In this review, we describe a variety of models or theoretical approaches to transport in disordered media and discuss the implication to modern organic devices. There are far too many models or variations, so our aim is not to try to cover them all. Instead, we show that when the different models are presented along with the assumptions included while being developed, they can all teach us and help us to develop some intuition regarding what goes on in nonordered materials. One may encounter debates regarding a model being wrong, but it is our belief that only when the models are used out of context (not within their basic assumptions) the obtained results could be false.One of the things one encounters while starting to study organic semiconductors is that the textbook models taught in semiconductor-device courses have to be revisited, and one has to look for ''old'' books that were written before silicon technology took over. With this spirit, we start a few years back, or a century ago. In 1900, three years after the discovery of the electron by Thomson, Drude proposed a model that explained the known conductivity phenomenon in metals and other types of materials.[1] This model was based on the assumption that electrons classically accelerate under an applied electric field and collide with the lattice's heavy positive ions. Upon collision, the electrons were assumed to scatter into a random angle and at a speed that was on average consistent with the local temperature. It would then go on accelerating until the next scattering event. This model, although erroneous in the assumption that the basic scattering centers were the lattice ions, was able to physically explain the already known Ohm's law and the Joule heating effect. Along with the debut of quantum mechanics came the quantum mechanical description of matter and the realization that in a well-ordered lattice electrons should be mathematically described as Bloch waves, and that the scattering was not the result of collisions with any lattice ion but rather scattering from defects, contaminations, and phonons. Nevertheless, the Drude model, under the semiclassical approximation, is conceptually appropriate for describing electron transport through crystal lattices, that is, freely roaming charge carriers that scatter upon collisions with defects, contaminations, and phonons. The carriers earn the name ''free'' whenever the material properties are such that the mean free path between collisions, L, is much longer than the typical carrier's Bloch wavelength, thus the carriers have very broad wavefunctions extending over many lattice units.However, as was historically elucidated by Anderson, [2] introducing disorder into the lattice and breaking the crystal symmetry results in the wavefunctions becoming localized and in the formation of energy states in the forbidden band-gap. The Drude concepts, and others deriving on its intuitive approach, can no longer serve us in explaining transport under such circumstances. Since the materials we are interested in a...

We investigate the density of states (DOS) for hole transport in undoped and doped amorphous organic films using high lateral resolution Kelvin probe force microscopy. Measurements are done on field effect transistors made of N,N1-diphenyl-N, N1-bis(1-naphthyl)-1,10-biphenyl-4,4II-diamine undoped or p doped with tetrafluoro-tetracyanoquinodimethane. We determine the DOS structure of the undoped material, including an anomalous peak related to interfaces between regions of different surface potential, the DOS doping-induced broadening, and doping-induced sharp peaks on the main DOS distribution.

We present self consistent picture of charge injection and transport in low mobility disordered organic based devices. We demonstrate the importance of accounting for charge density effects in both modeling and analysis of devices. We outline a method for the analysis of LEDs and FETs.

We propose a semi-implicit model for hopping transport in disordered media with application to organic semiconductors. The results show excellent agreement with both Monte Carlo and standard master-equation calculations. In organic LEDs the applied field would result in heating of the charge carrier population by up to 100°C above the lattice temperature and is more effective at lower temperatures. We show that the voltage dependence of the mobility in space charge limited LEDs is largely due to carrier heating and not to the previously considered charge density or barrier lowering effects. At the end we look into the effect of accounting for the soft nature of organic materials via the inclusion of polaronic rate ͑binding energy͒ and we find that carrier heating is suppressed at polaron binding energies above 0.1 eV.

We present time-of-flight-type calculations of the transport master equation applied to thin film disordered materials. We show that the energetic disorder in conjunction with a thin film results in electronic inhomogeneity. This inhomogeneity manifests itself as dispersive transport which can be described as a linear sum of close to normal-transport paths. Namely, in thin films of disordered materials the transport parameters do not converge to the infinite sample parameters but present a dispersive mesoscopic phenomenon. By defining a spatial distribution function of the charge velocity ͑mobility͒ we are able to examine the effect of the degree of disorder and film thickness on the electronic inhomogeneity. We postulate that in a given sample the spatial distribution characteristic of holes and the one characteristic of electrons are most likely nonidentical. Hence, in organic thin-film light-emitting diodes the energetic disorder is a limiting factor concerning charge recombination and efficiency.

Electronic line-up in light-emitting diodes with alkali-halide/metal cathodes

The potential across an organic thin-film transistor is measured by Kelvin probe force microscopy and is used to determine directly the pinch-off voltage at different gate voltages. These measurements lead to the determination of a generalized threshold voltage, which corresponds to molecular level shift as a function of the gate voltage. A comparison between measured and calculated threshold voltage reveals a deviation from a simple Gaussian distribution of the transport density of states available for holes.

A general representation of the current in an amorphous semiconductor pn diode is developed. This expression is applied to examples of density of states functions ͑exponential, Gaussian, and Gaussian with exponential tail͒ commonly found in conjugated molecules and other amorphous materials. We find that the ideality factor could be voltage dependent and that its functional form is closely related to the shape of the density of states.