Charge Transport in Disordered Organic Materials and Its Relevance to Thin-Film Devices: A Tutorial Review By Nir Tessler,* Yevgeni Preezant, Noam Rappaport, and Yohai Roichman 1. General Introduction 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 pho- nons. 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 are disordered in nature, we shall devote the discussion to some phenomena and physical theories relating to the transport of charge carriers through disordered media. As stated at the beginning, we do not aim to cover all existing theories or variations, but rather discuss only those that would help in developing some intuitive understanding of the transport in amorphous organic materials. The discussion in the following section starts in an abstract mode, so to help the reader place it in the right context we outline, briefly, how one could represent a film of conjugated polymers (or molecules) by a map of sites a charge would go through while drifting with the electric field. Figure 1a shows schematically a distribution of conjugated polymer chains as might be found in a small section of a polymer film. It is well known that the conjugated polymer is not a single electronic wire but that it is rather broken into subunits (by chemical or physical defects) that are called conjugation units, and the number of monomers making this unit is called the conjugation length. Figure 1b shows how the polymer chains would be broken into subconjugation units. Namely, we have now many small electronic units that can also be thought of as small molecules distributed across the film. The ‘‘only’’ role that was played by the polymer chain was to REVIEW www.advmat.de [*] Prof. N. Tessler, Y. Preezant, Dr. N. Rappaport, Dr. Y. Roichman Electrical Engineering Department Nanoelectronic Center Technion, Haifa 32000 (Israel) E-mail: nir@ee.technion.ac.il DOI: 10.1002/adma.200803541 Semiconducting polymers and small molecules form an extremely flexible class of amorphous materials that can be used in a wide range of applications, some of which are display, radio-frequency tags, and solar cells. The rapid progress towards functional devices is occurring despite the lack of sufficient understanding of the physical processes and very little experience in device engineering. This tutorial review aims to provide sufficient intuitive back- ground to draw more researchers to look into the fundamental aspects of device physics and engineering. Adv. Mater. 2009, 21, 2741–2761 ß 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2741