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Department of Electronics

Nanoelectronics 02. Atsufumi Hirohata. Department of Electronics. 12:00 17/January/2014 Friday (D/L 002). Quick Review over the Last Lecture. Nano-scale miniaturisation : reduction of ( effective electron paths ) reduction of ( electron scattering )

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Department of Electronics

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  1. Nanoelectronics 02 Atsufumi Hirohata Department of Electronics 12:00 17/January/2014 Friday (D/L 002)

  2. Quick Review over the Last Lecture • Nano-scale miniaturisation : • reduction of ( effective electron paths ) • reduction of ( electron scattering ) • ( faster ) operation • nano-fabrication ; ( complicated ) processes ( higher ) cost ( larger ) distributions in device properties • ( leakage ) current • ( Joule ) heating • electron ( confinement ) • Electron transport : • ( diffusive ) transport  ( electron scattering ) • ( ballistic ) transport  ( negligible electron scattering )

  3. Contents of Nanoelectronics I. Introduction to Nanoelectronics (01) 01 Micro- or nano-electronics ? II. Electromagnetism (02 & 03) 02 Maxwell equations 03 Scalar and vector potentials III. Basics of quantum mechanics (04 ~ 06) IV. Applications of quantum mechanics (07, 10, 11, 13 & 14) V. Nanodevices (08, 09, 12, 15 ~ 18) Lecture notes and files can be found at http://www-users.york.ac.uk/~ah566/

  4. 02 Maxwell Equations • Electromagnetic field • Origins of an electromagnetic field • Boundary conditions of an electromagnetic field

  5. Maxwell Equations Maxwell equations are proposed in 1864 : E : electric field, B : magnetic flux density, H : magnetic field, D : electric flux density, J : current density and  : charge density Supplemental equations for materials :  Definition of an electric flux density  Definition of a magnetic flux density  Ohm’s law * http://www.wikipedia.org/

  6. Maxwell Equations - Origins of an electromagnetic field i H dH i E Maxwell equations : For a time-independent case,  Ampère’s law  Biot-Savart law Gauss law : An electrical charge induces an electric field.

  7. Maxwell Equations - Boundary conditions of an electromagnetic field magnetic field force N magnetic field current N S current force S Maxwell equations : Faraday’s law of induction : Gauss law for magnetism : Conservation of magnetic flux * http://www.wikipedia.org/

  8. Maxwell Equations in Free Space Maxwell equations : In free space (no electron charge, and ,  and  : constant), By differentiating the first equation with t and substituting the second equation,

  9. Maxwell Equations in Free Space (Cont'd) Electric field Magnetic field Propagation direction Here, the left term can be rewritten as Similarly, For an ideal insulating matrix,  Electromagnetic wave propagation speed : in a vacuum, * http://www.molphys.leidenuniv.nl/monos/smo/index.html

  10. Electromagnetic Wave * http://www.wikipedia.org/

  11. Essence of the Maxwell Equations Maxwell equations unified electronics and magnetism :  Further unification with the other forces  Einstein’s theory of relativity

  12. Michelson-Moley Experiment In 1881, Albert A. Michelson and Edward W. Morley precisely designed experiment to prove the presence of Ether : Ether was believed exist as a matrix to transfer an electromagnetic wave.  No interference between parallel / perpendicular to Ether flow  No sign of Ether  No relative speed ! * http://www.wikipedia.org/

  13. Einstein's Theory of Relativity In 1905, Albert Einstein proposed the theory of special relativity : Lorentz invariance for Maxwell’s equations (1900) Poincaré proved the Lorentz invariance for dynamics.  Lorentz invariance in any inertial coordinates Speed of light (electromagnetic wave) is constant. * http://www.wikipedia.org/

  14. Unified Theory beyond the Maxwell Equations Big bang and Grand Unification Theory 10-12 s 10-35 s 10-43 s Gravity Weak nuclear force -decay Strong nuclear force nucleus 0 Big bang Electromagnetic force Maxwell Equation Weinberg-Salam Theory * http://map.gsfc.nasa.gov

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