The performance of nanoscale and microscale diodes depends largely on the interplay between quantum tunneling and thermal effects. While resonant tunneling can greatly enhance current densities, the accompanying electrode heating threatens device stability and may trigger thermal runaway at high currents. This makes the joint treatment of tunneling and heat transport essential for reliable device design. To address this challenge, we derive a general quantum potential within the Schr & ouml;dinger equation, and develop analytical formulations for diode current at different electrode temperatures. The approach yields exact current-voltage characteristics, explicitly accounts for reverse tunneling at low anode voltages, and incorporates electrode materials with distinct Fermi energies and work functions. Coupling these results with a ballistic heat transport model, we predict electrode heating under realistic operating conditions. Our analysis shows that resonant tunneling increases current but also intensifies heating. Materials with high thermal conductivity, such as diamond or BeO, have been shown to mitigate overheating and extend stable operation. These findings provide a predictive framework for understanding the coupled quantum-thermal behavior of tunneling diodes and offer guidelines for designing advanced electron sources and nanoscale power devices where current amplification must be balanced with thermal stability.

The corrections to Casimir pressure (force) on two plates of real metal described by the dielectric constant of the Drude, Drude-Lorentz, Drude-Smith and plasma models at the finite temperature and conductivity are considered. We consider the contour integral lost in the Lifshitz formula and discuss inconsistencies for the corrections to the Casimir force given in the literature. Numerical and analytical results in the near and far zones are presented. The two first-order correction obtained due to the actual dielectric constant of the metal coincided with the literature data.

Based on the van Kampen-Schram method, a formula for the Casimir force between two plane-layered structures is obtained, which includes the sum of the Matsubara frequencies and a contour integral. It is shown that the contour integral is not taken into account in the Lifshitz formula. Taking it into account gives a small contribution at high temperatures when the Lifshitz formula is approximately correct. However, at low temperatures, its contribution is significant, and the Lifshitz formula for the finite temperature does not transform into the Lifshitz formula at zero temperature. An example of interaction of metal plates is considered.1

The flat metasurfaces described by tensor surface conductivity, the transverse size of which is small compared to the wavelength, are considered. In this case, we introduce two-dimensional surface conductivity for them, as well as for infinitely thin conductive sheets of graphene type. The method of Green's tensor functions of electrodynamics connecting fields and current densities, as well as the mode matching technique, are used. Conductive films on substrates are considered, including layered substrates of finite thickness with periodic layers and infinite substrates, as well as gradient substrates with a dependence of the dielectric constant on the thickness. Two-dimensional periodic structures of conductive films and dielectric films doped with nanoparticles are also analyzed. The possibility of applying the method to diffraction of surface plasmons on metasurface inhomogeneities is analyzed.

We present a nonlinear model of thermal field emission in resonant tunneling nanostructures with multiple barriers and potential wells, based on an accurate determination of the quantum potential shape and a rigorous solution of the Schrödinger equation, while considering thermal balance. The model applies to vacuum and semiconductor resonant tunnel diode and triode structures with two and three electrodes and to the general case of two-way tunneling with electrode heating. The complete balance of heat release and transfer is accounted for, with heat transport considered ballistic. This approach can also be extended to the non-stationary case, incorporating the influence of space charge. The short flight time of electrons in such structures makes them promising for the fabrication of THz devices.

We consider the linear and nonlinear response of a weighted graphene sheet under the normal incidence of a plane electromagnetic wave in the form of a quasi-monochromatic pulse of long duration with a sharp edge and harmonic filling. The generation of odd harmonics in the reflected and transmitted spectra is obtained. The coefficient of transformation of the first harmonic into the third harmonic at a frequency of 10 Hz is of the order of 10-3. We use perturbative theory based on the quantum Wallace strong coupling model with field amplitude expansion and integration over the entire Brillouin zone (BZ), solving the kinetic Boltzmann equation with a collision integral in the Bhatnagar-Gross-Crook (BGK) form. The electromagnetic field is considered classically, while its vector potential changes the quasi-pulse in the dispersion equation.

