Ultrahigh Dielectric Permittivity of a Micron-Sized Hf0.5Zr0.5O2 Thin-Film Capacitor After Missing of a Mixed Tetragonal Phase
Corresponding Author: An Quan Jiang
Nano-Micro Letters,
Vol. 18 (2026), Article Number: 6
Abstract
Innovative use of HfO2-based high-dielectric-permittivity materials could enable their integration into few-nanometre-scale devices for storing substantial quantities of electrical charges, which have received widespread applications in high-storage-density dynamic random access memory and energy-efficient complementary metal–oxide–semiconductor devices. During bipolar high electric-field cycling in numbers close to dielectric breakdown, the dielectric permittivity suddenly increases by 30 times after oxygen-vacancy ordering and ferroelectric-to-nonferroelectric phase transition of near-edge plasma-treated Hf0.5Zr0.5O2 thin-film capacitors. Here we report a much higher dielectric permittivity of 1466 during downscaling of the capacitor into the diameter of 3.85 μm when the ferroelectricity suddenly disappears without high-field cycling. The stored charge density is as high as 183 μC cm−2 at an operating voltage/time of 1.2 V/50 ns at cycle numbers of more than 1012 without inducing dielectric breakdown. The study of synchrotron X-ray micro-diffraction patterns show missing of a mixed tetragonal phase. The image of electron energy loss spectroscopy shows the preferred oxygen-vacancy accumulation at the regions near top/bottom electrodes as well as grain boundaries. The ultrahigh dielectric-permittivity material enables high-density integration of extremely scaled logic and memory devices in the future.
Highlights:
1 Ferroelectric-to-nonferroelectric transition occurs in a micron-sized Hf0.5Zr0.5O2 thin-film capacitor with the generation of a giant dielectric permittivity.
2 Synchrotron X-ray micro-diffraction patterns show missing of a mixed tetragonal phase in the capacitor.
3 The stored charge density of the capacitor is as high as 183 μC cm-2 at an operating voltage/time of 1.2 V/50 ns at cycle numbers of more than 1012 without inducing dielectric breakdown.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
- W. Cao, H. Bu, M. Vinet, M. Cao, S. Takagi et al., The future transistors. Nature 620(7974), 501–515 (2023). https://doi.org/10.1038/s41586-023-06145-x
- S.K. Kim, M. Popovici, Future of dynamic random-access memory as main memory. MRS Bull. 43(5), 334–339 (2018). https://doi.org/10.1557/mrs.2018.95
- G. Ribes, J. Mitard, M. Denais, S. Bruyere, F. Monsieur et al., Review on high-k dielectrics reliability issues. IEEE Trans. Device Mater. Reliab. 5(1), 5–19 (2005). https://doi.org/10.1109/TDMR.2005.845236
- M. Hoffmann, F.P.G. Fengler, M. Herzig, T. Mittmann, B. Max et al., Unveiling the double-well energy landscape in a ferroelectric layer. Nature 565(7740), 464–467 (2019). https://doi.org/10.1038/s41586-018-0854-z
- S.S. Cheema, N. Shanker, L.-C. Wang, C.-H. Hsu, S.-L. Hsu et al., Ultrathin ferroic HfO2-ZrO2 superlattice gate stack for advanced transistors. Nature 604(7904), 65–71 (2022). https://doi.org/10.1038/s41586-022-04425-6
- K. Tomida, K. Kita, A. Toriumi, Dielectric constant enhancement due to Si incorporation into HfO2. Appl. Phys. Lett. 89(14), 142902 (2006). https://doi.org/10.1063/1.2355471
