Lecture_7

Lecture_7 - 3. Optical absorption, emission, and refraction...

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1 Prof. J. S. Harris 1 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Direct gap optical absorption Indirect gap optical absorption Kramers-Kronig relationships Excitons Free carrier absorption Optical emission-Einstein A and B coef±cients Stimulated emission Spontaneous emission Optical Absorption-Einstein A and B coefficients Optical refraction Reading-Ch 3 Notes, Bhattacharya pp 114-150 3. Optical absorption, emission, and refraction processes Prof. J. S. Harris 2 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Spectrum of GaAs, direct gap semiconductor which has abrupt absorption onset just below E g and a smooth rise above E g . It also has a relatively strong peak near the bandgap energy, especially at low temperatures optical absorption of GaAs at various temperatures Absorption does not have the smoothly rising curve predicted by non-excitonic model - instead almost step-like rise, followed by a much “straighter” increase with increasing photon energy. explanation - excitonic effects Excitons
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2 Prof. J. S. Harris 3 EE243. Semiconductor Optoelectronic Devices (Winter 2010) We made a simplistic assumption in the non-excitonic model that the initial state is electron in a particular state in valence band and Fnal state is with that same electron in a speciFc state in the conduction band, which is an incorrect model Better view Initial state is crystal with full valence and empty conduction bands ±inal state is crystal in which an electron-hole pair has been added Optical absorption not only adds an electron to conduction band it also adds a hole to the valence band Correct description- we created an electron-hole pair Possible Fnal states are all possible states of an electron-hole pair Why not simply an electron in a k-state and a hole in a k-state? The electron and the hole have strong Coulomb attraction to one another. Without this, the non-excitonic model would actually produce the correct answer. Origin of excitonic effects Prof. J. S. Harris 4 EE243. Semiconductor Optoelectronic Devices (Winter 2010) Quantum mechanical problem for states of a pair of particles, of given masses (e.g., m e for the electron, and m h for the hole), with equal and opposite charges of ² e This is similar to the hydrogen atom problem - an exactly solvable quantum mechanics problem (of which there are few ) Here we use 1) electron and hole effective masses instead of electron and proton masses 2) medium with a dielectric constant different from vacuum (e. g., ~ 13 in GaAs) The form of solutions is identical, but the numbers are different -- ±irst conclusion There is a set of discrete energies for the electron-hole pair that correspond to energy levels in the hydrogen atom States of electron-hole pair
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3 Prof. J. S. Harris 5 EE243. Semiconductor Optoelectronic Devices (Winter 2010) The single most important state is that corresponding to hydrogen ground state The ground state (1S) of hydrogen atom has energy below lowest energy of free electron and proton (hole) by the binding energy (13.6 eV = Rydberg) for the hydrogen atom
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This note was uploaded on 06/05/2010 for the course EE 243 taught by Professor Harris,j during the Winter '10 term at Stanford.

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Lecture_7 - 3. Optical absorption, emission, and refraction...

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