Key factors of spontaneous polarization magnitude in wurtzite materials

KANG Yao; CHEN Jian; TONG Yi; WANG Xinpeng; DUAN Kun; WANG Jiaqi; WANG Xudong; ZHOU Dayu; YAO Man

doi:10.7498/aps.74.20241520

Abstract

Emerging wurtzite ferroelectric materials have aroused significant interest due to their high spontaneous polarization magnitude (P_s). However, there is a limited understanding of the key factors that influence P_s. Herein, a machine-learning regression model is developed to predict the P_s using a dataset consisting of 40 binary and 89 simple ternary wurtzite materials. Features are extracted based on elemental properties, crystal parameters and electronic properties. Feature selection is carried out using the Boruta algorithm and distance correlation analysis, resulting in a comprehensive machine learning model. Furthermore, SHapley Additive exPlanations analysis identifies the average cation-ion potential (IPi_Aave) and the lattice parameter (a) as significant determinants of P_s, with IPi_Aave having the most prominent effect. A lower IPi_Aave corresponds to a lower P_s in the material. Additionally, a exhibits an approximately negative correlation with P_s.This multifactorial analysis fills the existing gap in understanding the determinants of P_s, and makes a foundational contribution to the evaluating emerging wurtzite materials and expediting the discovery of high-performance ferroelectric materials.The dataset in this work can be accessed in the Scientific Data Bank https://www.doi.org/10.57760/sciencedb.j00213.00073.

Keywords:

Authors and contacts

1.
School of Materials Science and Engineering, Dalian University of Technology, Dalian 116081, China
2.
Suzhou Laboratory, Suzhou 215123, China

Corresponding author: ZHOU Dayu, zhoudayu@dlut.edu.cn ; YAO Man, yaoman@dlut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51974056, 51474047, 52472120), the Fundamental Research Funds for the Central Universities of China (Grant No. DUT24LAB117), and the Suzhou Laboratory Project (Grant No. SK-1202-2024-012).

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References

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图 1 (a)初始筛选元素在元素周期表内的体现, 其中蓝色代表阳离子, 橙色代表阴离子; (b)元素筛选的条件和具体流程; (c) 二元纤锌矿材料合理的元素组成

Figure 1. (a) The representation of initial screening elements in the periodic table, where blue represents cations and orange represents anions; (b) the conditions and specific process for screening; (c) reasonable composition elements of binary wurtzite materials obtained through screening.

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图 2 (a) AB, (b) A₁A₂B, (c) AB₁B₂体系的P_s数值; (d)单价、二价、三价阳离子和整个数据集的箱线图

Figure 2. P_s of (a) AB, (b) A₁A₂B, and (c) AB₁B₂ systems; (d) box plots of P_s for monovalent, divalent, and trivalent cations as well as all systems.

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图 3 四面体结构参数示意图

Figure 3. Schematic diagram of tetrahedral structure parameters

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图 4 曲线路径示意图

Figure 4. Schematic diagram of curve path.

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图 5 组内距离自相关系数热图　(a) 元素基本属性特征; (b) 晶体结构特征; (c) DC特征; (d) COHP, BC, ELF特征; (e) DOS特征. (f) 保留特征的组间距离自相关系数热图

Figure 5. Heatmap of distance correlation coefficients: (a) element properties; (b) crystal parameters; (c) DC properties; (d) COHP, BC, ELF properties; (e) DOS properties. (f) Feature preserving inter group distance autocorrelation coefficient heat map.

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图 6 6种含105特征机器学习模型的(a) R², (b) RMSE, (c) XGBR模型的预测散点图; 6种含10特征机器学习模型的(d) R², (e)RMSE, (f) XGBR模型的预测散点图

Figure 6. (a) R² and (b) RMSE values of six machine-learning models and (c) scatter plot of the XGBR model with 105 features; (d) R² and (e) RMSE values of six machine-learning models and (f) scatter plot of the XGBR model with 10 features.

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图 7 含10个特征XGBR模型的 (a) SHAP散点图和(b) SHAP特征重要性; (c) IPi_Aave, (d) a, (e) IPi_Bave特征的部分依赖图

Figure 7. (a) SHAP summary plot, (b) SHAP feature importance of XGBR model with 10 features; partial dependence plots for the top three important features of (c) IPi_Aave, (d)a, (e) IPi_Bave.

