An appropriately parameterized compact analytical equation (APAE) is suggested to account for charge carrier mobility in organic disordered semiconductors (ODSs). This equation correctly reproduces the effects of temperature $T$, carrier concentration $n$, and electric field $F$ on the carrier mobility $\mu(T,F,n)$, as evidenced by comparison with analytical theories and Monte Carlo simulations. The set of material parameters responsible for charge transport is proven to be at varience to those used in the so-called extended Gaussian disorder model (EGDM) approach, which is widely exploited in commercially distributed device--simulation algorithms. While EGDM is only valid for cubic lattices with a specific choice of parameters, APAE describes charge transport in systems with spatial disorder in a wide range of parameters. APAE is user-friendly and, thus, suitable for incorporation into device-simulation algorithms.

The space- and temperature-dependent electron distribution n(r,T) determines optoelectronic properties of disordered semiconductors. It is a challenging task to get access to n(r,T) in random potentials, while avoiding the time-consuming numerical solution of the Schrödinger equation. We present several numerical techniques targeted to fulfill this task. For a degenerate system with Fermi statistics, a numerical approach based on a matrix inversion and one based on a system of linear equations are developed. For a non-degenerate system with Boltzmann statistics, a numerical technique based on a universal low-pass filter and one based on random wave functions are introduced. The high accuracy of the approximate calculations are checked by comparison with the exact quantum-mechanical solutions.

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 century and are not at hand for newcomers even nowadays. In the so-called pedestrian approach for newcomers, we start from relativistic kinematics and analyze elastic and inelastic scattering processes in different reference frames to derive the relativistic energy-mass relation. We extend the analysis to Compton scattering between a massive particle and a photon, and a massive particle emitting two photons. Using the Doppler formula, it follows that E = & hbar;omega for photons at angular frequency omega where & hbar; is the reduced Planck constant. We relate our work to other derivations of Einstein's formula in the literature.

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 Halperin and Lax (HL) and the so-called localization landscape technique (LLT) have received most recognition in the community. We prove that the HL approach becomes equivalent to the LLT for the specific case of a Lorentzian filter when applied to the Schrödinger equation with a constant mass. Advantageously, the low-pass filter approach allows further optimization beyond the Lorentzian shape. We propose the global HL filter as optimal filter with only a single length scale, namely, the size of the localized wave packets. As an application, we design an optimized potential landscape for a (semi-)classical calculation of the number of strongly localized states that faithfully reproduce the exact solution for a random white-noise potential in one dimension.

We have generalized the results of the previous work [arXiv:2302.12209] to the case of three-dimensional (3D) spacetime with two spatial and one temporal coordinates. We have found that the flat Minkowski 3D spacetime is "well-stitched", which means that it possesses a structure described by 24 causal relations between 12 events. We have proved that a 3D spacetime is "well-stitched" if and only if it is conformally flat. The concept of a "well-stitched" spacetime does not rely on metrical information about lengths, times, etc., and does not belong to the metric geometry, but rather to geometry of incidence. We therefore have "translated" an important concept of a conformally-flat spacetime from the "metric" language of Riemannian geometry to the "non-metric" language of the geometry of incidence. The results of this paper provide a tool for detecting the curvature of the 3D spacetime on the basis of causal relations only, without any measurement instruments like rulers and clocks, provided that the spacetime is not conformally flat.

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 century and are not at hand for newcomers even nowadays. In a pedestrian approach, we start from relativistic kinematics and analyze elastic and inelastic scattering processes in different reference frames to derive the relativistic energy-mass relation. We extend the analysis to Compton scattering between a massive particle and a photon, and a massive particle emitting two photons. Using the Doppler formula, it follows that $E=\hbar \omega$ for photons at angular frequency $\omega$ where $\hbar$ is the reduced Planck constant. We relate our work to other derivations of Einstein's formula in the literature.

