Doping in controlling the type of conductivity in bulk and nanostructured thermoelectric materials

Highlights

• Bulk and nano-grained TE materials were analyzed by DFT.

• The electronic effects on both PbTe and TiNiSn were demonstrated.

• The role of impurities on the conductivity type was analyzed.

• Interfacial states in nano-grained PbTe affect the conductivity type.

Abstract

Doping of materials for thermoelectric applications is widely used nowadays to control the type of conductivity. We report the results of ab-initio calculations aimed at developing the consistent scheme for determining the role of impurities that may change the type of conductivity in two attractive thermoelectric classes of materials. It is demonstrated that alloying of TiNiSn with Cu makes the material of n-type, and alloying with Fe leads to p-type conductivity. Similar calculations for PbTe with small amount of Na substituting for Pb leads to p-type conductivity, while Cl substituting for Te makes PbTe an n-type material. It is shown also that for nano-grained materials the n-type conductivity should be observed. The effect of impurities segregating to the grain boundaries in nano-structured PbTe is also discussed.

Introduction

Thermoelectric energy based on a direct conversion of heat (or thermal gradient) into electricity is one possible solution for the problem of affordable, environmentally clean energy. A number of compounds have been investigated in the search for potential thermoelectric materials, including the half-Heusler (HH) and chalcogenide-type alloys, capable of operation at elevated temperatures with adequate chemical, structural and mechanical stability. Due to the relatively easy alloying techniques of these materials with different elements substituting for its constituents, new ways are considered to optimize their thermoelectric properties.

Favorable high temperature thermoelectric properties of TiNiSn-based HH compounds were systematically reported, for example, in [1]. In [2] 36 HH compounds were investigated, where the electronic structures and electrical transport properties were studied using ab initio calculations and the Boltzmann transport equation under the constant relaxation time approximation for charge carriers. Some compositional optimization attempts of the thermoelectric properties are described in [3], where Hf alloying on the Ti site and Sb doping on the Sn site of TiNiSn enhanced the thermoelectric performance. For the case of Pd and Pt partially substitute for Ni, the reduction of the lattice thermal conductivity by the increase of mass-defect scattering was further investigated. Due to specific features of the band structure of this and similar compounds, changing the width of the band gap, regulating the number of charge carriers, increasing the slope of the density of states (DOS) for electrons in the vicinity of the bottom of conduction band, varying the scattering of electrons and phonons, etc. are also considered as possible design directions for improving the thermoelectric properties. The review [4] demonstrates the recent tendency of enhancement the thermoelectric properties by a combined optimization of the electronic properties and the phases’ morphology for engineering not only the band structure but also other properties determining the efficiency of thermoelectric materials. A simple theoretical analysis of experimental results, performed in [3], allowed the calculations of the effective mass and mobility of carriers, clarifying the influence of alloying on the electrical properties of materials obtained by casting or by powder metallurgy methods. In a more recent paper [5] a close relation of the electronic structure and the transport properties of these compounds was demonstrated, where measured temperature dependences of the thermal conductivity, k(T), electrical conductivity, σ(T), and Seebeck coefficient, S(T), were compared with all-electron ab initio density functional calculations. The results show the possibility to create n-type and p-type thermoelectric materials within one compound series. It is mentioned also that the open challenge to theory and experiment is to find new concepts that depress the thermal conductivity and, at the same time, improve the electrical conductivity of half-Heusler compounds.

Morphological modifications of the solid solution, the size, shape and the distribution of inclusions can all affect the thermal conductivity, k and consequently influent the thermoelectric figure of merit more efficiently as compared with expensive doping of TiNiSn that may manage the band structure of this compound. As discussed in [6], [7] k of thermoelectric materials can be reduced significantly by nano-scale structures, which effectively increase the phonon scattering. In fact, TiNiSn based nanocomposites were reported to possess a lower k and higher figure of merit than the conventional counterparts [8]. As mentioned in [9] the observed k reduction can be attributed to an enhancement of the phonon scattering. Actually, the developed network of interfaces may influence on the band structure of the material as well. This problem still remains one of the greatest challenges to the theory of thermoelectric materials.

