Gilles Horowitz

In this communication, a new theoretical model for the ac transit frequency of organic rectifier diodes is proposed. The model is built upon a full description of the drift-diffusion current in the rectifier diode for the entire forward bias regime. Such a method precisely correlates the transit frequency to a number of materials, geometrical, and operational parameters in particular the charge-Injection barriers. By systematic variation of parameters, it is found that a rectifier operating beyond 1 GHz is observable only with a highly injecting anode. Other parameters to reach that regime of operation are discussed. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1AB07048877), and by Materials, Components & Equipment Research Program funded by the Gyeonggi Province.

Correct parameterization of the Gaussian disorder model (GDM) on spatially random sites is necessary for a complete description of charge transport in disordered materials and concomitant device characteristics. Because the GDM on spatially random sites considers both energetic and spatial disorder, it is superior to the GDM on a cubic lattice. However, analytical arguments and experimental evidence are still lacking for correct parameterization of the model over a wide range of model parameters, energetic and spatial disorder, and electric fields. We show that the model requires a set of parameters to correctly account for high mobility and its charge density dependence, and we develop such a model. The model is implemented in a numerical simulation tool for comparison with the measured device characteristics. Accurate agreement with experimental data, particularly with the high mobility values in organic field-effect transistors, is achieved throughout a wide range of temperature by adjusting both the localization length and the attempt-to-escape frequency.

We study the effect of Gaussian energetic disorder on the organic field-effect transistors (OFETs) with surprisingly high field-effect mobility and the low contact resistance. The numerical device simulation assumes the thermally assisted hopping transport and injection in disordered semiconductors. The results are analyzed with the power-law field-effect mobility and the asymptotic power-law contact resistance model. Transistor parameters extracted by the models reveal that a higher Gaussian disorder, which leads to a lower injection barrier and a larger mobility enhancement, is the origin of the high field-effect mobility and the low contact resistance.

The injection barrier is a key parameter that governs the charge and current density in organic field-effect transistors (OFETs). However, the energetic disorder of organic disordered semiconductors (ODSs) hinders a clear definition of the injection barrier. We study the validity of effective injection barrier at the metal/organic disordered semiconductor by means of systematic numerical simulation of OFETs in full consideration of the Gaussian density-of-states. The contact resistance from the numerical simulation and analytical model are compared to verify this procedure. By varying the Gaussian width, the effective injection barrier is validated for low degree of disorder at which the semiconductor is under non-degenerate condition. The position of Fermi level with respect to the Gaussian width distinguishes the non-degenerate and degenerate condition of ODSs, indicating clearly the range of validity of the effective injection barrier.

In this review, recent advances in compact modeling of organic field-effect transistors (OFETs) are presented. Despite the inherent strength for printed flexible electronics and the extremely aggressive research conducted over more than three decades, the OFET technology still seems to remain at a relatively low technological readiness level. Among various possible reasons for that, the lack of a standard compact model, which effectively bridges the device-and system-level development, is clearly one of the most critical issues. This paper broadly discusses the essential requirements, up-to-date progresses, and imminent challenges for the OFET compact device modeling toward a universal, physically valid, and applicable description of this fast-developing technology.

We present a drain current model and a consistent parameter extraction method for organic field-effect transistors (OFETs) considering the gate voltage-dependent contact resistance and mobility by power-law. The physical origin of the asymptotic power-law dependence of contact resistance is elaborated based on the current crowding model. The parameters of a new model can be completely extracted without ambiguity by the proposed extraction method based on the linear fitting. Pentacene-based OFETs with the Au source/drain contact in a staggered configuration experimentally validate the proposed model and the extraction method, which further reveal the bulk resistivity as the major contribution to contact resistance.

We report an in-depth study of three-dimensional (3D) inkjet-printed flexible organic field-effect transistors (FETs) and integrated circuits (ICs), and demonstrate the necessity, the feasibility and the key aspects of modelling-driven design and analysis. In particular, we performed compact modelling of the flexible printed organic FETs to determine transistor parameters from measured electrical characteristics, and to optimize the design of transistors for a balanced inverter. We also conducted a SPICE simulation of both static and dynamic behaviours of flexible printed organic complementary inverters and ring oscillators. This study revealed design rules to guide fabrication of the 3D structure of the inverter. The study also showed that the parasitic capacitances are dominant factors that determine the transient behaviour of the ring oscillator. Our work provides insights that can guide further improvement of flexible printed organic FETs and ICs towards the realisation of increasingly complex organic ICs and unconventional electronic applications.

Contact resistance is a major characteristic of organic transistors, and its importance has received renewed attention due to the recent revelation of mobility overestimation. In this article, we propose a method to describe the contact resistance as a closed-form compact equation of the materials, interfaces, and geometrical parameters. The proposed model allows us to quantitatively understand the correlation between charge-injection and transport properties, while providing a tool for performance prediction and optimization. This theory is applied to a set of experimentally fabricated devices to exemplify how to utilize the model in practice.

We develop a numerical model for the current-voltage characteristics of organic electrochemical transistors (OECTs) based on steady-state Poisson’s, Nernst’s and Nernst–Planck’s equations. The model starts with the doping–dedoping process depicted as a moving front, when the process at the electrolyte–polymer interface and gradually moves across the film. When the polymer reaches its final state, the electrical potential and charge density profiles largely depend on the way the cations behave during the process. One case is when cations are trapped at the polymer site where dedoping occurs. In this case, the moving front stops at a point that depends on the applied voltage; the higher the voltage, the closer the stopping point to the source electrode. Alternatively, when the cations are assumed to move freely in the polymer, the moving front eventually reaches the source electrode in all cases. In this second case, cations tend to accumulate near the source electrode, and most of the polymer is uniformly doped. The variation of the conductivity of the polymer film is then calculated by integrating the density of holes all over the film. Output and transfer curves of the OECT are obtained by integrating the gate voltage-dependent conductivity from source to drain.

Because the conductivity of organic semiconductors is very low, a useful model for the organic diode consists of treating the organic layer as an insulator, an approximation often referred to as the metal-insulator-metal (MIM) model. Moreover, the dominant charge carrier injection process is diffusion, so that a modified Schottky theory can be used to derive a simple analytical equation for the current voltage curve of the diode. Here, we carried out a full analysis of the MIM model for the organic diode. We show that Schottky theory is only valid when charge injection is poor, that is, for high injection barriers. When the injection barrier is lowered, the current given by Schottky theory is still valid in the weak injection regime, when the applied potential is lower than the diffusion potential. However, it becomes largely overestimated in the strong injection regime. We also show that in the strong injection regime, the current given by the MIM model merges with Mott-Gurnery space-charge-limited regime.