Electric field dependence of charge carrier hopping transport within the random energy landscape in an organic field effect transistor

Abstract

We extended our analytical effective medium theory [Phys. Rev. B 81, 045202 (2010)] to describe the temperature-dependent hopping charge carrier mobility at arbitrary electric fields in the large carrier density regime. Special emphasis was made to analyze the influence of the lateral electric field on the Meyer-Neldel (MN) phenomenon observed when studying the charge mobilities in thin-film organic field-effect transistors (OFET). Our calculations are based on the average hopping transition time approach, generalized for large carrier concentration limit finite fields, and taking into account also spatial energy correlations. The calculated electric field dependences of the hopping mobility at large carrier concentrations are in good agreement with previous computer simulations data. The shift of the MN temperature in an OFET upon applied electric field is shown to be a consequence of the spatial energy correlation in the organic semiconductor film. Our calculations show that the phenomenological Gill equation is clearly inappropriate for describing conventional charge carrier transport at low carrier concentrations. On the other hand a Gill-type behavior has been observed in a temperature range relevant for measurements of the charge carrier mobility in OFET structures. Since the present model is not limited to zero-field mobility, it allows a more accurate evaluation of important material parameters from experimental data measured at a given electric field. In particular, we showed that both the MN and Gill temperature can be used for estimating the width of the density of states distribution.

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

“…The EMA theory with correlated disorder also predicts a mobility which is fi eld dependent and effectively charge-carrier independent at the DOS widths found for PFB and PFMO. [ 11 ] Hence, the presence of correlated disorder might offer a possible explanation of charge-carrier density independent transport in amorphous fl uorene-triarylamine copolymers. Recent structural investigations of a noncrystalline high mobility polymer show longrange alignment between the chains.…”

“…[ 8 ] These again predict a mobility which increases with increasing charge-carrier density, additionally showing that the temperature dependency of charge transport should simultaneously decrease, [ 9 ] and that correlated energetic disorder and polaronic effects will vary the behavior. [ 6,8,[10][11][12] Experimentally, OFETs probe the high charge-carrier density regime between about 10 17 and 10 20 cm −3 , while diodes (OPVs and OLEDs) probe the low charge-carrier density between about 10 15 and 10 17 cm −3 . The total number of transport states (based on the molecular or conjugation length density) is about 5 × 10 20 cm −3 , so in OFETs there is about 1 carrier per 10-100 sites, while in diodes there is about 1 carrier per 10 000-100 000 sites.…”

“…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.…”

Effect of source-drain electric field on the Meyer–Neldel energy in organic field effect transistors

“…Recently Fishchuk et al 7 extended the above theoretical model to consider the OFET mobility at arbitrary electric fields, viz., lateral field caused by source-drain voltage. In the present letter, we report on experimental and theoretical investigation of the influence of the lateral electric field on the MN energy in OFETs.…”

“…7 The model is based on effective medium formalism and takes also into account spatial energy correlation effects using the results of recent computer simulations 11 of charge-carrier transport in energy correlated system at large carrier concentrations ͑see for calculation details in Ref. 7͒.…”