1.School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China 2.Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, Beijing 100081, China
Abstract:Ferroelectric domain structures and ferroelectric properties in the hetero-epitaxially constrained ferroelectric thin films can be manipulated by substrate misfit strain. In this work, three kinds of phase structures of PbZr(1–x)TixO3 thin films, including tetragonal, tetragonal- rhombohedral-mixed and rhombohedral phases, are investigated. Firstly, the ferroelectric domain structures at different substrate misfit biaxial strains are obtained by the phase-field simulation. Then we calculate the polarization-electric field hysteresis loops at different misfit strains, and obtain the coercive field, saturation polarization, and remnant polarization. In the tetragonal PbZr(1–x)TixO3 (x = 0.8) thin film, compressive strain contributes to the formation of out-of-plane c1/c2 domain, and tensile strain favors in-plane a1/a2 domain formation. With the increase of compressive strain, the tetragonal phase and the rhombohedral phase coexist in PbZr(1–x)TixO3 (x = 0.48) film near the morphotropic phase boundary, while the tensile strain reduces the rhombohedral domain size. In the rhombohedral PbZr(1–x)TixO3 (x = 0.2) film, the rhombohedral domains are steady states under compressive strain and tensile strain. As the misfit strain changes from –1.0% to 1.0%, the value of the coercive field, saturation polarization and remnant polarization decrease. Among them, for tetragonal-rhombohedral mixed phase, the reductions of saturation field and remnant polarization are larger than for tetragonal phase and rhombohedral phase. The coercive field of mixed phase decreases rapidly under the compressive strain, but deceases slowly under the tensile strain. It is worth noting that the remnant polarization decreases faster than the saturation polarization in three components of ferroelectric thin film. Due to the electromechanical coupling, when x = 0.48 at the morphotropic phase boundary it is shown that the remnant polarization reduction is faster than those of the other two types of ferroelectric thin films, and the small coercive field is obtained in the case of large tensile strain. Therefore, tensile strain can effectively improve the energy storage efficiency in ferroelectric thin films, and the efficiency of x = 0.48 thin film increases significantly compared with that of x = 0.8 or 0.2 thin film. Both the ratio of rhombohedral/tetragonal phase and the domain size will play a significant role in ferroelectric performance. Therefore, our results contribute to the understanding of the electromechanical coupling mechanism of PbZr(1–x)TixO3, and provide guidance for the experimental design of ferroelectric functional thin film materials. Keywords:phase-field simulation/ misfit strain/ ferroelectric domain structure/ hysteresis loops
表1三种成分PZT铁电薄膜介电刚度系数和电致伸缩常数 Table1.Corresponding material constants for the Landau free energy, the electrostrictive coefficients of three components PZT thin films.
在充分了解基底失配应变对PZT薄膜中微观畴结构的影响之后, 接下来利用相场模拟研究其对PZT薄膜宏观铁电性能的影响. 图4展示了不同基底应变(εsub = ± 0.1%, ± 0.5%, ± 1.0%)下PZT (x = 0.8, 0.48, 0.2)薄膜的电滞回线. 在压应变情况下(如图4(a)—(c)所示), 随着Ti比例的降低, PZT薄膜的矫顽场、饱和极化值以及剩余极化值都相应减小. 对于PZT (x = 0.8)和PZT (x = 0.48)薄膜, 矫顽场受压应变的调控比PZT (x = 0.2)薄膜更敏感, 这主要是因为在这两种成分的PZT薄膜中, 基底面内压应变使得c畴比例明显增加. 然而相比于PZT (x = 0.8)和PZT (x = 0.2)薄膜, PZT (x = 0.48)薄膜的饱和极化和剩余极化值对压应变要更敏感, 这是由于PZT (x = 0.48)薄膜在准同型相界处的强力电耦合效应, 畴结构对应变响应较为敏感[38,47,48]. 这主要体现在面内压应变使得PZT (x = 0.48)薄膜中T相比例增加, 而R相比例减小. 而在施加基底拉应变情况下, 与PZT (x = 0.48)和PZT (x = 0.2)薄膜相比, PZT (x = 0.8)薄膜展现出更大的饱和极化和剩余极化值, 这是因为其主要由T畴构成, 而前两者主要由R畴构成. 随着拉应变增加, PZT (x = 0.8)薄膜中面内a畴比例增加, 同时面外c畴比例减小. 而PZT (x = 0.48)薄膜R畴尺寸减小, 同时伴随畴壁密度增大, 所以这两个成分的PZT薄膜矫顽场对拉应变都非常敏感. 而PZT (x = 0.2)薄膜中, R相畴尺寸随拉应变变化不是很明显, 所以其对应的矫顽场的变化幅度也最小. 图 4 室温下PZT铁电薄膜四方相(x = 0.8), 混合相(x = 0.48)以及菱方相(x = 0.2)在不同的基底失配应变下(εsub = ± 0.1%, ± 0.5%, ± 1.0%)的电滞回线, 其中P *和E *表示归一化后的极化强度和电场强度值 (a)?(c)分别表示压应变下四方相、混合相和菱方相的电滞回线; (d)?(f)分别表示拉应变下四方相、混合相和菱方相的电滞回线 Figure4. Hysteresis loops of PZT thin films with three Ti components at different substrate biaxial misfit strains (εsub = ± 0.1%, ± 0.5%, ± 1.0%), and P * and E * are normalized polarization and electric field: (a)?(c) The case of compressive strains; (d)?(f) the case of tensile strains.