An emerging approach for improving the desired properties of functional materials is by using nanostructured materials that show also new, sometimes unexpected properties and open new directions for their applications. This concerns metallic systems (see, for example, [10], [11], [12], [13], [14]), ceramics (see, for example, [15], [16], [17], [18]), and others. The concept of nanostructuring of thermoelectric materials has drawn much attention primarily due to the prediction that quantum confinement of charge carriers in low dimensional structures within a given matrix could drastically increase, the thermoelectric figure of merit, ZT (=S²σT/k, where T– temperature) of the composite through a large enhancement of the power factor (PF=S²σ) [19], [20]. Although, the exploration of this concept led to significant increases in the ZT of bulk thermoelectric materials [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32] and thin film superlattices, [7], [33], these improvements were mainly originated from large reductions in k rather than an enhancement in the PF as was originally predicted. Therefore, the concept of quantum confinement and the mechanism by which nanostructuring can be used to enhance the PF of thermoelectric materials is still poorly understood. ZT enhancement through large reductions in k using nanostructuring while minimizing reductions in the PF has therefore dominated thermoelectric research over the past 15 years, and the mechanism by which phonons are scattered at matrix/inclusion interfaces is now better understood [6], [34], [35], [36], [37], [38], [39], [40]. Despite the encouraging results obtained by applying this strategy [6], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [41], [42], [43], [44], the overall maximum ZT in most of the reported material systems still does not reach the targeted goal of ZT≥3. The solution of the problem must now come from a drastic increase of the PF simultaneously with a significant decrease of k. However, PF enhancement must originate from a dramatic increase in S as opposed to a large increase in σ if the goal of ZT≥3 is to be achieved. This is due to the fact that by increasing σ, the electronic part of k is also increased, while an increase in S does not directly affect k. It is therefore imperative to design and implement innovative concepts that could lead to large enhancements in the PF through (i) drastic increases in S while mitigating losses in σ or (ii) significant increase of both S and σ, simultaneously with large reductions in k. A comprehensive review of the latest developments in the field of nanostructured thermoelectrics may be found in [45].

An excellent example enlightening the complexity of the problem was recently reported in [46], where large enhancements in the S and σ of HH phases were simultaneously achieved at high temperatures through a coherent insertion of nanometer scale full-Heusler (FH) inclusions within the matrix. The S enhancement of the HH/FH nanocomposites arises from a drastic reduction in the “effective” carrier concentration around 300 K. At the same time it was found that the mobility increases drastically, which compensates for the decrease in the carrier concentration and minimizes the drop in the electric conductivity. The embedded FH nanostructures also induce a moderate reduction in the thermal conductivity leading to a drastic increase in the ZT of these HH/FH nanocomposites [47], [48]. A δ–function type shape in the DOS near the Fermi energy in nano-grained TiNiSn was identified in this highly efficient thermoelectric configuration [48]. As formulated in [49] a peak on top of a background density of states may become an optimal choice to increase the figure of merit when the background is two orders of magnitude smaller than the integrated contribution of the peak.

Analysis of the band structure of HH alloys and its link with their stability has a long lasting history. Probably, in [50] the first calculations of the band structure of MNiSn (M=Ti, Zr, or Hf) compounds using a pseudopotential method were reported showing that these compounds are semiconductors. A nice review of the results of an ab initio study of the structural stability of Ni-containing HH compounds may be found, for example, in [51] where also the nature of chemical bonding in these compounds is discussed and the energies of formation of different antisite defects are calculated. In a review paper [52] the calculation results of structural, elastic and electronic properties of TiNiSn and CoVSn HH compounds in the framework of the density functional theory (DFT) using the full-potential linear muffin-tin orbital (FP-LMTO) method were presented, demonstrating a very good agreement of theory with experimental data. The results of the electronic structure and Seebeck coefficient of (Ti_0.5Hf_0.5)NiSn and related HH phases based on full potential linearized augmented plane wave (FP LAPW) method for ordered structures using the WIEN2k software [53] and KKR-CPA methodology [54], [55] are presented in [56].

