Anylasis and comparison of several methods for calculation of positron bulk lifetime in perfect crystals

Huang Shi-Juan; Zhang Wen-Shuai; Liu Jian-Dang; Zhang Jie; Li Jun; Ye Bang-Jiao

doi:10.7498/aps.63.217804

Abstract

Positron annihilation lifetime spectroscopy, which takes positron lifetime as a detected object, has been widely applied to the study on micro-defects of semiconductors and other materials, and is very sensitive to the type of crystal structure, defect types, and temperature, and so on. Therefore, the analysis of fast and accurate calculation of positron lifetime theoretically combined with the experimental data is particularly necessary. In this paper, the superposed neutral atom model, the pseudo-potential model, and the full-potential model are used to deal with the positron local potential. While the positron wave function is solved self-consistently by the finite difference method, the positron-electron correlation potential and its enhancement factor are handled within the frame work of the local density approximation and the generalized gradient approximation. We have respectively calculated the positron bulk lifetime of three kinds of single crystal solid: the alpha iron of a body-centered cubic structure, the aluminum of a face-centered cubic structure, and the silicon of a double face-centered cubic structure. Calculation results agree well with the published experimental data. At the same time, the impact on positron bulk lifetime due to electron density grid point accuracy, positron-electron correlation potential and enhancement factor is analyzed carefully. Finally, we discuss the advantages and disadvantages of the three methods for calculating the positron bulk lifetime. In summary, an effective and reasonable calculation for the positron bulk lifetime should take into account the electron density, positron-electron correlation potential, and enhancement factor, etc. especially the enhancement factor.

Keywords:

positron bulk lifetime /
perfect crystals /
positron-electron correlation potential /
enhancement factor

Authors and contacts

1.
State Key Laboratory of Particle Detection and Electronics(IHEP &USTC), University of Science and Technology of China, Hefei 230026, China;
2.
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;
3.
Institute of Plasma Physics, University of Science and Technology of China, Hefei 230026, China
Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175171, 11105139).

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[73]	Zhang J, Liu J D, Chen X L, Ye B J 2010 Chin. Phys. B 19 117802
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[75]
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[79]	Kuriplach J, Barbiellini B 2014 Phys. Rev. B 89 155111
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[91]
[92]	Campillo-Robles J M, Ogando E, Plazaola F 2012 Solid State Sciences 14 982
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[94]	Lu T, Chen F W 2012 J. Comp. Chem 33 580
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[96]	Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson G A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J L, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery J A, Peralta Jr, J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam J M, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A D, Farkas , Foresman J B, Ortiz J V, Cioslowski J, Fox D J, Gaussian, Inc., Wallingford CT 2009
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[107]	Blaha P, Schwarz K, Sorantin P, Trickey S B 1990 Comput. Phys. Commun. 59 399
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Cited By

