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AIP Advances ARTICLE pubs.aip.org/aip/adv
Stress modulation of hafnium-based ferroelectric
material orientation in 3D cylindrical capacitor
Cite as: AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610
Submitted: 25 November 2024 •Accepted: 20 January 2025 •
Published Online: 5 February 2025
Wenqi Li,1,2 Zhiliang Xia,3,a) Meiying Liu,3Yong Cheng,3Bao Zhang,1Yuancheng Yang,3
Lei Liu,3and Zongliang Huo1,3,a)
AFFILIATIONS
1Institute of Microelectronics of the Chinese Academy of Sciences, Beijing 100029, China
2University of Chinese Academy of Sciences, Beijing 100049, China
3Yangtze Memory Technologies Innovation Research Institute, Wuhan 30070, China
a)Authors to whom correspondence should be addressed: albert_xia@ymtc.com and huozongliang@ime.ac.cn
ABSTRACT
Hafnium-based ferroelectric materials have attracted a lot of attention, but the distributions of the materials need to be tuned for commer-
cialization, including phase distribution and polarization orientation distribution. The orientation of ferroelectric materials plays a significant
role in memory device performance; however, there have been no reliable methods to control this orientation until now. This paper investi-
gates the control of ferroelectric phase polarization orientation in 3D cylindrical capacitors. This optimization is made possible because the
3D cylindrical capacitor allows stress application in the tangential, axial, and radial directions, offering a wider range of adjustment options
than 2D planar structures. The study focuses on how stress distribution affects ferroelectric phase orientation in hafnium-based materials
when the diameters of cylindrical capacitors are varied. First, stress simulations are conducted to analyze the stress distribution in cylindrical
capacitors with different diameters. The results indicate that the hafnium oxide layer experiences increased radical stress as the capacitor
diameter decreases. Subsequently, capacitors with two different diameters are fabricated, significantly improving the polarization orienta-
tion in the thinner one. It is found that the capacitor diameter and the polarization orientation are strongly related through the correlation
analysis. Finally, we demonstrate the improvement in the polarization orientation of ferroelectric thin films by radical stress through first-
principles calculations. This study provides valuable insights into how stress distribution influences polarization orientation in hafnium-based
ferroelectric films and is crucial for advancing the use of ferroelectric materials in future technologies.
©2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0230610
INTRODUCTION
Since the discovery of ferroelectricity in doped HfO2ultra-
thin layers,1polycrystalline HfO2films doped with various ele-
ments (e.g., zirconium,2,3 aluminum,4yttrium,5etc.), as well as
undoped HfO2, have been shown to have ferroelectricity as well.6
Hafnium-based ferroelectric materials have attracted a lot of atten-
tion for their COMS compatibility and scalability. Devices based
on hafnium-based ferroelectric materials, such as FeRAMs, FeFETs,
and FTJs, have been investigated and extended to areas such as
in-memory computing.7–10 Ferroelectricity in HfO2-based materi-
als is believed to be contributed by the space group Pca21, which
is a polar orthorhombic phase (O-phase) that coexists in the
films with a tetragonal phase (T-phase) and monoclinic phases
(M-phase).11,12 The ferroelectric O-phase is a metastable state
formed through a complicated process involving modifications to
doping,13 thickness,14–17 stress,18–22 annealing,23,24 and other factors.
Stress plays a crucial role in the creation of ferroelectrics in this
process.
Hafnium-based ferroelectric films exhibit not only phase distri-
bution due to the metastable ferroelectric phase but also polarization
orientation distribution. The theoretically calculated polarization
intensity of hafnium-based ferroelectric materials is around 55
μC/cm2,25 while experimentally measured values are generally in the
range of 20–30 μC/cm2,26–28 and the difference is related to the dis-
tribution in the ferroelectric material. The residual polarization of
the capacitor is influenced by the polarization orientation of these
films, which is directly linked to the memory window in ferroelectric
AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610 15, 025109-1
© Author(s) 2025
AIP Advances ARTICLE pubs.aip.org/aip/adv
memory devices, such as FeRAMs and FeFETs. Controlling polariza-
tion orientation is essential for the commercialization of ferroelectric
memory devices.