Chalcogenides, especially based on PbTe compound comprise another class of materials in the focus of interest with respect to their thermoelectric applications. This class of materials has been the mostly studied, [57], [58] including recent results considering nanostructuring [38] and band modifications [59] demonstrating exceptional figure of merit, ZT in both n-type [21], [60] and p-type [61], [62] compositions. The p- or n-type conductivities of doped and/or Pb- or Te-saturated PbTe were systematically studied in the early 70th (see, for example, [63]) on the basis of Hall coefficient measurements. The review article [64] and more recent review [65] give a comprehensive description of lead telluride as a useful thermoelectric material for power generation applications. Significant theoretical efforts were applied to reproduce correctly the peculiarities of the electronic density of states (DOS) in this narrow-band semiconductor (see, for example, [66]). The importance to account spin-orbit coupling in this system was also demonstrated. In [67] systematic calculations of the DOS changes upon doping of PbTe were attributed to different mechanisms including: Pb and Te vacancies, Pb substituted by monovalent (alkalis, Cu), divalent (s-type Zn, Cd, Hg, and p-type Ge, Sn) or trivalent (group III Ga, In, Tl, and group V As, Sb, Bi) atoms, and Te substituted by S, Se, or I. These calculations yielded a systematic understanding of the originated defect states while screening across or down the periodic table, upon introducing different impurity atoms. The role of doping in manipulating the type of conductivity and the link of the obtained results with the recent measurements of the thermopower in several PbTe-based compounds was discussed. The reported ab initio calculations predict drastic changes in the DOS near the band-gap region, which should affect the transport properties quantitatively.

Analyzing the stability of PbTe with respect to the formation of vacancies or interstitial defects also got recently a renewed attention. Different point defect complexes, including Schottky dimer and Schottky pair defects were considered in [68], while the influence of vacancies on the phase stability was discussed in [69]. The impact of doping by group IIIA elements (Al, Ga, In and Tl) on the electronic structure and stability of PbTe by first principles calculations was investigated in [70]. The impurity-induced defect level changes as a function of the charge state of the impurity. It was demonstrated that Al and In prefer to act as donors while Ga and Tl tend to act as acceptors in PbTe. A more sophisticated influence of the doping effectiveness on the electronic conductivity and thereby on the thermoelectric potential of such alloys was recently demonstrated both in experiments and by a theoretical study. It was found that in spite of a significant influence of additives on the type of conductivity, an improvement of thermoelectric properties may occur or not. In [71] the electronic structure of PbTe alloyed by Ti is considered, and is contrasted with the recently published results for thallium doped PbTe [72]. In both cases, impurity atoms, Ti and Tl, create resonant states in PbTe. However, in the Tl doped PbTe, the thermopower (and consequently the thermoelectric efficiency) was found to increase, compared to other, non-resonant impurities. On the other hand, in Ti doped PbTe, no increase in the thermopower above the Pisarenko line (i.e., the thermopower as a function of the carrier concentration) was found. As demonstrated in [71] Ti 3d-states form a dispersionless, flat, and narrow impurity band, characterizing localized states. Also, the electronic states which appear in the Brillouin zone of PbTe upon substitution of Pb with Ti show a very small hybridization with the Te electronic states, confirming the isolated character of this impurity. The formation of resonant states upon the introduction of transition-metal impurities into PbTe was reported also for Cr [73], [74], [75], [76], Fe [77], [78], and Sc [79]. It is noteworthy that small fractions of Ti do not enhance the thermopower above that of similarly doped PbTe, suggesting that the electrons of Ti are localized. Delocalized electrons appear again when the Ti concentration is increased, suggesting an appearance of an impurity-band conduction [80]. This tendency change upon increasing the Ti doping level of PbTe was not explained in [71].

Not only doping but also co-doping is widely used and experimentally studied for manipulating the type of conductivity of these materials, as discussed, for example in [81]. In this case the interplay of different mechanisms influencing the conductivity type should be analyzed and taken into account. In particular, the enhancement of ZT may be attributed to nanostructuring due to phase segregation and/or alloying disordering effects, reducing the lattice thermal conductivity. Recently co-doping and a nanostructuring approach were shown to be very effective for the enhancement of thermoelectric performance through synergy of resonance levels and band convergence in p-type SnTe [82]. It was demonstrated that in co-doping of this material with In and Cd these elements play different but complementary roles in modifying the valence band structure of SnTe.

