Thermoelectric Energy Harvesting

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James Watt. William Thomson. (Lord Kelvin). William John. Macquorn Rankine. Rev Robert Stirling. John Logie Baird. Rev John Kerr. Adam Smith. Joseph Black ...
Thermoelectric Energy Harvesting Douglas J. Paul School of Engineering University of Glasgow, U.K.

D.J. Paul School of Engineering

The University of Glasgow Established in 1451 6 Nobel Laureates 16,500 undergraduates, 5,000 graduates and 5,000 adult students £130M research income pa 400 years in High Street

Moved to Gilmorehill in 1870 Neo-gothic buildings by Gilbert Scott

Famous Glasgow Scholars

William Thomson (Lord Kelvin)

Rev John Kerr

James Watt

Joseph Black

William John Macquorn Rankine

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Rev Robert Stirling

Adam Smith

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750m2 cleanroom - pseudo-industrial operation 18 technicians + 5 research technologists (PhD level process engineers)

E-beam lithography

Large number of process modules Processes include: Si/SiGe/Ge, III-V, II-VI, piezoelectric MMICs, optoelectronics, metamaterials, MEMS Commercial access through KNT

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James Watt Nanofabrication Centre @Glasgow In School of Engineering £53M active research grant portfolio (£14M pa, industry ~£1M) 2nd highest cited E&EE Department in UK after Cambridge World Bests:

Smallest electron-beam lithography pattern – 3 nm Best layer-to-layer alignment accuracy (0.42 nm rms) Smallest diamond transistor (50 nm gate length) Lowest loss silicon optical waveguide (< 0.9 dB/cm) Fastest mode locked laser (2.1 THz) Highest Q silicon nanowire cavity (Q = 177,000)

JWNC@Glasgow Nanofabrication Probing molecules

Measured linewidth vs dose 9 8

HSQ

7 6 5 4 3 16000

Sub-5nm e-beam lithography 20000

24000

28000

Dose (µC cm-2 )

Penrose tile: 0.46 nm rms alignment

22 nm T-gate HEMTs

Photonic bandgaps N Tapered outside Cavity, NTO

Si nanowire cavity Q = 177,000 Tapered within Cavity, NTI

Cavity length, c

SiO2 1 µm

Thermoelectrics History: Seebeck effect 1822 heat –> electric current Peltier (1834): current –> cooling Physics: Thomson (Lord Kelvin) 1850s Ioffe: physics (1950s), first devices 1950s - 1960s, commercial modules 1960s Present applications: Peltier coolers (telecoms lasers, rf / mm-wave electronics, beer! etc...) Thermoelectric generators – some industrial energy harvesting As renewable energy interest increases, renewed interest in thermoelectrics D.J. Paul School of Engineering

Why Use Thermoelectrics? No moving parts –> no maintenance Peltier Coolers: fast feedback control mechanisms –> ΔT < 0.1 ˚C Scalable to the nanoscale –> physics still works (some enhancements) but power ∝ area Most losses result in heat Most heat sources are “static” Waste heat from many systems could be harvested home, industry, background D.J. Paul School of Engineering

Background Physics Fourier thermal transport

Q = −κA∇T

Joule heating

Q = I2 R

Q = heat (power i.e energy / time)

R = resistance

EF = chemical potential

I = current (J = I/A)

V = voltage

q = electron charge

κ = thermal conductivity σ = electrical conductivity α = Seebeck coefficient

g(E) = density of states

f(E) = Fermi function

kB = Boltzmann’s constant

µ(E) = mobility

A = area

D.J. Paul School of Engineering

The Peltier Effect heat transfer, Q Material 1 Hot reservoir Th

I => Π M

ate

2 l ia

er t a

ria

l2

Cold reservoir Tc

M I

Peltier coefficient,

Π=

Q I

units: W/A = V

Peltier coefficient is the energy carried by each electron per unit charge & time D.J. Paul School of Engineering

The Peltier Coefficient Full derivation uses relaxation time approximation & Boltzmann equation

� 1

Π = − q (E − σ=



σ(E)dE = q



σ(E) EF ) σ dE

g(E)µ(E)f (E)[1 − f (E)]dE

This derivation works well for high temperatures (> 100 K)

