Contribution for Sputtering Due to Undeveloped Collision Cascade
Takahiro KENMOTSU
(Received March 4, 2010)
The existing theoretical models for sputtering are derived from the general Boltzmann transport equation based on the well developed collision cascade. Experimental results have indicated that the theories describe sputtering phenomenon well in high energy, and nearly unity mass ratio of the projectile to the targetile. However, the collision cascades do not developed well in low-energy and/or light ion injections into metal targets. The reason for observing the deviation from theories is considered in these cases. In order to quantify the deviation, a Monte Carlo simulation code ACAT has been used to calculate sputtering due to low energy and/or light ions incidences. The ACAT code numerically calculates trajectories of atoms colliding in an amorphous target based on the binary collision approximation. The ACAT results have indicated that energy distributions of sputtered atoms were different from Thompson-Sigmund theory due to low-energy light ions incidence.
.
.H\ZRUGsputtering, collision cascade, Monte Carlo simulation
࢟
࣮࣮࢟࣡ࢻ㸸
ࢫࣃࢵࢱࣜࣥࢢ㸪⾪✺࢝ࢫࢣ࣮ࢻ㸪ࣔࣥࢸ࣭࢝ࣝࣟࢩ࣑࣮ࣗࣞࢩࣙࣥ
ᑡ
ᑡᩘᅇ⾪✺ᶵᵓࡼࡿࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࡢᐤ ᐤ
ᣢ ㈗ᘯ
㸯
㸯㸬 ࡣ ࡣࡌࡵ
㐠ື࢚ࢿࣝࢠ࣮ࢆࡶࡗࡓ⢏Ꮚࡀᅛయࢱ࣮ࢤࢵ
ࢺ⾲㠃ࡽධᑕࡍࡿ㸪ࢱ࣮ࢤࢵࢺཎᏊ⾪✺ࡍࡿ
ࡇࡼࡗ࡚㊴ཎᏊࢆ⏕ᡂࡍࡿ㸬⏕ᡂࡉࢀࡓ㊴ ཎᏊࡣධᑕ⢏Ꮚྠࡌാࡁࢆࡋ㸪ูࡢࢱ࣮ࢤࢵࢺཎ Ꮚ⾪✺ࡍࡿࡇࡼࡗ࡚᪂ࡓ㊴ཎᏊࢆ⏕ࡳ
ฟࡍ㸬ࡇࡢᅛయෆ࡛ࡢ⾪✺ࡢ㐃㙐ࡢࡇࢆ⾪✺࢝ࢫ ࢣ࣮ࢻ࠸࠸㸪ࡇࡢ⾪✺࢝ࢫࢣ࣮ࢻࡀࢱ࣮ࢤࢵࢺ⾲
㠃ࡲ࡛Ⓨ㐩ࡋ㸪⾲㠃᪉ྥࢱ࣮ࢤࢵࢺཎᏊࡀࡣࡌࡁ ฟࡉࢀࡓࡁ㸪ࡑࡢ㊴ཎᏊࡀ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮
ࡼࡾࡁ࡞࢚ࢿࣝࢠ࣮ࢆࡶࡗ࡚࠸ࡿሙྜ㸪ࢱ࣮ࢤࢵ
ࢺཎᏊࡣᅛయ⾲㠃ࡽᨺฟࡉࢀࡿ㸬ࡇࡢ⌧㇟ࢆࢫࣃ
ࢵࢱࣜࣥࢢ࠸࠺㸬ࡇࡢࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࡣ⌧
ᅾ㸪ⷧ⭷స〇㸪ᚤ㔞ศᯒ࡞ࡢᕤᴗศ㔝ᗈࡃ ᛂ⏝ࡉࢀ࡚࠸ࡿ㸬ࡲࡓ㸪᰾⼥ྜᐇ㦂⨨ࡢቨᮦᩱ㸱
ࡸ㸪↷᫂ᶵჾࡢᨺ㟁ࡢ㟁ᴟࡢᦆ⪖㸲࡞ࡶ㸪ࢫࣃ
ࢵࢱࣜࣥࢢࡼࡗ࡚ᘬࡁ㉳ࡇࡉࢀࡿࡇࡀ▱ࡽࢀ
࡚࠸ࡿ㸬
ࢫࣃࢵࢱࣜࣥࢢࡢཎᅉࡣ㸪㐠ື࢚ࢿࣝࢠ࣮ࢆࡶ
ࡗࡓධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ↷ᑕࡉࢀࡿࡇࡼ
