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 use digital holographic microscopy and Mie scattering theory to simultaneously characterize and track individual colloidal particles. Each holographic snapshot provides enough information to measure a colloidal sphere's radius and refractive index to within 1%, and simultaneously to measure its three-dimensional position with nanometer in-plane precision and 10 nanometer axial resolution.

The ratio between mobility and diffusion parameters is derived for a Gaussianlike density of states. This steady-state analysis is expected to be applicable to a wide range of organic materials (polymers or small molecules) as it relies on the existence of quasi-equilibrium only. Our analysis shows that there is an inherent dependence of the transport in trap-free disordered organic-materials on the charge density. The implications for the contact phenomena and exciton generation rate in light emitting diodes as well as channel-width in field-effect transistors is discussed. a) Email: nir@ee.technion.ac.il. W.pg: http://tiger.technion.ac.il/~nir/

We demonstrate both theoretically and experimentally that gradients in the phase of a light field exert forces on illuminated objects, including forces transverse to the direction of propagation. This effect generalizes the notion of the photon orbital angular momentum carried by helical beams of light. We further demonstrate that these forces generally violate conservation of energy, and briefly discuss some ramifications of their non-conservativity.Light's ability to exert forces has been recognized since Kepler's De Cometis of 1619 described the deflection of comet tails by the sun's rays. Maxwell demonstrated that the momentum flux in a beam of light is proportional to the intensity and can be transferred to illuminated objects, resulting in radiation pressure that pushes objects along the direction of propagation. This axial force has been distinguished from the transverse torque exerted by helical beams of light carrying orbital angular momentum (OAM) [1]. We demonstrate theoretically and confirm experimentally that OAM-induced torque is a special case of a general class of forces arising from phase gradients in beams of light. We also demonstrate that phase-gradient forces are generically non-conservative, and combine them with the conservative forces exerted by intensity gradients to create novel optical traps with structured force profiles.Our experimental demonstrations of phase-gradient forces make use of extended optical traps created through shape-phase holography [2,3,4] in an optimized [5] holographic optical trapping [6,7] system. Holographically sculpted intensity gradients enable these generalized optical tweezers [8] to confine micrometer-scale colloidal particles to one-dimensional curves embedded in three dimensions. Independent control over the intensity and phase profiles along the curve then provide an ideal model system for characterizing the forces generated by phase gradients in beams of light. OPTICAL FORCES DUE TO PHASE GRADIENTSThe vector potential describing a beam of light of frequency ω and polarizationε may be written in the form A(r, t) = A(r) exp (i ωt)ε.(1)Assuming uniform polarization (and therefore a form of the paraxial approximation), the spatial dependence,is characterized by a non-negative real-valued amplitude, u(r), and a real-valued phase Φ(r). For a plane wave propagating in theẑ direction, Φ(r) = −kz, where k = n m ω/c is the light's wavenumber, c is the speed of light in vacuum, and n m is the refractive index of the medium. Imposing a transverse phase profile ϕ(r) on the wavefronts of such a beam yields the more general formwhereẑ · ∇ϕ = 0 and where the the direction of the wavevector,now varies with position. The associated electric and magnetic fields are given in the Lorenz gauge by E(r, t) = − ∂A(r, t) ∂t and (5)where µ is the magnetic permeability of the medium, which we assume to be linear and isotropic. Following the commonly accepted Abraham formulation [9], the momentum flux carried by the beam iswhere I(r) = u 2 (r) is the light's intensity, and where w...

We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This non-equilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by non-conservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.Most discussions of the dynamics of optically trapped particles assume at least implicitly that the forces exerted by an optical tweezer [1] are path-independent and therefore conserve mechanical energy. Optical forces due to gradients in the intensity are manifestly conservative in this sense [2]. Radiation pressure, by contrast, is not [2,3]. The experimental studies described in this Letter demonstrate that the non-conservative component of the optical force has measurable consequences for the dynamics of optically trapped colloidal spheres. In particular, the probability density for a sphere trapped in a static optical tweezer exhibits steady-state toroidal currents, a phenomenon we call a fountain of probability. We use the Fokker-Planck formalism to explain how nonconservative forces bias random thermal fluctuations to induce circulating probability currents. Figure 1 schematically represents the deceptively simple system. A single colloidal sphere is drawn to the focus of a converging laser beam by forces arising from gradients in the beam's intensity [1,2]. These intensitygradient forces establish a three-dimensional potential energy well, V (r), determined by the local intensity, I(r). A particle trapped in this well also experiences radiation pressure that drives it downstream with a force proportional to I(r). In the absence of thermal fluctuations, a trapped particle would come to rest at a stable mechanical equilibrium downstream of the focus.Treating the displaced equilibrium point as the origin of an effective potential energy well is tempting but misleading. To appreciate the problem, consider a thermally driven trajectory such as the example shown schematically in Fig. 1. Were the system in thermodynamic equilibrium, forward and reverse trajectories around this loop would have equal probability. Because the light is more intense near the optical axis, however, radiation pressure biases the random walk in the forward direction. This departure from detailed balance should induce irreversible circulation in the particle's otherwise random fluctuations [4].We demonstrate this effect by observing the motions of colloidal silica spheres 2.2 µm in diameter (Bangs Lab-

We introduce optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction-limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. Unlike other collimated beams of light, appropriately designed solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light's propagation. We demonstrate this through video microscopy observations of a colloidal sphere moving upstream along a holographically projected optical solenoid beam.

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 describe a method for projecting single-beam optical traps whose potential energy wells are extended along one-dimensional curves. This technique exploits shape-phase holography in which computer-generated phase-only diffractive optical elements are used to implement complex and amplitude-only holograms. The resulting optical traps can have specified intensity and phase profiles along their lengths and can extend along curves in three dimensions. We demonstrate the extended traps' operation and characterize their potential energy profiles through digital video microscopy of trapped colloidal spheres.