explorations in quantum transport – phenomena and methods
DESCRIPTION
Explorations in quantum transport – phenomena and methods Sokrates T. Pantelides Department of Physics and astronomy , Vanderbilt University, Nashville, TN and Oak Ridge National Laboratory, Oak Ridge, TN Collaborators: Yoshihiro Gohda Zhong-yi Lu - PowerPoint PPT PresentationTRANSCRIPT
Explorations in quantum transport – phenomena and methods
Sokrates T. Pantelides Department of Physics and astronomy, Vanderbilt University, Nashville, TN
andOak Ridge National Laboratory, Oak Ridge, TN
Collaborators: Yoshihiro Gohda Zhong-yi Lu
Kalman Varga
Supported in part by Department of Energy
MOORE’S LAW
• Phenomena (using the Lippmann-Schwinger method)
• Charging of molecules during transport (Gohda)
• Transport through ultra-thin films (Lu)
• New method (Varga)
The Lippmann-Schwinger method
• Norton Lang, 1981 –
t
r
• Di Ventra, Lang, and Pantelides, 2000-2002
0 ,
ik z ik zr r
ik zl
e re z
te z
FR
FL
E
E
rrdErJ )]()(Im[2)( *
Experiment: Reed et al (2000)
T=190 K T=300 K
90°
0°
0°
90°
Theory
Nature 417, 72 (2002)
“The current is strongly suppressed up to a threshold V, then it increases in steps”
Coulomb blockade in a quantum dot
GaAs-AlGaAs-InGaAs-AlGaAs-GaAs
Barner and Ruggiero, 1987
LUMO LUMO
V=2.4V
V=1.2[V] V=3.6[V]
LUMO LUMO
AFTER SELF-CONSISTENCY,
MOLECULE IS NEUTRAL!
ELECTRODES ARE NEUTRAL!
EXCITED STATE?
C6H5S
ELIMINATE CONTACT ON LEFT
C6H4(NO2)S
-6 -4 -2 0 2
Energy (eV)
C6H5-S C6H4(NO2)-S
Energy (eV)
-3 -2 -1 0 1
0.6V0 e
1.8V1 e
4.2V1 e
Vsd = 0.1 V
Using a gate voltage
Q=0
0.3
0.8 1.2
Fowler-Nordheim tunneling
JE
J/E2 = Aexp(-B/E)
M O S
n-Si
MetalSiO2
EF
Ec
Ev
I
V
ln(J/E2)
1/E
Ohmic
Fowler-Nordheim
J/E2 = Aexp(-B/E)
I=V/R
8-layer Si(001)
Ohmic
Effective potential
EF
J
The dash-dot lines are boundary
EF
8 layers Si(001)
V=5.0v
V=1.0v
V=0.1v
Current vs thickness [Si(001)]
Bias=1.0V
I-V curve through SiO2 nano-film
Three regions:(1) 0.0 to 0.5V quasi-linear;(2) 0.5 to 4.0V non-linear;(3) Over 4.0V quasi-linear
Fowler-Nordheim I-V plot
Effective potential
J
The dash-dot lines are boundary
EF
SiO2
V= 4.0v
nano-film
V=0.5v
1.2 n m (SiO 2)
1.5 n m (SiO2)
0.9 n m (vacuum)
1.2 n m (vacuum)
1.5 n m (vacuum)
0 1 2 3 4 5
G. Timp et al (Bell Lab) 1998 calculation
The Lippmann-Schwinger method
t
r
0 ,
ik z ik zr r
ik zl
e re z
te z
FR
FL
E
E
rrdErJ )]()(Im[2)( *
0 J EVERYWHERE
DENSITY FUNCTIONAL THEORYFOR STEADY-STATE TRANSPORT
(CURRENT-DENSITY FUNCTIONAL)
[ ] [ ] 0 0E J E J A 21
2{ ( ) }xc ext H xcH i V V V A A
Static external potential ( )extV x + B.C.
( )xc J j A A *Im ( )
j
2HV 2 ( ) 0 A A J J
*
[ , ]xc
EV
J [ , ]
xc
E
J
AJ
MAP TRANSPORT ONTO AN EIGENVALUE PROBLEM
2W ( ) ))2
IW x L x R
J
( )H iW
Schrödinger equation with imaginary potential:
Source Sink
Battery!
Na wire
Real-space DFT calculationJellium electrodesBias Voltage
Experiment
(Reed et al.)
Benzene ring -- IV characteristics