This paper explores nanodiode and nanotriode structures with incorporated dielectric films in vacuum electronics. Such emission structures allow for very high (on the order of 10(12) A /m(2) and more) current densities and differ greatly from conventional field emitters. For all structures considered, we derive the electrostatic Green's function, construct potential barrier profiles, calculate tunneling coefficients, and determine the volt-ampere (VAC) characteristics, taking into account the distribution of electron energies. This work presents novel results, including a precise formula for the potential distribution in a structure with a dielectric film. This formula accounts for the finite conductivity of the semiconductor film and incorporates the reverse tunnel current within the structure. Considering this effect in nanostructures is crucial, particularly at low anodic voltages.

Peculiarities of 1D vacuum tunneling and calculation of the tunnel current in barrier quantum structures with one and two wells are considered. The structures are formed by several electrodes (cathode, anode, and two grids). The multiple imaging method is used for plotting the potential profiles. The equations for eigenlevels and metastable levels of the structure with an arbitrary potential profile are derived. For complete resonant tunneling, metastable levels must fall into the electron kinetic energy distribution region at the cathode, which is observed in one-well structures zero anode voltage or for a low anode voltage as compared to the grid voltage. An appreciable voltage at the anode leads to an asymmetric structure and to an incomplete resonant tunneling. In this case, the two-well structure with a double grid makes it possible to obtain complete resonant tunneling for some energies and to increase the tunnel current by orders of magnitude.

Magnetoplasmons moving along a thin metal or well-conducting semiconductor film, as well as along this film on a dielectric substrate, placed in a strong magnetic field parallel to the film are considered. Dispersion equations for hybrid waves have been derived by a strict method and in the thin film approximation by introducing surface conductivities. The possibility of existing slow microwave and terahertz magnetoplasmons has been demonstrated. The considered structures can be used as slowing systems for traveling wave amplifiers, in particular, a traveling-wave tube amplifier.

The conditions of resonant (almost complete) tunneling of photons (plane monochromatic electromagnetic waves) through layered dielectric and metal-dielectric structures are considered. Resonant tunneling occurs at frequencies at which the resonance conditions for the corresponding structures of open resonators are met. For metal-dielectric structures, the possibility of tunneling in the optical range with a strong barrier in the IR range is shown, which can be used to control the transmission of window panes. Keywords: dielectric permittivity, homogenization, resonant tunneling, plasmons, metal nanoparticles, window panes.

We consider the diffraction of a plane wave on a layer of symmetric hyperbolic metamaterial made of metal and SiO2 layers. It is shown that the reflection coefficient depends not only on the angle of incidence, but also on the direction of incidence relative to the anisotropy axis. In an arbitrary fall, a plate of an asymmetric hyperbolic metamaterial creates scattered waves of both polarizations.

We analyse the steady-state thermal regime of a one-dimensional triode resonant tunnelling structure. The high currents generated by resonant tunnelling produce a large amount of heat that could damage the structure. Establishing the conditions under which it can operate at optimum efficiency is therefore a problem of great relevance for applications. The tunnel current is found via eigenvalues of the Schrödinger equation in quantum wells. By calculating the current generated in the device and using the energy conservation law in the electrodes, the temperature reached is obtained for different types of electrodes and the importance of heat conduction and thermal radiation is analysed. In the cases discussed, conduction is dominant. When the electrode material is copper, the temperature reached is similar to that of the thermostat for a wide range of electrode lengths, whereas when the cathode material is diamond-graphite and the anode material is copper, the temperature increases significantly as a function of length. The results obtained allow the temperature to be controlled for optimum performance of the field-emitting triode structures.

We consider the diffraction of a plane wave on a layer of symmetric hyperbolic metamaterial made of metal and SiO 2 layers. It is shown that the reflection coefficient depends not only on the angle of incidence, but also on the direction of incidence relative to the anisotropy axis. In an arbitrary fall, a plate of an asymmetric hyperbolic metamaterial creates scattered waves of both polarizations. Keywords: hyperbolic metamaterial, diffraction, effective permittivity tensor, homogenization.

