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密度泛函理论研究ZnGeP2晶体中缺陷的稳定性及迁移机制

马天慧 雷作涛 张晓萌 付秋月 布和巴特尔 朱崇强 杨春晖

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密度泛函理论研究ZnGeP2晶体中缺陷的稳定性及迁移机制

马天慧, 雷作涛, 张晓萌, 付秋月, 布和巴特尔, 朱崇强, 杨春晖

Investigation of stability and migration mechanism of defects in ZnGeP2 crystals by density functional theory

Ma Tian-Hui, Lei Zuo-Tao, Zhang Xiao-Meng, Fu Qiu-Yue, Bu Hebateer, Zhu Chong-Qiang, Yang Chun-Hui
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  • ZnGeP2晶体是3—5 μm中红外激光输出的最好频率转换材料, 可实现激光器的全固态化和大功率输出. 但在8—12 μm处由于本证缺陷导致的吸收带与光参量振荡器的抽运波长交叠, 限制了光参量振荡器的应用性能, 使其无法实现远红外激光输出. 本论文采用密度泛函理论讨论了ZnGeP2晶体6种缺陷结构的形成能与缺陷迁移机制. 结果表明$ {{\text{V}}_{\text{P}}} $和VGe两种缺陷结构较难形成, $ {\text{V}}_{\text{Zn}}^{-} $, $ {\text{Z}}{{\text{n}}_{{\text{Ge}}}} $, $ {\text{Ge}}_{{\text{Zn}}}^{+} $$ {\text{G}}{{\text{e}}_{{\text{Zn}}}}{\text{ + }}{{\text{V}}_{{\text{Zn}}}} $四种缺陷容易形成. 当Ge原子微富余Zn原子, 温度为10 K, 500 K和600 K时, $ {\text{V}}_{\text{Zn}}^{-} $形成能小于$ {\text{Ge}}_{{\text{Zn}}}^{+} $, 当温度为273 K和400 K时, $ {\text{Ge}}_{{\text{Zn}}}^{+} $形成能小于$ {\text{V}}_{\text{Zn}}^{-} $. 晶体的体积膨胀率与缺陷形成能的关系为负相关, 即晶体体积膨胀率越大, 缺陷形成能越低. 差分电荷密度分析显示GeZn和VZn + GeZn两种缺陷结构中原子间电子云密度增强, 空位缺陷(VZn和VGe)与反位缺陷(GeZn和ZnGe)结合形成联合缺陷后, 空位缺陷格点处电子云密度增强. 当温度为10 K时, ZnGeP2晶体的吸收光谱显示VGe, VZn, ZnGe和GeZn四种缺陷结构在0.6—2.5 µm有较明显吸收. VZn的迁移能最低, VGe迁移能最高. VP在迁移过程中迁移能与空间位阻有关, 而VGe和VZn的迁移能与原子间距离有关.
    ZnGeP2 crystals are the frequency conversion materials with the excellent comprehensive performances in a range of 3–5 μm. However, the overlap of the absorption band and the pump wavelength range of optical parametric oscillator at 8–12 μm limits the application performance of the optical parametric oscillator and makes it impossible to achieve a far-infrared laser output. In this work, the formation energy and migration mechanism of six kinds of defects of ZnGeP2 crystal are discussed by density functional theory. The results show that two defective structures of $\rm{V_P}$and $\rm{V_{Ge}}$ are difficult to form, while four defective structures of $\rm V_{\rm Zn}^ -$, $\rm{Z{n_{Ge}}}$, $ {\rm Ge}_{\rm Zn}^ + $ and $\rm{ G{e_{\rm Zn}} + {V_{\rm Zn}}}$ are easy to create. When the number of Ge atoms are slightly more than that of Zn atoms in ZnGeP2 crystals, the vacancy defects $\rm V_{\rm Zn}^ -$ form more easily than antistructure defects $ {\rm Ge}_{\rm Zn}^ + $ at 10 K, 500 K and 600 K, but the antistructure defects $ {\rm Ge}_{\rm Zn}^ + $ are easier to form than the vacancy defects $ {\text{V}}_{\text{Zn}}^{-} $ at 273 K and 400 K. There is a negative correlation between the volume expansion rate and the defect formation energy of ZnGeP2 crystal. The larger the volume expansion rate, the lower the defect formation energy is. The differential charge density shows that the electron cloud density among the atoms is enhanced in the defective structures of GeZn and VZn+GeZn. The electron cloud density at the lattices of vacancy defects is enhanced when the vacancy defects (VZn and VGe) and antistructure defects (GeZn and ZnGe) form the joint defects. Comparing with the defect-free cells, the charge of Zn atoms increases significantly, that of Ge is significantly reduced, and that of P does not change in the antistructure defect ZnGe or GeZn. The absorption spectra of ZnGeP2 crystal at 10K show that there is the significant absorption in a wavelength range from 0.6 μm to 2.5 μm for the four defective structures: VGe, VZn, ZnGe and GeZn, while the absorption in this range is small for the defective structures VP and GeZn+VZn. The VZn has the lowest migration energy, while VGe has the highest. The difficulty for VP to migrate depends on the space resistance, while the difficulty for VGe and VZn to migrate depend on the inter-atomic distance. This may be related to the small radius and high proportion of P atoms and the large radius and low proportion of Ge and Zn atom in ZnGeP2 crystal.
      通信作者: 马天慧, matianhui1972921@163.com
    • 基金项目: 国家自然科学基金(批准号: 52172002)、黑龙江省科学基金项目(批准号: LH2019E079, YQ2020B002)、黑龙江省省属高等学校基本科研业务费科研项目(批准号:2021GJ03)、中央支持地方高校改革发展资金人才培养项目(批准号: 2021GSP13)和黑龙江省重点研发计划指导类项目(批准号: GZ20210140)资助的课题.
      Corresponding author: Ma Tian-Hui, matianhui1972921@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52172002), the Science Foundation Project of Heilongjiang Province, China (Grant Nos. LH2019E079, YQ2020B002), Basic scientific research project of Heilongjiang Province(Grant No.2021GJ03), the Talent Training Project of the Central Government for the Reform and Development of Local Colleges and Universities (Grant No. 2021GSP13), and the Key Research and Development Plan of Heilongjiang province (Grant No. GZ20210140).
    [1]

