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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 1883.
2) Placed 7th in a ranking of 106 UK Universities.
Cardiff University
Quantum mechanics of atomsPlanck constant = 1.054 10 g cm /s. -27 2
Length scale: a 0.5nm (Bohr radius)B
Energy scale: I /(m a ) (Rydberg)2 2
0 B
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 : 1840.0
(Figs. by Teachers Slide Show)
Crystal Lattices
K Hermann et al., Gallery of BALSAC
1cm contains about 10 atoms3 23
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 uniformlyspread off than those in semiconductors.
Si Al
GaAsAg
Figures byA Fox, HVEM, Laurence Berkeley Laboratory E Kaxiras, Harward UniversityM Blaber, 1996
Electrons in a crystal latticeelectrons
Brillouin-Bloch electrons, i.e., electrons “dressed” by an atomic lattice:
m m0 eff
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 quantumdots 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)
Cr3+
(Ruby) Nd3+Nd3+
(frequency doubled)
532nm 1064nm694nm
InxGa1-xN360-580nm
InxGa1-xAs850-1300nm
InxGa1-xP600-700nm
Lasers(Light Amplification by Stimulated Emission of Radiation)
Vertical-Cavity Surface-Emitting Laser (VCSEL)
Distributed Bragg ReflectorsGaAs 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)