6
n ˘ Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101 ^1>A5[˜ * !c 0 · ( B²˘n˘, #.1>fÆE˜/, B 550025 ) ( 2011 c 6 23 F´; 2012 c 2 4 F´?Uv ) ^!gU PIC/MCC (particle-in-cell with Monte Carlo collision) {, [^1>L§, :?ºŒØ>>>6K. [(JL², dm^|lrfCz, >l4m>>L4m>>. 3LG, ØA ^ˇ'O 0.67 Pa 0.05 T; XO, >>6kO², L 2.5 Pa , > 6m'O~; 4>O, >>6Cq5O\. c: ^, 1>, O¯[, G' PACS: 51.50.+v, 52.20.Hv, 52.65.-y 1 X>fu, ^¨E 2A^u«Æ ¥ [1] . du^|P^, ^>3 $>e?1. {D {, ^{kp!$§üw˝ A:, ˜(, p, U3. ¨?¿7Æ7Æ [2,3] . k^ ¯n˜:8¥3XJpq¡>6' !5, lJpqÆ|^˙; XO\ Nmlz˙9f$˙, l Jp˙; X3!! , lƒEz. øK, kuØ^>A5?1\˜. ^ >Æu~1>˘, Œ[·˜ >L§kˆª. Œ[¡Øü f$˜-E?1l, ˜fN1; ,¡qØf$˜?1O, ˜ f8N1. 3>f*1 *Lym, Œ[ØX**x ø^, ¿¯u/˜^L§ «›{. f [ (PIC) Monte Carlo ( PIC/MCC (particle-in-cell with Monte Carlo collision) [4,5] {d Birdsall [6] Boswell [7] uı. lnw, PIC {˜u1n, ?bCq, lzf3\| §g-u|¥$˜, ˇLØ$˜f O²>A5*ºŒ. PIC/MCC {¥, f$˜d²; Newton-Lorentz $˜§ £ª, f-u|d²; Maxwell §|ƒ), fm-Ed Monte Carlo {£ª. XO ¯O;UJp, PIC/MCC {Ø$ !f>llfNL§[u/. Nı ˘^ PIC/MCC {˜^L§. 'z [2, 8, 9] Ø^>²m>' !>|'!>f'9q¡f6 '?1[?. k^3 ºŒ^e>=C˜. 'z [10] Ø ^¢*L², ^|r, ^ * I[g,˘˜7 (1O: 60766002)!EIS;˜7 (1O: 2008DFA52210)!B²E8 (1O: GY i [2011] 3015)!B²EM#<L;˜7 (1O: <L [2011] 4002) B²ISE8 (1O: G i [2012] 7004, G i [2009] 700113) ]ˇK' E-mail: [email protected] c 2012 ¥In˘Chinese Physical Society http://wulixb.iphy.ac.cn 165101-1

ŸŸŸ AAA555 - iphy.ac.cnwulixb.iphy.ac.cn/fileWLXB/journal/article/wlxb/2012/16/...ª 3 Ò4>ØØq¡lf6'Ù˙K‘ 0 4 0.2 Pa 1 Pa 3.5 Pa 8 12 16 b Ö 0 @ /10 20 m-2 S s-1 0 5 10 15

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  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    ^̂̂ííí���111>>>AAA555������[[[ïïïÄÄÄ*

    !c ��† �� 0 ´�

    ( B²ÆnÆ�, #.1>fá�EâïĤ, B� 550025 )

    ( 2011 c 6 � 23 F�; 2012 c 2 � 4 F�?Uv )

    æ^�!gU� PIC/MCC (particle-in-cell with Monte Carlo collision) {, �[^í�1>L§, :?Øóëêé>�ªÚ>>6�K. �[(JL², �óíØd��½m^|lr�fCz,>�ª¬lÒ4m>ÖÌ��>�ªLÞ��4m>ÖÌ��>�ª. 3LÞG�, éA�óíØ^ÏÝ©O 0.67 Pa Ú 0.05 T; XóíØ�O, >>6kO�ª²ï, �óíØL 2.5 Pa , >6m©óíØ�O~�; Ò4>ØO, >>6Cq5O\.

