Interpretation of electron diffusion coefficient in organic and inorganic semiconductors with broad distributions of states

Abstract

The carrier transport properties in nanocrystalline semiconductors and organic materials play a key role for modern organic/inorganic devices such as dye-sensitized (DSC) and organic solar cells, organic and hybrid light-emitting diodes (OLEDs), organic field-effect transistors, and electrochemical sensors and displays. Carrier transport in these materials usually occurs by transitions in a broad distribution of localized states. As a result the transport is dominated by thermal activation to a band of extended states (multiple trapping), or if these do not exist, by hopping via localized states. We provide a general view of the physical interpretation of the variations of carrier transport coefficients (diffusion coefficient and mobility) with respect to the carrier concentration, or Fermi level, examining in detail models for carrier transport in nanocrystalline semiconductors and organic materials with the following distributions: single and two-level systems, exponential and Gaussian density of states. We treat both the multiple trapping models and the hopping model in the transport energy approximation. The analysis is simplified by thermodynamic properties: the chemical capacitance, C m , and the thermodynamic factor, w n , that allow us to derive many properties of the chemical diffusion coefficient, D n , used in Fick's law. The formulation of the generalized Einstein relation for the mobility to diffusion ratio shows that the carrier mobility is proportional to the jump diffusion coefficient, D J , that is derived from single particle random walk. Characteristic experimental data for nanocrystalline TiO 2 in DSC and electrochemically doped conducting polymers are discussed in the light of these models.

Series resistance in organic bulk-heterojunction solar devices: Modulating carrier transport with fullerene electron traps

“…The above mentioned conduction mechanism is highly sensitive to the kinetics of trapping/release of trapped electrons at PCBM molecules. While the inclusion of fast traps does not modify the carrier conductivity [16], slow trapping would have large influence on the transport mechanisms producing conductivity changes. It is worth noting that similarity of 1 R values at forward bias allows discarding morphology effects as originating the 1 R differences observed.…”

Electron Transport in Dye-Sensitized Solar Cells Based on ZnO Nanotubes: Evidence for Highly Efficient Charge Collection and Exceptionally Rapid Dynamics

“…This value exceeds by ∼1000 times the largest values previously reported for DSC photoanodes. 4,41 The plausibility of this value may be weighed against the theoretically predicted diffusion coefficient for polycrystalline ZnO. Equation 7 can also be expressed as 41…”

Diffusion–Recombination Impedance Model for Solar Cells with Disorder and Nonlinear Recombination

“…In many cases, hopping systems can also be reduced to the multiple trapping model by using the concept of transport energy. [8,9,17] Next, we introduce some magnitudes that enter the expression of impedance. [4] First, the chemical capacitance is defined as follows [Eq.…”

“…A full theory that rationalizes the interpretation of measured coefficients and their relation to stochastic simulations was formulated thereafter. [5,8,9] In addition, it was shown that nonlinear recombination is the rule in systems such as DSCs and organic solar cells, [3,10,11] and such a nonlinear feature enhances inhomogeneous behavior. [12] In this paper, we provide a more general derivation of the impedance model that includes the trapping factors and that uses a nonlinear recombination rate.…”