What Can DP Do too? | How Interstitial Doping Reduces the Coercive Field of Ferroelectric Hafnium Oxide

The research group led by Shi Liu from the Department of Physics, School of Science, Westlake University has made the latest progress in revealing the mechanism by which interstitial doping reduces the coercive field of ferroelectric hafnium oxide. On February 4, the research results were published in Physical Review Letters under the title "Origin of Interstitial Doping Induced Coercive Field Reduction in Ferroelectric Hafnia".

In this study, the research group led by Shi Liu comprehensively used first-principles calculations and deep potential-based molecular dynamics to reveal the relationship between interstitial doping and the coercive field of ferroelectric hafnium oxide (HfO₂). It was found that interstitial hafnium doping significantly reduces the energy difference between the polar orthorhombic O phase (space group: Pca2₁) and the tetragonal T phase, thereby reducing the polarization reversal energy barrier and the coercive field. Compared with the theoretical model proposed in previous studies, which suggested that doping-induced rhombohedral R phase reduces the coercive field, this study proposed that the low-doped O phase can better explain the experimental observations of interstitial-doped hafnium-based thin films. Large-scale molecular dynamics simulations based on deep potential further indicated that interstitial hafnium doping can induce the formation of mobile Pbcn-type domain walls, thus reducing the polarization reversal electric field to less than 1 MV/cm. In addition, first-principles calculations revealed a negative correlation between the polarization reversal energy barrier and the radius of the doped atom, and several potential interstitial doping atoms that can effectively reduce the coercive field were screened out.

Tianyuan Zhu, an assistant researcher at Westlake University, and Liyang Ma, a doctoral student, are the co-first authors of the paper. Shi Liu, a distinguished researcher at Westlake University, is the corresponding author.

Paper address: https://doi.org/10.1103/PhysRevLett.134.056802

Research Background

In recent years, ferroelectric HfO₂ has become an ideal carrier for a new generation of ferroelectric memory devices due to its high compatibility with semiconductor processes, nanoscale ferroelectricity, and mature preparation technology. However, the high coercive field (E_c) required for polarization reversal in hafnium-based ferroelectric thin films remains the main obstacle to their practical applications. Generally, the E_c value of polycrystalline hafnium-based thin films prepared by atomic layer deposition exceeds 1 MV/cm, while that of high-quality epitaxial thin films prepared by pulsed laser deposition is as high as 2 - 5 MV/cm. Achieving polarization reversal requires applying a high electric field close to the breakdown strength of the material, which greatly limits the durability of its electric field cycling. Reducing E_c without sacrificing ferroelectric performance is an urgent challenge in promoting the wide application of hafnium-based ferroelectric materials.

In 2023, the journal Science reported that a coercive field as low as 0.65 MV/cm was achieved in ferroelectric thin films of Hf(Zr)_1+xO₂ rich in hafnium/zirconium [Science 381, 558 (2023)]. This discovery brought new ideas for the optimization of the coercive field of hafnium-based ferroelectrics. Combined with first-principles calculations, the reduction of the coercive field was attributed to the interstitial doping of hafnium/zirconium in the polar rhombohedral R phase. However, assuming the existence of a polar R phase in the thin film leads to significant differences between theory and experiment. In particular, the strain-free R phase is actually non-polar, and a polar R phase requires an out-of-plane tensile strain of up to 7%, which is quite different from the XRD characterization results of experimental thin films.

Research Method

Figure 1. Influence of interstitial hafnium doping on the phase stability and polarization reversal of hafnium oxide. (a) Relative energies of the monoclinic M, orthorhombic O, tetragonal T, rhombohedral R, and cubic C phases at different doping concentrations. The inset shows the doping sites of interstitial Hf atoms in the hafnium oxide lattice. (b) Energy changes along the polarization reversal path of the O - phase at different doping concentrations. (c) Comparison of the out - of - plane polarization and its reversal energy barrier of the polar O - phase and R - phase.

To clarify these differences, the research group led by Shi Liu first analyzed the phase stability of HfO₂ under interstitial hafnium doping. Considering the monoclinic M, orthorhombic O, tetragonal T, rhombohedral R, and cubic C phases (Figure 1a), for undoped HfO₂, the thermodynamic stability of each crystal phase shows a negative correlation with its crystal symmetry: from the M phase to the C phase, the thermodynamic stability gradually decreases as the symmetry increases. As the doping concentration increases, the energies of each phase gradually approach. This indicates that the formation energy of interstitial hafnium is higher in the low-symmetry M and O phases, while it is lower in the high-symmetry C and R phases.

