Quantum Confinement Examples

1. Quantum Confinement Examples

2. E Electron Scattering d Inverse Photoemission EVacuum EFermi Photoemission 0 /d k /a = zone boundary Quantization in a Thin Film An energy band with continuous k in the bulk is quantized into N discrete points kn in a thin film withN atomic layers. n = 2d/n kn = 2/n = n  /d N atomic layers with the spacing a = d/n N quantized states with kn≈ n/d (n=1,…,N)

3. layers = graphite Quantization in Thin Graphite Films 1 layer = graphene 2 layers EVacuum EFermi 3 layers Photoemission 0 /d k /a 4 layers N atomic layers with spacing a = d/n :  N quantized states with kn≈ N /d

4. Becomes continuous for N   Quantum Well States in Thin Films Discrete for small N Paggel et al. Science 283, 1709 (1999)

5. n n Counting Quantum Well States Periodic Fermi level crossing of quantum well states with increasing thickness Number of monolayers N

6. n 6 5 4 3 2 1 Quantum Well Oscillations in Electron Interferometers Fabry-Perot interferometer model: Interfaces act like mirrors for electrons. Since electrons have so short wavelengths, the interfaces need to be atomically precise. Himpsel Science 283, 1655 (1999) Kawakami et al. Nature 398, 132 (1999)

7. The Important Electrons in a Metal • Energy  EFermi • Energy Spread  3.5 kBT • Transport (conductivity, magnetoresistance, screening length, ...) • Width of the Fermi function: • FWHM  3.5 kBT • Phase transitions (superconductivity, magnetism, ...) • Superconducting gap: • Eg  3.5 kBTc (Tc= critical temperature)

8. Energy Bands of Ferromagnets Calculation Photoemission data Ni Energy Relative to EF [eV] 0.7 0.9 1.1 k|| along [011] [Å-1 ] States near the Fermi level cause the energy splitting between majority and minority spin bands in a ferromagnet (red and green).

9. Quantum Well States and Magnetic Coupling The magnetic coupling between layers plays a key role in giant magnetoresistance (GMR), the Nobel prize winning technology used for reading heads of hard disks. This coupling oscillates in sync with the density of states at the Fermi level. (Qiu, et al. PR B ‘92)

10. Spin-Polarized Quantum Well States Magnetic interfaces reflect the two spins differently, causing a spin polarization. Minority spins discrete, Majority spins continuous

11. Giant Magnetoresistance & Spin - Dependent Scattering Parallel Spin Filters  Resistance Low Opposing Spin Filters  Resistance High • Filtering mechanisms • Interface: Spin-dependent Reflectivity Quantum Well States • Bulk: Spin-dependent Mean Free Path  Magnetic “Doping”

12. Magnetoelectronics Spin currents instead of charge currents Magnetoresistance = Change of the resistance in a magnetic field Giant Magnetoresistance (GMR): (Metal spacer, here Cu) Tunnel Magnetoresistance (TMR): (Insulating spacer, MgO)

13. Quantum Confinement • Trap particles and restrict their motion • Quantum confinement produces new material behavior/phenomena • “Engineer confinement”- control for specific applications • Structures • Quantum dots (0-D) only confined states, and no freely moving ones • Nanowires (1-D) particles travel only along the wire • Quantum wells (2-D) confines particles within a thin layer (Scientific American)

14. Figure 11: Energy-band profile of a structure containing three quantum wells, showing the confined states in each well. The structure consists of GaAs wells of thickness 11, 8, and 5 nm in Al0.4  Ga0.6  As barrier layers. The gaps in the lines indicating the confined state energies show the locations of nodes of the corresponding wavefunctions. Quantum well heterostructures are key components of many optoelectronic devices, because they can increase the strength of electro-optical interactions by confining the carriers to small regions. They are also used to confine electrons in 2-D conduction sheets where electron scattering by impurities is minimized to achieve high electron mobility and therefore high speed electronic operation.

15. http://www.eps12.kfki.hu/files/WoggonEPSp.pdf

16. http://www.evidenttech.com/pdf/wp_biothreat.pdf http://www.evidenttech.com/why_nano/why_nano.php

17. February 2003 • Industrial Physicist • Magazine • Quantum Dots for Sale • Nearly 20 years after their discovery, semiconductor quantum dots are emerging as a bona fide industry with a few start-up companies poised to introduce products this year. Initially targeted at biotechnology applications, such as biological reagents and cellular imaging, quantum dots are being eyed by producers for eventual use in light-emitting diodes (LEDs), lasers, and telecommunication devices such as optical amplifiers and waveguides. The strong commercial interest has renewed fundamental research and directed it to achieving better control of quantum dot self-assembly in hopes of one day using these unique materials for quantum computing. • Semiconductor quantum dots combine many of the properties of atoms, such as discrete energy spectra, with the capability of being easily embedded in solid-state systems. "Everywhere you see semiconductors used today, you could use semiconducting quantum dots," says Clint Ballinger, chief executive officer of Evident Technologies, a small start-up company based in Troy, New York... http://www.evidenttech.com/news/news.php

