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Stochastic simulation of nonlinear electron transport in Ni/Al$$_2$$O$$_3$$ metal–dielectric varistors Full article

Journal Journal of Computational Electronics
ISSN: 1569-8025
Output data Year: 2026, Volume: 25, Number: 5, Article number : 188, Pages count : 14 DOI: 10.1007/s10825-026-02639-9
Tags Metal–dielectric varistor · Electron tunneling · Barrier conductivity · Monte Carlo simulation · Current–voltage characteristics · Nonlinear potential equation with field-dependent conductivity
Authors Sabelfeld Karl 1,2 , Abramkin Demid 3 , Kireeva Anastasya 1,2 , Zalyalov Timur 3
Affiliations
1 Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentiev Prosp. 6, Novosibirsk, Russia, 630090
2 Sobolev Institute of Mathematics, SBRAS, Koptyug str. 4, Novosibirsk, Russia, 630090
3 Rzhanov Institute of Semiconductor Physics, Lavrentiev Prosp. 13, Novosibirsk, Russia, 630090

Funding (2)

1 Министерство науки и высшего образования РФ 075-15-2025-348
2 Russian Science Foundation 24-11-00107

Abstract: A stochastic computational framework for nonlinear electron transport in heterogeneous metal dielectric varistors is developed based on Monte Carlo simulation of explicit electron trajectories coupled with a self-consistent nonlinear potential equation. The methods derived are applied to compute current–voltage (I–V) characteristics of a Ni/Al(2)O(3) metal–dielectric varistor. The approach couples a nonlinear potential equation with Monte Carlo simulation of electron transport in a medium with strongly heterogeneous conductivity. Electron transport inside semiconductor grains is described by standard drift mechanisms, while transport across thin insulating intergranular layers is modeled via quantum tunneling. The resulting multiscale formulation accounts explicitly for the strong contrast between conductive grains and highly resistive grain boundary regions. Two modeling strategies are investigated. The first is a simplified homogeneous approximation, which assumes a uniform voltage drop across regularly structured grain layers. The second is a random grain-size model, in which the potential distribution is obtained by solving a nonlinear elliptic equation with field-dependent conductivity, coupled to a stochastic representation of the microstructure. The proposed models are validated against experimental I–V characteristics. The random grain-size model shows good agreement with experimental data, while the homogeneous approximation is accurate only for idealized periodic grain structures. The results demonstrate that coupling stochastic electron transport with nonlinear potential modeling provides an effective framework for describing varistor behavior in strongly disordered microstructures.
Cite: Sabelfeld K. , Abramkin D. , Kireeva A. , Zalyalov T.
Stochastic simulation of nonlinear electron transport in Ni/Al$$_2$$O$$_3$$ metal–dielectric varistors
Journal of Computational Electronics. 2026. V.25. N5. 188 :1-14. DOI: 10.1007/s10825-026-02639-9 WOS Scopus OpenAlex
Dates:
Submitted: Jun 19, 2026
Accepted: Aug 31, 2026
Published print: Sep 16, 2026
Published online: Sep 16, 2026
Identifiers:
≡ Web of science: WOS:001877193400001
≡ Scopus: 2-s2.0-105051071286
≡ OpenAlex: W7213432670
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