HfO2铁电极化计算(最新)

本文中，我们主要计算 HfO2 这种铁电材料的极化，给出具体的计算细节。

 

HfO2 是一种高介电常数 (high k) 和宽带隙材料，由于它最可能替代硅基集成电路的核心器件 金属氧化物半导体场效应管 (MOSFET) 的栅极绝缘层 SiO2 ，可有效减小栅极的漏电， 而且它与现有 CMOS 工艺兼容，这样可解决 MOSFET 中传统 SiO2/Si 结构的发展的尺寸极限问题。

自 2011年，研究者在 Si 掺杂的 HfO2 体系中发现铁电性以来 (Appl. Phys. Lett. 99, 102903 (2011)) ，大量有关铁电 HfO2 的研究工作层出不穷，例如 FeRAM, FeFet 等等，引发了 Hf 基铁电材料的研究热潮。

HfO2 有着不同的相。在室温下，它是属于单斜晶系 (Monoclinic, P21/c)，它的亚稳相是属于正交晶系 (Orthorhomic, Pca21)。在高温下，它是属于四方晶系 (Tetragonal, P42/nmc, 大于 2050 K) 或者立方晶系 (Cubic, Fm3m, 大于 2803 K)。最稳定的是 M 相，其次是 O 相，T 相， C 相。现如今，大家普遍认为 HfO2 的铁电性是来源于非中心对称的亚稳相 O 相 (Pca21)，也有人认为 Pmn21 也是铁电相。

 

维基百科上的介绍:

Hafnia typically adopts the same structure as zirconia (ZrO2). Unlike TiO2, which features six-coordinate Ti in all phases, zirconia and hafnia consist of seven-coordinate metal centres. A variety of other crystalline phases have been experimentally observed, including cubic fluorite (Fm3m), tetragonal (P42/nmc), monoclinic (P21/c) and orthorhombic (Pbca and Pnma).[2] It is also known that hafnia may adopt two other orthorhombic metastable phases (space group Pca21 and Pmn21) over a wide range of pressures and temperatures,[3] presumably being the sources of the ferroelectricity observed in thin films of hafnia.

 HfO2不同的晶格结构

 图来源 Appl. Phys. Lett. 117, 252904 (2020)

 

文献给出的  HfO2 晶格结构参数如图所示

因此，o-HfO2 结构参数可设置为:

a = 5.29 b = 5.01 c = 5.08
Hf  0.9668 0.7337 0.1231
O1 0.1350 0.0666 0.2672
O2 0.7288 0.4633 0.8744

利用 VESTA 等建模软件进行结构搭建，接着再对其进行结构优化得到初始结构，为了直观看出区别，这里我们对晶格进行简单平移。(注意，平移与否对整体计算不影响)

晶格平移，移动至 Hf 原子位于原点 (0,0,0)

 

再根据该结构进行操作得到极化方向相反的末态结构。因为该 HfO2 极化沿着 c方向，直接将初始结构的 c 基矢方向改为 -c 方向 (有时候需要进行简单的平移就可得到末态结构)。具体结构信息见文章后部分。

 

这样我们得到了极化方向相反的两种结构 (上图中红色箭头代表极化方向) ，接着可以用 nebmake.pl 线性插值等等...，但是，需要注意晶格中的 O 原子是如何移动的，这也是之前 HfO2铁电极化计算 - ghzphy - 博客园 (cnblogs.com) 算的两种结果不同的根本原因。如下图所示，我们可以发现，O 原子可以上下移动得到极化相反的结构，且两种移动路径相反。

 

实际上，O 原子有多个移动路径，这里我们只假设这两条移动路径，Type1, Type2。现在，我们就可以通过 nebmake.pl 线性来插值多个结构，以便进行极化强度的计算。详细步骤见  BaTiO3极化强度计算 - ghzphy - 博客园 (cnblogs.com)。如图所示，移动路径的中间结构是中心反演相，空间群是 Pbcm。

 

 

该 HfO2 体积为 134.6075 Å3 

 

1)  沿着 Type-1 路径移动

 

energy.dat 文件为:

-121.96296965
-121.90928171
-121.75609214
-121.51768966
-121.21126645
-120.85669034
-120.47627374
-120.09420205
-119.73548972
-119.42458043
-119.18386190
-119.03148151
-118.97931886
-119.03148154
-119.18386200
-119.42458062
-119.73548992
-120.09420223
-120.47627393
-120.85669059
-121.21126675
-121.51768997
-121.75609243
-121.90928197
-121.96296989

dipole_c.dat文件为:

