Thermoelectric and thermal rectification properties of quantum dot junctions
description
Transcript of Thermoelectric and thermal rectification properties of quantum dot junctions
![Page 1: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/1.jpg)
Thermoelectric and thermal rectification properties of quantum dot junctions
David M T Kuo1 and Yia-Chung Chang2
1:Department of Electrical Engineering, National Central University, Taiwan
2:Research Center for Applied Science, Academic Sinica, Taiwan
The detail can be found in PRB 81, 205321 (2010)
![Page 2: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/2.jpg)
Urbana-2003-July
![Page 3: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/3.jpg)
References
• [1]A. J. Minnich, M. S. Dresselhaus, Z. F. Ren and G. Chen, Energy Environ Science, 2, 466 (2009)
• [2]G. Mahan, B. Sales and J. Sharp, Physics Today,50, 42 (1997).• [3]R. Venkatasubramanian, E. Siivola,T. Colpitts,B. O'Quinn, Nature
413,597 (2001).”BiTe/SbTe quantum well superlattice”• [4]A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J. K.Yu, W. A. Godda
rd III and J. R. Heath, Nature, 451, 168(2008).”Silicon quantum wire”
• [5]T. C. Harman, P. J. Taylor, M. P. Walsh, B. E.LaForge, Science 297, 2229 (2002).”PbSeTe Quantum dot superlattice “
• [6]K. F. Hsu,S. Loo,F. Guo,W. Chen,J. S. Dyck,C. Uher, T. Hogan,E. K. Polychroniadis,M. G. Kanatzidis, Science 303, 818(2004)
• .[7]A. Majumdar, Science 303, 777 (2004).• [8]G. Chen, M. S. Dresselhaus, G. Dresselhaus, J. P.Fleurial and T. Ca
illat, International Materials Reviews,48, 45 (2003)• [9]Y. M. Lin and M. S. Dresselhaus, Phys. Rev. B 68, 075304 (2003).
![Page 4: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/4.jpg)
1:System
Amorphous insulator
Large intradot and interdot Coulomb interactions
![Page 5: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/5.jpg)
1-0:Fabrication
![Page 6: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/6.jpg)
1-1:Hamiltonian (Anderson model)
The key effects included are the intradot and interdotCoulomb interactions and the coupling between the QDs with the metallic leads
There is one energy level within each QD
![Page 7: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/7.jpg)
1-2:Nonequilibrium Green’s function technique
Ref[1]D. M. T. Kuo and Y. C. Chang, Phys. Rev. Lett. 99,086803(2007)
Ref[2]Y. C. Chang and D. M. T Kuo, Phys. Rev. B 77,245412 (2008)
)(Lf )(Rf
![Page 8: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/8.jpg)
2:Linear response
ZT as a function of T for different detuning energies. Solid and dash lines correspond, respectively, without and with intradot Coulomb interactions .
EF
Eg
e
eTGSZT
2
Homogenous QD size, dilute QD density
1/ 0 TT
Ref[3]P. Murphy, S. Mukerjee, J. Morre, Phys. Rev. B 78, 161406 (2008).
Fg EE RL
0, ZT
![Page 9: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/9.jpg)
2-1:Interdot Coulomb interactions
(a) (b) (c) (d)
Side view
Top view
High QD density
(a)
(b)(c )
(d)
0, ZT
![Page 10: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/10.jpg)
2-2: ZT detuned by Eg
Noninteraction case
Eg
EFFg EE
High QD density
![Page 11: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/11.jpg)
2-3: Inelastic scattering effect on ZT
QD size fluctuations, defects between metallic electrodesand insulators and electron-phonon interactions,
)()(
1)( ,,
iellg
l
ielg
lrl iUE
N
iE
NG
![Page 12: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/12.jpg)
2-4: Electrical conductance, thermal power and thermal conductance
e
eTGSZT
2
These curves correspond to Fig.3.The temperature-dependence of ZT is similar to thatof the electrical conductivity.