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表 1 用于描述纤锌矿材料的特征类型——元素基本属性

Table 1. Parameters describing the characteristic types of wurtzite materials—Basic element attributes.

特征	定义	特征	定义
aN	原子序数	aM	相对原子质量
ICV	ICSD数据库内晶体体积	aD	原子密度
X	电负性	VE	价电子
R_c	共价半径	R_i	离子半径
R_a	原子半径	IPi	离子势(VE/Ri)
FIP	第一电离势	SIP	第二电离势
TIP	第三电离势	CP	化学势
FAE	自由原子能量	Men	门捷列夫数

DownLoad: CSV

表 3 用于描述纤锌矿材料的特征类型——电子结构参数

Table 3. Parameters describing the characteristic types of wurtzite materials—Electronic parameters.

分析	特征	定义	特征	定义
COHP分析	ICa, ICe	轴向键与平向键键强	ICa-ICe	轴向键与平向键键强的差值
COHP分析	ICa/ICe	轴向键与平向键键强的比值	IC	四面体内平均键强
BC分析	AtV	原子体积	Bad	巴德电荷
DOS分析	Bc_tot	总能带中心	Bc_out	外层轨道的能带中心
	Bw_tot	总能带宽度	Bw_out	外层轨道的能带宽度
	Bs_tot	总能带偏度	Bs_out	外层轨道的能带偏度
	Bk_tot	总能带峰度	Bk_out	外层轨道的能带峰度
ELF分析	ELF _Cat	阳离子位置的ELF值	ELF_Ani	阴离子位置的ELF值
	ELF_dCA	阴阳离子位置ELF值的差值	ELF_Max	ELF曲线峰值
	ELF_MP	ELF曲线峰值的位置	ELF_F	ELF曲线半峰全宽
DC分析	DC_Cat	阳离子位置的DC值	DC_Ani	阴离子位置的DC值
	DC_dCA	阴阳离子位置DC值的差值	DC_Max	DC曲线峰值
	DC_MP	DC曲线峰值的位置	DC_F	DC曲线半峰全宽

DownLoad: CSV

表 2 用于描述纤锌矿材料的特征类型——晶体结构参数

Table 2. Parameters describing the characteristic types of wurtzite materials—Crystal structure parameters.

特征	定义	特征	定义
c, a	晶胞参数	c/a	晶胞参数比值
V	晶胞体积	S	晶胞底面积
H_tetra	四面体高度	V_tetra	四面体体积
d	阳离子到四面体底部的距离	μ	四面体内部曲折度(d/H_tetra)
L_a, L_e	轴向键与平向键键长	L_a – L_e	轴向键与平向键键长的差值
L_a/L_e	轴向键与平向键键长的比值	L	四面体内平均键长
A_a, A_e	轴向键与平向键键角	A_a – A_e	轴向键与平向键键角的差值
A_a/A_e	轴向键与平向键键角的比值	A	四面体内平均键角

