE materials in this temperature range. However, the small band gap of n-type Bi 2 Te 2.7 Se 0.3 and p-type Bi 0.5 Sb 1.5 Te 3 inherently restricts their promise because of the detrimental ambipolar effect (i.e., the excitation of minority carriers). [ 66 ] In addition, the maximum zT of p-type Bi 2x Sb x Te 3 material needs to be shifted to higher temperatures. To this end, one can either broaden the band gap or increase the concentration of majority carriers. Notably, one can achieve both tasks via increasing the Sb content in Bi 2x Sb x Te 3 system, a high zT value of ≈1.3 was obtained near 380 K in HP-HD Bi 0.3 Sb 1.7 Te 3 ( Figure 11 a). [ 66 ] Li et al. also reported a zT value ≈1.33 at 373 K in mechanically alloyed Bi 0.3 Sb 1.7 Te 3 with SiC nanoparticles. [ 122 ] Compared to HP-HD sample, less Sb ( x = 1.6) is needed for the optimal carrier concentration in HD-ZM sample. [ 126 ] As mentioned above, powder metallurgy processing leads to a strong donor-like effect and thus a high n e , making n-type Bi 2 Te 3x Se x (0 < x < 1) more suitable for application of low-temperature power generation. [ 32 ] For instance, the n-type HD Bi 2 Te 2.3 Se 0.7 subject to BM has a peak zT of 1.2 at 445 K [ 32 ] (Figure 11 b). Combining melt-spinning (MS) and spark plasma sintering (SPS), Wang et al. reported a maximum zT of 1.0 at 460 K for n-type Bi 1.9 Sb 0.1 Te 2.55 Se 0.45 . [ 127 ] Yan et al. reported an ≈22% improvement in peak zT value from 0.85 to 1.04 at 398 K in n-type Bi 2 Te 2.7 Se 0.3 HD2 samples. [ 128 ]

Mid-Temperature Power Generation
Using V 2 VI 3 compounds in mid-temperature (above 500 K) applications demands a larger band gap E g . The binary Sb 2 Te 3 has the largest E g ≈ 0.20 eV among all the p-type Bi 2x Sb x Te 3 materials. [ 129 ] However, the binary Sb 2 Te 3 is plagued by the presence of numerous Sb Te ′ , which leads to a value of n h ≈ 10 20 cm -3 and thus a low α and a high κ el . [ 29,49 ] Doping by sulfur [ 130 ] or indium [ 71 ] can increase the E AS of Sb Te ′ and hence reduce the n h . The E g of Sb 2 Te 3 can be broadened by alloying with In 2 Te 3 ( E g ≈ 1.2 eV) [ 131 ] or Sb 2 S 3 ( E g ≈ 1.67 eV), [ 132 ] thereby suppressing the detrimental bipolar effect in mid-temperature range. As a result, a maximum zT ≈ 0.92 at 710 K and an average zT ≈ 0.8 between 500 and 710 K were obtained in (In, Ag) co-doped Sb 2 Te 3 (Figure 11 a). [ 94 ] Density functional theory calculations by Mehta et al. suggested that subatomic-percent Sulfur doping of nanostructured Sb 2 Te 3 holds the promise of zT ≈ 1.7 at 600 K and ≈1.6 at 800 K. [ 130 ] www.MaterialsViews.com www.advancedscience.com Adv. Sci. 2016, 3, 1600004   Figure 11. a) zT curves of p-type (Bi,Sb) 2 (Te,Se) 3 alloys. [ 13,15,66,94,112,122,126 ] b) zT curves of n-type (Bi,Sb) 2 (Te,Se) 3 -based alloys. [ 32,33,39,127,128 ] In n-type Bi 2 Te 3x Se x , increasing the Se content increases the E g and it increases the n e in conjunction with doping by iodine. The iodine-doped ZM Bi 2 Te 1.5 Se 1.5 shows a maximum zT of 0.86 at 600 K (Figure 11 b). [ 39 ] We showed that the repetitive HD Bi 2 Te 2 Se 1 material has a zT value of 1.0 at 513 K. [ 67 ] As a comparison, single crystalline Bi 2 Te 2 Se 1 is located right at the point of p-n transition that has the lowest σ and α , [ 32 ] the E g of single crystalline Bi 2 Te 3x Se x happens to reach its maximum at x = 1.0, above which the E g starts to decrease with increasing x value. [ 133 ] To ease this restriction, the HD process and thus the donor-like effect are utilized. [ 32 ] Liu et al. recently conducted a systematic study of n-type Bi 2 Te 3 -Bi 2 Se 3 -Bi 2 S 3 system. [ 134 ] These results showed that Bi 2 Te 2 S 1 has a peak zT value ≈ 0.8 at 573 K and Bi 2 Se 1 S 2 ≈ 0.8 at 773 K upon high energy BM followed by the HP process. It is plausible to infer that the donorlike effect plays a key role in these materials.

