G. Jeffrey Snyder California Institute of Technology

Pasadena, California, USA http://thermoelectrics.caltech.edu

EF

nH holes

Materials strategies for improving the overall device ZT

Lalonde, Pei, Wang, Snyder, Materials Today 14 526 (2011).

Carrier Concentration Desire High zT Figure of Merit T zT " 2#

=$

Conflicting Materials Requirements α Seebeck Coefficient

Need small n, large m* • Semiconductor (Valence compound)

8 2k 2 2 3# B T$ # '

= m*"3 2 & ) eh % 3n (

σ Electrical Conductivity Need large n, high µ

• Metal

" = neµ

κ Thermal Conductivity Optimum between Insulator and Metal Desire small κl, small n

" #" l + LTneµ

Snyder, Toberer Nature Materials 7, 105 (2008)

!

!

!

!

PbTe1-xIx Iodine (I) supplies one more electron than Tellerium (TE) Iodine (I-) replaces Te2- producing 1 e- 1018 - 1020 e-/cm3

Conduction Band

EF

nH electrons

Valence Band From Room Temperature Hall Effect

Carrier Concentration Tuning

zT of n-type PbTe1-xIx

Lalonde, Pei, Snyder Energy and Environmental Science 4, 2090 (2011)

Peak zT ~ 1.4 at 800K due to low thermal conductivity

Unattended operation for over 10 years

Quality Factor and n* Maximum zT depends on Optimized

Quality Factor carrier concentration n* ~ N 2/3m * T3/2

v b

B ~ NV

m*b!L

Multi Valley Fermi Surface with Valley Degeneracy Nv

m* 2=m*

bN 3V

because µ decreases with m* e" 1

µ = " #m* 2b m*

3 /b

Acoustic Phonon Scattering

! Mahan, “Good Thermoelectrics” Solid State Physics 51, p 81 (1998). !

Lalonde, Pei, Wang, Snyder, Materials Today 14 526 (2011).

Effective mass LaxPb1-xTe vs. PbTe1-xIx

Both n-type L-band

20% lower m*

LaxPb1-xTe

PbTe1-xIx

1µ! N

m*5/2B ~ V

b m*b!L

30% higher µ PbTe1-xIx

LaxPb1-xTe

20% Higher zT

PbTe1-xIx

LaxPb1-xTe

Heavy and Light holes in PbTe Valence Band Maximum is at L point

•  “Light Band” NV = 4, mb* = 0.14 me Second valence band occurs at Σ line

•  “Heavy Band” NV = 12 , mb* = 0.28 me

m* * 2= m 3

bandNV

Transition from single to multiple band occurs at nH ~ 3 x 1019 holes/cm3

-0.1

0.0

0.1

0.2

0.3

E (e

V)

L K!

Eg

Conduction Band

Heavy Valence Band

Light Valence Band

!

Pei, Snyder, et al.. Energy Environ. Science 4, 2085 (2011). Pei, Snyder, et al. Nature 473, p66 (2011).

Valley Convergence with composition PbTe convergence changes with alloying

• Slight shift in energy of C, L and Σ bands • Will change Convergence Temperature

– Increases Tconvg with PbSe alloying – Decreases Tconvg with MgTe alloying

-0.1

0.0

0.1

0.2

0.3

E (e

V)

L K!

Eg

Conduction Band

Heavy Valence Band

Light Valence Band -0.2

0.0

0.2 0.30 0.15CC

ΔEC-Σ

Energy(e

V)

xSe

LΣΣ

L

C

Σ

L

ΔEC-L

0

300 K

PbTe1-xSex

Pei, Snyder, et al. Nature 473, p66 (2011).

p-type PbTe-PbSe ZT (average zT) Peak zT is high but device ZT (average zT) is not really improved zT at low temperature reduced by increasing Tconvg!

Pei, Snyder, et al. Nature 473, p66 (2011).

0.0

0.2

0.4

0.6

0.8

1.0

Biswas, PbTe:Na/SrTePei, PbTe

0.85Se

0.15:Na

Pei, PbTe:NaHeremans, PbTe:Tl

ZT

b This work, Pb0.97

Mg0.03

Te:Na

!

Device Figure of Merit ZT #T 1+ ZT %1

" = $ Th 1+ ZT +Tc Th

ZT = zT is approximation for α(T), ρ(T), κ(T), are constant

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250

Commercial p-(Sb,Bi)2Te

3 zT

Figu

re o

f Mer

it zT

T(C)

actual zT

approximate zT

ZT

Real materials: zT ≠ ZT especially max zT ≠ ZT Beware conclusions about changing ∆T

Materials figure of merit zT 2

zT "= T #$

Determines maximum reduced efficiency at any given point 1max + zT # 1 "r =

1 + zT + 1Actual efficiency is less

•  series current not optimal everywhere

0

5

10

15

20

0 50 100 150 200 250

Commercial p-(Sb,Bi)2Te

3 Reduced Efficiency

Red

uced

Effi

cien

cy (%

)

T(C)

maximum

actualZT

approximation

!

zT vs. ZT

!

!

Goldsmid, H. J. Applications of Thermoelectricity (Methuen, London, 1960).

