Electrons, phonons, and photons in solids

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

2. 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

3. United Kingdom Cardiff University: 1) Established by Royal Charter in 1883. 2) Placed 7th in a ranking of 106 UK Universities. Cardiff

4. Cardiff University

5. Quantum mechanics of atoms . -27 2 Planck constant h = 1.054 10 g cm /s Length scale: a ] 0.5nm (Bohr radius) B 2 Energy scale: I [ h /(m a ) (Rydberg) 2 0 B (Fig. by P Christian, 2000) Particle-wave duality: de Broglie wavelength l = 2p/p should be compared with a relevant length scale. One cannot describe the optical and electrical properties of solids without applying quantum mechanics.

6. 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 : 1840. 0 (Figs. by Teachers Slide Show)

7. Crystal Lattices 3 23 1cm contains about 10 atoms K Hermann et al., Gallery of BALSAC

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

9. Phonons as quantum (quasi-) particles 1) Phonons are quantized vibrations of lattice atoms: Momentum is h(2p/l) ; Energy is hW. 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.

10. 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)

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

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

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

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

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

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

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

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

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

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

21. Nd3+ (frequency doubled) Cr3+ (Ruby) Nd3+ 532nm 694nm 1064nm InxGa1-xN 360-580nm InxGa1-xP 600-700nm InxGa1-xAs 850-1300nm Lasers (Light Amplification by Stimulated Emission of Radiation)

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

23. Vertical-Cavity Surface-Emitting Lasers 1-10mm (Fig. by Huw Summers, Cardiff University) (Figs by C-K Kim, KAIST)

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