Mobility–diffusivity relationship for heavily doped organic semiconductors

Consistent double Gaussian model with non-symmetric potential barriers at contacts for organic diodes

“…3 also shows that the ratio of D/m deviates from the ER value kT/q, and the GER appears. However, the ratio also differs from the one in previous references, [33][34][35] in which the GER is due to degenerate effect of carriers. Since the viewpoint on GER is controversial in literature, [33][34][35][36] and the latest experiment 37 supports the ER for free carriers, the theoretical model dividing carriers into free and trapped types is consistent with the experiment.…”

“…However, the ratio also differs from the one in previous references, [33][34][35] in which the GER is due to degenerate effect of carriers. Since the viewpoint on GER is controversial in literature, [33][34][35][36] and the latest experiment 37 supports the ER for free carriers, the theoretical model dividing carriers into free and trapped types is consistent with the experiment. 37 The model of Nicolai et al 20,21 does not consider the asymmetric barriers at contacts, and adopted symmetric Ohmic contacts with W le ¼ W right .…”

“…It should be pointed out that trap-modulated mobilities were introduced decades ago, 1,2,4,[23][24][25][26] although not within the Gaussian DOS leading to eqn ( 29), and there are many possible GERs, for example eld-depend mobility. [33][34][35][36][37] Eqn (29) shows that although the mobility m 0 in the original model in eqn ( 14) and ( 15) is a constant, where the carriers are divided into free and trapped types, the effective mobility m and diffusion coefficient D in the transformed eqn (24) become functions of density of carriers. In Fig.…”

“…In the DDM, the ratio between the diffusion coefficient D and the mobility m is given by the Einstein relationship (ER), D/m ¼ k B T/q. Some authors [33][34][35][36] have proposed that the ER should be replaced by the generalized Einstein relation (GER) with the ratio k B T/q multiplied by a factor. However, Neumann et al 37 have disproved the GER through theoretical analysis.…”

Modeling the low-voltage regime of organic diodes: Origin of the ideality factor

“…Several recent papers discussed the validity of this relation in the case of organic semiconductors. [21][22][23] In general, it was found that a deviation from Einstein relation occurs with increased disorder (as measured by the variance of a Gaussian density of states) and charge carrier concentration. Here, we will assume that the semiconductor is partially ordered (or polycrystalline) and the carrier concentration is low enough (undoped or unintentionally doped semiconductor).…”