introduction to...
TRANSCRIPT
![Page 1: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/1.jpg)
Introduction to thermoelectricity!
Ecole thématique!«Thermoélectricité»!1-6 juin 2014, Annecy!
!B. Lenoir !
Institut Jean Lamour, Ecole des Mines, [email protected]!
!
![Page 2: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/2.jpg)
• Electrical and thermal conduction. Thermoelectric effects (description and qualitative interpretation)!• Dimensionneless figure of merit ZT. n, p thermocouple and performance of
thermoelectric devices!• Selection criteria!
• From conventional materials to new directions!• Thermoelectric converters: technological aspects, avantages/drawbacks, applications. !
Outline!
Suggestion of books:!- Recent Trends in Thermoelectric Materials Research, Semiconductors and Semimetals, Academic Press, Ed. T. Tritt, Vol. 69 -71 (2001)!- Thermoelectrics Handbook « Macro to Nano », Ed. M. Rowe, CRC Press (2006)!- Introduction to thermoelectricity, H.J. Goldsmid, Springer (2010)!- Thermoelectrics Handbook « Thermoelectrics and its energy harvesting », Ed. M. Rowe, CRC Press (2012)!
![Page 3: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/3.jpg)
Electrical and thermal conduction
E [V/m]: electric field!V [V]: electric potential!j [A/m2]: current density!ρ [Ω.m]: electrical resistivity!σ [Ω-1.m-1]: electrical conductivity!
ρ =1
σ≈1
neµ
Local Ohm’s law!
§ Electrical conduction (Ohm1827)!
j = j
x
i
E = −
∇V = −
∂V
∂x
i
j =σ
E =
E
ρ
n [cm-3]: charge carrier!e [C]: elementary charge!µ [m2/V.s]: carrier mobility !
T = cst ( T = 0)!
Assumption : Homogeneous and isotropic material!
Eric Alleno
Georg Simon Ohm!(1789-1854)!
![Page 4: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/4.jpg)
Bism
uth!
Arse
nic!
Ag, C
u, A
u, N
a!
10-8! 10-6! 10-4! 10-2! 100! 102! 104! 106! 108! 1010! 1012! 1014! 1016!
Pur g
erm
aniu
m !
Hig
hly
dope
d ge
rman
ium!
Pur s
iliciu
m !
Gla
ss!
Teflo
n!
TiO
2!
ρ (Ω.m)
Insulators (or large gap SC)!!
Semiconductors (SC)!Semi-metals!Metals!
EF: chemical potential or Fermi energy!
E!
EG > 2 eV!EF!
EF!EF!
EF!
EG: gap!
EG ~ 0-2 eV!
Electrical resistivity: order of magnitude at T = 300 K!
Band structure!
p-type SC!
n-type SC!
Dia
man
t!
AgBr!
BC!
BV! BV: valence band!BC: conduction band!
intrinsic SC!
![Page 5: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/5.jpg)
q [J/s.m2]: heat flux !T [K]: temperature!λ [W/mK]: thermal conductivity
€
q = −λ
∇ T
€
q = q e + q r ⇒ λ = λe +λr
Wiedemann-Franz law!λe ≈LTρ
(L ≈ 2,5.10−8V 2K −2 )
€
λr ≈1
3cl v
Semiconductors and semimetals!
Fourier’s law!
§ Thermal conduction (Fourier 1822)!
Heat transport mechanisms:!
Metals è transport by charge carriers (electrons) !
Insulators è transport by « lattice vibrations » (phonons)!
c [J/K.m3]: volumetric specific heat !l [m]: mean free path!v [m/s]: sound velocity
(Kinetic theory of gases)!
j = 0!∇T =
∂T
∂x
i
q = qx
i
Joseph Fourier!(1768-1830)!
Sami Merabia Jesus Montana Stéphane Pailhes
![Page 6: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/6.jpg)
0.01 0.1 1 10 100 1000
Conductivité thermique (W/mK)
Pur metals!
Pu!(5.2)!
Al!(237)!
Ag!(436)!
Metallic alloys!
Fibers!Foams!
Insulators!
Liquids!
Hg!(8.3)!
H20!(0.61)!Oils!
H2!(0.18)!
Gas!
O2!(0.03)!
