1982 年 51 巻 5 号 p. 1544-1550
We analyze the low-energy tail of the exciton absorption spectra calculated numerically on the standard model of exciton-phonon interaction. The empirical Urbach rule is established in its exponential decay for several orders of magnitude with a decay constant proportional to inverse temperature T−1 in two and three dimesnions and to T−2⁄3 in one dimension. A posteriori, the exponential tail is unambiguously ascribed to the “momentarily localized” excitons by considering the behaviour of the average oscillator strength per state. We introduce the steepness index s which relates the steepness coefficient σ and the exciton-phonon coupling constant g through σ=s⁄g. Our calculated values of 1.24 for square and 1.50 for simple cubic lattices enable us to correlate experimental observations on Urbach behaviour and self-trapping consistently.
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