    'c: ^í�, 1>, OÅ�[, G�©Ù

    PACS: 51.50.+v, 52.20.Hv, 52.65.−y

    1 Ú ó

    X>f��×uÐ, ^í�ÈEâ�2A^u«��á�Ú��ì��¥ [1]. du^|�åP^, ^í�>±3�$�íØÚ>Øe?1. 'ý�Û{�DÚ��{, ^í�{äkp!$§üwÍA:, �Ä(ÜÐ, Ýp, U3ØÓ�.þÈ?¿7á½7á��� [2,3]. k'^í�ÅnïÄ��:Ì8¥3XÛJpq¡>6©ÙÝ�þ!5, lJpqá|^Ç; XÛO\óíN�mlzÇ9í��f�Ñ$Ç, lJpí��Ç; XÛ3ºÝþ¼�þ!!���, l¦í�Eâ�z. ù¯K�)û, Ñkué^í�>A5?1�\�ïÄ. ^í�>áu~1>Æ, ê�[´ïÄ>L§�k�Ãã. ê�[¡±éüâf�$ÄÚ-E?1l, ïÄâf�N1;,¡q±éþâf�$Ä?1ÚO, ïÄþâf�8N1. 3>âf�*1Ú÷

    *Lym, ê�[å�éX*Ú÷*�xù^, ¿ÅìuФïÄ^í�åL§�«{.

    â f � [ (PIC) Monte Carlo ( Ü� PIC/MCC (particle-in-cell with Monte Carlocollision)[4,5] {d Birdsall � [6] Ú Boswell � [7]

    uÐÚ�õ. l�nþw, PIC {Äu1�n,Ø?Ûb�ÚCq, �lzâf3\|Ú§g�-u|¥�$Ä, ÏLéþ$ÄâfÚO²þ��>A5�÷*ëê. PIC/MCC {¥, âf$Äd²;� Newton-Lorentz $ħ£ã, âf-u�|d²; Maxwell §|¦),âfm-Ed Monte Carlo {£ã. XOÅOÝÚ;Uå�Jp, PIC/MCC {é$íØ!f>l�lfNL§�[®uФÙ. NõÆö^ PIC/MCC {ïÄ^í��åL§.©z [2, 8, 9] é^í�>²ï��m>³©Ù!>|©Ù!>âfÝ©Ù9q¡âf6©Ù?1[�?Ø. k'^í�3ØÓóëê^e>�ª=C�ïÄ��. ©z [10] é^í��¢�*ÿL², �^|rÝ��, ^

    * I[g,ÆÄ7 (1OÒ: 60766002)!EÜISÜ;Ä7 (1OÒ: 2008DFA52210)!B²Eô'8 (1OÒ: `Ü GYi [2011] 3015)!B²EM#

  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    í�>´�Ç�p��4m>ÖÌ��> (PSC) �ª; , >?3�Ç�$�Ò4m>ÖÌ��> (NSC) �ª. ©z [11] æ^ PIC {é¶é¡6^í�>L§?1

    �[, uy�^|rÝ�±ØC, XóíØ�O, >l NSC �ªÅìLÞ� PSC �ª.�©Äu PIC/MCC {, æ^�mI, nÝI (2d3v) �·>�., 鲡6^í��1>L§?1�[, X?ØØÓóëêé^í�>�ªÚq¡>6�K.

    2 �[�.

    2.1 ���[[[666§§§

    3 PIC/MCC O¥, zâfL 106—109 ý¢�âf. äN�OÚ½ [12,13,14]: 1)ÏLéЩâf� ©ÙÚÝ©Ù�, ¦�m�:�>ÖÝ ρ Ú>6Ý j; 2) â�:� ρ Ú j, ) Maxwell §|, ¦�m�:�>| E Ú^ÏÝ B; 3) âm�:� EÚ B, ¦�âf¤3 �>|Ú^ÏÝ,(½âf¤É��å; 4) ) Newton-Lorentz §, íÄâf, ��âf#� ©ÙÚÝ©Ù;5) >.u�, é-�>.�âfA^A�>.^; 6) -Eu�, éu)-E�âfA^ MCC {, N�âf�Ý. d, JpOÝ, ±æ^ÉÚI{!ØÓ�âf!-E!¿1{�{ [12].

