Exciton spectrum

Thus in either formulation the exciton spectrum consists of a series of bands, but the optical absorption spectrum consists of a series of lines because the selection rule... 

On the other hand, molecular crystals are characterized by the existence of strongly bound (Frenkel type) excitons, and it has been shown that the lower-energy part of the absorption spectrum (say, the first 2 eV) is completely dominated by these excitons [168], even to the extent that the absorption corresponding to electron-hole pair generation is completely hidden in the exciton spectrum [128] and is revealed only by such methods as modulated electrorefletance [169]. The only states in the exciton bands that are accessible by photon absorption are those at the center of the Brillouin zone, so the absorption is not a continuous band as for semiconductors, but a sharp line. The existence of this sharp line therefore does not mean that the exciton band is narrow (i.e., that its dispersion relation in the Brillouin zone is flat). On the contrary, since that dispersion is caused by dipolar interactions, exciton bandwidths can be several eV [168,170] the total bandwidth is four times the coupling term. This will be particularly... 

In consequence, a state with an exciton /ik has energy E (k) which can be computed by solving eqns (3.62) with regard to the conditions (3.60). The function Efj,(k) characterizes the excitonic spectrum, i.e. the dependence of the exciton energy on the excitonic quasimomentum ftk. 

For the discussion of the excitonic spectrum in a one-dimensional molecular crystal (with one molecule per unit cell) we use the following Hamiltonian ... 

Photoluminescence could be due to the radiative annihilation (or recombination) of excitons to produce a free exciton peak or due to recombination of an exciton bound to a donor or acceptor impurity (neutral or charged) in the semiconductor. The free exciton spectrum generally represents the product of the polariton distribution function and the transmission coefficient of polaritons at the sample surface. Bound exciton emission involves interaction between bound charges and phonons, leading to the appearance of phonon side bands. The above-mentioned electronic properties exhibit quantum size effect in the nanometric size regime when the crystallite size becomes comparable to the Bohr radius, qb- The basic physics of this effect is contained in the equation for confinement energy,... 

The last term in the exciton spectrum given elsewhere represents the spectrum of a hole undergoing oscillations of frequency. ... 

When using TDDFT to calculate the optical response of insulators, local approximations have again been shown to fail badly. Most noticeably, local approximations do not describe excitonic effects, or the exciton spectrum within the band gap. Moreover, the computed gap is usually much smaller than experiment because adiabatic approximations cannot change the gap size from its KS value. 

Historically, the first conflicted picture to be resolved was whether the photogeneration of carriers proceeded as a result of a direct transition from the valence band to the conduction band (band-to-band, BB) (2, p. 470). In anthracene, it was known that the absorption spectrum was essentially explicable in terms of transitions to bound, neutral, Frenkel exciton states the BB transition would thus have to be weak since the final states would be buried in the Frenkel exciton spectrum. An alternative hypothesis was that carrier generation requires the excitation of a Frenkel exciton that could dissociate if its energy was degenerate with that of a pair of uncorrelated carriers. 

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