Strain tuning of negative capacitance in epitaxial PbZr0.2Ti0.8O3 thin films

Lin Cui; Bai Gang; Li Wei; Gao Cun-Fa

doi:10.7498/aps.70.20210810

Abstract

In order to continue Moore’s Law, the reducing of power consumption is concerned by many researchers, and the discovery of ferronegative negative capacitance effect (NCE) provides a solution. Strain engineering has been widely studied as an effective means to regulate the physical properties of ferroelectric thin films. But the relevant mechanism of strain to ferroelectric negative capacitance regulation is not clear. Recently, the experimental results have shown that it is possible to stabilize the transient NCE in resistance-ferroelectric networks. In this work, we use the Landau-Khalatnikov theory to study the microscopic domain evolution and the influence of strain and temperature on NCE in a ferroelectric film. It is shown that compressive strain enhances NCE while NCE becomes weaker under a tensile strain. However, a larger compressive strain will give rise to a higher coercive voltage that hinders the NCE from forming. In addition, under a certain strain, the NCE becomes stronger at lower temperature. This work provides the theoretical basis for designing the negative capacitance devices and scaling towards nanoscale dimensions in future.

Keywords:

Authors and contacts

1.
College of Microelectronics, College of Electronic and Optical Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
2.
Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
3.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Corresponding author: Bai Gang, baigang@njupt.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51602159)

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References

[1]	Moore G 1965 Electronics 38 114 Google Scholar
[2]	Waldrop M 2016 Nature 530 144 Google Scholar
[3]	Tu L, Wang X, Wang J, Meng X, Chu J 2018 Adv. Electron. Mater. 4 1800231 Google Scholar
[4]	Zhirnov V, Cavin R 2008 Nat. Nanotechnol. 3 77 Google Scholar
[5]	Salahuddin S, Datta S 2008 Nano Lett. 8 405 Google Scholar
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[9]	Hoffmann M, Pesic M, Chatterjee K, Khan A I, Salahuddin S, Slesazeck S, Schroeder U, Mikolajick T 2016 Adv. Funct. Mater. 26 8643 Google Scholar
[10]	Hoffmann M, Khan A, Serrao C, Lu Z, Salahuddin S, Pesic M, Slesazeck S, Schroeder U, Mikolajick T 2018 J. Appl. Phys. 123 184101 Google Scholar
[11]	Zhou J, Han G, Li Q, Peng Y, Lu X, Zhang C, Zhang J, Sun Q, Zhang D, Hao Y 2016 IEEE International Electron Devices Meeting San Francisco, CA, USA, December 3–7, 2016 p16651211
[12]	Arimoto Y, Ishiwara H 2004 MRS Bull. 29 823 Google Scholar
[13]	Tanaka K, Kubota T, Sakabe Y 2002 Sens. Actuators, A 96 179 Google Scholar
[14]	Hoshyarmanesh H, Ghodsi M, Kim M, Cho H, Park H 2019 Sensors 19 2805 Google Scholar
[15]	Rath M, Varadarajan E, Premkumar S, Shinde S, Natarajan V, Rao R 2019 Ferroelectrics 551 17 Google Scholar
[16]	Janolin P 2009 J. Mater. Sci. 44 5025 Google Scholar
[17]	Choi K, Biegalski M, Li Y, Sharan A, Schubert J, Uecker R, Peiche P, Chen Y, Pan X, Gopalan V, Chen L, Schlom D, Eom C 2004 Science 306 1005 Google Scholar
[18]	Sharma A, Ban Z, Alpay S 2004 J. Appl. Phys. 95 3618 Google Scholar
[19]	Pertsev N, Zembilgotov A, Tagantsev A K 1998 Phys. Rev. Lett. 80 1988 Google Scholar
[20]	Pertsev N, Zembilgotov A, Tagantsev A 1999 Ferroelectrics 223 79 Google Scholar
[21]	Ban Z, Alpay S 2002 J. Appl. Phys. 91 9288 Google Scholar
[22]	Ban Z, Alpay S 2003 J. Appl. Phys. 93 504 Google Scholar
[23]	Pertsev N, Kukhar V, Kohlstedt H, Waser R 2003 Phys. Rev. B 67 054107 Google Scholar
[24]	Guo R, You L, Zhou Y, Lim Z, Zou X, Chen L, Ramesh R, Wang J 2013 Nat. Commun. 4 1990 Google Scholar
[25]	Chang S, Avci U, Nikonov D, Manipatruni S, Young I 2018 Phys. Rev. Appl. 9 014010 Google Scholar
[26]	Hoffmann M, Fengler F, Herzig M, Mittmann T, Max B, Schroeder U, Negrea R, Lucian P, Slesazeck S, Mikolajick T 2019 Nature 565 464 Google Scholar
[27]	Lo V 2003 J. Appl. Phys. 94 3353 Google Scholar
[28]	Zhang W, Bhattacharya K 2005 Acta Mater. 53 185 Google Scholar
[29]	Rabe K, Ahn C, Triscone J 2007 Physics of Ferroelectrics (Berlin Heidelberg: Springer-Verlag) pp366–368
[30]	Haun M, Zhuang Z, Furman E 1989 Ferroelectrics 99 45 Google Scholar
[31]	Qiu Q, Alpay S, Nagarajan V 2010 J. Appl. Phys. 107 114105
[32]	Liu C, Wang J 2021 Acta Mater. 206 116607 Google Scholar
[33]	Pertsev N, Contreras J, Kukhar V, Hermanns B, Kohlstedt H, Waser R 2003 Appl. Phys. Lett. 83 3356 Google Scholar

