023051010008 - Doors

THE SCIENCE AND ENGINEERING REVIEW OF DOSHISHA UNIVERSITY, VOL. 51, NO. 1 April 2010
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
ᑡᩘᅇ⾪✺ᶵᵓ࡟ࡼࡿࢫࣃࢵࢱࣜࣥࢢ⌧㇟࡬ࡢᐤ
ᐤ୚
๢ᣢ ㈗ᘯ
ᅾ㸪ⷧ⭷స〇 㸪ᚤ㔞ศᯒ ࡞࡝ࡢᕤᴗศ㔝࡟ᗈࡃ
㸯㸬ࡣࡌࡵ࡟
㐠ື࢚ࢿࣝࢠ࣮ࢆࡶࡗࡓ⢏Ꮚࡀᅛయࢱ࣮ࢤࢵ
ᛂ⏝ࡉࢀ࡚࠸ࡿ㸬ࡲࡓ㸪᰾⼥ྜᐇ㦂⿦⨨ࡢቨᮦᩱ㸱
ࢺ⾲㠃࠿ࡽධᑕࡍࡿ࡜㸪ࢱ࣮ࢤࢵࢺཎᏊ࡜⾪✺ࡍࡿ
ࡸ㸪↷᫂ᶵჾࡢᨺ㟁᫬ࡢ㟁ᴟࡢᦆ⪖㸲࡞࡝ࡶ㸪ࢫࣃ
ࡇ࡜࡟ࡼࡗ࡚཯㊴ཎᏊࢆ⏕ᡂࡍࡿ㸬⏕ᡂࡉࢀࡓ཯㊴
ࢵࢱࣜࣥࢢ࡟ࡼࡗ࡚ᘬࡁ㉳ࡇࡉࢀࡿࡇ࡜ࡀ▱ࡽࢀ
ཎᏊࡣධᑕ⢏Ꮚ࡜ྠࡌാࡁࢆࡋ㸪ูࡢࢱ࣮ࢤࢵࢺཎ
࡚࠸ࡿ㸬
Ꮚ࡜⾪✺ࡍࡿࡇ࡜࡟ࡼࡗ࡚᪂ࡓ࡟཯㊴ཎᏊࢆ⏕ࡳ
ࢫࣃࢵࢱࣜࣥࢢࡢཎᅉࡣ㸪㐠ື࢚ࢿࣝࢠ࣮ࢆࡶ
ฟࡍ㸬ࡇࡢᅛయෆ࡛ࡢ⾪✺ࡢ㐃㙐ࡢࡇ࡜ࢆ⾪✺࢝ࢫ
ࡗࡓධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ࡟↷ᑕࡉࢀࡿࡇ࡜࡟ࡼ
ࢣ࣮ࢻ࡜࠸࠸㸪ࡇࡢ⾪✺࢝ࢫࢣ࣮ࢻࡀࢱ࣮ࢤࢵࢺ⾲
ࡗ࡚⏕ࡳฟࡉࢀࡿ⾪✺࢝ࢫࢣ࣮ࢻࡀᅛయ⾲㠃࡛Ⓨ
㠃ࡲ࡛Ⓨ㐩ࡋ㸪⾲㠃᪉ྥ࡟ࢱ࣮ࢤࢵࢺཎᏊࡀࡣࡌࡁ
㐩ࡍࡿࡇ࡜࡟ࡼࡿ㸬⌧ᅾࡲ࡛ࡢ࡜ࡇࢁ㸪ࡇࡢࢫࣃࢵ
ฟࡉࢀࡓ࡜ࡁ㸪ࡑࡢ཯㊴ཎᏊࡀ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮
ࢱࣜࣥࢢ⌧㇟࡟ᑐࡍࡿ⌮ㄽⓗ࡞ྲྀࡾᢅ࠸ࡣ㸪༑ศ⾪
ࡼࡾ኱ࡁ࡞࢚ࢿࣝࢠ࣮ࢆࡶࡗ࡚࠸ࡿሙྜ㸪ࢱ࣮ࢤࢵ
✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋࡓሙྜ࡟ᑐࡋ࡚ࡔࡅ᭷ຠ࡛
ࢺཎᏊࡣᅛయ⾲㠃࠿ࡽᨺฟࡉࢀࡿ㸬ࡇࡢ⌧㇟ࢆࢫࣃ
࠶ࡾ 㸪ධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ሙྜࡸ㸪ධᑕ⢏Ꮚࡀ
ࢵࢱࣜࣥࢢ࡜࠸࠺㸬ࡇࡢࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࡣ⌧
Ỉ⣲ཎᏊ࡞࡝ࡢ㍍࢖࢜ࣥࡢሙྜࡣ㸪ࡇࡢ⾪✺࢝ࢫࢣ
*Department
of Biomedical Engineering
Telephone: +81-774-65-6687, E-mail: [email protected]
58 ）
（ 少数回衝突機構によるスパッタリング現象への寄与
59
య⾪✺㏆ఝ
࣮ࢻࡀ༑ศ࡟Ⓨ㐩ࡏࡎ㸪ࡑࡢሙྜࡢࢫࣃࢵࢱࣜࣥࢢ
ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ ACAT ࡣ๓㏙ࡢ㏻
⌧㇟ࡣ⌮ㄽⓗ࡟ண ࡉࢀࡿ᣺ࡿ⯙࠸࡜␗࡞ࡿࡶࡢ
ࡾࣔࣥࢸ࢝ࣝࣟἲࢆᇶ࡟㸪ᅛయෆࡢཎᏊ⾪✺࡟㛵ࡋ
࡜⪃࠼ࡽࢀࡿ㸬
ᮏ◊✲࡛ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸
࡚ 2 య⾪✺㏆ఝ 9)ࢆ᥇⏝ࡋ࡚࠸ࡿ㸬⢏Ꮚࡀᅛయෆ࡟
పධᑕ࢚ࢿࣝࢠ࣮㸪㍍࢖࢜ࣥࢫࣃࢵࢱࣜࣥࢢ࡟ࡘ࠸
ධᑕࡉࢀࡿ࡜㸪⾪✺࢝ࢫࢣ࣮ࢻ࡜࿧ࡤࢀࡿ⾪✺㐃㙐
࡚㸪ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ ACAT ࢆ⏝࠸࡚㸪ࢫ
ࡀ㉳ࡇࡿ㸬2 య⾪✺㏆ఝࡣ㸪Fig. 2 ࡟♧ࡉࢀࡿࡼ࠺
ࣃࢵࢱࣜࣥࢢ࡟ᑐࡍࡿᑡᩘᅇ⾪✺ࡢᐤ୚࡟ࡘ࠸࡚
࡟㐠ືࡋ࡚࠸ࡿ⢏Ꮚ࡜㟼Ṇࡋ࡚࠸ࡿᶆⓗཎᏊࡢ 2
ゎᯒࢆ⾜࠸㸪⌮ㄽ࡜ࡢ㐪࠸ࢆ᳨ドࡋࡓ㸬
ࡘࡢࡳࢆ⪃៖ࡋ㸪ཎᏊ⾪✺ࢆᶍᨃࡍࡿ㸬2 య⾪✺㏆
ఝࡣ㸪ධᑕ⢏Ꮚࡢ㐠ື࢚ࢿࣝࢠ࣮E ࡀᩘⓒ eV ௨ୖ
㸬ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ $&$7
࡛ࡼ࠸㏆ఝࢆ୚࠼ࡿ࡜࠸ࢃࢀ࡚࠸ࡿ㸬୍᪉㸪ධᑕ࢚
ࢫࣃࢵࢱࣜࣥࢢࡢࢩ࣑࣮ࣗࣞࢩࣙࣥゎᯒ࡟㛵
ࢿࣝࢠ࣮ࡀ 100 eV ௨ୗࡢప࢚ࢿࣝࢠ࣮࡛ࡣ㸪ධᑕ
ࡋ࡚㸪⌧ᅾࡲ࡛࡟ 2 య⾪✺㏆ఝἲ࡜ࣔࣥࢸ࢝ࣝࣟἲ
⢏Ꮚࡢ࿘ࡾ࡟࠶ࡿࢱ࣮ࢤࢵࢺཎᏊ࠿ࡽࡢᐤ୚ࡀ↓
ࢆࡶ࡜࡟ࡋࡓࢩ࣑࣮ࣗࣞࢩࣙࣥࢥ࣮ࢻࡀᗄࡘ࠿㛤
ど࡛ࡁ࡞ࡃ࡞ࡾ㸪㏆ఝࡣᝏࡃ࡞ࡿ㸬
Ⓨࡉࢀ࡚࠾ࡾ㸪ࢫࣃࢵࢱࣜࣥࢢ཰㔞࡞࡝ከࡃࡢ᭷⏝
࡞ࢹ࣮ࢱࡀ⏕ᡂࡉࢀ࡚࠸ࡿ
6)
㸬௦⾲ⓗ࡞ࡶࡢ࡟
⾪✺ᚋࡢ࢚ࢿࣝࢠ࣮ E㸫T
ACAT ࢥ࣮ࢻ 㸦Atomic Collision in Amorphous
7)
Target㸧㸪TRIM ࢥ࣮ࢻ 8)㸦Transport in Material㸧
ࡀᣲࡆࡽࢀࡿ㸬௨ୗ࡟㸪௒ᅇゎᯒ࡟⏝࠸ࡓ ACAT
ධᑕ⢏Ꮚࡢ㌶㊧
ධᑕ࢚ࢿࣝࢠ࣮ E
ᐇ㦂⣔ࡢᩓ஘ゅ T
ࢥ࣮ࢻࣔࢹࣝࡢ୺せ࡞㒊ศࢆㄝ᫂ࡍࡿ㸬
ACAT ࢥ࣮ࢻࡣ㸪Fig. 1 ࡟♧ࡍࡼ࠺࡟ࢱ࣮ࢤࢵ
⾪✺ಀᩘ p
ࢺࢆ 1 ㎶ R0㸦=N-1/3㸧ࡢࣘࢽࢵࢺࢭࣝ࡟ศ๭ࡋ㸪ࣘ
42
㸦㔜ᚰ⣔ࡢᩓ஘ゅ 4 㸧
ࢽࢵࢺࢭࣝ࡟஘ᩘࢆ⏝࠸࡚ࢱ࣮ࢤࢵࢺཎᏊࢆ 1 ࡘ
ᐇ㦂⣔ࡢ཯㊴ゅ I
ࣛࣥࢲ࣒࡟㓄⨨ࡉࡏ㸪࢔ࣔࣝࣇ࢓ࢫ㸦㠀⤖ᬗ㸧ࢱ࣮
ࢱ࣮ࢤࢵࢺཎᏊࡢ
ࢤࢵࢺࢆᵓᡂࡍࡿ㸬ࡇࡇ࡛㸪N ࡣࢱ࣮ࢤࢵࢺࡢᩘᐦ
ึᮇ఩⨨
཯㊴⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ T
Fig. 2. Binary collision approximation.
