Gaussian distribution, charge transport

An alternative approach [28, 50-54] is based on the assumption that the density of states can be modelled by a Gaussian distribution. Charge carrier transport occurs via direct hopping between the localized sites. In general, the differences between the two models are too small to be detected experimentally. Since our data can be quantitatively explained within the framework of multiple trapping we will restrict the discussion to this model. 

Usually, in amorphous molecular materials, charge transport is described by a disorder formalism that assumes a Gaussian distribution of energetic states of the molecules between which the charges jump [246]. The mobility is then given by... 

The choice of a Gaussian distribution can be justified by the observation that the optical absorption profiles of well-defined conjugated moieties are Gaussian. Charge transport is treated as a biased random walk amongst the conjugated moieties, which have random site energies described by Equation... 

Vs//2. The energetic disorder o can be imderstood as the width of the Gaussian distribution of the density of energy states for the transport sites the positional disorder E can be treated as the geometric randomness arising from structural or chemical defects [28,29]. In essence, only two material parameters, viz., a and E, are used to describe the randomness of the amorphous organic charge transporter. The PF slope, Ppp, is now replaced with P in Equation 3.7, and in the context of the GDM, it is related to the disorders of tire material. From Equations 3.6 and 3.7, o can be determined from the slope of the plot of p(0,T) vs l/T, while E can be determined from the x-intercept of a plot of P vs (cs/k Tf. 

Millis et al. [21] suggested that the evidence of lattice involvement in charge transport may be observed in the Debye-Waller (DW) factor. Indeed Dai et al. [25] reported an anomalous temperature dependence of the DW factor and concluded that polarons must be formed. However, the evidence provided by the DW factor is qualitative as we discussed earlier. The DW approximation assumes a harmonic (Gaussian) distribution of atomic displacements. If only a small number of atoms deviate significantly from the average positions, the DW approximation greatly underestimates the actual displacements. 

One of the easiest ways to model charge transport in a random distribution of localized states is via Monte Carlo simulation [7, 8]. The essential input parameter is the width a of the DOS, which is usually assumed to be of Gaussian shape ... 

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