In the organic disordered materials, the charge transport is occurred by variable range hopping (VRH) of charge carriers between strongly localized states [22-25, 30, 58-61]. The VRH model proposed by Vissenberg and Matters model that considers the hopping percolation of thermally activated carriers between localized states is the most model used for describing charge transport in the disordered organic semiconductors and modeling the electrical characteristics OTFTs [27, 58]. Indeed, the notion of VRH implies that a free carrier either may over a long distance with low activation energy or hop over a short distance with high activation energy [22-25, 58]. A crucial feature of the VRH model is the determination of the density of states (DOS).
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However, the presence of a dipole layer can affect the charge transport properties, induce a deviation in the DOS distribution and broaden the tail states of the DOS in the organic semiconductors [70-71]. Generally, a given electric dipole refers to a separation of electric charges. The dipole moment P that represents a measure of the separation of positive and negative electrical charges in a system of electric charges is defined as …show more content…
For a given hopping site, under dipole moment effect, the probability density, W(r), of having the nearest carrier trapped at a distance r is determined by the Poisson distribution as [72-75]:
W(r)=4πr^2 N_t exp(-4/3 πr^3 N_t) (15) where r is the relative position of the dipole with respect to the charge. As a carrier trapped by a localized state, the potential energy of the Coulomb interaction between the carrier and dipole moment can be expressed as [73-75]:
E_CC=-(qP cosθ)/(4πε_0 ε_r r^2 ) (16) where q is the elementary charge, ε_0 is the dielectric permittivity, and ε_r is the relative dielectric permittivity, and θ is the angle between vector L ⃗ and r ⃗.
Thanks to the random distribution of dipole orientation, the total energy of the interaction between charge and the total dipole moment in the dipole layer of the interface is calculated as [72-74]:
E_C=∫_(-π/2)^(π/2)▒∫_0^(π/2)▒E_CC □(24&dθ□(24&dφ=)) ∫_(-π/2)^(π/2)▒∫_0^(π/2)▒(-(qP cosθ)/(4πε_0 ε_r (t⁄cosφ )^2 )) □(24&dθ□(24&dφ= qP/(8ε_0 ε_r t^2 )))
However, the presence of a dipole layer can affect the charge transport properties, induce a deviation in the DOS distribution and broaden the tail states of the DOS in the organic semiconductors [70-71]. Generally, a given electric dipole refers to a separation of electric charges. The dipole moment P that represents a measure of the separation of positive and negative electrical charges in a system of electric charges is defined as …show more content…
For a given hopping site, under dipole moment effect, the probability density, W(r), of having the nearest carrier trapped at a distance r is determined by the Poisson distribution as [72-75]:
W(r)=4πr^2 N_t exp(-4/3 πr^3 N_t) (15) where r is the relative position of the dipole with respect to the charge. As a carrier trapped by a localized state, the potential energy of the Coulomb interaction between the carrier and dipole moment can be expressed as [73-75]:
E_CC=-(qP cosθ)/(4πε_0 ε_r r^2 ) (16) where q is the elementary charge, ε_0 is the dielectric permittivity, and ε_r is the relative dielectric permittivity, and θ is the angle between vector L ⃗ and r ⃗.
Thanks to the random distribution of dipole orientation, the total energy of the interaction between charge and the total dipole moment in the dipole layer of the interface is calculated as [72-74]:
E_C=∫_(-π/2)^(π/2)▒∫_0^(π/2)▒E_CC □(24&dθ□(24&dφ=)) ∫_(-π/2)^(π/2)▒∫_0^(π/2)▒(-(qP cosθ)/(4πε_0 ε_r (t⁄cosφ )^2 )) □(24&dθ□(24&dφ= qP/(8ε_0 ε_r t^2 )))