Chapter 9: Quantum Wells & Band-Structure Modelling
This chapter covers quantum wells and band-structure modelling in OghmaNano, including quantum confinement, k·p theory, strain, semiconductor band structures, optical transitions, gain, scattering and quantum-well model selection.
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9.1.1 Quantum wells and confinement
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9.1.2 Parabolic bands and the effective-mass approximation
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9.1.3 From the Schrödinger equation to a finite-difference matrix
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9.1.4 Introduction to k·p perturbation theory
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9.1.5 Basis states, envelope functions and multiband Hamiltonians
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9.1.6 The 8-band zincblende k·p model
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9.1.7 The 10-band zincblende / dilute-nitride model
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9.1.8 The 8-band wurtzite k·p model
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9.1.9 Pseudomorphic epitaxy and strain tensors
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9.1.10 The Bir–Pikus strain Hamiltonian
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9.1.11 The six-valley silicon conduction-band model
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9.1.12 The six-band Luttinger–Kohn valence model
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9.1.13 Sparse matrices, shift-invert and Rayleigh–Ritz
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9.1.14 Eigenstates, normalisation and state character
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9.1.15 Optical matrix elements and selection rules
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9.1.16 Absorption, stimulated emission and optical gain
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9.1.17 Scattering, relaxation times and mobility
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9.1.18 Material parameters and where they enter the solvers
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9.1.19 Choosing a quantum-well model
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9.1.20 References and further reading