-15.967830
-16.358750
-6.598370
-6.979300
-7.353280
-7.719840
-8.079210
-8.432200
-8.780040
1.022980
0.681080
0.340330
0.000000
-0.340330
-0.681080
-1.022980
8.780040
8.432200
8.079210
7.719840
7.353280
6.979300
6.598370
16.358750
15.967830

 

算出来的极化强度为 0.51497  C/m2

 

2) 沿着 Type-2 路径移动

energy.dat 文件为:

-121.96296965
-121.84675969
-121.72211035
-121.56976256
-121.40113853
-121.22709090
-121.05796273
-120.90350321
-120.77261245
-120.67297565
-120.61060785
-120.58938298
-120.61060788
-120.67297571
-120.77261253
-120.90350329
-121.05796280
-121.22709098
-121.40113863
-121.56976269
-121.72211052
-121.84675988
-121.93148949
-121.96296989

 

dipole_c.dat 文件为

-15.967830
-15.375560
-14.815460
-14.284380
-23.925520
-23.440250
-22.971300
-22.514340
-22.065350
-21.620920
-31.325650
-30.883640
0.000000
30.883640
31.325650
21.620920
22.065350
22.514340
22.971300
23.440250
23.925520
14.284380
14.815460
15.375560
15.967830

 算出来的极化强度为 0.6928  C/m2

 

 最后绘制两条路径下的 Energy-Polarization 曲线:

 

 

相关文件

 

最初始的 HfO2 POSCAR

HfO2
1.0
        5.2899999619         0.0000000000         0.0000000000
        0.0000000000         5.0100002289         0.0000000000
        0.0000000000         0.0000000000         5.0799999237
   Hf    O
    4    8
Direct
     0.966799965         0.733699974         0.123099996
     0.033200027         0.266300026         0.623099973
     0.466799965         0.266300026         0.123099996
     0.533200035         0.733699974         0.623099973
     0.135000003         0.066666002         0.267200000
     0.865000008         0.933333981         0.767199976
     0.634999992         0.933333981         0.267200000
     0.365000008         0.066666002         0.767199976
     0.728799991         0.463300006         0.874400058
     0.271200009         0.536699994         0.374400011
     0.228800059         0.536699994         0.874400058
     0.771200009         0.463300006         0.374400011

 

 

优化后的 HfO2 POSCAR

HfO2
   1.00000000000000
     5.2579484990322491    0.0000000000000000    0.0000000000000000
     0.0000000000000000    5.0458878475769300    0.0000000000000000
     0.0000000000000000    0.0000000000000000    5.0735889134678560
   Hf   O
     4     8
Direct
  0.9665121273103635  0.7328363467754023  0.1245850412467532
  0.0334878646896359  0.2671636532245980  0.6245850182467547
  0.4665121273103634  0.2671636532245980  0.1245850412467532
  0.5334878726896365  0.7328363467754023  0.6245850182467547
  0.1337959760166546  0.0696552925038741  0.2657885608673933
  0.8662040349833502  0.9303446904961210  0.7657885368673911
  0.6337959650166498  0.9303446904961210  0.2657885608673933
  0.3662040349833501  0.0696552925038741  0.7657885368673911
  0.7329597305601193  0.4612420383779082  0.8743264518858560
  0.2670402694398805  0.5387579616220919  0.3743264048858554
  0.2329597985601178  0.5387579616220919  0.8743264518858560
  0.7670402694398807  0.4612420383779082  0.3743264048858554

 

移动 Hf 原子至原点的 POSCAR

HfO2
1.0
        5.2579483986         0.0000000000         0.0000000000
        0.0000000000         5.0458879471         0.0000000000
        0.0000000000         0.0000000000         5.0735888481
   Hf    O
    4    8
Direct
     0.5000000000000000         0.465672693550804         0.0000000000000000
     0.5669757373792725         0.000000000000000         0.4999999770000015
     0.0000000000000000         0.000000000000000         0.0000000000000000
     0.0669757453792730         0.465672693550804         0.4999999770000015
     0.6672838487062912         0.802491639279276         0.1412035196206401
     0.3996919076729868         0.663181037271523         0.6412034956206379
     0.1672838377062864         0.663181037271523         0.1412035196206401
     0.8996919076729867         0.802491639279276         0.6412034956206379
     0.2664476032497559         0.194078385153310         0.7497414106391028
     0.8005281421295172         0.271594308397494         0.2497413636391022
     0.7664476712497544         0.271594308397494         0.7497414106391028
     0.3005281421295173         0.194078385153310         0.2497413636391022

 

