Toward Accelerated Thermoelectric Materials and Process Discovery

Thermoelectric materials have the ability to convert heat energy to electrical power and vice versa. While the thermodynamic upper limit is defined by the Carnot efficiency, the material figure of merit, zT, is far from this theoretical limit, typically limited by a complex interplay of non-equilibrium charge and phonon-scattering. Materials innovation is a slow, arduous process due to the complex correlations between crystal structure, microstructure engineering, and thermoelectric properties. Many physical concepts and materials have been unearthed in this path to discovery, supported ably by innovations in technology over many decades, revealing important material and transport descriptors. In this review, we look back at some case studies of inorganic thermoelectric materials employing a bird’s-eye view of complementary advancements in scientific concepts and technological advancements and conclude that most high values of zT have emerged from developed scientific models fueled by moderately mature technologies. On the basis of this conclusion, we then propose that the recent emergence of data-driven approaches and high-throughput experiments, encompassing synthesis as well as characterization, with machine learning guided inverse design is perfectly suited to provide an accelerated pathway toward the discovery of next-generation thermoelectric materials, potentially providing a feasible alternative source of energy for a sustainable future.


Introduction
Thermoelectrics (TE) is a field at the forefront of materials chemistry, novel physics and engineering. 1 This is because development of new thermoelectric technologies not only requires deep understanding of how materials are put together, but also requires in-depth knowledge of out-of-equilibrium transport phenomena: of how heat and charge transport and scattering occurs, as well as engineering of devices. The efficiency of heat-to-power (and vice versa) conversion of a thermoelectric material is gauged by the figure of merit zT at a thermodynamic temperature T, defined as S 2 σT/κ, where S is Seebeck coefficient representing how much entropy is carried by a majority carrier (typically in a semiconducting material), σ is the electrical conductivity and κ is the thermal conductivity. 2 The thermal conductivity has two components, that which is carried by the charge carriers (electronic thermal conductivity, κe) and lattice vibrations or phonons (lattice thermal conductivity, κl). 3 A zT value of 4 or more can be competitive with existing energy generation and/or cooling technologies, providing a viable sustainable energy alternative. 4 The technology is immensely attractive as it involves non-moving parts and solid-state devices.
Innovation in thermoelectrics is limited by discovery of new materials and even though device architectures have been considered and studied in some details 5-7 , the major challenge is to design a high performance TE material -this involves a complex process of identifying the key material and transport descriptors that can be used to predict a new thermoelectric material.
For instance, an ideal thermoelectric is a 'phonon glass electron crystal' where charges can flow unimpeded, while a large temperature gradient can be maintained across the material. 8 preserved. For instance, the word "chalcogenide" could be preferentially associated to "thermoelectrics" as opposed to "ferroelectrics". The most successful case of the application of NLP techniques to materials science has been carried out by Tshitoyan and collaborators.
By collecting, processing and deploying unsupervised ML techniques on almost 3.3 million scientific abstracts, they could capture complex underlying concepts, such as structureproperty relationships in the materials. 33 Another crucial resource in data mining is the wellestablished Inorganic Crystal Structure Database (ICSD), which compiles experimental data on every crystal structure ever experimentally characterized. 34 Since a crystal structure contains fundamental high quality data, such as the space group of a material, the Wyckoff positions of the atoms in the unit cell and the crystallographic parameters amongst others, having the ICSD data provides an important link to experimental verification.
On the other hand, if the target is to optimize the phase, microstructure and doping once the material is identified, the data frame needs to be thought about differently. Obtaining the right stoichiometry and doping level to achieve optimized thermoelectric performance is a trial-anderror process that involves navigating experimental parameters depending on the method being used, where the input-output parameter space can be defined as a set of experimental conditions and the output, for instance, being the right XRD spectrum of the material synthesized and the correct doping level. Recent work has catalogued a database of experimentally synthesized thermoelectric materials, with an easy-to-access API (tedesignlab.com) [35][36][37] , but much remains to be done. Text-based mining of recipes for materials synthesis provides an interesting alternative to manually curating data and has recently garnered interest, although this has not been applied to the specific case of thermoelectrics yet. 38 Therefore, innovation can be a complex and tortuous path, progressing through identification of a new material followed by developing a synthesis process, driven by a knowledge of materials and transport descriptors.
The two driving forces for the discovery of new materials are the scientific principles behind the high performance and the synthesis and characterization techniques at one's disposal. For instance, larger zT values started to be reported with the development of the laser flash technique, thus enabling the accurate measurement of the thermal conductivity. In the scientific side of the story, larger zT values were reported by using band convergence as the necessary strategy for optimized electronic power factor. 10 Herein, we scrutinized the technological developments and scientific advances that enabled high zT in traditional and emerging TE materials. We established a rating system ranging from 'novel' to 'mature' in both categories.
While individual values are only a guide, the trends they exhibit are illuminating. Conceptually unique physical advances are rated higher in our scale whilst old concepts are rated as mature.
For instance, alloying to reduce the lattice thermal conductivity 39 has a low rating while a Peierls instability as source of strong electron-phonon coupling is rated high. 40 Technological developments are rated according to their originality. In this case, established techniques such as the temperature-gradient methods for single-crystal synthesis 41 are rated low while highthroughput methods, such high-throughput bulk synthesis are highly rated. 42 The reasoning behind these choices is obvious: novel ideas will deepen the knowledge of the materials and thus will lead to new, more efficient strategies for the enhancement of the performance. The technological advances are rated in order to enable the prediction of how the new paradigm in automation, leading to the idea of a self-driven lab, support the discovery of new materials by reducing the time between discovery and commercialization as well as the overall cost. 43 Building upon this analysis, we now define the guidelines that the innovation path in TE materials may follow. To do so, we first discuss the material and transport descriptors that define good thermoelectrics in detail. Then, we revisit the historical evolution of some chalcogen-based cornerstone materials for TE applications (hereinafter called "Case Studies") and analyze the depth of knowledge and the technological progress that led to their success, therefore providing a perspective to future researchers on where the key bottlenecks lie.
In order to accelerate thermoelectrics materials development, a combination of data generation, machine learning, high-throughput experimentation (including synthesis and characterization) and high-performance computing needs to be employed. We find that the path of innovation in TE materials has typically been driven by novel, unexplored physical and chemical phenomena and executed via deployment of mature technological processes. Figure 1. Path towards the accelerated discovery of new TE materials. The Y-axis ("Scientific Advances") represents the novelty of the physical and/or chemical strategy deployed for the attainment of high zT in a material. The X-axis ("Technological Developments") represents the maturity of the experimental technique used for the synthesis of a material. The size of the bubble is directly proportional to the zTmax in a material. However, for visualization purposes the zTmax have been magnified by a factor of 50. The colours have been arbitrarily chosen and they represent a class of materials (e.g. SnSe and alloys appear in yellow). The solid red arrow is a guide for the reader and points at the sector where most materials with high zT values lie. The discontinuous purple and teal arrows depict the historical evolution of a particularly chosen material. The size of the arrow's head indicates a material with higher zT.

