Nature of Charge Carriers in Disordered Molecular Solids: Are Polarons Compatible with Observations?

Abstract

Polaronic theories for charge transport in disordered organic solids, particularly molecularly doped polymers, have been plagued by issues of internal consistency related to the magnitude of physical parameters. We present a natural resolution of the problem by showing that, in the presence of correlated disorder, polaronic carriers with binding energies Delta approximately 50-500 meV and transfer integrals J approximately 1-20 meV are completely consistent with the magnitudes of field and temperature dependent mobilities observed.

Charge-carrier concentration dependence of the hopping mobility in organic materials with Gaussian disorder

“…͑5͒ in Ref. 16 37 and Parris et al 38 provided further support for the latter approach by showing that the exp͓␥ ͱ F͔ field dependence is obtained over an extended field range if it is assumed that the site energies show a certain degree of spatial correlation. These results were argued to be in good qualitative agreement with experimental findings from time-of-flight measurements ͑TOF͒ on molecularly doped polymers ͑see Ref.…”

On the unipolarity of charge transport in methanofullerene diodes

“…Marcus-Hush theory and the Gaussian Disorder Model (GDM) 27 have been applied to a 3D network of molecules with energetic disorder σ. 28 The charge carrier mobility is dependent on energetic disorder σ as follows…”

Charge‐Carrier Density Independent Mobility in Amorphous Fluorene‐Triarylamine Copolymers

“…The original Gaussian disorder model (GDM) developed by Bässler for hopping transport in a Gaussian density of states (DOS) distribution was a single carrier approach, [ 1 ] as were the models based on it which considered both correlated energetic disorder, [ 2 ] with a smoothly varying energy landscape (see Figure 1 a), and the effect of polaronic relaxation. [ 3 ] The percolation model developed by Vissenberg and Matters for transport involving an exponential DOS instead considered multiple carriers, [ 4 ] and this predicted a mobility which has a power-law dependency on the charge-carrier density. The measured transistor mobility falls two to three orders of magnitude below that predicted from the charge-carrier density dependent model, and does not follow the expected power-law relationship.…”

“…Such energetic disorder will directly impact charge transport and mobility. [1][2][3][4][5][6][7][8][9][10][11][12] For such energetically disordered OSCs, one feature predicted by many charge transport models is a charge-carrier density dependent mobility. The original Gaussian disorder model (GDM) developed by Bässler for hopping transport in a Gaussian density of states (DOS) distribution was a single carrier approach, [ 1 ] as were the models based on it which considered both correlated energetic disorder, [ 2 ] with a smoothly varying energy landscape (see Figure 1 a), and the effect of polaronic relaxation.…”