Thermoelectric Energy Transport in Nanostructures

Ali ShakouriBaskin School of Engineering, University of California, Santa CruzHttp://quantum.soe.ucsc.edu

Int. Workshop on Nanoscale Energy Conversion and Information Processing DevicesNice, France, 24 September 2006

AcknowledgementPostdocs/Students: Zhixi Bian, James Christofferson, Mona Zebarjadi, Rajeev Singh,

Xi Wang, Daryoosh Vashaee, Yan Zhang, Kazuhiko Fukutani, Tammy Humphrey

Collaborators: John Bowers, Art Gossard, Arun Majumdar, Venky Narayanamurti, Rajeev Ram, Tim Sands, Avi Bar-Cohen, Stefan Dilhaire, Ed Croke, Peidong Yang, Holger Schmidt

Sponsors: ONR/MURI, Intel, Canon, National, Packard Foundation, DARPA/Heretic, NSF

2

AS 9/24/2006Motivation: Microprocessor Evolution

Source: IntelSource: Intel

1,000,0001,000,000

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11

1 Billion 1 Billion TransistorsTransistors

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Source: IntelSource: Intel

1,000,0001,000,000

100,000100,000

10,00010,000

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1 Billion 1 Billion TransistorsTransistors

80868086

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Electronic/Optoelectronic devices → Generate high/ localized heat density

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Possible ApplicationsPossible Applications

• Waste heat recovery

• Electric power generator with no moving part

• Microscale power sources

Direct Conversion of Heat into ElectricityDirect Conversion of Heat into Electricity

Significant amount of heat generated as by product of any energy conversion.

Thermal

Electrical

Optical

Magnetic Mechanical

Chemical/biological

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RejectedEnergy 61%

Total 91.4 quad(↑ x3) 1950

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ab

a

I

Q Q

ab a b Q

I

STdS

dTT

Peltier:

Peltier and Seebeck Effects Peltier and Seebeck Effects

Thomson:

Commercial TE Module• T=72C • Cooling density <10W/cm2

• Efficiency 6-8% of Carnot

RTGs (space power)

S VT

Seebeck: ab

V

T1T2

a

6

AS 9/24/2006Efficiency of TE Power GenerationEfficiency of TE Power Generation

ZT = 1.2-3.6

ZT = 0.3-0.9

Z S2

Z (Seebeck)2 (electrical conductivity)

(thermal conductivity)

Efficiency (COP) depends on a single ratio (Z)

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AS 9/24/2006

PbTe/PbTeSe Quantum DotSuperlattices

Ternary: ZT=1.3-1.6Quaternary: ZT=2T=43.7 K, Bulk T=30.8 KT.C. Harman, Science, 2002

T=32.2 K, ZT ~2-2.4R. Venkatasubramanian, Nature, 2001

Nanostructure Bulk

Power Factor (W/cmK2) 25.5 28 40 50.9Thermal Conductivity (W/mK) 0.5 2.0 0.5 1.26

PbTe/PbSeTe Bi2Te3/Sb2Te3 Superlattice Bulk

In-plane geometry Cross-plane geometry

(From M. S. Dresselhaus, Rohsenow Symposium, 2003)

Superlattices/ Quantum Dot Thermoelectrics T. C. Harman (2002) and R. Venkatasubramanian (2001)

8

AS 9/24/2006Thermionic Emission for Energy Conversion

Cathode Barrier Anode

Energy

Hot electron

Cold electron

Metal/Semiconductor Superlattice, Embedded Nanostructures

Low work function Vacuum (ions) Low work function

Metal/ Deg. Semicond

Metal/ Deg. Semicond

Solid-State

Vacuum

HotHot ColdCold

• Selective emission of hot electrons over a potential barrier can generate electrical power from temperature difference •Thermodynamic reverse process: evaporative cooling of electrons

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AS 9/24/2006

Si/SiGeC Superlattice Structures for Heterostructure Thermionic Filtering

150x SiGeC/Si Superlattice(10nm/10nm)

Barrier

SiCathode

Si (001) SubstrateAnode

• MBE Grown 5” Substrate

• Material and Processing Compatible with SiGe HBTs. 1 µm

Hot Electron

Cold Electron

Funded by ONR and DARPA/ARMY HERETIC

Si

Si0.89Ge0.1C0.01

X. Fan, E.Croke, J.E. Bowers, A. Shakouri, et al., “SiGeC/Si superlattice micro cooler,” Applied Physics Lett. 78 (11), 2001. Featured in Nature Science Update, Physics Today, AIP April 2001