    Kolesnikov A V, Vasilenko A P, Trukhanov E M, Lei Z T, Zhu C Q, Yang C H, Verozubova G A 2022 J. Cryst. Growth 580 126479Google Scholar

    [2]

    Cao Z H, Yang H, Sun S L, Liu Y H, Zhang M, Dai X J 2020 Opt. Mater. 110 110383Google Scholar

    [3]

    Lei Z T, Kolesnikov A, Vasilenko A, Zhu C Q, Verozubova G, Yang C H 2018 J. Appl. Cryst. 51 1043Google Scholar

    [4]

    Zinoviev M, Yudin N, Gribenyukov A, Podzyvalov S, Dyomin V, Polovtsev I, Suslyaev V, Zhuravlyova Y 2021 Opt. Mater. 111 110662Google Scholar

    [5]

    Shimony Y, Raz O, Kimmel G, Dariel M P 1999 Opt. Mater. 13 101Google Scholar

    [6]

    Rakowsky M H, Kuhn W K, Lauderdale W J, Halliburton L E, Edwards G J, Scripsick M P, Schunemann P G, Pollak T M, Ohmer M C, Hopkins F K 1994 Appl. Phys. Lett. 64 1615Google Scholar

    [7]

    Halliburton L E, Edwards G J, Scripsick M P, Rakowsky M H, Schunemann P G, Pollak T M 1995 Appl. Phys. Lett. 66 2670Google Scholar

    [8]

    Gehlhoff W, Azamat D, Hoffmann A 2003 Phys. Status Solidi B 235 151Google Scholar

    [9]

    Giles N C, Halliburton L E, Schunemann P G, Pollak T M 1995 Appl. Phys. Lett. 66 1758Google Scholar

    [10]

    Setzler S D, Giles N C, Halliburton L E, Schunmann P G, Pollak T M 1999 Appl. Phys. Lett. 74 1218Google Scholar

    [11]

    Gehlhoff W, Pereira R N, Azamat D, Hoffmann A, Dietz N 2001 Physica B 310 1015

    [12]

