J. O. Oelerich

Concentration dependence of the transport energy level for charge carriers in organic semiconductors

The concept of the transport energy (TE) has proven to be one of the most powerful theoretical approaches to describe charge transport in organic semiconductors. In the recent paper L. Li, G. Meller, and H. Kosina [Appl. Phys. Lett. 92, 013307 (2008)] have studied the effect of the partially filled localized states on the position of the TE level. We show that the position of the TE is essentially different to the one suggested by L. Li, G. Meller, and H. Kosina [Appl. Phys. Lett. 92, 013307 (2008)] We further modify the standard TE approach taking into account the percolation nature of the transport path. Our calculations show that the TE becomes dependent on the concentration of charge carriers n at much higher n values than those, at which the carrier mobility already strongly depends on n. Hence the calculations of the concentration-dependent carrier mobility cannot be performed within the approach, in which only the concentration dependence of the TE is taken into account.

Theoretical tools for the description of charge transport in disordered organic semiconductors

Hopping conduction is widely considered the dominant charge transport mechanism in disordered organic semiconductors. Although theories of hopping transport have been developed in detail for applications to inorganic amorphous materials, these theories are often out of scope for the community working with organic amorphous systems. Theoretical research on charge transport in organic systems is overwhelmed by phenomenological fittings of numerical results by equations, which often make little physical sense. The aim of the current review is to bring analytical theoretical methods to the attention of the community working with disordered organic semiconductors.

STEMsalabim: A high-performance computing cluster friendly code for scanning transmission electron microscopy image simulations of thin specimens.

We present a new multislice code for the computer simulation of scanning transmission electron microscope (STEM) images based on the frozen lattice approximation. Unlike existing software packages, the code is optimized to perform well on highly parallelized computing clusters, combining distributed and shared memory architectures. This enables efficient calculation of large lateral scanning areas of the specimen within the frozen lattice approximation and fine-grained sweeps of parameter space.

Energy position of the transport path in disordered organic semiconductors

The concept of transport energy is the most transparent theoretical approach to describe hopping transport in disordered systems with steeply energy dependent density of states (DOS), in particular in organic semiconductors with Gaussian DOS. This concept allows one to treat hopping transport in the framework of a simple multiple-trapping model, replacing the mobility edge by a particular energy level called the transport energy. However, there is no consensus among researchers on the position of this transport level. In this article, we suggest a numerical procedure to find out the energy level most significantly contributing to charge transport in organic semiconductors. The procedure is based on studying the effects of DOS modifications on the charge carrier mobility in straightforward computer simulations. We also show why the most frequently visited energy, computed in several numerical studies to determine the transport energy, is not representative for charge transport.

Fundamental characteristic length scale for the field dependence of hopping charge transport in disordered organic semiconductors

Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field μ(F )/μ(0) in a system of random sites is determined by the localization length a, and not by the concentration of sites N . This result is in drastic contrast to what is usually assumed in the literature for a theoretical description of experimental data and for device modeling, where N−1/3 is considered as the decisive length scale for μ(F ). We show that although the limiting value μ(F → 0) is determined by the ratio N−1/3/a, the dependence μ(F )/μ(0) is sensitive to the magnitude of a, and not to N−1/3. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field F and the real temperature T on the hopping transport via spatially random sites can contain the electric field only in the combination eFa.

Charge transport mechanism in lead oxide revealed by CELIV technique.

Although polycrystalline lead oxide (PbO) belongs to the most promising photoconductors for optoelectronic and large area detectors applications, the charge transport mechanism in this material still remains unclear. Combining the conventional time-of-flight and the photo-generated charge extraction by linear increasing voltage (photo-CELIV) techniques, we investigate the transport of holes which are shown to be the faster carriers in poly-PbO. Experimentally measured temperature and electric field dependences of the hole mobility suggest a highly dispersive transport. In order to analyze the transport features quantitatively, the theory of the photo-CELIV is extended to account for the dispersive nature of charge transport. While in other materials with dispersive transport the amount of dispersion usually depends on temperature, this is not the case in poly-PbO, which evidences that dispersive transport is caused by the spatial inhomogeneity of the material and not by the energy disorder.

Theory to carrier recombination in organic disordered semiconductors

A theoretical description for recombination kinetics of charge carriers in a disordered system with a broad energy distribution of localized states (DOS) is suggested. This kinetics is governed by the exchange of carriers between transport states and traps. Concentration transients in systems with Gaussian DOS, typical for organic semiconductors, appear much steeper than those obtained for systems with exponential DOS. This difference in recombination kinetics is caused by the difference in thermalization kinetics for these two types of the DOS functions. The comparison of the recombination transients for mobile and trapped carriers in exponential and Gaussian DOS might help to distinguish between these two possible shapes of the DOS using experimental data for transient photoconductivity and photoabsorption.

Influence of surface relaxation of strained layers on atomic resolution ADF imaging

Surface relaxation of thin transmission electron microscopy (TEM) specimens of strained layers results in a severe bending of lattice planes. This bending significantly displaces atoms from their ideal channeling positions which has a strong impact on the measured annular dark field (ADF) intensity. With the example of GaAs quantum wells (QW) embedded in a GaP barrier, we model the resulting displacements by elastic theory using the finite element (FE) formalism. Relaxed and unrelaxed super cells served as input for state of the art frozen phonon simulation of atomic resolution ADF images. We systematically investigate the dependencies on the sample´s geometric parameters, i.e. QW width and TEM sample thickness, by evaluating the simulated intensities at the atomic column´s positions as well as at the background positions in between. Depending on the geometry the ADF intensity can be affected in a range several nm from the actual interface. Moreover, we investigate the influence of the surface relaxation on the angular distribution of the scattered intensity. At high scattering angles we observe an intensity reduction at the interface as well as in the GaP barrier due to de-channeling. The amount of intensity reduction at an atomic column is directly proportional to its mean square displacement. On the contrary we find a clearly increased intensity at low angles caused by additional diffuse scattering. We discuss the implications for quantitative evaluations as well as strategies to compensate for the reduced intensities.

Transport of electrons in lead oxide studied by CELIV technique

Although polycrystalline lead oxide (PbO) has a long history of application in optoelectronics and imaging, the transport mechanism for electrons in this material has not yet been clarified. Using the photo-generated charge extraction by linear increasing voltage (photo-CELIV) technique, we provide the temperature- and field-dependences of electron mobility in poly-PbO. It is found that electrons undergo dispersive transport, i.e. their mobility decreases in the course of time. Multiple trapping of electrons from the conduction band into the developed band tail is revealed as the dominant transport mechanism. This differs dramatically from the dispersive transport of holes in the same material, dominated by topological factors and not by energy disorder.

Surface relaxation of strained Ga(P,As)/GaP heterostructures investigated by HAADF stem

The surfaces of thin transmission electron microscopy (TEM) specimens of strained heterostructures can relax. The resulting bending of the lattice planes significantly influences high‐angle annular dark field (HAADF) measurements. We investigate the impact by evaluating the intensities measured at the atomic columns as well as their positions in high‐resolution HAADF images. In addition, the consequences in the diffraction plane will be addressed by simulated position averaged convergent beam electron diffraction (PACBED) patterns.