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)