沿着 Type 1 路径得到极化相反的 POSCAR

HfO2
1.0
        5.2579483986         0.0000000000         0.0000000000
        0.0000000000         5.0458879471         0.0000000000
        0.0000000000         0.0000000000         5.0735888481
   Hf    O
    4    8
Direct
     0.5000000000000000         0.465672693550804         0.0000000000000000
     0.5669757373792725         0.000000000000000         0.5000000229999985
     0.0000000000000000         0.000000000000000         0.0000000000000000
     0.0669757453792730         0.465672693550804         0.5000000229999985
     0.8996919076729867         0.802491639279276         0.3587965043793621
     0.1672838377062864         0.663181037271523         0.8587964803793600
     0.3996919076729868         0.663181037271523         0.3587965043793621
     0.6672838487062912         0.802491639279276         0.8587964803793600
     0.3005281421295173         0.194078385153310         0.7502586363608978
     0.7664476712497544         0.271594308397494         0.2502585893608972
     0.8005281421295172         0.271594308397494         0.7502586363608978
     0.2664476032497559         0.194078385153310         0.2502585893608972

 

沿着 Type 2  路径得到极化相反的 POSCAR

HfO2
1.0
        5.2579483986         0.0000000000         0.0000000000
        0.0000000000         5.0458879471         0.0000000000
        0.0000000000         0.0000000000         5.0735888481
   Hf    O
    4    8
Direct
     0.5000000000000000         0.465672693550804         0.0000000000000000
     0.5669757373792725         0.000000000000000         0.5000000229999985
     0.0000000000000000         0.000000000000000         0.0000000000000000
     0.0669757453792730         0.465672693550804         0.5000000229999985
     0.6672838487062912         0.802491639279276         -0.1412035196206400
     0.3996919076729868         0.663181037271523         0.3587965043793621
     0.1672838377062864         0.663181037271523         -0.1412035196206400
     0.8996919076729867         0.802491639279276         0.3587965043793621
     0.3005281421295173         0.194078385153310         0.7502586363608978
     0.7664476712497544         0.271594308397494         0.2502585893608972
     0.8005281421295172         0.271594308397494         0.7502586363608978
     0.2664476032497559         0.194078385153310         0.2502585893608972

 

Type 1 路径上的中间相

Hf    O
1.0
   5.2579483986000000   0.0000000000000000   0.0000000000000000
   0.0000000000000000   5.0458879470999998   0.0000000000000000
   0.0000000000000000   0.0000000000000000   5.0735888481000000
Hf    O
4  8
Direct
  0.5000000000000000  0.4656726935508080  0.0000000000000000
  0.5669757373792730  0.0000000000000000  0.5000000000000140
  0.0000000000000000  0.0000000000000000  0.0000000000000000
  0.0669757453792741  0.4656726935508080  0.5000000000000140
  0.7834878781896180  0.8024916392792750  0.2500000120000220
  0.2834878726896330  0.6631810372715210  0.7499999880000200
  0.2834878726896410  0.6631810372715210  0.2500000120000220
  0.7834878781896610  0.8024916392792750  0.7499999880000200
  0.2834878726896410  0.1940783851533110  0.7500000234999790
  0.7834879066896150  0.2715943083974960  0.2499999764999790
  0.7834879066896580  0.2715943083974960  0.7500000234999790
  0.2834878726896260  0.1940783851533110  0.2499999764999790

 

Type 2 路径上的中间相

Hf    O
1.0
   5.2579483986000000   0.0000000000000000   0.0000000000000000
   0.0000000000000000   5.0458879470999998   0.0000000000000000
   0.0000000000000000   0.0000000000000000   5.0735888481000000
Hf    O
4  8
Direct
  0.5000000000000000  0.4656726935508080  0.0000000000000000
  0.5669757373792730  0.0000000000000000  0.5000000000000140
  0.0000000000000000  0.0000000000000000  0.0000000000000000
  0.0669757453792741  0.4656726935508080  0.5000000000000140
  0.6672838487062900  0.8024916392792750  0.0000000000000355
  0.3996919076729880  0.6631810372715210  0.5000000000000360
  0.1672838377062860  0.6631810372715210  0.0000000000000355
  0.8996919076729880  0.8024916392792750  0.5000000000000360
  0.2834878726896410  0.1940783851533110  0.7500000234999790
  0.7834879066896150  0.2715943083974960  0.2499999764999790
  0.7834879066896580  0.2715943083974960  0.7500000234999790
  0.2834878726896260  0.1940783851533110  0.2499999764999790

 

posted @ 2022-06-04 01:09  ghzphy  阅读(3729)  评论(0)  编辑  收藏  举报