    2.2 ���[[[ëëëêêê

    �[¥Xeb�: x ¶ÏLqá¥%²1uq¡; y ¶Ruq¡; qá»� 60 mm, qáÚ.m�ål 60 mm. �g>fu�Xê� γ = 0.1, mÚ ∆x = ∆y = 0.1 mm, mÚ ∆t = 10−10 s. du>f$ÄÝ'lfݯ�õ, �>fz£Ä 10 gíÄlf 1 g, =� ∆te = 10∆ti = ∆t. Щ>f§Ý� 5 eV, �lf§Ý� 0.026 eV. Щ>fÝÚ�lfÝÑ 1015 m−3, þ!©Ù3>m¥, §�ЩÝÑl Maxwell ©Ù. �[¥ÄXeâfm�-E:

    e + Ar → Ar + e, (1)

    e + Ar → Ar+ + e + e, (2)

    Ar+ + Ar → Ar + Ar+. (3)

    3ïÄ>�ª�=C, Bå, À^þ!�^|©Ù. ?Øóëêé>>6�K, Ä>m¥ý¢�^|©Ù, [^N3>m¥�^|©Ùdk�©Û^ ANSYS�[��.

    3 �[(J?Ø

    3.1 óóóëëëêêêééé>>>���ªªª���KKK

    � ± ^ Ï Ý B = 0.03 T Ø C, ó íØ p = 0.1—5 Pa SCz, ïÄØÓóíØé>�ª�K. �[(JL²: �íØ�$,>>ØÜ©üá3C.��4, /¤²w��4 ü«, d�>�ª NSC �ª. XóíØ�ÅìO, �4 ü«�>³�m©~�. dÓ, CqáÒ4à�>³á�m©O, /¤Ò4 ü«. �óíØ p = 0.67 Pa m, �4 ü«ÚÒ4 ü«�>³�Cq�,3>m¥UÓ*�²w��4 ü«ÚÒ4 ü«. d�, XóíØ�UYO, �4 ü«Åì, � p = 4 Pa m, U*�²w�Ò4 ü«, d, >ÅnLÞ� PSC �ª. ã 1 ÑóíØ p = 0.13, 0.67 Ú 4.0 Pa >m¥�>³©Ù, ©OL NSC �ª!LÞ�ªÚ PSC �ª.

    �±óíØ p = 0.67 Pa ØC, ^ÏÝ B3 0.01—0.1 T SCz, ïÄØÓ^|rÝé>�ª�K, (JXã 2 ¤«. � B ��, >?u PSC �ª; � B O\� 0.05 T , UÓ*�²w��4 üÚÒ4 ü, >?uLÞ�ª; � B O\� 0.1 T , Ò4 ü, >>ØÜ©üá3�4 ü«, >�ª= NSC �ª.

    óíØÚ^|rÝé>�ª�K±^>âf3��>^|¥�[£Ç5½5)º.^ µ′ L«>âf3k^|3R^|�[£Ç, µ L«>âf3Ã^|�[£Ç.K µ′ Ú µ 3Xe'X:

    µ′ =µ

    1 + (ω/ν)2

    165101-2

  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    电势/V

    0 0

    (a)

    20

    -500

    -400

    -300

    -200

    -100

    0

    20

    4060

    4060

    x/mm y/mm

    电势/V

    0 0

    (b)

    20

    -500

    -400

    -300

    -200

    -100

    0

    20

    4060

    40 60x/mmy/mm

    电势/V

    0 0

    (c)

    20

    -500

    -400

    -300

    -200

    -100

    0

    20

    4060

    4060

    x/mmy/m

    m

    ã 1 ØÓóíØ^e�>³©Ù, B = 0.03 T(a) p = 0.13 Pa; (b) p = 0.67 Pa; (c) p = 4.0 Pa

    电势/V

    0 0

    (a)

    20

    -500

    -400

    -300

    -200

    -100

    0

    20

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    60

    4060

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    电势/V

    0 0

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    40 60x/mm

    y/mm

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    0

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    4060

    4060

    x/mmy/mm

    ã 2 ØÓ^ÏÝ^e�>³©Ùã, p = 0.67 Pa(a) B = 0.02 T; (b) B = 0.05 T; (c) B = 0.1 T

    Ù¥ ω >âf�£^ªÇ, ν >âf¥5íN�-EªÇ. Ã^|3, >fÚlf�[£Ç©O µe = q/meνen, µi = q/miνin, ª¥ qü >Ö>þ, me, mi ©O>fÚ�lfþ, νen, νin ©O>fÚ�lf¥5íN�-EªÇ. du mi À me, �k µe À µi, =Ã^|, >f3>|¥�¤£Ý¬��ulf�¤£Ý. �>�²ï, >6Åð¦lfÝÚ>fÝ�, ùÒI3qáNCk�>³�5\lf�$Ä, 3.NC, du>fÝ®v¯, ØI�>³�\, Ïd,Ü©>>Øüá�qáNC, /¤Ò4 ü