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AS 9/24/2006Microrefrigerator on a chip

• Temperature resolution: 0.006oC• Spatial resolution: submicron

High resolution thermal imaging

Thermal imaging camera; J. Christofferson, A. Shakouri, Review of Scientific Instruments Feb 2005. Nanoscale heat transport and microrefrigerators on a chip; A. Shakouri, Proceedings of IEEE, 2006

• Maximum cooling: 4C (300K), 12 (500K)

• Cooling power density: >500 W/cm2

• Response time: < 20-40s• Materials: SiGe, SiGeC, InGaAs, InP• Fabrication: IC compatible

ZT~0.08-0.1

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J. Snyder (2003) http://www.its.caltech.edu/~jsnyder/thermoelectrics/science_page.htm

I

Z S2

Z (Seebeck)2 (electrical conductivity)

(thermal conductivity)For almost all materials, if doping is increased, electrical conductivity increases but Seebeck coefficient is reduced.

S

S2

How to improve ZT?How to improve ZT?

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Energy

Density of States

Ef High doping

Doped Bulk Semiconductor/ Metal

Highly-Doped Tall Barrier Superlattice

Ef

Ebarrier

Metallic Superlattices for Thermionic Energy Conversion

Distance

Energy

Symmetry of DOS near Fermi energy is the main factor determining Seebeck coefficient.

Ef Low doping

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Program Manager: Mihal Gross

D. Vashaee., A. Shakouri, Physical Review Letters March 12, 2004

Non-planar Barrier

UCSC Berkeley Harvard MIT NCSU Purdue UCSB

Director:A. Shakouri

ZT for metallic superlattices with non-planar barriersZT for metallic superlattices with non-planar barriers

Thermionic Energy Conversion Center MURIThermionic Energy Conversion Center MURI Assume: lattice=1W/mK, mobility ~10 cm2/Vs

Planar Barrier

Planar barriers are not ideal for hot electron filtering. ZT>5 is possible with metallic structures with non-planar barriers.

Hot and cold electrons in equilibrium

Hot electron filter

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TEM/HAADF of Semimetallic ErAs Nanoparticles in InGaAs Matrix

In,GaAsEr

STEM images show that the ErAs particles have the rock salt structure. The As sublattice is continuous across the interface.

STEM images show that the ErAs particles have the rock salt structure. The As sublattice is continuous across the interface.

110

001

1nm

D. O. Klenov, D. C. Driscoll, A. C. Gossard, S. Stemmer, Appl. Phys. Lett. 86, 111912 (2005)

HAADFHAADF

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0.4 ML 40 nm

0.1 ML 10 nm

In0.53Ga0.47As

Kim et al., Physical Review Letters, 30, 045901 (2006)

In0.53Ga0.47As

0.3 % ErAs

3.0 % ErAs

3.0 % ErAs:In0.53Ga0.28Al0.19As

Thermal Conductivity of ErAs:InThermal Conductivity of ErAs:In0.530.53GaGa0.470.47AsAs

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AS 9/24/2006ErAs: InGaAs/InGaAlAs SL

n-InP substrate

50nm 5E18 n-InGaAs

20nm n-InGaAs/ErAs 0.3%

10nm InGaAlAs

20nm n-InGaAs Cap layer

• Sample 1– 1E19

• Sample 2 – 4E18

• Sample 3 – 2E18

Add superlattice energy filtering to increase the thermoelectric power factor.

Joshua Zide, Daryoosh Vashaee, Gehong Zeng et al., submitted to PRB 2006

70x

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AS 9/24/2006Cross-plane/ In-plane Seebeck Characterization

J. Zide et al., (UCSB, UCSC) submitted to Physical Review B, 2006

Theory/Experiment Seebeck II, ┴ (300K)

ErAs: InGaAs/InGaAlAs Superlattices

0

0.5

1

1.5

2

300 400 500 600 700 800

2e184e186e188e181e19

ZT

Temperature (K)

1e19 cm-3

2e18 cm-3

6e18 cm-3

Theoretical ZT

ZT

Temperature (K)

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AS 9/24/2006Thermoelectric single element characterizationThermoelectric single element characterization

• ErAs generates significantly more power despite the lower effective

Seebeck

• BiTe degrades rapidly at higher temperatures while ErAs improves with

temperature

0 50 100 150 200 250 300 3500

1

2

3

4

5

T (K)Pow

er

densi

ty (

W/c

m2)

-ErAs (SL+substrate)-SiGe (SL+substrate)-BiTe (bulk)

