Fig. 1. (Color online) Ferroelectric behaviors of HfO₂ systems with different dopants. (a)P–E andC–E loop of Zr:HfO₂ with increasing concentration.P_r is enhanced until the atom ratio of Hf : Zr reaches 1 : 1. For higher doping concentration antiferroelectricity emerges. (b) Polarization and coercive field for La:HfO₂ with increasing La doping. A larger doping window of 12 mol% is observed for La compared to Si, Al and Gd. (a) is reprinted with permission from Ref. [20], copyright 2012 American Chemical Society. (b) is reprinted with permission from Ref. [53], copyright 2018 American Chemical Society.

Fig. 2. (Color online) 2P_r and o/t/m-phase fraction of (a) 5.5, (b) 10, (c) 17, (d) 25 nm HZO films annealing with different temperature.P_r is enhanced in the 400–600 °C section and the ratio of m-phase significantly increases with higher annealing temperature. Reprinted with permission from Ref. [37], copyright 2013 AIP Publishing LLC.

Fig. 3. (a)P–V loops and (b) GIXRD patterns for Y:HfO₂ undergoing 600 °C PMA and PDA process with different doping concentration. Y:HfO₂ adopting PDA still shows stableP_r and considerable o-phase fraction with doping concentration from 3.6 mol% to 5.2 mol%. But Y:HfO₂ after PMA shows a largerP_r at the same Y concentration level, which reaches 24μC/cm² at 5.2 mol%. Reprinted with permission from Ref. [58], copyright 2011 American Institute of Physics.

Fig. 4. (Color online) (a) The experimental and (b) computed equilibrium phase diagrams ofHfO2. (c) The regimes in which the free energy difference betweenPca21 andPmn21 phases, and the equilibrium phases are small (i.e.,kBT/5). (d–h) The schematic structures of m, t, oI, oII, oIII phases ofHfO2 respectively. (a) is reprinted with permission from Ref. [124], copyright 2023 The American Ceramic Society. (b) and (c) are reprinted with permission from Ref. [14], copyright 2014 American Physical Society.

Fig. 5. (Color online) Thin film energies, computed via the energy model considering the interfacial energies and bulk energies, as a function of film thickness forIr/HfO2/Ir stacks. The bulk energy of m phase is set as the zero point of bulk energies. Reprinted with permission from Ref. [131], copyright 2019 Royal Society of Chemistry.

Fig. 6. (Color online) The computed phase diagram ofHfO2 under the influence of electric field and in-plane stress. The red, yellow, and green colors respectively mark the regions where the m, the oI, and the oIII phase are the equilibrium state. Reprinted with permission from Ref. [132], copyright 2017 American Chemical Society.

Fig. 7. (Color online) Formation energy of various dopants. The dopant above the red line tends to form a substitutional defect, while the dopant below the red line tends to form an interstitial defect. The red line should be located atEformrel=0, but Falkowskiet al. set it to 8.5 eV to compensate DFT (density functional theory) error and match experimental findings. Reprinted with permission from Ref. [147], copyright 2017 American Chemical Society.

Fig. 8. (Color online) (a, b) Oxygen-deficient polar orthorhombic phase with different polarization orientation. (c) Total energy of the o (oI), f (oIII) and t phase relative to the m phase at different vacancy concentrations. (d) Polarization and switching barrier of the f (oIII) phase at different vacancy concentrations. Reprinted with permission from Ref. [105], copyright 2019 Elsevier B.V.

Fig. 9. (Color online) Oxygen vacancy induced polarization and the ferroelectric switching process. Reprinted with permission from Ref. [36], copyright 2018 IEEE.

Fig. 10. (Color online) Phase diagram ofHfO1.75. Reprinted with permission from Ref. [17], copyright 2021 American Physical Society.

Fig. 11. (Color online) Transition barrier of M–O transition (black curve, corresponds to NEB image 10–20), M1 phase switching (black curve, corresponds to NEB image 0–10) and O phase switching (red curve). Blue curve is the M–O transition in stoichiometricHfO2. Reprinted with permission from Ref. [17], copyright 2021 American Physical Society.

