1.Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Ministry of Education, School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China 2.Dalian Neusoft University of Information, Dalian 116023, China 3.NaMLab gGmbH, Dresden 01187, Germany
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 51972037)
Received Date:18 January 2021
Accepted Date:09 March 2021
Available Online:16 June 2021
Published Online:20 June 2021
Abstract: From physical point of view, the “0, 1” read/write operation of ferroelectric memory is based on the polarization switching of ferroelectric memory. Therefore, the reliability of device relies directly on the stability of polarization switching behavior. The polarization behaviors of HfO2-based ferroelectric thin films subjected to bipolar cyclic electric field often exhibit wake-up, fatigue and split-up of transient switching current. These unstable switching properties seriously restrict the practical application of this new-type ferroelectric material in memory devices. It therefore becomes the critical task to explore the mechanism behind the complex evolution of polarization switching and find out possible approaches to optimizing the stability. However, it will be extremely difficult to accomplish the task by the traditional characterization methods. First-order reversal curve (FORC) diagram is regarded as “fingerprint identification” in the study of hysteresis systems, and has been used successfully to analyze the characteristic parameters of magnetic materials. The FORC diagram can intuitively determine the type, size and domain status of magnetic particles from distribution of both coercive field and interaction field. Moreover, it is also found that the FORC diagram is sensitive to measuring temperature. In this work, first, the Preisach model and implementation method of the FORC diagram are introduced. Then using Keithley 4200-SCS equipped with a remote pulse measurement unit, 60 FORCs are recorded for Si-doped HfO2 ferroelectric thin films experiencing different external field loading histories. By the mathematical treatment, switching density distributions determined by FORC measurements are obtained to explore the evolution of coercive field and bias field. The FORC diagram of pristine film contains three distribution regions with different bias fields, which merge into one distribution with an almost zero bias field after 104 wake-up cycles. Two oppositely biased regions can be observed after 2 × 109 sub-cycling treatments. Surprisingly, the bias fields nearly vanish again after 104 wake-up cycles. The main change of bias field instead of coercive field indicates that the migration of oxygen vacancies is likely to be the dominant mechanism behind the complex polarization switching behavior for HfO2-based ferroelectric thin films. Keywords:first-order reversal curve diagram/ ferroelectric thin film/ hafnium oxide/ polarization switching
2.Preisach模型经典Preisach模型是FORC图谱法的理论基础, 该模型以无穷多个迟滞算子为基本的组成单元, 输入和输出呈现多分支非线性关系. 如图1(a)所示, 铁电材料中具有相同自发极化响应Ps的电畴单元对应于Preisach模型中的基本迟滞算子, 其中α和β分别对应于翻转场E和回转场Er, 模型规定α ≥ β. 每个电畴单元具有以下特性: 当输入电场单调递增时, 极化响应沿a-b-c-d-e路线进行; 当输入电场单调递减时, 极化响应沿e-d-f-b-a路线进行. 可以发现, 电畴单元的极化响应Pαβ[E(t)]只有+Ps和–Ps两个输出值, 具体取何值不仅取决于输入电场E(t)与特征场强α和β的大小关系, 而且与输入的历史路径有关. 图 1 以铁电材料为例的Preisach模型示意图 (a) 电畴单元对外电场的极化翻转响应; (b) 材料对外电场的总极化响应 Figure1. Schematic diagrams of Preisach model for ferroelectric materials: (a) Polarization switching response of a domain element to applied electric field; (b) total polarization switching response of materials to applied electric field.
规定P(i = 1)为0. 利用软件自带的加权移动平均法对积分得到的极化强度响应P(i)数据进行平滑处理以消除噪声, 采用二次多项式函数对平滑后的曲线进行拟合, 公式为${P}_{\rm{polyfit}}\left({E}_{\rm{r}}, E\right)\!={a}_{1}+\! {a}_{2} \cdot {E}_{\rm{r}}\;+ $$ {a}_{3} \cdot {{E}_{\rm{r}}}^{2}+\!{a}_{4} \cdot E+\!{a}_{5} \cdot {E}^{2}-\!{a}_{6} \cdot {E}_{\rm{r}} \cdot E$, 代入(2)式可得分布密度$\rho \left({E}_{\rm{r}}, E\right)=- {{a}_{6}}/{2}$. 由此, 对分布密度函数作图得到$ \rho \left({E}_{\rm{r}}, E\right) $-$ {E}_{\rm{r}} $-E的三维坐标图和二维投影等值线图. 图4给出了经过1 kHz, 3 MV/cm强电场循环加载104次wake-up处理后Si:HfO2铁电薄膜的实测FORC图谱, 图4(a)为实际测得的瞬态翻转电流I-E曲线, 图4(b)为利用(3)式积分得到的P-E电滞回线, 图4(c)和图4(e)分别为以E -Er和Ebias-Ec为x -y坐标的三维分布密度图, 图4(d)和图4(f)分别是对应于图4(c)和图4(e)的二维投影等值线图. 图 4 wake-up处理后Si掺杂HfO2铁电薄膜的FORC实测图 (a) 实际测得的I-E瞬态电流响应曲线; (b) 利用Matlab软件对瞬态电流I进行简单积分得到的P-E曲线; (c), (d)以E和Er为坐标的三维和二维分布密度图谱; (e), (f)以Ebias和Ec为坐标的三维和二维分布密度图谱 Figure4. FORC measurement of Si doped HfO2 ferroelectric thin films after wake-up treatment: (a) Measured I-E transient current response curves; (b) P-E curves obtained by simple integration of transient current I by using MATLAB software; (c) three- and (d) two-dimensional diagrams of distribution density with E and Er as coordinates; (e) three- and (f) two-dimensional diagrams of distribution density with Ebias and Ec as coordinates.
