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

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Quick Review over the Last Lecture Nano-scale miniaturisation : 4 reduction of ( effective electron paths ) 4 reduction of ( electron scattering ) ( faster ) operation 8 nano-fabrication ; ( complicated ) processes ( higher ) cost ( larger ) distributions in device properties 8 ( leakage ) current 8 ( Joule ) heating 8 electron ( confinement ) Electron transport : ( diffusive ) transport ( electron scattering ) ( ballistic ) transport ( negligible electron scattering )

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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

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02 Maxwell Equations Electromagnetic field Origins of an electromagnetic field Boundary conditions of an electromagnetic field

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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 Ohms law

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Maxwell Equations - Origins of an electromagnetic field Maxwell equations : For a time-independent case, Ampères law H i i dHdH Biot-Savart law Gauss law : An electrical charge induces an electric field. E

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Faradays law of induction : Maxwell Equations - Boundary conditions of an electromagnetic field Maxwell equations : NS current force magnetic field current force magnetic field Gauss law for magnetism : Conservation of magnetic flux * N S

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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,

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Maxwell Equations in Free Space (Cont'd) Here, the left term can be rewritten as Similarly, For an ideal insulating matrix, * Electric field Magnetic field Propagation direction Electromagnetic wave propagation speed : in a vacuum,

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Electromagnetic Wave *

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Essence of the Maxwell Equations Maxwell equations unified electronics and magnetism : Further unification with the other forces ElectronicsMagnetism Electron chargeSourceMagnetic dipole moment Force (Coulombs law) Field Potential Flux (Gauss law) Einsteins theory of relativity

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

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Einstein's Theory of Relativity In 1905, Albert Einstein proposed the theory of special relativity : Speed of light (electromagnetic wave) is constant. * Lorentz invariance for Maxwells equations (1900) Poincaré proved the Lorentz invariance for dynamics. Lorentz invariance in any inertial coordinates

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Unified Theory beyond the Maxwell Equations Big bang and Grand Unification Theory * Big bang s s s 0 Gravity Strong nuclear force nucleus Weak nuclear force -decay Electromagnetic force Weinberg-Salam Theory Maxwell Equation

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