    Gehlhoff W, Azamat D, Hoffmann A, Dietz N 2003 J. Phys. Chem. Solids 64 1923Google Scholar

    [13]

    Jiang X S, Miao M S, Lambrecht W R L 2005 Phys. Rev. B 71 205212

    [14]

    Jiang X S, Miao M S, Lambrecht W R L 2006 Phys. Rev. B 73 193203

    [15]

    Jiang X S, Lambrecht W R L 2009 Solid State Commun. 149 685

    [16]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [17]

    Vanderbilt D 1990 Phys. Rev. B 41 7892Google Scholar

    [18]

    Laasonen K, Pasquarello A, Car R, Lee C, Vanderbilt D 1993 Phys. Rev. B 47 10142Google Scholar

    [19]

    Yan Y F, Wei S H 2008 Phys. Stat. Sol. B 245 641

    [20]

    Wang C, Sun J, Gou H Y, Wang S P, Zhang J, Tao X T 2017 Phys. Chem. Chem. Phys. 19 9558Google Scholar

    [21]

    Setzler S D, Schunemann P G, Pollak T M, Ohmer M C, Goldstein J T, Hopkins F K, Stevens K T, Halliburton L E, Giles N C 1999 J. Appl. Phys 86 6677Google Scholar

    [22]

    Giles N C, Bai L H, Chirila M M, Garces N Y, Stevens K T, Schunemann P G, Setzler S D, Pollak T M 2003 J. Appl. Phys 93 8975Google Scholar

  • 图 1  缺陷形成能与温度的关系曲线

    Fig. 1.  Dependent curves of defect formation energy and temperature.

    图 2  ZnGeP2缺陷晶胞体积变化率

    Fig. 2.  Volume change rates of defective cells for ZnGeP2.

    图 3  ZnGeP2晶胞 (a) 273 K完美晶胞; (b) 273 K时VP晶胞; (c) 500 K完美晶胞; (d) 500 K时VP晶胞

    Fig. 3.  Unit cells of ZnGeP2 (a) Perfect cell at 273 K; (b) cell containing VP at 273 K; (c) perfect cell at 500 K; (d) cell containing VP at 500 K.

    图 4  无缺陷晶胞和含缺陷晶胞(200)晶面的差分电荷密度分布图(红色圆圈为缺陷位置)

    Fig. 4.  Differential charge density distribution of perfect cells and defective cells for (200) plane (red circles are defect positions) .

    图 5  ZnGeP2缺陷晶胞的吸收谱

    Fig. 5.  Absorption spectra of defective cells for ZnGeP2.

    图 6  (010)面P原子标记图(采用2 × 1 × 1超胞体系)

    Fig. 6.  Map of positions of P atoms for (010) plane (super cells of 2 × 1 × 1 are used).

    图 7  (010)面P1格点空位向P4, P6, P8迁移的过渡态 (a) P1-P4; (b) P1-P6; (c) P1-P8

    Fig. 7.  Transition states for migrations from P1 vacancy lattice to P4, P6 and P8 lattices for (010) plane: (a) P1-P4; (b) P1-P6; (c) P1-P8.

    图 8  (100)面Ge原子标记图

    Fig. 8.  Map of positions of Ge atoms for (100) plane.

    图 9  (100)面Ge1格点空位向Ge2, Ge3, Ge4, Ge7迁移的过渡态和中间体 (a) Ge1-Ge2过渡态; (b) Ge1-Ge3过渡态; (c) Ge1-Ge4中间体; (d) Ge1-Ge7中间体

    Fig. 9.  Transition states and intermediate products for migrations from Ge1 vacancy lattice to Ge2, Ge3, Ge4 and Ge7 lattices for (100) plane: (a) Transition state of Ge1-Ge2; (b) transition state of Ge1-Ge3; (c) intermediate product of Ge1-Ge4; (d) intermediate product of Ge1-Ge7.

    图 10  (100)面Zn原子标记图

    Fig. 10.  Map of positions of Zn atoms for (100) plane.