    «, >�ª PSC �ª. 3^|¥, du^|�åP^, �^|�½íØ�$¬k ωe À νen,>f3^|¥�[£Ç µ′e 'Ã^|� µe ¬k4~�. lfduþé, ^|élf�Ké�, �lf3^|¥�[£Ç µ′i ÚÃ^|� µi 'Ä��±ØC. ù�, X^|�O½óíØ�~�, >f[£Ç¬~�lf[£ÇCq±ØC. � µ′e < µ′i , >f.�Ñ$Ý�ulfqá�Ñ$Ý. d, �y>²ï>fÝÚlfÝ�, ÒI3.NCk�>³�5\>f�$Ä, �4 ü«/¤, >�ªLÞ� NSC �ª.

    165101-3

  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    3.2 óóóëëëêêêééé>>>>>>666���KKK

    3.2.1 q¡lf6©Ù

    ïÄý¢^|©Ù^eóíØÚÒ4>Øé^í�>>6�K. [^N�)�^|3>m�©Ùdk�©Û^ ANSYS �[��. �[�^í�C¥IÆ�!�Ƥìï¥%ï� JGP560C VIII .í£�pýõq^í�Û�XÚ. ã 3 Úã 4 ©OÑØÓÒ4>ØÚóíØéq¡lf6©Ù�K. ±wÑ, XÒ4>Ø�O, q¡lf6Cq5O, �óíØO, lf6kO�~�. ©z[2] ¥é6^í��ê�[���©aq�©Ù. �>ØO,>f±3>m¥��õ�Uþ, óíNu)õ�lz-E, �)õ�lf. d, �>ØO, lf�q¡�ݬO,

    0

    0

    5

    5

    10

    10

    15

    15

    x/mm

    氩离子流

    /

    20 m

    -2Ss

    -1

    20

    20

    25

    750 V

    600 V

    450 V

    30

    ã 3 Ò4>Øéq¡lf6©Ù�K

    0

    4

    0.2 Pa

    1 Pa

    3.5 Pa

    8

    12

    16

    氩离子流

    /

    20 m

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    -1

    0 5 10 15

    x/mm

    20 25 30

    ã 4 óíØéq¡lf6©Ù�K

    �>ØO, q¡lf6O. �óíØ�$, >f�£^ªÇ�u>fóíN�-EªÇ, =k ωe À νen. ù«¹e, ^|é>fåP^ér, >f�$ÄÌd>|Ú^|û½.�óíØO, >fóíN-E�VÇC, õ�-E�)õ�lf. dd, �óíØ�$, XóíØO, q¡lf6O. UYOóíØ, >f¥5íN�-EªÇ νen ¬×O, 3½�^|(�e,ωe ØC. �óíØO�½, νen Åì�C ωe, >^|é>f�åP^Åì~f, ��´>f¥5íNþÃ5K�-E. du�^|�åP^, >f3>m¥�Æ·Cá,¥5íN-E�gê¬~�. Ïd�óíØL½�, XóíØ�O, q¡lf6~�. ?Ú��[y¢ù:.ã 5 ÑóíØ p = 1 Ú 4 Pa >m¥�>fÝ©Ù. lã 5 ±wÑ, p = 1 Pa , ^|é>f�åP^ér, ^|�r�:éA�>fÝ�, 3^|r�ü:/¤üwÍ�©Ù¸; � p = 4 Pa , >m¥>f©Ùªþ!, `²^|é>fåP^~f.

    电子密度

    /16 m

    3

    0

    0 0

    (a)

    2020

    4060

    4060

    1

    2

    3

    x/mmy/m

    m

    电子密度

    /16 m

    3

    0

    0 0

    (b)

    20 20

    4040

    6060

    2

    4

    6

    8

    x/mm y/mm

    ã 5 ØÓóíØ^e�>fÝ©Ù (a) p = 1Pa; (b) p = 4 Pa

    165101-4

  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    3.2.2 q¡>6�Oq¡>6Ý j(r) = qniυi , ª¥, q ü >

    Ö>þ, ni Ú υi �q¡�lfÝ9ÙéA�Ý. >6Ý3q¡¥¶é¡©Ù, q¡o>6

    I =∫ R

    0

    2πrj(r)dr,

    ª¥ R qá». �[Oq¡>6óíØÚÒ4>Ø�'X, ¿¢�ÿþêâ?1'�, ¤�(JXã 6 Úã 7 ¤«.