ࡗ࡚⏕ࡳฟࡉࢀࡿ⾪✺࢝ࢫࢣ࣮ࢻࡀᅛయ⾲㠃࡛Ⓨ
㐩ࡍࡿࡇࡼࡿ㸬⌧ᅾࡲ࡛ࡢࡇࢁ㸪ࡇࡢࢫࣃࢵ
ࢱࣜࣥࢢ⌧㇟ᑐࡍࡿ⌮ㄽⓗ࡞ྲྀࡾᢅ࠸ࡣ㸪༑ศ⾪
✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋࡓሙྜᑐࡋ࡚ࡔࡅ᭷ຠ࡛
࠶ࡾ㸪ධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ሙྜࡸ㸪ධᑕ⢏Ꮚࡀ Ỉ⣲ཎᏊ࡞ࡢ㍍࢜ࣥࡢሙྜࡣ㸪ࡇࡢ⾪✺࢝ࢫࢣ
*Department of Biomedical Engineering
Telephone: +81-774-65-6687, E-mail: tkenmots@mail.doshisha.ac.jp
.H\ZRUG
࣮࣮࢟࣡ࢻ㸸
ᑡᩘᅇ⾪✺ᶵᵓࡼࡿࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࡢᐤ
㸯㸬 ࡣࡌࡵ
࣮ࢻࡀ༑ศⓎ㐩ࡏࡎ㸪ࡑࡢሙྜࡢࢫࣃࢵࢱࣜࣥࢢ
⌧㇟ࡣ⌮ㄽⓗண ࡉࢀࡿࡿ⯙࠸␗࡞ࡿࡶࡢ
⪃࠼ࡽࢀࡿ㸬
ᮏ◊✲࡛ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸
పධᑕ࢚ࢿࣝࢠ࣮㸪㍍࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡘ࠸
࡚㸪ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻACATࢆ⏝࠸࡚㸪ࢫ
ࣃࢵࢱࣜࣥࢢᑐࡍࡿᑡᩘᅇ⾪✺ࡢᐤࡘ࠸࡚
ゎᯒࢆ⾜࠸㸪⌮ㄽࡢ㐪࠸ࢆ᳨ドࡋࡓ㸬
㸬
㸬ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ
$$&$7 ࢫࣃࢵࢱࣜࣥࢢࡢࢩ࣑࣮ࣗࣞࢩࣙࣥゎᯒ㛵 ࡋ࡚㸪⌧ᅾࡲ࡛2య⾪✺㏆ఝἲࣔࣥࢸ࢝ࣝࣟἲࢆࡶࡋࡓࢩ࣑࣮ࣗࣞࢩࣙࣥࢥ࣮ࢻࡀᗄࡘ㛤
Ⓨࡉࢀ࡚࠾ࡾ㸪ࢫࣃࢵࢱࣜࣥࢢ㔞࡞ከࡃࡢ᭷⏝
࡞ࢹ࣮ࢱࡀ⏕ᡂࡉࢀ࡚࠸ࡿ 6)㸬௦⾲ⓗ࡞ࡶࡢ
ACATࢥ࣮ࢻ7)㸦Atomic Collision in Amorphous Target㸧㸪TRIMࢥ࣮ࢻ8)㸦Transport in Material㸧 ࡀᣲࡆࡽࢀࡿ㸬௨ୗ㸪ᅇゎᯒ⏝࠸ࡓ ACAT ࢥ࣮ࢻࣔࢹࣝࡢせ࡞㒊ศࢆㄝ᫂ࡍࡿ㸬
ACATࢥ࣮ࢻࡣ㸪Fig. 1♧ࡍࡼ࠺ࢱ࣮ࢤࢵ
ࢺࢆ1 ㎶R0㸦=N-1/3㸧ࡢࣘࢽࢵࢺࢭࣝศࡋ㸪ࣘ
ࢽࢵࢺࢭࣝᩘࢆ⏝࠸࡚ࢱ࣮ࢤࢵࢺཎᏊࢆ 1 ࡘ
ࣛࣥࢲ࣒㓄⨨ࡉࡏ㸪ࣔࣝࣇࢫ㸦㠀⤖ᬗ㸧ࢱ࣮
ࢤࢵࢺࢆᵓᡂࡍࡿ㸬ࡇࡇ࡛㸪Nࡣࢱ࣮ࢤࢵࢺࡢᩘᐦ ᗘ㸦atoms/cm3㸧࡛࠶ࡿ㸬
Fig. 1. Unite Cell model (ACAT).
య య⾪✺㏆ఝ
ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ ACAT ࡣ๓㏙ࡢ㏻
ࡾࣔࣥࢸ࢝ࣝࣟἲࢆᇶ㸪ᅛయෆࡢཎᏊ⾪✺㛵ࡋ
࡚2య⾪✺㏆ఝ9)ࢆ᥇⏝ࡋ࡚࠸ࡿ㸬⢏Ꮚࡀᅛయෆ
ධᑕࡉࢀࡿ㸪⾪✺࢝ࢫࢣ࣮ࢻࡤࢀࡿ⾪✺㐃㙐 ࡀ㉳ࡇࡿ㸬2య⾪✺㏆ఝࡣ㸪Fig. 2♧ࡉࢀࡿࡼ࠺
㐠ືࡋ࡚࠸ࡿ⢏Ꮚ㟼Ṇࡋ࡚࠸ࡿᶆⓗཎᏊࡢ 2 ࡘࡢࡳࢆ⪃៖ࡋ㸪ཎᏊ⾪✺ࢆᶍᨃࡍࡿ㸬2య⾪✺㏆
ఝࡣ㸪ධᑕ⢏Ꮚࡢ㐠ື࢚ࢿࣝࢠ࣮EࡀᩘⓒeV௨ୖ
࡛ࡼ࠸㏆ఝࢆ࠼ࡿ࠸ࢃࢀ࡚࠸ࡿ㸬୍᪉㸪ධᑕ࢚
ࢿࣝࢠ࣮ࡀ100 eV௨ୗࡢప࢚ࢿࣝࢠ࣮࡛ࡣ㸪ධᑕ
⢏Ꮚࡢ࿘ࡾ࠶ࡿࢱ࣮ࢤࢵࢺཎᏊࡽࡢᐤࡀ↓
ど࡛ࡁ࡞ࡃ࡞ࡾ㸪㏆ఝࡣᝏࡃ࡞ࡿ㸬
Fig. 2. Binary collision approximation.
2య⾪✺㏆ఝࡼࡿ㔜ᚰ⣔ࡢᩓゅ
4
ࡣ㸪ḟᘧ࡛ᐃ⩏ࡉࢀࡿ㸬
> @
(1)2
0
2 1
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r
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f4 S
ࡇࡇ࡛㸪pࡣ⾪✺ᚄᩘ㸬rࡣཎᏊ㛫㊥㞳㸪r0ࡣ᭱㏆᥋
㊥㞳࡛࠶ࡾ㸪㏆᪥Ⅼࡶࡤࢀ㸪g(r0) 0ࢆ‶ࡓࡍ㸬 ࡇࢀࡽࢆᶍᘧⓗFig. 2♧ࡍ㸬Fig. 2୰Tࡣᩓ
