Electronic Strategies for High Thermoelectric zT in Bulk Materials G. Jeffrey Snyder, Caltech Successful Strategies for TE

Zintl Phases Band Engineering nano-composite

Large Unit Cell Band Structure Nano Lamallae

Three routes to high zT: • Structural complexity - good for low κ •Different length scales ~ 1nm up to > 100nm •Eric Toberer 2:30pm • Band Structure Engineering - Electronic Properties Snyder, Toberer Nature Materials, 7, p. 105, (2008) Conventional Thermoelectric Material

Desire High zT Figure of Merit " 2#T zT = $ “Electron Crystal - Phonon Glass”

! α Seebeck Coefficient κ Thermal Conductivity High in Crystalline Semiconductor Low for Glass 2 2 2 3 8# k * $ # ' " = B m T & ) 3eh 2 % 3n ( Carrier " # " + L$T Concentration l σ Electrical Conductivity Tuning High In Crystalline Metal See Eric Toberer 2:30 ! ne2# " = neµ = Band! m* Structure Engineering

! Carrier Concentration

Desire High zT Figure of Merit " 2#T zT = $ Conflicting Materials Requirements α Seebeck Coefficient Need small n, large m* ! • Semiconductor (Valence compound) 2 2 2 3 8# k * $ # ' " = B m T & ) 3eh 2 % 3n (

σ Electrical Conductivity Need large n, high µ, low m* ! • Metal " = neµ κ Thermal Conductivity Carrier Concentration Tuning

Desire small κl, small n using ! Zintl Chemistry " # " l + LTneµ

! Valence Semiconductors General Valence Rule Vc = ec " bc Valence Conduction Accounts for Band Band Va = ea + ba " 8 Number of electrons donated (+) Ionic anion cation or needed (-) to fill valence band states states states • e valence electrons in atom! Polar Either/Both • each bond b reduces |valence|! by 1 Covalent Interpretation Valence Semiconductors Covalent bonding antibonding Stoichiometric balance of valences states states • ionic In3+Sb3-; covalent In1-Sb1+ Ionic MX Polar SC MX Semicond. X 3+ 2- 0 La 2Te 3 InSb Eg ~ 0.2 eV Ge Eg ~ 0.7 eV Conduction Band

+ M MIII antibonding X*

Eg X- XV bonding X

Valence Band

Toberer, May, Snyder Chem. Mat., 22, p. 624 (2010) TE: Valence Metals with Band Gap Thermoelectric materials are typically: Off Valence Balance compounds Where concentration of valence imbalance = free carrier concentration

• free Carrier Concentration measured by Hall Effect nH Transport properties are metallic • Heavily doped, degenerate semiconductors Zintl electron counting rules apply • Poly anions, Metal-Metal bonding

Ionic MX Polar MX Semicond. X La3Te4 “Zn4Sb3” Ge-clathrates electrons Conduction Band nH

+ EF M EF nH holes

X- EF Valence Band

Toberer, May, Snyder Chem. Mat., 22, p. 624 (2010) Zintl Phases for Low Cost Thermoelectrics Ca5Al2Sb6 valence balance

Zintl-Klemm valence counting gives valence balanced structure

Cation Valence = electron - bonds Anion Valence = electrons + bonds - 8 Sb2- Al as cation Ca Al Sb1,2 Sb3 electrons 2 3 5 5 Al3+ bonds 0 0 0 1 Ca2+ valence 2 3 -3 -2 Sb3- total 10 6 -12 -4

Net Valence = 0 Ca5Al2Sb6 cation doping

Ca Al Sb Eg 5 2 6 Sb2-

3+ Ca2+ Al Sb3-

Replace with NaxCa5-xAl2Sb6 1+ + EF Na + hole Induces free carriers Resistivity and Seebeck Coefficient

Resistivity Seebeck Coefficient

x = 0 x = 0

x = 0.05 x = 0.05

x =0.25 x =0.25

Heavily doped semiconductor: linear resistivity and Seebeck with T

• x=0.05: Seebeck peak at 800K gives Eg = 0.4 eV

E g = 2eTmax" max

! Seebeck vs. Carrier Concentration

Effective mass: m*= 2.2me

k & (2 + #)F ($) ) " = ( 1+# %$+ e ' (1+ #)F# ($) * $ r Fr (") = % # f o(")d# 0 3 / 2 ! 4 # 2"m*kT & n = % 2 ( F1/ 2()) " $ ! ' !

