Electric field and grain size dependence of Meyer-Neldel energy in C(60) films.

Meyer-Neldel rule for charge carrier mobility measured in C(60)-based organic field-effect transistors (OFETs) at different applied source drain voltages and at different morphologies of semiconducting fullerene films was systematically studied. A decrease in the Meyer-Neldel energy E(MN) from 36 meV to 32 meV was observed with changing electric field in the channel. Concomitantly a decrease from 34 meV to 21 meV was observed too by increasing the grain size and the crystallinity of the active C(60) layer in the device. These empiric findings are in agreement with the hopping-transport model for the temperature dependent charge carrier mobility in organic semiconductors with a Gaussian density of states (DOS). Experimental results along with theoretical descriptions are presented.

Introduction

Meyer–Neldel (MN) rule [1] has been typically observed in Arrhenius plots of the charge carrier mobility (μ) with changing carrier density in organic field-effect transistors (OFETs) [2,3]. In context of the charge transport in OFETs, the Meyer–Neldel rule suggests an empirical relation between the Arrhenius activation energy E and the mobility prefactor as described below by Eq. (1).More specifically, MNR implies that the Arrhenius-type (log(μ) vs 1/T) dependences, measured at different gate voltages and, concomitantly, at different charge carrier densities, intersect at a given finite isokinetic temperature TMN. Recent studies of the MN effect in C60 OFETs showed that the characteristic parameter called Meyer–Neldel energy “EMN = kBTMN” can be used to determine the width of the density-of-state (DOS) distribution, σ, in the conductive channel of an organic semiconducting film [4,5]. Temperature dependence of mobility measurements in C60 films grown at different conditions have revealed a significant shift of the Meyer–Neldel energy (and consequently change in the energetic disorder parameter σ) with changing film morphology [5]. Thus it was proposed [5] that ‘EMN’ can be used as an important material characterizing parameter for active organic semiconductor layers in OFETs independent of the device geometry [6].

The theoretical consideration of the Meyer–Neldel effect [4] in organic materials was based on a Gaussian disorder model with accounting for the carrier concentration dependence of the OFET mobility, however, it was limited to zero-electric field implying thus it is justified just for a very low lateral field. Recently Fishchuk et al. [7] extended the theoretical model described by Eq. (1) to consider the OFET mobility at arbitrary electric fields, viz. lateral field caused by source-drain voltage. In the present paper we report on experimental investigation of the influence of the lateral electric field on the Meyer–Neldel energy in OFETs with different active film morphology. The shift of the Mayer–Neldel temperature in an OFET upon applied lateral electric field was found for the first time and described successfully by the extended analytic model of Fishchuk et al. [7,15] that accounts for the field dependence of the OFET mobility. We have shown that the observed electric field dependence of the Meyer–Neldel energy is a consequence of the spatial energy correlations in the organic semiconductor film which features a Poole–Frenkel behavior for OFET mobility upon applied source-drain field (F). Since this model is not limited to zero-field, it allows a more accurate evaluation of energetic disorder parameters from experimental data measured at a given electric field.

Experimental setup

The charge carrier mobility in C60 OFETs was evaluated from the transfer characteristics in the linear regime (V ≫ V, where Vg and Vd are the gate and drain source voltages respectively) in order to ensure a homogeneous charge distribution in the conductive channel. In order to maintain the linear regime conditions we used low source drain voltages. These OFET devices, schematically shown in Fig. 1, were fabricated using divinyltetramethyldisiloxane-bis(benzocyclobutane) (BCB) as gate dielectric on ITO/glass substrates and C60 thin films as active organic semiconductor were grown by Hot Wall Epitaxy (HWE) system as described in [2,3].

Fig. 1

OFET geometry (a) with different fabrication layers and AFM images of C60 films grown by HWE system at a substrate temperature of (b) 130 °C and (c) 250 °C.

Results and discussion

The observation of different Arrhenius activation energies for charge carrier mobility in OFETs at different carrier concentrations leads to the phenomenological MN rule.

Fig. 2(a) shows the MN type behavior of charge carrier mobility in C60 OFET at a source-drain voltage of 2 V and Fig. 2(b) shows the MN behavior at a source-drain voltage of 10 V. A shift in the Meyer–Neldel temperature from 409 K to 372 K is clearly visible in both Arrhenius plots Fig. 2(a) and (b).

Fig. 2

Meyer Neldel rule behavior of charge carrier mobility measured in OFETs at different applied source-drain voltages (a) 2 V (b) 10 V.

Fig. 3 shows, on one hand, the Arrhenius activation energy of charge carrier mobility decreases with increasing V, which can be explained by the fact of filling up the DOS with increasing charge carrier concentration and consequently shifting the Fermi level closer to the effective transport energy level [8,9]. This decreases the activation energy which charge carriers have to overcome in order to obtain higher mobility. On the other hand, the activation energy decreases with increasing electric field in the film, which can be explained by the fact, that the electric field lowers the average barrier height for energetic uphill jumps in the field direction [10]. Fig. 3 shows a Poole–Frenkel type behavior of the activation energy which decreases linearly with square-root of the source-drain voltage.

Fig. 3

Arrhenius activation energy measured as a function of gate voltage V at different applied source-drain voltages Vd.

The Mayer–Neldel energy measured in C60 OFETs at different source-drain voltages is plotted in Fig. 4 (symbols). The “EMN” was found to shift from 35 meV to 32 meV with increasing lateral electric field in these devices.