ᚋࢱ࣮ࢤࢵࢺཎᏊࡀᚓࡿ㐠ື࢚ࢿࣝࢠ࣮࡛࠶ࡿ㸬 ࡋࡓࡀࡗ࡚㸪ᩓᚋࡢධᑕ⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ࡣE㸫 T࡛࠼ࡽࢀࡿ㸬ࡲࡓ㸪㛵ᩘg(r)ࡣ
) 2 ) (
1 ( ) (
2 1
2 2
»»
¼ º
««
¬
ª
Er
r V r r p
g ධᑕ࢜ࣥ
R0
㊴⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ T ධᑕ࢚ࢿࣝࢠ࣮ E
⾪✺ಀᩘp
⾪✺ᚋࡢ࢚ࢿࣝࢠ࣮ E㸫T
ᐇ㦂⣔ࡢᩓゅ T
ᐇ㦂⣔ࡢ㊴ゅ I 42
㸦㔜ᚰ⣔ࡢᩓゅ 4㸧
ࢱ࣮ࢤࢵࢺཎᏊࡢ
ึᮇ⨨
ධᑕ⢏Ꮚࡢ㌶㊧
࡛࠼ࡽࢀࡿ㸬ࡇࡇ࡛㸪V(r)ࡣཎᏊ㛫࣏ࢸࣥࢩࣕࣝ
࡛ACATࢥ࣮ࢻ࡛ࡣ㸪᩺ຊ࣏ࢸࣥࢩࣕࣝࡢࡳࡀ⪃៖
ࡉࢀࡿ㸬ཎᏊ㛫࣏ࢸࣥࢩࣕࣝ㛵ࡋ࡚ࡣ㸪ḟ⠇࡛ヲ ࡋࡃ㏙ࡿ㸬
ᘧ㸦2㸧୰ࡢErࡣ┦ᑐ࢚ࢿࣝࢠ࣮࡛㸪 ) 3 1 E (
A Er A ¸
¹
¨ ·
©
§
ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪㉁㔞ẚAࡣ㸪ධᑕ⢏Ꮚࡢ㉁
㔞M1ᶆⓗ⢏Ꮚࡢ㉁㔞M2ࡢẚ࡛㸪A M2 M1࡛
࠶ࡿ㸬ᘧ㸦1㸧ࡽᚓࡽࢀࡿ㔜ᚰ⣔ࡢᩓゅ4ࡽ㸪 ᐇ㦂ᐊ⣔ࡢᩓゅT㊴࢚ࢿࣝࢠ࣮Tࡣ㸪
) 4 cos (
1 tan 1 sin
4
4 A T A
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2 ¸
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¨ ·
©
§ 4
E
A T A
࡞ࡿ㸬
ཎᏊ㛫ຊ࣏ࢸࣥࢩࣕࣝ
ACATࢥ࣮ࢻ࡛ࡣ㸪ཎᏊ㛫స⏝ࡍࡿ᩺ຊࢆホ ౯ࡍࡿ2య㛫࣏ࢸࣥࢩࣕࣝࡋ࡚㸪ࢺ࣮࣐ࢫ࣭ࣇ࢙
࣑ࣝࣔࢹࣝࡼࡿ㐽ⶸࢡ࣮࣏ࣟࣥࢸࣥࢩࣕࣝ 10)ࢆ ᥇⏝ࡍࡿ㸬ཎᏊ␒ྕZ1㸪Z2ࡢ2ࡘࡢཎᏊ㛫ാࡃ᩺
ຊ࣏ࢸࣥࢩࣕࣝࡣ㸪
) 6 ( )
(
2 2
1 ¸
¹
¨ ·
©
§ a r r
e Z r Z
V I
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪Ir a ࡣ㐽ⶸ㛵ᩘ࡛㸪a ࡣ 㐽ⶸ㛗ࡉ(Å)࡛࠶ࡾ㸪Firsov11)ࡼࡗ࡚
0.465812223 (7)2 1
1 Z
Z
a
࠼ࡽࢀ࡚࠸ࡿ㸬ཎᏊ᰾ࡢṇ㟁Ⲵࡀ㸪࿘ࡾᏑᅾ ࡍࡿ㟁Ꮚࡢ㈇㟁Ⲵࡼࡗ࡚㐽ⶸࡉࢀࡿຠᯝࢆྲྀࡾ
ධࢀࡓᙧ࡞ࡗ࡚࠸ࡿ㸬ࡋࡓࡀࡗ࡚㸪ཎᏊ㛫ࡢ㊥㞳 ࡀ㞳ࢀ࡚࠸ࡿሙྜࡣཎᏊ᰾ࡢṇ㟁Ⲵࡣ㟁Ꮚࡢ㈇㟁 Ⲵ㐽ⶸࡉࢀ㸪⾪✺┦ᡭࡢཎᏊࡽࡳࡿ୰ᛶぢ
࠼㸪ẁࠎཎᏊ㛫㊥㞳ࡀ㏆࡙ࡃࡘࢀ㐽ⶸࡢຠᯝࡀ ῶᑡࡋ࡚࠸ࡃ㸬
㐽ⶸ㛵ᩘࡘ࠸࡚ࡣ㸪ከࡃࡢ㛵ᩘᙧࡀᥦࡉࢀ
࡚࠾ࡾ㸪ACATࢥ࣮ࢻ࡛ࡣ㸪௨ୗࡢ5ࡘࡢ㐽ⶸ㛵ᩘ
ࢆ᥇⏝ࡍࡿࡇࡀ࡛ࡁࡿ㸬ᮏ◊✲࠾࠸࡚ࡣ㸪
Moriereࡢ㐽ⶸ㛵ᩘ12)ࢆ⏝࠸ࡓ㸬
(1) Moliere࣏ࢸࣥࢩࣕࣝ
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Mol e e e
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ࢆ⏝࠸ࡿ㸬ZBL( Ziegler㸪Biersak, Littmark)࣏ࢸࣥࢩ
ࣕࣝ13)௨እࡣ㸪ࡇࡢFirsovࡢ㐽ⶸ㛗ࡉࢆ⏝࠸ࡿ㸬
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(4) ZBL࣏ࢸࣥࢩࣕࣝ
Ziegler㸪Biersak, Littmark ࡼࡗ࡚ᥦࡉࢀࡓ ཎᏊ㛫ຊ࣏ࢸࣥࢩ࡛ࣕࣝ㸪௨ୗ࡛ᐃ⩏ࡉࢀࡿ㸬
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ᐃ⩏ࡋ࡚⏝࠸ࡿ㸬
(5) AMLJ㸦Averaged Modified Lenz-Jensen 㸧࣏ࢸࣥ
ࢩࣕࣝ16)
(13)
exp 1x 2x32 3x2
x AMLJ D D D
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0 10.169 20.169
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(16)
244 .
