Geminate electron-hole pairs

Optical absorption and recombination processes involve two or more particles and so may include correlation effects. Electron-hole pairs form excitons in a crystal, with the result that the absorption and emission spectra are not described by the one-particle density of states distributions. Although excitons can exist in an amorphous material (see Chapter 3), they are not detected in the optical spectra and the absorption is described by the convolution of the one-particle densities of valence and conduction band states. The correlation effects in 

The absorption of a photon creates an electron-hole pair whose wavefunctions initially overlap. After the absorption process, the electron and hole thermalize to the band edge and diffuse apart. The different thermalization mechanisms in extended and localized states are reflected in the diffusion properties. In the extended states, the thermalization time, required to emit the excess energy AE as n phonons is 

After this time, the carrier crosses the mobility edge and is trapped in localized states, so that further movement is much slower, although the distance between the sites is larger. During thermalization in extended states the carriers diffuse apart a distance. 

Due to their close proximity, the electron-hole pair is bound by their mutual Coulomb interaction as shown in Fig. 8.7. When the potential is strong enough, the particles diffuse together, giving geminate recombination. Otherwise the electron and hole diffuse apart and any subsequent recombination is non-geminate. The Onsager (1938) model 

The Coulomb potential model in Fig. 8.7 does not take into account quantum effects. The binding potential does not increase indefinitely as the electron and hole difiuse together, but instead an exciton is formed of binding energy E. The exciton can either dissociate thermally with rate exp (— E x/ T), or else can recombine with rate fV. An additional condition for geminate recombination is therefore. 

---

Rubel O, Baranovskii SD, Stolz W, Gebhard F (2008) Exact solution for hopping dissociation of geminate electron-hole pairs in a disordered chain. Phys Rev Lett 100 196602... 

In course of subsequent work Bubeck, Tieke, and Wegner discovered that the action spectrum for photopolymerization of undoped diacetylene multilayers extends into the visible provided some polymer formed in course of previous UV-irradiation is present. Since obviously excitation of the polymer can sensitize the reaction this effect has been termed self-sensitization. Checking the absorption spectrum of the polymer produced via self-sensitization assured that the final product is identical with the product obtained under UV excitation of the monomer. Later work by Braunschweig and Bassler demonstrated, that the effect is not confined to multilayer systems but is also present in partially polymerized single crystalline TS-6, albeit with lower efficiency. Interestingly, the action spectrum of self-sensitization follows the action spectrum for excitation of an electron from the valence band of the polymer backbone to the conduction band rather than the excitonic absorption spectrum of the polymer which is the dominant spectral feature in the visible (see Fig. 21). The quantum yield is independent of the electric field, whereas in a onedimensional system the yield of free carriers, determined by thermal dissociation of optically produced, weakly bound geminate electron-hole pairs, is an linear function of an applied electric field 29.30,32,129) Apparently, the sensitizing action does not... 

In organic photoreceptors photoinduced charge generation occurs through an excited state to produce a geminate electron-hole pair bound by their coulombic attraction. These separate into free carriers by a combination of diffusion and drift... 

After ionization of the excitons, the spatial separation of electrons and holes is small, i.e. <10 nm. Therefore, the charges attract each other by Coulomb interaction, and cannot be thought of as two independent freely moving species (Figure 13.2b). In the literature on organic solar cells this situation is described as bound electron-hole pairs , or geminate electron-hole pairs . The separation of electron and hole can be so small that their... 

A. Kadashchuk, A. Vakhnin, 1. Blonski, D. Beljonne, Z. Shuai, J.L. Bredas, V.l. Arkhipov, P. Heremans, E.V. Emelianova, and H. Bassler, Singlet-triplet splitting of geminate electron-hole pairs in conjugated polymers, Phys. Rev. Lett., 93, 066803 (2004). 

S. Difley, D. Beljonne, and T. Van Voorhis, On the singlet-triplet splitting of geminate electron-hole pairs in organic semiconductors, J. Am. Chem. Soc., 130, 3420-3427 (2008). 

It has been pointed out above that the deactivation of excitons may result in the formation of geminate electron/hole pairs that can eventually form free charge carriers. This process proceeds with strong competition from charge recombination and can be affected by an external electric field. According to the Onsager theory [31], the probability Pr of recombination can be estimated with the aid of Eq. (2-4). 

Hertel D, Soh EV, Bassler H, Rothberg LJ (2002) Electric field dependent generation of geminate electron-hole pairs in a ladder-type n -conjugated polymer probed by fluorescence quenching and delayed field collection of chaige carriers. Chem Phys Lett 361 99... 

A second issue is the efficiency of charge generation at the interface. The geminate electron-hole pair, represented by < D+A-, at the interface can dissociate... 

---