At low temperatures phonon drag effects must be added see H. Fritzsche, Solid State Comm. 9, 1813 (1971) D.J. Paul School of Engineering

The Seebeck Effect Material 1 Hot reservoir Th

α => I M

ate

ria

e

l a i r

at

l2

2

Cold reservoir Tc

M V

Open circuit voltage, V = α (Th – Tc) = α ΔT

Seebeck coefficient,

Seebeck coefficient =

D.J. Paul School of Engineering

α=

dV dT

units: V/K

1 Q x entropy ( ) transported with charge carrier q T

Measuring Seebeck Coefficient

heater Iσ



Cu block

sample

Iheater

Physically heat one side of sample

thermocouple Th

Cold sink at the other side of sample

ΔT thermocouple Tc

Thermocouples top and bottom to measure ΔT

Cold reservoir Cu block

D.J. Paul School of Engineering

4 terminal electrical measurements

The Seebeck Coefficient Full derivation uses relaxation time approximation, Boltzmann equation

α=

− kqB σ=

� �

(E −

σ(E) EF ) σ dE



σ(E)dE = q g(E)µ(E)f (E)[1 − f (E)]dE

For electrons in the conduction band, Ec of a semiconductor

α=

− kqB



Ec −EF kB T

+

R∞ 0

(E−Ec ) kB T σ(E)dE R∞ σ(E)dE 0



for

E > Ec

see H. Fritzsche, Solid State Comm. 9, 1813 (1971)

D.J. Paul School of Engineering

The Seebeck Coefficient for Metals df f (1 − f ) = −kB T dE

Expand

g(E)µ(E) in Taylor’s series at E = EF 2

α = − π3

kB q kB T



d ln(µg) dE



EF

(Mott’s formula) Mott and Jones, 1958

i.e. Seebeck coefficient depends on the asymmetry of the current contributions above and below EF Using the energy-independent scattering approximation:

α=

D.J. Paul School of Engineering

� � 8π 2 k2 π − 3eh2B m∗ T 3n 3 2

n=carrier density M. Cutler et al., Phys. Rev. 133, A1143 (1964)

Semiconductor Example: SiGe Alloys Seebeck coefficient, α (µV K–1)

Mott criteria ~ 2 x 1018 cm–3

Degenerately doped p-Si0.7Ge0.3

α decreases for higher n

For SiGe, α increases with T

α= J.P. Dismukes et al., J. Appl. Phys. 35, 2899 (1964) D.J. Paul School of Engineering

� π �3 8π 2 k2 ∗ B 3eh2 m T 3n 2

The Thomson Effect Hot reservoir Th

dx

Cold reservoir Tc

Q I

T dT α is temperature dependent

dQ dx

=

dT βI dx

Thomson coefficient, β

D.J. Paul School of Engineering

x

dQ = βIdT

units: V/K

The Kelvin Relationships Derived using irreversible thermodynamics

Π = αT

β=

dα T dT

These relationships hold for all materials

Seebeck, α is easy to measure experimentally

Therefore measure α to obtain Π and β

D.J. Paul School of Engineering

Peltier Effect, Heat Flux and Temperature If a current of I flows through a thermoelectric material between hot and cold reservoirs: Heat flux per unit area =

Area, A hot side

( = Peltier + Fourier )

Q A

current, I Heat (energy/t) = Q but

cold side

D.J. Paul School of Engineering

= ΠJ − κ∇T

Π = αT

and

J=

Q = αIT − κA∇T

I A

Semiconductors and Thermoelectrics Seebeck effect: electricity generation

Peltier effect: electrical cooling

heat source Th

heat source Th

metal

metal

p

n

n

metal metal heat sink Tc I Load

D.J. Paul School of Engineering

p

metal metal heat sink Tc I

+



Battery

Heat transfer Q

Conversion Efficiency power supplied to load η= heat absorbed at hot junction heat source Th Power to load (Joule heating) = I2RL

metal n Rn

p Heat absorbed at hot junction = Peltier heat + heat withdrawn from hot junction

Rp

metal metal heat sink Tc I Load, RL R = Rn + Rp D.J. Paul School of Engineering

Peltier heat

I=

= ΠI = αITh

α(Th −Tc ) R+RL

(Ohms Law)