Thermoelectric Material and Transport Descriptors
Thermoelectric (TE) descriptors allow the rapid assessment of the potential of a material by utilizing the appropriate combination of one or more fundamental parameters. 44 It is desirable to have a one-to-one correlation between the descriptor and zT. 12 Some of the TE descriptors that have been used so far are: -Band gap (Eg): The band gap of a semiconductor is defined as the difference in energy between the bottom of the conduction band (CBM) and the top of the valence band (VBM) and is important as it determines the upper limit to optimum temperature for a TE material.
Goldsmith and Sharp determined that the maximum Seebeck coefficient that a material could reach at a given temperature is: Where Smax is the maximum value of Seebeck coefficient, Tmax is the absolute temperature at which Smax occurs and e is the electron charge. Based on this, loosely it was identified that the optimum bandgap for a TE material should satisfy the criteria > 10 . 45 However, Gibbs et. al. showed that significant deviations from this may occur when dealing with narrow Eg materials as bipolar conduction is not negligible. 46 Therefore, care must be taken when using band gap in identifying a promising material for a target operating temperature T.
-Weighted mobility (U): Introduced by Slack and defined as: where µ0 is the intrinsic mobility, mS * is the density of states effective mass and me is the electron mass. 47 U is tied to a fundamental property of a material, the bond-weighted difference in electronegativity (Δχ) between its elemental constituents. 47 Slack attributed the variation of U with Δχ to the difference in the bonding of the compounds. For larger values of Δχ, the electron charge transfer between the ions is larger. For a given T, the phonons in the lattice will produce modulations in the local electrostatic field thus increasing charge carrier scattering. As a consequence, U will decrease with increasing Δχ. Thus, in principle, the lower the Δχ the more promising a material is for TE applications. An intuitive correlation between weighted mobility and electronegativity difference from a chemical bonding perspective can be estimated, although the use of this is limited. Large electronegativity difference will generally result in ionic-like bonding where carriers tend to be localized and vice versa for small electronegativity difference. This is expected to affect the deformation potential which can be linked to intrinsic carrier mobility in the deformation potential scattering regime, via the following expression: where µc is the classical mobility, κl is the lattice thermal conductivity and T is the absolute temperature in K. Recently, in 2013, this parameter was popularized again thanks to the work by Wang et. al. 44 The authors assumed that the scattering is dominated by acoustic phonons (r = -0.5) and that the bands were parabolic with a spherical Fermi surface. These assumptions allowed them to describe the quality factor, B, as: where mS * is the density of states effective mass and m * C is the inertial effective mass. The larger the Fermi surface complexity factor for a material, the more chances it may be a good thermoelectric material. This is because it indicates a large value of N v * (thus a larger number of carrier pockets are contributing for a fixed T and chemical potential) and a large value of K * (larger deviation from the canonical spherical shaped Fermi pocket). 51 While Nv * can be estimated directly from the bandstructure, determining K * would require precise DFT calculation of the band structure as well as non-trivial averaging model to quantitatively represent the anisotropy factor, especially for non-parabolic band. 52 -Anharmonicity: most of the recent achievements in TE have been due to the suppression of the lattice thermal conductivity, sometimes to the point of reaching the amorphous limit and thus approaching a phonon glass. A rather convenient way to quantify the anharmonicity in a material is by looking into the dimensionless Grüneisen parameter (γ = αGV/Cv, with α the thermal expansion coefficient, G the bulk modulus, V the volume and Cv the heat capacity) , which quantifies the change in the phonon dispersion as a consequence of a change in volume. 53 In general, the larger the Grüneisen parameter the more anharmonicity is present in the material and thus the lower the values of lattice thermal conductivity, due to softer phonon modes as well as enhanced phonon-phonon Umklapp scattering. 54 Recently, Nielsen et. al. discussed that the lattice thermal conductivity could be also be effectively minimized in materials with lone pairs. 55 While the exact mechanism by which the lone pairs induce anharmonicity in the structure is not exempt of debate and can be material-specific, the preservation of long-range symmetry to conserve electron mean free paths, but simultaneously distorting local ordering to induce anharmonicity could provide a great knob to tune TE properties. 54 -Energy dependent scattering, r: for a real crystal (with acoustic and optical phonons, defects, impurities and grain orientations and varied grain sizes) carriers travel for certain distance (mean free path) before they are scattered. It is often useful to consider the relaxation time between collisions (τ) in its energy-dependent form: where τ0 is the constant (energy independent) relaxation time, kB is the Boltzmann constant, T is the absolute temperature, E is the energy and r is a characteristic exponent that describes the particular scattering. For a material in which transport happens in 3D and the bands can be modelled with parabolas, r = -0.5 for acoustic phonon scattering, 0.5 for polar optical phonon scattering and 1.5 for ionized impurity scattering. 13 Mobility and relaxation time are directly proportional (µ = eτ/m * C). 13 Thus, a larger scattering time will maximize the mobility and in turn the electrical conductivity. Interestingly, in the Seebeck coefficient, the value of 0 does not matter and only the energy-dependence of the scattering time affects the entropy per charge. Therefore, identifying and tabulating this energy-dependence for real crystals can provide a valuable descriptor to segregate potential TE materials.
-Electron fitness function (t): introduced by Xing et. al. this descriptor can be directly evaluated from first principles and Boltzmann transport theory, thus not requiring any experiment. 56 It is defined as: where N is the volumetric electronic density of states. For its calculation, the authors assume single parabolic band approximation and the constant relaxation time approximation (CRTA).

