MIT OpenCourseWare http://ocw.mit.edu 3.23 Electrical, Optical, and Magnetic Properties of MaterialsFall 2007For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.•3.23 Fall 2007 – Lecture 24 LUMINESCENCE Last time • Optical processes Optical processes, optical materialsoptical materials • Complex dielectric constant, Kramers-Kronig relations • Interband absorption, direct and indirect transitions • Fermi’s golden rule, perturbing Hamiltonian 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 1 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)•Study • FoxFox, Optical Properties of Solids: Chapter 5Optical Properties of Solids: Chapter 5 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Direct and indirect transitions Image removed due to copyright restrictions. Please see: Fig. 3.2 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 2Transition rates: perturbing Hamiltonian 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Transition rate for direct absorption 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 3Transition rate for direct absorption Image removed due to copyright restrictions. Please see: Fig. 3.5 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Dipole-allowed selection rules These are for atomsThese are for atoms… • Parity of initial and final state are opposite • Δm=-1, 0 or 1 • Δl=-1 or 1 • Δms E.g. phosphorence involves dipole-forbidden transitions that are mediated by higher order terms (magnetic dipole, electronic quadrupole) 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 4 Please also see any diagram of GaAs energy bands, such as http://ecee.colorado.edu/~bart/book/book/chapter2/gif/fig2_3_6.gif.Joint Density of States 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Frequency dependence of band edge absorption Image removed due to copyright restrictions. Please see: Fig. 3.6 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 5Indirect gap semiconductors 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Indirect gap semiconductors Image removed due to copyright restrictions. Please see: Fig. 3.10 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 6Absorption above the band edge Image removed due to copyright restrictions. Please see: Fig. 3.11 and 3.12 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Excitons Image removed due to copyright restrictions. Please see: Fig. 4.1 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 7Excitons 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Excitons absorption Image removed due to copyright restrictions. Please see: Fig. 4.4 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 8Light emission in solids Image removed due to copyright restrictions. Please see: Fig. 5.1 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Interband luminescence Image removed due to copyright restrictions. Please see: Fig. 5.2 and 5.3 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 9Indirect band gap materials Image removed due to copyright restrictions. Please see: Fig. 5.4 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Photoluminescence: excitation, relaxation Image removed due to copyright restrictions. Please see Fig. 5.5 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 10Low-carrier density case Image removed due to copyright restrictions. Please see: Fig. 5.6 in Fox, Mark. Optical Properties of Solids.Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) Degeneracy Image removed due to copyright restrictions. Please see: Fig. 5.7 and 5.8 in Fox, Mark. Optical Properties of Solids. Oxford, England: Oxford University Press, 2001. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)