0 10.0418 20.0418 2
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ࡇࡇ࡛㸪x{r aB ࡛࠶ࡾ㸪aB 0.529 Å㸦࣮࣎
༙ᚄ㸧ࢆ⏝࠸ࡿ㸬
࢚ࢿࣝࢠ࣮ᦆኻ
㐠ືࡋ࡚࠸ࡿ⢏Ꮚࡀ㟼Ṇࡋ࡚࠸ࡿࢱ࣮ࢤࢵࢺ ཎᏊ⾪✺ࡍࡿࡇࡼࡿ㐠ື࢚ࢿࣝࢠ࣮ࡢᦆኻ ࡣ㸪⾪✺ࡢ๓ᚋ࡛㐠ື࢚ࢿࣝࢠ࣮㐠ື㔞ࡀಖᏑࡉ
ࢀࡿᙎᛶ⾪✺ࡼࡿࡶࡢ㸪㐠ື㔞ࡀಖᏑࡉࢀ࡞࠸
㠀ᙎᛶ⾪✺ࡀ࠶ࡿ㸬ᙎᛶ⾪✺ࡼࡗ࡚㸪ࢱ࣮ࢤࢵ
ࢺཎᏊ࠼ࡿ࢚ࢿࣝࢠ࣮ࡣᘧ㸦5㸧࡛࠼ࡽࢀࡿ㸬 㠀ᙎᛶ⾪✺ࡣ㸪㟁Ꮚⓗ࢚ࢿࣝࢠ࣮ᦆኻࡶゝࢃࢀ㸪 ධᑕ࢚ࢿࣝࢠ࣮ࡀࡁࡃ࡞ࡿࡘࢀ࡚ࢱ࣮ࢤࢵࢺ ཎᏊࡢཎᏊ᰾ࡢࡲࢃࡾᏑᅾࡍࡿ㟁Ꮚ⣔㸪ບ㉳࣭
㟁㞳࠸࠺㐣⛬ࢆ⤒࡚࢚ࢿࣝࢠ࣮ࡀࡉࢀࡿࡼ
࠺࡞ࡿ㸬㟁Ꮚ⣔࢚ࢿࣝࢠ࣮ࡀࡉࢀࡿሙྜࡣ㸪 㟁Ꮚࡢ㉁㔞ࡀධᑕ⢏Ꮚẚ࡚ᅽಽⓗᑠࡉ࠸ࡓ
ࡵ㸪ධᑕ⢏Ꮚࡣ┤㐍ࡍࡿ⪃࠼࡚ࡼ࠸㸬
ධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ୰ࢆ༢㛗ࡉᙜࡓࡾ㐍
ࡴࡢኻ࠺࢚ࢿࣝࢠ࣮ࢆ㜼Ṇ⬟࠸࠸㸪
) 17 ( )
( 2
)
³
( N T p pdp Ns E dx
dE S
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪xࡣධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ
୰ࢆ㐍ࢇࡔ㛗ࡉ㸪N[atoms/cm3]ࡣࢱ࣮ࢤࢵࢺࡢᩘᐦ ᗘ࡛㸪T(p)ࡣ⾪✺ಀᩘp࠾ࡅࡿ㊴࢚ࢿࣝࢠ࣮㸪 s(E)[eVcm2]ࡣ㜼Ṇ᩿㠃✚ࡤࢀࡿ㸬ᘧ㸦17㸧
ࡣ㸪ᙎᛶ⾪✺ࡼࡿ࢚ࢿࣝࢠ࣮ᦆኻ㸪㠀ᙎᛶ⾪✺
ࡼࡿ࢚ࢿࣝࢠ࣮ᦆኻࡀྵࡲࢀ࡚࠾ࡾ㸪๓⪅ࢆ᱁ⓗ
㜼Ṇ⬟
dE dxn㸪ᚋ⪅ࢆ㟁Ꮚⓗ㜼Ṇ⬟dE dxeࡪ㸬㜼Ṇ⬟ࢆࡇࢀࡽࡘࡢせ⣲ศࡋ࡚⾲ࡍ㸪
s (E) s E (18) dx NdE dx
dE dx dE
e n e
n
¸
¹
¨ ·
© §
¸¹
¨ ·
©
§
࡞ࡿ㸬
㟁 Ꮚ ⓗ 㜼 Ṇ ⬟ ࡢ ⌮ ㄽ ࡋ ࡚ 㸪Lindhard㸪 Scharff㸪Schiøttࡼࡗ࡚ᥦࡉࢀࡓ LSSࡢ㜼Ṇ⬟
බᘧ7)ࡀ᭷ྡ࡛࠶ࡿࡀ㸪ACATࢥ࣮ࢻ࠾࠸࡚ࡣ㸪 Ziegler㸪Biersak, Littmark (ZBL)ࡼࡗ࡚࠼ࡽࢀࡓ ᗈ࠸࢚ࢿࣝࢠ࣮⠊ᅖரࡗ࡚㐺⏝࡛ࡁࡿᐇ㦂ࢹ࣮
ࢱࢆᇶࡋࡓබᘧ17)ࢆ᥇⏝ࡋ࡚࠸ࡿ㸬ࡇࡢᐇ㦂ᘧࡢ
㜼Ṇ᩿㠃✚ࢆsZBL(E)ࡍࡿ㸪ධᑕ⢏Ꮚࡀࢱ࣮ࢤ
ࢵࢺ୰ࢆ'xࡔࡅ㐍ࡴ㛫ኻ࠺㟁Ꮚⓗ࢚ࢿࣝࢠ࣮ᦆ ኻ'Eࡣ㸪
) 19 ( )
(E x Ns
E ZBL ' '
⾲ࡉࢀࡿ㸬
ࢫࣃࢵࢱࣜࣥࢢ㔞ࡢホ౯ᘧ
ACAT ࢥ࣮ࢻ࡛ィ⟬ࡉࢀࡓࢫࣃࢵࢱࣜࣥࢢ
㔞ࡢጇᙜᛶࢆ᳨ドࡍࡿࡓࡵ㸪⤖ᯝࢆᐇ㦂ࢹ࣮ࢱ㸪ཬ ࡧ ᐇ 㦂 ࢹ ࣮ ࢱ ࢆ ࡼ ࡃ ⌧ ࡍ ࡿ ࡇ ࡛ ▱ ࡽ ࢀ ࡿ
Yamamura ➼ࡼࡗ࡚ᥦࡉࢀࡓබᘧ 6)ࡢ⤖ᯝẚ
㍑ࡋࡓ㸬ࡇࡢࢫࣃࢵࢱࣜࣥࢢබᘧࡣ㸪ᆶ┤ධᑕࡢࢫ
ࣃࢵࢱࣜࣥࢢ㔞ࢆホ౯ࡋ㸪⥺ᙧ࢝ࢫࢣ࣮ࢻ⌮ㄽ5)
ࡽᑟࢀࡿ㛵ᩘᙧ㸪ᐇ㦂ࢹ࣮ࢱࢆᇶỴࡵࡽࢀ
ࡓࣇࢵࢸࣥࢢࣃ࣓࣮ࣛࢱࢆྵࡴ༙⌮ㄽ༙ᐇ㦂 ᘧ࡛࠶ࡿ㸬ࡇࡢࣇࢵࢸࣥࢢࣃ࣓࣮ࣛࢱ㛵ࡋ࡚
ࡣ㸪ཧ⪃ᩥ⊩6)ᩘ್⾲ࡀ࠶ࡾ㸪ࢱ࣮ࢤࢵࢺẖ᭱
㐺್ࡀ♧ࡉࢀ࡚࠸ࡿ㸬 Yamamuraබᘧ࡛࠼ࡽࢀ
ࡿࢫࣃࢵࢱࣜࣥࢢ㔞ࡣᘧ㸦20㸧࡛࠼ࡽࢀࡿ㸬
) 20 ( 1
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ࡇࡇ࡛㸪Y(E) [atoms/ion]ࡣධᑕ࢚ࢿࣝࢠ࣮E [eV]ࡢ
ࡁࡢࢫࣃࢵࢱࣜࣥࢢ㔞㸪Q㸪s ࡣࢱ࣮ࢤࢵࢺཎ Ꮚ౫Ꮡࡍࡿࣃ࣓࣮ࣛࢱ࡛࠶ࡿ㸬ࡲࡓ㸪Us[eV]ࡣࢱ
࣮ࢤࢵࢺཎᏊࡢ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮࡛㸪㏻ᖖࡣ᪼⳹
࢚ࢿࣝࢠ࣮ࡀ⏝࠸ࡽࢀࡿ㸬Eth[eV]ࡣࢫࣃࢵࢱࣜࣥࢢ ࡢࡋࡁ࠸್࢚ࢿࣝࢠ࣮࡛㸪