-Inertial Effective Mass (mc * )
Building on earlier works by Gibbs et.al. 14 , by analyzing and calculating polycrystalline averaged data mined from 1617 n-type and p-type compounds from Materialsproject.org, Suwardi et.al., found that in addition to conventional understanding that low inertial effective mass results in high carrier mobility, it also facilitates sensitive power factor enhancements (i.e. given the same magnitude of band alignment, the enhancements to the power factor is larger for lower effective mass compounds). 13 This conclusion can be explained by the fact that it takes lower amount of doping to move the chemical potential of a compound with low effective mass than its heavier effective mass counterpart. Therefore, given all other parameters remain equal, the optimal carrier concentration of compounds with low effective mass is lower compared to the ones with heavy effective mass, which results in higher intrinsic mobility and thus higher power factor. It's efficacy as a descriptor was also proposed by Samsonidze and Kozinsky for half-Heusler compounds. 57

-Mechanical Properties:
Significant progress has been recently achieved by obtaining high zT values for thermoelectric materials. Most of these materials, however, deteriorate at temperatures near peak zT values, which is a serious challenge to make reliable TE devices. In reality, TE materials could be exposed to thermal and mechanical stresses which may cause reduction in device efficiency. 58 For instance, in waste heat recovery applications, sublimation of TE materials at the hot side of the device may occur, and hence, reducing the cross-sectional area at the semiconductormetal junction, that leads to lower electrical power. 59 Therefore, considering the mechanical robustness as a design principle by the thermoelectric community will aid in obtaining robust and highly efficient TE devices. Several studies focused previously on how to experimentally measure the mechanical properties of materials. [60][61][62] Mechanical properties of TE materials, such as Young's modulus, strength, fracture toughness, etc, are linked with the material's crystal structure and bonds between atoms. 60,63 For instance, the relationship between stress and strain in the linear elasticity regime is defined as Young's modulus. 58 Therefore, it would be very interesting to use the relationship between the 'macroscopic' mechanical properties and the 'atomic' level parameters, such as the change in stiffness in the material as a function of atomic displacement and establish them as screening descriptors while searching for promising candidates to ensure stable TE devices. Now, armed with this deep understanding of TE descriptors, we progress to consider test cases of specific chalcogen-based materials and the technologies that enabled significant progress in their thermoelectric performance.

