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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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 interdot
Coulomb 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
f L ( )
f R ( )
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)
2:Linear response
 T / T 0  1
Homogenous QD size, dilute QD density
  Eg  EF
L  R  
Eg
EF
2
ZT 
S G eT
e
ZT as a function of T for different detuning energies. Solid and dash lines
correspond, respectively, without and with intradot Coulomb interactions .
Ref[3]P. Murphy, S. Mukerjee, J. Morre, Phys. Rev. B 78, 161406 (2008).
ZT   ,
  0
2-1:Interdot Coulomb interactions
High QD density
Side view
(a)
(b)
(c )
(d)
(a)
(c)
(b)
ZT   ,
Top view
 0
(d)
2-2: ZT detuned by Eg
Noninteraction case
High QD density
Eg
EF
  Eg  EF
2-3: Inelastic scattering effect on ZT
QD size fluctuations, defects between metallic electrodes
and insulators and electron-phonon interactions,
G l ( ) 
r
1  N l ,
  E g  i (  l   ie )

N l ,
  E g  U l  i (  l   ie )
2-4: Electrical conductance, thermal power
and thermal conductance
2
ZT 
S G eT
e
These curves correspond to Fig.3.
The temperature-dependence of ZT is similar to that
of the electrical conductivity.
2-5: Ge, S and Ke as a function of gate
voltage
  30 
Ge: Coulomb oscillation
S: Sawtooth-like shape
Ke: Sensitive to T
2-6:Midway between the good and poor
conductors
2.7 Without vacuum layer
L , 0
t L ,R
R , 0
2.8 Different dot sizes
2nm
2.9 Thickness of SiO2
3-1:Thermal rectification effect  T / T
0
1
Two dot case
 A , L   ,  AR  0
B ,L  B ,R  
U
A
 U B  30 k B T 0
U
TL
TR
T  TL  TR  0
AB
TL
T  TL  TR  0
Q /  B   (1  N B )[( 1  2 N A )( E B  E F ) f LR ( E B )  2 N A ( E B  U
Q /  B   (1  N B )( E B  E F )( f L ( E B )  f R ( E B ))  eq .( 8 )
AB
 15 k B T 0
TR
 E F ) f LR ( E B  U
AB
)]  eq .( 7 )
3-2: Thermal rectification efficiency
(2 dots)
U A  U B  30 k B T 0
Q 
Q (  T  0 )  | Q (  T  0 |)
Q (T  0)
U
AB
 15 k B T 0
 A , L   ,  AR  0
B ,L  B ,R  
TL
TR
Q (T  0)
TL
TR
Q ( T  0 )
Ref[4] R. Scheiber et al, New. J. Phys. 10, 083016 (2008)
3-3: Thermal rectification (three QDs)
U
AB
U
AC
 15 k B T 0
U BC  8 k B T 0
E C  E F  120 
Dot A
E B  E F  80 
E A  E F  40 
3-4:The shift of QD energy levels caused by
electrochemical potential
U BC  10 k B T
Solid curves including
Dashed curves excluding
S 
V
T
TL
VH
TH
VL
TH
TL
VL
VH
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 efficiency
3 dots
2 dots
4:Conclusion
(A) Figure of merit, ZT
[1]The optimization of ZT depends not only on the temperature but
also on the detuning energy   E g  E F
[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
electrodes.
[2] Large energy level separation between dots
[3]Strong interdot Coulomb interactions
4. Thermal rectification
4.1 Tunneling rates
V  VL  VR  0
TH
V  VL  VR  0
TL
TH
TL
4.2 Tuning energy level
4.3 Three-dots with uniform size
Q 
Q (T  0)
Q (T  0)
The dot-dashed line indicates the junction
system without asymmetrical heat current,
when dots are identical.
4.4: Different sizes
E A  E F  40 
E B  E F  80 
Ca 
E C  E F  120 
Q 
Q (T  0)
Q (T  0)
Cb 
Q (  T  30  )
| Q (  T   30  ) |
Q (  T  20  )
Q (  T   20  )
4.5 :Gate voltage
eV g  50 
eV g  60 
eV g  70 
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: G (T ), S (T ) and 
e
e
(T )
5.2:Detuning energy
  Ed  EF
5.3: G (T ), S (T ) and 
e
e
(T )
5.4
5.5
5.6:
5.7: S to resolve high order
phonon assisted tunneling