The difference in the formation energy of interstitial hafnium in the T and O phases significantly reduces the energy barrier for O-phase polarization reversal (usually with the T phase as an intermediate phase) (Figure 1b), thus promising to reduce the coercive field of HfO₂. Further comparison of the out-of-plane polarization and its reversal energy barrier of the polar O and R phases (Figure 1c) shows that compared with the R phase, the O phase already has a polarization reversal energy barrier comparable to that of the 7% strained and 8% doped R phase at a lower doping concentration (3 - 6%), and has a higher spontaneous polarization out of the plane, which is highly consistent with the experimental results.

Figure 2. Interstitial hafnium doping induces the formation of Pbcn - type domain walls to facilitate polarization reversal. (a) Polarization reversal electric fields of hafnium oxide under different distributions of interstitial doping. (b) Alternating arrangement of non - polar (NP) and polar (P) oxygen atoms in the O - phase unit cell. (c - f) Local displacement distributions of oxygen atoms when introducing two - dimensional distributed interstitial Hf: (c) without an external electric field; (d) applying an electric field of 3.1 MV/cm; (e) removing the electric field; (f) reapplying an electric field of 0.8 MV/cm. The left inset in (c) shows the Pbcn - type structure around interstitial Hf; the top inset in (e) shows the atomic structure of the mobile Pbcn - type domain wall.

Due to the limitation of computational cost, first-principles calculations based on density functional theory (DFT) can only focus on relatively small supercells. This naturally raises a question: How will the decrease in the energy difference between the T and O phases predicted by DFT present in larger supercells and at higher temperatures, which are more representative of the real situation of experimental samples?

To answer this question, the research group led by Shi Liu carried out large-scale finite-temperature molecular dynamics simulations (Figure 2). A supercell with a 0.5% interstitial doping concentration consisting of 20,772 atoms was studied, considering different distributions of doped atoms. The deep neural network-based potential (deep potential) can accurately reproduce the energy change of Hf_1+xO₂ along the reversal path. For undoped HfO₂, the reversal electric field (E_s) is 5.3 MV/cm. Introducing a uniformly distributed 0.5% interstitial doping reduces E_s to 4.4 MV/cm. The local enrichment of interstitial doping further reduces E_s: cluster-like and two-dimensional distributions reduce E_s to 2.8 MV/cm and 3.1 MV/cm, respectively. In addition, simple prepolarization treatment can induce mobile Pbcn-type domain walls, reducing E_s to an even lower value, approximately 0.8 MV/cm. The understanding of the interaction between interstitial doping and the domain wall dynamics in HfO₂ provides guidance for optimizing the coercive field of this silicon-compatible ferroelectric oxide.

Figure 3. Energy differences between the T - phase and O - phase under different types of doping. (a) Relationship between the energy difference and the radius of the impurity atom under interstitial doping. (b) Relationship between the energy difference and the radius of the impurity ion under substitutional doping.

Summary

The above results show that the energy difference between the T and O phases can be used as an effective descriptor for regulating E_c. In order to screen more types of interstitial doping to regulate the E_c of ferroelectric HfO₂, the research group led by Shi Liu further carried out DFT calculations covering a variety of doped atoms (Figure 3). The results show that there is a significant negative correlation between the energy difference of the T and O phases in interstitial doping and the radius of the doped atom: Interstitial doping with larger atomic radii (such as H_f, Zr, and Ti) tends to reduce the energy difference, thereby reducing E_c; while smaller doped atoms (such as Si, Ge, and Sn) tend to increase the energy difference, which may lead to a higher E_c. It is worth noting that the negative correlation between the energy difference and the size of the doped atom in interstitial doping is in sharp contrast to substitutional doping. In substitutional doping, the energy difference between the T and O phases shows a volcano-like dependence on the radius of the doped ion (mostly positive correlation). Only a few relatively small substitutional dopants (such as Si) can effectively reduce the energy difference. This difference further emphasizes the unique potential of interstitial doping in regulating the coercive field of ferroelectric hafnium oxide.

This research was funded by the Young Scientists Project of the Key Research and Development Program of the Ministry of Science and Technology, the International Cooperation and Exchange Project, the General Project of the National Natural Science Foundation of China, and the Key Project of the Natural Science Foundation of Zhejiang Province. It was also supported by the High-Performance Computing Center of Westlake University.