Five-Lecture Course on the Basic Physics of Nanoelectromechanical Devices

1. Five-Lecture Course on the Basic Physics of Nanoelectromechanical Devices • Lecture 1: Introduction to nanoelectromechanical systems (NEMS) • Lecture 2: Electronics and mechanics on the • nanometer scale • Lecture 3: Mechanically assisted single electronics • Lecture 4: Quantum nano-electro-mechanics • Lecture 5: Superconducting NEM devices

2. Lecture 3: Mechanically Assisted Single Electronics Outline • Electric charge quantization in solids (important historical events) • Self-assembled nanocomposites – new materials with special electronic and mechanical properties • Nanoelectromechanicalcoupling due to tunneling of single electrons • Shuttlingof single electrons in NEM-SET devices • Electromechanics of suspended carbon nanotubers(CNT)

3. Lecture 3: Electronics and Mechanics on the Nanometer Scale Millikan’s Oil-Drop Experiment(Nobel Prize in 1923) The electronic charge as a discrete quantity: In 1911, Robert Millikan of the University of Chicago published* the details of an experiment that proved beyond doubt that charge was carried by discrete positive and negative entities of equal magnitude, which he called electrons. The charge on the trapped droplet could be altered by briefly turning on the X-ray tube. When the charge changed, the forces on the droplet were no longer balanced and the droplet started to move. *Phys. Rev. 32, 349-397 (1911) See also http://nobelprize.org/physics/laureates/1923/press.html

4. Electrically Controlled Single-Electron Charging Lecture 3: Electronics and Mechanics on the Nanometer Scale Experiment: L.S.Kuzmin, K.K.Likharev, JETP Lett. 45, 495(1987): T.A.Fulton, C.J.Dolan, PRL, 59,109(1987); L.S.Kuzmin, P.Delsing, T.Claeson, K.K.Likharev, PRL,62,2539(1989); P.Delsing, K.K.Likharev, L.S.Kuzmin & T.Claeson, PRL, 63, 1861, (1989) Dot e2/C Theory: R.Shekhter., Soviet Physics JETP 36, 747(1973); I.O.Kulik, R.Shekhter, Soviet Physics JETP 41, 308(1975); D.V.Averin, K.K.Likharev, J.LowTemp.Phys. 62, 345 (1986)

5. Gate Repulsion at the dot Electron Dot Cost Attraction to the gate At the energy cost vanishes ! Lecture 3: Electronics and Mechanics on the Nanometer Scale Coulomb Blockade Single-electron transistor (SET)

6. Lecture 3: Electronics and Mechanics on the Nanometer Scale Single Molecular Transistors with OPV5 and Fullerenes Nature 425, 628 (2003)

7. Self-Assembled Metal-Organic Composites Lecture 3: Electronics and Mechanics on the Nanometer Scale Molecular manufacturing – a way to design materials on the nanometer scale Encapsulated 4nm Au particles self-assembled into a 2D array supported by a thin film, Anders et al., 1995 Scheme for molecular manufacturing

8. Basic Characteristics Materials properties: Electrical – heteroconducting Mechanical – heteroelastic Electronic features: Quantum coherence Coulomb correlations Electromechanical coupling Lecture 3: Electronics and Mechanics on the Nanometer Scale

9. Lecture 3: Electronics and Mechanics on the Nanometer Scale Nanoelectromechanical Devices Quantum ”bell” Single C60Transistor A. Erbe et al., PRL 87, 96106 (2001); D. Scheible et al. NJP 4, 86.1 (2002) H. Park et al., Nature 407, 57 (2000) Here: Nanoelectromechanics caused by or associated with single-charge tunneling effects

10. CNT-Based Nanoelectromechanics Lecture 3: Electronics and Mechanics on the Nanometer Scale A suspended CNT has mechanical degrees of freedom => study electromechanical effects on the nanoscale. B. J. LeRoy et al., Nature 432, 371 (2004) V. Sazonova et al., Nature 431, 284 (2004)

11. Lecture 3: Electronics and Mechanics on the Nanometer Scale Fullerene Empty CNT

12. Shuttling of Single Electrons in NEM-SET Devices Lecture 3: Electronics and Mechanics on the Nanometer Scale 12/35

13. Millikan’s Set-up on a Nanometer Length Scale Lecture 3: Electronics and Mechanics on the Nanometer Scale If W exceeds the dissipated power an instability occurs Gorelik et al., PRL, 80, 4256(1998)

14. Lecture 3: Electronics and Mechanics on the Nanometer Scale The Electronic Shuttle

15. Circuit Model for the Shuttle Lecture 3: Electronics and Mechanics on the Nanometer Scale Electrostatic energy of the charged grain Electronic tunneling rate:

