锑空位复合体对锗晶体物性影响的第一性研究
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摘要
利用第一性原理软件CASTEP系统研究了锑掺杂锗晶体中锑原子与空位的相互作用,对单空位、双空位可能出现的结构模型进行了计算,通过对结合能的比较分析了相应的结构模型的稳定性。结果表明,在锑掺杂锗晶体中由于锑的引入,空位倾向于聚集在锑原子周围,形成锑-空位复合体。当体系仅含有一个空位时,空位处于锑原子的第一近邻晶格位点时形成最稳定的结构其结合能为-1.10 eV。当体系含有两个空位时,双空位分别位于锑原子同一共价键方向上的第一、第二近邻晶格位点形成最稳定的结构其结合能为-2.03 eV。使用Voigt-Reuss-Hill近似计算相应单空位、双空位模型的弹性模量并与无缺陷锗晶体的弹性模量相比较,根据Pugy判据可知无缺陷锗晶体的B/G(体模量/剪切模量)值为1.38,由于锑空位复合体的引入使单空位双空位模型的B/G值增加到1.59～1.73的范围之内,由此表明锑空位复合体可以提高锗晶体的塑性,这也与利用柯西压力判定脆塑性得到的结论一致。
The first-principle theory software(CASTEP) was used to systematically study interaction between antimony and vacancies in germanium crystal, the possible structure models of monovacancy and divacancy were calculated, and the stability of related models were analyzed by comparing the binding energy. As the results showed, because of the introducing of antimony atom, vacancies tended to gather around with antimony atom, and formed antimony-vacancy complex in Ge crystal. For monovacancy case, the most stable structure was formed when the vacancy was located in the first nearest-neighboring of antimony atom, and the binding energy was-1.10 eV. For divacancy case, the most stable structure was formed when the divacancy was respectively located in the first and second nearest-neighboring of the same covalent bond branch of antimony atom, and the binding energy was-2.02 eV. Voigt-Reuss-Hill approximation was used to calculate elastic modulus of monovacancy, divacancy and defect free case in Sb doped Ge crystal, and the related elastic modulus were compared. According to Pugy criterion, the B/G(bulk modulus/shear modulus) value increased from 1.38 for defect free case to a range of 1.59～1.73 for monovacancy and divacancy case, and the results showed that the antimony-vacancy complex could improve the plasticity of Ge crystal. This was also consistent with the conclusion obtained by using the Cauchy pressure to determine brittle and plasticity.
The first-principle theory software(CASTEP) was used to systematically study interaction between antimony and vacancies in germanium crystal, the possible structure models of monovacancy and divacancy were calculated, and the stability of related models were analyzed by comparing the binding energy. As the results showed, because of the introducing of antimony atom, vacancies tended to gather around with antimony atom, and formed antimony-vacancy complex in Ge crystal. For monovacancy case, the most stable structure was formed when the vacancy was located in the first nearest-neighboring of antimony atom, and the binding energy was-1.10 eV. For divacancy case, the most stable structure was formed when the divacancy was respectively located in the first and second nearest-neighboring of the same covalent bond branch of antimony atom, and the binding energy was-2.02 eV. Voigt-Reuss-Hill approximation was used to calculate elastic modulus of monovacancy, divacancy and defect free case in Sb doped Ge crystal, and the related elastic modulus were compared. According to Pugy criterion, the B/G(bulk modulus/shear modulus) value increased from 1.38 for defect free case to a range of 1.59～1.73 for monovacancy and divacancy case, and the results showed that the antimony-vacancy complex could improve the plasticity of Ge crystal. This was also consistent with the conclusion obtained by using the Cauchy pressure to determine brittle and plasticity.
引文
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[23] Fulcher B D,Cui X Y,Delley B,Stampfl C.Hardness analysis of cubic metal mononitrides from first principles [J].Physical Review B,2012,85(18):1614.
[24] Chen S,Lu J S,Xie M,Xia L,Pan Y,Hu J Q.First-principle investigation on mechanical performances of platinum-rhodium alloys [J].Chinese Jounal of Rare Metals,2015,39(3):276.(陈松,陆建生,谢明,夏璐,潘勇,胡洁琼.铂铑合金系基本力学性能的第一性原理研究 [J].稀有金属.2015,39(3):276.)
[25] Pugh S F.XCII.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J].Philosophical Magazine,2009,45(367):823.
[26] Pettifor D G.Theoretical predictions of structure and related properties of intermetallics [J].Metal Science Journal,1992,8(4):345.
[2] Markevich V P,Peaker A R,Hamilton B,Litvinov V V,Pokotilo Y M,Lastovskii S B,Coutinho J,Carvalho A,Rayson M J,Briddon P R.Tin-vacancy complex in germanium [J].Journal of Applied Physics,2011,109(8):201.
[3] Chroneos A,Bracht H,Grimes R W,Uberuaga B P.Vacancy-mediated dopant diffusion activation enthalpies for germanium [J].Applied Physics Letters,2008,92(17):172103.