Case Study 1: Bismuth antimony telluride (BST)
Bi2Te3 was recognized as a potential layered TE material (see Figure 2(a)) in the 1950s for TE refrigeration. 64 Several material-engineering approaches have been investigated to optimize the TE performance of Bi2Te3 such as doping, alloying, and nanostructuring. 65 Making alloys of Bi2Te3 was one of the first strategies to tune its electronic properties. For instance, pressing and sintering of Sb2Te3-Sb2Se3 and Bi2Se3 create p and n-type Bi2Te3 alloys, respectively. The maximum values of the figure of merit for the p and n-type samples are 0.51 and 0.92 at 300 and 575 K, respectively. 66 After seven decades of intensive research on Bi2Te3, a high record zT of 1.86 at 320 K was reported for p-type Bi0.5Sb1.5Te (BST, see Figure  2(b)). 67 This remarkable zT value was achieved by introducing dense dislocation arrays at the grain boundaries to effectively scatter phonons with a wider range of frequencies without hindering the electronic transport. Nanostructuring approach showed that the zT of BST can be improved by reducing the thermal conductivity. Poudel et. al. revealed that the maximum zT of 1.2 at 373 K can be achieved in nanocrystalline BST made by hot pressing nanopowders prepared by ball milling (see Figure 2(b)). 31 Furthermore, doping Bi2Te3 by resonant impurities such as Sn induces a sharp excess in the DOS below the valence band (~15 meV), and hence resulting in enhanced Seebeck coefficient. 68 The TE power factor can be optimized by alloying Bi2Te3 with Sb2Te3, which causes the substitution of Bi with Sb, resulting two valence maxima (with the same energy) in the electronic DOS, and therefore increasing the band degeneracy from N=6 to 12. 69 Additionally, the figure of merit of (Bi0.25Sb0.75)2Te3 was improved by optimizing the converging valence bands of Bi2Te3 and Sb2Te3. The excess of Te was selected to tune the carrier concentration and obtaining the optimum zT of 1.05 at 300 K without nanostructuring. 70 Son et al investigated the effect of grain size in p-type bismuth telluride alloy made by sintering. They optimized the grain size by controlling the ball milling time, which in principle revealed how grain size rules thermal transport, and hence zT of 1.14 was found near room temperature. 71 Hence, in the case of Bi2Te3/Sb2Te3 and their complementary alloys, zT has gone up from 0.5 to 1.8 over a span of seven decades (see Figure 2(c)). The key advancements have been both a combination of novel physics such as DOS distortion, band convergence, phonon scattering by nanostructuring as well as new processing techniques such as spark plasma sintering, and nanostructuring through milling. This is an example where even in well-established material systems, there is room to explore new phenomena in physics, where process innovation has been a key driver to push the zT up by 400%. This case study provides a prime example of a known material system springing surprises over many decades, and we can predict that using machine learning, high-throughput experiments and process optimization, similar development of other known material systems could potentially be sped up significantly with the use of new tools. demonstrated by the distortion of the electronic DOS by incorporating thallium impurity levels, where purportedly the Thallium impurity level introduced resonant scattering, thus enhancing the Seebeck coefficient significantly, as shown in Figure 3(d). 79 Subsequently, a zT of 2.2 at 800 K was obtained for AgPbmSbTe2+m due to concurrent enhancement in electrical conductivity and Seebeck coefficient, which was attributed to the change in the DOS structure and the effective doping. 80 In 2012, Biswas et al demonstrated mesoscale engineering of nanostructured PbTe to improve the zT further (2.2 at 915 K, see Figure 3(b) and 3(c)). This high zT was obtained due to the huge reduction in the lattice thermal conductivity by scattering phonons with a broad frequency spectrum in a hierarchical nanostructuring approach. 81 Very recently, Liu-Cheng Chen et al have shown that a prominent enhancement in zT (1.7 at room temperature) for Cr doped PbSe can be achieved by applying external pressure. They attributed this enhancement to the topological phase transition driven by the external pressure that promotes electrical conduction. 82 Structurally analogous to PbTe (see Figure 3(a)), tin telluride (SnTe) has attracted a lot of attention due to its potential to perform as well as PbTe, with the benefit of being lead-free and therefore non-toxic. 83 The lower performance of SnTe has been attributed to a larger valence band offset between the light-hole L band and the heavy hole Σ band, when compared to that of PbTe (0.30 eV and 0.15 eV, respectively), hindering band convergence and thus reducing the maximum power factor via reduction of the number of available valleys (Nv). In addition to this, SnTe has an intrinsically high concentration of Sn vacancies, leading to overdoping and high thermal conductivity. 84 However, researchers have deployed a plethora of strategies in order to enhance the performance of SnTe. One of the very first strategies was the introduction of nanostructures, that would act as phonon scattering centres and reduce the lattice thermal conductivity. Tan et. al. showed that alloying with 3% mol Cd, band convergence can be achieved and moreover, introducing endotaxially nanostructured CdS effectively suppresses phonon scattering and therefore reduces the lattice thermal conductivity. The combination of these strategies led the authors to a zT of 1.3 at 873K. 84 In addition, synergistic band engineering in addition to a clever manipulation of the intrinsic defects has been proved effective to this end. Tang and co-workers demonstrated that alloying SnTe with 5% of GeTe increases the solubility of the SnTe-MnTe alloy, with an overall reduction of the band offset, thus achieving band convergence and increasing the power factor. In addition, alloying with Cu2Te reduces the lattice thermal conductivity down to its amorphous limit, rendering a zT of 1.8 at 900K. 85 Hence, in the cases of PbTe/Se and SnTe, higher zT has mostly been enabled by the emergence of new physics coupled with materials engineering to control charge and phonon scattering.
This presents a case where seeding and testing of new ideas is necessary to push the boundaries of knowledge in existing materials, similar to the BST case study.

