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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�$,>>ØÜ©üá3C.��4, /¤²w��4 ü«, d�>�ª NSC �ª. XóíØ�ÅìO, �4 ü«�>³�m©~�. dÓ, CqáÒ4à�>³á�m©O, /¤Ò4 ü«. �óíØ p = 0.67 Pa m, �4 ü«ÚÒ4 ü«�>³�Cq�,3>m¥UÓ*�²w��4 ü«ÚÒ4 ü«. d�, XóíØ�UYO, �4 ü«Åì, � p = 4 Pa m, U*�²w�Ò4 ü«, d, >ÅnLÞ� PSC �ª. ã 1 ÑóíØ p = 0.13, 0.67 Ú 4.0 Pa >m¥�>³©Ù, ©OL NSC �ª!LÞ�ªÚ PSC �ª.
�±óíØ p = 0.67 Pa ØC, ^ÏÝ B3 0.01—0.1 T SCz, ïÄØÓ^|rÝé>�ª�K, (JXã 2 ¤«. � B ��, >?u PSC �ª; � B O\� 0.05 T , UÓ*�²w��4 üÚÒ4 ü, >?uLÞ�ª; � B O\� 0.1 T , Ò4 ü, >>ØÜ©üá3�4 ü«, >�ª= NSC �ª.
óíØÚ^|rÝé>�ª�K±^>âf3��>^|¥�[£Ç5½5)º.^ µ′ L«>âf3k^|3R^|�[£Ç, µ L«>âf3Ã^|�[£Ç.K µ′ Ú µ 3Xe'X:
µ′ =µ
1 + (ω/ν)2
165101-2
Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101
电势/V
0 0
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20
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-400
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ã 1 ØÓóíØ^e�>³©Ù, B = 0.03 T(a) p = 0.13 Pa; (b) p = 0.67 Pa; (c) p = 4.0 Pa
电势/V
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ã 2 ØÓ^ÏÝ^e�>³©Ùã, p = 0.67 Pa(a) B = 0.02 T; (b) B = 0.05 T; (c) B = 0.1 T
Ù¥ ω >âf�£^ªÇ, ν >âf¥5íN�-EªÇ. Ã^|3, >fÚlf�[£Ç©O µe = q/meνen, µi = q/miνin, ª¥ qü >Ö>þ, me, mi ©O>fÚ�lfþ, νen, νin ©O>fÚ�lf¥5íN�-EªÇ. du mi À me, �k µe À µi, =Ã^|, >f3>|¥�¤£Ý¬��ulf�¤£Ý. �>�²ï, >6Åð¦lfÝÚ>fÝ�, ùÒI3qáNCk�>³�5\lf�$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
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5
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20
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600 V
450 V
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ã 3 Ò4>Øéq¡lf6©Ù�K
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1 Pa
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8
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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�$, XóíØO, q¡lf6O. UYOóíØ, >f¥5íN�-EªÇ νen ¬×O, 3½�^|(�e,ωe ØC. �óíØO�½, νen Åì�C ωe, >^|é>f�åP^Åì~f, ��´>f¥5íNþÃ5K�-E. du�^|�åP^, >f3>m¥�Æ·Cá,¥5íN-E�gê¬~�. Ïd�óíØL½�, XóíØ�O, q¡lf6~�. ?Ú��[y¢ù:.ã 5 ÑóíØ p = 1 Ú 4 Pa >m¥�>fÝ©Ù. lã 5 ±wÑ, p = 1 Pa , ^|é>f�åP^ér, ^|�r�:éA�>fÝ�, 3^|r�ü:/¤üwÍ�©Ù¸; � p = 4 Pa , >m¥>f©Ùªþ!, `²^|é>fåP^~f.
电子密度
/16 m
3
0
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2020
4060
4060
1
2
3
x/mmy/m
m
电子密度
/16 m
3
0
0 0
(b)
20 20
4040
6060
2
4
6
8
x/mm y/mm
ã 5 ØÓóíØ^e�>fÝ©Ù (a) p = 1Pa; (b) p = 4 Pa
165101-4
Ô n Æ � Acta Phys. Sin. Vol. 61, No. 16 (2012) 165101
3.2.2 q¡>6�Oq¡>6Ý j(r) = qniυi , ª¥, q ü >
Ö>þ, ni Ú υi �q¡�lfÝ9ÙéA�Ý. >6Ý3q¡¥¶é¡©Ù, q¡o>6
I =∫ R
0
2πrj(r)dr,
ª¥ R qá». �[Oq¡>6óíØÚÒ4>Ø�'X, ¿¢�ÿþêâ?1'�, ¤�(JXã 6 Úã 7 ¤«.
ã 6 >>6óíØ�'X
dd±wÑ, p < 0.5 Pa , >>6óíØ�,p×O, �>>6ªu²ï,�ó p > 2.5 Pa , >>6m©óíØ�,p~�. �Ò4>ØO, >>6Cq5
O.
ã 7 >>6Ò4>Ø�'X
4 ( Ø
é^í�1>L§��[L², �>m¥^|�r½óíØ�$, >�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
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[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
[9] Zhao H Y, Mu Z X 2008 Chin. Phys. B 17 1475[10] Wasa K, Kitabatake M 2003 Thin Film Materials Technology
(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