Precipitates in PbTe can Increase ZT Higher average zT

Higher Device ZT

Pei, Snyder, et al, Energy and Environmental Science 4, 3640 (2011)"Pei, Snyder, et al, Adv. Funct. Mat.,21, 241 (2011)"

p-type

n-type

Decreasing Tconvg with Mg MgxPb1-xTe shifts valence L band to convergence with Σ at 300K

S vs n (Pisarenko) looks like single heavy band

Continues to go below Σ at high temperature But band gap (between C and Σ) increases, helps S at high T

1018 1019 10200

50

100

150

200

250

300

350

Biswas, PbTe:Na/SrTe

Crocker,Mg0.034

Pb0.966

Te

3 Band Model, Mg0.03

Pb0.97

Te

Rogers,Mg

xPb

1-xTe, 0.01<x<0.04

This workMg

0.03Pb

0.97Te:Na

PbTe:Na

a

S(µV

/K)

1/eRH ( cm-3)

300 K

!

-0.2

0.0

0.2 0.06 0.03CC

!EC-"

Energy(

eV)

xMg

L "

"L

C

"L

!EC-L

0

a

300 K

300 400 500 600 700 80050

100

150

200

250

300

3.7e19 5.8e19 7.8e19 9.0e19 1.0e20 1.2e20

Pei, PbTe:Na, 7.5e19

b

S(µV

/K)

T ( K) !

Pei, Snyder, et al. Advanced Materials 23, 5674 (2011)

!

Increasing ZT by stabilizing n* Lower Tconvg: Reduces T of NV

enhancement Keeps n* from increasing

with T so fast Higher average zT

0.0

0.2

0.4

0.6

0.8

1.0

Biswas, PbTe:Na/SrTe

b This work, Pb0.97

Mg0.03

Te:NaPei, PbTe

0.85Se

0.15:Na

Pei, PbTe:NaHeremans, PbTe:Tl

ZT

!

300 400 500 600 700 800 9000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Biswas, PbTe:Na/SrTe

a

Pei, PbTe0.85Se0.15:NaPei, PbTe:Na

3.7e19 5.8e19 7.8e19 9.0e19 1.0e20 1.2e20

zT

T ( K)

Heremans, PbTe:Tl

!

Pei, Snyder, et al. Advanced Materials 23, 5674 (2011)

Optimized carrier

concentration n ~ Nv

2/3mb* T3/2

TE Handbook (1995)

Self-Tuning n* via Composites

Ag, Ag2Te particles in PbTe

!

Pei, Snyder, et al. Advanced Energy Materials 1, 291 (2011)

Temperature dependent dopant solubility Pb, Te, Ag, Cu in PbTe B, P in SiGe

At solubility limit, n increases with T

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 200 400 600 800 1000

zT

Temperature (°C)

SiGe

p-Type Metal

CeFe4Sb

12

TAGS p-Type zT

Compatibility Factor High Efficiency from zT 1+ zT "1only with compatible s s =

#Toperating current must match

0.70.80.91.0

2.0

3.0

4.05.06.0

0 200 400 600 800 1000

Com

patib

ility

Fac

tor s

Temperature (°C)

SiGe

CeFe4Sb

12

TAGS

Factorof Two

p-Type s

p-Type Metal

!

0

2

4

6

8

10

12

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

Constant Temperature I-V curve

Voltage

Power (mW)

Vol

tage

Power (m

W)

Current (mA)

Ukraine 1205° C

1.17 W heat

0.86 W heat

Snyder Applied Physics Letters 84, 2436 (2004)

0

5

10

15

20

0 50 100 150 200 250

Commercial p-(Sb,Bi)2Te

3 Reduced Efficiency

Red

uced

Effi

cien

cy (%

)

T(C)

maximum

actualZT

approximation

SiGe has small s compared to other TE cant be segmented

Summary Many levels of complexity for ZT

higher order effects relevant for high Optimized

carrier concentration

n ~ Nv2/3mb* T3/2

B ~ NV

mb*!L

efficiency applications Peak zT

carrier concentration for peak zT quality factor maximization

High average zT carrier conc. tuning functionally grading *self-tuning composites

Band Engr. for ZT quality factor engr for avg zT nanostructures for low temp *stabilizing n*

Compatibility effects ZT not a simple average of zT

Pei, Snyder, et al. Advanced Materials 23, 5674 (2011) Pei, Snyder, et al. Advanced Energy Materials 1, 291 (2011) Lalonde, Pei, Wang, Snyder, Materials Today 14 526 (2011)

Acknowledgements Postdocs

Yanzhong Pei Aaron Lalonde Shiho Iwanaga Eric Toberer

Students Heng Wang Alex Zevalkink Nick Heinz Greg Pomrhen Andrew May

Collaborations/discussions Lidong Chen Xiaoya Shi (SIC-CAS) Norb Elsner Joseph Heremans Mercuri Kanatzidis Yaniv Gelbstein David Singh (ORNL) Jean-Pierre Fleurial Sabah Bux (JPL) Axel van de Walle (Caltech)

Funded by NASA-JPL Beckman Foundation, Caltech DARPA Sandia National Laboratories AFOSR MURI

Greg Pomrhen Nick Heinz

Eric Toberer

Alex Zevalkink

Yangzhong PEI

Heng WANG

Shiho IWANAGA

Aaron Lalonde