Heat withdrawn from hot junction

= κA (Th − Tc ) − 12 I2 R

NB half Joule heat returned to hot junction

heat source Th

Conversion Efficiency

power supplied to load power supplied to load η= = heat absorbed at hot junction Peltier + heat withdrawn

I 2 RL 2R αITh +κA(Th −Tc )− 1 I 2

η= For maximum value

ηmax = =

dη R d( RL )

Carnot

D.J. Paul School of Engineering

x

heat sink RL

=0

√ Th −Tc √ 1+ZT−1 Tc Th 1+ZT+ T h

p

n

Tc I

T = 12 (Th + Tc )

where

Z=

Joule losses and irreversible processes

α2 RκA

=

α2 σ κ

Thermoelectric Power Generating Efficiency

η=

heat source Th metal

Temperature difference, !T (˚C)

p

n

40

0

35

I

Figure of merit α2 σ ZT = κ T

30

Efficiency (%)

metal metal heat sink Tc

Load

√ ∆T √ 1+ZT −1 Tc Th 1+ZT + T

25

50

100

150

200

250

300

450

500

550

600

ZT=0.5 ZT=1 ZT=2 ZT=3 ZT=4 ZT=5 Carnot

20 15 10 5 0 300

350

400

Temperature (K) D.J. Paul School of Engineering

h

Heat Transfer in Thermoelectric Element But n-type and p-type materials are seldom identical heat source

area, An

Qn = −αn IT −κn An dT dx

Th

Ln

p

heat sink

Tc

n

area, Ap

Lp

Z for a couple depends on relative dimensions Z is maximum for D.J. Paul School of Engineering

Ln Ap Lp Am

=



σn κn σp κp

Qp = αp IT −κp Ap dT dx

Maximising ZT for an Unbalanced Couple heat source Th area, Ap area, An

n

Ln

p

heat sink



Ln Ap Lp Am

=

ZT =

(αp −αn )2 T hq κ i √ κn p + σp σn

σn κn σp κp

Lp

Tc

We need good ZT for both n- and p-type semiconductors

D.J. Paul School of Engineering

Maximum Temperature Drop As the system has thermal conductivity κ a maximum ΔT which can be sustained across a module is limited due to heat transport

∆Tmax = 12 ZT2c

heat source Th metal

The efficiency cannot be increased indefinitely by increasing Th The thermal conductivity also limits maximum ΔT in Peltier coolers Higher ΔTmax requires better Z materials

D.J. Paul School of Engineering

n

p

metal metal heat sink Tc

Zfdd\ekXip

Thermodynamic Efficiency: The Competition 80

Carnot efficiency Thermodynamic limit ZT=infinity

70

Efficiency (%)

60

ZT=20, unlikely Coal/Rankine

50 40

Solar/Stirling Nuclear/Rankine Solar/Rankine

30

Solar/Brayton Nuclear/Brayton+Rankine ZT=4, ambitious ZT=2, plausible eventually

20 10 0 300

ZT=0.7, available today

Cement/Org. Rankine Geothermal/Kalina Geothermal/Org. Rankine 400

500

600

700 800 900 1,000 Heat source temperature (K)

1,100

1,200

1,300

ZT of 4 start to become seriously competitive

=`^li\)s8jj\jj`e^k_\idf\c\Zki`Zj% 30% of car’s electrical requirement 5% reduction in fuel consumption through removing alternator D.J. Paul School of Engineering

NASA Radioisotope Thermoelectric Generator Radioisotope heater –> thermoelectric generator –> electricity Voyager – Pu238 Half-life = 87 years Pu238 fuel pellet

470 W @ 30 V on launch, after 33 years power = D.J. Paul School of Engineering

470 ×

− 33 2 87 = 361 W

Energy Conversion: Electricity: The Rankine Cycle Temperature needs to be reduced by 80 ˚C for carbon capture

Cooling towers –> throw heat away –> added losses Energy stored in fuel D.J. Paul School of Engineering

heat

kinetic energy

electric energy

U.K. Electricity Generation 2007

Coal 36%

Other 1% Nuclear 16% Oil 1%

Renewables 3%

Nuclear Other Coal Renewables Gas Oil

80% generate CO2 Gas 43%

97% use the Rankine Cycle http://www.berr.gov.uk/energy/statistics/

D.J. Paul School of Engineering

Main Strategies for Optimising ZT Reducing thermal conductivity faster than electrical conductivity: e.g. skutterudite structure: filling voids with heavy atoms Low-dimensional structures: 2

