F. Gebhard

• Philipps University of Marburg

An appropriately parametrized analytical equation (APAE) is suggested to account for charge-carrier mobility in organic disordered semiconductors. This equation correctly reproduces the effects of temperature T, carrier concentration n, and electric field F on the carrier mobility μ(T,F,n), as evidenced by comparison with analytical theories and Mo...

There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, $E=mc^2$. Noether's theorem applied to the relativistic Lagrange function provides an unambiguous and straightforward access to energy and momentum conservation laws but those tools were not available at the beginning of the twentieth centur...

The space- and temperature-dependent electron distribution n(r,T) is essential for the theoretical description of the optoelectronic properties of disordered semiconductors. We present two powerful techniques to access n(r,T) without solving the Schrödinger equation. First, we derive the density for nondegenerate electrons by applying the Hamiltoni...

The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical solution of the Schrödinger equation. Among various approaches suggested so far, the low-pass filter approach of...

The space- and temperature-dependent electron distribution $n(\mathbf r,T)$ is essential for the theoretical description of the opto-electronic properties of disordered semiconductors. We present two powerful techniques to access $n(\mathbf r,T)$ without solving the Schr\"odinger equation. First, we derive the density for non-degenerate electrons b...

The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical solution of the Schr\"odinger equation. Among various approaches suggested so far, the low-pass filter approach...

Amorphous oxide semiconductors, such as InGaZnO (IGZO) materials, are distinguished in the broad class of disordered semiconductors due to high values of charge carrier mobility that makes IGZOs unique for various device applications. In spite of numerous experimental and theoretical studies, the charge transport mechanism in IGZOs was, for a long...

Studying optoelectronic properties in FAPb$_{1-x}$Sn$_x$I$_3$ perovskites as a function of the lead:tin content, Parrott et al. observed the broadest luminescence linewidth and the largest luminescence Stokes shift in mixed compositions with Sn $ < 25$% and with $> 0.85$%. Since the largest effects of alloy disorder were expected for the 50:50 comp...

In Phys. Rev. B 93, 140206(R) (2016), electron transport governed by nuclear tunneling was claimed to be a more realistic transport mechanism in semiconducting polymers as compared to Marcus and Miller-Abrahams transport mechanisms. The conclusion was based on the analysis of the field-dependent charge carrier mobility. We point out the unjustified...

Charge transport in amorphous oxide semiconductors is often described as the band transport affected by disorder in the form of random potential barriers (RB). Theoretical studies in the framework of this approach neglected so far the percolation nature of the phenomenon. In this article, a recipe for theoretical description of charge transport in...

The charge transport mechanism in amorphous oxide semiconductors (AOS) is a matter of controversial debates. Most theoretical studies so far neglected the percolation nature of the phenomenon. In this paper, a recipe for theoretical description of charge transport in AOSs is formulated using the percolation arguments. Comparison with the previous t...

Charge transport in amorphous oxide semiconductors is often described as the band transport affected by disorder in the form of random potential barriers (RB). Theoretical studies in the framework of this approach neglected so far the percolation nature of the phenomenon. In this article, a recipe for theoretical description of charge transport in...

The charge transport mechanism in amorphous oxide semiconductors (AOS) is a matter of controversial debates. Most theoretical studies so far neglected the percolation nature of the phenomenon. In this article, a recipe for theoretical description of charge transport in AOSs is formulated using the percolation arguments. Comparison with the previous...

Trapping of electrons in localized states strongly affects optoelectronic phenomena in disordered semiconductors. In this paper, it is shown by numerical simulations and by analytical calculations that the release of the trapped electrons into the conduction band can be substantially enhanced by hopping of electrons between the traps. The effect st...

Charge transport in disordered inorganic semiconductors is governed by the multiple trapping (MT) of carriers from delocalized states in the conduction band into localized traps in the band tail. Although it is well known that carrier mobility in these materials strongly depends on electric field, a consistent description of this effect in the MT r...

Semiconductor compounds, such as Ga(NAsP)/GaP or GaAsBi/GaAs, are in the focus of intensive research due to their unique features for optoelectronic devices. The optical spectra of compound semiconductors are strongly influenced by the random scattering potentials caused by compositional and structural disorder. The disorder potential is responsibl...

The theoretical description of the effect of the electric field F on the hopping mobility μ belongs to the not-yet-resolved problems related to charge transport in disordered materials. An often proposed solution is to simulate hopping transport via sites placed on regular grids and to fit the results by phenomenological equations. This approach cu...

Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $\mu(F)/\mu(0)$ in a system of random sites is determined by the localization length $\alpha$ and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature...

An analytical theory is suggested for carrier recombination in organic bulk heterojunction (BHJ) structures taking into account the spatial separation of recombining species. In BHJ systems, electrons and holes are confined to two different material phases, and the nongeminate recombination can happen only at the interfaces between the phases. The...

Modern optoelectronic devices are usually based on multi-component alloys. Local statistical fluctuations in the concentrations of chemically different components cause energy fluctuations experienced by charge carriers. So far the theory for compositional disorder has been developed for compounds, in which atoms of only two chemically different ty...

A mechanism of light absorption at THz frequencies in nematic liquid crystals based on intermolecular dynamics is proposed. In this mechanism, the energy conservation is supplied by acoustic phonons, whereas momentum conservation is provided by static spatial fluctuations of the director field. The mechanism predicts a continuous absorption spectru...

The apparent order δ of non-geminate recombination higher than δ = 2 has been evidenced in numerous experiments on organic bulk heterojunction (BHJ) structures intensively studied for photovoltaic applications. This feature is claimed puzzling, since the rate of the bimolecular recombination in organic BHJ systems is proportional to the product of...

