1. Molecular electronics by the Numbers
Sokrates T. Pantelides, Massimiliano Di Ventra, Norton D. Lang and Sergey N. Rashkeev
IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 1, NO. 1, MARCH 2002

2. Molecular electronics by the Numbers Sokrates T
Molecular electronics by the Numbers Sokrates T. Pantelides, Massimiliano Di Ventra, Norton D. Lang and Sergey N. Rashkeev
Molecules for nanoscale electronics device.
Experimental measurements  rich structure and diverse behavior.
I-V characteristic computed  understanding of transport in molecules.
Informations obtained:
molecule-electrode contacts;
three-terminal molecular device;
factors that control the performance.

3. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

4. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

5. The solid-state and silicon-based technology follows the Moore’s Law:
Introduction
The solid-state and silicon-based technology follows the Moore’s Law:
The number of transistors that can be fabricated on a silicon integrates circuit is doubling every 18 to 24 months.  This cannot go on forever.
1970
1975
1980
1985
1990
1995
2000
2005
2010
103
104
105
106
107
108
109
Transistors per chip
Year
Pentium
Pro
80786
80486
Pentium
80386
80286
8086
8080
4004

6. Quantum phenomena such as tunneling
Introduction
Problems:
Heat dissipation
Quantum phenomena such as tunneling
Control of doping in ultra-small regions
Fabrication of efficient smaller silicon transistors and interconnections
Expensive and difficult lithography
Short inversion-channel effect

7. New era of Nanotecnology
Introduction
Future computational systems will consist of superdense, superfast and very small logic devices.
New era of Nanotecnology
Molecules as individual active devices are obvious candidates for the ultimate ultra-small components in nanoelectronics.
The advantage using organic molecular wires rather than carbon nanotubes is that they are so much smaller.

8. To construct basic electronic devices from individual molecules.
Introduction
Goal:
To construct basic electronic devices
from individual molecules.
First theoretical papers on molecular electronics:
Aviram and M. A. Ratner,
“Molecular rectifiers,”
Chem. Phys. Lett., vol. 29, p. 277, 1974.
Since then the research in this area has increased exponentially.

9. Experimental measurements  recent Semiempirical methods  various
Introduction
Functioning an extremely small electronic device demands tremendous control over the I-V characteristics of the device:
Experimental measurements  recent
Semiempirical methods  various
Practical method  N. D. Lang
[N. D. Lang, “Resistance of atomic wires,” Phys. Rev. B, Condens. Matter, vol. 52, p. 5335, 1995.]

10. Transport in molecules whose core is a single benzene ring.
Introduction
Transport in molecules whose
core is a single benzene ring.
Reed et al.: first quantitative electrical measurements of this molecule witch was fabricated by self-assembly.

11. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

12. Single benzene rings  calculations practical.
Transport in a Single Benzene Ring
M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, “Conductance of a molecular junction,” Science, vol. 278, p. 252, 1997.
Benzene
C6H6
Single benzene rings  calculations practical.
Experimental data are available for two-terminal configurations
Benzene-1,4-dithiolate
between metallic
gold contacts.

13. Experiment: room temperature
Transport in a Single Benzene Ring
Experiment:
room temperature
mechanically controllable break junction (MCB)
benzene-1,4-dithiol was adsorbed from solution in tetrahydro-furan onto the gold electrodes
One molecule forms the bridge between the electrodes

14. Experimental current-voltage (I-V) characteristic
Transport in a Single Benzene Ring
Experimental current-voltage (I-V) characteristic
Experimental conductance G(V) (=dI/dV).
I(V): Gap of ~0.7 V.
Electrons traveled without generating heat by interacting or colliding.
G(V): Step-like structure:
Lower step ~22.2 MΩ (0.045 μS);
Higher step ~13.3 MΩ (0.075 μS).
No negative differential resistance.
Reproducibility of the G(V) 
One active molecules.
Lower step: 22.2, 22.2 and 22.7 MΩ.
Higher step: 12.5, 13.3 and 14.3 MΩ.
One singular observation:
configuration of two non-interacting self-assembled molecules in parallel.