Semiconductors (small and large gap)!
Ge!(60)!
Si!(150)!
Diamant!(2000)!
Bi2Te3!(2.0)!
Pt!(72)!
Thermal conductivity: order of magnitude at T = 300 K!
Crystalline or amorphous materials!
Thermal conductivity (W/mK)!
Amorphous!
Glass!(1.2)!
GeTe4!(0.1)!
S!(0.27)!
![Page 7: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/7.jpg)
Thermelectric effects
T+dT! T!
dV
dV = −α dTE =α
∇T
V [V]: voltage!E [V/m]: electric field!α [V/K]: Seebeck coefficient! or thermopower!
§ Seebeck effect (1824)!
Experimentally no direct access to α !!!!!T+dT! T!
dV
dV = (α −α fil ) dTT!
α ≥ 0 ou < 0!intrinsic transport property!
If we replace the voltmeter by an ammeter, one observed an electrical current. A temperature gradient causes not only a heat flux but also an electrical current !!!
Exercice !Show that :!
Voltmeter !
j = 0!
Eric Alleno
Thomas Yohann Seebeck!(1770-1831)!
![Page 8: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/8.jpg)
Thermopower: order of magnitude at 300 K!
Ag, Cu, Au!
IαI (V/K)
Constantan (Cu – Ni)!
10-7!
10-6!
10-5!
10-4!
10-3!
10-2!
10-1!
Pur Ge and Si!
Bi2Te3!
Semiconductors!
Semimetals!
Metals!
Bismuth!
5!
5!
5!
5!
5!
5!
Nickel!
Insulators!
n! IαI
![Page 9: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/9.jpg)
π [V]: Peltier coefficient q = π
j
τ [V/K]: Thomson coefficient!dQ = −τ I dT
I! T+dT!T!
dQ
§ Peltier effect (1834)!
§ Thomson effect (1854 -1856)!
€
Q = (π a −πb )I = π ab Ia b
I!
a b I!
πa> π
b> 0
€
π = αT
τ = Tdα
dT
Kelvin’s relations:!
π ≥ 0 ou < 0, intrinsic property!
τ ≥ 0 ou < 0!
A potentiel gradient creates an electrical current but also a heat flux !!
T = cst ( T = 0)!j = j
x
i
q = qx
i
Q [W]: thermal power!I [A]: electrical current!
Consequence:!Jean Charles Peltier!
(1785-1845)!
William Thomson (Lord Kelvin)!(1824-1907)!
![Page 10: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/10.jpg)
Interpretation of thermoelectric effets!
€
E = ρ
j +α ∇ T
q = π j − λ ∇ T
Si
€
∇ T =
0
€
E = ρ
j
q = π j
Ohm law Peltier effect Si
€
j = 0
€
E = α
∇ T
q = −λ
∇ T
Seebeck effect Fourier law
E = ρ
j +α
∇T
q = π
j −λ
∇T
Anisotropic materials
: tensors of rank 2 x
Thermodynamic approach
€
π = αT
τ = Tdα
dT
with the Kelvin’s relations:
Thermoelectric effects: coupling between thermal and electrical phenomena (out of equilibrium phenomena)è irreversible thermodynamic!
(reciprocity Onsager relations)!
(energy conservation)!
Christophe Goupil
Fundamental relations of thermoelectricity!Isotropic materials
Microscopic approach !Connect the electronic transport coefficients (σ, α et λe) to the D.O.S., the distribution of Fermi-Dirac, the energy and the relaxation time (Boltzmann formalism). Starting point: j et q!
!!
Laurent Chaput - Joseph Heremans
![Page 11: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/11.jpg)
-e!
Electron diffusion: !
Hot cold !
+!+!+!
+!Cold hot !
Stationary state:
€
E
j =jc→ f +
j f→c =
0
E =α
∇T
€
( f = (−e)
E )
€
∇ T
Metal (free electron gas)!
Mechanism responsible for PTE: diffusion, lattice PTE or «phonon-drag », magnon-drag !
€
j c→ f
€
j f →c
Seebeck effect: qualitative interpretation!
-e! -e!-e! -e!
-e!-e!
-e!
-e!
(here α < 0 but if holes α > 0 !!)!(open circuit !)!
