Th Thermal Energy Transport in Nanostructured and l E T t i N t - - PowerPoint PPT Presentation

Th l E T t i N t t d d Thermal Energy Transport in Nanostructured and Complex Crystals

Li Shi Department of Mechanical Engineering & Texas Materials Institute The University of Texas at Austin

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Thermoelectric Energy Conversion

Waste Heat Recovery

Metal Semi- conductor Insulator

• n

p Waste Heat Recovery

Heat Source

EC EF

• n

p

• +

I I

S σ EV + +

I I

Heat Sink

S σ S2σ Figure of Merit (ZT)

Seebeck coefficient Electrical conductivity

κ

T S ZT κ σ

2

≡

κe κp

κ

Thermal conductivity

p

Carrier concentration (n)

ZT Progress and Materials Issues

• ZT enhancement in complex or

p nanostructured bulk materials is caused by lattice thermal conductivity suppression.

• Thallium (Tl) doping in PbTe increases

S2σ and ZT. 2 Bi2T 3 1.5

T

Bi2Te3 SiGe Complex crystals Nano‐bulk telluride 1

Peak ZT

Nano bulk telluride Tl doped PbTe 0.5 1950 1970 1990 2010

Year

• Tellurium and germanium are costly. Thallium is toxic.
• Low-cost, abundant, and environmentally-friendly materials with ZT > 1.5 are needed for

large-scale deployment of thermoelectric generators.

Thermal Conductivity (κ) +

κ (W/m-K) @ 300 K

κ ≈ κE+κl

Lattice vibration or phonon Electronic κ (W/m-K) @ 300 K 1000 Diamond, Graphene, CNTs, Graphite 100 Cu Si

i max

λ

Spectral specific heat Wavelength 100 Si Bi InAs

∑ ∫ =

i i i x i l

i i

d l v C

max, min,

) ( ) ( ) (

, λ

λ λ λ λ κ

Alloy limit κalloy

10 Bi CrSi2 Group velocity m.f.p. λ Polarizations

y

alloy

Bi2Te3, PbTe, MnSi1.75 SiGe Si vx,i(λ) = speed of sound li(λ) = λ/2 Amorphous limit κα 1 α-Si

• κl << κα has been demonstrated in disordered, layered thin films.

0.1 Polymer Air

• The question is how much κl can be lowered without considerable

reduction of the charge mobility.

Nanowire Model Systems

• Bi2Te3 NW Sample 3

210

• Electrodeposited
• Single crystalline
• Growth direction

003

<110>

[120] Zone Axis

B d tt i f

• Boundary scattering m.f.p.:

for 1 1 → → − + = p d d p p lb

• At 300 K, phonon wavelength (λ)
• Effective m.f.p.:

( )

1 1 1 1

) (

− − − −

+ + =

b i U

l l l l ω

~1 nm ~ surface roughness (δ)

• Ziman’s surface specularity:

d l v C

i i x i l

ZBi

∑ ∫ = ) ( ) ( ) (

,

ω ω ω ω κ

ω

• Callaway-type model:

) / 16 exp(

2 2 3

≥ − = λ δ π p

d lb

diffuse i

→ → when

,

κ

Thermal Measurement of Individual NWs

T Th

Th’

x Ts

Th Ts’

I

Th Ts

Th Ts T0 Ts’ Th’

I RNW

h s

RC2 RC1

T0

RBeams Q

s h

Contact Thermal Resistance and Seebeck Measurements

T Th

Th’

x Ts

Th Ts’

I

V14

T

Mavrokefalos et al., Rev. Sci.

Th Ts

V23 / V14

• Instr. 78, 034901 (2007):

(Th’-Ts’)/ (Th-Ts) S V /(T T ) Th Ts T0 Ts’ Th’

I

S ≈ V14/(Th-Ts) V23

• Electrical contact was made between

RNW

h s

RC2 RC1

T0

RBeams Q

s h

• Electrical contact was made between

the NW and the pre-patterned Pt electrodes via annealing in hydrogen.

Single-crystal NW

• Polycrystalline NW
• Majority of the NW oriented within

3o along the binary direction

003

Seebeck Coefficient and Fermi Level (EF)

• Hall measurements cannot be

used to obtain carrier concentration & mobility in NWs. & mobility in NWs.

