Semiconductors, Optical Properties - Introduction to Solid State Physics - Lecture Slides, Slides of Solid State Physics

Download Semiconductors, Optical Properties - Introduction to Solid State Physics - Lecture Slides and more Slides Solid State Physics in PDF only on Docsity! Semiconductors: optical properties: log a _—— =e docsity.com http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm Figure VI-1-1: Different types of optical absorption phenomena; (1) transitions of high- lying bands, (2) excitons, (3) fundamental absorption (VB-to-CB transition and Urbach- tail), (4) impurity absorption, (5) free-carrier absorption and (6) Reststrahlen absorption. docsity.com http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm Figure VI-2-1: Direct absorption in a semiconductor. !! photon = Eg + !2k2 2me * + !2k2 2mh * !! photon = Eg + !2k2 2µ ; 1 µ = 1 me * + 1 mh * Parabolic bands: D E( ) = 0; !! < Eg D E( ) = 1 2" 2 2µ !2 # $% & '( 3/2 !! ) Eg( )1/2 ; !! > Eg Joint density of states: Matrix element: docsity.com Calculating band gap from absorption and transmission spectra: In very clean samples at very low temperatures, onset of absorption is sharp and BG identification is trivial, but under other conditions, extraction is harder. It can be shown (e.g. Cardona and Yu) that the imaginary part of the dielectric constant (proportional to absorption coefficient α, remember) for a DIRECT GAP semiconductor is ! '' "( ) = A Eg E # $% & '( 2 E Eg )1 # $ % & ' ( 1/2 *+ Comes from density of states Comes from matrix element docsity.com BaCuSF thin film 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 200 300 400 500 600 700 800 900 Wavelength (nm) T, dir (stack) R, spec T/(1-R) Optical Spectrum of BaCuSF film e!"d Reflection Transmission thin film interference is removed in T/(1-R)=e-ad docsity.com Calculating band gap from absorption and transmission spectra: It can be shown (e.g. Cardona and Yu) that the imaginary part of the dielectric constant (proportional to absorption coefficient a, remember) for a INDIRECT GAP semiconductor is ! '' "( )#$ # E ± Ephonon % Eg( ) 2 !1/2 " E + Eph # Eg( ) A plot of the square root of the absorption coefficient against the photon energy is a straight line, and intersects the energy axis at E = Eg - Eph docsity.com http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm Figure VI-2-6: The left diagram shows the perturbation of the band edges by Coulomb interaction with inhomogeneously distributed impurities. This leads to the formation of tails of states shown on the right side. The dashed lines show the distribution of states in the unperturbed case. docsity.com Mobility Edges/ Minimum Metallic Conductivity A D(E) Delocalized states Localized states A Mobility edge ® docsity.com Figure VI-1-1: Different types of optical absorption phenomena; (1) transitions of high- lying bands, (2) excitons, (3) fundamental absorption (VB-to-CB transition and Urbach- tail), (4) impurity absorption, (5) free-carrier absorption and (6) Reststrahlen absorption. docsity.com Absorption coeff. vs. photon energy at different doping levels, n-InSb, T = 130K: 1. 6.6·1013 cm-3; 2. 7.5·1017 cm-3; 3. 2.6·1018 cm-3; 4. 6·1018 cm-3; (Ukhanov [1977]). http://w w w .ioffe.rssi.ru/S VA /N S M /S em icond/InS b/optic.htm l docsity.com Figure VI-1-1: Different types of optical absorption phenomena; (1) transitions of high- lying bands, (2) excitons, (3) fundamental absorption (VB-to-CB transition and Urbach- tail), (4) impurity absorption, (5) free-carrier absorption and (6) Reststrahlen absorption. docsity.com http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm Figure VI-4-1: (a) The band structure in the independent electron picture and (b) the Coulombic interaction between electron and hole, which modifies the band structure. Figure VI-4-2: Band structure including the exciton levels. docsity.com http://kottan-labs.bgsu.edu/teaching/workshop2001/chapter6.htm Figure VI-4-3: A conceptual picture of the periodic envelope function extent of Frenkel and Mott excitons. En = ! µred m0 1 "r 2 RH n2 = RX n2 rn = m0 µred "rn 2aH = n 2aX docsity.com http://www.cusbo.polimi.it/us/research/quantum.html We have performed investigation of optical nonlinearities induced by exciton or carrier photogeneration in InGaAs/InP QW structures by using the infrared femtosecond optical parametric amplifier. The absorption spectrum shows clearly visible heavy and light hole exciton peaks docsity.com