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)

Urbana-2003-July

References

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• [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).

1:System

Amorphous insulator

Large intradot and interdot Coulomb interactions

1-0:Fabrication

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

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

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

2-1:Interdot Coulomb interactions

(a) (b) (c) (d)

Side view

Top view

High QD density

(a)

(b)(c )

(d)

0, ZT

2-2: ZT detuned by Eg

Noninteraction case

Eg

EFFg EE

High QD density

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

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.

2-5: Ge, S and Ke as a function of gate voltage

Ge: Coulomb oscillation S: Sawtooth-like shapeKe: Sensitive to T

30

2-6:Midway between the good and poor conductors

2.7 Without vacuum layer

0,L 0,RRLt ,

2.8 Different dot sizes

2nm

2.9 Thickness of SiO2

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

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)

3-3: Thermal rectification (three QDs)

Dot A

015 TkUU BACAB

08 TkU BBC

40FA EE

80FB EE

120FC EE

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

3-5: Interdot Coulomb interactions

Solid line UAC=15kBT0

Dashed line UAC=10kBT0

Dotted line UAC=5kBT0

Dot-Dashed line UAC=0

3-6: Thermal rectification efficiency2 dots3 dots

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

4. Thermal rectification

4.1 Tunneling rates

0 RL VVV

TH TLTH

TL

0 RL VVV

4.2 Tuning energy level

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.

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

4.5 :Gate voltage

50geV 60geV 70geV

4.6: Interdot Coulomb interactions

4.7:Energy level shifted by electrochemical potential

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).

5.1: )()(),( TandTSTG ee

5.2:Detuning energy

Fd EE

5.3: )()(),( TandTSTG ee

5.4

5.5

5.6:

5.7: S to resolve high order phonon assisted tunneling