Cited By

图 1 铁电负电容瞬态响应模型及其等效电路图

Figure 1. Transient response model of ferroelectric negative capacitance and its equivalent circuit diagram.

DownLoad: Full-Size Img PowerPoint

图 2 (a)在T = 300 K, S_m = –0.011, 外加脉冲$ {V_{\text{S}}} = 14\;{\text{V}} $下$ {V_{\text{f}}} $与时间t的局部关系图; (b)—(f)不同时间段的铁电极化分布($ t = 0.545 $, $ 4.85 $, $ 11.0 $, $ 14.3 $, $16.5\;{\text{μ} }{\rm{ s}}$)

Figure 2. (a) Local relationship diagram with time under applied pulse; (b)–(f) ferroelectric polarization distribution in different time periods ($ t = 0.545 $, $ 4.85 $, $ 11.0 $, $ 14.3 $, $16.5\;{\text{μ} }{\rm{ s}}$).

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图 3 恒定应变$ {S_{\text{m}}} = 0.011 $以及不同温度下, (a), (c), (e)外加电压$ {V_{\text{S}}} = 14\;{\text{V}} $时铁电材料PbZr_0.2Ti_0.8O₃的${V_{\text{f}}} \text{-} t$关系图、${i_{\rm R}} \text{-} t$关系图、${Q_{\text{f}}} \text{-} t$关系图; (b), (d), (f)外加电压$ {V_{\text{S}}} = 10\;{\text{V}} $时铁电材料PbZr_0.2Ti_0.8O₃的${V_{\text{f}}} \text{-} t$关系图、${i_{\rm R}} \text{-} t$关系图、${Q_{\text{f}}} \text{-} t$关系图

Figure 3. Under constant strain $ {S_{\text{m}}} = 0.011 $ and different temperatures, (a), (c), (e) the ${V_{\text{f}}}\text{-} t$ relationship diagram, ${i_{\rm R}} \text{-} t$ relationship diagram and ${Q_{\text{f}}} \text{-} t$ relationship diagram of ferroelectric materials PbZr_0.2Ti_0.8O₃ when the applied voltage $ {V_{\text{S}}} = 14\;{\text{V}} $, respectively; (b), (d), (f) the ${V_{\text{f}}} \text{-} t$ relationship diagram, ${i_{\rm R}} \text{-} t$ relationship diagram and ${Q_{\text{f}}} \text{-} t$ relationship diagram of ferroelectric materials PbZr_0.2Ti_0.8O₃ when the applied voltage $ {V_{\text{S}}} = 10\;{\text{V}} $, respectively.

