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Coulomb repulsion and Wigner glass of localized electrons and holes in hafnia at room temperature

Vladimir A. Gritsenko

Damir R. Islamov ^*, Mahmood M. Mahmoodian , Andrei A. Gismatulin , Timur M. Zalyalov , and Matvey V. Entin

Mehrdad M. Mahmoodian

Mikhail S. Lebedev

Rzhanov Institute of Semiconductor Physics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russian Federation and Novosibirsk State Technical University, Novosibirsk 630073, Russian Federation

Rzhanov Institute of Semiconductor Physics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russian Federation

Rzhanov Institute of Semiconductor Physics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russian Federation and Novosibirsk State University, Novosibirsk 630090, Russian Federation

Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russian Federation

^*Contact author: damir@isp.nsc.ru

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Phys. Rev. Materials 10, 115001 – Published 9 November, 2026

DOI: https://doi.org/10.1103/v31x-71nc

Abstract

Hafnium oxide ${HfO}_{2}$ , a high- $κ$ dielectric, replaced ${SiO}_{2}$ and now is a key dielectric in modern silicon devices. ${HfO}_{2}$ contains deep traps. The effect of electron and hole localization on traps in ${HfO}_{2}$ is studied for the use as a storage medium in modern charge trap flash memory devices (CTFM). In this study, we demonstrate that electrons and holes localized on traps in ${HfO}_{2}$ exhibit Coulomb repulsion. Due to Coulomb repulsion, the surface concentration of traps filled with electrons and holes is an order of magnitude lower than the total trap concentration. This effect significantly changes our understanding of the physics of CTFM programming processes. Analysis of the correlation distribution function of localized electrons indicates Wigner crystallization of electrons and holes localized in ${HfO}_{2}$ . Due to the disordered arrangement of traps, electrons and holes localized on traps in ${HfO}_{2}$ form a Wigner glass. In contrast to the Wigner crystal of free electrons, which is formed at helium temperatures, the Wigner glass of electrons and holes localized in ${HfO}_{2}$ , due to deep traps $W_{t} = 1.25 eV$ , is observed at room temperature.

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References (45)

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Coulomb repulsion and Wigner glass of localized electrons and holes in hafnia at room temperature

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