Joseph Heremans
![Page 12: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/12.jpg)
Seebeck effect: sign and electrical analogy!
Sign: if the hot end is > 0 / to the cold end, α < 0 (n-type). Otherwise, α > 0 (p-type). !
Equivalent electrical scheme:
n-type!
Tc! Tf!p-type!
€
Tc! Tf!
Tc! Tf!
Tc! Tf!+!-!
+!-!
useful to determine the electrical properties of a material with two types of carrier (1 and 2)
σ =σ1 +σ 2
α =α1σ1 +α2σ 2
σ1 +σ 2
€
1!
2!
Tc! Tf!Tc! Tf!
α1 σ1
α2σ 2
Exercice !Show that:!
Ιe.m.f. Ι = Ια dTΙ
Two channels of conduction !
![Page 13: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/13.jpg)
Peltier effect: qualitative interpretation!
metal/n-type SC contact!
I !
Ec!
Ev!
µ = EF (Fermi level)!
Heating of the junction!
I!
Ec!
Ev!
EF!
Cooling of the junction!
EG!
métal
I!
SC (n)
I!
SC (p) Metal! Metal!
Spontaneous formation of e-h pairs!
metal/p-type SC contact!
![Page 14: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/14.jpg)
Thomson effect: qualitative interpretation !
€
∇ T
€
j
è The Thomson effect appears like a continuous Peltier effect inside the material.!
In general, the Thomson effect is negligeable compared to Joule effect (if ΔT is not too large).!
π(Τ)
€
j
π(Τ’)
Only one material traveled by an electrical current and submitted to a thermal gradient è π(T) varies from one point to the other in the material. !
Peltier effect!
![Page 15: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/15.jpg)
Performance criteria: dimensionless figure of merit ZT!
Electrical energy conversion ! Cooling or heating using Peltier effect!(refrigerator, air conditionner, heat pumps)!
Electrical power generation using Seebeck effect!(electric generator)!
Thermal energy conversion!
P +Qf =Qc
C.O.P.=Qf
P
€
Qc = Pu +Qf
η =Pu
Qc
n!
Tfroid!
Tchaud!
Qc!
I!P!
Qf!
Pu!
Tfroid!
Tchaud!
Qc!
I!Qf!
n!RC!
Refrigeration (Peltier effect) Power generation (Seebeck effect)
L!
S!n!
Cuivre!
Cuivre!
Cuivre!
Cuivre!
Tc !
Tf !
+!-!
![Page 16: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/16.jpg)
€
C.O.P.=Qf
P=
−αTf I − KΔT −1
2RI
2
RI2−αΔT I
n!
Tfroid!
Tchaud!
Qc!
I!P!
Qf!
Approximated modelling of the performances!
Assumptions:!!ü Heat exchanges limited to the 2 thermostats (Cu) !ü Heat transfert along the x direction!ü α, ρ and λ are temperature independant and IαI >> IαcuI!ü Absence of contact resistances!ü Stationnary state!
Approach (to be done at least one time !):!!
€
q = π j − λ ∇ T
€
Qf = q(x = 0).S = −αTf I − λdT
dx
x=0
S
Energy balance:!
€
−λSd2T
dx2
=I2ρ
S
€
T (x)
€
P =UI = RI2−αΔT I
0!
L!
x!
€
Qf = −αTf I − KΔT −1
2RI
2
Case of the refrigerator!
Cuivre!
Cuivre!
€
j
∇T
T c!
T f!
+!-!
![Page 17: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/17.jpg)
Optimization of C.O.P.:!
€
(C.O.P.)max =Tf
Tc −Tf
1+ ZTm −Tc
Tf
1+ ZTm +1
€
ηmax
=Tc −Tf
Tc
1+ ZTm −1
1+ ZTm +Tc
Tf
€
∂C.O.P.
∂I
= 0 Optimization of η:
€
∂η
∂Rc
= 0
€
C.O.P.=Qf
P=
−αTf I − KΔT −1
2RI
2
RI2−αΔT I
€
η =Pu
Qc=
RcI2
KΔT −αTcI −1
2RI
2
Case of the refrigerator! Case of the generator!
Carnot! Carnot!
Z: figure of merit [K-1]!
Z =!α2!