In n-doped (Zn,Mn)Se, the (s,d) exchange influences the ground state level of the donor-bound electrons in an external B-field, depending on their local Mn environment. Due to the statistical Mn arrangement, this should induce a broadening of the donor energy distribution, inducing a magneto-resistance in transport, and also a broadening of the ene...

The effect of a large positive magnetoresistance (MR) in materials in the hopping regime is studied experimentally and theoretically. A possible mechanism of this effect has been recently suggested [Nenashev et al., Phys. Rev. B 88 (2013) 115210] [4] based on the increase of energy disorder in the distribution of dopant levels caused by the exchang...

Magnetoresistance in dilute magnetic semiconductors is studied in the hopping transport regime. Measurements performed on Cl-doped Zn(1-x)Mn(x)(S)e with x < 8% are compared with simulation results obtained by a hopping transport model. The energy levels of the Cl donors are affected by the magnetization of Mn atoms in their vicinity via the s-d exc...

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, a...

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, re...

We suggest a mechanism causing large positive magnetoresistance (MR) in dilute magnetic semiconductors when hopping via nonmagnetic donor impurities dominates the conductivity. The effect is due to the increase in the characteristic width σ of the donor energy distribution with increasing magnetic field B, caused by exchange interactions between ma...

Hopping of carriers between localized states dominates charge transport in amorphous organic and inorganic semiconductors. We suggest a comprehensive description of this transport regime based on the percolation approach that allows one to determine not only very pronounced exponential dependencies of the hopping conductivity on material parameters...

The compositional dependence of the properties of metastable Ga(N,As,P) has been characterized optically by means of temperature dependent absorptive and emissive techniques. By assuming a two-scaled disorder within the alloy caused by microscopic composition fluctuations on the one hand and a fluctuation of strain fields or the well width on the o...

Ga(NAsP) grown lattice-matched on (001) silicon substrate is a very promising material for future integrated, electrically pumped lasers on silicon. Here, we present experimental and theoretical studies of the time-resolved photoluminescence in Ga(NAsP)/Si quantum well structures. The experimental results obtained at 10 K show a strong nonexponenti...

In many-component semiconductor heterostructures photoluminescence (PL) is strongly affected by the disorder potentials caused by compositional fluctuations. We present an experimental study on the temperature-dependent PL in the Ga(N,P,As)/GaP quantum well which indicates the intriguing feature that the energy scale of the disorder decreases with...

Photoluminescence (PL) in many-component semiconductor heterostructures is strongly affected by disorder potential caused by compositional fluctuations. Our experimental study of the temperature-dependent PL in Ga(N,P,As)/GaP QW indicates the intriguing feature that the scale of disorder potential decreases with increasing concentration of the fluc...

The quantum efficiency of the free-carrier-photogeneration in amorphous selenium avalanche blocking structures is studied experimentally in a wide range of wavelengths (380–600 nm) at high electric fields (10−112.5Vμm−1). While at comparatively small excitation wavelengths (up to ≃ 540nm), our experimental results are consistent with the Onsager th...

The decisive feature of any material designed for photovoltaic applications is the dissociation efficiency of photogenerated excitons. This efficiency is essentially governed by the Coulomb attraction between electrons and holes. Because the dielectric constant in organic materials is rather low (ε r ≈ 3), the exciton binding energy is much larger...

It is a matter of controversy why excitons can efficiently dissociate into free electrons and holes at an intrinsic donor-acceptor interface despite the strong Coulomb interaction between the charges provided by the low dielectric constant in organic materials. We suggest an analytic theory based on the recently developed exact solution for the dis...

The photoluminescence behavior of Ga(NAsP) compound material lattice matched to silicon for solar cell applications is studied experimentally and theoretically. The temperature‐dependent PL spectra show some peculiarities that can not be described by the conventional theoretical model assuming the single energy and spatial scales of disorder. The e...

The metastable quaternary Ga(N,As,P) has been studied experimentally as well as theoretically as promising material for integration of optoelectronics with Si-based microelectronics. The optical studies reveal unusual peculiarities in the photoluminescence response and its temperature dependence. The disorder-induced features have been analyzed by...

The effect of electric field on diffusion of charge carriers in disordered materials is studied by Monte Carlo computer simulations and analytical calculations. It is shown how an electric field enhances the diffusion coefficient in the hopping transport mode. The enhancement essentially depends on the temperature and on the energy scale of the dis...

Interband tunnel diodes are widely used to electrically interconnect the individual subcells in multi-junction solar cells. Tunnel diodes have to operate at high current densities and low voltages, especially when used in concentrator solar cells. They represent one of the most critical elements of multi-junction solar cells and the fluctuations of...

Current-voltage characteristics of GaAs tunnel diodes are studied experimentally and theoretically. In theoretical calculations contributions of three different transport mechanisms are considered: direct tunneling processes, nonresonant multiphonon tunneling processes via defects, and resonant tunneling processes through defects. The comparison be...

Tunnel diodes play a decisive role in many semiconductor devices. Energy levels in the band gap of the diodes caused by impurities or defects are responsible for the device properties, particularly for the current/voltage characteristics. We present a simple analytical theory that provides a simple estimate for the position of energy levels in the...

Current-voltage characteristics of Ga0.99In0.01As tunnel diodes are studied experimentally and theoretically. Three possible tunneling mechanisms are considered: direct band-to-band tunneling, phonon-assisted tunneling through defects, and resonant tunneling through defects. Comparison between theoretical results and experimental data reveals reson...

A universal theoretical description of the dissociation problem for electron-hole pair on a one-dimensional chain in the hopping regime is proposed. Widely used results of Frenkel and Onsager theories are obtained as particular cases of the general solution. The application of the analytical theory to disordered chains shows that disorder enhances...