Deep traps limits

TABLE II. Intensity Distribution in the Deep-trap Limit. 

Concerning ices, it has been discussed that they must be amorphous (Smoluchowski 1983) in the interstellar medium and not crystalline. This implies that the adsorbed H atoms are localized in deep traps so that their wavefunctions have a limited spatial extent. This fact reduces significantly their mobility and hence the interaction with another H atom absorbed on another site is slow as compared to the residence time unless the two atoms happens to be localized near each other. This phenomenon reduces the rate of H2 formation by several orders of magnitude when compared to the situation on crystalline surfaces. Computational simulations on soft and hard ice model surfaces have shown that for a cross-section of 4,000 nm2 the reaction probability is 1 (Takahashi et al. 1999). Furthermore, the H2 formed, due to the high amount of energy liberated is rapidly desorbed in an excited state from the ice mantle in timescales of 500 fs (Takahashi et al. 1999). 

The conclusion that the photocurrents are limited by recombination has been verified recently by Karl and Sommer (1971) who also determined the value of the bimolecular electron-hole recombination constant. The shapes of the transients observed in these experiments are similar to those which are characteristic of damaged surface layers (see p. 181). In a similar way many workers have observed non-linear field dependences of the collected charge. In their study of durene, Burshtein and Williams (1977) show that a consideration in terms of Onsager s (1938) theory of geminate surface recombination appears to be unsatisfactory the results are best explained in terms of efficient deep trapping and/or recombination in a narrow region near the illuminated surface. 

Fig. 2. The energy levels as a function of trap depth S for the onedimensional mixed crystal with guest concentration The manifold shown belongs to r = 0. The dotted curves are plots of the shallow-trap (left-hand) and deep-trap (right-hand) limiting approximations.

As the trap is made deeper the intensity spreads more widely over the levels of the band. In treating deep traps it is convenient to begin with the hypothetical limit of the infinitely deep trap, based on the wave functions (17) of the residual host, and to consider transitions to them from the ground state. The transition... 

Reucroft and Takahashi (1975) reported room temperature hole mobilities of PVK. The mobilities were field dependent and described by a power-law relationship. The studies of Reucroft and Takahashi and Mort and Emerald (1974) are two of few references in the literature to a field dependence of log t °< PE. The presence of deep traps at 5 to 10 x 1012 cm-3 was reported. It was suggested that the traps were due to either small molecule impurities, impurity monomer units incorporated into the polymer chain, or localized regions of compression introduced by polymer chain entanglements. The lower limit of the trap cross section was reported as 10 A2. It was suggested that the traps were primarily located in surface regions. 

From picosecond transient photoconductivity measurements on PPP films,22 we know that mobile charged states decay within 110 ps. In conventional routes to PPPs, defects like branched chains and large torsion angles of neighboring rings are known to occur. These defects act as shallow or deep traps for positive and negative polarons,38,39 which limit the mobility of charge carriers.40 The synthetic route toward the PPP-type ladder-polymers prevents the described defects and leads to a trap concentration of less than 1 trap per 1000 monomer units,28 whereas substi-... 

For some choices of the parameters, it is possible to obtain very small values for the axial vibrations of the ion along the channel. As we will see, band states for these systems correspond to the nearly free ion limit. On the other hand, it is possible to find other axial frequencies reaching nearly 20 cm 1. In these cases, we have treated (post) the bands in the tight binding limit. With distortions of the channel walls in the vicinity of the ion, a case not specifically illustrated here, it is possible to see the formation of deep traps of several decades in axial frequency. In these cases, the ion transfer along the chain would occur via an activated site-hopping mechanism. The formalism... 

Photoconductivity and SCLC experiments have been used to obtain information on localized states in the bulk of organic crystals. However, information about the surface states that are relevant to the OFET operation is stiU very limited. Fortunately, the calculation of several basic OFET parameters does not require a detailed knowledge of the trap spectrum. For example, the field-effect threshold voltage is determined by the total density of deep traps... 

The oxygen vacancy defects appear to function as deep traps for holes and recombination centers for electrons and shallow traps for electrons [66] (the limited dispersion of time constants in transient current experiments has been attributed to the absence of deep electron traps). No optical absorbance is associated with occupied defects but instead a bleaching of the absorption... 

From equation 5, it can be seen that maximization of Letr for a given grating spacing requires maximization of the fx-r product or application of a large external field. Because of the dispersive nature of the transport, fx and x are not easily defined quantities in polymers (78). The mobilities are field dependent, often in a highly nonlinear way, and the presence of significant trapping in a polymer complicates their determination (33,79). Furthermore, r in many polymers may be effectively limited by the presence of deep traps from which further photoionization is inhibited. 

Transient electrical data collected under different bias conditions contain enough information to determine the density of states with the aid of a transient device model. One study has shown that by simultaneously fitting a number of transient current measurements, as well as steady-state device response, a non-trivial best fit for the densities of sub gap electron and hole states could be obtained [86]. In a further application of the transient device simulation it has been shown that in certain conditions the transient current extracted from a solar cell device accurately reflects the density of states of the carrier type with the greater density of deep trap states [160]. In those conditions where this approximation is true, then transient current data can be modelled with a simple expression for current due to thermally emitted charge carriers, and the current transient mapped onto a density of states function [51, 52]. However, the approximation fails in the limit of significant recombination or low electric fields. 

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