Excitation and Recombination of Charge Carriers

Accordingly, the recombination rate as well as the lifetime of a band-band recombination process depends strongly on the carrier density. 

The trapping rate for electrons from the conduction band into traps is proportional to the electron density in the conduction band and to the number of empty traps. We have then 

C can be related to C by analyzing the equilibrium state which is determined by R = Rg. Applying this condition, we have 

The carrier density for a Fermi level located just at the trap level ( p = ,) is given by 

If the equilibrium of a semiconductor is disturbed by excitation of an electron from the valence to the conduction band, the system tends to return to its equilibrium state. Various recombination processes are illustrated in Fig. 1.16. For example, the electron may directly recombine with a hole. The excess energy may be transmitted by emission of a photon (radiative process) or the recombination may occur in a radiationless fashion. TTie energy may also be transferred to another free electron or hole (Auger process). Radiative processes associated with direct electron-hole recombination occur mainly in semiconductors with a direct bandgap, because the momentum is conserved (see also Section 1.2). In this case, the corresponding emission occurs at a high quantum yield. The recombination rate is given by 

In the case of semiconductors with an indirect gap, recombination occurs primarily via deep traps (Fig. 1.16). Here, an electron is first captured by the trap in a second 

---

The situation is quite different if minority carriers are involved. Then electrons and holes are not in equilibrium and their quasi-Fermi levels become different. In the case of an n-type semiconductor, f,p can be located above or below depending on the minority carrier process, i.e. on whether minority carriers are extracted from or injected into the semiconductor. However, quasi-Fermi levels have been qualitatively used in the theory of non-equilibrium processes in solid state devices, such as the excitation and recombination of electrons and holes (see Section 1.6), and also for the descriptions of charge transfer processes in p-n junctions (see Section 2.3). In this section a quantitative analysis of reactions at n- and p-type electrodes in terms of quasi-Fermi levels will be derived [19, 54]. 

Thus weak disorder may be the main source of localization and conjugation length limitation. The variations in electronic properties such as absorption will then not always follow laws such as those given in Section II.C N 1 variations are well verified for polyenes, but then would not give the correct extrapolation for N — °°. Weak disorder also localizes excitations for instance, photoexcited charge carriers. It will induce the presence of polarons even if they were not bound states of the perfect chain, or of bipolarons, modify the transport properties, and increase the lifetime of charge carriers against recombination [98]. 

The operation of organic light-emitting diodes (OLEDs) involves charge injection from electrodes, transport of charge carriers, recombination of holes and electrons to generate electronically excited states or excitons, followed by their deactivation by emission of either fluorescence or phosphorescence. The main factors that determine luminous and external quantum efficiencies are the following ... 

Thus, in case of weak excitation the lifetime of electrons and holes is controlled, in general, by nonradiative recombination centers and equals to the corresponding value T r. The effect of stabilization of the effective lifetime of charge carriers in homogeneously doped superlattices is more pronounced compared with... 

---