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Department of Electronics

Nanoelectronics 14. Atsufumi Hirohata. Department of Electronics. 12:00 28/ February/ 2014 Friday (D/ L 002). Quick Review over the Last Lecture. Contents of Nanoelectonics. I. Introduction to Nanoelectronics (01) 01 Micro- or nano-electronics ?. II. Electromagnetism (02 & 03)

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Department of Electronics

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  1. Nanoelectronics 14 Atsufumi Hirohata Department of Electronics 12:00 28/February/2014 Friday (D/L 002)

  2. Quick Review over the Last Lecture

  3. Contents of Nanoelectonics I. Introduction to Nanoelectronics (01) 01 Micro- or nano-electronics ? II. Electromagnetism (02 & 03) 02 Maxwell equations 03 Scholar and vector potentials III. Basics of quantum mechanics (04 ~ 06) 04 History of quantum mechanics 1 05 History of quantum mechanics 2 06 Schrödinger equation IV. Applications of quantum mechanics (07, 10, 11, 13 & 14) 07 Quantum well 10 Harmonic oscillator 11 Magnetic spin 13 Quantum statistics 1 14 Quantum statistics 2 V. Nanodevices (08, 09, 12, 15 ~ 18) 08 Tunnelling nanodevices 09 Nanomeasurements 12 Spintronic nanodevices

  4. 14 Quantum Statistics 2 • Boson • Fermion • Bose-Einstein condensation • Fermi degeneracy • Fermi liquid • Ideal quantum gas

  5. Fermions / Bosons If electrons were bosons... If photons were fermions... If protons / neutrons were bosons... In particle physics, Fermions : 1 fermion occupies 1 quantum state (Fermi-Dirac statistics) Particles, which consist of materials; e.g., protons, neutrons and electrons Bosons : Several bosons occupy 1 quantum state (Bose-Einstein statistics) Particles, which transfer particle-interactions; e.g., photons and gluons * http://www.wikipedia.org/

  6. Fermions / Bosons (Cont'd) Particles consisting of even numbers of fermions : bosons e.g., He 4 Particles consisting of odd numbers of fermions : fermions e.g., He 3 * http://www.sci.osaka-cu.ac.jp/phys/ult/invitation/helium/helium.html

  7. Low-Temperature Generation By using 3-He and 4-He, a dilution refrigerator is realised (< 100 mK) : * http://www.sci.osaka-cu.ac.jp/phys/ult/invitation/cryo/dr.html

  8. Dilution Refrigerator Oxford Instruments SM4000-8 with Heliox TL : Temperature : < 350 mK Magnetic field : ± 8 T

  9. Bose-Einstein Condensation - He 3 superfluid In boson systems, all bosons fall into the lowest energy state at very low temperature.  Bose-Einstein condensation e.g., superfluid of He 4 (1938 Fritz W. London) e.g., superfluid of He 3 (1972 Douglas D. Osheroff, Robert C. Richardson and David M. Lee) 2 He-3 fermions form a Cooper pair  quasi-particle  superconducting state * http://photos.aip.org/

  10. Bose-Einstein Condensation - Rb atom In 1995, B-E condensation observed in Rb atom by Eric A. Cornell and Carl E. Wieman :  Reduced speed by photon-momentum absorption * http://www.wikipedia.org/ ** http://jila.colorado.edu/content/bec-transporter *** R. Baierlein, Thermal Physics (Cambridge University Press, Cambridge, 1999).

  11. Bose-Einstein Condensation - Na atom In 1995, Wolfgang Ketterle also observed B-E condensation in Na atom : * http://www.wikipedia.org/ ** http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm

  12. Bose-Einstein Condensation - Superconductor Cooper pair in a superconductor : * http://www.phys.shimane-u.ac.jp/mutou_lab/ ** http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/coop.html

  13. Superconductor and Heavy-Electron System Heavy-electron system : Cooper pair in a superconductor :  Lattice deformation  Quadra-pole rigid lattice  Dipole Cooper pair  Mott insulator * http://www.lanl.gov/news/index.php/fuseaction/1663.article/d/20075/id/10392 ** http://www.lorentz.leidenuniv.nl/~pjhdent/

  14. Magnetic Quantum Critical Point Fermi liquid : Phase diagram : Mott insulator  Conventional metals Frustrated spin system : * http://physicsworld.com/cws/article/print/3504/1/pw1501092 ** http://kotai2.scphys.kyoto-u.ac.jp/index.php?Research *** http://www.jst.go.jp/kisoken/presto/complete/soshiki/theme/first_r/07nantoh/link011.htm

  15. Fermi Liquid In 2D and 3D, Landau proposed electron behaviour as liquid : Electron states can be defined by the competition among ； • Kinetic energy  Liquid • Coulomb interaction  Solid crystal • Potential randomness  Amorphous glass At very low temperature, Coulomb interaction becomes negligible.  Fermi liquid

  16. Fermi Degeneracy T ≠ 0 Fermi-Dirac distribution : E T = 0 EF Pauli exclusion principle  Fermi degeneracy • Free electrons in a metal at room temperature • Higher energy states are occupied. • Heat capacity becomes smaller than expected from the classical model. • Magnetic susceptibility becomes smaller (Pauli paramagnetism). • Star cores even at 10 9 K • Very high density  degeneracy pressure • After nuclear fusion, • white dwarf stars by electron degeneracy pressure • neutron stars by electron degeneracy pressure  black holes

  17. Ideal Quantum Gas E T Equation of states for ideal gas : where P : gas pressure, V : volume, N : number of particles, kB : Boltzman constant and T : temperature Energy E satisfies : (classical model) Fermions : Fermions Compared with the classical model E increases / P increases Bosons = Repulsive force between particles  Pauli exclusion law Bosons : Compared with the classical model = Attractive force between particles E decreases / P decreases

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