) 21 ( for
7 . 5 1
2 1 2
1
M M M U
Eth M s
d
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7 . 6
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࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪Jࡣᙎᛶ⾪✺࠾ࡅࡿ࢚ࢿ
ࣝࢠ࣮⛣⾜ᅉᏊ࡛㸪
(23)
4
2 2 1
2 1
M M
M M J
࠶ࡿ㸬ࡑࡢࡢࣃ࣓࣮ࣛࢱࡣḟࡢࡼ࠺ᐃ⩏ࡉࢀࡿ㸬
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ࡇࡇ࡛㸪M1㸪M2[a.m.u]ࡣධᑕ⢏Ꮚࢱ࣮ࢤࢵࢺཎ Ꮚࡢ㉁㔞࡛࠶ࡿ㸬᰾ⓗ㜼Ṇ᩿㠃✚ Sn(E) [eV·Å/cm2] ࡣ㸪
84.78 22312 1 1 2 ( ) (26)3 2 1
2
1 n H
n s
M M
M Z
Z
Z E Z
S
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪Z1㸪Z2ࡣධᑕ⢏Ꮚࢱ࣮ࢤ
ࢵࢺཎᏊࡢཎᏊ␒ྕ࡛࠶ࡿ㸬ࡲࡓ㸪⟬᰾ⓗ㜼Ṇ᩿
㠃✚sn(H)ࡣ㸪
) 27 ( )
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. 6 1
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2 1
1 H
H H
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n n
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࡛࠼ࡽࢀࡿ㸬ࡇࡇ࡛㸪⟬࢚ࢿࣝࢠ࣮Hࡣ
0.0325522312 1 1 2 (28)3 2 2 1 1
M E M
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Z
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࡛࠶ࡿ㸬ࡲࡓ㸪
7 (29)1 M1 3 W
*
࡛࠼ࡽࢀ㸪ࣇࢵࢸࣥࢢࣃ࣓࣮ࣛࢱ W ࡣࢱ࣮
ࢤࢵࢺཎᏊ౫Ꮡࡍࡿ㸬keࡣLindhardࡢ㟁Ꮚⓗ㜼Ṇ
⬟ಀᩘ࡛࠶ࡾ㸪
(30)
079 .
0 23 34
2 3 2 1
2 1 2 3 2 1 2
1 2 2 3 1
2 3 2 1
Z Z
Z Z M
M M ke M
࡛࠶ࡿ㸬
4㸬ゎᯒ⤖ᯝ
ACATࢥ࣮ࢻࢆ⏝࠸࡚㸪⾪✺࢝ࢫࢣ࣮ࢻࡀ༑ศ
Ⓨ㐩ࡋ࡞࠸ሙྜ࠾࠸࡚㸪ࢫࣃࢵࢱࣜࣥࢢࡀ⌮ㄽ
ࡢࡼ࠺␗࡞ࡿࢆゎᯒࡋࡓ㸬⾪✺࢝ࢫࢣ࣮ࢻࡀ
༑ศⓎ㐩ࡋ࡞࠸ሙྜࡋ࡚㸪ධᑕ⢏Ꮚࢆప࢚ࢿࣝࢠ
࣮ࡢAr+࢜ࣥ, H+࢜ࣥࡋ㸪ࢱ࣮ࢤࢵࢺࡣ㖡ࢆ
㑅ࢇࡔ㸬
㸬 $U㸫&X
ࢫࣃࢵࢱࣜࣥࢢ
Fig. 3㸪Ar+࢜ࣥࢆ㖡ࢱ࣮ࢤࢵࢺ⾲㠃ᑐ
ࡋ࡚ᆶ┤ධᑕࡉࡏࡓሙྜࡢ㖡ཎᏊࡢࢫࣃࢵࢱࣜ
ࣥ ࢢ 㔞 ࡢ ᐇ 㦂 ࢹ ࣮ ࢱ 18-20)㸪ACAT ࢹ ࣮ ࢱ 㸪
Yamamuraබᘧࡼࡾᚓࡽࢀࡓ⤖ᯝࢆ♧ࡍ㸬Fig. 3
ࡼࡾ㸪ACAT ࢹ࣮ࢱ㸪Yamamura බᘧࡶ㸪ⱝᖸ ࡢᕪࡣぢࡽࢀࡿࡀ㸪ᐇ㦂ࢹ࣮ࢱࡢㄗᕪ࡞ࢆ⪃៖ࡍ
ࡿ㸪ᐇ㦂ࢹ࣮ࢱࡼࡃ୍⮴ࡋ࡚࠸ࡿ㸬ࡇࡢሙྜ
⏝࠸ࡓ Yamamuraබᘧࡢࣇࢵࢸࣥࢢࣃ࣓࣮ࣛ
ࢱࡢ್ࡣ㸪Q=1.0㸪W=0.73㸪s=2.5 ࡛࠶ࡿ㸬ࡲࡓ㸪
ACATࢥ࣮ࢻYamamuraබᘧࡘ࠸࡚ࡶ㸪ࡼࡃ
୍⮴ࡋ࡚࠾ࡾ㸪ࢫࣃࢵࢱࣜࣥࢢ㔞ࡢゎᯒ㛵ࡋ࡚㸪 ACAT ࢥ࣮ࢻ㸪Yamamura බᘧࡶ᭷⏝࡛࠶ࡿ
⪃࠼ࡽࢀࡿ㸬
Fig. 3. Sputtering yields of Cu bombarded by Ar+ ions at 0°.