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 by applying the Hamiltonian recursively to random wave functions (RWF). Second, we obtain a temperature-dependent effective potential from the application of a universal low-pass filter (ULF) to the random potential acting on the charge carriers in disordered media. Thereby, the full quantum-mechanical problem is reduced to the quasi-classical description of $n(\mathbf r,T)$ in an effective potential. We numerically verify both approaches by comparison with the exact quantum-mechanical solution. Both approaches prove superior to the widely used localization landscape theory (LLT) when we compare our approximate results for the charge carrier density and mobility at elevated temperatures obtained by RWF, ULF, and LLT with those from the exact solution of the Schr\"odinger equation.

We demonstrate how one can distinguish a curved 4-dimensional spacetime from a flat one, when it is possible, relying only on the causality relations between events. It is known that it is possible only for spacetimes that are not conformally flat. We prove that if a spacetime is not conformally flat, then its non-flatness can be verified by only a few (sixteen) measurements of causal relations. Therefore the results of this paper clarify what can be said about flatness or non-flatness of the spacetime after a finite number of measurements of causal relations.

Here we show that the concepts behind such terms as entanglement, qubits, quantum gates, quantum error corrections, unitary time evolution etc., which are usually ascribed to quantum systems, can be adequately realized on a set of coupled classical pendulums.

The study of semiconductor alloys is currently experiencing a renaissance. Alloying is often used to tune the material properties desired for device applications. It allows, for instance, to vary in broad ranges the band gaps responsible for the light absorption and light emission spectra of the materials. The price for this tunability is the extra disorder caused by alloying. In this minireview, we address the features of the unavoidable disorder caused by statistical fluctuations of the alloy composition along the device. Combinations of material parameters responsible for the alloy disorder are revealed, based solely on the physical dimensions of the input parameters. Theoretical estimates for the energy scales of the disorder landscape are given separately for several kinds of alloys desired for applications in modern optoelectronics. Among these are perovskites, transition-metal dichalcogenide monolayers, and organic semiconductor blends. While theoretical estimates for perovskites and inorganic monolayers are compatible with experimental data, such a comparison is rather controversial for organic blends, indicating that more research is needed in the latter case.

Studying optoelectronic properties in FAPb 1− x Sn x I 3 and in FA 0.83 Cs 0.17 Pb 1− x Sn x I 3 perovskites as a function of the lead:tin content, Parrott et al. (2018) and Savill et al. (2020) observed the broadest luminescence linewidth and the largest Stokes shift in mixed compositions with Sn <25% and with >85%. It is in contrast to the intuitive expectation of the largest effects of alloy disorder for the 50:50 composition. This comment addresses the alloy disorder caused by statistical local spatial fluctuations of the alloy composition and shows that the largest effects of alloy disorder for perfectly random fluctuations in FAPb 1− x Sn x I 3 and FA 0.83 Cs 0.17 Pb 1− x Sn x I 3 are, in fact, expected for x < 0.25 and for x > 0.85. It can be one of the reasons why Pb‐rich and Sn‐rich Sn‐Pb perovskites typically show shorter photoluminescence (PL) lifetimes, broader emission, increased Stokes shifts, reduced PL quantum yield, and higher Urbach tails, compared with their lead‐only counterparts.

Ordered arrays of Ge quantum dot groups (QDs) were grown on pit-patterned silicon-on-insulator (SOI) substrates with deep pits, prepared by electron beam lithography (EBL) and plasma-chemical etching (PCE). Experiments were carried out for the square and hexagonal pit lattices with the lattice period varied. The QDs were found to be sited at the periphery of pits. It was demonstrated that for both pit lattice types the number of QDs per pit can be controlled by varying the period of the pit lattice. The Monte Carlo (MC) simulations of QDs growth on pit-patterned Si substrates were carried out, using the model, which takes strain into account. The island patterning depending on the inter-pit distance is interpreted as the result of competition between stress driven QD nucleation and Ge migration downward into the pits, which serve as the sinks for Ge atoms.

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 period, a matter of controversial debates. Only recently, a comprehensive theory of charge transport in IGZOs has been developed based on the percolation theory. Our chapter is dedicated to a detailed description of this approach. Theoretical results are compared to experimental data revealing parameters of disorder potential in IGZO materials.

