Modeling of current-voltage characteristic of the intergranular barrier in metal oxide varistor ceramics

Abstract

Purpose -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. Design/methodology/approach -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. Findings -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. Originality/value -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 effect of negative capacitance in varistor structure on the basis of its models with voltage drop on the intergranular interlayer

“…Thus, to the ohmic (prebreakdown) region of I-V characteristic can be match Region 1 of C-V characteristic where capacitance varies only slightly with increasing voltage, the low-nonlinear (prebreakdown) region -Region 2 (increased capacitance) and the beginning of the highly nonlinear (breakdown) region -Region 3 (drop size). This link shows the generality of electronic processes that are responsible for the analyzed field effects and thus, the dependence of the dielectric constant (or capacitance), which are observed, can be interpreted in terms of models known for I-V characteristics (Kvaskov, 1988;Gupta, 1990;Clarke, 1999;Tonkoshkur and Ivanchenko, 2014).…”

“…Band diagram of the varistor element is shown in Figure 1. It includes intergranular barrier represented by two counter included the depletion regions of the space charge, separated by a thin nanoscale (Δd~20 Å) dielectric interlayer of the intergranular phase (Gupta, 1990;Ponce et al, 2010;Tonkoshkur and Ivanchenko, 2014). And it also includes the neutral area of the highly conductive crystallite (grain) with a linear size d s from~10 μm (Ivon, 2000).…”

Percolation effects in dc degradation ofZnOvaristors

“…The presence of Bi-rich thin-film phase is detected for GB with highly nonlinear IðUÞ characteristics with a threshold voltage 3.2 -3.6 V. 29 The space variation of the donor density and band bending in the surface regions were calculated by solving the system of the Poisson equation and the continuity equation for migrating ions. 25 Earlier suggested computation scheme 47 was used for the calculation of IðUÞ characteristic. Its peculiarity was that it allowed to take into account the voltage drop on the intergranular layer.…”

“…They are the effective medium approximation, 41,42 the network models based on Kirchhoff equations [43][44][45] and percolation theory approach. 34,[46][47][48] Using ideas of percolation, a phenomenological approach to nonOhmic conduction in ZnO varistor was developed and expression J ¼ 0 E expðEÞ (here J is the current density and E is the electric field) was obtained. 49 The mentioned methods were used for the analysis of current-voltage (IðUÞ) characteristic 34,[41][42][43][44][45][46][47]49 and temperature dependence of conductivity 48 in ZnO varistor.…”

“…34,[46][47][48] Using ideas of percolation, a phenomenological approach to nonOhmic conduction in ZnO varistor was developed and expression J ¼ 0 E expðEÞ (here J is the current density and E is the electric field) was obtained. 49 The mentioned methods were used for the analysis of current-voltage (IðUÞ) characteristic 34,[41][42][43][44][45][46][47]49 and temperature dependence of conductivity 48 in ZnO varistor. However, application of such models to a study of degradation in varistor ceramics seems to be promising.…”