ḟ㸪100 eV㸪5 keVࡢAr+࢜ࣥࢆ㖡ࢱ࣮ࢤ
ࢵࢺᆶ┤ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉࢀࡓ 㖡ཎᏊࡢゅᗘศᕸࢆ ACAT ࢥ࣮ࢻ࡛ゎᯒࡋࡓ⤖ᯝ
ࢆFig. 4㸪5♧ࡍ㸬ࡲࡓ㸪༑ศⓎ㐩ࡋࡓ⾪✺࢝ࢫ
ࢣ࣮ࢻࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉࢀࡓࢫࣃࢵࢱ࣮⢏Ꮚ ࡢゅᗘศᕸࢆ⌧ࡍࡿࡋ࡚⌮ㄽⓗᑟࢀࡿࢥ
4㸬ゎᯒ⤖ᯝ
㸬 $U㸫&X
ࢫࣃࢵࢱࣜࣥࢢ
ࢧࣥศᕸ 12)ࡶేࡏ࡚♧ࡍ㸬ࢥࢧࣥศᕸࡣᴟゅ T
T
T
㹼
d 㸪᪉ゅI㹼
IdI୰ᨺฟࡉࢀࡿ⢏Ꮚᑐࡍࡿࢫࣃࢵࢱ⋡ࢆY
T, Iࡋ࡚㸪) 31 ( cos
) ,
(T I dTdI TdTdI
Y v
࡛⾲ࡉࢀࡿ㸬ࡇࡇ࡛㸪ゅᗘTࡣᅛయ⾲㠃ᑐࡋ࡚ᆶ
┤᪉ྥࢆ0rࡋ㸪ྑഃࢆ0r㹼90r㸪ᕥഃࢆ 0r
㹼㸫90rࡍࡿ㸬ᅗ୰♧ࡉࢀࡿࢥࢧࣥศᕸࡣ㸪 ゅᗘศᕸࡢᆶ┤ᡂศ୍⮴ࡍࡿࡼ࠺つ᱁ࡋ࡚
࠶ࡿ㸬ᅗ♧ࡉࢀࡿࡼ࠺㸪ධᑕ࢚ࢿࣝࢠ࣮ࡀ1 keV ࡢሙྜࡣ㸪ࡰࢥࢧࣥศᕸ୍⮴ࡋ࡚࠸ࡿࡢᑐ ࡋ࡚㸪100 eV ࡢሙྜࡣ㸪ゅᗘศᕸࡢᆶ┤ᡂศࡀᢚ
࠼ࡽࢀࡓࣥࢲ࣮࣭ࢥࢧࣥศᕸࢆ♧ࡋ࡚࠸ࡿ㸬ࡇ
ࢀࡣධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ࡓࡵ㸪ᅛయෆ࡛⾪✺࢝
ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡏࡎ㸪ධᑕ᪉ྥࡢ㐠ື㔞ᡂศࡀ ከࡃṧࡗ࡚࠸ࡿࡓࡵ࡛࠶ࡿ㸬
Fig. 4. Calculated angular distributions of sputtered Cu atoms bombarded by 100 eV Ar+ions at 0°.
ධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ࡓࡵ㸪⾪✺࢝ࢫࢣ࣮
ࢻࡀⓎ㐩ࡋ࡞࠸ࡇࡢᙳ㡪ࡣ㸪ࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚
ࢿࣝࢠ࣮ศᕸࡶ⌧ࢀࡿ㸬ゅᗘศᕸྠᵝධᑕ࢚
ࢿࣝࢠ࣮100 eV1 keVࡢAr+࢜ࣥࢆ㖡ࢱ࣮ࢤ
ࢵࢺᆶ┤ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉࢀࡓ 㖡ཎᏊࡢ࢚ࢿࣝࢠ࣮ศᕸࢆ ACAT ࢥ࣮ࢻ࡛ゎᯒࡋ
ࡓ⤖ᯝࢆFig. 6㸪7♧ࡍ㸬༑ศⓎ㐩ࡋࡓ⾪✺࢝ࢫ
ࢣ࣮ࢻࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉࢀࡓ⢏Ꮚࡣ⌮ㄽⓗ
ᑟࢀࡿࢺࣥࣉࢯࣥࡢබᘧ 12)ᚑ࠺ࡇࡀ▱ࡽࢀ
࡚࠾ࡾ㸪ࢺࣥࣉࢯࣥࡢබᘧࡣ
(32)
)
( 3
Us
E dE E E
Y v
࡞ࡿ㸬ࡇࡇ࡛㸪Eࡣࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚ࢿࣝࢠ࣮㸪
Usࡣࢱ࣮ࢤࢵࢺཎᏊࡢ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮࡛࠶ࡿ㸬
Fig. 5. Calculated angular distributions of sputtered Cu atoms bombarded by 1 keV Ar+ions at 0°.
ࡲࡓ㸪ࢺࣥࣉࢯࣥࡢබᘧ࡛࠼ࡽࢀࡿ࢚ࢿࣝࢠ࣮
ศᕸࡢࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧࢆ࢚
ࢿࣝࢠ࣮㛵ࡋ࡚ᚤศࡋ࡚ᴟ್ࢆồࡵࡿࡇ࡛ᚓ
ࡽࢀ㸪ࡑࡢ್ࡣUs 2࡞ࡿ㸬ࢱ࣮ࢤࢵࢺࡀ㖡ࡢሙ
ྜ㸪⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮ࡣ3.49 eV࡛࠶ࡾ㸪⌮ㄽⓗ
ண ࡉࢀࡿࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ1.75 eV࡛࠶ࡿ㸬
Fig. 6♧ࡉࢀࡿࡼ࠺㸪ධᑕ࢚ࢿࣝࢠ࣮1 keVࡢ
ሙྜࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧࡼࡃྜ⮴ࡋ࡚࠸ࡿࡇ
ࡀศࡿ㸬
Fig. 6. Calculated energy distributions of sputtered Cu atoms bombarded by 1 k eV Ar+ions at 0°.