    图 11  (100)面Zn1格点空位向Zn2和Zn3迁移的过渡态 (a) Zn1-Zn2; (b) Zn1-Zn3

    Fig. 11.  Transition states for migrations from Zn1 vacancy lattice to Zn2 and Zn3 lattices for (100) plane: (a) Zn1- Zn2; (b) Zn1- Zn3

    表 1  $ {\text{Z}}{{\text{n}}_{{\text{Ge}}}} $$ {\text{G}}{{\text{e}}_{{\text{Zn}}}} $的缺陷晶胞替换元素电荷和对应的键长

    Table 1.  Charge of substitution element and corresponding bond length of defective cells containing $ {\text{Z}}{{\text{n}}_{{\text{Ge}}}} $ and $ {\text{G}}{{\text{e}}_{{\text{Zn}}}} $.

    温度/K 元素电荷化学键键长/nm元素电荷 元素电荷化学键键长/nm元素电荷
    273无缺陷晶体Ge40.69Ge4-P62.35899P6–0.32ZnGeZn90.13Zn9-P82.48614P8–0.34
    Ge4-P42.35999P4–0.36Zn9-P62.50023P6–0.4
    Ge4-P82.34575P8–0.32Zn9-P122.49713P12–0.38
    Ge4-P32.28732P3–0.35Zn9-P112.42738P11–0.33
    Zn30.01Zn3-P42.31271P4–0.36GeZnGe10.37Ge1-P62.69564P6–0.36
    Zn3-P32.34784P3–0.35Ge1-P32.62636P3–0.32
    Zn3-P62.40425P6–0.32Ge1-P82.57614P8–0.32
    Zn3-P82.46926P8–0.32Ge1-P42.51162P4–0.35
    600无缺陷晶体Ge40.68Ge4-P62.23412P6–0.37ZnGeZn50.15Zn5-P82.3525P8–0.37
    Ge4-P42.34218P4–0.32Zn5-P62.65332P6–0.32
    Ge4-P82.40672P8–0.34Zn5-P122.6305P12–0.34
    Ge4-P32.34169P3–0.31Zn5-P112.54137P11–0.36
    Zn20Zn2-P52.48759P5–0.33GeZnGe10.37Ge1-P72.57682P7–0.33
    Zn2-P72.37797P7–0.37Ge1-P52.65679P5–0.34
    Zn2-P32.3425P3–0.31Ge1-P82.56753P8–0.33
    Zn2-P82.40251P8–0.34Ge1-P32.49967P3–0.29
    下载: 导出CSV

    表 2  (010)面P原子间距与迁移能

    Table 2.  P atomic spacing and migration energy for (010) plane.

    原子间距/(10–10 m)迁移能/eV原子间距/(10–10 m)迁移能
    /eV
    原子间距/(10–10 m)迁移能
    /eV
    P1-P23.7292.48595P1-P34.0242.54995P1-P43.7573.31980
    P2-P13.7292.45433P3-P14.0242.74953P4-P13.7573.24897
    P1-P53.8812.75197P1-P63.5542.28346P1-P73.7812.35649
    P5-P13.8812.67016P6-P13.5542.66777P7-P13.7812.27400
    P1-P83.6332.08976P1-P93.9472.68005
    P8-P13.6332.01885P9-P13.9472.87954
    下载: 导出CSV

    表 3  (100)面Ge原子间距与迁移能

    Table 3.  Ge atomic spacing and migration energy for (100) plane.

    原子间距/(10–10 m)迁移能
    /eV
    原子间距/(10–10 m)迁移能/eV原子间距/(10–10 m)迁移能
    /eV
    Ge1-Ge23.6682.41507Ge1-Ge36.6824.84944Ge1-Ge46.7205.76056
    Ge2-Ge13.6682.16555Ge3-Ge16.6824.77747Ge4-Ge16.7205.68664
    Ge1-Ge53.8572.85194Ge1-Ge63.9062.67506Ge1-Ge75.5055.15750
    Ge5-Ge13.8572.80361Ge6-Ge13.9062.62691Ge7-Ge15.5055.15696
    Ge1-Ge86.6354.50346
    Ge8-Ge16.6354.21664
    下载: 导出CSV

    表 4  (100)面Zn原子间距与迁移能

    Table 4.  Zn atomic spacing and migration energy for (100) plane.

