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Title: Effective mass and Fermi surface complexity factor from ab initio band structure calculations

Abstract

The effective mass is a convenient descriptor of the electronic band structure used to characterize the density of states and electron transport based on a free electron model. While effective mass is an excellent first-order descriptor in real systems, the exact value can have several definitions, each of which describe a different aspect of electron transport. Here we use Boltzmann transport calculations applied to ab initio band structures to extract a density-of-states effective mass from the Seebeck Coefficient and an inertial mass from the electrical conductivity to characterize the band structure irrespective of the exact scattering mechanism. We identify a Fermi Surface Complexity Factor: N* vK* from the ratio of these two masses, which in simple cases depends on the number of Fermi surface pockets (N* v) and their anisotropy K*, both of which are beneficial to high thermoelectric performance as exemplified by the high values found in PbTe. The Fermi Surface Complexity factor can be used in high-throughput search of promising thermoelectric materials.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [2];  [5]; ORCiD logo [3]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
  2. Univ. catholique de Louvain, Louvain-la-Neuve (Belgium)
  3. Northwestern Univ., Evanston, IL (United States)
  4. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  5. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  6. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1476581
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
npj Computational Materials
Additional Journal Information:
Journal Volume: 3; Journal Issue: 1; Related Information: © 2017 The Author(s).; Journal ID: ISSN 2057-3960
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Gibbs, Zachary M., Ricci, Francesco, Li, Guodong, Zhu, Hong, Persson, Kristin, Ceder, Gerbrand, Hautier, Geoffroy, Jain, Anubhav, and Snyder, G. Jeffrey. Effective mass and Fermi surface complexity factor from ab initio band structure calculations. United States: N. p., 2017. Web. doi:10.1038/s41524-017-0013-3.
Gibbs, Zachary M., Ricci, Francesco, Li, Guodong, Zhu, Hong, Persson, Kristin, Ceder, Gerbrand, Hautier, Geoffroy, Jain, Anubhav, & Snyder, G. Jeffrey. Effective mass and Fermi surface complexity factor from ab initio band structure calculations. United States. doi:10.1038/s41524-017-0013-3.
Gibbs, Zachary M., Ricci, Francesco, Li, Guodong, Zhu, Hong, Persson, Kristin, Ceder, Gerbrand, Hautier, Geoffroy, Jain, Anubhav, and Snyder, G. Jeffrey. Thu . "Effective mass and Fermi surface complexity factor from ab initio band structure calculations". United States. doi:10.1038/s41524-017-0013-3. https://www.osti.gov/servlets/purl/1476581.
@article{osti_1476581,
title = {Effective mass and Fermi surface complexity factor from ab initio band structure calculations},
author = {Gibbs, Zachary M. and Ricci, Francesco and Li, Guodong and Zhu, Hong and Persson, Kristin and Ceder, Gerbrand and Hautier, Geoffroy and Jain, Anubhav and Snyder, G. Jeffrey},
abstractNote = {The effective mass is a convenient descriptor of the electronic band structure used to characterize the density of states and electron transport based on a free electron model. While effective mass is an excellent first-order descriptor in real systems, the exact value can have several definitions, each of which describe a different aspect of electron transport. Here we use Boltzmann transport calculations applied to ab initio band structures to extract a density-of-states effective mass from the Seebeck Coefficient and an inertial mass from the electrical conductivity to characterize the band structure irrespective of the exact scattering mechanism. We identify a Fermi Surface Complexity Factor: N*vK* from the ratio of these two masses, which in simple cases depends on the number of Fermi surface pockets (N*v) and their anisotropy K*, both of which are beneficial to high thermoelectric performance as exemplified by the high values found in PbTe. The Fermi Surface Complexity factor can be used in high-throughput search of promising thermoelectric materials.},
doi = {10.1038/s41524-017-0013-3},
journal = {npj Computational Materials},
number = 1,
volume = 3,
place = {United States},
year = {2017},
month = {2}
}

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Cited by: 39 works
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Works referenced in this record:

First-principles study on band structures and electrical transports of doped-SnTe
journal, June 2016


Temperature dependent band gap in PbX (X = S, Se, Te)
journal, December 2013

  • Gibbs, Zachary M.; Kim, Hyoungchul; Wang, Heng
  • Applied Physics Letters, Vol. 103, Issue 26
  • DOI: 10.1063/1.4858195

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Raising the Thermoelectric Performance of p-Type PbS with Endotaxial Nanostructuring and Valence-Band Offset Engineering Using CdS and ZnS
journal, September 2012