DownLoad: Full-Size Img PowerPoint

图 4 恒定温度$ T = 300\;{\text{K}} $以及不同应变下, (a), (c), (e)外加电压$ {V_{\text{S}}} = 14\;{\text{V}} $时铁电材料PbZr_0.2Ti_0.8O₃的${V_{\text{f}}} \text{-} t$关系图、${i_{\rm R}} \text{-} t$关系图、${Q_{\text{f}}} \text{-} t$关系图; (b), (d), (f)外加电压$ {V_{\text{S}}} = 10\;{\text{V}} $时铁电材料PbZr_0.2Ti_0.8O₃的${V_{\text{f}}} \text{-} t$关系图、${i_{\rm R}} \text{-} t$关系图、${Q_{\text{f}}} \text{-} t$关系图

Figure 4. Under constant temperature $ T = 300\;{\text{K}} $ and different strains, (a), (c), (e) the ${V_{\text{f}}} \text{-} t$ relationship diagram, ${i_{\rm R}} \text{-} t$ relationship diagram and ${Q_{\text{f}}} \text{-} t$ relationship diagram of ferroelectric materials PbZr_0.2Ti_0.8O₃ when the applied voltage $ {V_S} = 14\;{\text{V}} $, respectively; (b), (d), (f) the ${V_{\text{f}}} \text{-} t$ relationship diagram, ${i_{\rm R}} \text{-} t$ relationship diagram and ${Q_{\text{f}}} \text{-} t$ relationship diagram of ferroelectric materials PbZr_0.2Ti_0.8O₃ when the applied voltage $ {V_{\text{S}}} = 10\;{\text{V}} $, respectively.

DownLoad: Full-Size Img PowerPoint

图 5 自由能U与极化P的关系图　(a)恒定应变$ {S_{\text{m}}} = 0.011 $, 不同温度下$U \text{-} P$图; (b)恒温$ T = 300\;{\text{K}} $, 不同应变下$U \text{-} P$图

Figure 5. Relationship between free energy U and polarization P: (a) $U\text{-} P$ diagram with constant strain $ {S_{\text{m}}} = 0.011 $ at different temperatures; (b)$U \text{-} P$ diagram with constant temperature $ T = 300\;{\text{K}} $ at different strains.

DownLoad: Full-Size Img PowerPoint

表 1 PbZr_0.2Ti_0.8O₃材料的相关系数(温度T的单位为K)

Table 1. Correlation coefficient of PbZr_0.2Ti_0.8O₃ material (The unit of temperature T is K).

Coefficients	PbZr_0.2Ti_0.8O₃	Units	Reference
a₁	3.44(T – 729.5)	10⁵ C^–2·m²·N	[29]
a₁₁	–3.050	10⁷ C^–4·m⁶·N	[29]
a₁₁₁	2.475	10⁸ C^–6·m¹⁰·N	[29]
s₁₁	8.2	10^–12 m²/N	[29]
s₁₂	–2.6	10^–12 m²/N	[29]
Q₁₂	–0.0245	m⁴/C²	[30]
$ {t_{{\text{FE}}}} $	60	nm	[7]
A	30²	${\text{μ}}{ {\text{m} }^2}$	[7]
R	50	${\rm{k } }\Omega$	[7]
k	$ 1.26 \times {10^{ - 7}} $	$ {{\text{m}}^3}/{\text{F}} $
${\rho{'} }$	70	${\rm{k } }\Omega$
$ \Delta x $	$ 150 $	$ {\text{nm}} $
$ \Delta y $	$ 150 $	$ {\text{nm}} $
$ {N_x} $	200
$ {N_y} $	200
$ \Delta t $	$ 5 $	$ {\text{ns}} $

