🔬 materials science

Thermally stimulated depolarization in hafnium oxide: experiment and numerical simulation

This paper combines experimental and numerical studies of thermally stimulated depolarization in hafnium oxide to demonstrate that the multiphonon ionization mechanism of isolated traps best explains the observed behavior, yielding similar thermal energies of approximately 1.3 eV for both electron and hole traps.

Original authors: Yu. N. Novikov, D. E. Temnov, E. A. Volgina, M. S. Lebedev, V. A. Gritsenko

Published 2026-09-15

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CC BY 4.0

Original authors: Yu. N. Novikov, D. E. Temnov, E. A. Volgina, M. S. Lebedev, V. A. Gritsenko

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the tiny circuits that power our modern world, from smartphones to artificial intelligence, lies a thin layer of material that acts as a gatekeeper. This material, hafnium oxide, is a ceramic-like substance used to control the flow of electricity in computer chips. Its job is to hold an electrical charge in place, much like a dam holds back water, allowing information to be stored and retrieved. However, for these devices to work reliably, scientists must understand exactly how electricity moves through this material and why it sometimes leaks away. The key to this mystery lies in "traps"—tiny imperfections or defects within the crystal structure of the oxide that catch passing electrons or holes (the absence of an electron) and hold them there. When these trapped charges are released, they create a current that can be measured, and understanding how they escape is crucial for building faster, more efficient memory devices.

A team of researchers in Russia set out to solve a specific puzzle regarding how these trapped charges escape from hafnium oxide when the material is heated. They used a technique called thermally stimulated depolarization, which involves charging the material, cooling it down, and then slowly warming it up while measuring the current that flows as the trapped charges are freed. The goal was to determine which physical mechanism drives this release. For decades, the scientific community has largely relied on a model known as the Frenkel effect, which suggests that an electric field helps pull a trapped charge over an energy barrier, similar to how a strong wind might help a ball roll over a hill. However, the researchers suspected this old model might not tell the whole story for hafnium oxide.

To test their hypothesis, the scientists created thin films of hafnium oxide on silicon wafers using a precise chemical process called atomic layer deposition. They then charged these films with either electrons or holes using a special plasma setup that avoids injecting extra particles directly into the material. As they heated the samples from room temperature up to 220 degrees Celsius, they recorded the flow of current. They then compared their experimental data against three different theoretical models. The first was the traditional Frenkel model, which they modified to include a process where charges tunnel through barriers with the help of heat. The second model described how a single isolated trap releases a charge by absorbing multiple vibrations from the surrounding atoms, a process known as multiphonon ionization. The third model considered what happens when traps are packed very closely together, allowing charges to hop from one trap to another through a combination of heat and tunneling.

The results were clear and decisive. When the researchers applied the traditional Frenkel model to their data, the mathematical curves did not match the real-world measurements unless they used a value for the frequency of atomic vibrations that was physically impossible, far too small to make sense. Similarly, the model for closely packed traps, which assumes charges jump between neighbors, predicted a current that rose and fell too slowly compared to what they observed in the lab. The only model that fit the experimental data perfectly was the one describing the release of charges from isolated traps through the absorption of multiple atomic vibrations. This mechanism, known as the multiphonon ionization of isolated traps, successfully predicted the shape and timing of the current peaks for both electrons and holes.

The study revealed that the energy required to free an electron from a trap is nearly identical to the energy needed to free a hole, both sitting at approximately 1.3 electronvolts. This finding suggests that the defects trapping these charges behave in a specific way: when a charge is captured, the surrounding atoms shift their positions to accommodate it, creating a stable state that requires a significant amount of thermal energy to break. The researchers also found that the energy needed to release a charge using light (optical energy) is about twice the energy needed to release it using heat (thermal energy). This specific ratio points to the fact that these traps are "polaronic," meaning the trapped charge and the distorted lattice of atoms around it move together as a single unit. By ruling out the older, more common theories and confirming the multiphonon mechanism, this work provides a more accurate map of how charge moves through hafnium oxide, offering essential insights for engineers designing the next generation of high-speed memory and artificial intelligence hardware.