The propagation of a strong plane electromagnetic wave from vacuum through a bounded plasma layer is considered taking into account nonlinearity under tunneling and transparency conditions. The plasma is considered to be cold and nonmagnetic, and the electromagnetic pulse to be quasi-monochromatic, but short (i.e., not heating the plasma layer during its passage through it). The temperature dependence is not taken into account. The nonlinearity is taken into account phenomenologically as a dependence of the plasma frequency and collision rate on the field square averaged over the period. Associated stationary nonlinear integral equations for field harmonics, as well as a nonlinear integral equation for a nonstationary process, are obtained. The rate and time of tunneling in linear and nonlinear cases, the field distribution, and the third harmonic generation coefficient are determined. It is shown that tunneling takes longer than the passage through a transparent layer, and the nonlinear tunneling is a longer process compared to linear tunneling, while in all cases the time of the wave passage is longer when the time of passage through the equivalent length in vacuum at the speed of light.

The features of one-dimensional vacuum tunneling and calculation of the tunneling current in barrier quantum structures with one and two wells are considered. The structures are formed by several electrodes: the cathode, the anode and two grids. The potential profiles are constructed by the method of multiple images. Equations for eigenvalues and metastable levels of a structure with an arbitrary potential profile are found. For full resonant tunneling, the metastable levels must fall into the region of the electron kinetic energy distribution at the cathode, which occurs in single-well structures in the absence of an anode voltage or at a low anode voltage compared to the voltage on the grids. A significant voltage at the anode leads to an asymmetric structure and incomplete resonant tunneling. In this case, a two-well structure with a double grid allows obtaining full resonant tunneling for a number of energies and increasing the tunneling current by orders of magnitude.

A new rigorous model for calculating Casimir-Lifshitz forces for thin dielectric or conductive filaments based on the Lorentz force is proposed. We use the formulas of G.T. Markov and the fluctuation-dissipation theorem. The only approximation used is the small ratio of the radii to the distance between the threads, which allowed the transverse structure of the fields in the threads to be considered constant. The results are obtained for metallic and dielectric filaments, as well as for carbon nanotubes.

A new method for determining the dispersion interaction between arbitrary bodies of an arbitrary shape, based on the theory of excitation of cavities, is proposed. The Rytov–Levin–Lifshitz approach with introducing fluctuation current sources into Maxwell’s equations was used, which gave equations for determining correlations of fluctuation currents, and correlations of the fields were obtained. Determining the correlations is an inverse problem, formulated on the basis of Kirchhoff’s detailed equilibrium principle.

Methods of inversion of integrodifferential operators of thin linear antennas and also related to the dispersion interaction of the Casimir–Lifshitz force between two thin linear objects described by the dielectric constant in the form of Drude–Lorentz are considered. A new rigorous model for calculating Casimir–Lifshitz forces for thin dielectric or conductive filaments based on the Lorentz force is proposed. To determine correlations, the formulas of G.T. Markov, the fluctuation–dissipation theorem, and the principle of detailed equilibrium with a thermal field were used. Analytical estimates of the obtained spectral integrals are performed in the far zone.

Volumetric integral and integro-differential equations are considered that describe problems of diffraction by three-dimensional bodies with given macroscopic permittivity and magnetic permeability, as well as problems on free vibrations of such bodies. Similar equations are obtained for waveguide structures: hollow shielded waveguides with dielectric filling, dielectric waveguides (optical beamguides), photonic-crystal waveguides. Dominantly stationary linear electromagnetic problems are considered. Non-stationary and nonlinear problems are mentioned casually. Numerical results are given for oscillations H01delta and H011 of a cylindrical dielectric resonator, for waves of a rectangular dielectric waveguide and a plasmonic waveguide, dispersion in a photonic crystal, and diffraction by a rectangular dielectric cylinder. Keywords: ...