S. D. Baranovskii’s research while affiliated with Philipps University of Marburg and other places

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Publications (227)


A derivation of E = mc2 without electrodynamics
  • Article

September 2024

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27 Reads

European Journal of Physics

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Sergei D Baranovskii

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Florian Gebhard

There are several ways to derive Einstein’s celebrated formula for the energy of a massive particle at rest, E = mc2. 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 = ℏω for photons at angular frequency ω where ℏ is the reduced Planck constant. We relate our work to other derivations of Einstein’s formula in the literature.


Parametrization of the charge-carrier mobility in organic disordered semiconductors

July 2024

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49 Reads

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1 Citation

Physical Review Applied

S.D. Baranovskii

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[...]

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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 Monte Carlo simulations. The set of material parameters responsible for charge transport is proven to be at variance with those used in the so-called extended-Gaussian-disorder-model (EGDM) approach, which is widely exploited in commercially distributed device-simulation algorithms. While the EGDM is valid only for cubic lattices with a specific choice of parameters, the APAE describes charge transport in systems with spatial disorder in a wide range of parameters. The APAE is user-friendly and, thus, suitable for incorporation into device-simulation algorithms.


Figure 1. Sketch of matrixˆUmatrixˆ matrixˆU for the one-dimensional case. White and black squares represent zeros and unities, respectively.
Figure 4. Realization of the white-noise disorder potential on a one-dimensional strip. Insert: the wave function ψ(x) of the state with the lowest energy in the region 275 ≤ x ≤ 325. The coordinate x is dimensionless in the units given by Equation (2).
Figure 6. Comparison between the exact effective potential (solid blue lines) and the filtered potential (dashed red lines) for a one-dimensional sample with white-noise potential. Reprinted with permission from [14]. Copyright (2023) by the American Physical Society.
Computation of the Spatial Distribution of Charge-Carrier Density in Disordered Media
  • Article
  • Full-text available

April 2024

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56 Reads

Entropy

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.

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A pedestrian approach to Einstein's formula E=mc2E=mc^2 with an application to photon dynamics

August 2023

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176 Reads

There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, E=mc2E=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=ωE=\hbar \omega for photons at angular frequency ω\omega where \hbar is the reduced Planck constant. We relate our work to other derivations of Einstein's formula in the literature.


Quantum states in disordered media. II. Spatial charge carrier distribution

February 2023

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29 Reads

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11 Citations

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 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 quasiclassical description of n(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 Schrödinger equation.


Quantum states in disordered media. I. Low-pass filter approach

February 2023

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24 Reads

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13 Citations

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.


FIG. 2. Possible arrangement of a swarm of satellites near the Earth, enabling one to detect the curvature of the space due to the Earth's gravity. One group of satellites is located on a circle (violet dashed line), another one -on the axis of symmetry of this circle (green dashed line). Yellow arrows show the directions of optical signals between the satellites. L is the size of the swarm, and R is the distance from the Earth's center.
FIG. 7. Illustration of time delay δtP Q. A light signal emitted at event P passes in a vicinity of event Q. The event when this signal comes to the point of space of event Q is denoted as Q. Time delay δtP Q is the difference in time between events Q and Q.
FIG. 8. A complete quadrilateral in a curved space. Solid lines OAB, OCD, AE1D and BE2C are geodesics. Dashed lines show that geodesics AB and CD would intersect in some point (event) E0 if the spacetime were flat. Points E1 and E2 are chosen in a vicinity of point E0. Unit vectors b1 and b2 (not shown) are perpendicular both to a1 and to a2.
How to detect the spacetime curvature without rulers and clocks

February 2023

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73 Reads

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.



Energy Scales of Compositional Disorder in Alloy Semiconductors

December 2022

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94 Reads

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7 Citations

ACS Omega

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 mini-review, 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.


FIG. 3. Comparison between LLT and a global Lorentzian filter. The random potential VR(x) of Fig. 1(a) is shown as a blue line. The red line is the result of LLT, WR(x), from the solution of Eq. (40). The yellow line shows the potential W L R (x) using a Lorentzian filter, see eq. (36), where L = 0.436 wp is calculated from eqs. (49) and (50).
FIG. 5. Relation between the exact energies for the lowestlying localized states ej and the corresponding standard deviations HL,j of the wave packets in the Halperin-Lax wave function in one dimension, see eq. (68). Also shown is the median of the data (red dots) and the Halperin-Lax relation HL(e) = 1/ √ −e, see eq. (69).
FIG. 8. Integrated particle density N (e) up to energy e = E/T in a one-dimensional random white-noise potential. The exact result (73) is compared with the semi-classical state counting using eqs. (78) and (79) for a Halperin-Lax filter with HL = 1.2 wp (dashed line) and with HL = 1.0 wp (full line) (SL = 1), averaged over 1.000 configurations with 2.000 sites for L = 200.
FIG. 9. Localized state in a one-dimensional random whitenoise potential. (a) sketch of potential V (x); (b) wave function ψ(x) that corresponds to the nth eigenstate whose energy is approximately equal to e; (c) function y(x) = −ψ (x)/ψ(x). The particle is confined between infinite walls at x = 0 and x = L. The zeros of the wave function are labeled by x1, x2, et cetera.
Quantum states in disordered media. I. Low-pass filter approach

December 2022

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80 Reads

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 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 Schr\"odinger 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.