依据上述模拟结果, 进一步统计了基底失配应变(εsub = ± 0.1%, ± 0.5%, ± 1.0%)对不同成分的PZT (x = 0.8, 0.48, 0.2)薄膜矫顽场、饱和极化值以及剩余极化值的影响. 如图5所示, 随基底失配应变从压应变逐渐过渡到拉应变, PZT (x = 0.8, 0.48, 0.2)薄膜中矫顽场、饱和极化值以及剩余极化值都呈现出减小的趋势. 结合上面对图3与图4的讨论可知, 这主要与PZT (x = 0.8, 0.48, 0.2)薄膜中T相与R相的相对比例以及R相畴的尺寸随应变的变化是密切相关的. 对于PZT (x = 0.48, 0.2)薄膜来讲, 所有随应变变化的函数曲线(包含矫顽场、饱和极化与剩余极化)都存在一个交点(图5中蓝色和紫色曲线). 在交点左侧, PZT (x = 0.48)薄膜的相关铁电性能(矫顽场、饱和极化和剩余极化)都优于PZT (x = 0.2)薄膜. 在压应变情况下, 虽然这两个R相薄膜中都有T相畴的形成, 但PZT (x = 0.48)薄膜中T相畴的比例更高, 所以造成上面的现象. 而在交点右侧, PZT (x = 0.2)薄膜的相关铁电性能要优于PZT (x = 0.48)薄膜. 这是因为随着拉应变的增加, PZT (x = 0.2)薄膜中R相畴的尺寸变化不大, 而PZT (x = 0.48)薄膜中R相畴的尺寸急剧减小, 畴壁密度迅速增加所导致的. PZT (x = 0.2)薄膜中, 随着应变从–1.0%变化到1.0%时, 矫顽场、剩余极化值和饱和极化值都缓慢降低, 而对于PZT (x = 0.48)薄膜随应变增加, 矫顽场、剩余极化值以及饱和极化值显著降低. 从自由能角度分析, 准同型相界处PZT (x = 0.48)双势阱能垒小于PZT (x = 0.8)和PZT (x = 0.2), 在能量双势阱中能垒被拉平(图2(h)), 准同型相界处PZT薄膜对应变响应更为敏感, 其铁电极化强度也更容易翻转. 因此, x = 0.48时PZT薄膜随基底失配应变从–1.0%变化到1.0%, 矫顽场、饱和极化和剩余极化等值的变化速率大于另外两种PZT薄膜. 图 5 三种相PZT铁电薄膜的矫顽场、饱和极化和剩余极化值与基底应变的关系 (a) 矫顽场Ec*; (b) 饱和极化值Ps*; (c) 剩余极化值Pr* Figure5. Normalized coercive field (Ec*), saturation polarization (Pr*), and remnant polarization (Ps*) as a function of substrate misfit strain (εsub), where three PZT ferroelectric thin films with x = 0.8, 0.48 and 0.2 Ti component are considered: (a) Coercive field vs. strain; (b) saturation polarization vs. strain; (c) remnant polarization vs. strain.
我们继续探讨应变调控PZT铁电薄膜在储能方面的应用. 储能密度和储能效率之间的计算公式为
$\eta = \frac{{w1}}{{w1 + w2}} \times 100\% ,$
其中η表示储能效率, w1为可放电能量密度, w2为损失能量密度, 具体定义可见文献[49]. 图6(a)表示电滞回线中对应的能量储存示意图, 其中绿色面积表示可放电能量密度, 黄色区域表示放电过程中损失能量密度. 图 6 (a)电滞回线中充放电过程中储能示意图; (b) 三种PZT薄膜材料能量存储效率与基底应变之间的关系 Figure6. (a) Schematic of P-E loop used for energy storage; (b) the energy storage efficiency as a function of substrate misfit strain.