π Increase α through enhanced DOS ( α = − 3

kB q kB T

Make α and σ almost independent Reduce



d ln(µg) dE



EF )

κ through numerous interfaces to increase phonon scattering

Energy filtering:

α = − kqB

enhance



Ec −EF kB T

+

R∞ 0

(E−Ec ) kB T σ(E)dE R∞ σ(E)dE 0



Y.I. Ravich et al., Phys. Stat. Sol. (b) 43, 453 (1971)

Carrier Pocket Engineering – strain & band structure engineering D.J. Paul School of Engineering

Length Scales: Mean Free Paths 3D electron mean free path

� = vF τ m = �=

3D phonon mean free path

1 µm∗ � 2 3 m∗ (3π n) q

1 �µ 2 3 (3π n) q

Λph =

3κph Cv �vt �ρ

Cv = specific heat capacity = average phonon velocity ρ = density of phonons A structure may be 2D or 3D for electrons but 1 D for phonons (or vice versa!) D.J. Paul School of Engineering

2 0 100

Complex Crystal 200 300 400 500 Structures: Reducing Temperature °C

 l (W m–1 K–1 )

SiGe

CeFe3CoSb12 2

 l (W m–1 K–1 )

− CoSb3 filling voids Skutterudite structure: 8 − Doped CoSb3 with heavy − Ruatoms 0.5Pd0.5Sb3

3

6

Hf0.75Zr0.25NiSn

1

− FeSb2Te − CeFe3CoSb12

4

Co Zn Yb

2 0 100

Bi2Te3

κph

Sb REVIE

200 300 400 Temperature °C

500

PbTe TAGS

Ag9TlTe5

La3–xTe4 Yb14MnSb11

0 0

Zn4Sb3 200

400

Ba8Ga16Ge30 600 800

Temperature °C

p-Yb14MnSb11 – ZT ~ 1 @ 900 ˚C

mal conductivity. a, Extremely low thermal conductivities are found inSnyder the recently materia G.J. et al., Nat.identified Mat. 7, 105complex (2008) 8Ga16Ge30, ref. 79; and Zn4Sb3, ref. 80; Ag9TlTe5, ref. 40; and La3–xTe4, Caltech unpublished data) compared wit D.J. Paul ublished data; PbTe, crystal ref. 81; TAGS, ref. 69; SiGe, ref. 82 or the half-Heusler alloy Hf ref.in the 83). b, Th 0.75Zr0.25NiSn, Figure 2 Complex structures that yield low lattice thermal conductivity. a, Extremely low thermal conductivities are found recently School of Engineering cal conductivity is asoptimized by 45; doping (doped CoSb3).16The thermal conductivity is further lowered by alloying systems (such Yb14MnSb11, ref. CeFe3CoSb Ge30, ref. 79; and Zn 12, ref. 34; Ba8Ga 4Sb3, ref. 80; Ag9TlTe5, ref. 40; and La3–xTe4, Caltech unpub state-of-the-art thermoelectric data;isPbTe, ref. 81; TAGS, 69; SiGe, ref. 82 or the alloy H 2Te3, Caltech unpublished spacesmost (CeFe CoSb ) (ref. 34). c,alloys The(Biskutterudite structure composed of ref. tilted octahedra of half-Heusler CoSb creatin

Electron Crystal – Phonon Glass Materials Principle: trying to copy “High Tc” superconductor structures

REVIEW ARTICLE Heavy ion / atom layers for phonon scattering

The low, glas phase, a distinct accomp dynami conduct and neu the Zn CaxYb1-xZn2Sb2 NaxCoO2 conduct Only small improvements to ZT observed from hi Figure 3 Substructure approach used to separate the electron-crystal and G.J. Snyder et al., Nat. Mat. 7, 105 (2008) distortio phonon-glass attributes of a thermoelectric. a, NaxCoO2 and b, CaxYb1–xZn2Sb2 cell, Zn structures both contain ordered layers (polyhedra) separated by disordered cation D.J. Paul Sb fram monolayers, creating electron-crystal phonon-glass structures. School of Engineering One High mobility electron layers for high electrical conductivity