Silver (TAGS)
GeTe-based compounds (TAGS -Tellurium-Antimony-Germanium-Silver) have been identified as potentially good thermoelectric 88 since 1960s 89 and has been widely explored recently. 90 In terms of application, it was used as RTG in Pioneer10 space probe to Jupiter and numerous space-applications afterwards. It was mainly explored as an isostructural (see Figure   4(a)) alternative to the toxic PbTe (at high temperature) and the lack of high temperature stability of p-type PbTe. Alloy of (0.15) AgSbTe2 -(0.85) GeTe (TAGS 85) was found to display robust high temperature performance as well as relatively low thermal expansion coefficient (15 x 10-6 K-1 compared to 29 x 10-6 K-1 for PbTe) which is beneficial for mechanical stability at high temperature. 89 Unlike SiGe, TAGS was mainly used for intermediate temperature application (below 525 C) due to its low phase transition temperature (510 K) and high sublimation rate at high temperature, compromising its compositional stability.
The rationale of alloying GeTe with AgSbTe2 were due to the fact that pristine GeTe has low power factor due to excessive carrier concentration induced by Ge vacancies. [91][92][93][94] In most studies and applications, the process condition used was mainly melting stoichiometric amount of alloy ingot in ampules since sintering and cold pressing were found to be unsatisfactory for fabricating TAGS legs. 89 Prior to 2008, most works on TAGS were based on the concept of alloying-induced lattice strain which leads to low lattice thermal conductivity. Hence, most reports were focused on the phase transformation (see Figure 4(b)) and thermoelectric properties of these system, not on the process related microstructure. 95,96 In 2008, Yang et. al examined the effects of the microstructures of TAGS by quenching and pulverizing molten ingots into micron sized particles followed by hot pressing. It was found that in situ formed nanodomains and inhomogeneities in the order of 10 nm was the main reason for low thermal conductivity in this system. 97 Subsequently, carrier and phonon engineering with AgSbTe2 alloy lead to high performance by simultaneously optimizing carrier concentration and introduces phonon scattering centres through alloying. 98 In addition to de-doping of GeTe, parallel efforts to improve the Seebeck coefficients such as introducing resonant states by introducing Dy in AgSbTe2-GeTe 114 as well as Ce and Yb in TAGS-85 was reported. 115 Furthermore, band convergence was achieved by doping 3 mol% Bi2Te3 into Ge0.87Pb0.13Te. 116 Hitherto, the record breaking zT of 2.4 at 600 K for GeTe based compound was reported by Yanzhong Pei, et.al. in 2018. By utilizing slight symmetry-breaking near the rhombohedralcubic transition temperature to synergistically achieve band-convergence and reduce lattice thermal conductivity. 117,118 This is an incredible study considering the processing condition was simply using hand ground and hot pressing. More recently, crystal-field engineering and ferroelectric instability has been touted as another route to improve the performance of GeTe. 119 Last but not least, entropy engineering (by increasing configurational entropy via alloying) have also be shown to improve power factor. 120,121 Overall, over the years, breakthroughs in scientific understanding (e.g. alloying and doping to optimize carrier concentration, band convergence, and phonon-scattering) has enabled the zT of this material system to increase dramatically. More importantly, some of the new scientific breakthroughs (i.e. nanoscale grains to scatter phonons) were enabled by adoption of relatively mature technologies (i.e. ball milling, spark plasma sintering) that subsequently enabled scientists to investigate new physical mechanisms to improve the thermoelectric performance.

Case Study 4: Silicon-Germanium (SiGe)
An example of a traditional compound which has wide range of applications can be found in cubic SiGe (See Figure 5(a)). 123 SiGe is a tried and tested compound with primary application in radioisotope thermoelectric generator used by NASA in 1976. 59,124 The main draw to using this compound lies in its high temperature mechanical and performance stability (up to 1300 K). In the early days, hot pressing was mainly used to fabricate polycrystalline bulk while preparation from melts was used for the study of silicon-germanium mixed-crystals or "alloys" as possible materials for thermoelectric generators by Ioffe and Ioffe. Initially, powder metallurgy (hot pressing) was intended as a way to change carrier concentration, as the dopant solubility changes near the liquidus line. Later, this powder metallurgy processing was used to improve electrical properties via density increase as well as decreased thermal conductivity via optimizing grain size. With the evolution and advancements of materials processing technologies, higher performance SiGe were obtained using the combination of mechanical alloying + powder metallurgy (SPS). 125,126 The evolution of processing technique for this compound can be summarized as follows: Preparation or alloying from melts (single crystal)  Powder metallurgy process  Mechanical Alloying (i.e. ball milling)  Thin films/superlattices.
In terms of thermal transport, the lattice thermal conductivity of SiGe mixed crystal was found to be lower than its respective parent pure crystals, reaching the alloy limit 39 , while the carrier mobility was found out to be just slightly lower, which justifies the alloying of Si and Ge. 127 The resulting optimal zT at that time were 0.5 (p-type) and 0.9 (n-type). 89 In 1978, Pisharody and Garvey proposed that dissolving small amount of GeP into SiGe to further reduce lattice thermal conductivity. 128 However, no reduction in thermal conductivity was observed: instead, adding GeP inadvertently optimized the carrier concentration and hence zT.
As technologies progressed, nanostructuring in the form of SiGe superlattices to exploit quantum effects was studied. Advancements in vacuum systems enabled Superlattices of SiGe to be grown from as early as 1970's via ultra-high vacuum evaporation techniques. 129 Later on, with the advent of Molecular Beam Epitaxy, more precise control of composition and thickness could be achieved. Building upon the physical intuitions derived from nanostructuring techniques, then-record zT for nanostructured bulk p-type and n-type SiGe bulk alloys of 0.95 and 1.3, was achieved in 2008 and 2009, respectively. [130][131][132] The spectacular progress in zT enhancement owes a lot to a key development in materials processing: advancement in ballmilling, which enables nano-grains to be achieved. This, combined with other state-of-the-art process back then (DC hot-press) was used to form nanocrystalline alloys. In retrospect, both hot pressing and mechanical alloying have already existed for more than 20 years by this point in time. To date, the record zT for bulk material ~ 1.84 for n-type SiGe at 1073 K was achieved by multi-frequency (broadband) phonon scattering using the combination of point defects, dislocations, and grain boundaries (see Figure 5(b) and 5(c)). 124 In the case of SiGe, like other material case studies, technological progress indeed enabled new scientific directions that were previously not accessible.