Electron Concentration (n) and Mobility (μ)

) ( ) 2 ( 4

2 / 3

F T k ζ π

∗

) ( ) 2 ( 4

2 / 1 2 / 3 3 e B e

F T k m h n ζ π

∗

=

~0 for the highly doped EF

h e

pe ne μ μ σ + =

ne / σ μ =

• The measured σ can only be

fitted with the higher EF

ne

e

/ σ μ =

fitted with the higher EF.

• The mobility of the single-crystal NW 3 is

~19% lower than the bulk value.

• The electron m.f.p. is reduced from 60 nm

in bulk to 40 nm in NW 3 because of partially specular electron surface scattering partially specular electron-surface scattering.

Electronic and Lattice Thermal Conductivity (κe & κl)

• For the polycrystalline NW 2, κ < κbulk

mainly because of κ suppression mainly because of κe suppression.

• For the single crystal NW the obtained κ is
• κe calculated

from the W-F law

• For the single-crystal NW, the obtained κl is

suppressed by <20% because of the short Umklapp m.f.p. (lu~3 nm), so that the size ff d i il i h 50 effects on κl and μ are similar in the 50-nm diameter Bi2Te3 NW.

• Symbols: κl =κ −κe
• Lines: Callaway model

Lines: Callaway model

• μ of the NW is close to bulk values along the same
• μ of the NW is close to bulk values along the same

direction.

• Hole effective mass m*= 5m0 large p & low bulk μ
• σ is high because of a large m* and p
• μ and τ in NWs were dominated by acoustic phonon

scattering instead of boundary scattering.

Thermal Conductivity and ZT of CrSi2 Nanowires

• Phonon m.f.p. in bulk CrSi2 is less than 10 nm < d.
• Compared to the hot pressed bulk powder sample small ZT enhancement was
• Compared to the hot pressed bulk powder sample, small ZT enhancement was

found in two NWs of <100 nm diameter mainly because of the slightly suppressed κ without mobility reduction without mobility reduction.

• κl suppression in a NW is rather small unless d ≤ the umklapp scattering m.f.p. (lu).

l

pp pp g p ( u)

Complex Silicide Nanowires of Large Effective Mass

A HRTEM MnSi1 75 nanowires C

Mn27Si47

A HRTEM MnSi1.75 nanowires C

Novotony Chimney Ladder

5 nm

phases of MnSi1.75 (004) (112)

11.79 nm 11.79 nm Mn15Si26 Mn15Si26 Mn11Si19 Mn11Si19

B

5 nm 5 nm 5 nm 5 nm

Mn Si

• J. M. Higgins, A. Schmitt, S. Jin,

JACS (2008)

Mn4Si7 Selected Area Electron Diffraction

• Large unit cell size (c) along

the c axis of a MnSi1.75 NW

• Numerous phonon modes of low group velocity and enhanced

phonon-phonon scattering results in low κ = 2−4 W/m-K and ZT = 0.7 at 800 K in bulk MnSi1.75.

Phonon-Glass Behavior in MnSi1.75 NRs and NWs

• For MnSi1.75 NWs and NRs, κ ~ κα = 0.7 W/m-K calculated with l = λ/2 and v = speed of

d sound.

• The group velocity of the numerous optical phonons is much smaller than the speed of sound.

Th f f ti h ld b till it l i b lk M Si d i d d b

• The m.f.p. of acoustic phonons could be still quite long in bulk MnSi1.75, and is reduced by

diffuse surface scattering in the nanostructure.

Summary

• It appears to be possible to achieve phonon-glass, electron-crystal

behavior in silicide NWs of complex crystals that have a large effective mass and abundant on earth mass and abundant on earth.

• In such NWs, κl can be suppressed to κα via the combination of

l l it ti l h ith ll f ti f ti numerous low-velocity optical phonons with a small fraction of acoustic phonons of suppressed m.f.p.

• While it remains to be verified, the large effective mass can potentially

lead to large carrier concentration and low-medium bulk mobility that is not reduced much in a NW, so that the power factor is not reduced as much , p as κl suppression.