DownLoad: CSV

[1]	Ishiwara H 2012 J. Nanosci. Nanotechnol. 12 7619 Google Scholar
[2]	Arimoto Y, Ishiwara H 2004 Mrs. Bull. 29 823 Google Scholar
[3]	Song S, Kim K H, Chakravarthi S, Han Z, Kim G, Ma K Y, Shin H S, Olsson R H, Jariwala D 2023 Appl. Phys. Lett. 123 183501 Google Scholar
[4]	Muralt P 2000 J. Micromech. Microeng. 10 136 Google Scholar
[5]	Takayama R, Tomita Y, Iijima K, Ueda I 1991 Ferroelectrics 118 325 Google Scholar
[6]	Han X, Ji Y, Yang Y 2022 Adv. Funct. Mater. 32 2109625 Google Scholar
[7]	钟维烈 1996 (北京: 科学出版社) 第1页 Zhong W L 1996 Physics of Ferroelectric Materials (Beijing: Science Press) p1
[8]	李飞, 张树君, 徐卓 2020 物理学报 69 217703 Google Scholar Li F, Zhang S J, Xu Z 2020 Acta Phys. Sin. 69 217703 Google Scholar
[9]	Fan Y T, Tan G J 2022 Mater. Lab 1 220008
[10]	Fichtner S, Wolff N, Lofink F, Kienle L, Wagner B 2019 J. Appl. Phys. 125 114103 Google Scholar
[11]	Zhao Z, Chen Y R, Wang J F, Chen Y W, Zou J R, Lin Y X, Xing Y F, Liu C W, Hu C M 2022 IEEE Electr. Device L 43 553 Google Scholar
[12]	Hayden J, Hossain M D, Xiong Y H, Ferri K, Zhu W L, Imperatore M V, Giebink N, Trolier-McKinstry S, Dabo I, Maria J P 2021 Phys. Rev. Mater. 5 044412 Google Scholar
[13]	Wang D, Mondal S, Liu J N, Hu M T, Wang P, Yang S, Wang D H, Xiao Y X, Wu Y P, Ma T, Mi Z 2023 Appl. Phys. Lett. 123 033504 Google Scholar
[14]	Wang D, Wang P, Wang B Y, Mi Z 2021 Appl. Phys. Lett. 119 111902 Google Scholar
[15]	Ferri K, Bachu S, Zhu W L, Imperatore M, Hayden J , Alem N, Giebink N, Trolier-McKinstry S, Maria J P 2021 J. Appl. Phys. 130 044101 Google Scholar
[16]	Zhang Y L, Zhu Q X, Tian B B, Duan C G 2024 Nano-Micro Lett. 16 227 Google Scholar
[17]	Yasuoka S, Shimizu T, Tateyama A, Uehara M, Yamada H, Akiyama M, Hiranaga Y, Yasuo C, Funakubo H 2020 J. Appl. Phys. 128 114103 Google Scholar
[18]	Ye K H, Han G, Yeu I W, Hwang C S, Choi J H 2021 Phys. Status Solidi R 15 2100009 Google Scholar
[19]	Wang P, Wang D, Vu N M, Chiang T, Heron J T, Mi Z 2021 Appl. Phys. Lett. 118 223504 Google Scholar
[20]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[21]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[22]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[23]	Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A 2013 APL Mater. 1 011002 Google Scholar
[24]	Dreyer C E, Janotti A, Van de Walle C G, Vanderbilt D 2016 Phys. Rev. X 6 021038
[25]	Fichtner S, Yassine M, Van de Walle C G, Ambacher O 2024 Appl. Phys. Lett. 125 040501 Google Scholar
[26]	Liu Z J, Wang X Y, Ma X Y, Yang Y R, Wu D 2023 Appl. Phys. Lett. 122 122901 Google Scholar
[27]	Calderon S, Hayden J, Baksa S M, Tzou W, McKinstry S T, Dabo I, Maria J P, Dickey E C 2023 Science 380 1034 Google Scholar
[28]	Lee C W, Yazawa K, Zakutayev A, Brennecka G L, Gorai P 2024 Sci. Adv. 10 eadl0848 Google Scholar
[29]	Lee C W, Din N U, Yazawa K, Brennecka G L, Zakutayev A, Gorai P 2024 Matter 7 1644 Google Scholar
[30]	Spaldin N A 2012 J. Solid State Chem. 195 2 Google Scholar
[31]	Kursa M B, Rudnicki W R 2010 J. Stat. Softw. 36 1
[32]	Kim Y, Kim Y 2022 Sustain. Cities Soc. 79 103677 Google Scholar
[33]	Moriwake H, Yokoi R, Taguchi A, Ogawa T, Fisher C AJ, Kuwabara A, Sato Y, Shimizu T, Hamasaki Y, Takashima H, Itoh M 2020 APL Mater. 8 121102 Google Scholar
[34]	Kang Y, Chen J, Sui J Y, Wang X D, Zhou D Y, Yao M 2024 ACS Appl. Mater. Interfaces. 16 49484 Google Scholar
[35]	Sun J A, Zhang J F, Yan J Y, Wang Y L, Lou J Z, Yan X B, Guo J X 2022 Phys. Status. Solidi. B 259 2200079 Google Scholar
[36]	Kirklin S, Saal J E, Meredig B, Thompson A, Doak J W, Aykol M, Rühl S, Wolverton C 2015 NPJ Comput Mater. 1 15010 Google Scholar
[37]	杨自欣, 高章然, 孙晓帆, 蔡宏灵, 张凤鸣, 吴小山 2019 物理学报 68 210502 Google Scholar Yang Z X, Gao Z R, Sun X F, Cai H L, Zhang F M, Wu X S 2019 Acta Phys. Sin. 68 210502 Google Scholar

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