15. Transport in a Single Benzene Ring
Theoretical modeling.
M. Di Ventra, S. T. Pantelides, and N. D. Lang, “First-principles calculation of transport properties of a molecular device,” Phys. Rev. Lett., vol. 84, p. 979, 2000.
Analytical I-V characteristic of single benzene-1,4-dithiol molecule between two ideal metallic contacts.
The molecule stands perpendicular to the metal surfaces.

16. Three distinct regions in the calculated conductance curve:
Transport in a Single Benzene Ring
experimental characteristics
calculated characteristics
The shapes of experimental and calculated I-V curves are the same but differ of 2 orders of magnitude.
Three distinct regions in the calculated conductance curve:
1. Initial slow rise: Ohmic behavior; small but smooth DOS
2. Peak and valley: resonant tunneling through π* antibonding states.
3. Other peak  resonant tunneling with π bonding states.
The bonding σ and π states are altered by the bias .

17. Limitations of the local-density approximation Geometry Chemistry
Transport in a Single Benzene Ring
The discrepancy between the theoretical and experimental characteristics:
Limitations of the local-density approximation
Geometry
Chemistry
Temperature
Local disorder in the Au metal near the contacts
The experimental measurements have an uncertainty of at least a factor of 2.

18. Single gold atom between the sulfur and the metal surface.
Transport in a Single Benzene Ring
Single gold atom between the sulfur and the metal surface.
Same shape
Absolute value of G(V) decreases by 2 orders of magnitude.
The p states of the sulfur atoms that are parallel to the metal surfaces do not couple to the gold s states, thus breaking the π scattering channel.
with Au
without Au

19. between the sulfur and the metal surface.
Transport in a Single Benzene Ring
Single aluminum atom
between the sulfur and the
metal surface.
The p orbitals of Al atoms forms π states with the p orbitals of the sulfur atoms similarly oriented.
S atom in front of the center
of a triangular pad of three
gold atoms on each electrode
surface.
The calculated resistance is nearly the same as the one for the sulfur attached to the model metal.

20. Molecules determine the shape of the
Transport in a Single Benzene Ring
Molecules determine the shape of the
I-V characteristic, but the nature of individual atoms at the molecule-
electrode contact determines the
absolute magnitude of the current.
Molecules attached to the gold electrodes through sulfur end group  convenient thiol-gold self-assembly scheme
A S atom is commonly used  there are other better choices.
Find anchoring groups to build devices with the desired properties.

21. Benzene connected to two Au leads through S, Se, and Te.
Transport in a Single Benzene Ring
Yongqiang Xue, and Mark A. Ratner, “End group effect on electrical transport through individual molecules: A microscopic study,” cond-math/ v1 (2003).
Devices formed by attaching the benzene molecule onto two semi-infinite gold electrodes through oxygen (O) and fluorine (F) end atoms and the isocyanide (C-N) and hydroxile (OH) end group: OΦO, HOΦOH, FΦF, CNΦNC and NCΦCN (Φ stands for benzene ring)
S.-H. Ke, H.U. Baranger and W. Yang, “Molecular Conductance: Contact Atomic Structure and Chemical Trends of Anchoring Groups,” cond-mat/ (2004)
Benzene connected to two Au leads through S, Se, and Te.

22. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

23. Three-terminal device:
Desired device for many of the applications of molecules in electronics
Not investigated  difficulty of realizing a gate terminal
At a fixed small source-drain bias, the gate voltage must be able to amplify the current by orders of magnitude
M. Di Ventra, S. T. Pantelides, and N. D. Lang, “The benzene Molecule as a molecular resonant-tunneling transistor,” Appl. Phys. Lett., vol. 76, p. 3448, 2000.