Technical Summary: Thermally Stimulated Depolarization in Hafnium Oxide

Problem Statement
Hafnium oxide (HfO₂) is a critical material for modern semiconductor applications, serving as a gate dielectric in silicon devices, a storage medium in flash memory, and an active layer in memristors for artificial intelligence. A fundamental challenge in utilizing HfO₂ is understanding the mechanisms of charge transport and trap ionization within the dielectric. While the majority of existing interpretations rely on the Frenkel model (ionization of Coulomb charged traps in an electric field), alternative mechanisms such as multiphonon ionization have been proposed for other dielectrics. There remains uncertainty regarding the specific ionization mechanism in HfO₂, the contribution of electrons versus holes to conductivity, and the precise thermal energies of the associated traps. Resolving these mechanisms is essential for accurately modeling leakage currents in field-effect transistors and predicting information retention in memory devices.

Methodology
The study employs a combined experimental and theoretical approach to investigate thermally stimulated depolarization (TSD) in HfO₂.

Experimental Setup: Thin HfO₂ films (46 nm) were deposited on Si (100) substrates using Atomic Layer Deposition (ALD) with TDEAH and H₂O precursors. The films were characterized as polycrystalline monoclinic with carbon-free composition. TSD measurements were conducted using a silicon-dielectric-corona plasma system. This configuration allowed for the injection of electrons or holes from the silicon substrate into the dielectric without direct injection from the corona plasma. Samples were polarized at 20°C under a positive corona field and subsequently heated to 220°C at a rate of 9°C/min while recording depolarization currents.
Theoretical Modeling: The experimental TSD currents were analyzed by numerically solving transport equations coupled with the Poisson equation. Three distinct models for trap ionization probability were evaluated:
1. Frenkel Model: Including both thermal ionization over the Coulomb barrier and thermally assisted tunneling (TAT).
2. ME-L Model: Multiphonon ionization of isolated traps, applicable at low trap concentrations (Macram-Ebeid and Lannoo model).
3. N-G Model: Phonon-assisted tunneling between neighboring traps, applicable at high trap concentrations (Nasyrov-Gritsenko model).

Key Contributions and Results
The study systematically compared experimental TSD spectra against calculations derived from the three models:

Frenkel Model Analysis: When applied to the experimental data, the Frenkel model (with or without TAT) failed to reproduce the experimental peak shapes accurately. Achieving agreement required either an anomalously small frequency factor ( $\nu \approx 10^7$ s⁻¹) or unphysically high trap energies ( $\approx 1.9$ eV) that resulted in peak widths narrower than observed experimentally. The authors conclude that the Frenkel model is inapplicable for describing TSD spectra in HfO₂ under these conditions.
N-G Model Analysis: The N-G model, which assumes high trap concentrations and tunneling between adjacent traps, predicted TSD signals significantly broader than the experimental data. The low ionization probability calculated for this model, attributed to the large distance between traps at the tested concentrations, rendered it unsuitable for interpreting the HfO₂ spectra.
ME-L Model Success: The multiphonon ionization mechanism of isolated traps (ME-L model) provided the best agreement between theory and experiment. The calculated TSD spectra matched the experimental peak positions and widths using reasonable physical parameters.
- Trap Energies: The analysis yielded similar thermal energies for electron and hole traps: $W_{et} \approx 1.39$ eV and $W_{ht} \approx 1.29$ eV (averaging to $\approx 1.3$ eV).
- Optical/Thermal Ratio: The ratio of optical to thermal ionization energies was found to be approximately 2.0, consistent with the polaronic nature of the traps.

Significance and Claims
The paper claims that the mechanism governing trap ionization in HfO₂ is the multiphonon ionization of isolated traps, rather than the traditionally assumed Frenkel effect or high-concentration phonon-assisted tunneling.

Mechanism Identification: The study establishes that the ME-L model is the correct physical description for TSD in HfO₂, resolving the discrepancy between experimental data and previous theoretical interpretations based on the Frenkel model.
Trap Characterization: The work provides reliable values for the thermal ionization energies of both electron and hole traps in HfO₂ ( $\approx 1.3$ eV). These values are consistent with previous findings from luminescence spectroscopy, pulsed injection methods, and deep level transient spectroscopy (DLTS) cited in the literature.
Physical Nature of Defects: The derived ratio of optical to thermal energy supports the conclusion that the traps in HfO₂ possess a polaronic nature, implying significant lattice relaxation upon charge capture.
Implications: By identifying the correct ionization mechanism and trap parameters, the study provides a more reliable foundation for modeling leakage currents in modern field-effect transistors and predicting the storage time of information in flash memory devices utilizing HfO₂.

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