Exciton oscillator strength

Since in quantum wells electrons and holes can freely move only within the quantum well plane, bound electron-hole states, i.e. excitons, become two-dimensional in nature as well. The exciton binding energy is enhanced four-fold in the ideal two-dimensional case compared to a conventional three-dimensional case. In addition, the exciton oscillator strength is also enhanced. In the optical spectra, this leads to pronounced excitonic features which are usually observed even at room temperature. 

Fig. 10 Room temperature absorption spectra of P4 (upper two panels), P8 (two central panels), and Pi6 (bottom panels) estimated according to Eq. (66) and in using adiabatic exciton energies and oscillator strengths. The overall spectrum (thick line) follows as the sum of single exciton level contributions (thin lines). The left column of figures shows spectra without including the modulation of the chromophore excitation energy by a coupling to the solvent. The right column of figures shows spectra where this effect is inciuded.

When 2e < (U+J), the exciton state is lower in energy than the corresponding exciplex state. Also, we can see from this analysis how an exciplex state can acquire oscillator strength to the ground state through mixing with ipo- Taking e —> 0 as in the case of the homo-dimer,... 

In the crude Born-Oppenheimer approximations, the oscillator strength of the 0-n vibronic transition is proportional to (FJ)2. Furthermore, the Franck-Condon factor is analytically calculated in the harmonic approximation. From the hamiltonian (2.15), it is clear that the exciton coupling to the field of vibrations finds its origin in the fact that we use the same vibration operators in the ground and the excited electronic states. By a new definition of the operators, it becomes possible to eliminate the terms B B(b + b ), BfB(b + hf)2. For that, we apply to the operators the following canonical transformation ... 

Microscopic disorder We consider a lattice the sites of which have disordered resonance energies, with a distribution of width Ae, but have the same intersite interactions (same dipole orientation and oscillator strength) as the perfect lattice. This is the so-called substitutional disorder model.122 We assume the disorder width to be smaller than the excitonic bandwidth (4< Be) and examine the bottom of the excitonic band, where the emitting and the absorbing K 0 states lie. In a renormalization-group scheme, we split the lattice into isometric domains of n sites, on which the excitation is assumed to be localized, and write the substitutional-disorder hamiltonian in this basis we thereby obtain a new disorder width An Aen-1/2 and a... 

The absorption is observed at the poles of t, at the energy oj, shifted relative to coB (4.101) by the local field. If a>, is close to an excitonic transition of the host crystal, the absorption resonates strongly for to/ tuke in fact, the impurity transition is polarized according to the host excitonic transition in its vicinity.16 (In other words, the impurity borrows oscillator strength, and more or less spatial extension, from the host band.184... 

We must remark that the broadening is in general nonlorentzian and asymmetric, particularly when the optical transition occurs at the boundary of the excitonic band (as in the case of the anthranene crystal). Lastly, the analyticity of the CPA method assures that (4.118) satisfies the Kramers-Kronig relations, and that the total oscillator strength of the transition, redistributed on the two bands, is conserved. 

---