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
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JWNC@Glasgow Nanofabrication Probing molecules
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HSQ
7 6 5 4 3 16000
Sub-5nm e-beam lithography 20000
24000
28000
Dose (µC cm-2 )
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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
Vσ
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