- Y. Yun, P. Buragohain, M. Li, Z. Ahmadi, Y. Zhang et al., Intrinsic ferroelectricity in Y-doped HfO2 thin films. Nat. Mater. 21(8), 903–909 (2022). https://doi.org/10.1038/s41563-022-01282-6
- J. Müller, U. Schröder, T.S. Böscke, I. Müller, U. Böttger et al., Ferroelectricity in yttrium-doped hafnium oxide. J. Appl. Phys. 110(11), 114113 (2011). https://doi.org/10.1063/1.3667205
- T.S. Böscke, J. Müller, D. Bräuhaus, U. Schröder, U. Böttger, Ferroelectricity in hafnium oxide thin films. Appl. Phys. Lett. 99(10), 102903 (2011). https://doi.org/10.1063/1.3634052
- P. Polakowski, J. Müller, Ferroelectricity in undoped hafnium oxide. Appl. Phys. Lett. 106(23), 232905 (2015). https://doi.org/10.1063/1.4922272
- D. Martin, E. Yurchuk, S. Müller, J. Müller, J. Paul et al., Downscaling ferroelectric field effect transistors by using ferroelectric Si-doped HfO2. Solid State Electron. 88, 65–68 (2013). https://doi.org/10.1016/j.sse.2013.04.013
- S.S. Cheema, D. Kwon, N. Shanker, R. dos Reis, S.-L. Hsu et al., Enhanced ferroelectricity in ultrathin films grown directly on silicon. Nature 580(7804), 478–482 (2020). https://doi.org/10.1038/s41586-020-2208-x
- Y. Watanabe, H. Ota, S. Migita, Y. Kamimuta, K. Iwamoto et al., Achievement of higher-k and high-Φ in phase controlled HfO2 film using post gate electrode deposition annealing. ECS Trans. 11(4), 35–45 (2007). https://doi.org/10.1149/1.2779546
- S.S. Fields, T. Cai, S.T. Jaszewski, A. Salanova, T. Mimura et al., Origin of ferroelectric phase stabilization via the clamping effect in ferroelectric hafnium zirconium oxide thin films. Adv. Electron. Mater. 8(12), 2200601 (2022). https://doi.org/10.1002/aelm.202200601
- J. Müller, T.S. Böscke, U. Schröder, S. Mueller, D. Bräuhaus et al., Ferroelectricity in simple binary ZrO2 and HfO2. Nano Lett. 12(8), 4318–4323 (2012). https://doi.org/10.1021/nl302049k
- Y.-H. Chen, C.-Y. Chen, C.-L. Cho, C.-H. Hsieh, Y.-C. Wu et al., Enhanced sub 20-nm FinFET performance by stacked gate dielectric with less oxygen vacancies featuring higher current drive capability and superior reliability. 2015 IEEE International Electron Devices Meeting (IEDM). December 7–9, 2015, Washington, DC, USA. IEEE, (2015), 21.3.1–21.3.4.
- H.J. Lee, M. Lee, K. Lee, J. Jo, H. Yang et al., Scale-free ferroelectricity induced by flat phonon bands in HfO2. Science 369(6509), 1343–1347 (2020). https://doi.org/10.1126/science.aba0067
- P. Nukala, M. Ahmadi, Y. Wei, S. de Graaf, E. Stylianidis et al., Reversible oxygen migration and phase transitions in Hafnia-based ferroelectric devices. Science 372(6542), 630–635 (2021). https://doi.org/10.1126/science.abf3789
- Y. Wei, P. Nukala, M. Salverda, S. Matzen, H.J. Zhao et al., A rhombohedral ferroelectric phase in epitaxially strained Hf0.5Zr0.5O2 thin films. Nat. Mater. 17(12), 1095–1100 (2018). https://doi.org/10.1038/s41563-018-0196-0
- M. Pešić, L. Larcher, Root causes for ferroelectricity in doped HfO2. in ferroelectricity in doped hafnium oxide: materials, properties and devices, U. Schroeder, C.S. Hwang, & H. Funakubo, eds. (Woodhead Publishing, Cambridge, 2019), pp. 399–411.
