Exceptionally High Average Power Factor and Thermoelectric. Figure of Merit in n-type PbSe by the Dual Incorporation of Cu

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Supporting information of

Exceptionally High Average Power Factor and Thermoelectric

Figure of Merit in n-type PbSe by the Dual Incorporation of Cu

and Te

Chongjian Zhou,‡,¶_{Yuan Yu}

,ᴨ,¶ Yea-Lee Lee,Ψ,¶ Bangzhi Ge,‡,ǂWeiqun Lu,‡ Oana

Cojocaru-Mirédin,ᴨ_{Jino Im,}Ψ_{Sung-Pyo Cho,}§_{Matthias Wuttig,}ᴨ,∆_{Zhongqi Shi,}ǂ_{and In}

Chung†,‡,*

†_{Center for Nanoparticle Research, Institute for Basic Science (IBS), Seoul 08826,}

Republic of Korea

‡_{School of Chemical and Biological Engineering, and Institute of Chemical Processes,}

and §_{National Center for Inter-University Research Facilities, Seoul National University,}

Seoul 08826, Republic of Korea

ᴨ_{Institute of Physics (IA), RWTH Aachen University, 52056 Aachen, Germany}

∆_{JARA-FIT Institute Green-IT,} _{RWTH Aachen University and Forschungszentrum Jülich,}

52056 Aachen, Germany

Ψ_{Chemical Data-Driven Research Center, Korea Research Institute of Chemical}

Technology, Daejeon 34114, Republic of Korea

ǂ_{State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University,}

Xi’an 710049, China

* To whom correspondence should be addressed: [email protected] ¶These authors contributed equally to this work

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Figure S1. Schematic illustration of cluster algorithm for identifying the cluster in a system containing two element species. For clarity, the illustration is drawn in a two-dimensional plane. (a) The atomic distribution in a volume reconstructed by atom probe tomography. A red sphere is defined as a center atom. If the distance between neighboring red spheres and the central red sphere is less than the user defined radius Dmax, they will be categorized

into one group. (b) The process is repeated to traverse every red sphere in the dataset. Only the group with atom number larger than the user defined threshold value Nmin will be

regarded as a cluster. (c) Meshing the volume into an array of grids envelops the associated atoms into the clusters. The clusters identified in (b) are mapped to the grid, and the yellow area indicates the grid they occupied. The atoms not belonging to the cluster but inside the yellow grid are added into the cluster. (d) An erosion algorithm removes the artificial shell of the matrix atoms, leaving the identified clusters. A more detailed analysis procedure is well-documented elsewhere.1

Figure S2. Atom probe tomography analysis repeated on an additional Cu0.005PbSe0.99Te0.01 sample. (a)The spatial element distribution of Pb (cyan), Se (orange),

Te (green) and Cu (red) atoms within the 3D APT reconstructed volume. (b) Cu cluster analysis showing Cu atoms form a high degree of clusters with a density of ~3.1 × 1022

cm3_{, which is consistent with the results in the main text.}

Figure S3. Seebeck coefficients as a function of temperature and carrier concentration calculated by solving Boltzmann transport equation for pristine PbSe, PbSe0.99Te0.01,

Cu0.004PbSe, and Cu0.004PbSe0.99Te0.01. The same legends are applied to all the panels.

Figure S4. Conduction band electron effective mass as a function of temperature for Cu0.004PbSe0.99Te0.01. The lattice parameter at the elevated temperatures for the calculations

was extracted from the previous report with the temperature-dependent X-ray diffraction patterns.4

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samples. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) total thermal conductivity, and (d) ZT. Three specimens were independently synthesized from the different batches, and characterized. These results show excellent reproducibility of thermoelectric properties of Cu0.005PbSe0.99Te0.01 sample.

Figure S6. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor, and (d) thermal conductivity for the Cu0.005PbSe0.99Te0.01 sample upon the

consecutive heating and cooling cycles, validating the high thermal and chemical robustness of thismaterial.

Figure S7. Typical photographs of spark plasma sintered (SPS) high density specimens, which were cut and polished for thermoelectric property measurements. (a) The diameter and (b) height of typical SPS processed cylinder-shaped specimens. (c) Typical photograph of cut and polished SPS samples for measuring thermoelectric properties.

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1. Calculation Details

Calculations for Pisarenko relation based on a single Kane band model (SKB).

Pisarenko relation is calculated employing a single Kane band model, assuming acoustic phonons dominate scattering mechanism. The carrier concentration (n), Seebeck coefficient (S), carrier mobility (), Lorenz number (L), electrical conductivity (), and power factor (PF) can be approximated by the equations (1) – (5):2

(2) * 3/2 0 3/2 0 2 3 (2 ) 3 B m k T n F   h (3) 1 1 2 0 1 2 [ ] B k F S e F      (4) 4 1 1 2 * * 3/2 2 0 1 2 2 3 (2 ) l I b B eC F m m k T F       h (5) 2 1 1 1 2 2 2 2 0 1 0 1 2 2 (kB) [ F ( F ) ] L e F F       (5) /2 2 2 0 ( ) (1 2 ) 2 k n m n m k f F

  



d



 _   _ _  _ _  _   _   



In the equations, ħis the reduced Planck constant, T is the absolute temperature,kBisthe