Emerging materials Tin Selenide (SnSe) and Tin Sulphide (SnS)
Tin selenide (SnSe) is a layered orthorhombic material that historically, unlike other traditional TE materials like PbTe or Bi2Te3, has been less explored. 133,134 It was prepared for the first time by Albers et. al. in 1962, employing traditional single crystal methods, and not much work was done thereafter. 135,136 In 2014, Zhao et. al. reported an ultralow lattice thermal conductivity in pristine single crystals along the b-axis (≈ 0.23 W m -1 K -1 at 973K). They selected this material because traditionally, materials with layered structures (such as Bi2Te3) are good TE materials. In the case of pristine SnSe, a zT of 2.6 ± 0.3 at 923 K was achieved as a consequence of the large anharmonicity and anisotropy in the strong covalent bonding between Sn and Se in the b-axis. 137 The same authors, two years later and employing the same technique, managed to introduce sodium (Na) as hole dopant, increasing the value of zT average but without further increase in zTmax. 138 Other than Na, only silver (Ag) was found to be a good dopant for SnSe. Chen et. al. deployed a melting and hot-pressing strategy for the doping of polycrystalline bulk SnSe with 1% mol Ag, reporting a zT of 0.6 at 750 K. 139  break the record zT. The synergistic enhancement of m* without a dramatic decrease in mobility, combined with a suppression of the thermal conductivity due to softening of optical phonons enabled them to reach the current zT record of ~2.8 ± 0.5 at 773 K for n-type single crystal SnSe (see Figure 6 (a)). 41 Similar work was conducted by He et. al. for the synthesis of low cost, Earth abundant SnS0.91Se0.09 single crystals and found that Se had the same effect that Br in SnSe: it enabled the two-band convergence, two-band divergence, and two-band crossing interplay (see Figure 6(b)) that led to a zTmax of 1.6 at 873 K. 142 Thus, we conclude that the combination of new chemical phenomena (large bond anharmonicity in the b-axis) and the synthesis of high-quality samples by means of a mature technology are the main driving forces for the discovery of the material with highest zT at the moment. This is in line with our observations from Figure 1 and reinforces the idea that new, high performing TE materials are to be explored by scientific advances as opposed to technological.

Magnesium antimonide and alloys (Mg3Sb2 -Mg3Bi2)
Magnesium antimonide (Mg3Sb2) and its alloys are a recent material that is set to substitute bismuth telluride and its alloys for low T applications. 143 The main factor hindering the replacement is the complex synthesis and processing of the compounds, as the high vapour pressure and causticity of Mg introduces defects and boundary phases that have a negative impact on the transport properties. 144,145 Most of the efforts have been centred on classical alloying approaches in order to reduce the thermal conductivity and increase the grain size, thus improving the electrical properties. Shi et. al. utilized a combination of melting, annealing and hot pressing to achieve a zT of 1.1 in the 300K-500K range for the n-type Sc-doped Mg3Sb2−Mg3Bi2 alloy. This was realized due to the coarse-grain structure enabled by the synthesis and processing conditions. 146 Another step towards better performance in Mg3Sb2 was achieved by simply changing the processing conditions, revealing that a clever optimization of the synthesis is a key parameter for obtaining high performance TE materials. 147 Here, Shi and co-workers employed tantalum tubes as sealing units for melting of the elemental precursors for the synthesis of polycrystalline Mg3.05Sb2−x−yBiy−xTex (x ≤ 0.04, y ≤ 1.5) alloys. This sealing prevents oxidation during hot press sintering and Mg from evaporating, thus reducing the vacancies that could be created. This led to an enhancement in mobility due to the reduction of grain boundaries, that enabled them to achieve a zT of 0.72 at 300K and a zTmax of 1.31 at 500K. 148  This case study is a prime example of how when a new material is discovered enabled by new physics, existing processing techniques and technological advancements can be adopted quickly to further optimize the TE properties.

Discussion
Our case studies reveal that breakthroughs in thermoelectrics mostly seem to emerge from new scientific ideas when supported by technologies that are moderately evolved; for instance a brand new technology would not (by itself) be sufficient to push an existing material towards high values of zT -therefore materials discovery via new physics, especially of nonequilibrium charge scattering and material/transport descriptors remains the key advancing step. This is consistent with our conclusion from Figure 1 It is also to be noted that in terms of device fabrication, manual p and n legs in series have been the tried and tested method for decades of thermoelectric device applications. More recently, some emerging techniques have been developed including electrochemical deposition-based technique to fabricate micro-legs 151 , CMOS fabrication techniques 152 , and 3D printed legs. 153 With the advancement and expected maturity of 3D printing technologies, we expect it to play a pivotal role for large scale, facile thermoelectric device fabrication in the near future.
To this end, it is highly encouraging that many recent reports in thermoelectric research go beyond reporting zT to include device characteristics as well as efficiency. 150 For instance, either power generation or cooling performance can be included to support the claim for zT and applicability of the thermoelectric material for a real-world application. This serves a dual purpose: as a confirmation for the reported zT as well as going further to demonstrate viability of device fabrication. In addition, in the presence of good device models, as is possible in thermoelectrics, machine learning can be used to perform system level diagnostics to directly determine limiting factors affecting device performance (such as large contact resistance, imperfect load matching conditions, etc. 154 )