与PZT等传统钙钛矿型铁电材料类似, HfO2基铁电薄膜同样具有显著的唤醒[28] (wake-up)和疲劳[29] (fatigue)效应, 还有新发现的饱和极化翻转电流峰劈裂[13,14] (split-up)等效应. 图5给出了Si:HfO2铁电薄膜在交变电场循环加载下P-E电滞回线和I-E瞬态电流曲线的演变过程, 可以清晰地看到wake-up, fatigue和split-up三种效应. 初始未极化样品的电滞回线在矫顽场处向内收缩呈“束腰”状, 并且正负矫顽场强度不一致; 对应的I-E曲线在正负电场方向均存在两个或多个极化翻转电流峰. 在3 MV/cm, 1 kHz的强场循环加载过程中, 电滞回线逐渐打开、变得饱满对称, 并伴随着剩余极化值Pr的增加和正负矫顽场强趋于一致; I-E曲线中正向和负向的翻转电流峰不断靠近, 呈现合并为单峰的趋势, 初始未极化样品在低频强电场循环加载下出现的上述P-E和I-E曲线演变过程称之为wake-up效应[11,30]. 如图5(c)和图5(d)所示, 对经过wake-up处理的样品施加2 MV/cm, 50 kHz的低幅值高频循环电场, 如采用1 kHz的相同场强(即2 MV/cm)监测P-E/I-E曲线的演变, 随着电场循环次数的增加可以观察到剩余和饱和极化强度均明显降低, 瞬态翻转电流峰的高度也显著下降, 即发生疲劳(fatigue)效应. 如图5(e)和图5(f)所示, 同样是在上述的2 MV/cm, 50 kHz电场循环加载过程中, 如采用3.5 MV/cm (1 kHz)的强场进行监测, 可以发现饱和P-E电滞回线会产生明显的扭曲变形现象, 相应地在饱和I-E曲线中正/负电场方向的单个翻转电流峰劈裂为两个峰. 在上述低幅值高频电场循环加载过程中, 铁电薄膜内只有部分电畴被反复翻转, 这种循环加载过程被称之为低场亚循环(sub-cycling), 而被强场监测到的饱和极化翻转电流峰劈裂的现象被称为split-up效应[31]. 如果对经过wake-up处理后的样品按幅值由高到低的降序依次施加多个低电场亚循环加载, 饱和极化翻转电流将由单峰劈裂为多个峰, 饱和P-E电滞回线的扭曲变形也更加明显[13]. 图 5 10 nm厚Si:HfO2铁电薄膜在循环电场载荷下的P-E电滞回线和I-E瞬态电流曲线的演变 (a), (b)初始未极化样品在3 MV/cm, 1 kHz电场循环加载下的wake-up效应; 对wake-up处理后的样品施加2 MV/cm, 50 kHz的循环电场, (c), (d)在2 MV/cm, 1 kHz电场下测试观察到的fatigue效应, (e), (f)在3.5 MV/cm, 1 kHz电场下测试观察到的split-up效应; 上方插图展示了具体的电场循环和测试顺序 Figure5. Evolution of P-E/I-E hysteresis loops of 10 nm thick Si:HfO2 ferroelectric thin films subjected to bipolar electric field cycling. (a), (b) Wake-up effect observed for pristine sample subjected to 3 MV/cm and 1 kHz bipolar field cycling. For woken-up sample subjected to 2 MV/cm and 50 kHz, (c), (d) fatigue effect monitored by 2 MV/cm and 1 kHz field, (e), (f) split-up effect monitored by 3.5 MV/cm and 1 kHz field. Details of cycling and measurement sequences are shown on top of the figures.