[4] Chroneos A,Grimes R W,Tsamis C.Atomic scale simulations of donor-vacancy pairs in germanium [J].Journal of Materials Science Materials in Electronics,2007,18(7):763.
[5] Markevich V P,Hawkins I D,Peaker A R,Emtsev K V,Emtsev V V,Litvinov V V,Murin L I,Dobaczewski L.Vacancy-group-V-impurity atom pairs in Ge crystals doped with P,As,Sb,and Bi [J].Physical Review B,2004,70(70):155.
[6] Chroneos A,Grimes R W,Uberuaga B P,Bracht H.Diffusion and defect reactions between donors,C,and vacancies in Ge.II.Atomistic calculations of related complexes [J].Physical Review B,2008,77(23):235208.
[7] Brotzmann S,Bracht H.Intrinsic and extrinsic diffusion of phosphorus,arsenic,and antimony in germanium [J].Journal of Applied Physics,2008,103(3):3275.
[8] Tahini H,Chroneos A,Grimes R W,Schwingenschl?gl U,Bracht H.Diffusion of E centers in germanium predicted using GGA+U approach [J].Applied Physics Letters,2011,99(7):33508.
[9] Chen J,Wu T,Ma X,Wang L,Yang D.Ge-vacancy pair in Ge-doped Czochralski silicon [J].Journal of Applied Physics,2008,103(12):123519.
[10] Wang J,Fang F,Zhang X.An experimental study of cutting performance on monocrystalline germanium after ion implantation [J].Precision Engineering,2015,39:220.
[11] Fujita F E.Generation of vacancies in high-speed plastic deformation [J].Materials Science & Engineering A,2003,350(2):216.
[12] Zhu P P,Guo X F,Cui H B.Effect of point defects on physical and mechanical properties of B2-CoSc intermetallic studied by first-principles method [J].The Chinese Journal of Nonferrous Metals,2017,(8):1589.(朱攀攀,郭学锋,崔红保.点缺陷对B2-CoSc化合物物性影响的第一性原理研究 [J].中国有色金属学报,2017,(8):1589.)
[13] Clark S J,Segall M D,Pickard C J,Hasnip P J,Probert M I J,Refson K,Payne M C.First principles methods using CASTEP [J].Zeitschrift für Kristallographie,2005,220(5):567.
[14] Pfrommer B G,C?té M,Louie S G,Cohen M L.Relaxation of crystals with the quasi-newton method [J].Journal of Computational Physics,1997,131(1):233.
[15] Singh H P.Determination of thermal expansion of germanium,rhodium and iridium by X-rays [J].Acta Crystallographica,1968,24(4):469.
[16] Mattsson T R,Mattsson A E.Calculating the vacancy formation energy in metals:Pt,Pd,and Mo [J].Physical Review B Condensed Matter,2002,66(21):214110.
[17] Chroneos A,Uberuaga B P,Grimes R W.Carbon,dopant,and vacancy interactions in germanium [J].Journal of Applied Physics,2007,102(8):473.
[18] Chroneos A.Isovalent impurity-vacancy complexes in germanium [J].Physica Status Solidi.,2007,244(9):3206.
[19] Chroneos A,Grimes R W,Uberuaga B P,Brotzmann S,Bracht H.Vacancy-arsenic clusters in germanium [J].Applied Physics Letters,2007,91(19):195203.
[20] Nichols C S,Van de Walle C G,Pantelides S T.Mechanisms of dopant impurity diffusion in silicon [J].Physical Review B,1989,40(8):5484.
[21] Hill R.The elastic behaviour of a crystalline aggregate [J].Proceedings of the Physical Society,2002,65(5):349.
[22] Zhao H,Zhao Y H,Yang X M,Sui H M,Hou H,Han P D.First-principles study on elastic properties and electronic structure of Ca,Sr and Ba doped Mg2Si [J].Rare Metal Materials and Engineering,2015,(3):638.(赵慧,赵宇宏,杨晓敏,眭怀明,侯华,韩培德.Ca,Sr和Ba掺杂Mg2Si弹性性能和电子结构的第一性原理研究 [J].稀有金属材料与工程,2015,(3):638.)
[23] Fulcher B D,Cui X Y,Delley B,Stampfl C.Hardness analysis of cubic metal mononitrides from first principles [J].Physical Review B,2012,85(18):1614.
[24] Chen S,Lu J S,Xie M,Xia L,Pan Y,Hu J Q.First-principle investigation on mechanical performances of platinum-rhodium alloys [J].Chinese Jounal of Rare Metals,2015,39(3):276.(陈松,陆建生,谢明,夏璐,潘勇,胡洁琼.铂铑合金系基本力学性能的第一性原理研究 [J].稀有金属.2015,39(3):276.)
[25] Pugh S F.XCII.Relations between the elastic moduli and the plastic properties of polycrystalline pure metals [J].Philosophical Magazine,2009,45(367):823.
[26] Pettifor D G.Theoretical predictions of structure and related properties of intermetallics [J].Metal Science Journal,1992,8(4):345.