Recombination at defects

Even when is large, the concentration gradient only extends for about the diffusion length Ljj. Surface recombination is a weak effect in a-Si H, because Lj, is small and is confined to carriers created close to the surface. This occurs particularly at low temperature when the diffusion length is less than 100 A. This contrasts with the situation in a crystal, in which the diffusion length is large and can lead to a high recombination rate even when is small. 

Surface recombination reduces the luminescence intensity when the excitation light has a very short absorption length. The effect is weak because of the low carrier mobility and diffusion length, so that although there are many defects at the surface of a-Si H, the effect on the luminescence intensity is only 10-20% (Dunstan 1981). A measure of the surface recombination is the product, aLp, of the optical absorption coefficient and the diffusion length. In most situations in a-Si H, and particularly at low temperature, aLp is less than unity, whereas in crystals it is often much greater. 

The surface recombination of a-Si H is greatly enhanced in multilayer structures which constrain the electron-hole pair to be near an interface. For example a thin a-Si H film sandwiched between a-Sig N4 layers, has a luminescence intensity which drops rapidly when the layer thickness is less than 200 A. These results are discussed further in the next chapter (Section 9.4.1) and show that surface recombination effects extend 100-200 A into the film, and that electron-hole pairs created farther from the surface are not influenced by the surface at low temperature. As the carriers become more mobile at higher temperatures, the diffusion length increases and surface recombination is more significant. 

Defects provide the dominant recombination path when their density is above about 10 cm or when the temperature is higher than about 100 K. The recombination mechanism depends on the temperature and on the mobility of the carrier. The low temperature mechanism is discussed first. 

---

Fig. 3 depicts low-temperature PL spectra of the implanted samples. A broad band at 0.92 eV with small intensity is observed in the as-implanted sample. It can be attributed to radiative recombination at defects induced by ion implantation. 

Fig. 1. The energy levels in a semiconductor. Shown are the valence and conduction bands and the forbidden gap in between where represents an occupied level, ie, electrons are present O, an unoccupied level and -3- an energy level arising from a chemical defect D and occurring within the forbidden gap. The electrons in each band are somewhat independent, (a) A cold semiconductor in pitch darkness where the valence band levels are filled and conduction band levels are empty, (b) The same semiconductor exposed to intense light or some other form of excitation showing the quasi-Fermi level for each band. The energy levels are occupied up to the available voltage for that band. There is a population inversion between conduction and valence bands which can lead to optical gain and possible lasing. Conversely, the chemical potential difference between the quasi-Fermi levels can be connected as the output voltage of a solar cell. Fquilihrium is reestabUshed by stepwise recombination at the defect levels D within the forbidden gap.

A representative example for the information extracted from a TRMC experiment is the work of Prins et al. [141] on the electron and hole dynamics on isolated chains of solution-processable poly(thienylenevinylene) (PTV) derivatives in dilute solution. The mobility of both electrons and holes as well as the kinetics of their bimolecular recombination have been monitored by a 34-GHz microwave field. It was found that at room temperature both electrons and holes have high intrachain mobilities of fi = 0.23 0.04 cm A s and = 0.38 0.02 cm / V s V The electrons become trapped at defects or impurities within 4 ps while no trapping was observed for holes. The essential results are (1) that the trap-free mobilities of electrons and holes are comparable and (2) that the intra-chain hole mobility in PTV is about three orders of magnitude larger than the macroscopic hole mobility measured in PTV devices [142]. This proves that the mobilities inferred from ToF and FET experiments are limited by inter-chain hopping, in addition to possible trapping events. It also confirms the notion that there is no reason why electron and hole mobilities should be principally different. The fact... 

The recombination of electrons and holes is a rather complicated process. We have to distinguish between (a) the direct recombination of electrons and holes, occurring in particular at high concentrations of charge carriers (b) recombination via defect states which depends, among other factors, on the densities and capture cross-sections of the defects (recombination centers) located in the bulk of the solid or on its surface. 

Recombination at and excitation from deep levels are emphasized. Nonradiative transitions at defect levels—Auger, cascade capture, and multiphonon emission processes—are discussed in detail. Factors to be considered in the analysis of optical cross sections which can give information about the parity of the impurity wave function and thus about the symmetry of a particular center are reviewed. 

Strictly speaking, it is correct in the case of complete particle recombination at the black sphere only partial particle reflection is discussed by Doktorov and Kotomin [50]. Incorporation of the back reactions into the kinetics of geminate recombination has been presented quite recently by [74, 75]. The effective radius for an elastic interaction of defects in crystals, (3.1.4), was calculated by Schroder [3], Kotomin and Fabrikant [76],... 

In equation (7.1.6) the first and the last term in the r.h.s. turns out to zero as cto —> 00 The integral terms contain functions 52,2 in which there exist several defects A in the recombination sphere around B which, in their turn, have partners to recombine at r tq. In the limit of instant annihilation such functions have another order of magnitude in Oq. ... 

Equation (7.1.16) is asymptotically (cto — oo) exact. It shows that the accumulation kinetics is defined by (i) a fraction of AB pairs, 1 — u>, created at relative distances r > r0, (ii) recombination of defects created inside the recombination volume of another-kind defects. The co-factor (1 - <5a - <5b ) in equation (7.1.16) gives just a fraction of free folume available for new defect creation. Two quantities 5a and <5b characterizing, in their turn, the whole volume fraction forbidden for creation of another kind defects are defined entirely by quite specific many-point densities pmfl and po,m > he., by the relative distribution of similar defects only (see equation (7.1.17)). 

The quantum efficiency of the band tail luminescence is largest at low temperature, low excitation intensity, and in samples of low defect density. Other conditions cause competing non-radiative processes which quench the luminescence intensity. Direct recombination to defect states in samples of high defect density is discussed in Section 8.4.1. The other main non-radiative mechanism is thermal... 

Fig. 8.20 shows the dependence of the band tail luminescence intensity on the defect density as measured by the g = 2.0055 ESR resonance in undoped a-Si H. The luminescence intensity drops rapidly when the defect density is above 10 cm" , becoming unobservable at defect densities above 10 cm" (Street et al. 1978). These data establish that the defect provides an alternative recombination path competing with the radiative band tail transition. At the low temperatures of the measurements, the electrons and holes are trapped in the band tails and are immobile. Both the radiative and the non-radiative transitions must therefore occur by tunneling. Section... 

---