Boltzmann constant, m*_{is the density of states effective mass given band degeneracy,}_C l

(9.1 × 1010 _{Pa for PbSe) is a parameter determined by combining elastic constants,}3_e_{is the}

elementary positive charge, α is the reciprocal reduced band gap given by kBT/Eg, in which

Eg is the band gap. Ξ is the deformation potentials for multivalley systems, describing

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2. Table S1. Density of the CuxPbSe0.99Te0.01 (x = 0.0025, 0.004, and 0.005) samples

consolidated by an SPS process.

x Density (g cm–3₎ Relative density to the

theoretical value (%)

0.0025 8.10 100.0

0.004 8.09 99.8

0.005 8.09 99.8

Table S2. Defect formation energy (∆HD) for all the possible locations of Cu atom in the

PbSe0.99Te0.01 lattice. CuInt, CuPb, CuSe, and CuTe stand for Cu atom at the interstitial, Pb,

Se, and Te sites, respectively. Int1 (Pb1) indicates the interstitial site (Pb site) close to the Te anion while Int2 (Pb2) near Se anion.

Site CuInt1 CuInt2 CuPb1 CuPb2 CuSe CuTe

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3. Figures S1

−

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Figure S1. Schematic illustration of cluster algorithm for identifying the cluster in a system containing two element species. For clarity, the illustration is drawn in a two-dimensional plane. (a) The atomic distribution in a volume reconstructed by atom probe tomography. A red sphere is defined as a center atom. If the distance between neighboring red spheres and the central red sphere is less than the user defined radius Dmax, they will be categorized

into one group. (b) The process is repeated to traverse every red sphere in the dataset. Only the group with atom number larger than the user defined threshold value Nmin will be

regarded as a cluster. (c) Meshing the volume into an array of grids envelops the associated atoms into the clusters. The clusters identified in (b) are mapped to the grid, and the yellow area indicates the grid they occupied. The atoms not belonging to the cluster but inside the yellow grid are added into the cluster. (d) An erosion algorithm removes the artificial shell of the matrix atoms, leaving the identified clusters. A more detailed analysis procedure is well-documented elsewhere.1

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Figure S2. Atom probe tomography analysis repeated on an additional Cu0.005PbSe0.99Te0.01 sample. (a)The spatial element distribution of Pb (cyan), Se (orange),

Te (green) and Cu (red) atoms within the 3D APT reconstructed volume. (b) Cu cluster analysis showing Cu atoms form a high degree of clusters with a density of ~3.1 × 1022

cm3_{, which is consistent with the results in the main text.}

Figure S3. Seebeck coefficients as a function of temperature and carrier concentration calculated by solving Boltzmann transport equation for pristine PbSe, PbSe0.99Te0.01,

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Figure S4. Conduction band electron effective mass as a function of temperature for Cu0.004PbSe0.99Te0.01. The lattice parameter at the elevated temperatures for the calculations

was extracted from the previous report with the temperature-dependent X-ray diffraction patterns.4

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Figure S5. Reproducibility of thermoelectric properties of the Cu0.005PbSe0.99Te0.01

samples. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) total thermal conductivity, and (d) ZT. Three specimens were independently synthesized from the different batches, and characterized. These results show excellent reproducibility of thermoelectric properties of Cu0.005PbSe0.99Te0.01 sample.

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Figure S6. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor, and (d) thermal conductivity for the Cu0.005PbSe0.99Te0.01 sample upon the

consecutive heating and cooling cycles, validating the high thermal and chemical robustness of thismaterial.

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Figure S7. Typical photographs of spark plasma sintered (SPS) high density specimens, which were cut and polished for thermoelectric property measurements. (a) The diameter and (b) height of typical SPS processed cylinder-shaped specimen. (c) Typical photograph of cut and polished SPS samples for measuring thermoelectric properties.

4. References

(1) Philippe, T.; De Geuser, F.; Duguay, S.; Lefebvre, W.; Cojocaru-Mirédin, O.; Da Costa, G.; Blavette, D. Clustering and Nearest Neighbour Distances in Atom-Probe Tomography. Ultramicroscopy 2009, 109, 1304.

(2) Zhang, Q.; Song, Q.; Wang, X.; Sun, J.; Zhu, Q.; Dahal, K.; Lin, X.; Cao, F.; Zhou, J.; Chen, S.; Chen, G.; Mao, J.; Ren, Z. Deep Defect Level Engineering: A Strategy of Optimizing the Carrier Concentration for High Thermoelectric Performance. Energy Environ. Sci. 2018, 11, 933.

(3) Wang, H.; Pei, Y.; LaLonde, A. D.; Snyder, G. J. Weak Electron-Phonon Coupling Contributing to High Thermoelectric Performance in n-Type PbSe. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 9705.

(4) Gayner, C.; Sharma, R.; Mallik, I.; Das, M. K.; Kar, K. K. Exploring the Doping Effects of Copper on Thermoelectric Properties of Lead Selenide. J. Phys. D. Appl. Phys. 2016, 49, 285104.

Exceptionally High Average Power Factor and Thermoelectric. Figure of Merit in n-type PbSe by the Dual Incorporation of Cu

Supporting information of