Fig. 4

Meyer–Neldel energy as a function of the lateral electric field measured in C60-based OFET (symbols) and the theoretical fit based on our extended model as described by Eqs. (1) and (2). Dashed curve 2 was calculated by neglecting any energy correlation effects.

Recently Fishchuk et al. extended their analytic model, which was originally suggested for a zero-electric field limit, to consider the temperature dependent OFET mobility also at arbitrary electric fields [7]. Their 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 charge carrier concentrations [7]. Energy correlations in organic disordered solids imply slowly varying static spatial fluctuation in the potential energy landscape and can arise due to charge–dipole [12] or charge–quadrupole interactions or fluctuations (inhomogenity) in electronic polarization energy, resulting from molecular density fluctuations in an organic material due to microscopic regions that are under compression or dilation [13].

In particular, the analytic model [7] accounts for a reduced local variance in the energy distribution of nearby hopping sites due to the correlation-induced smoothing of the energy landscape in a disordered organic solid and, what was found to be of special relevance for the description of the presented experimental results, is that it accounts for a decrease of the slope of the Pool–Frenkel-type field dependence with increasing carrier density [11]. The latter was found to be an immediate reason giving rise to the lateral field (F) dependence of the Meyer–Neldel energy. This dependence can be parameterized in the following form [7] for a/b = 5:where e is the elementary charge, a is an average intermolecular distance assumed for C60 films to be similar to C60 crystals, viz. a = 1.4 nm [14], and b is the carrier localization radius. The width of the DOS σ can be determined asEqs. (2) and (3) are valid for eaF/σ > 0.25, i.e. when the Poole–Frenkel-type field dependence of the OFET mobility is obeyed. At lower fields, the charge mobility tends to saturate upon approaching zero-field and thus deviates from the Poole–Frenkel low [7,11]. Consequently, the actual zero-field mobility differs from that obtained by extrapolations of plots to F → 0. It should be noted that the present extended theoretical model yields EMN/σ ≅ 0.33 for zero-field mobility. Previous theoretical treatment limited to zero-field case [4], which disregarded the energy correlations and percolation effects, yielded a somewhat different ratio EMN/σ ≅ 0.40. Solid curve 1 in Fig. 4 shows the calculated lateral electric field dependence of EMN using Eqs. (2) and (3) at q = 256 and a = 1.4 nm, and it demonstrates a remarkably good fitting of the experimental data by the present analytic model for F = V/L > 500 V cm−1, when dependence for the OFET mobility takes place. The calculated field dependence of EMN for the system, devoid of any spatial energy correlations, is given by he dashed curve 2 in Fig. 4. Thus, the experimentally observed decrease of the Meyer–Neldel energy with increasing electric field results from the presence of spatial energy correlations.

Thus, the experimentally determined EMN at a finite electric field can directly be used for the evaluation of the energy disorder parameter σ by Eq. (3) without the necessity of an extrapolation of the experimental data to zero-electric field [15].

The charge carrier mobility strongly depends on the active film morphology. Temperature dependence of the mobility in these films results into different disorder and ultimately into different EMN in different films [5]. Fig. 5(a) shows the electric field dependence of charge carrier mobility in OFETs with different morphology of C60 films (as shown in Fig. 1(b) and (c)) and Fig. 2(b) shows the evaluated Meyer–Neldel energy of these devices form the temperature dependence of the charge carrier mobility with changing carrier concentration to change activation energy. We observed that the electric field dependence of EMN shows relatively strong dependence in OFETs with small grain size of active film than in OFETs fabricated from bigger grain size films which were grown at higher substrate temperatures. This leads to the fact that disorder present in the active film is crucial in charge transport studies. The variance in different charge transport parameters in more ordered films is less and the obtained devices give a better efficiency. It should be noted, that for the quantitative description of the lateral-field dependence of the OFET mobility one has to involve a concept of a strong inhomogeneity of the lateral electric field inside the accumulation layer formed in an OFET caused by an inhomogeneous morphology of the semiconductor, which results in strong local fields confined to specific places having the largest energetic barrier heights and, hence, controlling the overall (effective) hopping charge mobility through the OFET channel [7]. Thus, it is actually the effective local field that should be used in Eq. (3) instead of the average applied electric field. The ratio q between the local electric field strength and that averaged over the transistor channel V/L can be readily determined from the field dependence of EMN. In fact, a set of just two EMN values measured at two different electric fields inserted into Eq. (3) enables calculating σ and q parameters.

Fig. 5

(a) Field effect mobility and (b) Meyer–Neldel energy as a function of lateral electric field in C60-based OFETs. Red curves with circular points show the sample with C60 film grown at 250 °C (bigger grain size) substrate temperature and black curves with square points show sample grown at 130 °C (smaller grain size). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

Conclusion

In conclusion, the Meyer–Neldel behavior for the temperature dependent FET mobility has been studied in C60 films at different applied lateral electric fields. The characteristic Meyer–Neldel energy “EMN” is found to change from 35 meV → 32 meV by increasing the applied source drain electric field. The experimental results are in excellent agreement with the predictions of the recent theoretical model [7] which was extended to account for the dependence of the OFET mobility upon the applied lateral electric field in organic semiconductors with a Gaussian DOS distribution. Moreover, experimental results in two devices with different active film morphology show that the electric field dependence of EMN is smaller in highly ordered active film devices in comparison to less ordered devices. The active film morphology is obviously the main reason behind this phenomenon. The experimental results also show that the present model from Fishchuk et al. is superior to the previously suggested one as it allows a more accurate evaluation of important material parameters from experimental data measured at any electric field and does not require an extrapolation of the experimental data to zero-electric fields.