24. The calculated I–EG characteristic (VD-S = 10 mV):
Three-Terminal Device
The calculated I–EG characteristic (VD-S = 10 mV):
Initial slow rise  ohmic behavior: small but smooth DOS
Peak (1.1 V/Å): due to resonant tunneling through π* antibonding states that shift in energy and enter into resonance with the states
Valley (1.5 V/Å): the resonant-tunneling condition is lost
The current increase further  linear dependence on the gate bias: quasifree electron states enter the window of energy between the Fermi levels and can contribute to transport.

25. Effect of symmetry of model molecular transistors, on the
Three-Terminal Device
Effect of symmetry of model molecular transistors, on the
I-V and the I-E characteristics.
Benzene-1,4-dithiolate molecule substituting one or two hydrogen atoms by hydroxile groups (OH). The gate is applied perpendicular to the molecule plane as a capacitor field.
S. N. Rashkeev, M. Di Ventra, and S. T. Pantelides, “Transport in a molecular transistor: Symmetry effects and nonlinearities,” Phys. Rev. Lett., submitted for publication.

26. Same behavior of the I-E curves: region of a constant high resistance
Three-Terminal Device
The calculated I-V curves are very similar despite the different symmetry but:
The amplification of the current at the resonant tunneling regime is a few times larger in the asymmetric molecule.
Resonant tunneling occurs at much lower voltage than in the symmetric molecule.
When the gate field is applied, both molecules behave as resonant-tunneling transistors.
Same behavior of the I-E curves:
region of a constant high resistance
the current increases
reaches a peak
drops to a valley
increases almost linearly
VG = 0 V
VD-S = 0.01 V

27. Shape of I-E curves determined by resonant-tunneling processes.
Three-Terminal Device
Shape of I-E curves determined by resonant-tunneling processes.
Asymmetric molecule: the DOS has a broad hump at ~1 eV due to antibonding O-H orbitals hybridized with the π state of the benzene ring  peak and valley of the I-E curve at lower gate fields.
Symmetric molecule: the DOS curve is flat above the Fermi level with the antibonding π* state of the benzene ring at about 2.7 eV  the I-E curve is similar to that of the BDT molecule. A field twice as large is needed to reach the resonant-tunneling condition.
The current for the asymmetric molecule are 2 to 3 times larger than for the symmetric one  larger DOS value at resonant tunneling.
VD-S = 0.01 V

28. Asymmetric molecule: the current grows at low values of the gate field
Three-Terminal Device
I-E curve depends on the value of VS-D. When E is applied, the I changes in a different way.
Asymmetric molecule: the current grows at low values of the gate field
Symmetric molecule: the current drops at low values of the gate field  for the voltage 2.4 V the π states of the carbon ring are in resonance with the left Fermi level. The resonant-tunneling condition for this peak is not satisfied anymore, with consequent reduction in the current.
VS-D = 2.4 V
The external gate field can either increase or decrease the resistance of the device due to the nonlinear effects intrinsic in resonant tunneling.

29. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

30. Use of advanced microfabrication and self-assembly techniques.
Benzene Ring With a Ligand
Use of advanced microfabrication and self-assembly techniques.
Electronic measurements in a nanostructure: metal top contact, self-assembled monolayer (SAM) active region, metal bottom contact  fabricated with a nanopore.
Small number of self-assembled molecules (~1000); no defect.
Stable devices  can be loaded into cryogenic systems for measurements at different temperatures.

31. Nanopore process Benzene Ring With a Ligand 3. 1. 4. 2.
1. The silicon wafer
with the nanopore.
2. The molecular
junction.
3. SEM of bottom view
of 1.
4. SEM of the pore.

