Perturbation theory predicts rates of transitions between eigenstates of the unperturbed Hamiltonian, which in the independent electron model for a crystal are nonlocal Bloch wave functions or linear combinations of them that extend throughout the crystal. However, photon absorption is localized. With radiation normally incident on a semiconductor, the photon flux N(E;x) decreases with depth according to $$\frac {dN(E;x)}{dx} = -α(E;x)N(E;x)$$ So in a thin layer of thickness dx , ##α(E;x)N(E;x)## photons of energy E (or in a narrow interval dE) will be absorbed per unit volume in unit time. If each photon of energy E absorbed in dx generates a conduction band electron (and/or a valence band hole) in dx, the local rate of generation is then $$G(E;x) = α(E;x)N(E;x)$$(adsbygoogle = window.adsbygoogle || []).push({});

While it can be shown that Fermi’s Golden Rule, provided by perturbation theory, applies to one-electron transitions if the initial one-electron state is a wave packet, e.g. a valence band wave packet, at least under certain assumptions, it appears to me that the possible final state must be an eigenfunction of the unperturbed Hamiltonian, which is nonlocal. Yet I see a number of texts apply perturbation theory, i.e. Fermi’s Golden Rule, to predict local rates of photon absorption and carrier generation (I assume wave packets). How is this justified? How are localized carriers, which I think are wave packets, generated by light absorption? These seem like fundamental questions but I have not been able to extract the answers from books so far.

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# Localized absorption of photons and carrier generation

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