  • Zhao, Li-Dong; He, Jiaqing; Hao, Shiqiang
  • Journal of the American Chemical Society, Vol. 134, Issue 39
  • DOI: 10.1021/ja306527n

Low effective mass leading to high thermoelectric performance
journal, January 2012

  • Pei, Yanzhong; LaLonde, Aaron D.; Wang, Heng
  • Energy & Environmental Science, Vol. 5, Issue 7
  • DOI: 10.1039/c2ee21536e

Highly effective Mg 2 Si 1 x Sn x thermoelectrics
journal, July 2006


High Band Degeneracy Contributes to High Thermoelectric Performance in p-Type Half-Heusler Compounds
journal, August 2014

  • Fu, Chenguang; Zhu, Tiejun; Pei, Yanzhong
  • Advanced Energy Materials, Vol. 4, Issue 18
  • DOI: 10.1002/aenm.201400600

Band convergence in the non-cubic chalcopyrite compounds Cu 2 MGeSe 4
journal, January 2014

  • Zeier, Wolfgang G.; Zhu, Hong; Gibbs, Zachary M.
  • J. Mater. Chem. C, Vol. 2, Issue 47
  • DOI: 10.1039/C4TC02218A

Cyclotron Resonance Experiments in Silicon and Germanium
journal, November 1956


Designing high-performance layered thermoelectric materials through orbital engineering
journal, March 2016

  • Zhang, Jiawei; Song, Lirong; Madsen, Georg K. H.
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms10892

Tuning bands of PbSe for better thermoelectric efficiency
journal, January 2014

  • Wang, Heng; Gibbs, Zachary M.; Takagiwa, Yoshiki
  • Energy Environ. Sci., Vol. 7, Issue 2
  • DOI: 10.1039/C3EE43438A

Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites
journal, October 2015

  • Tang, Yinglu; Gibbs, Zachary M.; Agapito, Luis A.
  • Nature Materials, Vol. 14, Issue 12
  • DOI: 10.1038/nmat4430

Connecting Thermoelectric Performance and Topological-Insulator Behavior: Bi 2 Te 3 and Bi 2 Te 2 Se from First Principles
journal, January 2015


Cyclotron Resonance of Electrons and Holes in Silicon and Germanium Crystals
journal, April 1955


Convergence of electronic bands for high performance bulk thermoelectrics
journal, May 2011

  • Pei, Yanzhong; Shi, Xiaoya; LaLonde, Aaron
  • Nature, Vol. 473, Issue 7345, p. 66-69
  • DOI: 10.1038/nature09996

High Three-Dimensional Thermoelectric Performance from Low-Dimensional Bands
journal, April 2013


Band Engineering of Thermoelectric Materials
journal, October 2012


Convergence of Conduction Bands as a Means of Enhancing Thermoelectric Performance of n -Type Mg 2 Si 1 x Sn x Solid Solutions
journal, April 2012


Evaluation of Half-Heusler Compounds as Thermoelectric Materials Based on the Calculated Electrical Transport Properties
journal, October 2008

  • Yang, Jiong; Li, Huanming; Wu, Ting
  • Advanced Functional Materials, Vol. 18, Issue 19, p. 2880-2888
  • DOI: 10.1002/adfm.200701369

Electronic structure and transport in the low-temperature thermoelectric Cs Bi 4 Te 6 : Semiclassical transport equations
journal, May 2006


Lead telluride alloy thermoelectrics
journal, November 2011


Theory of band warping and its effects on thermoelectronic transport properties
journal, April 2014


Comparative study of defect transition energy calculation methods: The case of oxygen vacancy in In 2 O 3 and ZnO
journal, July 2012


Band parameters for III–V compound semiconductors and their alloys
journal, June 2001

  • Vurgaftman, I.; Meyer, J. R.; Ram-Mohan, L. R.
  • Journal of Applied Physics, Vol. 89, Issue 11, p. 5815-5875
  • DOI: 10.1063/1.1368156

Shubnikov-de Haas Effect in Bismuth
journal, September 1962


High ZT in p-Type (PbTe) 1–2 x (PbSe) x (PbS) x Thermoelectric Materials
journal, February 2014

  • Korkosz, Rachel J.; Chasapis, Thomas C.; Lo, Shih-han
  • Journal of the American Chemical Society, Vol. 136, Issue 8
  • DOI: 10.1021/ja4121583

BoltzTraP. A code for calculating band-structure dependent quantities
journal, July 2006