- T. Shiraishi, K. Katayama, T. Yokouchi, T. Shimizu, T. Oikawa et al., Impact of mechanical stress on ferroelectricity in (Hf0.5Zr0.5)O2 thin films. Appl. Phys. Lett. 108(26), 262904 (2016). https://doi.org/10.1063/1.4954942
- G. Walters, A. Shekhawat, S. Moghaddam, J.L. Jones, T. Nishida, Effect of in situ hydrogen plasma on the ferroelectricity of hafnium zirconium oxide films. Appl. Phys. Lett. 116(3), 032901 (2020). https://doi.org/10.1063/1.5135709
- K.-Y. Chen, P.-H. Chen, R.-W. Kao, Y.-X. Lin, Y.-H. Wu, Impact of plasma treatment on reliability performance for HfZrOx-based metal-ferroelectric-metal capacitors. IEEE Electron Device Lett. 39(1), 87–90 (2018). https://doi.org/10.1109/LED.2017.2771390
- S. Kang, W.-S. Jang, A.N. Morozovska, O. Kwon, Y. Jin et al., Highly enhanced ferroelectricity in HfO2-based ferroelectric thin film by light ion bombardment. Science 376(6594), 731–738 (2022). https://doi.org/10.1126/science.abk3195
- J. Hur, P. Wang, N. Tasneem, Z. Wang, A.I. Khan et al., Exploring Argon plasma effect on ferroelectric Hf0.5Zr0.5O2 thin film atomic layer deposition. J. Mater. Res. 36(5), 1206–1213 (2021). https://doi.org/10.1557/s43578-020-00074-5
- S.S. Cheema, N. Shanker, S.-L. Hsu, J. Schaadt, N.M. Ellis et al., Giant energy storage and power density negative capacitance superlattices. Nature 629(8013), 803–809 (2024). https://doi.org/10.1038/s41586-024-07365-5
- M.D. Glinchuk, A.N. Morozovska, A. Lukowiak, W. Stręk, M.V. Silibin et al., Possible electrochemical origin of ferroelectricity in HfO2 thin films. J. Alloys Compd. 830, 153628 (2020). https://doi.org/10.1016/j.jallcom.2019.153628
- W. Wei, X. Ma, J. Wu, F. Wang, X. Zhan et al., Spontaneous polarization enhancement in ferroelectric Hf0.5Zr0.5O2 using atomic oxygen defects engineering: an ab initio study. Appl. Phys. Lett. 115(9), 092905 (2019). https://doi.org/10.1063/1.5115293
- W.D. Zhang, Z.Z. Song, S.Q. Tang, J.C. Wei, Y. Cheng et al., Ultrahigh dielectric permittivity in Hf0.5Zr0.5O2 thin-film capacitors. Nat. Commun. 16(1), 2679 (2025). https://doi.org/10.1038/s41467-025-57963-8
- J. Kim, S. Saremi, M. Acharya, G. Velarde, E. Parsonnet et al., Ultrahigh capacitive energy density in ion-bombarded relaxor ferroelectric films. Science 369(6499), 81–84 (2020). https://doi.org/10.1126/science.abb0631
- A.Q. Jiang, X.B. Liu, Q. Zhang, Nanosecond-range imprint and retention characterized from polarization-voltage hysteresis loops in insulating or leaky ferroelectric thin films. Appl. Phys. Lett. 99(14), 142905 (2011). https://doi.org/10.1063/1.3647577
- W. Hamouda, A. Pancotti, C. Lubin, L. Tortech, C. Richter et al., Physical chemistry of the TiN/Hf0.5Zr0.5O2 interface. J. Appl. Phys. 127(6), 064105 (2020). https://doi.org/10.1063/1.5128502
- A.K. Jonscher, Dielectric relaxation in solids. J. Phys. D Appl. Phys. 32(14), R57–R70 (1999). https://doi.org/10.1088/0022-3727/32/14/201
- Y. Cheng, Z. Gao, K.H. Ye, H.W. Park, Y. Zheng et al., Reversible transition between the polar and antipolar phases and its implications for wake-up and fatigue in HfO2-based ferroelectric thin film. Nat. Commun. 13(1), 645 (2022). https://doi.org/10.1038/s41467-022-28236-5
- M. Stengel, D. Vanderbilt, N.A. Spaldin, Enhancement of ferroelectricity at metal-oxide interfaces. Nat. Mater. 8(5), 392–397 (2009). https://doi.org/10.1038/nmat2429
- M. Stengel, N.A. Spaldin, Origin of the dielectric dead layer in nanoscale capacitors. Nature 443(7112), 679–682 (2006). https://doi.org/10.1038/nature05148
- A.A. Sirenko, C. Bernhard, A. Golnik, A.M. Clark, J. Hao et al., Soft-mode hardening in SrTiO3 thin films. Nature 404(6776), 373–376 (2000). https://doi.org/10.1038/35006023
- C.S. Hwang, Thickness-dependent dielectric constants of (Ba, Sr)TiO3 thin films with Pt or conducting oxide electrodes. J. Appl. Phys. 92(1), 432–437 (2002). https://doi.org/10.1063/1.1483105
- L.J. Sinnamon, R.M. Bowman, J.M. Gregg, Investigation of dead-layer thickness in SrRuO3/Ba0.5Sr0.5TiO3/Au thin-film capacitors. Appl. Phys. Lett. 78(12), 1724–1726 (2001). https://doi.org/10.1063/1.1356731
- C.A. Mead, Anomalous capacitance of thin dielectric structures. Phys. Rev. Lett. 6(10), 545–546 (1961). https://doi.org/10.1103/physrevlett.6.545