Approaches beyond Intrinsic Point Defect Engineering
The focus of Section 6 is on the underheeded role of intrinsic point defects in the (i) nanostructuring approach and (ii) texturing approach. Extensively employed in V 2 VI 3 materials but without explicitly containing "intrinsic point defects" in their names, the nanostructuring and texturing approach involve powder metallurgy processes such as BM, HD, HP. These processes are the same ones we employ to create intrinsic point defects (cf. Section 3.3 and 3.4). Hence the proper assessment of nanostructuring and texturing approach is subject to a proper assessment of donor-like effect and recovery effect.
While the nanostructuring approach was initially proposed to enhance the electrical properties of TE material via quantum confi nements, [ 135,136 ] most advances in enhancing zT are attained by the reduction of κ ph in nanostructured TE material. On one hand, the nanostructuring process introduces numerous grain boundaries that strongly scatter heat-carrying phonons. On the other hand, it is risky to assert that grain boundary scattering is the primary mechanism underlying the reduction of κ ph . A good example is the reduction of κ ph in Bi 2 Te 3 nanocrystals (cf. Section 4.2), [ 120 ] in which the deformation-induced vacancies dominate over grain boundaries.
Nanostructuring approach can be categorized into two basic classes: bottom-up and top-down. In a typical bottom-up approach, nanostructures are fi rstly prepared by BM, [137][138][139] or MA [140][141][142][143] before consolidation to yield nanostructured bulk materials. A high zT value of 1.4 using ZM ingots as the feedstock [ 13 ] and a high zT value of 1.3 using elemental chunks as the feedstock [ 138 ] were attained in p-type Bi 2− x Sb x Te 3 nanocomposites by a highenergy-BM-HP procedure. In comparison, HD is an effective topdown approach for creating nanostructures and enhancing the zT of both p-and n-type (Bi,Sb) 2 (Te,Se) 3 -based materials. The signifi cant reduction in κ ph of HD-ZM sample is ascribed to effective phonon scattering by multi-scale microstructures. [ 33 ] Texture refers to the misorientation between grains. To the fi rst order approximation, texture is independent of intrinsic point defects. Texture is found to be crucial for the carrier mobility µ , [144][145][146][147][148][149][150][151] intrinsic point defects are shown to affect the carrier concentration n (cf. Section 2 and 3) while they both control the anisotropy of { σ , α , κ }. The commercial V 2 VI 3 TE materials are fabricated by unidirectional crystal growth methods such as Bridgman, [ 152 ] Czochralsky, [ 153 ] and zone-melting (ZM) [ 154 ] technique, which lead to textures in the as-grown ingots. Advanced powder metallurgy methods, including HP, [ 155 ] SPS, [ 156 ] hot extrusion, [157][158][159][160][161][162] shear extrusion, [ 163,164 ] powder extrusion, [ 165 ] and equal channel angular extrusion [ 166,167 ] have been utilized to introduce textures in V 2 VI 3 materials. It is plausible to assume that these deformation processes involves the donor-like effect (cf. Section 3.3). For example, Zhao et al. prepared fi ne-grained n-type Bi 2 Te 3 materials with preferred grain orientation by using SPS as a hot forging tool. [ 104 ] We have employed HD process to obtain high performance p-and n-type V 2 VI 3 materials. [ 2,32,66,67 ] The degree of texture can be controlled by the HD temperature, [ 2 ] the number of times of HD, [ 67 ] and also the deformation strain. [ 66 ] Notably, the carrier concentration n strongly affects the anisotropy of { σ , α , κ }. [ 124,125 ] Increasing the n deforms the Fermi surface topology, making it more prolate and warped from an ellipsoidal shape. As a result, the anisotropy ratio in both σ and κ increases with increasing n given the same degree of texture. [ 124,125 ] As for the α , it is nearly isotropic in the extrinsic region, [ 168 ] and highly anisotropic in the intrinsic region. [ 169,170 ] The α anisotropy is attributed to the presence of minority carriers and the difference in the ratio of hole to electron mobility along the two principal directions. [ 169 ] Hence a synergistic implementation of texture and intrinsic point defects would help simultaneously attain an optimal µ and an optimized anisotropy of { σ , α , κ }.

Conclusions
Defects, ubiquitous and often wrongly conceived as performance limiters, are the key performance enhancer in diverse functional materials upon proper implementation. This review focuses on the underexplored intrinsic point defects (i.e., vacancies and antisite defects) in V 2 VI 3 semiconductors and their derivatives, regarding the compositional, mechanical and thermal control as well as their interplay with other defects towards higher thermoelectric performance. It is not our aim to emphasize the significance of intrinsic point defects over other types of defects; rather, we intend to clarify the causal chain in the synthesis-structureproperty correlation. We summarized our understanding of intrinsic point defects in a ( χ, r )-model and discussed the donorlike effect and the recovery effect in V 2 VI 3 compounds.
The study of intrinsic point defects in V 2 VI 3 compounds is not yet complete, especially regarding the role of intrinsic point defects in nanostructuring and texturing approaches (cf. Section 6), which warrants further investigations. Nonetheless, the new insights derived herein open a promising avenue for further improving the thermoelectric performance of other compounds and, in a wider context, contribute to the development of advanced functional materials by rational defect design in the long run.