Valence Bands in Lead Telluride
journal, October 1961

  • Allgaier, R. S.
  • Journal of Applied Physics, Vol. 32, Issue 10
  • DOI: 10.1063/1.1777039

Hall Coefficient Behavior and the Second Valence Band in Lead Telluride
journal, January 1966

  • Allgaier, R. S.; Houston, B. B.
  • Journal of Applied Physics, Vol. 37, Issue 1
  • DOI: 10.1063/1.1707831

Characterization and analysis of thermoelectric transport in n -type Ba 8 Ga 16 x Ge 30 + x
journal, September 2009


Magnetoresistance in PbS, PbSe, and PbTe at 295°, 77.4°, and 4.2°K
journal, November 1958


Ab initio Studies of the Band Parameters of III–V and II–VI Zinc-Blende Semiconductors
journal, January 2005


The panoscopic approach to high performance thermoelectrics
journal, January 2014

  • Zhao, Li-Dong; Dravid, Vinayak P.; Kanatzidis, Mercouri G.
  • Energy Environ. Sci., Vol. 7, Issue 1
  • DOI: 10.1039/C3EE43099E

Optimization of thermoelectric efficiency in SnTe: the case for the light band
journal, January 2014

  • Zhou, Min; Gibbs, Zachary M.; Wang, Heng
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 38
  • DOI: 10.1039/C4CP02091J

High-Mobility Bismuth-based Transparent p -Type Oxide from High-Throughput Material Screening
journal, December 2015


Thermoelectric alloys between PbSe and PbS with effective thermal conductivity reduction and high figure of merit
journal, January 2014

  • Wang, Heng; Wang, Jianli; Cao, Xianlong
  • Journal of Materials Chemistry A, Vol. 2, Issue 9
  • DOI: 10.1039/c3ta14929c

Thinking Like a Chemist: Intuition in Thermoelectric Materials
journal, April 2016

  • Zeier, Wolfgang G.; Zevalkink, Alex; Gibbs, Zachary M.
  • Angewandte Chemie International Edition, Vol. 55, Issue 24
  • DOI: 10.1002/anie.201508381

Valence-band structure of highly efficient p -type thermoelectric PbTe-PbS alloys
journal, January 2013


Weak electron-phonon coupling contributing to high thermoelectric performance in n-type PbSe
journal, May 2012

  • Wang, H.; Pei, Y.; LaLonde, A. D.
  • Proceedings of the National Academy of Sciences, Vol. 109, Issue 25
  • DOI: 10.1073/pnas.1111419109

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996


Benefits of Carrier-Pocket Anisotropy to Thermoelectric Performance: The Case of p -Type AgBiSe 2
journal, June 2015


Material descriptors for predicting thermoelectric performance
journal, January 2015

  • Yan, Jun; Gorai, Prashun; Ortiz, Brenden
  • Energy & Environmental Science, Vol. 8, Issue 3
  • DOI: 10.1039/C4EE03157A

Extraordinary role of Hg in enhancing the thermoelectric performance of p-type SnTe
journal, January 2015

  • Tan, Gangjian; Shi, Fengyuan; Doak, Jeff W.
  • Energy & Environmental Science, Vol. 8, Issue 1
  • DOI: 10.1039/C4EE01463D

Identification and design principles of low hole effective mass p-type transparent conducting oxides
journal, August 2013

  • Hautier, Geoffroy; Miglio, Anna; Ceder, Gerbrand
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3292

Heavy Doping and Band Engineering by Potassium to Improve the Thermoelectric Figure of Merit in p-Type PbTe, PbSe, and PbTe 1– y Se y
journal, June 2012

  • Zhang, Qian; Cao, Feng; Liu, Weishu
  • Journal of the American Chemical Society, Vol. 134, Issue 24
  • DOI: 10.1021/ja301245b

A high-throughput infrastructure for density functional theory calculations
journal, June 2011


Understanding thermoelectric properties from high-throughput calculations: trends, insights, and comparisons with experiment
journal, January 2016

  • Chen, Wei; Pöhls, Jan-Hendrik; Hautier, Geoffroy
  • Journal of Materials Chemistry C, Vol. 4, Issue 20
  • DOI: 10.1039/C5TC04339E

Chemical composition tuning in quaternary p-type Pb-chalcogenides – a promising strategy for enhanced thermoelectric performance
journal, January 2014

  • Yamini, Sima Aminorroaya; Wang, Heng; Gibbs, Zachary M.
  • Phys. Chem. Chem. Phys., Vol. 16, Issue 5
  • DOI: 10.1039/C3CP54493A

