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Quantum Confined Laser DevicesOptical gain and recombination in semiconductors$
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Peter Blood

Print publication date: 2015

Print ISBN-13: 9780199644513

Published to Oxford Scholarship Online: November 2015

DOI: 10.1093/acprof:oso/9780199644513.001.0001

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Optical transitions in quantum wells

Optical transitions in quantum wells

(p.172) 11 Optical transitions in quantum wells
Quantum Confined Laser Devices

Peter Blood

Oxford University Press

Optical transitions in quantum wells occur between closely spaced states associated with unconfined motion in the plane of the well within sub-bands formed by confinement across the well. The energy spacing of the unconfined states is much less than the homogeneous linewidth, so the transition rate is given by Fermi’s Golden Rule. Initial and final states must have the same in-plane k-vector (k-selection) and this leads to definition of the transition density. The transition probability is also determined by the overlap integral between initial and final confined state envelope functions, which limits transitions in rectangular wells to sub-bands of the same index. Confinement also produces polarisation dependence of the momentum matrix element, which depends upon whether the valence band is light or heavy hole in character. Expressions are derived for modal gain and spontaneous emission together with the spectrally integrated emission rate at low carrier density using the Boltzmann approximation.

Keywords:   Fermi’s Golden Rule, momentum matrix element, overlap integral, k-selection, transition density, Boltzmann approximation, heavy hole, light hole, modal gain, spontaneous emission

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