![Page 13: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/13.jpg)
2-5: Ge, S and Ke as a function of gate voltage
Ge: Coulomb oscillation S: Sawtooth-like shapeKe: Sensitive to T
30
![Page 14: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/14.jpg)
2-6:Midway between the good and poor conductors
![Page 15: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/15.jpg)
2.7 Without vacuum layer
0,L 0,RRLt ,
![Page 16: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/16.jpg)
2.8 Different dot sizes
2nm
![Page 17: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/17.jpg)
2.9 Thickness of SiO2
![Page 18: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/18.jpg)
3-1:Thermal rectification effect
TL TR TL TR
0 RL TTT0 RL TTT
Two dot case
0,, ARLA
RBLB ,,
015 TkU BAB
030 TkUU BBA
)8.())()()()(1(/
)7.()]()(2)())(21)[(1(/
eqEfEfEENQ
eqUEfEUENEfEENNQ
BRBLFBBB
ABBLRFABBABLRFBABB
1/ 0 TT
![Page 19: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/19.jpg)
3-2: Thermal rectification efficiency(2 dots)
)0(
|)0(|)0(
TQ
TQTQQ
)0( TQ)0( TQ
TL TR TLTR
0,, ARLA
RBLB ,,
030 TkUU BBA
015 TkU BAB
Ref[4] R. Scheiber et al, New. J. Phys. 10, 083016 (2008)
![Page 20: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/20.jpg)
3-3: Thermal rectification (three QDs)
Dot A
015 TkUU BACAB
08 TkU BBC
40FA EE
80FB EE
120FC EE
![Page 21: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/21.jpg)
3-4:The shift of QD energy levels caused by electrochemical potential
TH TLTHTL
VHVLVH VL
TkU BBC 10
Solid curves includingDashed curves excluding
T
VS
![Page 22: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/22.jpg)
3-5: Interdot Coulomb interactions
Solid line UAC=15kBT0
Dashed line UAC=10kBT0
Dotted line UAC=5kBT0
Dot-Dashed line UAC=0
![Page 23: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/23.jpg)
3-6: Thermal rectification efficiency2 dots3 dots
![Page 24: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/24.jpg)
4:Conclusion
(A) Figure of merit, ZT[1]The optimization of ZT depends not only on the temperature but a
lso on the detuning energy [2]Inelastic scattering effect of electron-phonon interactions, QD size
fluctuations, and defects lead to a considerable reduction to the ZT values
(B)Thermal rectification [1] Very strong asymmetrical coupling between the dots and the elect
rodes. [2] Large energy level separation between dots
[3]Strong interdot Coulomb interactions
Fg EE
![Page 25: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/25.jpg)
4. Thermal rectification
![Page 26: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/26.jpg)
4.1 Tunneling rates
0 RL VVV
TH TLTH
TL
0 RL VVV
![Page 27: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/27.jpg)
4.2 Tuning energy level
![Page 28: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/28.jpg)
4.3 Three-dots with uniform size
)0(
)0(
TQ
TQQ The dot-dashed line indicates the junction
system without asymmetrical heat current,when dots are identical.
![Page 29: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/29.jpg)
4.4: Different sizes
)0(
)0(
TQ
TQQ
120
80
40
FC
FB
FA
EE
EE
EE
|)30(|
)30(
TQ
TQCa
)20(
)20(
TQ
TQCb
![Page 30: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/30.jpg)
4.5 :Gate voltage
50geV 60geV 70geV
![Page 31: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/31.jpg)
4.6: Interdot Coulomb interactions
![Page 32: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/32.jpg)
4.7:Energy level shifted by electrochemical potential
![Page 33: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/33.jpg)
5:A single molecular QD
(a)Hard to scaling up the thermal devices.(b)Hard to integrate with silicon based electronics.
[1]P. Murphy, S.Mukerjee and J. Morre, Phys. Rev. B 78, 161406 (2008).
![Page 34: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/34.jpg)
5.1: )()(),( TandTSTG ee
![Page 35: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/35.jpg)
5.2:Detuning energy
Fd EE
![Page 36: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/36.jpg)
5.3: )()(),( TandTSTG ee
![Page 37: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/37.jpg)
5.4
![Page 38: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/38.jpg)
5.5
![Page 39: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/39.jpg)
5.6:
![Page 40: Thermoelectric and thermal rectification properties of quantum dot junctions](https://reader036.fdocuments.net/reader036/viewer/2022081419/56815a92550346895dc809d1/html5/thumbnails/40.jpg)
5.7: S to resolve high order phonon assisted tunneling