Slow Ion Capture by an Overcharged Complex

For analysing slow processes it is sufficient to consider the last reaction (29) describing the capture of a mobile ion by the overcharged complex. The equilibrium constant is given by 

This process can be important only if the equilibrium lies on the side of the complex D , which means for 3(0, ) =(Cp /Cp, ) 1. The time constant for the formation of the neutral complex Dj is, according to (6), given by = (k c ) . On the other hand, the time constant for the decay of 

Several mechanisms for the hysteresis effeets have been proposed in the literature, in most cases as verbal statements without mathematical formulation and numerical evaluation. Typical statements are that trap recharging or mobile ions are likely to cause the hysteresis. Additionally we have proposed that formation and dissociation of bipolarons in the accumulation layer can cause this effeet. 

Numerical simulations on the trap recharging mechanism in MIS capacitors and transistors indicate that energetically distributed traps in particular can lead to hysteresis in these devices. On the other hand, the form of the simulated hysteresis deviates from the observed one and extreme parameter values are needed either for the total trap concentration or for the product from capture cross section and thermal velocity. We conclude that it is more likely that trap recharging can modify a hysteresis caused by another mechanism than being the main origin of the hysteresis. 

A revisal of the equilibrium between polarons and doubly charged states of the polymer chains shows that the previous assumptions on the extension of polaron, bipolarons and polaron pairs were not justified. A more general formulation is presented for the equilibrium concentrations and the kinetics. But the differences are almost negligible up to the maximum charge concentrations that can be achieved in accumulation layers. The resulting rate constants for formation and dissociation of (immobile) bipolarons can be estimated using a rate constant for the bipolaron formation determined recently by Salleo and Street, and indicate that these processes can cause the hysteresis on the time scale of the measurements. 

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