Understanding Mott's law from scaling of variable-range-hopping currents and intrinsic current fluctuations

We have used the master equation to simulate variable-range hopping (VRH) of charges in a strongly disordered d-dimensional energy landscape (d=1,2,3). The current distribution over hopping distances and hopping energies gives a clear insight into the difference between hops that occur most frequently, dominate quant. in the integral over the mobility distribution, or are crit. ones that still need to be considered in that integral to recover the full low-temp. mobility. The recently reported scaling with temp. of the VRH-current distribution over hopping distances and hopping energies is quant. analyzed in 1D and 2D, and accurately confirmed. Based on this, we present an anal. scaling theory of VRH, which distinguishes between a scaling part of the distribution and an exponential tail, sepd. by crit. currents that set the scale and that follow self-consistently at each temp. This naturally renders Mott's law for the low-temp. mobility, in a way and with a phys. picture different from that of the established crit.-percolation-network approach to VRH. We argue that current fluctuations as obsd. in simulations are intrinsic to VRH and play an essential role in this distinction. [on SciFinder (R)

Universality of AC conductivity: random site-energy model with Fermi statistics

The universality of the frequency-dependent (AC) conduction of many disordered solids in the extreme-disorder limit has been demonstrated exptl. Theor., this universality has been established with different techniques and for various models. A popular model that has been extensively investigated and for which AC universality was established is the sym. random-barrier model without Fermi statistics. However, for the more realistic model of random site-energies and Fermi statistics AC universality has never been rigorously established. In the present work we perform a numerical study of the latter model for a regular lattice in two dimensions. In addn., we allow for variable-range hopping. Our main conclusion is that AC universality appears to hold for this realistic model. The obtained master curve for the cond. and the one obtained for the random-barrier model in two dimensions appear to be the same. [on SciFinder (R)

Understanding the doping dependence of the conductivity of conjugated polymers: dominant role of the increasing density of states and growing delocalization

In variable-range-hopping theories for the dc conductivity, the extension of sites where the charges are located and the energy dependence of the density of states (DOS) are usually neglected. We show that these dependences are the dominant factors for understanding the strong doping dependence, and present an analytical theory for arbitrary DOS. We verify the theory with systematic data over a broad range of temperature and doping for FeCl3-doped poly(p-phenylene vinylene). By combining theory and data, we reconstruct the energy-dependent DOS and the extension of sites

Mesoscopic modelling of 2-CN-PPV/PPV polymer LED

Although optoelectronic devices made of polymers are very attractive ones (low cost, easy to make), problems related to charge transport, exciton quenching, among others, can be an obstacle for their performance. The use of heterojunctions made of two polymers can be a strategy for improving the efficiency of polymer light emitting diodes (PLEDs) at low bias. Here we present a theoretical study of the influence of bilayer structure in a PLED made of PPV and 2-CN-PPV, by adopting a mesoscopic approach. Our results show that the presence of the polymer/polymer interface improves charge injection and leads to a confinement of charges near it, which will increase the number recombination events in the middle of the device compared to the equivalent single-layer PLEDs.Fundação para a Ciência e a Tecnologia (FCT) Programa Operacional “Ciência , Tecnologia, Inovação” POCTI/CTM/41574/2001, CONC-REEQ/443/EEI/2001 e SFRH/BD/22143/200

Transport properties of copper phthalocyanine based organic electronic devices

Ambipolar charge carrier transport in Copper phthalocyanine (CuPc) is studied experimentally in field-effect transistors and metal-insulator-semiconductor diodes at various temperatures. The electronic structure and the transport properties of CuPc attached to leads are calculated using density functional theory and scattering theory at the non-equilibrium Green's function level. We discuss, in particular, the electronic structure of CuPc molecules attached to gold chains in different geometries to mimic the different experimental setups. The combined experimental and theoretical analysis explains the dependence of the mobilityand the transmission coefficient on the charge carrier type (electrons or holes) and on the contact geometry. We demonstrate the correspondence between our experimental results on thick films and our theoretical studies of single molecule contacts. Preliminary results for fluorinated CuPc are discussed.Comment: 18 pages, 16 figures; to be published in Eur. Phys. J. Special Topic