Fig. 12. (Color online) (a) HAADF-STEM of a pristine Gd:HfO₂ grain with O and M regions separated by boundaries indicated by white arrows. (c) Magnified view of the O1/O2 boundary from (a), with (d). (b, e) Magnified regions from (a) where planes are indicated with lines and the polar direction by arrows. (f) Experiment and simulated PACBED patterns corresponding to O1 and O2 regions. Reprinted with permission from Ref. [26], copyright 2018 John Wiley & Sons, Inc.

Fig. 13. (Color online) The direct observation of oxygen atoms of single orthorhombic (O-) phase grain in TiN/Hf_0.5Zr_0.5O₂ (HZO, 15 nm)/TiN device. HAADF- and ABF-STEM images of single O-phase grain (a, b) in pristine, (d, e) after wake-up process, and (f–h) after fatigue process. (c) The atomic models of thePbc2₁ andPbca phases along [010] direction. Reprinted with permission from REF. [177], copyright 2022 Springer Nature Limited.

Fig. 14. (Color online) (a) Sawyer-Tower circuit. (b) A circuit for transientI–V measurement. (c) A typicalP–V loop of ferroelectric capacitor. (d) A typical transient response of ferroelectric capacitor under triangle wave.

Fig. 15. (Color online) (a) TypicalI–V–t graph of PUND test: the applied voltage waveform (black line) and the corresponding transient current response (red line). (b) TheP–V loop of a HZO ferroelectric capacitor obtained from PUND measurement.

Fig. 16. P–E andC–E curves of (a, b) ferroelectrics and (c, d) anti-ferroelectrics

Fig. 17. (a) First order reversal curve (FORC) test waveform, (b) FORCI–V plot, (c) FORCP–V loop, and (d) the extracted Preisach density. Reprinted with permission from Ref. [198], copyright 2015 American Chemical Society.

Fig. 18. (Color online) 4-cap retention test. Reprinted with permission from Ref. [204], copyright 2013 IEEE.

Fig. 19. (Color online) Minor loops are simulated by a linear scaling from the saturated polarization-voltage hysteresis loop. ↑/↓ indicates forward/reverse branch respectively. The switching dynamics are captured using a RC delay. Reprinted with permission from Ref. [221], copyright 2018 IEEE.

Fig. 20. (Color online) (a)P–E characteristics in the FE-HfO₂-based MFIM structure with ferroelectric thickness of 30 nm and dielectric thickness of 5 nm. (b) Voltages, (c) electric fields, and (d) polarization charges as a function of time operated by triangular voltage waveform at frequency of 1 MHz. (e) Polarization domain patterns during the polarization switching corresponding to the stages label in (d). Reprinted with permission from Ref. [247], copyright 2021 Science China Press.

Fig. 21. (Color online) Simulated wake-up of the device: (a) vacancy diffusion and (b) corresponding electric field evolution within the device with the field cycling of the FeCap in three different points in time at 4 MV/cm external applied field. (c) ResultingI–V andP–V characteristics obtained by removing the charges from the interface and changing the k-value of the grains undergoing the phase transformation. Reprinted with permission from Ref. [104], copyright 2016 John Wiley & Sons, Inc.

Fig. 22. (Color online) (a) Simulated evolution of remanent polarization during the electric cycles. (b) Simulated V_O distribution at different device states corresponding to the points in (a). Reprinted with permission from Ref. [36], copyright 2018 IEEE.

Fig. 23. (Color online) Whether percolation exists (a) or not (b) impacts theV_th states. (c) Summary of percolation in FeFET. Reprinted with permission from Ref. [265], copyright 2021 IEEE.

Fig. 24. (Color online) (a) 3D Al:HfO₂ trench capacitor with trench number up to 10⁵ and aspect ratio of 13 : 1. MeasuredP_r of 12 nm Al:HfO₂ with 100k trenches is 150μC/cm². (b) 1T1C FeRAM using 1X nm node DRAM technology. At lower pulse amplitude (0.6 V) the operation of FeRAM with 5 nm HZO is possible with 2P_r of 5μC/cm². (a) is reprinted with permission from Ref. [293], copyright 2014 IEEE. (b) is reprinted with permission from Ref. [294], copyright 2021 IEEE.

