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The purpose of this paper is to develop the models of the dielectric permittivity dispersion of heterogeneous systems based on semiconductors to a level that would allow to apply effectively the method of broadband dielectric spectroscopy for the study of electronic processes in ceramic and composite materials.

The new approach for determining the complex dielectric permittivity of heterogeneous systems with semiconductor particles is used. It includes finding the analytical expression of the effective dielectric permittivity of the separate semiconductor particle of spherical shape. This approach takes into account the polarization of the free charge carriers in this particle, including capturing to localized electron states. This enabled the authors to use the known equations for complex dielectric permittivity of two-component matrix systems and statistical mixtures.

The presented dispersion equations establish the relationship between the parameters of the dielectric spectrum and electronic processes in the structures like semiconductor particles in a dielectric matrix in a wide frequency range. Conditions of manifestation and location of the different dispersion regions of the complex dielectric heterogeneous systems based on semiconductors in the frequency axis and their features are established. The most high-frequency dispersion region corresponds to the separation of free charge carriers at polarization. After this region in the direction of reducing of the frequency, the dispersion regions caused by recharge bulk and/or surface localized states follow. The most low-frequency dispersion region is caused by recharging electron traps in the boundary layer of the dielectric matrix.

Dielectric dispersion models are developed that are associated with: electronic processes of separation of free charge carriers in the semiconductor component, recapture of free charge carriers in the localized electronic states in bulk and on the surface of the semiconductor and also boundary layers of the dielectric at the polarization. The authors have analyzed to situations that correspond applicable and promising materials: varistor ceramics and composite structure with conductive and semiconductor fillers. The modelling results correspond to the existing level of understanding of the electron phenomena in matrix systems and statistical mixtures based on semiconductors. It allows to raise efficiency of research and control properties of heterogeneous materials by dielectric spectroscopy.

The purpose of this paper is modeling the effect of negative capacitance in the capacitance-voltage characteristic of the intergranular potential barrier of varistor structure.

The modeling of the capacitance-voltage characteristic of the intergranular barrier in metal oxide varistor ceramics is based on the development of the algorithm. It includes all the known mechanisms of electrotransfer in a wide range of voltages and currents, and also takes into account the voltage drop on the intergranular interlayer of intergranular potential barrier.

The models and algorithms for calculating the capacitance-voltage characteristics of a single intergranular potential barrier with the use of the most established understanding used at the interpretation of the nonlinear conductivity intergranular barrier are developed. The results of the capacitance-voltage characteristics modeling correspond to the existing understanding of the electrical properties on the ac current varistor ceramics are based on zinc oxide. The model allows to predict the behavior of varistors on the alternating current (voltage).

It is established that the recharge of the surface localized states occurs when a voltage is applied to the varistor structure, it can lead to a relaxation decrease in the width of the potential barrier overcome by tunneling electrons in the field emission from the conduction band of the one crystallite in the conduction band of the other crystallite and thus to the current backlog of applied voltage on the phase (i.e. the expression of the negative capacitance effect).

The purpose of this paper is to develop a generalized model of the nonlinear conductivity of varistor ceramic suitable for solving problems of prediction and control of ceramic nonlinearity, stability of varistor properties.

The modeling of current-voltage characteristic of the intergranular barrier in metal oxide varistor ceramics is based on the development of the algorithm. It includes all the known mechanisms of electrotransfer in a wide range of voltages and currents of the current-voltage characteristics, and also takes into account the deviation of the barrier form the Schottky barrier.

The models of double Schottky barrier and double barrier of arbitrary form, as well as the algorithms for calculating the current-voltage characteristics of a single intergranular potential barrier and a separate “microvaristor” with the use of the most well-established understanding of the main mechanisms of electrical are developed. The results of current-voltage characteristics modeling correspond to the existing understanding of the nonlinear electrical conductivity varistor ceramics are based on zinc oxide. The model of double barrier of arbitrary form takes into account the deviation of the barrier form the Schottky barrier which is important in predicting the deformation of the current-voltage characteristics of the varistor products in the process of degradation.

The relation between the form of the current-voltage characteristic and the distribution profile of the donor concentration in the surface regions of the semiconductor crystallites constituting the intergranular potential barrier is established. The accumulation of donors in the space charge region leads to the increase in the current on the prebreakdown region of the current-voltage characteristic and the reduction of voltage corresponding to the breakdown region beginning of the current-voltage characteristic. The significant role of the interlayer in the formation of current-voltage characteristic of the intergranular potential barrier is shown.

The purpose of this study is to model the dependences of the output voltage, temperature, current and electrical power dissipation of a voltage limiter based on a two-layer varistor–posistor structure on time and analysis the influence of operating modes and design parameters of such a limiter on these characteristics.

The behavior of the limiting voltage, temperature and other parameters of the voltage limiter when an input constant overvoltage is applied is studied by the simulation method. The voltage limiter was a two-layer construction. One layer was a zinc oxide ceramic varistor. The second layer was a posistor polymer composite with a nanocarbon filler of PolySwitch technology.