- M.M. Saad, P. Baxter, R.M. Bowman, J.M. Gregg, F.D. Morrison et al., Intrinsic dielectric response in ferroelectric nano-capacitors. J. Phys. Condens. Matter 16(41), L451–L456 (2004). https://doi.org/10.1088/0953-8984/16/41/l04
- J. Junquera, P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422(6931), 506–509 (2003). https://doi.org/10.1038/nature01501
- E.D. Grimley, T. Schenk, X. Sang, M. Pešić, U. Schroeder et al., Structural changes underlying field-cycling phenomena in ferroelectric HfO2 thin films. Adv. Electron. Mater. 2(9), 1600173 (2016). https://doi.org/10.1002/aelm.201600173
- T. Mizoguchi, M. Saitoh, Y. Ikuhara, First-principles calculation of oxygen K-electron energy loss near edge structure of. J. Phys. Condens. Matter 21(10), 104212 (2009). https://doi.org/10.1088/0953-8984/21/10/104212
References
W. Cao, H. Bu, M. Vinet, M. Cao, S. Takagi et al., The future transistors. Nature 620(7974), 501–515 (2023). https://doi.org/10.1038/s41586-023-06145-x
S.K. Kim, M. Popovici, Future of dynamic random-access memory as main memory. MRS Bull. 43(5), 334–339 (2018). https://doi.org/10.1557/mrs.2018.95
G. Ribes, J. Mitard, M. Denais, S. Bruyere, F. Monsieur et al., Review on high-k dielectrics reliability issues. IEEE Trans. Device Mater. Reliab. 5(1), 5–19 (2005). https://doi.org/10.1109/TDMR.2005.845236
M. Hoffmann, F.P.G. Fengler, M. Herzig, T. Mittmann, B. Max et al., Unveiling the double-well energy landscape in a ferroelectric layer. Nature 565(7740), 464–467 (2019). https://doi.org/10.1038/s41586-018-0854-z
S.S. Cheema, N. Shanker, L.-C. Wang, C.-H. Hsu, S.-L. Hsu et al., Ultrathin ferroic HfO2-ZrO2 superlattice gate stack for advanced transistors. Nature 604(7904), 65–71 (2022). https://doi.org/10.1038/s41586-022-04425-6
K. Tomida, K. Kita, A. Toriumi, Dielectric constant enhancement due to Si incorporation into HfO2. Appl. Phys. Lett. 89(14), 142902 (2006). https://doi.org/10.1063/1.2355471
Y. Yun, P. Buragohain, M. Li, Z. Ahmadi, Y. Zhang et al., Intrinsic ferroelectricity in Y-doped HfO2 thin films. Nat. Mater. 21(8), 903–909 (2022). https://doi.org/10.1038/s41563-022-01282-6
J. Müller, U. Schröder, T.S. Böscke, I. Müller, U. Böttger et al., Ferroelectricity in yttrium-doped hafnium oxide. J. Appl. Phys. 110(11), 114113 (2011). https://doi.org/10.1063/1.3667205
T.S. Böscke, J. Müller, D. Bräuhaus, U. Schröder, U. Böttger, Ferroelectricity in hafnium oxide thin films. Appl. Phys. Lett. 99(10), 102903 (2011). https://doi.org/10.1063/1.3634052
P. Polakowski, J. Müller, Ferroelectricity in undoped hafnium oxide. Appl. Phys. Lett. 106(23), 232905 (2015). https://doi.org/10.1063/1.4922272
D. Martin, E. Yurchuk, S. Müller, J. Müller, J. Paul et al., Downscaling ferroelectric field effect transistors by using ferroelectric Si-doped HfO2. Solid State Electron. 88, 65–68 (2013). https://doi.org/10.1016/j.sse.2013.04.013
S.S. Cheema, D. Kwon, N. Shanker, R. dos Reis, S.-L. Hsu et al., Enhanced ferroelectricity in ultrathin films grown directly on silicon. Nature 580(7804), 478–482 (2020). https://doi.org/10.1038/s41586-020-2208-x
Y. Watanabe, H. Ota, S. Migita, Y. Kamimuta, K. Iwamoto et al., Achievement of higher-k and high-Φ in phase controlled HfO2 film using post gate electrode deposition annealing. ECS Trans. 11(4), 35–45 (2007). https://doi.org/10.1149/1.2779546
S.S. Fields, T. Cai, S.T. Jaszewski, A. Salanova, T. Mimura et al., Origin of ferroelectric phase stabilization via the clamping effect in ferroelectric hafnium zirconium oxide thin films. Adv. Electron. Mater. 8(12), 2200601 (2022). https://doi.org/10.1002/aelm.202200601
J. Müller, T.S. Böscke, U. Schröder, S. Mueller, D. Bräuhaus et al., Ferroelectricity in simple binary ZrO2 and HfO2. Nano Lett. 12(8), 4318–4323 (2012). https://doi.org/10.1021/nl302049k
Y.-H. Chen, C.-Y. Chen, C.-L. Cho, C.-H. Hsieh, Y.-C. Wu et al., Enhanced sub 20-nm FinFET performance by stacked gate dielectric with less oxygen vacancies featuring higher current drive capability and superior reliability. 2015 IEEE International Electron Devices Meeting (IEDM). December 7–9, 2015, Washington, DC, USA. IEEE, (2015), 21.3.1–21.3.4.