For electronic fine tuning of the carrier concentration values and thereby controlling the p- or n-type conductivities different rather complicated multicomponent PbTe-based compounds are considered. To enhance the thermoelectric properties of PbTe, many methods have been used including hot-pressing of fine powder particles and heavy doping [83], [84], [85], [86]. At the same time, there are many low-dimensional structures which can be artificially produced in PbTe for the purpose of enhancing its thermoelectric properties [41], [87], [88]. Comparing to other preparation methods of thermoelectric materials, the method of high pressure and high temperature (HPHT) has many advantages. This method can restrain the disorder, phase separation and other complicating factors during the preparation of materials. In [89] it was reported that n-type lead telluride (PbTe) compounds without doping were successfully prepared at high pressure and high temperature (HPHT). The carrier type was assumed to be induced by the effect of pressure. The results of the electrical conductivity, Seebeck coefficient, thermal conductivity for n-type PbTe, which were measured at room temperature, show that the PbTe samples prepared by HPHT exhibit the same characteristics as heavily doped semiconductors. In this context it is interesting to mention that in the case of co-doping, a different type of conductivity at the same doping level of PbTe may be obtained depending on the processing of the final material. A good example for this is a comparison of the results reported in [90] and in [81]. In [90] co-sputtering of PbTe and a small amount of NaCl on a preheated to 200 °C substrate, was used for producing doped PbTe films, yielding p-type conductivity. In [81] similar compositions were synthesized by arc melting, further they were flipped and re-melted more than five times to ensure homogeneity. Each synthesized ingot was crushed by a mortar and pestle and filtered through a 60 mesh sieve. The sieved powder was spark plasma sintered (SPS) under a mechanical pressure of 25 MPa at 550 °C for 60 min, resulting in high density values of >95% of the theoretical density. n-type conductivity of the final samples was observed in this case. A broad discussion on the recent developments and current research in high performance bulk thermoelectric materials, including nanostructuring, band engineering and other key strategies for improving the thermoelectric performance is presented in [91].

This brief review, even being not a comprehensive, clearly illustrates the high interest in these materials for thermoelectric applications. It should be noted that in order to realize thermoelectric modules based on these compounds, both n- and p-type materials should be developed.

Design of such new materials and new synthesis techniques that leapfrog technical barriers is therefore required. Such a progress may be achieved only with the aid of a highly innovative basic research. This area clearly requires a paradigm shift from the trial and error approach, which delivers only incremental evolutionary improvements of devices, to serious, consistent, very fundamental research, in addition to the commonly involved applied research. Of a particular importance is the need to understand on the microscopic level, the link between the morphology of the nanostructured materials to the specific changes that happen when materials are alloyed with different elements (this may happen in the process of their synthesis) with tailored properties suitable for use in thermoelectric devices with much improved (and potentially tunable) efficiency.

For that purpose, rigorous, state of the art, large scale first-principles computations are required to gain fundamental understanding of the factors governing the electronic properties of nanostructured materials. Such a comprehensive study is of an extreme significance due to the fact that most of the DFT calculations for thermoelectric materials are carried out for monocrystals. Investigating the electronic contribution of interfaces in modern nano-crystalline materials is still lacking.

At present, several codes exist for DFT calculations employing pseudopotentials and plain waves (for example, CASTEP, VASP and Wien2k packages [92], [93], [94]), and the only input required for computing is a structural model. The computation scheme, on which the codes are based, allows a relaxation of the lattice parameters. Besides, the coordinates of atoms in the cell may be varied. This relaxation is terminated when the system energy reaches its minimum, thus resulting in the geometrical optimization of the tested structure. The consistency between the theoretically optimized cell dimensions and the measured properties may approve the validity of the model and may serve as a justification of the applied method of calculations.

Keeping in mind that both TiNiSn and PbTe are highly sensitive with respect to doping, to formation of point defects, and to the fabrication process of doped samples, there is still a lot of room for investigation of the physics and chemistry that regulates these effects. The aim of our paper is three-fold: i) we report the results of a comparative DFT study of doping of TiNiSn HH by Cu and Fe for illustrating the influence of noble and transition metals on the type of conductivity; ii) we investigated the effects that occur in PbTe upon co-doping by Na and Cl and explain the difference in the type of conductivity obtained in experiments with materials fabricated in different processes; iii) we discuss the results of doping of nano-structured PbTe by Na and Cl and demonstrate that formation of broken bonds at the interfaces between the grains is responsible for an n-type conductivity which is not affected by the small amount of excess Na or Cl atoms or NaCl molecules segregating to the interfaces.