Acknowledgement

Current Graduate Students and Post-doc Fellows: Arden Moore, Jae Hun Seol, Michael Pettes, Yong Lee, JaeHyun Kim, Mir Mohammad Sadeghi, Patrick Jurney Alumni: Alumni: Anastassios Mavrokefalos, Feng Zhou, Choongho Yu, Jianhua Zhou, Sanjoy Saha, Huijun Kong Collaborations for Nanowire Studies: Jeremy Higgins, Jeannine Szczech, Song Jin (UW-Madison) Wei Wang, Xiaoguang Li (USTC) Laura Qi Ye (NASA) au a Q e (N S ) Natalio Mingo (CEA-Grenoble) Derek Stewart (Cornell) Heiner Linke, Kimberley Thelander, Jessica, Ann Persson, Linus Fröberg, Lars Samuelson (Lund) Research Sponsors:

Power Factor (S2σ)

• Electrical conductivity:

* m dE

E

∝ ∫ = σ σ

Conduction band EF

E

∫

Differential conductivity

Valence E

Effective mass

• Seebeck coefficient:

band k

Seebeck coefficient: Th Tc

V S

E

∂ Δ σ

• -
• ΔV

E T V S

E

∂ ∂ ∝ Δ = σ

E E

• D(E)f(E)

D(E)f(E)

E

E D S ⎟ ⎞ ⎜ ⎛ ∂ ∂ ) ( σ

F

E E

E E S ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∝ ∂ ∝ ) (

Th lli (Tl) d i i PbT di t t th d it f t t i i S2 d ZT

• Thallium (Tl) doping in PbTe distorts the density of states, increasing S2σ and ZT.

Diffuse surface limit for random surface roughness: l d 22

• Monte Carlo phonon

transport simulation.

δ1 d θ δ1 d θ

l d = 22 nm

transport simulation.

δ2 d δ2 θ δ2 d δ2 θ

Phonon backscattering at a sawtooth surface: l < d

• κ can be decreased by the sawtooth

roughness, but is still considerably higher than κα.

Johansson et al. Nature Nanotech 4, 50 (2009)

• κl << κα has been demonstrated.
• The question is how much κl can be lowered without

considerable reduction of the charge mobility.

• We use nanowires as model systems to investigate this

question because of the simple and well-characterized structure and interface.

Seebeck Coefficient and Fermi Level (EF)

• Hall measurements cannot be

h h e e

S S S σ σ +

Hall measurements cannot be used to obtain carrier concentration & mobility in NWs.

h e h h e e

S σ σ + =

• Two-band model:
• Single conduction band model:

⎟ ⎟ ⎟ ⎞ ⎜ ⎜ ⎜ ⎛ − + − =

+ e e r e B e

e

F r k S ζ ζ 3 ) ( ) 2 5 (

2 3

Single conduction band model: ⎟ ⎟ ⎠ ⎜ ⎜ ⎝ +

+ e r e

e

F r e ζ ) ( ) 2 3 (

2 1

EF ξ T kB

F e =

ξ

• Relaxation time:

e

r

E τ τ =

Relaxation time: re = -0.5 for phonon and boundary scattering

Structural &Thermal Characterization of MnSi1.75 NWs

• Mn Si

nanoribbon (NR)

• Mn39Si68 nanoribbon (NR)
• c ≈ 17 nm
• Growth direction perpendicular to {121} planes,

p p { } p ,

• r 63o from the c axis

Two-Dimensional Phonons in MnSi1.75 NWs?

• If the c axis is along a radial direction, 2c <λc = 2d /n < 2d:
• nly one or several phonon wavevectors allowed in the c direction.
• d l ti

i d d th i λ h h tt i modulation in d and thus in λc can enhance phonon scattering. κ is reduced.

50 nm

2 nm

• NW growth direction found to be <0001>

2 nm

Thermoelectric Energy Conversion

Waste Heat Recovery Waste Heat Recovery Th l t i G t n p Thermoelectric Generator

Heat Source

n p

• +

I I I I

Heat Sink

S σ

2

Seebeck coefficient Electrical conductivity

Figure of Merit (ZT)

T S ZT κ σ ≡

Thermal conductivity