Wigner crystallization due to electrons localized at deep traps in two-dimensional amorphous dielectric

Abstract

We calculated the spatial distribution of electrons localized at deep neutral traps in some amorphous dielectric films based on some fundamental physics in order to explain the phenomena such as space ordering of electrons. We showed that when the surface density of traps ͑N s ͒ is much larger than that of the trapped electrons ͑n s ͒, e.g., n s / N s Յ 0.001, Wigner crystallization occurs due to the Coulomb repulsion of trapped electrons and a two-dimensional quasiperiodic hexagonal lattice or Wigner glass can be formed.

Charge transport in amorphous Hf0.5Zr0.5O2

“…However, it should be noted that the number of filled bulk traps n b h Շ 3 Â 10 18 cm À3 is much lower than total trap density of N ¼ 3 Â 10 19 cm À3 . The possible explanation of this difference is the Coulomb repulsion of the charged particles with forming of Wignerglass-like structures 15 in the bulk of Hf 0.5 Zr 0.5 O 2 .…”

Charge Transport Mechanism of Stress Induced Leakage Current in Thermal Silicon Oxide

“…Here J is the total current density, s is the SILC area of the sample. Recently it was show that in spite of high trap density, trapped charge density in dielectric does not exceed 5×10 18 cm -3 due to strong electron-electron (Coulomb) interaction, while the charge carriers form Wigner glass hexagonal lattice (12)(13)(14).…”

(Invited) The Influence of Defects on the Electronic Properties of Hafnia

“…Despite the fact that obtained trap density is ~10 19 -10 20 cm -3 , C-V measurements shows that trapped charge density is ~5×10 18 cm -3 (9), (11). This phenomenon can be explained by the Coulomb repulsion of charge carriers, leading to the Wigner crystallization of trapped electrons to form a hexagonal glassy structure (14) as shown in Figure 9. These phenomena can explain the difference of difference of found values of effective mass: simulations [2] assumes that the electric field in the dielectric films is uniform, while the trapped charge deforms the electric field according to Poison equations.…”

“…However, the fitting parameters, obtained by experimental data analysis in terms of PF model, are far from realistic values. E.g., either the frequency factor in 5-7 order lower than expected, or trap density in [13][14][15][16] ECS Transactions, 69 (5) 197-203 (2015) orders lower than values obtained from capacitance-voltage (C-V) measurements. In Ref.…”