HfO2铁电极化计算

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。

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 HfO2 的研究工作层出不穷， 引发了 Hf 基铁电材料的研究热潮。HfO2 是一种高介电常数的铁电材料 (high k)，它与现有 CMOS 工艺兼容，能够在 Si 和 SiO2上稳定存在，所以被学术界和工业界广泛采纳。

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)。

 

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)

 

o-HfO2 结构来自 materialproject 数据库 (https://materialsproject.org/materials/mp-685097/)，对其进行结构优化得到初始结构，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 b 方向，直接将初始结构的 b 基矢方向改为 -b 方向，然后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。)

 

通过 nebmake.pl 线性插值多个结构，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)

HfO2 体积为 134.6082 Å3

energy.dat 文件为:

-121.96298683
-121.93156690
-121.84683984
-121.72215096
-121.56973571
-121.40102358
-121.22687016
-121.05762557
-120.90304789
-120.77204695
-120.67231812
-120.60988578
-120.58863508
-120.60987825
-120.67230380
-120.77202755
-120.90302597
-121.05760440
-121.22685283
-121.40101191
-121.56973070
-121.72215236
-121.84684706
-121.93157912
-121.96300277

 

dipole_b.dat 文件为:

44.916280
45.508530
46.068600
36.452470
36.958440
37.443650
37.912510
38.369380
28.671080
29.115390
29.557710
29.999570
30.441520
30.883480
21.178170
21.620480
22.064790
22.513670
22.970540
13.292240
13.777440
14.283410
14.814460
15.374530
5.819610

 

Energy-Polarization 关系

 


能看出，该体系的极化强度值为 0.69  C/m2，与 Appl. Phys. Lett. 104,092906 (2014) 文献中 DFT 计算出的 0.53 C/m2 相差较多，可能原因是体系的晶格常数不同。

 

相关文件:

materialproject 上的POSCAR

Hf4 O8
1.0
5.040138 0.000000 0.000000
0.000000 5.074451 0.000000
0.000000 0.000000 5.269276
Hf O
4 8
direct
0.267436 0.242569 0.033795
0.267436 0.742569 0.466205
0.732564 0.242569 0.533795
0.732564 0.742569 0.966205
0.072143 0.376847 0.367911
0.072143 0.876847 0.132089
0.459797 0.493584 0.733288
0.459797 0.993584 0.766712
0.540203 0.993584 0.266712
0.540203 0.493584 0.233288
0.927857 0.376847 0.867911
0.927857 0.876847 0.632089

 

结构优化 INCAR

ISTART =0
ICHARG =2
PREC   =Accurate
ENCUT  =520
EDIFF  =0.1E-07
ISMEAR =-5
LWAVE=.FALSE.
NSW = 300
POTIM = 0.2
IBRION = 2
ISIF = 3
NELM = 200

 

优化后的铁电相

Hf4 O8
   1.00000000000000
     5.0459958191765715    0.0000000000000000    0.0000000000000000
     0.0000000000000000    5.0735875525735814    0.0000000000000000
     0.0000000000000000    0.0000000000000000    5.2578653593600473
   Hf   O
     4     8
Direct
  0.2671591864390609  0.2406759038916039  0.0334817296699646
  0.2671591864390609  0.7406759038916039  0.4665182703300353
  0.7328408135609393  0.2406759038916039  0.5334817296699645
  0.7328408135609393  0.7406759038916039  0.9665182703300355
  0.0696363549573347  0.3819201241270918  0.3661788814237995
  0.0696363549573347  0.8819201241270920  0.1338211185762006
  0.4612473990478969  0.4904039719813039  0.7329635847515669
  0.4612473990478969  0.9904039719813039  0.7670364152484331
  0.5387526009521030  0.9904039719813039  0.2670364152484332
  0.5387526009521030  0.4904039719813039  0.2329635847515668
  0.9303636450426654  0.3819201241270918  0.8661788814237991
  0.9303636450426654  0.8819201241270920  0.6338211185762009

 

