Nanoelectronics 02 Atsufumi Hirohata Department of Electronic Engineering

Nanoelectronics 02 Atsufumi Hirohata Department of Electronic Engineering 09: 00 (online) & 12: 00 (SLB 118 & online) Monday, 18/January/2021

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

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/~ah 566/

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

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 : permittivity, : magnetic permeability, and : conductivity * http: //www. wikipedia. org/

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

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

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,

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 Electromagnetic wave propagation speed : Prop aga tion dire ctio n in a vacuum, * http: //www. molphys. leidenuniv. nl/monos/smo/index. html

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

Essence of the Maxwell Equations Maxwell equations unified electronics and magnetism : Electronics Magnetism Electron charge Source Force (Coulomb’s law) Field Potential Flux (Gauss’ law) Further unification with the other forces Einstein’s theory of relativity Magnetic dipole moment

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/

Michelson-Moley Experiment When the system is still with the Ether flow at the speed of v : Lorentz contraction

Einstein's Theory of Relativity In 1905, Albert Einstein proposed 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/

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