This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61804003, 61674008) and in part by China Postdoctoral Science Foundation (Grant Nos. 2019T120017, 2018M630034).
[1] Hoffman J, Pan X, Reiner J W. Ferroelectric Field Effect Transistors for Memory Applications. Adv Mater, 2010, 22: 2957-2961 CrossRef Google Scholar
[2] Salahuddin S, Datta S. Use of Negative Capacitance to Provide Voltage Amplification for Low Power Nanoscale Devices. Nano Lett, 2008, 8: 405-410 CrossRef ADS Google Scholar
[3] Yang H, Xiao M, Cui Y. Nonvolatile memristor based on heterostructure of 2D room-temperature ferroelectric α-In2Se3 and WSe2. Sci China Inf Sci, 2019, 62: 220404 CrossRef Google Scholar
[4] B?scke T S, Müller J, Br?uhaus D. Ferroelectricity in hafnium oxide thin films. Appl Phys Lett, 2011, 99: 102903 CrossRef ADS Google Scholar
[5] Wang L F, Luo Y, Wang J S. Temperature-dependent evolution of surface charge screening and polarization at ferroelectric surfaces. Sci China-Phys Mech Astron, 2019, 62: 987721 CrossRef ADS Google Scholar
[6] Zhang H, Long W J, Chen Y Q. Enhanced electrical properties in bilayered ferroelectric thin films. Sci China-Phys Mech Astron, 2013, 56: 551-555 CrossRef ADS Google Scholar
[7] Khan A I, Chatterjee K, Duarte J P. Negative Capacitance in Short-Channel FinFETs Externally Connected to an Epitaxial Ferroelectric Capacitor. IEEE Electron Device Lett, 2016, 37: 111-114 CrossRef ADS Google Scholar
[8] Zhou J R, Han G Q, Li Q L, et al. Ferroelectric HfZrO$_x$ Ge and GeSn PMOSFETs with Sub-60 mV/decade subthreshold swing, negligible hysteresis, and improved I$_{\rm~~DS}$. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), San Francisco, 2016. 310--313. Google Scholar
[9] Wang H, Huang Q, Yang M. Deep insight into the voltage amplification effect from ferroelectric negative capacitance. Sci China Inf Sci, 2019, 62: 089401 CrossRef Google Scholar
[10] Zhou J, Han G, Xu N. Incomplete Dipoles Flipping Produced Near Hysteresis-Free Negative Capacitance Transistors. IEEE Electron Device Lett, 2019, 40: 329-332 CrossRef ADS Google Scholar
[11] Zhou J, Han G, Li J. Negative Differential Resistance in Negative Capacitance FETs. IEEE Electron Device Lett, 2018, 39: 622-625 CrossRef ADS Google Scholar
[12] Zhou J, Han G, Li J. Comparative Study of Negative Capacitance Ge pFETs With HfZrOx Partially and Fully Covering Gate Region. IEEE Trans Electron Devices, 2017, 64: 4838-4843 CrossRef ADS Google Scholar
[13] Hoffmann M, Pe?i? M, Slesazeck S. On the stabilization of ferroelectric negative capacitance in nanoscale devices. Nanoscale, 2018, 10: 10891-10899 CrossRef Google Scholar
[14] Jin C J, Jang K, Saraya T, et al. Experimental study on the role of polarization switching in subthreshold characteristics of HfO$_2$-based ferroelectric and anti-ferroelectric FET. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), San Francisco, 2018. 723--726. Google Scholar
[15] Kalinin S V, Morozovska A N, Chen L Q. Local polarization dynamics in ferroelectric materials. Rep Prog Phys, 2010, 73: 056502 CrossRef ADS Google Scholar
[16] Zubko P, Stucki N, Lichtensteiger C. Phys Rev Lett, 2010, 104: 187601 CrossRef ADS Google Scholar