Previous research has explored altering doping elements,29
substrate materials,30 and other factors to enhance polarization ori-
entation. Popovici et al. found that the TiO2seed layer favorably
improves the grain orientation inside HZO, resulting in a higher
Prand reduced wake-up.31 Zhao et al. used MFM capacitors with
flat amorphous TiN and ensured the c-axis of the O-phase aligned
well along the deposition direction.32 Lee et al. demonstrated that
textured grains in ultrathin HZO films with (112) point in the out-
of-plane direction and proved that the hydroxyl adsorption during
the deposition process reduces the surface energy of (112)-oriented
films.15,33 Gao et al. employed in situ AC electric bias during rapid
thermal annealing treatment and effectively controlled the O-PA
orientation toward the out-of-plane E direction.33 However, these
studies have largely focused on 2D planar structures, which may not
apply to 3D capacitors.
The issue of polarization orientation may take a new turn
when the viewpoint is expanded from a 2D structure to a 3D
one.34 The performances of FeRAM devices in 2D and 3D archi-
tectures have been compared.35 A cylindrical capacitor exhibits a
different stress distribution in the ferroelectric layer from a pla-
nar capacitor, manifesting as a larger out-of-plane stress, which is
the direction radial to the capacitor hole. As a crucial element in
hafnium-based ferroelectric materials, stress can potentially adjust
the orientation of ferroelectric materials. Figure 1 illustrates the
stress distribution in the 2D planar capacitor and 3D cylindrical
capacitor.
This study examines how the orientation in 3D cylindrical
capacitors is affected by stress distribution. The stresses on hafnium
oxide in capacitor holes of various sizes were examined by stress sim-
ulation first. Next, ferroelectric cylindrical capacitors with two diam-
eters were experimentally fabricated to examine the texture using
precession electron diffraction (PED). In addition, we examined
the relationship between the profiles and orientation. Finally, first-
principles calculations demonstrate the modulating effect of radical
tensile stresses on polarization orientation. This study is significant
for the potential use of ferroelectric material for the revealing of how
stress distribution affects the polarization orientation in hafnium
materials.
FIG. 1. Schematic diagram of stress distribution in (a) 2D planar capacitor and (b)
3D cylindrical capacitor.
SIMULATIONS
In a cylindrical capacitor, the electrode thickness, filling struc-
ture, diameter of the capacitor holes, and other factors can be used
to modify the stress in axial, tangential, and radial directions. In
this study, a stress simulation was used to assess the stresses on
hafnium oxide under various capacitor diameters, and the simula-
tion structure is shown in Fig. 2. The capacitor hole diameter was
set to six values, increasing from ato f, when we built the structure
in COMSOL. The TiN and HZO films were incorporated into the
structure in a zero-stress state at their respective deposition temper-
atures. As they have different deposition temperatures and different
thermal expansion coefficients, different degrees of thermal strains
will be generated when the ambient temperature changes. Because
of the boundary constraints between the films, thermal strain can-
not occur freely, resulting in thermal stress. It has been shown that
the formation of the ferroelectric phase of hafnium oxide is affected
by the tensile stresses, which will be generated during the cooling
part of the annealing process.36 Therefore, the stress condition of
the hafnium oxide layer upon cooling to room temperature at 300 K
is analyzed.
Figures 3(a) and 3(b) show the axial, tangential, and radial
stress distribution of diameters aand d. Since the hafnium oxide
layer is the primary focus of our work, the stress applied to it
was extracted as shown in Fig. 3(c) to see the trend of the stress
in three directions with the diameter changed. As the diameter
shrinks, the tangential stress reduces and the axial and radial stresses
increase, as shown in Fig. 3(c). The radial stresses are generated
directly by the strain between the two layers of the film; the smaller
the diameter of the hole, the greater the diameter change and the
greater the radial stress. While the tangential stress, according to
the basic principle of elastic mechanics, the larger the diameter, the
larger the tangential stress. When studying the in-plane and out-
of-plane stresses, the radial stress, which is perpendicular to the
surface and represents the out-of-plane stress of the film, exhibits
a strong trend to increase with decreasing diameter. There is a
chance to optimize the orientation of the ferroelectric material in
FIG. 2. The simulated cylindrical capacitor structure.
AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610 15, 025109-2
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FIG. 3. Stress distribution mapping in three directions: radial, tangential, and axial, for diameters (a) aand (b) d. (c) The trends in radial, tangential, and axial directions with
the diameter changed.
cylindrical capacitors by decreasing the diameter for the increasing
out-of-plane stress.
EXPERIMENTS
In the previous section, we have shown that the stress distribu-
tion changes as the diameter of the capacitor changes. To test the
relationship between the stress distribution and the polarization ori-
entation, we have prepared cylindrical capacitors of two diameters, a
and d. This work involves the progressive deposition of silicon oxide,
polycrystalline silicon, and silicon oxide stacks on a substrate wafer,
followed by the etching of capacitor holes with aand dvalue diame-
ters. By ALD, a bottom electrode of ∼10 nm TiN was first deposited.
Next, a thin layer of Al2O3was deposited by ALD to enhance the
interfacial contact between TiN and HZO.37 Subsequently, ∼10 nm
of HZO was deposited with a Hf:Zr ratio of 1:1, followed by an
∼10 nm TiN top electrode. Then capacitors are annealed at 550 ○C to
crystallize the HZO thin films.38–41 Figure 4 displays the plane-view
TEM image and the process flow.
RESULTS AND DISCUSSION
Orientation results
The precession electron diffraction (PED) technique, which can
obtain electron diffraction patterns in TEM, was used to analyze the
ferroelectric capacitors prepared above. The crystal phase and ori-
entation can be determined by analyzing the diffraction pattern by
PED. Figure 5(a) shows the phase distribution of a single capacitor
hole. More than a dozen holes were analyzed to determine the aver-
aged phase distribution of the aand dcapacitors, with the result
shown in Table I. It can be seen that the average proportion of the
O-phase is 64% and 43% in the two cases aand d, respectively, with
aslightly higher than d.
FIG. 4. (a) Process flow for the manufacture of the structure and (b) TEM image of
the structure.
Following the analysis of the physical phase, we further ana-
lyzed the data for the O-phase in the holes, focusing on the orien-
tation in the a/b/c-axis, especially the polarization axis (c-axis). As
previously discussed, the angle formed by the c-axis in the O-phase
and the capacitor’s radial direction is crucial because it represents
each grain’s polarization contribution to the ferroelectric capacitor.
The phase analysis software provides polar and antipolar plots in all
directions directly for samples with 2D planar structure, reflecting
the texture of the sample.15,42 However, for the cylindrical capacitor
to be analyzed in this paper, the orientation for the radial direction of
the capacitor is not directly given by the software, so we have carried
out further data processing based on the source data given by PED.
The source data for PED are provided in the form of pixel points,
each of which contains information such as the type of phase and
the Euler angle of the site.
Data processing mainly consists of determining the O-phase
a/b/c-axis orientation as well as the radial direction of the
AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610 15, 025109-3
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FIG. 5. The distribution map in aand d
capacitors of (a) O/T/M phase and (b)
polarization orientation.
TABLE I. The averaged distribution of O/T/M phase and polarization orientation.
CD O-phase (%) T-phase (%) M-phase (%) Orientation
a 64 34 2 0.51
d 43 51 6 0.42
capacitor and then obtaining the angle of the a/b/c-axis to the radial
direction at each pixel point, drawing the orientation distribution in
one capacitor. Figure 5(b) shows the orientation distribution of the
polarization of the c-axis with the radial direction of one capacitor.
The direction of the a/b/c-axis of each pixel is determined through
the Euler angle provided by the PED, and the radial vector of each
pixel is determined through image recognition.