ρλ = !
λ
P!
Power factor [WK-2m-1]!
Tm: average temperature!
Exercice !Show that:!
Exercice !Show that:!
Iopt ~ 2-10 A!
![Page 18: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/18.jpg)
Thermoelectric performances: impact of ZT!
ZT è!
0.0
0.1
0.2
0.3
0.4
300 400 500 600 700 800 900 1000η
max
Tc (K)
0.1
0.5
1
2
ZT = 4
∞
Carnot! TF = 300 K!
0.0
0.5
1.0
1.5
0.4 0.5 0.6 0.7 0.8 0.9 1.0
(C.O
.P.)
max
Tf/T
c
ZT = 4 2 0.51 0.1∞ZT è!
Carnot!
Domestic refrigerator!ZT ~ 3!
High performance è high ZTm!Material’s criteria: high ZT (dimensionless figure of merit)!
(no limitation on the ZT values) !
![Page 19: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/19.jpg)
Class of interesting materials!
Best compromise highly doped semiconductors!
ZT =α 2
ρ(λe+λ
r)TKey material parameter:!
Good TE material: α ↑, ρ ↓, λ↓ but α ↑ ρ ↑ et ρ ↓ λ↑ !
€
⇔
€
⇔
Insulators! Semiconductors! Metals!
λe (Electronic thermal conductivity)
λr (Lattice thermal conductivity)
λ ΙαΙ
ρ
Carrier concentration (cm 3)!
ΙαΙ ρ λ ZT
ZT!
1014 1020 1018 1016! 1022
T = 300 K
!!ZiiT =
αii
2
ρiiλii
T
Anisotropic materials!
![Page 20: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/20.jpg)
n, p thermoelectric couple!
n! n! n! n! n!
Refrigeration!
Power generation!
I!
Rc!
n! n! n! n! n! n!I!
N N N N N N n! p! n! p! n! p!I!
1 – Electric and thermal parallel connection!
2 - Electric series and thermal parallel connection!!
n! n! n! n! n!
Problem with the current source!
Output voltage too low!
Work… but there is a risk of a thermal short-cut!
Best solution!
n!Evident that devices constituted with only one leg are not interesting in practice (Qf and Pu are too low)… it is better to associate severals legs together !!!
Refrigeration!
(Ileg ~ 2-10 A)!
![Page 21: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/21.jpg)
Ideal performance of thermoelectric devices!
p! n!
Tfroid!
Tchaud!
Qf!
Qc! I!
p! n!
Rc!I!
Tchaud!
Tfroid!
Refrigerator (Peltier effect) Power generation (Seebeck effect)
P! Pu!
Qc!
Qf!
P +Qf =Qc
C.O.P.=Qf
P
€
Qc = Pu +Qf
η =Pu
Qc
Lp = Ln = L!Sp, Sn!αp, αn!λp, λn!ρp, ρn!!
€
Qf = qp(x = 0)Sp +qn(x = 0)Sn
0!
L!
x!
!!
+ + + +!- +!-
![Page 22: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/22.jpg)
Optimization of C.O.P.:!
€
(η)max =Tc −Tf
Tc
1+ ZnpTm −1
1+ ZnpTm +Tc
Tf
€
∂C.O.P.
∂I
= 0 Optimization of η:
€
∂η
∂Rc
= 0
C.O.P.=Qf
P=α pnTf I − KΔT −
12RI 2
RI 2 −α pn ΔT I
€
η =Pu
Qc=
RcI2
KΔT +αpnTcI −1
2RI
2
Case of the refrigerator! Case of the generator!
Carnot!Carnot!
Figure of merit of the couple Znp!€
(C.O.P.)max =Tf
Tc −Tf
1+ ZnpTm −Tc
Tf
1+ ZnpTm +1
Znp =α p −αn( )
2
[(ρ pλp )12 + (ρnλn )
12 ]2
≈Zn + Zp2
leg geometry:!
and and
€
Sp
Sn=
ρpλn
ρnλp
€
Sp
Sn=
ρpλn
ρnλp
If the transport properties are similar!
leg geometry:!
![Page 23: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/23.jpg)
Thermoelectric materials : whose semiconductors ?!
Qualitative information from transport Boltzmann equation with only one type of charge carriers!!
