1. Nanostructured materials 0D: quantum dots 1D: Nanowires 2D: superlattices and heterostructures Nano-Photonics Magnetic nanostructures Magnetic nanostructures Nanofluidic devices and surfaces Nanofluidic devices and surfaces Copyright Stuart Lindsay 2009

2. Nanostructured materials derive their special properties from having one or more dimensions made small compared to a length scale critical to the physics of the process. Copyright Stuart Lindsay 2009

3. Development of electronic properties as a function of cluster size Each band has a width that reflects the interaction between atoms, with a bandgap between the conduction and the valence bands that reflects the original separation of the bonding ad antibonding states.

4. Electronic DOS and dimensionality Size effects are most evident at band edges (semiconductor NPs). DOS (dn/dE) as a function of dimensionality. 3D case is for free particles. Copyright Stuart Lindsay 2009

5. k-space is filled with an uniform grid of points each separated in units of 2π/L along any axis. The volume of k-space occupied by each point is: k-space r-space: k-space:

6. 3D DOS Copyright Stuart Lindsay 2009 Density of states in a volume V per unit wave vector: For a free electron gas:

7. 2D DOS Constant for each electronic band Copyright Stuart Lindsay 2009

8. 8 1D DOS At each atomic level, the DOS in the 1D solid decreases as the reciprocal of the square root of energy. Copyright Stuart Lindsay 2009

9. 0 D DOS In zero dimensions the energy states are sharp levels corresponding to the eigenstates of the system. Copyright Stuart Lindsay 2009

10. 0D Electronic Structures: Quantum Dots Light incident on a semiconductor at an energy greater than the bandgap forms an exciton, i.e. an electron-hole quasiparticle, representing a bound state.

11. Excitons can be treated as “Bohr atoms” Electronic energy gap When the size of the nanoparticle approaches that of an exciton, size quantization occurs. Intrinsic band gap NP radius electrostatic correction

12. 1-D Electronic Structures: Carbon Nanotubes Wrapping vector Wrapping vector: Diameter: The folding of the sheet controls the electronic properties of the nanotubes.

13. p z electrons hybridize to form π e π* valence and conduction bands that are separated by an energy gap of about 1V (semiconductor). For certain high simmetry directions (the K points in the reciprocal lattice) the material behaves like a metal. Conduction in CNTs Apex: at this point CB meets VB for graphene sheets (metal-like behavior) Allowed states wave vector perpendicular to the CNT long axis

14. D = diameter of the nanotube wave vector perpendicular to the CNT long axis The component of the wave vector perpendicular to the CNT long axis is quantized Metallic behavior: the allowed values of intersect the k points at which the conduction and valence bands meet.. CNTs can be either metals or semiconductors depending on their chirality.

15. Field effect transistor made from a single semiconducting CNT connecting source and drain connectors.

16. Semiconductor Nanowires Ga-P/Ga-As p/n nanojunctions Copyright Stuart Lindsay 2009 (IOP) TEM images Line profiles of the composition through the junction region

17. 17 2D Electronic Structures: superlattices and heterostructures Variation of electron energy in an MBE grown superlattice Superlattice: alternating layers of small bandgap semiconductors (GaAs) interdispersed with layers of wide bandgap semiconductors (GaAlAs). The thickness of each layer is considerably smaller than the electron mean free path.

18. Band splitting into sub-bands Modulation of the structure on the length scale d (thickness of the layer in the superlattice) gives rise to the formation of new bands inside the original Brillouin zone. Electrons can pass freely from one small bandgap region to another without scattering.

19. Resonant tunneling through different sub-bands Negative differential resistance Negative differential resistance: electrons slow down with increasing bias when approaching the first sub-band boundary (≈20mV). Low scattering in 2-D means reaching zone boundaries at reasonable fields, accelerating electrons at the band edges.

