Capture radius, Coulombic

An equation of the type (16) makes most physical sense when there exists a large capture radius Rc however, it can be applied to any diatomic capture case if regarded simply as a definition of Rc. Its utility is twofold. For one thing, physical common sense can sometimes give a value, or a bound, for Rc. When there is a Coulomb attraction between the reacting species, as for our case of H+ and A-, Rc can be plausibly estimated from... 

Consider first the fate of an H+. In a region with an average density nB of B- ions, each with a Coulomb capture radius of the order of 50A [from (17)], the mean lifetime rc of an H+ with respect to capture into BH will... 

The classic treatment of carrier recombination can be related to the notion of the recombination time. The recombination time represents a combination of the carrier motion time (im), i.e. the time to get the carriers within capture radius (it is often assumed to be the Coulombic radius rc = e2/An o kT), and the elementary capture time (tc) for the ultimate recombination event (actual annihilation of charge carriers), tree1 = m1 -I Tc 1 (cf. Fig. 3). Following the traditional description of recombination processes in ionized gases, a Langevin-like [22] and Thomson-like [23] recombination can be defined if Tcsolid-states physics, these two cases have been distinguished... 

For an organic semiconductor blend with an average dielectric constant of 3, this Coulomb capture radius is 19 nm at room temperature, which is somewhat larger than the typical exdton diffusion length of 10 nm. Of course for this estimation it... 

This process is referred to as auto-ionization (AI). It does not follow that all AI transitions lead to completely uncorrelated carrier pairs. Most of the emitted electrons will thermalize within the Coulomb capture radius of the geminate positive ion, forming a transient charge-transfer state that can either decay to the ground state or dissociate by the absorption of ambient energy. Following Jortner (3), the wavefunction of such an AI state can be written as... 

The value of 2q is referred to as the Coulombic capture radius r, and corresponds to the distance at which the kinetic energy of the diffusing particle is equal to the Coulombic attractive potential energy. For an electron moving with thermal energy kT,... 

Equations (10.2) and (10.3) describe the process when a pair of opposite charges encounter each other in space and recombine with the help of Coulomb attraction. According to the classical bimolecular recombination model, when the mean free path of charges in a material is smaller than the Coulomb capture radius bimolecular recombination will take place. The typical mean free path of organic semiconductors is about 1-2 nm, which is much smaller than r (10-20 nm at room temperature ), therefore bimolecular recombination is universally present in OSC devices. ... 

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