When n $ 1 and m $ 18, the composition high ZT values (!2) at elevated temperatures. is AgPb18SbTe20. These samples also possess The AgnPbmSbnTem#2n compounds possymsess an average NaCl structure (Fm3m AgPb – Nanoparticle Scattering? 18SbTe20 metry); the metals Ag, Pb, and Bi are disorFig. 4. (A) TEM image of dered in the structure on the Na sites, whereas the chalcogen atoms occupy the Cl sites (Fig. shown in the enclosed are 1A). The formula is charge-balanced because surrounding structure, whic the average charge on the metal ions is 2# with a unit cell parameter and on the chalcogen ions it is 2". The an extended region of a Ag AgnPbmBinTem#2n formulation can generate nm. In essence, the observ a large number of compositions by “dialing” Fig. 4. (A) TEM image of a AgPb SbTe sample showing a nano-sized region (a “nanodot” shown the enclosed area) of the crystal structure that is Ag-Sb–rich in the artificial PbSe/PbTe s m and n,in allowing considerable potential forin composition. The surrounding structure, which is epitaxially related to this feature, is Ag-Sb–poor in composition Fig. with a unit cell parameter of 6.44find Å, closethat to that of PbTe. (B) Compositional modulations over property control. We several memat least along the stacking an extended region of a AgPb SbTe specimen. The spacing between the bands is "20 to 30 and nm. In essence, the observed compositional modulation is conceptually akin to the one found bers inofthe this family are capable of achieving artificial PbSe/PbTe superlattices (15). In the latter, the compositional modulation exists (A) at least along the stacking direction. higher power factors and high ZT values at mop similar to those found in for the high-efficiency Monte Carlo Coulomb calculations in the th high materials, temperatures suitable tho αmaterials, = –335 µVK–1similar to in class of materials are in PbSe/PbTe MBE– grown thin films. The Ag Pb Sb Te tem Sb Te materials are derived by progress, toapplicaexplore the role of the Ag/Sb Ag Pb electrical heat–to– energy conversion σ = 30,000 S/m ions for isoelectronic substitution of Pb distribution and its general dispersing tendenPbSe/PbTe MBE– grown beck and Sb (or Bi) in the lattice. This Ag cies in the cubic lattice (21). tions. A series of AgPbmSbTe2#m (n $ 1) –1 –1 = 1.1 Wm K κAg materials may generates local distortions, both structural The Ag Pb Sb Te tudi Pb Sb Te materi samples were in which the lattice find potential applications in thermoelectric and electronic, that prepared are critical in determining n m n m'2n charge transport at 700 K atur . For expower generation from heat sources: for exthe properties of Ag Pb Sb Te or AgPb SbTe : parameters vary smoothly withample, m. vehicle Theexhaust, x-ray ample, at issue is how the Ag and Sb ions coal-burning installaisoelectronic substitution (%) and ther(usin are distributed in the structure, i.e., homogetions, electric power utilities, etc. With an mal conductivity pattern and unit ' 3' silve K. The data diffraction were neously or inhomogeneously. Arguably, one cell average parameter ZT of 2, a hot source of 900 K, and a and Sb (or Bi) in Ag (19). (C) Thermight expect an inhomogeneous distribution temperature difference across 500 K, a convariation for several members of the series cryo ZT, as a function given the different formal charges of '1/'3 version efficiency of more than 18% may be versus '2 arising (22). Additional amplification in ZT prov generates local distortion are shown (Fig.from1,Coulombic B andinteracC). achieved tions. A completely homogeneous Ag and should be possible with further exploration of K.F. Hsu et al., Science 303, 818 (2004) (thin in the Fm3m lattice would Sb dispersion e m ! 18 samples Ingots doping agents and n/m values. We have alwith the composition AgPb SbTe and electronic, that are crit 10 substantially 12 require the complete separation of the Ag ical conductivity; ready observed lower thermal pera and Sb pair over long distances, which 850 S/cm atFig. room conductivities (as much as 40 to 50% lower) 3. Variable-temperature charge (17) show an electrical conductivity of %520 transport sure members that could create charge imbalances in the vicinity er of #135 $V/KD.J. in other Ag Pb Sb Te Pb the properties of Ag Paul n mS S/cm and thermopower (i.e., coefficould further enhance ZT values. ofthermal these atoms. Therefore, barring any com- Seebeck value indicates an SbTe : and transport data for AgPb ther 18 20 Engineering pensationof effects from the Te sublattice, elecn the temperatureSchool ample, at issue is how the cient) of "154 at that room temperature, re- and thertroneutrality reasons&V/K alone require Ag smoothly, as exmadA (A) Electrical conductivity (%) and Sb ions be generally found near one onductor, whereas References and Notes2 . electrical conductivity, sulting in ((5 a topower factor of 12.3 &W/cm!K sam 1. ZT ! (%S /&)T, where % is the another 6 Å). Given the relatively dily in nearly a are distributed in the struc 10