    原子间距/(10–10 m)迁移能
    /eV
    原子间距/(10–10 m)迁移能
    /eV
    原子间距/(10–10 m)迁移能
    /eV
    Zn1-Zn23.8841.75494Zn1-Zn33.7302.03159Zn1-Zn43.9822.00985
    Zn2-Zn13.8841.81019Zn3-Zn13.7302.05914Zn4-Zn13.9822.04534
    Zn1-Zn55.5053.52642Zn1-Zn66.9065.04726
    Zn5-Zn15.5053.52635Zn6-Zn16.9065.12510
    下载: 导出CSV
  • [1]

    Kolesnikov A V, Vasilenko A P, Trukhanov E M, Lei Z T, Zhu C Q, Yang C H, Verozubova G A 2022 J. Cryst. Growth 580 126479Google Scholar

    [2]

    Cao Z H, Yang H, Sun S L, Liu Y H, Zhang M, Dai X J 2020 Opt. Mater. 110 110383Google Scholar

    [3]

    Lei Z T, Kolesnikov A, Vasilenko A, Zhu C Q, Verozubova G, Yang C H 2018 J. Appl. Cryst. 51 1043Google Scholar

    [4]

    Zinoviev M, Yudin N, Gribenyukov A, Podzyvalov S, Dyomin V, Polovtsev I, Suslyaev V, Zhuravlyova Y 2021 Opt. Mater. 111 110662Google Scholar

    [5]

    Shimony Y, Raz O, Kimmel G, Dariel M P 1999 Opt. Mater. 13 101Google Scholar

    [6]

    Rakowsky M H, Kuhn W K, Lauderdale W J, Halliburton L E, Edwards G J, Scripsick M P, Schunemann P G, Pollak T M, Ohmer M C, Hopkins F K 1994 Appl. Phys. Lett. 64 1615Google Scholar

    [7]

    Halliburton L E, Edwards G J, Scripsick M P, Rakowsky M H, Schunemann P G, Pollak T M 1995 Appl. Phys. Lett. 66 2670Google Scholar

    [8]

    Gehlhoff W, Azamat D, Hoffmann A 2003 Phys. Status Solidi B 235 151Google Scholar

    [9]

    Giles N C, Halliburton L E, Schunemann P G, Pollak T M 1995 Appl. Phys. Lett. 66 1758Google Scholar

    [10]

    Setzler S D, Giles N C, Halliburton L E, Schunmann P G, Pollak T M 1999 Appl. Phys. Lett. 74 1218Google Scholar

    [11]

    Gehlhoff W, Pereira R N, Azamat D, Hoffmann A, Dietz N 2001 Physica B 310 1015

    [12]

    Gehlhoff W, Azamat D, Hoffmann A, Dietz N 2003 J. Phys. Chem. Solids 64 1923Google Scholar

    [13]

    Jiang X S, Miao M S, Lambrecht W R L 2005 Phys. Rev. B 71 205212

    [14]

    Jiang X S, Miao M S, Lambrecht W R L 2006 Phys. Rev. B 73 193203

    [15]

    Jiang X S, Lambrecht W R L 2009 Solid State Commun. 149 685

    [16]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [17]

    Vanderbilt D 1990 Phys. Rev. B 41 7892Google Scholar

    [18]

    Laasonen K, Pasquarello A, Car R, Lee C, Vanderbilt D 1993 Phys. Rev. B 47 10142Google Scholar

    [19]

    Yan Y F, Wei S H 2008 Phys. Stat. Sol. B 245 641

    [20]

    Wang C, Sun J, Gou H Y, Wang S P, Zhang J, Tao X T 2017 Phys. Chem. Chem. Phys. 19 9558Google Scholar

    [21]

    Setzler S D, Schunemann P G, Pollak T M, Ohmer M C, Goldstein J T, Hopkins F K, Stevens K T, Halliburton L E, Giles N C 1999 J. Appl. Phys 86 6677Google Scholar

    [22]

    Giles N C, Bai L H, Chirila M M, Garces N Y, Stevens K T, Schunemann P G, Setzler S D, Pollak T M 2003 J. Appl. Phys 93 8975Google Scholar

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出版历程
  • 收稿日期:  2022-04-02
  • 修回日期:  2022-07-07
  • 上网日期:  2022-11-04
  • 刊出日期:  2022-11-20

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