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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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Quantum confinement

Quantum confinement

(p.110) 8 Quantum confinement
Quantum Confined Laser Devices

Peter Blood

Oxford University Press

The properties of the states produced by quantum confinement in double heterostructures are obtained by solving the spatial part of Schrödinger’s equation for a one-dimensional potential well with barriers of finite height. The apparently formidable task of dealing with the very large number of atoms in a solid is greatly simplified by exploiting the periodic nature of crystals through Bloch’s theorem and the envelope functions. Schrödinger’s equation gives, first, the wavefunctions that are used to calculate transition rates via the matrix element and, second, the energies of the confined states and hence the photon energies at which light interactions occur. This is used to develop simple models for the energy states in quantum dots with rectangular and parabolic potential profiles. Quantum wells provide confinement in only one dimension. Freedom in the other two dimensions produces a continuum of states characterised by a density-of-states function.

Keywords:   Schrödinger’s equation, Bloch’s theorem, envelope function, confined state, continuum of states, rectangular potential, parabolic potential, quantum dot, quantum well, density of states

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