Electrons, phonons, and photons in solids Optoelectronics Group Alex L Ivanov Department of Physics and Astronomy, Cardiff University Wales, United Kingdom

Outline A few words about Cardiff University Quantum mechanics: atoms and electrons Crystals and atomic lattices Phonons and electrons in a crystal Nanostructures and nanotechnology Semiconductor lasers

Cardiff United Kingdom Cardiff University: 1) Established by Royal Charter in ) Placed 7 th in a ranking of 106 UK Universities.

Cardiff University

Quantum mechanics of atoms Planck constant  = g cm /s Length scale: a  0.5nm (Bohr radius) B Energy scale: I   /(m a ) (Rydberg) 2 2 0B Particle-wave duality: de Broglie wavelength = 2  /p should be compared with a relevant length scale. One cannot describe the optical and electrical properties of solids without applying quantum mechanics. (Fig. by P Christian, 2000)

Bohr model H (Hydrogen) Be (Beryllium) 1) Electrons in an atom can occupy only discrete energy states, 2) By absorbing/emitting a photon an electron can “jump” between the energy states, 3) Proton (neutron) mass M is much larger than m: m : M = 1 : (Figs. by Teachers Slide Show)

Crystal Lattices K Hermann et al., Gallery of BALSAC 1cm contains about 10 atoms 323

Phonons in crystals Rayleigh (surface) phonons Transverse (bulk) phonons (amplitude is magnified by factor 10) K Hermann et al., Gallery of BALSAC

Phonons as quantum (quasi-) particles 1) Phonons are quantized vibrations of lattice atoms: Momentum is   Energy is   2) The number of phonons depends on temperature: Heat is mainly due to phonons. 3) Phonons can easily interact with electrons: Resistivity R in metals ; Zero resistivity in superconductors. 4) Some of phonons can resonantly interact with light.

Generation of phonons by a laser pulse The heat pulses (phonons of about 600GHz frequency) induced in a crystal film at T = 2K by a high-intensity laser (light) pulse. M Hauser and J Wolfe (University of Illinois)

In-plane heat propagation (the movie by M Hauser and J Wolfe, University of Illinois)

Electrons in solids Some of electrons move nearly free in the atomic lattice: “An electron sea”. Teachers Slide Show

Motion of electrons in a crystal (the movie by K Drews, 2001)

Electrons in solids Electron density distribution in Cr (Resolution – 0.5 nm). In metals the electrons are more uniformly spread off than those in semiconductors. Si Al GaAs Ag Figures by A Fox, HVEM, Laurence Berkeley Laboratory E Kaxiras, Harward University M Blaber, 1996

Electrons in a crystal lattice electrons Brillouin-Bloch electrons, i.e., electrons “dressed” by an atomic lattice: mm 0eff Fig. by T Hromadka, 1997

Electron-phonon interaction Electron-phonon interaction causes a) Resistivity in metals and semiconductors, b) Superconductivity in some solids at low temperatures. Fig. by P Moriarty, University of Nottingham

Quantum Wells InGaAs/GaAs multiple quantum well (Fig. by M Patra, Helsinky University) (Figs. by J F Zheng et al., Lawrence Berkeley Labs) The electron de Broglie wavelength is comparable with the quantum well width  a two-dimensional electron motion.

Quantum Dots InGaAs (self-assembled) quantum dots on a GaAs substrate. Self-organized SiGe quantum dots grown on Si. (Figs. by Matlab-Kjist) (Fig. by J A Floro, 1997) (Fig. by P Moriaty, University of Nottingham)

Quantum Dots Figs by M.C. Roco, Nanotechnology Initiative Figs by L Kouwenhoven

Quantum wires Cross-section (about 5nm) of the Si quantum wire. InAs/InP self-assembled quantum wires. (Fig. by S Greiner at al., ESRF) (Fig. by J Kedzierski and J Bokor, DARPA)

Cr 3+ (Ruby) Nd 3+ (frequency doubled) 532nm1064nm694nm In x Ga 1-x N nm In x Ga 1-x As nm In x Ga 1-x P nm Lasers (Light Amplification by Stimulated Emission of Radiation)

Vertical-Cavity Surface-Emitting Laser (VCSEL) Distributed Bragg Reflectors GaAs Multiple Quantum Well Light (Fig by G Vander-Rhodes et al, Boston University)

Vertical-Cavity Surface-Emitting Lasers (Fig. by Huw Summers, Cardiff University) (Figs by C-K Kim, KAIST)  m

GaN-based Blue Lasers GaN lasers were developed in Japan by S. Nakamura. (Fig. by Osram Opto Semiconductors) (Fig. by Nitride Semiconductor Research)