The output voltage across the varistor layer decreases and reaches some fixed value related to its breakdown voltage after applying a constant overvoltage to the structure over time. The temperature of the structure increases to some steady state value, while the current decreases significantly. The amplitude of the transient current pulse increases, its duration and energy of the transient process decrease with increasing overvoltage. An increase in the internal resistance of the overvoltage source can cause a decrease in the amplitude and an increase in the duration of transient currents.

The ranges of values for the activation energy of conduction of the varistor layer in weak electric fields, the intensity of heat exchange between the structure under study and the environment are determined to ensure the stable operation of this structure as a voltage limiter. The results obtained make it possible to select the necessary parameters of the indicated structures to ensure the required operating modes of the voltage limiter for various applications.

The purpose of this paper is to minimize and prevent current overloads (including the elimination of abnormal and fire hazardous situations) in photovoltaic solar arrays by using low-cost functional electronic elements, in particular, the new PolySwitch PPTC fuses.

The modeling method has been used to investigate the circuit solution of the use of PolySwitch type fuses to prevent and minimize current overloads in photovoltaic solar arrays.

It is shown that the limitation of the short-circuit current with parallel connection of photovoltaic components (photovoltaic cells or their modules) can be implemented when the following conditions are met: the resistance of the fuse in the conducting state is much lesser than the parallel connection of the series resistances of the photovoltaic components; and the tripping current of the fuse must be greater than the maximum current of the separate photovoltaic components and lesser than the current of a parallel connection of several photovoltaic components.

The influence of the magnitude of the resistance in the conducting state and the response current of the fuses to the current–voltage and volt–watt characteristics of parallel connections of the photovoltaic components (photovoltaic cells or their modules) is analyzed. The modeling results are confirmed by experimental data on the transformation research of light current–voltage and volt–watt characteristics of parallel connections of industrial photovoltaic modules using resettable fuses of the PolySwitch type.

The purpose of this paper is to explore and develop specific models of the kinetics of isothermal depolarization currents (IDC) and the corresponding methods for the diagnostics of the physical parameters of localized electronic states (LES) in heterogeneous materials and corresponding polycrystalline semiconductor materials and heterogeneous insulators with a conductive phase.

Analysis of the kinetics of isothermal depolarization on the basis of the models allowed the authors to establish a sufficient level of their information content. This also allowed the possibility of applying for research and testing of heterogeneous structures of electronic technique.

Optimal conditions (full charge of LES on one side of the object and full discharge on the other side) and the correction factors, allowed the researchers to find concentration of these states using the developed models.

This paper uses a particular method to determine and test the parameters of LES, including operations of determining the time constant of IDC signal from its frequency spectrum, finding the ionization energy and the capture coefficient of electrons from the temperature dependence of this time constant, determining the concentration based on the integration of the time dependence of current density of IDC in the time interval that boundaries are determined from the limited range of frequencies of the signal IDC spectrum has been proposed, validated and verified by numerical experiments.

The electromigration degradation model of nonlinear electrical properties of non‐uniform structures with intercrystallite potential barriers is developed. It allows connecting the increasing of near surfaces concentration of volume donors by their migration in electrical field at heating up structures by means of electrical current in the process of degradation. It results in experimentally observed deterioration varistoral properties, deterioration and asymmetrical deformation of currentvoltage characteristics during their exploitation.

In this article the electric properties of conducting polymeric compounds with graphite filler was studied to obtain the information of its structural distinctions. It was defined, that the temperature dependences of the electrical resistivity of the investigated composite materials, which had different content of conductive filler, had the posistor properties. Their frequency dependences of dielectric permittivity were found dispersed at low‐frequency area. This phenomenon was explained based on the availability of “built‐in” charges at the boundary region to the particles of graphite of polymeric layer. It was determined by outflow of free charge carries from graphite to localized states in the polymeric matrix. The estimated thickness of “built‐in” charge, in the context of the model of concentric system of conductive particles in dielectric matrix is about a micron.

The paper aims to substantiate optimization directions of resettable fuses parameters to protect solar arrays from overcurrent.

The method of modeling the electrophysical characteristics of resettable fuses is used.

Resettable fuses currently produced are of little use for protecting photovoltaic cells (PVC) in solar arrays from overcurrent. The volume fraction of the conductive filler should be about 0.15, near the percolation threshold. Thus, reducing the resistance by increasing the amount of filler is not possible. The matrix of the composite should consist of a material with a significant proportion of the crystalline phase to ensure a sharp increase in the composite's volume near the melting point. Using a polymer with a lower melting point instead of polyethylene can reduce the power required to switch a resettable fuses.

The possibility of using resettable fuses based on polymer composite materials with a positive temperature coefficient of resistance to protect photovoltaic solar cells from current overloads is considered. Modeling of the electrophysical characteristics of modern industrial fuses of this type based on polyethylene-nanocarbon composites has been carried out. The limits of their applicability for the protection of photovoltaic solar cells are analyzed. On the basis of the obtained results, the optimization directions of the resettable fuses parameters for use in the protection circuits of PVC of solar array are determined.