Understanding Mott's law from scaling of variable-range-hopping currents and intrinsic current fluctuations

We have used the master equation to simulate variable-range hopping (VRH) of charges in a strongly disordered d-dimensional energy landscape (d=1,2,3). The current distribution over hopping distances and hopping energies gives a clear insight into the difference between hops that occur most frequently, dominate quant. in the integral over the mobility distribution, or are crit. ones that still need to be considered in that integral to recover the full low-temp. mobility. The recently reported scaling with temp. of the VRH-current distribution over hopping distances and hopping energies is quant. analyzed in 1D and 2D, and accurately confirmed. Based on this, we present an anal. scaling theory of VRH, which distinguishes between a scaling part of the distribution and an exponential tail, sepd. by crit. currents that set the scale and that follow self-consistently at each temp. This naturally renders Mott's law for the low-temp. mobility, in a way and with a phys. picture different from that of the established crit.-percolation-network approach to VRH. We argue that current fluctuations as obsd. in simulations are intrinsic to VRH and play an essential role in this distinction. [on SciFinder (R)

Temperature and field dependence of the mobility in 1D for a Gaussian density of states

The temperature and field-dependent mobility of a charge carrier in a gaussian density of states has been analyzed, based on a numerically exact solution of the Master equation. In this way we get a microscopic insight into the origin of the mobility and find some new features pointing to relevance of the Fermi level and of variable-range hopping to sites further away than nearest ones

Universality of AC conductivity: random site-energy model with Fermi statistics

The universality of the frequency-dependent (AC) conduction of many disordered solids in the extreme-disorder limit has been demonstrated exptl. Theor., this universality has been established with different techniques and for various models. A popular model that has been extensively investigated and for which AC universality was established is the sym. random-barrier model without Fermi statistics. However, for the more realistic model of random site-energies and Fermi statistics AC universality has never been rigorously established. In the present work we perform a numerical study of the latter model for a regular lattice in two dimensions. In addn., we allow for variable-range hopping. Our main conclusion is that AC universality appears to hold for this realistic model. The obtained master curve for the cond. and the one obtained for the random-barrier model in two dimensions appear to be the same. [on SciFinder (R)

Temperature, charge carrier density, and electric field dependence of mobilities in disordered conjugated polymers: simulation results

We present the results of simulation studies of the dependence on temperature, charge carrier density, and electric field of the mobility µ in disordered conjugated polymers. The disorder is modeled by a Gaussian density of states (DOS) with width s. We base our analysis on an exact numerical solution of the Pauli Master equation. The recently experimentally determined carrier density dependence, ranging from densities typically found in light-emitting diodes (LEDs) up to those found in field-effect transistors (FETs), is fully reproduced. At low temperatures T, we find deviations from the generally accepted µexp[-const.(s/kT)2] behavior. Our calculations show that the electric field dependence does not play a prominent role at the driving voltages of polymer devices

Charge-carrier concentration dependence of the hopping mobility in organic materials with Gaussian disorder

It has recently been demonstrated that the hopping mobility in semiconducting organic materials depends on the charge-carrier concentration. We have analyzed this effect within the framework of six existing semianalytical models, for the case of a Gaussian density of states (DOS). These models were either not applied earlier to the case of a Gaussian DOS, or are shown to require a major modification. The mobility is constant below a certain concentration, which decreases with increasing ratio of the width of the DOS over the thermal energy kBT, and it increases for larger concentrations. At very high concentrations final state effects limit this increase or even give rise to a decrease. An analytical expression is given for the mobility, µ, in the form of the product of the mobility in the low concentration limit times a concentration (c) and -dependent enhancement factor. Depending on c, ln(µ) varies approximately linearly with 1/T or with 1/T2. This finding may lead to a solution for the long-standing controversy between polaron-based and disorder-based hopping models