Data Driven Approaches
With open source materials databases becoming more available and machine learning reaching maturity, we live in a privileged era of identifying key parameters that comprehensively describe thermoelectric materials (i.e. descriptors), leveraging upon existing physical understanding to derive new physical insights. A good example of the state-of-the-art physical insights based on data-driven study is the fermi surface complexity factor ( * * ). 14 The efforts to discover compounds with high * * values was built on earlier work in high-throughput thermoelectric compounds screening using DFT and BoltzTraP. 14,156,157 Other efforts focused on band-structure as descriptor. 158 While * * and band-structure are relatively insightful electronic descriptors for thermoelectrics, their interdependence with the scattering times renders them less comprehensive. A more recent study using the same dataset reveals the important role of inertial effective mass in obtaining both high * * and sensitive enhancements to power factor via band alignment. 51 It is important to qualify that at this stage, these data-driven insights are still largely DFT-based with some coarse assumptions (i.e. constant carrier relaxation time approximation as well as a rigid band). A more powerful approach can be envisaged by taking into account the electron-phonon interaction in the transport calculations that may give more realistic values of thermoelectric parameters, especially carrier mobility. Furthermore, recent reports using intuition-agnostic approaches based on unsupervised machine learning of word-embeddings from materials science literatures predicts several high performance thermoelectrics such as CuBiS2, CsGeI3, and TlSbSe2 that traditionally have never been reported in any thermoelectric literatures. 33 In addition, the idea of creating a comprehensive experimental database is alluring, yet a gargantuan undertaking. Mapping out the entire stoichiometric space for inorganic compounds by utilizing key chemical concepts and elemental attributes is one approach to overcome this complexity, allowing for advances in machine learning to pick out irreducible representations that can connect process to structure to property. 159 Overall, in addition to technological and scientific progress, creation and use of materials data provides a new dimension of discovery that can potentially lead to both new materials as well as new scientific/physics discovery.

Theoretical Calculations and Machine Learning for Predicting Efficient TE Materials
Theoretical calculations represent an essential step that inspires experimentalists to investigate research on promising candidate of thermoelectric materials. For example, the remarkable work by Dresselhaus et. al. drove research in the thermoelectric community towards nanostructuring to promote discretization in the electronic density of states that were expected to lead to superior TE performance. 78 Furthermore, complex TE materials (such as skutterudites, clathrates and Zintl phases) had been predicted to exhibit exceptional performance by breaking the intercorrelation between transport properties that determine zT. 2 In the previous decades in the history of TE research, conventional methods of theoretical calculations (such as density functional theory, molecular dynamics, etc) have been usually reliable options to predict or explain rigorously the interesting transport phenomena in TE materials. However, they are computationally expensive with limited scope of screening in the space of materials.
Recently, there have been several attempts to utilize machine learning tools to uncover nontraditional TE materials that surpass their traditional counterparts, that may not be captured by human intuition. 160 For instance, using materials descriptors 161 and deep neural networks to predict stability of mixed garnets and perovskites, 162 graph-based neural networks for inorganics 163 as well as organics 164 are some examples of using machine learning approaches to predict ground-state properties of materials. However, predicting functional properties such as in thermoelectrics, where charges and phonons are out of equilibrium, requires better datasets for machine learning approaches to learn from and are still in their infancy. 165,166