Assumptions: Single parabolic band, acoustic phonon scattering ! NaxCa5-xAl2Sb6 zT

zT vs Temperature zT vs Carrier Concentration

zT greater than 0.6 at 1000K for heavily doped sample

2 Input from x=0.25 sample: m*=1.9me µo=4.7 cm /Vs κl=0.76 W/mK Toberer, Zevalkink, Snyder Adv. Funct. Mat., (2010) 201000970 NaxCa3-xAlSb3

Ca AlSb4 No Sb-Sb bond zT vs Temperature

Similar structure and chemistry to Ca5Al2Sb6, except for no Sb-Sb bond higher mobility, lower effective mass leads to higher zT

2 Ca3Al1Sb3: m* = 0.8 me µo= 15 cm /Vs κl=0.78 W/mK 2 Ca5Al2Sb6: m* = 1.9 me µo= 4.7 cm /Vs κl= 0.76 W/mK

Zevalkink, Toberer, Snyder Energy. Environ. Sci., (2010) High Efficiency from Band Structure Engineering Enhancing Thermopower

Seebeck Thermopower increased by Typically described by effective m* • Single Parabolic Band 1. Larger band mass m* 2 2 2 3 But reduces mobility 8# kB * $ # ' " = 2 m T & ) 3eh % 3n ( ne2# " = neµ = * degenerate limit, m acoustic phonon scattering ! 2. Greater band degeneracy NV multiple parabolic bands • Need carrier concentration n ! * 2 – Typically use Hall nH 3 m* = mband NV

3. Scattering ! Energy dependence of τ p-PbTe Pisarenko Plot

Pisarenko 0.05 Parab DOS/dE/DOS Thermopower depends on carrier conc. n Res as dopant 0.04 Non Parabolic DOS -2/3 Resonant1. Increases seebeck state parabolic band metal α ∝ n 2. not strictly decreasing. 0.03 depending on width and intensity ofeffect resonant state 2 2 2 3 this can be a peak or a flat shelf 8# k * $ # ' 0.02 " = B m T & ) 3eh 2 % 3n ( Seebeck d(DOS)/dE/DOS Seebeck 0.01 α ∝ n-2/3 0.00 0 100 200 300 400 500 m* is the single Parabolic Band effective mass holes (arbitrary units) ! PbTe:Tl shows higher thermopower than other p-type dopants • Resonant state should alter thermopower from increased DOS

Change in slope α vs. n in PbTe:Na indicates multiple band behavior

Heremans, et al.. Science 321, p 554 (2008). Thermoelectric La3-xTe4

La3Te4 EF La3-xTe4 has high zT at high T Higher than SiGe used by NASA La2.73Te4 EF Highest zT for La2.73Te4

EF at edge of heavy band

• m* ~ 3.5 me

EF deep inside light band La2Te3 EF

• m* ~ 2 me

1.5

K 1.0 1273

zT 0.5

0.0 0.0 0.2 0.4 0.6 0.8 1.0 4 3 nH* 4 Te Te Te 2 3 2.73 La La La May et. al. Phys. Rev. B, 78, p. 125205, (2008) May et. al. Phys. Rev. B, 79, p. 153101, (2009) Heavy and Light holes in PbTe

Valence Band Maximum is at L point • “Light Band”

Second valence band occurs at Σ line • “Heavy Band”

Transition from single to multiple band 19 3 occurs at nH ~ 3 x 10 holes/cm

0.3 Conduction Band

0.2 Eg 0.1 (eV) Light E 0.0 Valence Band Heavy Valence Band -0.1 L ! K p-PbTe zT

NASA doping optimal Light band has peak zT at low n Range doping zT peak < 1 “2P-PbTe” used by NASA in 1960’s 19 3 nH < 4 x 10 holes/cm

Heavy band requires high n zT peak ~ 1.5 20 3 nH ≥ 1 x 10 holes/cm

Pei, Snyder, et al.. Energy Environ. Science (in press). p-PbSe

Similar light-band heavy-band in PbSe Leads to zT > 1 without expense of Te!

Wang, Snyder, et al.. Advanced Materials (in press). Summary

Three Strategies for advanced TE 1. Zintl Phases 2. Band structure Engineering 3. Nano composites

Zintl Phases New low cost, non-toxic TE systems

• NaxCa5-xAl2Sb6 zT 0.6 at 1000K

• NaxCa3-xAl1Sb3 zT 0.8 at 1000K

PbTe structure materials High zT without Tl or Te • Na:PbTe zT ~ 1.5 at 750K • Na:PbSe zT ~ 1.2 at 800K Acknowledgements

Postdocs Teruyuki Ikeda (JST) Eric Toberer Yanzhong Pei Aaron Lalonde Shiho Iwanaga Eric Toberer Yangzhong PEI Aaron Lalonde Students Shiho IWANAGA Heng Wang Alex Zevalkink Nick Heinz Greg Pomrhen Andrew May Collaborations Heng WANG Alex Zevalkink Nick Heinz Greg Pomrhen Norb Elsner Funded by Joseph Heremans Jessica Lensch-Falk, NASA-JPL Doug Medlin (Sandia CA) - TEM Beckman Foundation, Caltech David Singh (ORNL) DARPA Axel van de Walle (Caltech) Sandia National Laboratories Ø. Prytz, P. Rauwel Johan Taftø (Oslo) MURI Actual band structure Blue PbTe Red Tl:PbTe (minus one band) Supercell L is actually Gamma