20

12

n

n

m

n

m'2n

m

n

m'2n

2'

3'

'

n

18

n

20

m

n

'

m'2n

m

n

m'2n

3'

'

3'

'

3'

n

'

3'

2

m

n

m'2n

Downloaded from www.sciencemag.org on September 2, 2009

18

Low Dimensional Structures: 2D Superlattices Use of transport along superlattice quantum wells Higher α from the higher density of states Higher electron mobility in quantum well –> higher σ Lower

heat source metal n metal heat sink

Th

p metal Tc

κph through additional phonon scattering from heterointerfaces

Disadvantage: higher κel with higher σ (but layered structure can reduce this effect) Overall Z and ZT should increase

Figure of merit α2 σ ZT = κ T

L.D. Hicks and M.S. Dresselhaus, Phys. Rev. B 47, 12737 (1993) D.J. Paul School of Engineering

2D Bi2Te3 Superlattices EF2D = EF3D −

E Ec

�2 π 2 2 2m∗ za

Both doping and quantum well width, a can now be used to engineer ZT

0

a

z

mx = 0.021 m0 my = 0.081 m0 mz = 0.32 m0

κph = 1.5 Wm–1K–1 µa0 = 0.12 m2V–1s–1 ZT for 3D Bi2Te3

L.D. Hicks and M.S. Dresselhaus, Phys. Rev. B 47, 12737 (1993) D.J. Paul School of Engineering