ZT = α 2
ρ (λe +λr )T = ZT (EF , scattering mechanisms,λr )
Optimal carrier concentration such that EF (Fermi level) is near a band edge, α ~ ± 200 µV/K !!!
β ∝µ
λr
(m*)32 the largest possible!
Semiconductors with a high mobility (µ), a high effective mass (m*) and a low lattice thermal conductivity (λr)!
Energie!B.C.!B.V.!
Den
sity
of s
tate!
EG
EF! EF!
Optimization of!!
Type n!Type p!
Joseph Heremans
![Page 24: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/24.jpg)
Selection criteria!
§ Materials with rather covalent bondings (low electronegativity difference between elements) (µ ↑)!
§ Density of state at the Fermi level varying greatly (lαl ↑)!!§ Multivalley bands semiconductors (µ .m* 3/2 ↑) è crystalline structure with high symetries!
if 2 types of carrier (holes + electrons): lαl ↓ è ZT ↓ !
§ Large number of atoms N per cell, high average atomic mass M (v↓), (λr ~ M-1/2 N-2/3)!
§ Important mass fluctuations inside the lattice (solid solutions) (µ/λr↑)!
§ Gap (EG) appropriated to reduce the presence of minority carriers (5 kT < EG < 10 kT)!!
kx!
ky!
kz!
α < αn,α
p⇒ ZT ↓
Exercice !Show that:!
![Page 25: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/25.jpg)
1950 - 1995: Conventionnels n and p-type materials!
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 200 400 600 800 1000 1200
np
ZT
Temperature (K)
β-FeSi2
(Pb,Sn)(Te,Se)
TAGS(Bi,Sb)
2(Te,Se)
3BiSb
Si-Ge
0.2 T
TAGS : (AgSbTe2)1-x(GeTe)x!
• small gap SC + heavy elements!• operate in a limited temperature range!• At T = 300 K solid solutions based on Bi2Te3!• ZT ~ 1 (efficiency 5 – 7 %) è limit the field of applications!
60 - 75!
76 - 10! Bi2Te3!65 – …!
Sylvie Hébert - Romain Viennois
![Page 26: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/26.jpg)
1995, a corner for thermoelectricty…!
Environmental problems (Kyoto…), energy problems (development of new sources of energy) è Renewed interest for thermoelectricity (USA, Japon) !Proposals of new idea and new concepts with the aim to identify and develop new materials with high ZT (ZT > 1)!
Identification of new bulk materials!
Thermoelectricity of low dimensional systems and
nanostructured bulk materials!
3!
2!
1!
0!1940! 1960! 1980! 2000!
ZT!
?!
![Page 27: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/27.jpg)
Open and complex crystalline structures are part of the research to identify materials for which electrical and thermal properties are decoupled (concept of the «Phonon Glass Electron Crystal (PGEC)» G. Slack, 1994). !
Axe 1 : Advanced bulk materials!
✚ ✚ ✚ ✚ ✚
✚ ✚ ✚ ✚ ✚
✚ ✚ ✚ ✚ ✚
- - - -
- -
« Phonon Glass » è lphonon low !! ! λr low (glass) « Electron crystal » è lélevé high!
! ! µ high (SC)
![Page 28: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/28.jpg)
Open crystalline structures: « cage » materials!!
Interesting cage materials:!
400 K < T < 900 K!(ZT)max ≥ 1!
Materials containing polyedra in which reside an atom (or in which it is possible to insert atoms) weakly linked to his neighbours è greater freedom to oscillate around their atomic position (« rattlers ») è behave like Einstein oscillators that strongly scatter phonons èλr ↓. !
Phonon!Scattering!