20. Quantum Hall resistance of 2D electron gas Magnetic quantization in 2D electron gas A series of steps in the Hall resistance corresponding exactly at twice the Landauer frequency were observed. Copyright Stuart Lindsay 2009 : Electrons in a layer are accelerated by an applied magnetic field at a frequency: von Klitzing resistance Nobel in Physics 1985

21. Confinement on optical length scales Plasmonics plasma resonance Small (d<<λ) metal particles exhibit a phenomenon called plasma resonance, i.e. plasma-polariton resonance of the free electrons in the metal surface. resonant antennas A resonant metal particle can capture light over a region of many wavelengths in dimension even if the particle itself is only a fraction of a wavelength in diameter (resonant antennas). Free electrons in metals polarize excluding electric fields from the interior of the metal showing a negative dielectric constant. The polarizability of a sphere of volume V and dielectric constant ε r is:

22. For Ag  =-2 at 400 nm, but resonance moves to 700 nm for a/b=6. The resonance is tunable throughout the visible by engineering the particle shape. When ε r →-2  →∞ For d<<λ the resonant frequency is independent on the particle size, but depends on particle shape. For a prolate spheroid of eccentricity e: where:

23. Plasmon enhanced optical absorption Placing a chromophore near a resonant metal nanoparticle: Electric field surrounding a resonant nanoparticle (E=E z ) dye layer Enhanced fluorescence Reduced decay times

24. The increased absorption cross section is accompanied by a decrease in fluorescence lifetime. The plasmon resonance results in local enhancement of the electric field: doubling the electric field quadruples the light absorption. A single dye molecule is only visible in fluorescence when the gold NP passes over it. Enhanced fluorescence

25. 25 Photonic engineering In quantum dots all of available gain is squeezed into a narrow bandwidth. Performance of a solid-state laser material in various geometries. Lasing effect: the gain of the laser medium must exceed the cavity losses. Dashed lines: density of states Modern semiconductor lasers are made from semiconductors heterostructures designed to trap excited electrons and holes in the optically active part of the laser.3D 2D 1D 0D

26. Quantum dot laser The QDs are chosen to have a bandgap that is smaller than that of the medium. Excitons are stabilized in the optical cavity, because the electrons are confined to the low- energy part of the conduction band and the holes are confined to the top of the valence band. Quantum dots of the right size can place all of the exciton energies at the right value for lasing. Optical cavity

27. Photonic crystals: concentrating photon energy into bands Copyright Stuart Lindsay 2009 Opalescent materials from colloidal crystal (polystyrene latex beads) The concentration of modes into bands results in an increase in the density of states in the allowed bands, particularly near bands edges. Optical wavelengths require that materials should be structured on the half-micron scale. Opalescence comes from sharp (Bragg) reflection in only certain directions.

28. Bragg’s law hkl = Miller indices of the colloidal crystal lattice n = refraction index d hkl = spacing between Bragg planes in the hkl direction For a given spacing in some direction in the colloidal crystal lattice, the wavelength of the reflected beam is given by the Bragg law. Colloidal particles spaced with polymer spacers

29. 3D Photonic crystals Require “non spherical” atoms to give zero “structure factor” in directions where propagation must be suppressed Photonic crystals convert heat into light! See Optics Letters 28 1909, 2003. Optical dispersion in a crystal made by non spherical atoms. A 3D bandgap appear when structures are designed to have zero intensity in directions of allowed Bragg reflections. Repeat period is on the order of 30μm (3D optical bandgap in the far IR, limit of today technology).

30. Magnetic properties Diamagnetism Diamagnetism: Zero-spin systems give rise to circulating currents that oppose the applied field (negative magnetic susceptibility, Larmor diamagnetism). Paramagnetism: Paramagnetism: Free-electrons are magnetically polarized by an external magnetic field (positive magnetic susceptibility, Pauli paramagnetism). Ferromagnetism: Ferromagnetism: Spontaneous magnetic ordering due to electron-electron interactions. Antiferromagnetism: polarization alternates from atom to atom. No net macroscopic magnetic moment arises.

31. Magnetic Interactions Exchange (electron-electron) interaction (many-particle wavefunction antisymmetry) - atomic scales Dipole-dipole interactions between locally ordered magnetic regions Dipole interaction energy grows with the volume of the ordered region. The size of the individual domains is set by a competition between volume and surface energy effects. - hundreds of atoms to micron scales Magnetic Anisotropy energy Magnetization interacts with angular momentum of the atoms in the crystal. – many microns

32. Super-paramagnetic particles Ferromagnetic domains, created by d-electrons exchange interactions, develop only when a cluster of iron atoms reaches a critical size (ca. microns). The magnetic moment per atom decreases toward the bulk value as cluster size is increased. Stable domains cannot be established in crystals that are smaller than the intrinsic domain size.