18. Quantum Dots for SaleThe Industrial Physicist reports that quantum dots are emerging as a bona fide industry. Evident NanocrystalsEvident's nanocrystals can be separated from the solvent to form self-assembled thin films or combined with polymers and cast into films for use in solid-state device applications. Evident's semiconductor nanocrystals can be coupled to secondary molecules including proteins or nucleic acids for biological assays or other applications. http://www.evidenttech.com/why_nano/docs.php http://www.evidenttech.com/index.php

19. EviArrayCapitalizing on the distinctive properties of EviDots™, we have devised a unique and patented microarray assembly. The EviArray™ is fabricated with nanocrystal tagged oligonucleotide probes that are also attached to a fixed substrate in such a way that the nanocrystals can only fluoresce when the DNA probe couples with the corresponding target genetic sequence. http://www.evidenttech.com/why_nano/docs.php

20. EviDots - Semiconductor nanocrystalsEviFluors- Biologically functionalized EviDotsEviProbes- Oligonucleotides with EviDotsEviArrays- EviProbe-based assay system Optical Transistor- All optical 1 picosecond performanceTelecommunications- Optical Switching based on EviDotsEnergy and Lighting- Tunable bandgap semiconductor

21. Why nanowires? “They represent the smallest dimension for efficient transport of electrons and excitons, and thus will be used as interconnects and critical devices in nanoelectronics and nano-optoelectronics.” (CM Lieber, Harvard) General attributes & desired properties • Diameter – 10s of nanometers • Single crystal formation -- common crystallographic orientation along the nanowire axis • Minimal defects within wire • Minimal irregularities within nanowire arrays http://www.me.berkeley.edu/nti/englander1.ppt

22. Nanowire fabrication • Challenging! • Template assistance • Electrochemical deposition • Ensures fabrication of electrically continuous wires since only takes place on conductive surfaces • Applicable to a wide range of materials • High pressure injection • Limited to elements and heterogeneously-melting compounds with low melting points • Does not ensure continuous wires • Does not work well for diameters < 30-40 nm • CVD • Laser assisted techniques http://www.me.berkeley.edu/nti/englander1.ppt

23. Magnetic nanowires • Important for storage device applications • Cobalt, gold, copper and cobalt-copper nanowire arrays have been fabricated • Electrochemical deposition is prevalent fabrication technique • <20 nm diameter nanowire arrays have been fabricated Cobalt nanowires on Si substrate (UMass Amherst, 2000) http://www.me.berkeley.edu/nti/englander1.ppt

24. Silicon nanowire CVD growth techniques • With Fe/SiO2 gel template (Liu et al, 2001) • Mixture of 10 sccm SiH4 & 100 sccm helium, 5000C, 360 Torr and deposition time of 2h • Straight wires w/ diameter ~ 20nm and length ~ 1mm • With Au-Pd islands (Liu et al, 2001) • Mixture of 10 sccm SiH4 & 100 sccm helium, 8000C, 150 Torr and deposition time of 1h • Amorphous Si nanowires • Decreasing catalyst size seems to improve nanowire alignment • Bifurcation is common • 30-40 nm diameter and length ~ 2mm http://www.me.berkeley.edu/nti/englander1.ppt

25. Template assisted nanowire growth • Create a template for nanowires to grow within • Based on aluminum’s unique property of self organized pore arrays as a result of anodization to form alumina (Al2O3) • Very high aspect ratios may be achieved • Pore diameter and pore packing densities are a function of acid strength and voltage in anodization step • Pore filling – nanowire formation via various physical and chemical deposition methods http://www.me.berkeley.edu/nti/englander1.ppt

26. Al2O3 template preparation • Anodization of aluminum • Start with uniform layer of ~1mm Al • Al serves as the anode, Pt may serve as the cathode, and 0.3M oxalic acid is the electrolytic solution • Low temperature process (2-50C) • 40V is applied • Anodization time is a function of sample size and distance between anode and cathode • Key Attributes of the process (per M. Sander) • Pore ordering increases with template thickness – pores are more ordered on bottom of template • Process always results in nearly uniform diameter pore, but not always ordered pore arrangement • Aspect ratios are reduced when process is performed when in contact with substrate (template is ~0.3-3 mm thick) http://www.me.berkeley.edu/nti/englander1.ppt

27. The alumina (Al2O3) template (T. Sands/ HEMI group http://www.mse.berkeley.edu/groups/Sands/HEMI/nanoTE.html) alumina template Si substrate http://www.me.berkeley.edu/nti/englander1.ppt 100nm (M. Sander)

28. Bi2Te3 nanowire unfilled pore alumina template Electrochemical deposition • Works well with thermoelectric materials and metals • Process allows to remove/dissolve oxide barrier layer so that pores are in contact with substrate • Filling rates of up to 90% have been achieved http://www.me.berkeley.edu/nti/englander1.ppt (T. Sands/ HEMI group http://www.mse.berkeley.edu/groups/Sands/HEMI/nanoTE.html)