p-Bi2Te3 / Sb2Te3 Superlattices κph = 1.05 Wm–1K–1 Phonon mean free path

Lattice thermal conductivity

Bi2Te3

3/3 nm, 1/5 nm, 2/4 nm Bi2Te3 / Sb2Te3 periods almost identical

κph

R. Venkatasubramanium Phys. Rev. B 61, 3091 (2000) D.J. Paul School of Engineering

+9, + "! 0+)1* /2 !"(= ! !$ ! &'< :* /D.+69 +9 *) &/9,1&.606.K /2 !="G 'H &'"! P"!" B51- .5* &4 !"#$#$%&'#()*$+,-'-(./#$%./0$12*..*$+ 1./3(.3/-1 .5*4'+) &/9,1&.606.K 6- !#"% 'H &'"! P"!" B56B5* 4*-1).- /D.+69*, :6.5 .5* !$?@A#$?@ 86(B*=ACD(B*= -1;*4)+..6&*- 'F+S6- (X /2 D1)7 +))/K-(J V+9, '1&5 56E5*4 .5 2 3+9, 5/)* M&5+4E* 2 3 &+446*4-N !("# 'H &'"! P"! /D-*40*, 69 J$F?@F;*46/, ;F.K 69,6&+.* .5+. :* &+9 L9*F.19* .5* ;5/9/9 -1;*4)+..6&*- 69 4*2" (I< +9, 56E5*4 .5+9 .5+. , +9+)K-6- /2 ,+.+ 69 >6E-" (D< &" H* D*)6*0* .5+. .5*-* 3 9*+4F6,*+) -1;*4)+..6&* 69 .5* 86(B*=A Bulk Bi 1.0 2Te3 ZT ~69.*42+&*p-TeAgGeSb (ref.10) :5*4* .5* &/';/-6.6/9+) '/,6L&+.6/9- /2 *6.5* CeFe3.5Co0.5Sb12 (ref.10) Superlattice ZT = 2.6*9&)/-*, DK .5* B*QB 2.5 +&&/';)6-5*, :6.569 4*E6/9Bi2-xSbxTe3 (ref.11) D/9," B51-< 6. -5/1), D* ;/--6D)* ./ /D.+69 '644/4 CsBi4Te6 (ref.11) 69.*42+&*-< )*+,69E ./ ;/.*9.6+) 4*a*&.6/9 *22*&.- 2/4 2 Bi-Sb (ref.5) (IN" W9 &/9.4+-.< 69 .5* 86(B*=A86(B*#C*="# -K-.*'< : Bi2Te3/Sb2Te3 SL (this work) B* +4* *S;*&.*, ./ D* Phonons ;4*-*9. +. .5* 0+9 ,*4 H+ Electrons 1.5 +9.6&6;+.* '1&5 1969.*9,*, &/';/-6.6/9+) '6S 2V–1s–1 µ=383 cm.5*4'+) )+..6&* &/9,1&.606.K 6- )67*)K ./ D* '/4* .K 1 :+-nm 214.5*4 *06,*9. nm /D-*40+.6/9- / Λph =693 /14 = 11.4 � B56-6E96L&+9. 6';4/0*'*9. 69 *)*&.4/96& '/D6)6.6*- 6 0.5 ~ 0.5 ./ 9F.K;* 86 k86 ~ 7.6 kph Λ B*("%= C*$"!G -1;*4)+..6&*M&/';+4*, el(� 69 &/9.4+-. ./ + '+47*, *95+9&*'*9. /2 &+446*4 '/ 0 0 200 400 600 800 1,000 69 ;F.K;* 86(B*=ACDblocking => Phonon (B*= -1;*4)+..6&*- 4*)+.60* ./ ;F (! +))/K" B5*4*2/4*< *95+9&*'*9. /2 !"6 ./ !"3J 6 Temperature (K) )+..6&*- M24/' !! 2/4 D1)7 9F.K;* +))/KN +;;*+4- ./ 1 23/01 $4'5$" 678!"92:;8!"9 10 µm)

2 2 Pmax = 12 FN A ∆T α σ L

N.B. The thermal conductivity must also be considered for ΔTmax!

D.J. Paul School of Engineering

Generate Renewable Energy Efficiently using Nanofabricated Silicon (GREEN Silicon) D.J. Paul, J.M.R. Weaver, P. Dobson & J. Watling University of Glasgow, U.K. G. Isella, D. Chrastina & H. von Känel L-NESS, Politecnico de Milano, Como, Italy J. Stangl, T. Fromherz & G. Bauer University of Linz, Austria E. Müller ETH Zürich, Switzerland ETH Zürich - Info für Studieninteressierte

D.J. Paul – Co-ordinator GREEN Si EC FP7 ICT FET “2ZeroPowerICT” No.: 257750

GREEN Silicon Approach 100 nm Al gate

Al gate

SiO2 substrate

Low dimension technology Al gate

source

superlattice

quantum dot

nanowires

Module

Generator ETH Zürich - Info für Studieninteressierte

D.J. Paul – Co-ordinator GREEN Si EC FP7 ICT FET “2ZeroPowerICT” No.: 257750

drain

Al gate

Al gate

Summary Waste heat is everywhere –> enormous number of applications

Low dimensional structures are yet to demonstrate the predicted increases in α due to DOS Reducing κph faster than σ has been the most successful approach to improving ZT to date Heterointerface scattering of phonons has been successful in reducing κ

TE materials and generators are not optimised –> there is plenty of room for innovation D.J. Paul School of Engineering

Further Reading D.M. Rowe (Ed.), “Thermoelectrics Handbook: Macro to Nano” CRC Taylor and Francis (2006) ISBN 0-8494-2264-2

G.S. Nolas, J. Sharp and H.J. Goldsmid “Thermoelectrics: Basic Principles and New Materials Development (2001) ISBN 3-540-41245-X

M.S. Dresselhaus et al. “New directions for low-dimensional thermoelectric materials” Adv. Mat. 19, 1043 (2007)

D.J. Paul School of Engineering