33. Small particles can have very high magnetic susceptibility with permanent magnetic dipole. super-paramagnetism Small clusters consisting of a single ferromagnetic domain follow the applied field freely (super-paramagnetism). The magnetic susceptibility of superparamagnetic particles is orders of magnitude larger than bulk paramagnetic materials. Ferromagnetic limit Magnetic response for particles of increasing size (Gd clusters)

34. Superparamagnetic separations Magnetic sorting of cells labeled with superparamagnetic beads Induced magnetic moment: Magnetic force: Particle were pulled to point of highest field gradient Copyright Stuart Lindsay 2009 MFS: microfabricated ferromagnetic strips

35. Giant Magnetoresistance giant magnetoresistance sensor. Magnetic hard drives are based on a nanostructured device, called giant magnetoresistance sensor. Albert Fert, Peter Grünbers Nobel Prize in Physics 2007 Hitachi hard drive reading head Co, magnetic layer NiFe alloy, magnetic layer An easily re-alignable magnetization Cu, electrically conducting layer Layers have a width that is smaller than electron scattering length. The magnetization on the surface of the disk can be read out as fluctuations in the resistance of the conducting layer.

36. For antiparallel magnetic layers both spin polarizations are scattered, giving rise to super-resistance (II). Giant magnetoresistance occurs when the magnetic layers above and below the conductor are magnetized in opposite direction. Electron scattering in magnetic media is strongly dependent on spin polarization. When magnetic layers are parallely magnetized, only one spin polarization is scattered (I,III). III III

37. Nanofluidics Fluid flow in small structures is entirely laminar and dominated by the chemical boundaries of the channel. Reynolds number Reynolds number (Re), a dimensionless number quantifying the ratio of inertial to viscous forces that act on the volume of a liquid: viscosity density channel narrowest dimension Re >> 1: turbulence regime Re << 1: viscous regime

38. Re in a L=100nm channel with = 1mm/s not exceeds 10 -4 Flow in nanoscale channels is dominated by viscosity! Fluids do not mix in a nanofluidic device. The chemistry of the interface becomes critical and aqueous fluids will not generally enter a channel with hydrophobic surfaces. Kinematic viscosity (25°C) For water: ν =1·10 -6 m 2 s -1 (25°C)

39. 1-D Nanochannel devices. A significant stretching of large molecules can occur in a large ion gradient or electric field in a channel that is comparable to the radius of giration of the molecule. Ex. Ex. A 17μm DNA (fully stretched length) is equivalent to 340 freely jointed segments each of 5 nm length. The relative giration radius is: It can be significantly extended in a channel of 100 nm diameter, owing to the strong interaction between the fluid and the wall.

40. Time Mg ions introduced DNA + cutting enzymes introduced Microchannels distance DNA cutting starts Fluorescently labeled DNA at various times DNA is introduced through the microchannel and then transported through the nanochannels by an applied voltage. Continous time course of the cutting process

41. Nanopores: 0D fluidic nanostructure 2-nm diameter holes: only a single DNA molecule can pass through it at a given time. The passage of DNA molecules can be measured by the drops in currents that occur when a single DNA molecule occludes the hole. Polystyrene bead electrophoresis Optical tweezer

42. Flow in Carbon Nanotubes 42 The measured rate of water flow through 2nm-diameter CNTs was found to be 1000 times higher than predicted by classical hydrodynamics. A. A.Fabrication of a layer of CNTs penetrating a silicon nitride membrane; B. and C. SEM images before and after filling with silicon nitride; D. Individual finished device: E. An array of devices

43. 2D Nanostructures: Superhydrophobic surfaces contact angle The angle formed by a tangent to a flat surface of a drop of water at the point of contact (contact angle) is given in terms of the interfacial energies of the system by the Young equation: γ AB = air/surface interfacial tension γ AC = water/surface interfacial tension γ BC = air/water interfacial tension

44. Si NanowiresCoated Si surface (planar) Coated nanostructured surface (rough) Roughening on the nanoscale can greatly increase hydrophobicity. Water/surface repulsion (large interfacial tension) Water drop