[17] You W X, Su P. Intrinsic Difference Between 2-D Negative-Capacitance FETs With Semiconductor-on-Insulator and Double-Gate Structures. IEEE Trans Electron Devices, 2018, 65: 4196-4201 CrossRef ADS Google Scholar
[18] Rollo T, Wang H, Han G, et al. A simulation based study of NC-FETs design: off-state versus on-state perspective. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), San Francisco, 2018. 213--216. Google Scholar
[19] Saha A K, Sharma P, Dabo I, et al. Ferroelectric transistor model based on self-consistent solution of 2D Poisson's, non-equilibrium Green's function and multi-domain Landau Khalatnikov equations. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), San Francisco, 2017. 326--329. Google Scholar
[20] Xiao Y G, Tang M H, Li J C. Temperature effect on electrical characteristics of negative capacitance ferroelectric field-effect transistors. Appl Phys Lett, 2012, 100: 083508 CrossRef ADS Google Scholar
[21] Ota H, Ikegami T, Hattori J, et al. Fully coupled 3-D device simulation of negative capacitance FinFETs for sub 10 nm integration. In: Proceedings of IEEE International Electron Devices Meeting (IEDM), San Francisco, 2016. 318--321. Google Scholar
[22] Mehta R R, Silverman B D, Jacobs J T. Depolarization fields in thin ferroelectric films. J Appl Phys, 1973, 44: 3379-3385 CrossRef ADS Google Scholar
[23] Stephanovich V A, Luk'yanchuk I A, Karkut M G. Domain-Enhanced Interlayer Coupling in Ferroelectric/Paraelectric Superlattices. Phys Rev Lett, 2005, 94: 047601 CrossRef ADS arXiv Google Scholar
[24] Zhou G Z, Wang Y X, Liu C. On ferroelectric domain polarization switching mechanism subject to an external electric field by simulations with the phase-field method. Sci China Technol Sci, 2013, 56: 1129-1138 CrossRef ADS Google Scholar
[25] Park H W, Roh J, Lee Y B. Modeling of Negative Capacitance in Ferroelectric Thin Films. Adv Mater, 2019, 8: 1805266 CrossRef Google Scholar
[26] Woo C H, Zheng Y. Depolarization in modeling nano-scale ferroelectrics using the Landau free energy functional. Appl Phys A, 2008, 91: 59-63 CrossRef ADS Google Scholar
[27] Devonshire A F. XCVI. Theory of barium titanate. London Edinburgh Dublin Philos Mag J Sci, 1949, 40: 1040-1063 CrossRef Google Scholar
[28] Chang P, Zhang Y, Du G. Experiment and modeling of dynamical hysteresis in thin film ferroelectrics. Jpn J Appl Phys, 2020, 59: SGGA07 CrossRef ADS Google Scholar
[29] Batra I P, Wurfel P, Silverman B D. Phase Transition, Stability, and Depolarization Field in Ferroelectric Thin Films. Phys Rev B, 1973, 8: 3257-3265 CrossRef ADS Google Scholar
[30] Cano A, Jiménez D. Multidomain ferroelectricity as a limiting factor for voltage amplification in ferroelectric field-effect transistors. Appl Phys Lett, 2010, 97: 133509 CrossRef ADS arXiv Google Scholar
Figure 1
(Color online) (a) MFM and (b) MFIM structures, where top electrode is biased by $V_{\rm~App}\sin(2\pi~f\cdot~t)$, and bottom electrode is grounded. (c) Measured and simulated $P$-$E$ characteristics of MFM capacitor with 10 nm HZO film, showing the model calibration. Notice that measured slow switching of FE can be obtained by considering distribution of FE parameters.