Machine Learning and Process Optimization towards Inverse Design
Traditional characterization tools, which can investigate a wide range of physical properties (surface morphology, crystal structure, electrical/magnetic, optical properties etc), have played essential roles in understanding the structure-property correlation, and hence theories and models were established. However, in the era of Artificial Intelligence (AI) and ML, beside high-throughput (HT) materials synthesis or processing, HT characterization is the need-ofthe-hour to either test existing hypotheses or discover new phenomena. The current challenge is to make HT synthesis and characterization tools that can contribute effectively to accelerating research outputs. Piotr S. Gromski et al have proposed a universal approach (Chemputer) for chemical synthesis and discovery by having robots that can investigate chemical reactions and data analysis in a much faster manner than manual methods. By integrating multiple characterization tools in the loop, extensive size of data can be generated that would be fed into optimization algorithms to explore the multidimensional space of the chemical reactions. 167  novel polymers with desired cloud point temperatures ranges from K with a high accuracy that is limited to the systematic error in the experimental setup. 169 One of the key points of performing inverse design problems, along with having machine learning tools, is to be able to propose accurate materials descriptors that lead to superior properties. Such an integrated highthroughput screening approach has seen very promising initial success, for instance in molecular organic Light-Emitting Diode molecules 170 , and its proposed approach to energy materials . 171,172 Thus, with the emergence of HT synthesis methods and self-driven laboratories, the classical Edisonian approach to materials discovery has been progressively abandoned, in pursue of a better, more efficient method. 173 Despite the recent boom, combinatorial methods, embodying rapid synthesis and simultaneous, on-line tools for diagnosis are not brand new, having their origin in the phase diagram studies, back in the 1960s. 174 Historically, one of the first cases of combinatorial science applied to the discovery of solid-state inorganic materials is registered in 1995, when Xiang et. al. developed a mask-enabled physical evaporation technique for the discrete deposition of superconducting oxide thin films. 175 Their work produced a 128-member library and led to the discovery of two superconducting oxides (BiSrCaCuOx and YBa2Cu3Ox).
Many combinatorial approaches have been focused on oxides, with special mentions to efforts to replace amorphous SiOx as dielectric were conducted by van Dover and collaborators and the investigation on crystalline high-K dielectrics by Chang et. al. 176,177 However, no combinatorial method is complete without a high-speed characterization technique. 178 Thus, it is crucial to identify a descriptor (see "Thermoelectric Material and Transport Descriptors" section earlier) that evaluates the potential of a material for a specific application and develop a characterization technique for its rapid, accurate measurement. Danielson et. al. developed an automated combinatorial synthesis and characterization for the discovery of new luminescent materials. They deployed a combination of mask-assisted electron beam evaporation for the synthesis and high-throughput imaging of the visible spectrum with a CCD camera for optical characterization. Their work led to a discrete library consisting of 25,000 different oxides and the discovery of a new red phosphor (Y0.845Al0.070La0.060Eu0.025VO4) with quantum efficiency of 0.83 ± 0.04, comparable to the then state-of-the-art material. 179 More recently, Mao developed a combinatorial approach for the synthesis and characterization of photovoltaic materials as well as transparent conducting oxides. Their work is outstanding for many reasons, one of which being the fact that they developed systems for material characterization (band gap) and characterization of the functional property of the material (carrier mobility and lifetime). 180 Most combinatorial synthesis approaches use physical methods for synthesis. In addition to evaporation, pulsed laser deposition is often used for epitaxial growth of oxides. 181 All these techniques rely on vacuum technology, which increases both cost and synthesis/characterization time. Chemical methods such as continuous hydrothermal flow synthesis can alleviate these problems thanks to their atmospheric pressure operation and their ease to scale up, thus accelerating the commercialization of the materials. 182,183 Another alternative that has been deployed recently by Kremsner et. al. is microwave-assisted synthesis. 184 Whilst chemical methods offer the advantages of scalability and user-friendly operation conditions, they normally render materials with lower quality (compactness, adherence to the substrate, mixed phases) than the materials obtained by their physical synthesis counterpart methods. Therefore, a compromise between synthesis time/cost, material quality and scalability need to be reached before designing any combinatorial approach.
Developments in combinatorial synthesis for thermoelectric film materials have been very recently published by Adamczyk et. al. 185 They utilized an aerosol spray for the highthroughput deposition (very high rates of near 1 µm min -1 ) of PbTe-SnTe thick films (ca. 10 µm) on Al2O3 that were subsequently annealed in fused silica ampoules. They conducted conventional material (Scanning electron microscope, X-ray spectroscopy and X-ray diffraction) and thermoelectric characterization (Seebeck coefficient and electrical resistivity).
They concluded that the properties have a positive correlation with bulk samples and that after an optimization of the aerosol deposition conditions, it is a potential candidate for the highthroughput discovery of new thermoelectric thin films. However, the best commercially available TE materials yet remain bulk samples. This is due to the superior quality of bulk samples (dense, homogeneous composition) as opposed to thin films (porosity, element segregation leading to compositional inhomogeneities). Ortiz et. al. led an effort to achieve HT synthesis of bulk TE. A combination of automation of powder dispensing and parallelization of hot pressing and ball milling led to the astounding 5-10x increase in synthetic speed, obtaining 121 bulk samples within the PbTe-PnSe-SnSe-SnTe system. 42 They performed non-HT characterization in order to determine the quality factor (β) of the samples and represented the results in the form of heat maps. They arrived at the non-intuitive conclusion that the best performing alloy (Pb0.7Sn0.3Te0.9Se0.1) does not lie along any intuitive set of compositions. This demonstrates that HT experimentation is a useful tool to achieve process optimization as well as discovery of new, non-intuitive materials. Therefore, we expect that the combination of machine learning optimization, coupled with high-throughput calculations, synthesis and characterization is a necessary tool that needs to reach maturity to enable scientific discovery, leading to potential breakthroughs in thermoelectric materials (See Figure 7). The deployment of HT combinatorial methods is expected to lead to an increase in process optimization rate as well as accelerate the discovery of new, non-intuitive materials. Thus, we recommend working towards a closed-loop high-throughput experimentation methodology in order to unravel novel physicochemical phenomena in potential TE material candidates. In conclusion, we have established the guidelines towards the accelerated discovery of novel TE materials. We revisit both the scientific rationale and the technology employed for the realization of high zT values in case studies of key chalcogenide-based and state-of-the-art thermoelectric materials. We ascertain that the discovery of new TE with high performance is driven by novel scientific phenomena, catalyzed by mature technological processes. To this end, we propose the use of causality-built TE descriptors that can be experimentally measured, combined with closed-loop high-throughput experimentation for the discovery of unexplored, high performing TE materials.

Supporting Information
Supplementary Table 1: List of materials, publication years, temperature of peak zT, scientific and technological ratings, system and colour (for plotting purposes) and references.