32. 2’-amino-4-ethynylphenyl-4’-ethynylphenyl- 5’-nitro-1-benzenethiolate
Benzene Ring With a Ligand
J. Chen, M. A. Reed, A. M. Rawlett, and J. M. Tour, "Observation of a Large On-Off Ratio and Negative Differential Resistance in an Electronic Molecular Switch", Science, 286, 1550 (1999).
2’-amino-4-ethynylphenyl-4’-ethynylphenyl- 5’-nitro-1-benzenethiolate
Large reversible switching behavior.
NDR < -380 ohm∙cm2  strong NDR (negative differential resistance) behavior at low temperature.
Peak-to-valley ratio (PVR) = 1030:1.
The spike is found to broaden and shift on the voltage axis with increasing temperature  shift by about 1 V.
Nitro-amine Molecule

33. 2’-amino-4-ethynylphenyl-4’ ethynylphenyl-1-benzenethiolate
Benzene Ring With a Ligand
J. Chen, W. Wang, M. A. Reed, M. Rawlett, D. W. Price, and J. M. Tour, "Room-Temperature Negative Differential Resistance in Nanoscale Molecular Junctions", Appl. Phys. Lett., 77, 1224 (2000).
2’-amino-4-ethynylphenyl-4’ ethynylphenyl-1-benzenethiolate
The "nitro-only" molecule shows NDR at both low and room temperature
Resonant-tunneling peak depend with the temperature
Nitro-only Molecule

34. the rotation properties of the NO2 group
Benzene Ring With a Ligand
M. Di Ventra, S.-G. Kim, S. T. Pantelides, and N. D. Lang, “The temperature effects on the transport properties of molecules,” Phys. Rev. Lett., vol. 86, p. 288, 2001.
A three-benzene-ring molecule without ligands has effectively zero conductivity for all voltages  insertion of ligands produces significant differences in the shape of the I-V curve.
Single benzene ring with an NO2 ligand has the same behavior as the three-ring molecule measured by Chen. Rotation of the ligand, activated by temperature, causes a substantial shift in the resonant-tunneling voltage due to:
the rotation properties of the NO2 group
the different symmetry of the states on the NO2 group.

35. Benzene Ring With a Ligand
The atoms of the NO2 group lie on the same plane defined by the six-carbon ring.
Calculated I-V characteristic at zero temperature:
zero for voltages up to about 0.5 V.
increases almost linearly with external bias
Peak (3.8 V) and valley (4.2 V)
The resonant tunneling condition at zero temperature occurs at 3.8 V, at a higher voltage than in the experiment.

36. Benzene Ring With a Ligand
Contrary to BDT, the π bonding orbital lies close to the left Fermi level  presence NOp that push the π orbital higher in energy.
NOp do not contribute directly to transport.
peak  the π orbital enters in resonance
valley  the resonant tunneling condition is no longer satisfied

37. Benzene Ring With a Ligand
The rotation of the NO2 group can easily be activated by temperature.
In the I-V characteristics for the
90° rotation:
the peak-to-valley ratio is reduced;
the peak occurs at about 1 V less than at zero temperature.
The rotation of the NO2 group pushes the NOp very close to the ring π orbital  the benzene ring π orbital “forced” to reach the resonant tunneling condition at a lower bias.

38. Molecular electronics by the Numbers
Introduction
Transport in a Single Benzene Ring
Three-Terminal Device
Benzene Ring With a Ligand
Conclusion

39. Conclusion
Theory on molecular electronics has now advanced to the point where quantitative predictions can be made about transport in single molecules.
Such calculations are expected to play a major role in the evolution of molecular electronics.
Major advantages of molecular electronics = potential to build devices with the desired properties  exploration the feasibility of such device through molecular design of interfaces.

40. The need to built a three terminal transistor.
Conclusion
Enormous potential advantages of molecular devices, but significant obstacles:
The need to built a three terminal transistor.
Integration onto a microchip.
Heat limit: the fundamental limit for a molecule operating at room temp is about 50 picowatts and that gives roughly 100,000 times more than the number of transistors that can be packed on a chip (without this constraint this number would be much larger).
The lack of an appropriate addressing mechanism for the molecules.