简单操作变换后的极化方向相反的结构

Hf4 O8
   1.00000000000000
     5.0459958191765715    0.0000000000000000    0.0000000000000000
     0.0000000000000000    5.0735875525735814    0.0000000000000000
     0.0000000000000000    0.0000000000000000    5.2578653593600473
   Hf   O
     4     8
Direct
  0.2671591864390609  0.2406759038916039  0.0334817296699646
  0.2671591864390609  0.7406759038916039  0.4665182703300353
  0.7328408135609393  0.2406759038916039  0.5334817296699645
  0.7328408135609393  0.7406759038916039  0.9665182703300355
  0.0696363549573347  0.0994316836561160  0.3661788814237995
  0.0696363549573347  0.5994316836561158  0.1338211185762006
  0.4612473990478969  0.4909478358019038  0.7670364152484331
  0.4612473990478969  0.9909478358019038  0.7329635847515669
  0.5387526009521030  0.9909478358019038  0.2329635847515668
  0.5387526009521030  0.4909478358019038  0.2670364152484332
  0.9303636450426654  0.0994316836561160  0.8661788814237991
  0.9303636450426654  0.5994316836561158  0.6338211185762009

 

 

 

 

 

2022-05-23 的计算记录.

 

我们先构建了极化方向相反的两个结构:

 

具体计算过程参考: BaTiO3极化强度计算 - ghzphy - 博客园 (cnblogs.com)

 

HfO2 体积为 134.6068 Å3

 

energy.dat 文件为

-121.96299172
-121.91029520
-121.75987179
-121.52545097
-121.22358657
-120.87330577
-120.49585045
-120.11405352
-119.75146962
-119.43107594
-119.17407064
-118.99802372
-118.91513380
-118.93082266
-119.04310179
-119.24263236
-119.51373588
-119.83608381
-120.18660880
-120.54100496
-120.87525509
-121.16681751
-121.39548564
-121.54385285
-121.59772656

 

diople_b.dat 文件为

-15.965790
-16.364370
-6.611600
-7.000210
-7.381980
-7.756520
-8.124110
-8.485560
-8.842100
0.952050
0.601190
0.251460
-0.097750
-0.446770
-0.795910
-1.145820
8.649590
8.294530
7.934560
7.568260
7.194600
6.813160
6.424150
16.175670
15.774890

 

最后得到 Energy-Polarization 关系:

 

可以算出，HfO2 的极化强度大约为 0.5152 C/m2，与 Appl. Phys. Lett. 104,092906 (2014) 文献中DFT计算出的 0.53 C/m2 吻合.

 

 

相关文件:

 

铁电相 HfO2 的 POSCAR

Hf4 O8
1.0
        5.0459661484         0.0000000000         0.0000000000
        0.0000000000         5.0735898018         0.0000000000
        0.0000000000         0.0000000000         5.2578392029
   Hf    O
    4    8
Direct
     0.000000000         0.000000000         0.000000000
    -0.000000000         0.499999765         0.433025411
     0.465672455        -0.000000000         0.500000045
     0.465672455         0.499999765         0.933025457
     0.802489625         0.141206385         0.332707341
     0.802489625         0.641206432         0.100318093
     0.194072631         0.249741849         0.699493665
     0.194072631         0.749741849         0.733531792
     0.271599351         0.749741849         0.233531746
     0.271599351         0.249741849         0.199493642
     0.663182453         0.141206385         0.832707295
     0.663182453         0.641206432         0.600318116
Hf4 O8
1.0
        5.0459661484         0.0000000000         0.0000000000
        0.0000000000         5.0735898018         0.0000000000
        0.0000000000         0.0000000000         5.2578392029
   Hf    O
    4    8
Direct
     0.000000000         0.000000000         0.000000000
    -0.000000000         0.499999765         0.433025411
     0.465672455        -0.000000000         0.500000045
     0.465672455         0.499999765         0.933025457
     0.802489625         0.359309917         0.100318093
     0.802489625         0.859309917         0.332707341
     0.194072631         0.249741849         0.699493665
     0.194072631         0.749741849         0.733531792
     0.271599351         0.749741849         0.233531746
     0.271599351         0.249741849         0.199493642
     0.663182453         0.359309917         0.600318116
     0.663182453         0.859309917         0.832707295

 

posted @ 2022-05-23 12:20  ghzphy  阅读(1834)  评论(0)  编辑  收藏  举报