16. Formulation of the Problem Lecture 3: Electronics and Mechanics on the Nanometer Scale

17. Nanoelectromechanical Instability Lecture 3: Electronics and Mechanics on the Nanometer Scale Weak electromechanical coupling:

18. W pumping dissipation Lecture 3: Electronics and Mechanics on the Nanometer Scale Stable Shuttle Vibrations

19. Different Scenarios for a Shuttle Instability Lecture 3: Electronics and Mechanics on the Nanometer Scale ”HARD” instability ”SOFT” instability Only onestable mechanical regime is possible Tworegimes of locally stable mechanical operations

20. ”Soft” Onset of Shuttle Vibrations Lecture 3: Electronics and Mechanics on the Nanometer Scale

21. ”Hard” Onset of Shuttle Vibrations Lecture 3: Electronics and Mechanics on the Nanometer Scale

22. Shuttling of Electronic Charge Lecture 3: Electronics and Mechanics on the Nanometer Scale

23. Lecture 3: Electronics and Mechanics on the Nanometer Scale Electromechanical Instabilities of Suspended CNTs L. M. Jonsson et al. Nano Lett. 5,1165 (2005)

24. Model Lecture 3: Electronics and Mechanics on the Nanometer Scale • The model system. • An STM-tip, biased at–V/2 is placed above a suspended CNT with diameter Dand length L. • One end of the nanotube is connected to an electrode biased at V/2. • A gate electrode with potential Vg is used to control the electronic levels on the nanotube. • Only deformation of the tube in the plane is considered and the shape of the nanotube is given by u(z; t). • The nanotube is considered to be a metallic island between the STM and the electrode. • Tunnelling from the STM to the nanotube depends on tube deformation whereas the tunneling matrix elements connecting the nanotube and the electrode are constant.

25. Formulation of the Problem: Mechanics of Suspended CNT Lecture 3: Electronics and Mechanics on the Nanometer Scale E-the Youngs modulus; I-moment of inertia of the cross section Boundary conditions: Ansatz: Vibrational modes:

26. Normal Vibrations Lecture 3: Electronics and Mechanics on the Nanometer Scale We include a finite number of eigenmodes (flexural vibrations) The frequencies of the modes are determined by The fundamental mode Mechanics is described by a collection of harmonic oscillators Frequencies of different modes are incommensurable!

27. Formulation of the Problem: Electrostatics of Suspended CNT Lecture 3: Electronics and Mechanics on the Nanometer Scale The electrostatic energy Ec should be included in the Hamiltonian of the vibrating CNT.A deformation u(z,t) causes an extra charge Q on the tube. To linear order in Q the electrostatic energy Ec({u(z,t)},Q) is: In the limit of an STM size d much smaller than the length L of the CNT one can model K(z) as: (E - electric field in the vicinity of the STM tip)

28. Nanoelectromechanics of Suspended CNTModifiedcircuitmodel for the charge dynamics Lecture 3: Electronics and Mechanics on the Nanometer Scale • Equation for the mechanical vibrations: • Coupling of electrons to a set of vibrators • Vibrations in different modes are coupled • γ- damping of the mechanical vibrations

29. Nanoelectromechanical Instability Lecture 3: Electronics and Mechanics on the Nanometer Scale • Linearization with respect to Xn(t) • Weakelectromechanicalcoupling: • Thedynamics of different vibration modes decouple

30. Optimal Conditions for NEM Instability Lecture 3: Electronics and Mechanics on the Nanometer Scale • Optimal conditions: • Γ = ω1 • Symmetric tunneling rates

31. Instabilities of Different Modes Lecture 3: Electronics and Mechanics on the Nanometer Scale In the classical limit we find solutions on the form δn > 0 implies an instability. Threshold dissipation for mode n: L. M.Jonssonet al., New J.Phys. 9, 90 (2007) Different modes can be treated independently in the weak electromechanical limit!

32. Development of a Multimode InstabilityClassical approach Lecture 3: Electronics and Mechanics on the Nanometer Scale - Each mode is described by a driven and damped h.o. - Kinetic equation for charge Weak NEM coupling: Low frequency limit:

33. Nonlinear Multimode Dynamics Lecture 3: Electronics and Mechanics on the Nanometer Scale Ansatz + Averaging Development of two unstable modes

34. Selective Pumping of N Vibrational Modes Lecture 3: Electronics and Mechanics on the Nanometer Scale Evolution of the vibrations is described by vector: Only N points in the vector space are attracting focuses: THEOREM If at t=0 the condition holds: then for t>0 monotonically increases approaching value: and other amplitudes decay exponentially when t→∞:

35. Self-organization of Shuttle Vibrations with Three Unstable Modes Lecture 3: Electronics and Mechanics on the Nanometer Scale