Density of trapping states

Concerning the nature of electronic traps for this class of ladder polymers, we would like to recall the experimental facts. On comparing the results of LPPP to those of poly(para-phenylene vinylene) (PPV) [38] it must be noted that the appearance of the maximum current at 167 K, for heating rates between 0.06 K/s and 0.25 K/s, can be attributed to monomolecular kinetics with non-retrapping traps [26]. In PPV the density of trap states is evaluated on the basis of a multiple trapping model [38], leading to a trap density which is comparable to the density of monomer units and very low mobilities of 10-8 cm2 V-1 s l. These values for PPV have to be compared to trap densities of 0.0002 and 0.00003 traps per monomer unit in the LPPP. As a consequence of the low trap densities, high mobility values of 0.1 cm2 V-1 s-1 for the LPPPs are obtained [39]. 

Zeiger has recently published a theoretical examination of the effect of traps on the SL linewidth. Given a sufficient density of trap states within the optical mode volume, a result similar to the observed behavior is obtained if the trap decay rates are at least of the order of the power-independent linewidth. The motivation for the trapping theory came in part from the widely observed l/f behavior in the low frequency current, amplitude and frequency noise spectra of SL s. This is discussed in more detail shortly. Similar behavior in the current fluctuation noise in semiconductors has been related to the presence of trap levels. 

This resulted in penetration depths which could exceed the sample dimensions. The density of trapping states seems to be the more important parameter. The model can be extended to include surface states as well as bulk states or other nonuniform state distributions. Only if Vj and (T are known can the penetration depth and the density of states be calculated. If we consider the contact potential, Vc acting across a distance equal to the penetration depth, to be equivalent to an effective surface capacitance, Cs, the injecting field Vg/t > is neutralized by the injected charge 0/2e. 

For the simplest case of a single set of localized states sitnated at a particular energy Ei, the trap-limited drift mobility of carriers moving in extended states at is readily compnted from equation (3.3). If the effective density of extended states at Ep is Np and the trap concentration is N, then we may write... 

Analytical considerations applied to the full dynamics (where it is H rather than T that determines the time evolution) and computational results [45f] suggest that even when the coupling is allowed for, remnants of the zero-order dichotomy between promptly decaying and stable states do survive, that K states can either decay promptly, without much sampling of the bound space of N states, and that N - K states have a delayed decay. The larger is the density of bound states, the slower is the decay of the states that, in first order, are trapped. Figure 6 is the schematic case while Fig. 8 shows explicit computational results. 

Electron-hole recombination velocities at semiconductor interfaces vary from 102 cm/sec for Ge3 to 106 cm/sec for GaAs.4 Our first purpose is to explain this variation in chemical terms. In physical terms, the velocities are determined by the surface (or grain boundary) density of trapped electrons and holes and by the cross section of their recombination reaction. The surface density of the carriers depends on the density of surface donor and acceptor states and the (potential dependent) population of these. If the states are outside the band gap of the semiconductor, or are not populated because of their location or because they are inaccessible by either thermal or tunneling processes, they do not contribute to the recombination process. Thus, chemical processes that substantially reduce the number of states within the band gap, or shift these, so that they are less populated or make these inaccessible, reduce recombination velocities. Processes which increase the surface state density or their population or make these states accessible, increase the recombination velocity. 

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