Interaction between Photons and Electrons Uncertainty principle Heisenberg

Interaction between Photons and Electrons Uncertainty principle (Heisenberg): Wave packet 1

Spontaneous and Stimulated Emission of Light Spontaneous emission Stimulated emission Ø Wide angular distribution of emitted photons Ø Small angular distribution of emitted photons Ø Wide spectrum of frequencies Ø Narrow spectrum of frequencies (or a well-defined frequency) Ø Photons are incoherent (different phase shift of individual photons) Ø Good coherence of photons (phase shift complying with the wavelength) 2

Laser – Light Amplification by Stimulated Emission of Radiation 1. Electron in an excited state decay to a lower energy state under the emission of a photon (h 21). 2. The first emitted photon stimulate a second electron in an excited state to decrease the energy (to jump down). 3. Because it is a coupled process, both photons are coherent (have the same phase). 4. Photons still have a wide angular distribution (propagate in different directions). 3

Principle of a Laser Limitation of the angular range Improvement of coherence (emission time) three-step laser and four-step laser 4

5

Helium-Neon-Laser Ø Polarization of light at Brewster’s angle Ø Additional monochromatization 6

Semiconductor Laser 7

Semiconductor Laser Direct and indirect quantum jumps (band transitions) Direct: energy loss of electrons is converted into the energy of emitted photons Indirect: energy loss is connected to a change in impulse (or k vector) emission of a phonon (heat). 8

Semiconductor Laser Wavelength of emitted light in semiconductors with direct quantum jumps Absorption of light by glass Minimum at 1. 3 m and 1. 55 m 9

Semiconductor Laser Wavelength of emitted light in semiconductors with direct quantum jumps 10

11

Photoluminescence of Ga. In. NAs(Sb) III a: Ga, In V a: N, As, Sb Applications Ø VCSEL (Vertical Cavity Surface Emitting Laser), 10 GHz, 1. 3 µm communication technology, Raman spectroskopy Ø Optical amplifier for frequencies from 1. 2 to 1. 6 µm 12

Homojunctions and Heterojunctions Homojunction: semiconductor interface that occurs between layers of similar semiconductor material (equal band gaps) but with different doping. Heterojunction: interface between layers of dissimilar semiconductor material (different band gaps) with definite crystal structure and properties Only a part of the p-n transition is used. In the other parts electrons are absorbed these lasers have to be cooled Different index of refraction for single materials. These structures act as „waveguide“. Cons: large angular divergence of the light 13 beam (20 - 40)°

Quantum Structures „Quantum dots“ and „quantum wires“ Formation of new (additional) energy levels, as in doped semiconductors Quantum dots Extremely thin layer (dots) between thick layers (spacer) Surface tension self organized structures (dots) are energetically more favorable 14

Quantum Structures Materials: In. As/Al. As, In. As/In. Sb, …, solid solutions Crystal structure: cubic, space group F-43 m Different lattice parameters residual stress within the crystal lattice ordering of quantum dots a (In. As) = 6. 058 Å a (In. Sb) = 6. 4782 Å a (Ga. Sb) = 6. 095 Å a (Ga. As) = 5. 6538 Å 15

Materials for Self Organized Semiconductor Structures Typically based on the elements from the groups IIB, IIIA, IVA, VA and VIA. Al … 3 s 2, 3 p 1 Ga … 4 s 2, 4 p 1 In … 5 s 2, 5 p 1 Si … 3 s 2, 3 p 2 Ge … 4 s 2, 4 p 2 P … 3 s 2, 3 p 3 As … 4 s 2, 4 p 3 Sb … 5 s 2, 5 p 3 16

Quantum Structures Formation of atomic steps Materials: Ge/Si, Si 1 -x. Gex/Si Slanted cut of a single-crystal 17

Additional periodicity of the (crystal) structure leads to the structuring of the energy bands Density of states within the conduction band (CB) and the valence band (VB) for Ø a double heterojunction (DH), Ø a quantum well (QW) Ø a quantum wire (QWi) Ø a quantum box(QB) 18

Quantum Structures Methods of investigation AFM (atomic force microscopy) STM (scanning tunneling microscopy) X-ray diffraction TEM (transmission electron microscopy) Electron diffraction SEM (Scanning electron microscopy) X-ray scattering Applications Photodiodes Laser Fast transistors 19

Optical Memory Elements CD-ROM: Compact Disc Read Only Memory Height of “steps” = /4 Phase shift between the incident wave and the reflected wave = /2 destructive interference 1 0 20