Figure 2
(Color online) $P$-$E$ characteristics in the MFIM structure with (a) $T_F$ = 50 nm, (b) $T_F$ = 40 nm, (c) $T_F$ = 30 nm,protect łinebreak (d) $T_F$ = 15 nm, (e) $T_F$ = 5 nm, and (f) $T_F$ = 3 nm. Black square is the $P_F$-$E_F$, red circle is the $P_D$-$E_D$, blue triangle is the overall $P$-$E$ of FE-DE bilayer, green dash is the $P_F$-$E_F$ based on the LGD theory. All the simulation parameters are from Table
Figure 3
(Color online) (a) Critical ferroelectric thickness $T_{{\rm~cri},{\rm~A}}$ and $T_{{\rm~cri},{\rm~C}}$ for phase transition of MFIM with various gradient coefficient at equilibrium state ($V_{\rm~App}=0$). (b) Domain patterns at $V_{\rm~App}=0$ at the specified $T_F$ in (a) within region A, B and C, respectively.
Figure 4
(Color online) (a) Domain width versus ferroelectric thickness with different gradient coefficient at equilibrium state ($V_{\rm~App}=0$) for the region B in Figure
Figure 5
(Color online) (a) Voltages ($V_{\rm~DE}$and $V_{\rm~App}$, (b) electric fields, and (c) polarization charges as a function of time in MFIM with $T_F=30$ nm operated at frequency of 1 MHz as shown in Figure
Figure 6
(Color online) (a) $V_{\rm~DE}$-$V_{\rm~App}$ and (b) $A_{v}$-$V_{\rm~App}$ characteristics with different $T_F$.
Figure 7
(Color online) (a) Voltage window and (b) voltage amplification factor for hysteresis-free operation versus $T_F$ with different $k$.
Figure 8
(Color online) $P$-$E$ characteristics in the MFIM structure with different $T_D$ and $\varepsilon_{D}$, accounting for SiO$_2$, Al$_2$O$_3$, and HfO$_2$, respectively. (a)–(c) and (d)–(f) are the $T_D=1$ nm and 5 nm cases. All the simulation parameters are taken from Table
Figure 9
(Color online) (a), (b) $P$-$E$ and (c), (d) $V_{\rm~DE}$-$V_{\rm~App}$ characteristics in the MFIM structure with different values of $\varepsilon_{D}/T_D$ respectively. (a), (c) are the $\varepsilon_{D}/T_D$$\propto{3.9}$cases, and (b), (d) are the $\varepsilon_{D}/T_D$$\propto{10}$cases.
Figure 10
(Color online) (a)–(c) $P$-$E$ characteristics in the MFIM structure with different conductivity ($\Gamma=10$, 0.1 and 0.01 S/m)protect łinebreak operated at $f$ = 1M Hz. (d)–(f) $P$-$E$ characteristics with $\Gamma=10$ S/m operated at $f$ = 1k, 10M and 100M Hz. All the simulation parameters are taken from Table
Figure 11
(Color online) (a) Voltage window and (b) voltage amplification for hysteresis-free operation versus frequency with different $\Gamma$.
| Symbol | Quantity | Value |
| $\alpha$ | Landau constant of ferroelectric | $-2.9\times10^{8}$ V$\cdot~$m/C |
| $\beta$ | Landau constant of ferroelectric | $-4.0\times10^{8}$ V$\cdot$m$^{5}$/C$^{3}$ |
| $\gamma$ | Landau constant of ferroelectric | $6.0\times10^{10}$ V$\cdot~$m$^{9}$/C$^{5}$ |
| ıtshapek | Gradient coefficient of ferroelectric | $1\times10^{-10}$ V$\cdot~$m$^{3}$/C |
| ıtshape$\Gamma$ | Conductivity of polarization switching | 10 S/m |
| $\varepsilon_{\rm~Fb}$ | Dielectric constant of ferroelectric | 25 |
| $\varepsilon_{D}$ | Dielectric constant of dielectric | 25 |
| ıtshapeT$_F$ | Thickness of ferroelectric | 10 nm |
| ıtshapeT$_D$ | Thickness of dielectric | 5 nm |
| ıtshapeL | Lateral size of simulation region | 50 nm |
| ıtshapeV$_{\rm~App}$ | Amplitude of external applied voltage | 10 V |
| ıtshapef | Sweep frequency of applied voltage | $10^{6}$ Hz |
Download PDF