Fig. 25. (Color online) (a) Band diagram of metal/FE-HfO₂/SiO₂/Si FTJs, where the total tunneling current consists of tunneling current from the CBE (J_CBE), VBE (J_VBE) and VBH (J_VBH). (b) and (c) Comparison of the calculated and measured read current of FTJ based on MFIS(n+) and MFIS(p+). (d) and (e) Corresponding contributions ofJ_CBE,J_VBE and J_VBH to the total current. Reprinted with permission from Ref. [282], copyright 2020 IEEE.

Fig. 26. (Color online) Band diagrams of (a–d) n-type and (e–h) p-type MFIS-FTJ with various metal work functionΦ_M and remnant polarizationP_r at read voltage of |V_read| = 0.2 V. According to the overlap between metal Fermi levelE_fm and surface energy level of minority band in the semiconductor (E_vs in n-type device andE_cs in p-type device), the carrier transport can be respectively classified in to different conduction modes (I-IV). They are differentiated from the tunneling transmission of minority carriers, as represented by the shadow region of (d) and (h). Reprinted with permission from Ref. [283], copyright 2021 IEEE.

Fig. 27. (Color online) The storage class memory among the memory pyramid hierarchy. 1T1C FeRAM, 1T FeFET and 3D FeFET are located at M-SCM and S-SCM separately.

Fig. 28. (Color online) Ferroelectric based deep learning accelerator. (a) The partial polarization switching behavior in FeFET. (b) Symmetric analog weight modulation schemes. (c) VMM engines in analog and digital modes. (d) The macro circuits for the deep learning accelerator. (a) and (b) are reprinted with permission from Ref. [339], copyright 2017 IEEE. (c) and (d) are reprinted with permission from Ref. [340].

Fig. 29. (Color online) Logic gates based on the ferroelectric-capacitor. (a) Logic operation principle of single devices. (b) Circuit diagram of complementary ferroelectric-capacitor logic gate. (c) Measured results of complementary ferroelectric-capacitor logic gate. (a) is reprinted with permission from Ref. [354], copyright 2007 American Institute of Physics. (b) and (c) are reprinted with permission from Ref. [355], copyright 2004 IEEE.

Fig. 30. (Color online) Logic gates-based FeFET. (a) Logic operation principle based on single FeFET devices. (b) Circuit diagram of the FeFET based logic gate and the measured results of NOR logic operation. (c) Circuit diagram of XOR and XNOR gates. (d) The full adder based 2T-FeFET array. (a) and (b) are reprinted with permission from Ref. [356], copyright 2017 IEEE. (d) is reprinted with permission from Ref. [251].

Fig. 31. (Color online) FeFET based TCAM. (a) The architecture of a TCAM array. (b) The multi-bit FeFET CAM. (b) is reprinted with permission from Ref. [364], copyright 2020 IEEE.

Table 0. Selected formation energy of charged oxygen vacancies in m phaseHfO2 andZrO2 when Fermi level is at VBM. “M” stands for metal species (Hf orZr). The system is under extreme reducing condition whenμM=μM0, and is under extreme oxidation conditions whenμO=μO0. There are two types of oxygen vacancies in m phaseHfO2: threefold-coordinated vacancy and fourfold-coordinated vacancy. The lowest vacancy energy is listed. Data comes from Ref. [158].

Table 0. Comparison of HAADF- and ABF-STEM techniques^[167-169].

Table 0. Impact of substitutional dopant on the phase stability ofHfO2. “S” stands for “stabilization”, “D” stands for “destabilization”, and “–” means no data available. “Stabilization” means the relative energy between target phase and m phase lowers when dopant concentration increases. The dopant concentration falls in the range of 0%–6.25%.

Table 0. The basic functions of CTEM^[167,168].

Table 0. Ferroelectric HfO₂ with different fabrication conditions.