H.J. Lee, M. Lee, K. Lee, J. Jo, H. Yang et al., Scale-free ferroelectricity induced by flat phonon bands in HfO2. Science 369(6509), 1343–1347 (2020). https://doi.org/10.1126/science.aba0067
P. Nukala, M. Ahmadi, Y. Wei, S. de Graaf, E. Stylianidis et al., Reversible oxygen migration and phase transitions in Hafnia-based ferroelectric devices. Science 372(6542), 630–635 (2021). https://doi.org/10.1126/science.abf3789
Y. Wei, P. Nukala, M. Salverda, S. Matzen, H.J. Zhao et al., A rhombohedral ferroelectric phase in epitaxially strained Hf0.5Zr0.5O2 thin films. Nat. Mater. 17(12), 1095–1100 (2018). https://doi.org/10.1038/s41563-018-0196-0
M. Pešić, L. Larcher, Root causes for ferroelectricity in doped HfO2. in ferroelectricity in doped hafnium oxide: materials, properties and devices, U. Schroeder, C.S. Hwang, & H. Funakubo, eds. (Woodhead Publishing, Cambridge, 2019), pp. 399–411.
T. Shiraishi, K. Katayama, T. Yokouchi, T. Shimizu, T. Oikawa et al., Impact of mechanical stress on ferroelectricity in (Hf0.5Zr0.5)O2 thin films. Appl. Phys. Lett. 108(26), 262904 (2016). https://doi.org/10.1063/1.4954942
G. Walters, A. Shekhawat, S. Moghaddam, J.L. Jones, T. Nishida, Effect of in situ hydrogen plasma on the ferroelectricity of hafnium zirconium oxide films. Appl. Phys. Lett. 116(3), 032901 (2020). https://doi.org/10.1063/1.5135709
K.-Y. Chen, P.-H. Chen, R.-W. Kao, Y.-X. Lin, Y.-H. Wu, Impact of plasma treatment on reliability performance for HfZrOx-based metal-ferroelectric-metal capacitors. IEEE Electron Device Lett. 39(1), 87–90 (2018). https://doi.org/10.1109/LED.2017.2771390
S. Kang, W.-S. Jang, A.N. Morozovska, O. Kwon, Y. Jin et al., Highly enhanced ferroelectricity in HfO2-based ferroelectric thin film by light ion bombardment. Science 376(6594), 731–738 (2022). https://doi.org/10.1126/science.abk3195
J. Hur, P. Wang, N. Tasneem, Z. Wang, A.I. Khan et al., Exploring Argon plasma effect on ferroelectric Hf0.5Zr0.5O2 thin film atomic layer deposition. J. Mater. Res. 36(5), 1206–1213 (2021). https://doi.org/10.1557/s43578-020-00074-5
S.S. Cheema, N. Shanker, S.-L. Hsu, J. Schaadt, N.M. Ellis et al., Giant energy storage and power density negative capacitance superlattices. Nature 629(8013), 803–809 (2024). https://doi.org/10.1038/s41586-024-07365-5
M.D. Glinchuk, A.N. Morozovska, A. Lukowiak, W. Stręk, M.V. Silibin et al., Possible electrochemical origin of ferroelectricity in HfO2 thin films. J. Alloys Compd. 830, 153628 (2020). https://doi.org/10.1016/j.jallcom.2019.153628
W. Wei, X. Ma, J. Wu, F. Wang, X. Zhan et al., Spontaneous polarization enhancement in ferroelectric Hf0.5Zr0.5O2 using atomic oxygen defects engineering: an ab initio study. Appl. Phys. Lett. 115(9), 092905 (2019). https://doi.org/10.1063/1.5115293
W.D. Zhang, Z.Z. Song, S.Q. Tang, J.C. Wei, Y. Cheng et al., Ultrahigh dielectric permittivity in Hf0.5Zr0.5O2 thin-film capacitors. Nat. Commun. 16(1), 2679 (2025). https://doi.org/10.1038/s41467-025-57963-8