    ã 6 >>6óíØ�'X

    dd±wÑ, p < 0.5 Pa , >>6óíØ�,p×O, �>>6ªu²ï,�ó p > 2.5 Pa , >>6m©óíØ�,p~�. �Ò4>ØO, >>6Cq5

    O.

    ã 7 >>6Ò4>Ø�'X

    4 ( Ø

    é^í�1>L§��[L², �>m¥^|�r½óíØ�$, >�ªN´?u�Ç�$� NSC �ª, ,�r�^|¦>f£^»L�, Ø|u>fl>|��Uþ; óíØL�, >fíN-EVÇ~�, Ø|u>�±. Ïd3^í�(��OÚóëê�À�, ^|ØU�r, óíØØU�$. â�[���>>6óíØ�'X, Lp�óíج�>6eü, ü$í��Ç.éu²¡6^í�ó, �n�^ÏÝ 0.03 T m, óíØ 1.0 Pa m.

    [1] Shon C H, Lee J K 2002 Appl. Surf. Sci. 192 258[2] Kolev I, Bogaerts A 2009 J. Vac. Sci. Technol. A 27 20[3] Li Y P, Liu Z T, Zhao H L, Liu W T, Yan F 2007 Acta Phys. Sin. 56

    2937 (in Chinese) [o�², 4�,, ë°9, 4©x, A¸ 2007ÔnÆ� 56 2937]

    [4] Verboncoeur J P 2005 Plasma Phys. Contr. Fusion 47 A231[5] Jin X L, Yang Z H 2006 Acta Phys. Sin. 55 5930 (in Chinese) [7

    ¡�, ¥° 2006 ÔnÆ� 55 5930][6] Birdsall C K, Langdon A B 1985 Plasma Physics via Computer

    Simulation (New York: McGraw-Hill) p7

    [7] Boswell R W, Morey I J 1988 Appl. Phys. Lett. 52 21[8] Shon C H, Lee J K 1998 IEEE Trans. Plasma Sci. 26 1635

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    (Berlin: Springer Publishing) p130

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    165101-5

  • Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101

    Computer simulation of the glow dischargecharacteristics in magnetron sputtering∗

    Shen Xiang-Qian Xie Quan† Xiao Qing-Quan Chen Qian Feng Yun

    ( Institute of Advanced Optoelectronic Materials and Technology, College of Science, Guizhou University, Guiyang 550025, China )

    ( Received 23 June 2011; revised manuscript received 4 February 2012 )

    Abstract

    In this paper, the process of glow discharge in magnetron sputtering is studied by the particle-in-cell with Monte Carlo collision

    method. The proposed model is a two-dimensional and self-consistent approach. The results show that the discharge mode transits from

    the negative space-charge-dominated mode to positive space-charge-dominated mode with working pressure increasing or magnetic

    field weakening. At the transition state, working pressure and magnetic field are 0.67 Pa and 0.05 T, respectively. Discharge current

    increases as the cathode voltage increases. When pressure increases, discharge current first increases and then tends to balance. When

    the pressure is higher than 2.5 Pa, current begins to decreases with the increase of the pressure.

    Keywords: magnetron sputtering, glow discharge, computer simulation, state distributionPACS: 51.50.+v, 52.20.Hv, 52.65.−y

    * Project supported by the National Natural Science Foundation of China (Grant No. 60766002), the Special Foundation for International Cooper-

    ation of the Ministry of Science and Technology of China (Grant No. 2008DFA52210), the Science and Technology Research Project of Guizhou

    Province, China (Grant No. [2011] 3015), the Special Fund for Construction of Sci-Tech Innovative Talents Team of Guizhou Province, China

    (Grant No. [2011] 4002), and the Fund for International Sci-Tech Cooperation of Guizhou Province, China (Grant Nos. [2012] 7004, [2009]

    700113).

    † E-mail: [email protected]

    165101-6