29. Template-assisted, Au nucleated Si nanowires • Gold evaporated (Au nanodots) into thin ~200nm alumina template on silicon substrate • Ideally reaction with silane will yield desired results • Need to identify equipment that will support this process – contamination, temp and press issues • Additional concerns include Au thickness, Au on alumina surface, template intact vs removed Au dots Au 100nm 1µm http://www.me.berkeley.edu/nti/englander1.ppt template (top) (M. Sander)

30. Nanometer gap between metallic electrodes Before breaking SET with a 5nm CdSe nanocrystal After breaking Electromigration caused by electrical current flowing through a gold nanowire yields two stable metallic electrodes separated by about 1nm with high efficiency. The gold nanowire was fabricated by electron-beam lithography and shadow evaporation. http://www.lassp.cornell.edu/lassp_data/mceuen/homepage/Publications/EMPaper.pdf

31. Quantum and localization of nanowire conductance • Nanoscale size exhibits the following properties different from those found in the bulk: • quantized conductance in point contacts and narrow channels whose characteristics (transverse) dimensions approach the electronic wave length • Localization phenomena in low dimensional systems • Mechanical properties characterized by a reduced propensity for creation and propagation of dislocations in small metallic samples. • Conductance of nanowires depend on • the length, • lateral dimensions, • state and degree of disorder and • elongation mechanism of the wire. http://dochost.rz.hu-berlin.de/conferences/conf1/PDF/Pascual.pdf

32. Short nanowire “Long” nanowire Conductance during elongation of short wires exhibits periodic quantization steps with characteristic dips, correlating with the order-disorder states of layers of atoms in the wire. The resistance of “long” wires, as long as 100-400 A exhibits localization characterization with ln R(L) ~ L2 http://dochost.rz.hu-berlin.de/conferences/conf1/PDF/Pascual.pdf

33. Electron localization At low temperatures, the resistivity of a metal is dominated by the elastic scattering of electrons by impurities in the system. If we treat the electrons as classical particles, we would expect their trajectories to resemble random walks after many collisions, i.e., their motion is diffusive when observed over length scales much greater than the mean free path. This diffusion becomes slower with increasing disorder, and can be measured directly as a decrease in the electrical conductance. When the scattering is so frequent that the distance travelled by the electron between collisions is comparable to its wavelength, quantum interference becomes important. Quantum interference between different scattering paths has a drastic effect on electronic motion: the electron wavefunctions are localized inside the sample so that the system becomes an insulator. This mechanism (Anderson localization) is quite different from that of a band insulator for which the absence of conduction is due to the lack of any electronic states at the Fermi level. http://www.cmth.ph.ic.ac.uk/derek/research/loc.html

34. Molecular nanowire with negative differential resistance at room temperature http://research.chem.psu.edu/mallouk/articles/b203047k.pdf

35. Resistivity of ErSi2 Nanowires on Silicon ErSi2 nanowires on a clean surface of Si(001). Resistance of nanowire vs its length. ErSi2 nanowire self-assembled along a <110> axis of the Si(001) substrate, having sizes of 1-5nm, 1-2nm and <1000nm, in width, height, and length, respectively. The resistance per unit length is 1.2M/nm along the ErSi2 nanowire. The resistivity is around 1cm, which is 4 orders of magnitude larger than that for known resistivity of bulk ErSi2, i.e., 35 cm. One of the reasons may be due to an elastically-elongated lattice spacing along the ErSi2 nanowire as a result of lattice mismatch between the ErSi2 and Si(001) substrate. http://www.riken.go.jp/lab-www/surf-inter/tanaka/gyouseki/ICSTM01.pdf

36. Last stages of the contact breakage during the formation of nanocontacts. Conductance current during the breakage of a nanocontact. Voltage difference between electrodes is 90.4 mV Electronic conductance through nanometer-sized systems is quantized when its constriction varies, being the quantum of conductance, Go=2 e2/h, where e is the electron charge and h is the Planck constant, due to the change of the number of electronic levels in the constriction. The contact of two gold wire can form a small contact resulting in a relative low number of eigenstates through which the electronic ballistic transport takes place. http://physics.arizona.edu/~stafford/costa-kraemer.pdf

37. Setup for conductance quantization studies in liquid metals. A micrometric screw is used to control the tip displacement. Evolution of the current and conductance at the first stages of the formation of a liquid metal contact. The contact forms between a copper wire and (a) mercury (at RT) and (b) liquid tin (at 300C). The applied bias voltage between tip and the metallic liquid reservoir is 90.4 mV. http://physics.arizona.edu/~stafford/costa-kraemer.pdf

38. Conductance transitions due to mechanical instabilities for gold nanocontacts in UHV at RT: (a) between 0 and 1 quantum channel. (b) between 0 and 2 quantum channels. Conductance transitions due to mechanical instabilities for gold nanocontacts in UHV at RT: Transition from nine to five and to seven quantum channels. http://physics.arizona.edu/~stafford/costa-kraemer.pdf