DownLoad: CSV

[1]	Moore G 1965 Electronics 38 114 Google Scholar
[2]	Waldrop M 2016 Nature 530 144 Google Scholar
[3]	Tu L, Wang X, Wang J, Meng X, Chu J 2018 Adv. Electron. Mater. 4 1800231 Google Scholar
[4]	Zhirnov V, Cavin R 2008 Nat. Nanotechnol. 3 77 Google Scholar
[5]	Salahuddin S, Datta S 2008 Nano Lett. 8 405 Google Scholar
[6]	Meindl J, Chen Q, Davis J 2001 Science 293 2044 Google Scholar
[7]	Khan A, Chatterjee K, Wang B, Drapcho S, Long Y, Serrao C, Bakaul S, Ramesh R, Salahuddin S 2015 Nat. Mater. 14 182 Google Scholar
[8]	Khan A, Hoffmann M, Chatterjee K, Lu Z, Xu R, Serrao C, Smith S, Martin L, Hu C, Ramesh R, Salahuddin S 2017 Appl. Phys. Lett. 111 253501 Google Scholar
[9]	Hoffmann M, Pesic M, Chatterjee K, Khan A I, Salahuddin S, Slesazeck S, Schroeder U, Mikolajick T 2016 Adv. Funct. Mater. 26 8643 Google Scholar
[10]	Hoffmann M, Khan A, Serrao C, Lu Z, Salahuddin S, Pesic M, Slesazeck S, Schroeder U, Mikolajick T 2018 J. Appl. Phys. 123 184101 Google Scholar
[11]	Zhou J, Han G, Li Q, Peng Y, Lu X, Zhang C, Zhang J, Sun Q, Zhang D, Hao Y 2016 IEEE International Electron Devices Meeting San Francisco, CA, USA, December 3–7, 2016 p16651211
[12]	Arimoto Y, Ishiwara H 2004 MRS Bull. 29 823 Google Scholar
[13]	Tanaka K, Kubota T, Sakabe Y 2002 Sens. Actuators, A 96 179 Google Scholar
[14]	Hoshyarmanesh H, Ghodsi M, Kim M, Cho H, Park H 2019 Sensors 19 2805 Google Scholar
[15]	Rath M, Varadarajan E, Premkumar S, Shinde S, Natarajan V, Rao R 2019 Ferroelectrics 551 17 Google Scholar
[16]	Janolin P 2009 J. Mater. Sci. 44 5025 Google Scholar
[17]	Choi K, Biegalski M, Li Y, Sharan A, Schubert J, Uecker R, Peiche P, Chen Y, Pan X, Gopalan V, Chen L, Schlom D, Eom C 2004 Science 306 1005 Google Scholar
[18]	Sharma A, Ban Z, Alpay S 2004 J. Appl. Phys. 95 3618 Google Scholar
[19]	Pertsev N, Zembilgotov A, Tagantsev A K 1998 Phys. Rev. Lett. 80 1988 Google Scholar
[20]	Pertsev N, Zembilgotov A, Tagantsev A 1999 Ferroelectrics 223 79 Google Scholar
[21]	Ban Z, Alpay S 2002 J. Appl. Phys. 91 9288 Google Scholar
[22]	Ban Z, Alpay S 2003 J. Appl. Phys. 93 504 Google Scholar
[23]	Pertsev N, Kukhar V, Kohlstedt H, Waser R 2003 Phys. Rev. B 67 054107 Google Scholar
[24]	Guo R, You L, Zhou Y, Lim Z, Zou X, Chen L, Ramesh R, Wang J 2013 Nat. Commun. 4 1990 Google Scholar
[25]	Chang S, Avci U, Nikonov D, Manipatruni S, Young I 2018 Phys. Rev. Appl. 9 014010 Google Scholar
[26]	Hoffmann M, Fengler F, Herzig M, Mittmann T, Max B, Schroeder U, Negrea R, Lucian P, Slesazeck S, Mikolajick T 2019 Nature 565 464 Google Scholar
[27]	Lo V 2003 J. Appl. Phys. 94 3353 Google Scholar
[28]	Zhang W, Bhattacharya K 2005 Acta Mater. 53 185 Google Scholar
[29]	Rabe K, Ahn C, Triscone J 2007 Physics of Ferroelectrics (Berlin Heidelberg: Springer-Verlag) pp366–368
[30]	Haun M, Zhuang Z, Furman E 1989 Ferroelectrics 99 45 Google Scholar
[31]	Qiu Q, Alpay S, Nagarajan V 2010 J. Appl. Phys. 107 114105
[32]	Liu C, Wang J 2021 Acta Mater. 206 116607 Google Scholar
[33]	Pertsev N, Contreras J, Kukhar V, Hermanns B, Kohlstedt H, Waser R 2003 Appl. Phys. Lett. 83 3356 Google Scholar

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Strain tuning of negative capacitance in epitaxial PbZr_0.2Ti_0.8O₃ thin films

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Corresponding author: Bai Gang, baigang@njupt.edu.cn

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