To measure the orientation of the individual holes in the radial
direction, considering that the actual contribution of the grains to
the polarization intensity of the capacitor should ideally be the pro-
jection of the polarization in the radial direction of the capacitor,
we calculated the projection of the c-axis of all pixel points of one
capacitor in the radial direction and averaged them to measure the
polarization intensity that can be contributed. By calculating each
pixel’s projection along the c-axis in the radial direction and averag-
ing these projections, we obtained an estimate of the contribution
to the ferroelectric capacitor from such an orientation. The aver-
age values can be seen in Table I. This calculation is then extended
to the a/b-axes, where the orientation strength is measured by the
projected value of each axis relative to the radial direction.
The comparison shows that the c-axis orientation of the thin-
ner capacitor is significantly better than the diameter of the d
capacitor shown in Table I, which aligns with the stress simula-
tion results, speculating that it is related to the significant increase
in tensile stress in the radial direction. The effect of stress on the
texture of hafnium-based ferroelectric materials in 2D capacitors
has been studied previously, and the study using EBSD on the
TiN/HZO/TiN planar capacitor revealed that most grains were ori-
ented with the b-axis pointing out-of-plane.42 This texture may be
due to stress conditions during crystallization and phase transitions,
where the hafnium oxide layer aligns the longer axes in-plane to
compensate for tensile stresses. Since the b-axis is the shortest axis
in the Pca21cell, it is linked to the out-of-plane texture. In 3D
cylindrical capacitors, as indicated above, radial tensile stress
increases as the diameter decreases, which is favorable for polariza-
tion orientation.
Correlation analysis
It is found that the polarization orientation of the ferroelec-
tric phase is increased in capacitor holes with smaller diameters as
above. To further investigate the relationship between polarization
orientation and capacitor diameter, we examined the profile of each
dcapacitor hole and analyzed the relationship between capacitor
diameter and orientation. It is known that there is always a cer-
tain variation during the process, and the actual diameter of each
capacitor hole falls within a variation around diameter d. We cre-
ated a scatter plot in Fig. 6, and correlation coefficients can be seen
in images.
The direction of the c-axis exhibits a strong negative correla-
tion with the diameter, with a correlation coefficient of −0.904, as
shown in Fig. 6(a), indicating improved polarization orientation as
the diameter decreases. In contrast, the orientation of the O-phase’s
b-axis shows a positive correlation with the diameter, with a cor-
relation coefficient of 0.451, suggesting that the O-phase’s b-axis
tends to align an out-of-plane with a lager diameter when there is no
FIG. 6. The scatter plot of diameter and orientation of the (a) c-axis, (b) b-axis, and (c) a-axis in the O phase.
AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610 15, 025109-4
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FIG. 7. Energies of HZO cells with different orientations under in-plane tensile stresses. Oa/Ob/Ocmean the energy of a/b/c-axis points out-of-plane. (a) Oa–Ob, (b) Oc–Ob,
and (c) Oc–Oa.
significant out-of-plane tensile stress. In addition, there is almost no
correlation between the a-axis and the capacitor’s diameter, with a
correlation coefficient of −0.087.
The results of the correlation analysis between orientation and
capacitor diameter are largely in line with our expectations, with the
c-axis orientation in the radial direction increasing as the capacitor
diameter decreases, in contrast to the b-axis orientation decreas-
ing in the radial direction. It is speculated that this phenomenon is
related to the increase in radial tensile stress caused by the decrease
in capacitor diameter, and the radial stress has a modulating effect
on the polarization orientation of hafnium-based ferroelectric mate-
rials. First-principles calculations were performed to verify this
idea.
First-principles calculations
The research concerning energy change of O-phase HZO
supercells under the impact of stress is calculated by first-principle
calculations. To confirm that stress does affect the orientation
of the ferroelectric film in the 3D cylindrical capacitor, first-
principles calculations were conducted by density functional theory
(DFT) within the projector augmented waves (PAWs), as imple-
mented in the Vienna Ab initio Simulation Package (VASP).43–45
The Perdew–Burke–Ernzerhof (PBE) form of the generalized gra-
dient approximation (GGA)46 is utilized to describe the electron
exchange-correlation potential. The single-point calculations are
employed to acquire the energy values under different stresses with
a cut-off energy of 520 eV for the plane wave expansion and a 3 ×3
×3 k-point grid for Brillouin zone integrations. The criterion for the
energy convergence is 1.0 ×10−5eV/atom.
