Nanoelectronics 04. Atsufumi Hirohata Department of Electronics. Quick Review over the Last Lecture ' E = A. ' t gradφ ' ) / ' ) ε ρ
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1 Nanoelectronics 04 Atsufumi Hirohata Department of Electronics 09:00 Tuesday, 23/January/2018 (P/T 005) Quick Review over the Last Lecture Maxwell equations with ( scalar ) potential ( f ) and ( vector ) potential ( A ) : % B = rot A E = A Positive charge & ( t gradφ ( Scalar potential ).% 1 2 & c 2 t 2 ( 0 2 * A = µj 0 ) / 0 % 1 2 & c 2 t ( * φ = 1 ) ε ρ 1 ( Lorentz ) gauge : ( Electric field E ) div A + 1 φ c 2 t = 0 Electrical current ( Magnetic field H ) ( Vector potential )
2 Contents of Nanoelectonics 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) 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) V. Nanodevices (08, 09, 12, 15 ~ 18) 04 History of Quantum Mechanics 1 Black body radiation Light quantum Photoelectric effect Compton scattering De Broglie wave
3 Black Body Radiation In 1900, Max Planck reported energy unit of hn between light and a material : Black body : Non-uniform distribution : cannot be explained by statistical mechanics. in an equilibrium state, each degree of freedom holds E = kbt / 2 distribution If the energy unit is hn, for kbt < hn, for kbt > hn, distribution Einsteins Light Quantum Hypothesis In 1905, Albert Einstein explained that each photon has the energy of hn :
4 Photoelectric Effect - Experiments In 1887, Heinrich R. Hertz found ultraviolet light encourages discharge from a negative metallic electrode : In 1888, W. L. F. Hallwacks observed electron radiation by light. In 1902, Philipp E. A. von Lenard found radiated electron energy is independent of light intensity but dependent upon n. metal plate light source light source electrode glass bottle electrons Metallic foil electrons photons ** *** Photoelectric Effect - Theory In 1905, Albert Einstein proposed theories of light with using a light quantum : Light consists of a light quantum (photon). hν E = hν W W : work function for an electron to be released Light holds both wave and particle nature. Momentum of a photon is predicted to be.
5 Milikans Oil-Drop Experiment In 1916, Robert A. Millikan and Harvey Fletcher measured the Planck constant : In 1912, an electron charge measured to be : C ( C) oil spray ~ kv microscope uniform electric field A critical voltage, at which no electron motion (no photocurrent) is realised : E = hν W = ev 0 hν e W e = V 0 Compton Scattering In 1923, Arthur H. Compton measured the momentum of a photon : λ " λ = h m e c ( 1 cosθ) l : wavelength of a photon before scattering, l : wavelength of a photon after scattering, m e : electron mass, q : scattered photon angle, h : Planck constant and c : speed of light
6 Davisson-Germer experiment in 1927 : Electron Interference Electrons are introduced to a screen through two slits. - + Electron as a particle should not interfere. Photon (light) as a wave observed! Wave packet : De Broglie Wave contains number of waves, of which amplitude describes probability of the presence of a particle. where l : wave length, h : Planck constant and m 0 : mass of the particle. de Broglie hypothesis (1924 PhD thesis 1929 Nobel prize) According to the mass-energy equivalence : E = m 0 c 2 = m 0 c c = p λν where p : momentum and n : frequency. By using E = hn, λ = h p = h m 0 v
7 Schrödinger Equation In order to express the de Broglie wave, Schrödinger equation is introduced in 1926 : 2 2m 2 ψ + E V & ( )ψ = 0 2 = 2 ( ) z 2 + * x y E : energy eigenvalue and y : wave function Wave function represents probability of the presence of a particle ψ 2 = ψ * ψ y * : complex conjugate (e.g., z = x + iy and z * = x - iy) Propagation of the probability (flow of wave packet) : j = ( 2mi ψ* ψ ψ ψ * ) Operation = observation : 2 2m 2 ψ = E V ( )ψ ψ 2 = 1 : Scrödingers Cat Thought experiment proposed by Erwin R. J. A. Schrödinger in 1935 Radioactive substance Hydrocyanic acid The observer cannot know if a radioactive atom has decayed. if the vial has been broken and the hydrocyanic acid has been released. if the cat is killed. The cat is both dead and alive according to quantum law : superposition of states The superposition is lost : only when the observer opens the box and learn the condition of the cat. then, the cat becomes dead or alive. quantum
8 Comparison between Classical and Quantum Mechanics In order to express the de Broglie wave, Schrödinger equation is introduced in 1926 : Classical mechanics Coordinate Momentum Quantum mechanics Energy Variables Equation Amplitide / wavefunction Energy / probability
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