Calculation of dopant solubilities and phase diagrams of X–Pb–Se (X = Br, Na) limited to defects with localized charge

The control of defects, particularly impurities, to tune the concentrations of electrons and holes is of utmost importance in the use of semiconductor materials. To estimate the amount of dopant that can be added to a semiconductor without precipitating secondary phases, a detailed phase diagram is needed. The ability of ab initio computational methods to predict defect stability can greatly accelerate the discovery of new semiconductors by calculating phase diagrams when time-consuming experimental ones are not available. DFT defect energy calculations are particularly successful in identifying doping strategies by determining the energy of multiple defect charge states in large band gap semiconductors and insulators. In metals, detailed phase diagrams can be determined from such calculations but only one, uncharged defect is needed. In this work, we have calculated dopant solubilities of Br and Na in the thermoelectric material PbSe by mapping its solvus boundaries in different regions of the respective ternary phase diagrams using DFT defect energy calculations. The narrow gap PbSe provides an example where defects with nominal charge state (based on valence counting) have properly-localized charge states. However, defects with unexpected charge states produce delocalized electrons, which are then, in effect, defects with the expected charge state. Simply applying the methods for calculating multiple defect charge states in PbSe and treating them as separate defects fails to predict properties measured by experiments. Performing thermodynamic calculations using only the expected charge states, excluding others, enables accurate prediction of experimentally measured doping efficiencies and phase diagrams. Identifying which defect charge states to include in thermodynamic calculations will expedite the use of such calculations for other semiconductors in understanding phase diagrams and devising effective doping strategies

The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies

The Open Quantum Materials Database (OQMD) is a high-throughput database currently consisting of nearly 300,000 density functional theory (DFT) total energy calculations of compounds from the Inorganic Crystal Structure Database (ICSD) and decorations of commonly occurring crystal structures. To maximise the impact of these data, the entire database is being made available, without restrictions, at www.oqmd.org/download. In this paper, we outline the structure and contents of the database, and then use it to evaluate the accuracy of the calculations therein by comparing DFT predictions with experimental measurements for the stability of all elemental ground-state structures and 1,670 experimental formation energies of compounds. This represents the largest comparison between DFT and experimental formation energies to date. The apparent mean absolute error between experimental measurements and our calculations is 0.096 eV/atom. In order to estimate how much error to attribute to the DFT calculations, we also examine deviation between different experimental measurements themselves where multiple sources are available, and find a surprisingly large mean absolute error of 0.082 eV/atom. Hence, we suggest that a significant fraction of the error between DFT and experimental formation energies may be attributed to experimental uncertainties. Finally, we evaluate the stability of compounds in the OQMD (including compounds obtained from the ICSD as well as hypothetical structures), which allows us to predict the existence of ~3,200 new compounds that have not been experimentally characterised and uncover trends in material discovery, based on historical data available within the ICSD

Ab initio study of intrinsic point defects in PbTe: an insight into phase stability

The stability of intrinsic point defects in PbTe, one of the most widely studied and efficient thermoelectric material, is explored by means of Density Functional Theory (DFT). The origin of n- and p-type conductivity in PbTe is attributed to particular intrinsic charged defects by calculating their formation energies. These DFT calculated defect formation energies are then used in the Gibbs free energy description of this phase as part of the Pb-Te thermodynamic model built using the CALPHAD method, and in the resulting phase diagram it is found that its solubility lines and non-stoichiometric range agree very well with experimental data. Such an approach of using DFT in conjunction with CALPHAD for compound semiconductor phases that exhibit very small ranges of non-stoichiometry does not only make the process of calculating phase diagrams for such systems more physical, but is necessary and critical for the assessment of unknown phase diagrams

Role of Sodium Doping in Lead Chalcogenide Thermoelectrics

Center for Revolutionary Materials for Solid State Energy Conversion, an EFRC; U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-SC0001054]; 973 Program of the Ministry of Science and Technology of China [2012CB619401]; National Natural Science Foundation of China [U1232110]The solubility of sodium and its effects on phonon scattering in lead chalcogenide PbQ(Q = Te, Se, S) family of thermoelectric materials was investigated by means of transmission electron microscopy and density functional calculations. Among these three systems, Na has the highest solubility limit (similar to 2 mol %) in PbS and the lowest similar to 0.5 mol %) in PbTe. First-principles electronic structure calculations support the observations, indicating that Na defects have the lowest formation energy in PbS and the highest in PbTe. It was also found that in addition to providing charge carriers (holes) for PbQ, Na introduces point defects (solid solution formation) and nanoscale precipitates; both reduce the lattice thermal conductivity by scattering heat-carrying phonons. These results explain the recent reports of high thermoelectric performance in p-type PbQ materials and may lead to further advances in this class of materials

High Thermoelectric Performance of p‑Type SnTe via a Synergistic Band Engineering and Nanostructuring Approach