J. Kim, S. Saremi, M. Acharya, G. Velarde, E. Parsonnet et al., Ultrahigh capacitive energy density in ion-bombarded relaxor ferroelectric films. Science 369(6499), 81–84 (2020). https://doi.org/10.1126/science.abb0631
A.Q. Jiang, X.B. Liu, Q. Zhang, Nanosecond-range imprint and retention characterized from polarization-voltage hysteresis loops in insulating or leaky ferroelectric thin films. Appl. Phys. Lett. 99(14), 142905 (2011). https://doi.org/10.1063/1.3647577
W. Hamouda, A. Pancotti, C. Lubin, L. Tortech, C. Richter et al., Physical chemistry of the TiN/Hf0.5Zr0.5O2 interface. J. Appl. Phys. 127(6), 064105 (2020). https://doi.org/10.1063/1.5128502
A.K. Jonscher, Dielectric relaxation in solids. J. Phys. D Appl. Phys. 32(14), R57–R70 (1999). https://doi.org/10.1088/0022-3727/32/14/201
Y. Cheng, Z. Gao, K.H. Ye, H.W. Park, Y. Zheng et al., Reversible transition between the polar and antipolar phases and its implications for wake-up and fatigue in HfO2-based ferroelectric thin film. Nat. Commun. 13(1), 645 (2022). https://doi.org/10.1038/s41467-022-28236-5
M. Stengel, D. Vanderbilt, N.A. Spaldin, Enhancement of ferroelectricity at metal-oxide interfaces. Nat. Mater. 8(5), 392–397 (2009). https://doi.org/10.1038/nmat2429
M. Stengel, N.A. Spaldin, Origin of the dielectric dead layer in nanoscale capacitors. Nature 443(7112), 679–682 (2006). https://doi.org/10.1038/nature05148
A.A. Sirenko, C. Bernhard, A. Golnik, A.M. Clark, J. Hao et al., Soft-mode hardening in SrTiO3 thin films. Nature 404(6776), 373–376 (2000). https://doi.org/10.1038/35006023
C.S. Hwang, Thickness-dependent dielectric constants of (Ba, Sr)TiO3 thin films with Pt or conducting oxide electrodes. J. Appl. Phys. 92(1), 432–437 (2002). https://doi.org/10.1063/1.1483105
L.J. Sinnamon, R.M. Bowman, J.M. Gregg, Investigation of dead-layer thickness in SrRuO3/Ba0.5Sr0.5TiO3/Au thin-film capacitors. Appl. Phys. Lett. 78(12), 1724–1726 (2001). https://doi.org/10.1063/1.1356731
C.A. Mead, Anomalous capacitance of thin dielectric structures. Phys. Rev. Lett. 6(10), 545–546 (1961). https://doi.org/10.1103/physrevlett.6.545
M.M. Saad, P. Baxter, R.M. Bowman, J.M. Gregg, F.D. Morrison et al., Intrinsic dielectric response in ferroelectric nano-capacitors. J. Phys. Condens. Matter 16(41), L451–L456 (2004). https://doi.org/10.1088/0953-8984/16/41/l04
J. Junquera, P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422(6931), 506–509 (2003). https://doi.org/10.1038/nature01501
E.D. Grimley, T. Schenk, X. Sang, M. Pešić, U. Schroeder et al., Structural changes underlying field-cycling phenomena in ferroelectric HfO2 thin films. Adv. Electron. Mater. 2(9), 1600173 (2016). https://doi.org/10.1002/aelm.201600173
T. Mizoguchi, M. Saitoh, Y. Ikuhara, First-principles calculation of oxygen K-electron energy loss near edge structure of. J. Phys. Condens. Matter 21(10), 104212 (2009). https://doi.org/10.1088/0953-8984/21/10/104212