7
pnicogen position would reduce to (x=0, y=0.25, z=0.25). The similarities between the filled-
Fig. 3. Model of the filled skutterudite structure. The transition metal atoms (Fe, Ru, or Os -small
light blue spheres) are at the center of distorted octahedra formed by the pnicogen atoms (P, As,
Sb- green spheres). The lanthanide atoms (red spheres) are located at the center of a cage formed
by 12 pnicogen atoms. The skutterudite structure results if the lanthanide atoms are removed
from the structure and the transition metals (Fe, Ru or Os) are replaced by transition metals with
one more outer shell electron (Co, Rh or Ir).
skutterudite structure and the more familiar perovskite (e.g. CaTiO3) and ReO3 structures have
been discussed by Jeitschko and Braun 1977. In the ideal perovskite structure the eight octahedra
are not tilted which results in eight voids that are filled by Ca atoms. The tilting of the octahedra
in the skutterudite structure reduces the volume of six of these voids which become the centers of
rectangular pnicogen (P4, As4 or Sb4) groups. The remaining two voids are greatly enlarged and
can accommodate lanthanide atoms (fig. 4). Each lanthanide atom is located at the center of a
distorted icosohedron formed by 12 pnicogen atoms. The size of this icosohedral cage formed by
the pnicogen atoms increases as the pnicogen is changed from P to As to Sb. In many of the
antimonide compounds the atomic displacement parameters for the lanthanide atoms are
unusually large, indicating substantial “rattling” of the R atoms about their equilibrium positions
Skutterudites!(n,p - ☐Co4Sb12)
Clathrates!(n-Ba8Ga16Ge30!p-Ba8AuxGe46-x)!
Sylvie Hébert - Romain Viennois
![Page 29: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/29.jpg)
! !!!ü Zintl Phases (polar intermetallic compounds): β-Zn4Sb3, Yb14MnSb11!ü Half-Heusler: (Ti,Zr,Hf)Ni(Sn,Sb)!ü Silicides: Mg2Si!ü Oxides: family of NaxCoO2 (misfits) è metals with α ~ 100 µV/K at 300 K !! (origin: high electronic correlations) !
Complex crystalline structures! Sylvie Hébert - Romain Viennois
ü Conducting organic polymers (PDOT-PSS,…),!ü Oxychalcogenides (BiCuSeO)!ü SnSe…!
Other recent families of materials!
Type p! Type n!
Jernej Marvlje
Sylvie Hébert - Romain Viennois
![Page 30: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/30.jpg)
Axe 2: Low dimensional systems (2D,1D,0D)…!
3 D 2 D 1 D 0 D
- density of state (D.O.S.) more favorable (more pronounced energy variation )!è Increase of α!- further degree of freedom (size) to modulate the transport properties!- possibility to decrease λr through the scattering of phonons at interfaces!- possibility to induce semimetal/semiconductor transitions (bismuth)!- ZT0D > ZT1D > ZT2D > ZT3D !
D.O
.S.!
D.O
.S.!
D.O
.S.!
D.O
.S.!
E E E E
30 nm!
Spectacular results (ZT ~ 2 – 3.5) in superlattices through a strong reduction of the thermal conductivity but…results not reproduced !!!
Clotilde Boulanger
Guillaume Savelli
Sami Merabia
![Page 31: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/31.jpg)
Intensive research and promising results on several materials through a degradation of the thermal properties !!!
Lead chalcogenide compounds!
Idea: is it possible to achieve a reduction of the thermal conductivity in a bulk material containing features of nanometric size (grain size, dispersion of nanoparticules,…) ?!
Axe 2 : … to nanostructured bulk materials!
5 nm!
Conventional materials!
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
200 400 600 800 1000 1200 1400
ZT
Température (K)
n-SiGe
p-SiGe nano
p-SiGe
n-SiGe nano
PbTe
Bi2Te
3 nano PbTe/PbS
Pb1+x
SbyTe
Bi2Te
3
0,0
0,5
1,0
1,5
2,0
2,5
300 400 500 600 700 800 900
ZT
TempОrature (K)
LASTT
SALT-20PLAT-20
LAST-18
LAST-m : AgPbmSbTe2+m!LASTT-m : AgPbm SnSbTe2+m!PLAT-m : KPbmSbTe2+m!SALT-m : NaPbmSbTe2+m!!
Type p!
Lorette Sicard
David Berardan
![Page 32: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/32.jpg)
1995 - 2014: significant advances ?!
![Page 33: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/33.jpg)
Converters: technological aspects !
p n!Metallic electrodes
Electrical insulator (but good thermal conductor)!
Unicouple!Module with 3 couples!
Assembly!