୍᪉㸪100 eV ࡢሙྜࡣ㸪ࢫࣃࢵࢱ࣮⢏Ꮚࡢ㧗࢚
ࢿࣝࢠ࣮㒊ศࡢ㔞ࡀ㸪ࢺࣥࣉࢯࣥࡢබᘧࡽண ࡉࢀࡿࡶࡢẚ࡚ᑡ࡞࠸㸬ࡇࡢ㐪࠸ࡣ㸪ゅᗘศᕸ
ྠᵝ⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡚࠸࡞࠸ࡇ
㉳ᅉࡍࡿ㸬ࡲࡓ㸪࢚ࢿࣝࢠ࣮ศᕸࡢࣆ࣮ࢡ࢚ࢿࣝࢠ
࣮ࡣ㸪100 eV㸪1 keVࡢධᑕ࢚ࢿࣝࢠ࣮ඹ㸪ࢺࣥࣉ
ࢯࣥࡢබᘧࡽண ࡉࢀࡿ1.75 eV㏆࠸್ࢆ♧ࡍ㸬 ࡋࡓࡀࡗ࡚㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞࠸ࡇࡼ
ࡿ࢚ࢿࣝࢠ࣮ศᕸࡢᙳ㡪ࡣ㸪㧗࢚ࢿࣝࢠ࣮㒊ศࡢ
㔞⌧ࢀࡿ㸬
Fig. 7. Calculated energy distributions of sputtered Cu atoms bombarded by 1 00eV Ar+ions at 0°.
㸬
㸬+
+㸫㸫&
&Xࢫ ࢫࣃࢵࢱࣜࣥࢢ
⾪✺࢝ࢫࢣ࣮ࢻࡀᮍⓎ㐩࡞ࡿࡢࡣ㸪Ỉ⣲࢜
ࣥ࡞ࡢ㍍࢜ࣥࡼࡿࢫࣃࢵࢱࣜࣥࢢࡢሙྜࡶ
ྠᵝ࡛࠶ࡿ㸬Fig. 8㸪9100 eV H+࢜ࣥࢆ㖡ࢱ
࣮ࢤࢵࢺᆶ┤ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉ
ࢀࡓ㖡ཎᏊࡢゅᗘศᕸ࢚ࢿࣝࢠ࣮ศᕸࢆ♧ࡍ㸬
Fig. 8࡛♧ࡉࢀࡿࡼ࠺㸪㍍࡛࢜ࣥࢫࣃࢵࢱ࣮ࡉ
ࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡢゅᗘศᕸࡣ㸪100 eV ࡢప࢚
ࢿࣝࢠ࣮ࡶ㛵ࢃࡽࡎࢥࢧࣥ㏆࠸ศᕸࢆ♧ࡍ㸬 ࡇࡢゎᯒ⤖ᯝࡣ㸪Ar+࢜ࣥධᑕࡢሙྜ␗࡞ࡿഴ
ྥ࡛࠶ࡿ㸬ࡇࢀࡣFig. 10♧ࡉࢀࡿࡼ࠺㸪㍍
࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢ࣓࢝ࢽࢬ࣒ࡀᑡᩘᅇ⾪✺
ࡼࡿࡶࡢ࡛࠶ࡿࡇ㉳ᅉࡍࡿ㸬
㍍࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢሙྜ㸪ධᑕ⢏Ꮚࡢ㉁
㔞ࡀࢱ࣮ࢤࢵࢺཎᏊẚ࡚㍍࠸ࡓࡵࢱ࣮ࢤࢵ
ࢺཎᏊ⾪✺ࡋࡓ㝿ᚋ᪉ᩓࡉࢀࡿ⋡ࡀ㧗ࡃ
࡞ࡿ㸬ࡇࡢᚋ᪉ᩓࡉࢀࡓ㍍࢜ࣥࡢ᪉ྥࡣ㸪ࢱ
࣮ࢤࢵࢺཎᏊࡢ⾪✺⨨ࡼࡗ࡚ࡁࡃᙳ㡪ࡉࢀ
ࡿࡓࡵ㸪ഹ࡞⾪✺⨨ࡢ㐪࠸࠾࠸࡚ࡶ㸪ᩓ
ゅࡀ␗࡞ࡿ㸬⤖ᯝࡋ࡚㸪ᚋ᪉ᩓࡉࢀࡿ㍍࢜ࣥ
ࡢ᪉ྥࡣࣛࣥࢲ࣒࡞ࡾ㸪➼᪉ⓗ࡞ࡿ⪃࠼ࡽࢀ
ࡿ㸬ࡋࡓࡀࡗ࡚㸪ᚋ᪉ᩓࡉࢀࡓ㍍࢜ࣥࡼࡗ࡚
ࢫࣃࢵࢱ࣮ࡉࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡣప࢚ࢿࣝࢠ࣮
࡛࠶ࡗ࡚ࡶ㸪ゅᗘศᕸࡢᆶ┤᪉ྥᡂศࡢῶᑡࡣぢࡽ
ࢀ࡞࠸㸬ࡇࡢഴྥࡣධᑕ࢜ࣥࢱ࣮ࢤࢵࢺཎᏊࡢ
㉁㔞ᕪࡀࡁ࠸ሙྜࡸ㸪ධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ሙྜ
㢧ⴭ࡞ࡿ㸬
Fig. 8. Calculated angular distributions of sputtered Cu atoms bombarded by 100 eV H+ions at 0°.
Fig. 9. Calculated energy distributions of sputtered Cu atoms bombarded by 100 eV H+ions at 0°.