160x(10nm (InGaAs)0.6(InAlAs)0.4/20nm (n-InGaAs)0.97Er0.03) on 474 m doped InP substrate

200x(75Å SiGe0.16/ 75Å SiGe0.24) on 403 m doped Si substrate

Thot

V+

V-

Heater

OFHC copper

OFHC copper

TE sample

Al cold plate

Chilled water

Ceramic rails(insulating)

Peter Meyer, Rajeev Ram (MIT)

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AS 9/24/2006Thin film array generator 200 n-p couples, 5-10 microns ErAs:InGaAs/InAlAs superlattice thin films, 120x120m2, 12 ohm load

G. Zeng, J. Bowers, et al. (UCSB)Appl. Physics Letters 2006

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

400 element generator array10 m x 120 m x 120 m (R

L = 12 Ohm)

heat up (W/cm2)cooling down (W/cm2)

Po

wer

(W

/cm

2 )

T (K)

20

AS 9/24/2006Monte Carlo + Poisson Equation

InGaAs InGaAsP InGaAsH

eat Sin

kA

nod

eBias

Hot

Sou

rceC

athod

e

Cathode contactlayer

Anode contact layer

Barrier (main-layer)

+ Electron-phonon energy exchange (S) TJ

SJ

ph

ph

.

Goal: Range of validity for thermoelectric and thermionic transport formalisms

Mona Zebarjadi, Keivan Esfarjani, Ali Shakouri (UCSC)

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-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.25 0.5 0.75 1 1.25 1.5 1.75

length (um)

En

erg

y e

xch

an

ge

(1

E-9

W/C

m^2

)Electron-phonon energy exchange (S)

Peltier Cooling Peltier Heating

Non-equilibrium transport in the barrier

Energy relaxation length in cathode

Energy relaxation length in anode

Mona Zebarjadi, Keivan Esfarjani, Ali Shakouri (UCSC)

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Effective Seebeck Coefficient vs. Barrier Thickness

200

220

240

260

280

300

320

340

0 500 1000 1500 2000

Length(nm)

seeb

eck

(uv/

K)

Convectional Thermoelectric transport

Convectional Thermionic transport

Mona Zebarjadi, Keivan Esfarjani, Ali Shakouri (UCSC)

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Summary• Micro-refrigerator on a chip• Cooling 4 -7C , >500W/cm2, 20-40s

• Solid-state thermionic energy conv.Metallic SL and embedded nanoparticles

• ErAs: lattice thermal conductivity 6→ 2-3 W/mK • Increase ┴ Seebeck coefficient 200→600V/K • Power generation 1 element >5W/cm2 for T=300C

• Improvement in ZT: decouple S, , k

• Microscopic origin of TE/TI– Location and spatial extent of regions where

Peltier cooling/ heating occurs– Transition from TE to TI transport

• Statistical properties of reservoirs

Students/postdocsUCSC Zhixi Bian, Rajeev Singh, Mona Zebarjadi, Yan Zhang Younes Ezzahri, Daryoosh Vashaee,Tammy Humphrey

Berkeley Woochul KimSusanne Singer

Harvard Kasey Russel

MIT Peter Mayer

Purdue Vijay Rawat

UCSB Josh Zide, Gehong Zeng, J-H Bahk

Acknowledgement: ONR MURI (Dr. Mihal Gross), Packard, DARPA, Intel, Canon

SUMMARY

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kBTh ~ 75 meV kBTc ~ 25 meV

Why there is Carnot limit?

T=900K T=300K

Average Random Kinetic Energy of Carriers

If an electron is moved from hot reservoir to cold reservoir with “no dissipation”, on the average the maximum amount of energy per electron available to do work is: (KBTh-KBTc)/KBTh = (Th-Tc)/Th Carnot limit

Ali Shakouri, TE, TI and TPV energy conversion, MRS Fall 2005

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kBTh ~ 75 meV kBTc ~ 25 meV

hBlackBody~ 400 meV

Thermoelectric/Thermionic vs. TPV

0

2000

4000

6000

8000

10000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

I (W

m-2

m

-1)

E (eV)

np

hBlackBody~ 125 meV

T=900K T=300K

Photons emitted from hot source have higher average energy than electrons emitted at the same temperature.

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T=625C T=25C

Photon-Assisted Thermionic Power Generation

Solid State TI

Possibility to use both hot electrons and hot photons?Ali Shakouri, TE, TI and TPV energy conversion, MRS Fall 2005

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Possibility to use phase transition (change in internal degrees of

freedom, latent heat) in electron gas to improve TE energy conversion

efficiency?

Is there room temperature phase change for electrons?