To compare the energy of the O-phase with different orienta-
tions, including a/b/c-axis point out-of-plane, we first consider the
case of only being subjected to in-plane tensile stress in a 2D planar
capacitor. The energies of the three cases are marked as Oa, Ob, and
Oc, and the results are displayed in Fig. 7. As can be seen, Obhas the
lowest energy, and Oa–Ob/Oc–Obenergy increases as the in-plane
FIG. 8. Energies of HZO cells with different orientations under out-of-plane and in-plane tensile stresses. (a) 1% in-plane strains, (b) 2% in-plane strains, and (c) 3% in-plane
strains.
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tensile stress increases, which suggests that the b-axis will be more
likely to point out-of-plane as the in-plane tensile stress increases.
This finding demonstrates that under the stress distribution of a 2D
planar capacitor, ferroelectric HZO films will be more likely to have
a texture with the b-axis pointing out-of-plane.
To further demonstrate that a 3D cylindrical capacitor struc-
ture with the introduction of tensile stress in the out-of-plane
direction has the potential to improve the orientation of the c-axis
pointing out-of-plane, we gradually increase the value of the radi-
cal tensile stress with the in-plane tensile stress fixed and compare
the change in Oa/Ob/Ocenergy. The energy of the HZO supercell
without strain is used as a benchmark, and the change in energy
at different strains is compared. The results are shown in Fig. 8.
We set the in-plane tensile strain at 1%, 2%, and 3%, and the out-
of-plane tensile strain increases from 0% to 4%. It is found that
when the out-of-plane tensile strain is small, it is still the smallest
value of Ob, indicating the b-axis points out-of-plane most stably.
As the out-of-plane tensile strain increases, the Ocvalue gradu-
ally becomes the smallest, which means that the c-axis will tend
to point out-of-plane once the out-of-plane tensile strain reaches a
certain level. The results prove that the tensile stress in the out-of-
plane direction helps to improve the polarization orientation of the
ferroelectric films.
CONCLUSION
This study examined the impact of stress distribution across
different capacitor diameters on the ferroelectric O-phase’s polar-
ization orientation in hafnium oxide materials. Stress simulations
were conducted to analyze the stress distribution, revealing that
out-of-plane stress significantly increases as the diameter decreases.
Experimentally, capacitor holes with two diameters were prepared,
confirming that the decrease in capacitor diameter improves polar-
ization orientation in the material. Further investigation revealed
a strong negative correlation between the c-axis orientation of the
O-phase and the capacitor diameter, while the orientation of its b-
axis showed a certain positive correlation. Through first-principles
calculations, we reveal the role of out-of-plane tensile stress in reg-
ulating the polarization direction of hafnium-based ferroelectric
materials. This paper demonstrates that increasing the out-of-plane
stress helps to improve the polarization orientation of hafnium-
based ferroelectric materials and that smaller capacitor diameters
are an effective means of increasing the out-of-plane stress in 3D
structures.
ACKNOWLEDGMENTS
This work was supported by the National Key Research
and Development Program of China, under Grant No.
2023YFB4402500.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
All authors contributed equally to this work.
Wenqi Li: Data curation (equal); Formal analysis (equal); Valida-
tion (equal); Writing – original draft (equal). Zhiliang Xia: Fund-
ing acquisition (equal); Methodology (equal); Resources (equal);
Supervision (equal). Meiying Liu: Data curation (equal); Formal
analysis (equal); Validation (equal); Writing – review & editing
(equal). Yong Cheng: Data curation (equal); Software (equal); Val-
idation (equal); Writing – review & editing (equal). Bao Zhang:
Funding acquisition (equal); Resources (equal); Supervision (equal).
Yuancheng Yang: Methodology (equal); Project administration
(equal); Supervision (equal); Writing – review & editing (equal). Lei
Liu: Methodology (equal); Project administration (equal); Super-
vision (equal); Writing – review & editing (equal). Zongliang
Huo: Funding acquisition (equal); Methodology (equal); Resources
(equal); Supervision (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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AIP Advances 15, 025109 (2025); doi: 10.1063/5.0230610 15, 025109-7
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