㍍࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢሙྜࡢ࢚ࢿࣝࢠ࣮
ศᕸࡣࢺࣥࣉࢯࣥࡢබᘧࡁࡃ␗࡞ࡿ㸬࢚ࢿࣝࢠ
࣮ศᕸࡢࣆ࣮ࢡࢆ࠼ࡿ࢚ࢿࣝࢠ࣮ࡣࢺࣥࣉࢯࣥ
ࡢබᘧ࡛ࡣ1.75 eV࡛࠶ࡿࡢᑐࡋ࡚㸪ACATࡢ⤖
ᯝࡣప࢚ࢿࣝࢠ࣮ഃࢩࣇࢺࡋ࡚࠾ࡾ㸪0.5 eV㏆ഐ
㸬+㸫&X
ࢫࣃࢵࢱࣜࣥࢢ
࡛࠶ࡿ㸬ࡲࡓ㸪࢚ࢿࣝࢠ࣮ศᕸࡢ㧗࢚ࢿࣝࢠ࣮㒊ศ
ࡘ࠸࡚ࡶ㸪ACATࢥ࣮ࢻࡢゎᯒࡽᚓࡽࢀࡿศᕸ ࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧࡀ⦆ࡸῶᑡࡍࡿࡢᑐࡋ㸪 ᛴ⃭0᮰ࡍࡿ㸬
Fig. 10. Undeveloped collision cascade.
⤖
⤖ㄽ
ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻACATࢆ⏝࠸࡚㸪⾪
✺࢝ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸ሙྜ㸪ࡍ࡞ࢃࡕᑡᩘ
ᅇ⾪✺࡛⏕ࡌࡿࢫࣃࢵࢱࣜࣥࢢᐤࡀࡁ࠸ሙྜ
ࡢゎᯒࢆ⾜ࡗࡓ㸬ලయⓗࡣ㸪పධᑕ࢚ࢿࣝࢠ࣮㸪 ཬࡧ㍍࢜ࣥධᑕࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࢆᑐ㇟
ࡋࡓ㸬ࡲࡎ⾪✺࢝ࢫࢣ࣮ࢻࢆࡶࡋࡓ⌮ㄽࡢ㐪
࠸ࢆゎᯒࡋࡓ㸬ࢫࣃࢵࢱ࣮⢏Ꮚࡢゅᗘศᕸᑐࡋ࡚
ࡣ㸪Ⓨ㐩ࡋࡓ⾪✺࢝ࢫࢣ࣮ࢻࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉ
ࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡢゅᗘศᕸࡣࢥࢧࣥศᕸ
࡞ࡿࡇࡀ⌮ㄽⓗண ࡉࢀࡿࡀ㸪ప࢚ࢿࣝࢠ࣮
Ar+࢜ࣥࡢ㖡ࢱ࣮ࢤࢵࢺᆶ┤ධᑕࡢሙྜࡣ⾪✺࢝
ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸ࡓࡵ㸪ධᑕ᪉ྥࡢ㐠ື
㔞ᡂศࡀከࡃṧࡿ㸬ࡑࡢ⤖ᯝ㸪⾲㠃ᆶ┤ᡂศࡢ㔞 ࡀᑡ࡞࠸ࣥࢲ࣮ࢥࢧࣥศᕸࢆ♧ࡍ㸬୍᪉㸪H+
࢜ࣥࡢప࢚ࢿࣝࢠ࣮㖡ࢱ࣮ࢤࢵࢺᆶ┤ධᑕࡢሙ
ྜࡣ㸪ᑡᩘᅇ⾪✺ᶵᵓࡀᨭ㓄ⓗ࡞ࡾ㸪⤖ᯝⓗゅ ᗘศᕸࡣࢥࢧࣥศᕸ㏆࠸ศᕸࢆ♧ࡍ㸬
ࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ศᕸࡘ࠸࡚ࡣ㸪 ప࢚ࢿࣝࢠ࣮Ar+࢜ࣥࡢሙྜࡣ㸪࢚ࢿࣝࢠ࣮ศᕸ ࡢࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ⌮ㄽⓗண ࡉࢀࡿࢺࣥࣉ
ࢯࣥࡢබᘧࡼࡃ୍⮴ࡍࡿࡀ㸪㧗࢚ࢿࣝࢠ࣮㒊ศࡢ
㔞ࡀࢺࣥࣉࢯࣥࡢබᘧẚ࡚ᑡ࡞࠸㸬ࡇࡢഴྥ
ࡣ㍍࢜ࣥప࢚ࢿࣝࢠ࣮ධᑕࡢሙྜ࡛≉㢧ⴭ࡛㸪
㍍࢜ࣥࡢሙྜࡣ㸪ศᕸࡢࣆ࣮ࢡࢆ࠼ࡿ࢚ࢿࣝࢠ
࣮ࡶ㸪⌮ㄽⓗண ࡉࢀࡿ್ࡢ༙ศ௨ୗ࡞ࡿ㸬
㍍࢜ࣥධᑕࡢࢫࣃࢵࢱ࣮⢏Ꮚࡢゅᗘศᕸ
ࡘ࠸࡚ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞ࡃ࡚ࡶ㸪ᚋ ᪉ᩓࡉࢀࡿධᑕ⢏Ꮚࡢ㐠ື㔞ࡀ༑ศࣛࣥࢲ࣐
ࢬࡉࢀࡿࡇࡼࡗ࡚Ⓨ㐩ࡋࡓ⾪✺࢝ࢫࢣ࣮ࢻ
ྠࡌ⤖ᯝࢆ♧ࡍ㸬ࡋࡋ࡞ࡀࡽ㸪࢚ࢿࣝࢠ࣮ศᕸ
ᑐࡋ࡚ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞࠸ᙳ㡪ࡀ㢧 ⴭ⌧ࢀ㸪⌮ㄽⓗண ࡉࢀࡿࢺࣥࣉࢯࣥࡢබᘧ
ࡽࡁࡃእࢀࡓࡶࡢ࡞ࡿ㸬
ᮏ◊✲ࡢ୍㒊ࡣࠕ2008 ᖺᗘྠᚿ♫Ꮫ⌮ᕤᏛ◊✲
ᡤ◊✲ຓᡂ㔠㸦ಶே㸧ࠖࡢᨭࢆཷࡅࡓ㸬ࡇࡇ㸪 グࡋ࡚ㅰពࢆ⾲ࡍࡿ㸬
ཧ
ཧ⪃ᩥ⊩
1) ᑠᯘὒ㸪ⷧ⭷㸦ᇶ♏ࡢࡁࡑ㸧㸪㸦᪥หᕤᴗ᪂⪺♫㸪ᮾ
ி㸪2006㸧㸪p. 51.
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4) ᑠᯘὒ㸪ⷧ⭷㸦ᇶ♏ࡢࡁࡑ㸧㸪㸦᪥หᕤᴗ᪂⪺♫㸪ᮾ
ி㸪2006㸧㸪p. 52.
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Phys. 78,283(1932).
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Eff. 105,239-256 (1988) .
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