Materials: n- and p- types with high ZT on a broad ΔT. Similar physical properties (to have close geometry).!Auxiliary material conditions: thermaly and chemicaly stable, high mechanical strengh, low cost, abundant and easy preparation.!!Assembly: identification of electrodes (with similar coefficient of thermal expansion), diffusion barriers, control of interfaces (low thermal and electrical contact resistances), possibly identification of an electrical insulation.!
Commercial module!
Alumina !Copper + PbSn or BiSn brazing !
n- an p-legs based on Bi2Te3 + nickel plating !
Franck Gascoin
David Berardan
Heat exchangers (size, thermal resistance,…), associated electronics !
Guillaume Bernard-Granger
![Page 34: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/34.jpg)
Possible architectures:! ZT
T(°C)
1
200 400 600
p1 p2 p3 T (°C)
25 100
700
250
450 n1!p1!
p2!
p3!n2!
Rc!
T (°C)
25
100
700
250
450
n!p!p,
n (c
m-3
)!
Rc!
ü functionally graded materials
ü cascade
ü segmented materials
Rc!
p2!
p1!
n2!
n1!
RC1!
F. Gascoin
ü « Y » structure (versus « π »)
!! Compatibility of materials!
2008 DOE Merit Review:
BSST Waste Heat Recovery Program
27 February, 2008
This presentation does not contain any
proprietary or confidential information12
Performance Measures and AccomplishmentsPerformance Measures and Accomplishments22ndnd Generation BiGeneration Bi22TeTe33 SubassemblySubassembly
n-type Bi2Te3
p-type Bi2Te3
Current
flow
Heat exchanger
Surface- cold
Heat exchanger
Surface- hot
!j ⊥ !q
!j / / !q(versus )
![Page 35: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/35.jpg)
Avantages/drawbacks of thermoelectric devices!
§ Low performances!§ Cost !
§ Direct conversion of energy, solid state device, no moving parts, no vibration (silent)!
§ Reliable (long lifetime), no maintenance!§ Compact, working independant of the
position!§ Simple installation!§ No use of harmful gaz (CFC)!§ Precise control of the temperature!§ Reversibility (« heating » and « cooling »)!§ Recovery of heat lost!!
!
![Page 36: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/36.jpg)
Applications/cooling (200 – 250 M€/an)!
Electro-optic (localized cooling-stabilization of temperature)!Laser diodes, detectors (I.R., X, gamma), CCD cameras!Space telescopes!I.R cameras, night vision!Medical laser equipment …!
!Electronic (cooling)
Integrated circuits !Parametric amplifiers!Photodiodes…!
!Cooling of small volumes
Camping fridges, minibars, water fontains…!Medical refrigerator!Computers (iMac)!
!Air conditioning
Automobile seats (Amerigon, US)!Driver cabin for tube (Russiia)!
!
Répartition du marché des modules pour le refroidissement (Komatsu-2007)!
Automobile14%
Biens de consommation35%
Télécommunications16%
Industrie9%
Labo. médicaux& biologiques
12%
Semicond.8%
Défense&spatial
6%
Daniel Champier
Julien Ramousse
![Page 37: Introduction to thermoelectricitygdr-thermoelectricite.cnrs.fr/ecole2014/lac2014-Lenoir.pdfIntroduction to thermoelectricity! Ecole thématique! «Thermoélectricité»! 1-6 juin 2014,](https://reader034.vdocuments.us/reader034/viewer/2022042804/5f52e92fda7dff34614b654f/html5/thumbnails/37.jpg)
Applications/power generation (25-50 M€/an)!Civil!
Telecommunication industries* (power for communication systems!or emergency telecommunication systems in remote aeras, …)!Oil and gas industry* (cathodic protection) !Monitoring of environment* – Weather stations!Navigational aids (beacons, buoyes, landing zone,…)!Commercial products* (camping stove + radio,…)!Jewellery (Citizen, Seiko) !
Military!Supply for communication systems*!
Spatial (since 1960) Choice technology to power deep space probes (Transit…Voyagers I&II, Galiléo,…rover Curiosity)!RTG (« Radioisotope Thermoelectric Generators »), heat source: Pu238O2, high reliability!
!
!
Cassini mission!55 kg!P ~ 250 W!η ~ 7%!
*Heat source: burner powered by fossile fuel (P ~ 10 W – 5 KW)!