SnTe is a potentially attractive thermoelectric because it is the lead-free rock-salt analogue of PbTe. However, SnTe is a poor thermoelectric material because of its high hole concentration arising from inherent Sn vacancies in the lattice and its very high electrical and thermal conductivity. In this study, we demonstrate that SnTe-based materials can be controlled to become excellent thermoelectrics for power generation via the successful application of several key concepts that obviate the well-known disadvantages of SnTe. First, we show that Sn self-compensation can effectively reduce the Sn vacancies and decrease the hole carrier density. For example, a 3 mol % self-compensation of Sn results in a 50% improvement in the figure of merit <i>ZT</i>. In addition, we reveal that Cd, nominally isoelectronic with Sn, favorably impacts the electronic band structure by (a) diminishing the energy separation between the light-hole and heavy-hole valence bands in the material, leading to an enhanced Seebeck coefficient, and (b) enlarging the energy band gap. Thus, alloying with Cd atoms enables a form of valence band engineering that improves the high-temperature thermoelectric performance, where p-type samples of SnCd_0.03Te exhibit <i>ZT</i> values of ∼0.96 at 823 K, a 60% improvement over the Cd-free sample. Finally, we introduce endotaxial CdS or ZnS nanoscale precipitates that reduce the lattice thermal conductivity of SnCd_0.03Te with no effect on the power factor. We report that SnCd_0.03Te that are endotaxially nanostructured with CdS and ZnS have a maximum <i>ZT</i>s of ∼1.3 and ∼1.1 at 873 K, respectively. Therefore, SnTe-based materials could be ideal alternatives for p-type lead chalcogenides for high temperature thermoelectric power generation

Role of Sodium Doping in Lead Chalcogenide Thermoelectrics

The solubility of sodium and its effects on phonon scattering in lead chalcogenide PbQ (Q = Te, Se, S) family of thermoelectric materials was investigated by means of transmission electron microscopy and density functional calculations. Among these three systems, Na has the highest solubility limit (∼2 mol %) in PbS and the lowest ∼0.5 mol %) in PbTe. First-principles electronic structure calculations support the observations, indicating that Na defects have the lowest formation energy in PbS and the highest in PbTe. It was also found that in addition to providing charge carriers (holes) for PbQ, Na introduces point defects (solid solution formation) and nanoscale precipitates; both reduce the lattice thermal conductivity by scattering heat-carrying phonons. These results explain the recent reports of high thermoelectric performance in p-type PbQ materials and may lead to further advances in this class of materials

Origin of the High Performance in GeTe-Based Thermoelectric Materials upon Bi₂Te₃ Doping

As a lead-free material, GeTe has drawn growing attention in thermoelectrics, and a figure of merit (<i>ZT</i>) close to unity was previously obtained via traditional doping/alloying, largely through hole carrier concentration tuning. In this report, we show that a remarkably high <i>ZT</i> of ∼1.9 can be achieved at 773 K in Ge_0.87Pb_0.13Te upon the introduction of 3 mol % Bi₂Te₃. Bismuth telluride promotes the solubility of PbTe in the GeTe matrix, thus leading to a significantly reduced thermal conductivity. At the same time, it enhances the thermopower by activating a much higher fraction of charge transport from the highly degenerate Σ valence band, as evidenced by density functional theory calculations. These mechanisms are incorporated and discussed in a three-band (L + Σ + C) model and are found to explain the experimental results well. Analysis of the detailed microstructure (including rhombohedral twin structures) in Ge_0.87Pb_0.13Te + 3 mol % Bi₂Te₃ was carried out using transmission electron microscopy and crystallographic group theory. The complex microstructure explains the reduced lattice thermal conductivity and electrical conductivity as well

High <i>ZT</i> in p‑Type (PbTe)_{1–2<i>x</i>}(PbSe)_<i>x</i>­(PbS)_<i>x</i> Thermoelectric Materials

Lead chalcogenide thermoelectric systems have been shown to reach record high figure of merit values via modification of the band structure to increase the power factor or via nanostructuring to reduce the thermal conductivity. Recently, (PbTe)_1–<i>x</i>(PbSe)_<i>x</i> was reported to reach high power factors via a delayed onset of interband crossing. Conversely, the (PbTe)_1–<i>x</i>(PbS)_<i>x</i> was reported to achieve low thermal conductivities arising from extensive nanostructuring. Here we report the thermoelectric properties of the pseudoternary 2% Na-doped (PbTe)_{1–2<i>x</i>}(PbSe)_<i>x</i>(PbS)_<i>x</i> system. The (PbTe)_{1–2<i>x</i>}(PbSe)_<i>x</i>(PbS)_<i>x</i> system is an excellent platform to study phase competition between entropically driven atomic mixing (solid solution behavior) and enthalpy-driven phase separation. We observe that the thermoelectric properties of the PbTe–PbSe–PbS 2% Na doped are superior to those of 2% Na-doped PbTe–PbSe and PbTe–PbS, respectively, achieving a <i>ZT</i> ≈2.0 at 800 K. The material exhibits an increased the power factor by virtue of valence band modification combined with a very reduced lattice thermal conductivity deriving from alloy scattering and point defects. The presence of sulfide ions in the rock-salt structure alters the band structure and creates a plateau in the electrical conductivity and thermopower from 600 to 800 K giving a power factor of 27 μW/cmK². The very low total thermal conductivity values of 1.1 W/m·K of the <i>x</i> = 0.07 composition is accounted for essentially by phonon scattering from solid solution defects rather than the assistance of endotaxial nanostructures