Citations (77)


... with the factor C 0.6-0.7 being slightly dependent on the parameter ρα 3 [18][19][20][21][22]. Despite the successful utilization of the transport energy concept for describing transport phenomena, its existence and exact position have been difficult to confirm in direct kMC simulations. ...

Reference:

Variational encoder-decoder architecture for charge and energy transport in disordered materials
Parametrization of the charge-carrier mobility in organic disordered semiconductors
  • Citing Article
  • July 2024

Physical Review Applied

... Recently a new way to do the filtering was suggested 211 and later compared with the conventional one. 212 Chapter 13. The theory of nonlinear screening of a long-range potential developed in Chapters 3 and 13 was extended to nonlinear screening of the random potential of remote charged impurities by the 2DEG in QHE devices. ...

Quantum states in disordered media. I. Low-pass filter approach
  • Citing Article
  • February 2023

... It should be noted that there are indirect methods investigating the essential aspects of electron states in disordered structures without solving explicitly the Schrödinger equation, such as the localization landscape theory [25][26][27] or the low-pass filter approach [28,29]. However, since the energy band structure is one of our interests here, we focus on direct band-structure calculation methods. ...

Quantum states in disordered media. II. Spatial charge carrier distribution
  • Citing Article
  • February 2023

... In other words, the versatility in material and device designs comes with the unavoidable alloy disorder, which might not be fully controllable in the technological growth processes and which can negatively impact device performance due, e.g., to the broadening of optical transitions [19,20] or additional alloy scattering [21]. Therefore, understanding the effects of alloy disorder on electronic and optical properties is of crucial importance [22][23][24]. From the theoretical side, this is translated into the need of models able to properly integrate disorder effects at the Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. atomistic scale into the calculation of the electronic and optical properties of the relevant portion in the active region of a device, like a QW, a QD or a SL. ...

Energy Scales of Compositional Disorder in Alloy Semiconductors

ACS Omega

... 3,11 Therefore, further crystal growth optimization might not be helpful to diminish the effects of alloy disorder in FAPb 1−x Sn x I 3 and FA 0.83 Cs 0.17 Pb 1−x Sn x I 3 perovskites. 21 In other words, the samples have already achieved a high quality with respect to the effects of alloy disorder. If the parameters α, m, and N in eq 9 did not depend on x, ε 0 (x) would solely be proportional to x 2 (1 − x) 2 and would display a maximum at x = 0.5. ...

Comment on “Interplay of Structural and Optoelectronic Properties in Formamidinium Mixed Tin‐Lead Triiodide Perovskites”

... The low temperature (20 K) PL spectra of P1 indicate the presence of the neutral exciton X 0 and a trion X T at ≈30 meV lower than X 0 . The energy of X 0 and X T in P1 at low temperatures agrees well with earlier reports [23]. In the case of D1 at low temperature, the indirect exciton emission X 0 at ≈1.6 eV and another peak at ≈109 meV lower than X 0 , which we assign to an exciton bound to a charged defect X B , is observed. ...

Energy Scaling of Compositional Disorder in Ternary Transition‐Metal Dichalcogenide Monolayers

... The inner ring of the bearing is mounted on a trunnion (10). (d) The sample plate is based on commonly used Omicron-type sample plates (11) with a Teflon housing (14) to hold five spring-loaded contacts (15) with leads attached to the sample (16) in a four-point geometry with back-gating embedded in. (e) Close-up of the sample receptacle with a sample plate loaded. ...

Tunneling current modulation in atomically precise graphene nanoribbon heterojunctions

... 15,16 In particular, many studies provided a multi-scale description of electron transport with a realistic material morphology obtained from molecular dynamics simulations to calculate and analyze the charge mobility. [17][18][19][20][21][22][23][24][25] The charge carriers in conducting polymers are polarons representing quasiparticles that are localized over several monomer units because of the strong electron-phonon coupling that induces geometrical distortion of the chain (from aromatic to quinoid). 17 One of the central questions in the description of electron transport in conductive polymers is the calculation of the hopping rates polarons in the chains or between chains as. ...

Parametrization of the Gaussian Disorder Model to Account for the High Carrier Mobility in Disordered Organic Transistors
  • Citing Article
  • February 2021

Physical Review Applied

... Note that by "compact" models, we mean an effectively zero-dimensional description that takes in a voltage and returns a mobility using, for example, a numerical integration in energy rather than a compact analytical expression specifically intended for circuit design. Although initially there was a great deal of debate [3][4][5][6] as to the basic transport mechanisms dominant in a-IGZO, the bulk of current "compact" modeling research [3,[7][8][9][10][11][12][13] has largely settled on a certain agreed-upon conceptual picture. This picture envisions a-IGZO as having a conduction band-edge or so-called "mobility edge", E b (r), that spatially varies throughout the system such that its randomized value obeys a certain probability distribution. ...

Percolation description of charge transport in the random barrier model applied to amorphous oxide semiconductors