Magneto-transport properties were studied on thin films of a 3D topological insulator (TI) Bi2Se3 grown on graphene (Gr) by physical vapor deposition. It was shown that the main contribution to the conductance is from the bulk states, whereas magnetoresistance is determined by both surface and bulk channels. The input of the charge transport over the surface states in the Si/SiO2/Gr/Bi2Se3 structure reveals itself in the weak antilocalization effect. The transition from a weak antilocalization to a weak localization is observed with decreasing the film thickness. The band bending on both interfaces makes it possible to explain the contribution to a weak antilocalization from different surfaces at different TI film thicknesses.

We propose a method of constructing analytical, closed-form expressions for electrostatic/Newtonian potentials of non-uniform polyhedral bodies, in which the density distributions are polynomials of coordinates. Possible applications of the proposed method are spread from astronomy to nanotechnology. The method is based on the use of the generating function for the potential. Explicit expressions for the potential are derived in the case of quadratic or cubic coordinate dependence of the density within a polyhedral body.

A new approach to improve the light-emitting efficiency of Ge(Si) quantum dots (QDs) by the formation of an ordered array of QDs on a pit-patterned silicon-on-insulator (SOI) substrate is presented. This approach makes it possible to use the same pre-patterned substrate both for the growth of spatially ordered QDs and for the formation of photonic crystal (PhC) in which QDs are embedded. The periodic array of deep pits on the SOI substrate simultaneously serves as a template for spatially ordering of QDs and the basis for two-dimensional PhCs. As a result of theoretical and experimental studies, the main regularities of the QD nucleation on the pre-patterned surface with deep pits were revealed. The parameters of the pit-patterned substrate (the period of the location of the pits, the pit shape, and depth) providing a significant increase of the QD luminescence intensity due to the effective interaction of QD emission with the PhC modes are found.

Lateral heterojunctions of atomically precise graphene nanoribbons (GNRs) hold promise for applications in nanotechnology, yet their charge transport and most of the spectroscopic properties have not been investigated. Here, we synthesize a monolayer of multiple aligned heterojunctions consisting of quasi-metallic and wide-bandgap GNRs, and report characterization by scanning tunneling microscopy, angle-resolved photoemission, Raman spectroscopy, and charge transport. Comprehensive transport measurements as a function of bias and gate voltages, channel length, and temperature reveal that charge transport is dictated by tunneling through the potential barriers formed by wide-bandgap GNR segments. The current-voltage characteristics are in agreement with calculations of tunneling conductance through asymmetric barriers. We fabricate a GNR heterojunctions based sensor and demonstrate greatly improved sensitivity to adsorbates compared to graphene based sensors. This is achieved via modulation of the GNR heterojunction tunneling barriers by adsorbates.

Possibility of formation of pseudomorphous quantum well consisting of InGaAsP quaternary alloy during InAs deposition on GaP/Si epitaxial film surface with developed relief is demonstrated. Investigations of quantum well were performed by transmission electron microscopy and spectroscopy of cw photoluminescence. The appearance of quantum well segments of 2 types with different width and composition InGaAsP is demonstrated. Width increasing is accompanied by decreasing of In and As atoms fraction. Lateral sizes of quantum well segments are not lower than 20 nm. Different photoluminescence bands are corresponds to quantum well segments. Observed phenomenon are explained in the framework of suggestion about strain induced surface reorganization during InAs heteroepitaxy on terraced GaP surface.

The effect of magnetic field on the long-term photoconductance relaxation in two-dimensional arrays of Ge tunnel-coupled quantum dots grown on Si by molecularbeam epitaxy is studied. It was shown that the relaxation process can be slowed down as well as accelerated by magnetic field. The sign of changing the relaxation rate depends on the localization radius and the quantum dot occupancy. To explain an unusual acceleration effect we proposed a model based on the difference in probabilities of carrier transitions to single- or double-occupied quantum dots due to Zeeman effect.