Thermoelectrics from Abundant Chemical Elements: High-Performance Nanostructured PbSe–PbS
journal, July 2011

  • Androulakis, John; Todorov, Iliya; He, Jiaqing
  • Journal of the American Chemical Society, Vol. 133, Issue 28
  • DOI: 10.1021/ja203022c

High-Performance Pseudocubic Thermoelectric Materials from Non-cubic Chalcopyrite Compounds
journal, April 2014


High Thermoelectric Performance of p-Type SnTe via a Synergistic Band Engineering and Nanostructuring Approach
journal, May 2014

  • Tan, Gangjian; Zhao, Li-Dong; Shi, Fengyuan
  • Journal of the American Chemical Society, Vol. 136, Issue 19
  • DOI: 10.1021/ja500860m

Nanostructures Boost the Thermoelectric Performance of PbS
journal, March 2011

  • Johnsen, Simon; He, Jiaqing; Androulakis, John
  • Journal of the American Chemical Society, Vol. 133, Issue 10
  • DOI: 10.1021/ja109138p

How Does Chemistry Influence Electron Effective Mass in Oxides? A High-Throughput Computational Analysis
journal, September 2014

  • Hautier, Geoffroy; Miglio, Anna; Waroquiers, David
  • Chemistry of Materials, Vol. 26, Issue 19
  • DOI: 10.1021/cm404079a

Quasiparticle self-consistent GW calculations for PbS, PbSe, and PbTe: Band structure and pressure coefficients
journal, June 2010


On the tuning of electrical and thermal transport in thermoelectrics: an integrated theory–experiment perspective
journal, February 2016


Importance of non-parabolic band effects in the thermoelectric properties of semiconductors
journal, November 2013

  • Chen, Xin; Parker, David; Singh, David J.
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep03168

Heavily Doped p-Type PbSe with High Thermoelectric Performance: An Alternative for PbTe
journal, February 2011

  • Wang, Heng; Pei, Yanzhong; LaLonde, Aaron D.
  • Advanced Materials, Vol. 23, Issue 11, p. 1366-1370
  • DOI: 10.1002/adma.201004200

High-Performance Tellurium-Free Thermoelectrics: All-Scale Hierarchical Structuring of p-Type PbSe–MSe Systems (M = Ca, Sr, Ba)
journal, March 2013

  • Lee, Yeseul; Lo, Shih-Han; Androulakis, John
  • Journal of the American Chemical Society, Vol. 135, Issue 13
  • DOI: 10.1021/ja400069s

Python Materials Genomics (pymatgen): A robust, open-source python library for materials analysis
journal, February 2013


    Works referencing / citing this record:

    Transparent conducting materials discovery using high-throughput computing
    journal, June 2019

    • Brunin, Guillaume; Ricci, Francesco; Ha, Viet-Anh
    • npj Computational Materials, Vol. 5, Issue 1
    • DOI: 10.1038/s41524-019-0200-5

    Chalcogenide Thermoelectrics Empowered by an Unconventional Bonding Mechanism
    journal, August 2019

    • Yu, Yuan; Cagnoni, Matteo; Cojocaru‐Mirédin, Oana
    • Advanced Functional Materials
    • DOI: 10.1002/adfm.201904862

    An ab initio electronic transport database for inorganic materials
    journal, July 2017


    Insights into the design of thermoelectric Mg3Sb2 and its analogs by combining theory and experiment
    journal, July 2019

    • Zhang, Jiawei; Song, Lirong; Iversen, Bo Brummerstedt
    • npj Computational Materials, Vol. 5, Issue 1
    • DOI: 10.1038/s41524-019-0215-y

    Valleytronics in thermoelectric materials
    journal, February 2018


    Transparent conducting materials discovery using high-throughput computing
    journal, June 2019

    • Brunin, Guillaume; Ricci, Francesco; Ha, Viet-Anh
    • npj Computational Materials, Vol. 5, Issue 1
    • DOI: 10.1038/s41524-019-0200-5

    Insights into the design of thermoelectric Mg3Sb2 and its analogs by combining theory and experiment
    journal, July 2019

    • Zhang, Jiawei; Song, Lirong; Iversen, Bo Brummerstedt
    • npj Computational Materials, Vol. 5, Issue 1
    • DOI: 10.1038/s41524-019-0215-y

    Valleytronics in thermoelectric materials
    journal, February 2018


    An ab initio electronic transport database for inorganic materials
    journal, July 2017


    Chalcogenide Thermoelectrics Empowered by an Unconventional Bonding Mechanism
    text, January 2019