[1]	Zhang L J, Wang L H, Liu J D, Li Q, Cheng B, Zhang J, An Ran, Zhao M L, Ye B J 2012 Acta Phys. Sin. 61 237805 (in Chinese) [张丽娟, 王力海, 刘建党, 李强, 成斌, 张杰, 安然, 赵明磊, 叶邦角 2012 61 237805]
[2]	Zhang Y H, Li Y L, Gu Y, Chao Y S 2012 Acta Phys. Sin. 61 167502 (in Chinese) [张艳辉, 李彦龙, 谷月, 晁月盛 2012 61 167502]
[3]
[4]
[5]	Zhang M L, Yang R X, Li Z X, Cao X Z, Wang B Y, Wang X H 2013 Acta Phys. Sin. 62 117103 (in Chinese) [张明兰, 杨瑞霞, 李卓昕, 曹兴忠, 王宝义, 王晓晖 2013 62 117103]
[6]
[7]	Liu J D, Cheng B, Zhang J, Zhang L J, Weng H M, Ye B J 2011 Chin. Phys. B 20 108105
[8]	Gong J, Gong Z L, Yan X L, Gao S, Zhang Z L, Wang B 2012 Chin. Phys. B 21 107803
[9]
[10]
[11]	Yu W Z 2003 Positron Physics and its Application (Beijing: Science Press) p2 (in Chinese) [郁伟中 2003 正电子物理及其应用(北京: 科学出版社) 第2页]
[12]	Xiao C, Qin X M, Zhang J, An R, Xu J, Li K, Cao B X, Yang J L, Ye B J, Xie Y 2012 J. Am. Chem. Soc. 134 18460
[13]
[14]
[15]	Guan M L, Xiao C, Zhang J, Fan S J, An R, Cheng Q M, Xie J F, Zhou M, Ye B J, Xie Y 2013 J. Am. Chem. Soc. 135 10411
[16]	Nieminen R M, Boronski E, Lantto L J 1985 Phys. Rev. B 32 1377
[17]
[18]	Boronski E, Nieminen R M 1986 Phys. Rev. B 34 3820
[19]
[20]
[21]	Puska M J, Nieminen R M 1983 J. Phys. F: Met. Phys. 13 333
[22]	Fong C Y, Marvin. L. Cohen 1970 Phys. Rev. Lett. 24 306
[23]
[24]
[25]	Hamann D R, Schluter M, Chiang C 1979 Phys. Rev. Lett. 43 1494
[26]
[27]	David Vanderbilt 1990 Phys. Rev. B 41 7892
[28]	Blochl P E 1994 Phys. Rev. B 50 17953
[29]
[30]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[31]
[32]	Anderson O K 1975 Phys. Rev. B 12 3060
[33]
[34]
[35]	Weyrich K H 1988 Phys. Rev. B 37 10269
[36]	Wimmer E, Krakauer H, Weinert M, Freeman A J 1981 Phys. Rev. B 24 864
[37]
[38]
[39]	Jansen H J F, Freeman A J 1984 Phys. Rev. B 30 561
[40]
[41]	Daniuk S, Sob M, Rubaszek A 1991 Phys. Rev. B 43 2580
[42]	Barbiellini B, Puska M J, Torsti T, Nieminen R M 1995 Phys. Rev. B 51 7341
[43]
[44]	Rubaszek A, Szotek Z, Temmerman W M 1998 Phys. Rev. B 58 11285
[45]
[46]	Puska M J, Corbel C, Nieminen R M 1990 Phys. Rev. B 41 9980
[47]
[48]
[49]	Puska M J, Nieminen R M 1994 Rev. Mod. Phys. 66 841
[50]	Puska M J, Lanki P, Nieminen R M 1989 J. Phys.: Condens. Matter 1 6081
[51]
[52]
[53]	Chen X L, Xi C Y, Ye B J, Weng H M 2007 Acta Phys. Sin. 56 6695 (in Chinese) [陈祥磊, 郗传英, 叶邦角, 翁惠民 2007 56 6695]
[54]
[55]	Chen X L, Kong W, Weng H M, Ye B J 2008 Acta Phys. Sin. 57 3271 (in Chinese) [陈祥磊, 孔伟, 翁惠民, 叶邦角 2008 57 3271]
[56]	Chen X L, Guo W F, Du H J, Weng H M, Ye B J 2009 Matter. Sci. Forum 607 146
[57]
[58]
[59]	Chen X L, Kong W, Du H J, Ye B J 2009 Acta Phys. Sin. 58 7627 (in Chinese) [陈祥磊, 孔伟, 杜淮江, 叶邦角 2009 58 7627]
[60]
[61]	Chen X L 2009 Ph. D. Dissertation (Hefei: the University of Science and Technology of China) (in Chinese) [陈祥磊 2009 博士学位论文 (合肥:中国科学 17 与技术大学)]
[62]
[63]	Tang Z, Hasegawa M, Nagai Y, Saito M, Kawazoe Y 2002 Phys. Rev. B 65 045108
[64]
[65]	Tang Z, Hasegawa M, Nagai Y, Saito M 2002 Phys. Rev. B 65 195108
[66]
[67]	Liu J D 2010 Ph. D. Dissertation (Hefei: the University of Science and Technology of China) (in Chinese) [刘建党 2010 博士学位论文 (合肥:中国科学与技术大学)]
[68]
[69]	Liu J D, Zhang J, Zhang L J, Hao Y P, Guo W F, Cheng B, Ye B J 2011 Chin. Phys. B 20 57802
[70]	Zhang J 2013 Ph. D. Dissertation (Hefei: the University Science and Technology of China) (in Chinese) [张杰 2010 博士学位论文(合肥:中国科学与技术大学)]
[71]
[72]
[73]	Zhang J, Liu J D, Chen X L, Ye B J 2010 Chin. Phys. B 19 117802
[74]	Zhang J, Chen X L, Ye B J 2010 Chin. Phys. B 19 77806
[75]
[76]	Drummond N D, Lopez Rios P, Needs R J, Pickard C J 2011 Phys. Rev. Lett. 107 207402
[77]
[78]
[79]	Kuriplach J, Barbiellini B 2014 Phys. Rev. B 89 155111
[80]
[81]	Zhang W S, Liu J D, Zhang J, Huang S J, Li J, Ye B J 2014 JJAP Conference Proceedings of the 2nd Japan-China Joint Workshop on Positron Science Tsukuba, Japan, December 20-23, 2013 (会议文集)
[82]	David M. Schrader 1970 Phys. Rev. A 1 1070
[83]
[84]
[85]	Puska M J, Ari P. Seitsonen, Nieminen R M 1995 Phys. Rev. B 52 10947
[86]	Siegel R W 1980 Ann. Rev. Mater. Sci. 10 393
[87]
[88]	Hohenberg P, Kohn W 1964 Phys. Rev. B 136 864
[89]
[90]	Kohn W, Sham L J 1965 Phys. Rev. A 140 1133
[91]
[92]	Campillo-Robles J M, Ogando E, Plazaola F 2012 Solid State Sciences 14 982
[93]
[94]	Lu T, Chen F W 2012 J. Comp. Chem 33 580
[95]
[96]	Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson G A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J L, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery J A, Peralta Jr, J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam J M, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A D, Farkas , Foresman J B, Ortiz J V, Cioslowski J, Fox D J, Gaussian, Inc., Wallingford CT 2009
[97]
[98]
[99]	Kresse G, Hafner J 1993 Phys. Rev. B 47 R558
[100]
[101]	Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169
[102]	Blochl P E 1994 Phys. Rev. B 50 17953
[103]
[104]
[105]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[106]
[107]	Blaha P, Schwarz K, Sorantin P, Trickey S B 1990 Comput. Phys. Commun. 59 399
[108]	Campillo-Robles J M, Ogando E, Plazaola F 2007 J. Phys.: Condens. Matter 19 176222
[109]

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