ᗘ㸦atoms/cm3㸧࡛࠶ࡿ㸬
2 య⾪✺㏆ఝ࡟ࡼࡿ㔜ᚰ⣔ࡢᩓ஘ゅ 4 ࡣ㸪ḟᘧ
ධᑕ࢖࢜ࣥ
࡛ᐃ⩏ࡉࢀࡿ㸬
f
³>
@
1
4 S 2 p r 2 g r dr
(1)
r0
ࡇࡇ࡛㸪p ࡣ⾪✺ᚄᩘ㸬r ࡣཎᏊ㛫㊥㞳㸪r0 ࡣ᭱㏆᥋
㊥㞳࡛࠶ࡾ㸪㏆᪥Ⅼ࡜ࡶ࿧ࡤࢀ㸪g (r0 )
0 ࢆ‶ࡓࡍ㸬
ࡇࢀࡽࢆᶍᘧⓗ࡟ Fig. 2 ࡟♧ࡍ㸬Fig. 2 ୰ T ࡣᩓ஘
ᚋ࡟ࢱ࣮ࢤࢵࢺཎᏊࡀᚓࡿ㐠ື࢚ࢿࣝࢠ࣮࡛࠶ࡿ㸬
ࡋࡓࡀࡗ࡚㸪ᩓ஘ᚋࡢධᑕ⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ࡣ E㸫
R0
T ࡛୚࠼ࡽࢀࡿ㸬ࡲࡓ㸪㛵ᩘ g(r)ࡣ
Fig. 1. Unite Cell model (ACAT).
1
g (r )
59 ）
（ ª p 2 V (r ) º 2
«1 2 »
E r »¼
«¬ r
(2)
剣持貴弘
60
࡛୚࠼ࡽࢀࡿ㸬ࡇࡇ࡛㸪V(r)ࡣཎᏊ㛫࣏ࢸࣥࢩࣕࣝ
Moriere ࡢ㐽ⶸ㛵ᩘ 12)ࢆ⏝࠸ࡓ㸬
࡛ ACAT ࢥ࣮ࢻ࡛ࡣ㸪᩺ຊ࣏ࢸࣥࢩࣕࣝࡢࡳࡀ⪃៖
ࡉࢀࡿ㸬ཎᏊ㛫࣏ࢸࣥࢩࣕࣝ࡟㛵ࡋ࡚ࡣ㸪ḟ⠇࡛ヲ
(1) Moliere ࣏ࢸࣥࢩࣕࣝ
I x Mol
ࡋࡃ㏙࡭ࡿ㸬
ࡇࡇ࡛㸪r ࡣཎᏊ㛫㊥㞳࡛࠶ࡿ㸬ࡲࡓ x
ᘧ㸦2㸧୰ࡢ Er ࡣ┦ᑐ࢚ࢿࣝࢠ࣮࡛㸪
§ A ·
¸E
¨
© A 1¹
Er
r a ࡛࠶ࡾ㸪
ࢆ⏝࠸ࡿ㸬ZBL( Ziegler㸪Biersak, Littmark)࣏ࢸࣥࢩ
࡜ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪㉁㔞ẚ A ࡣ㸪ධᑕ⢏Ꮚࡢ㉁
ࣕࣝ 13)௨እࡣ㸪ࡇࡢ Firsov ࡢ㐽ⶸ㛗ࡉࢆ⏝࠸ࡿ㸬
M 2 M1 ࡛
࠶ࡿ㸬ᘧ㸦1㸧࠿ࡽᚓࡽࢀࡿ㔜ᚰ⣔ࡢᩓ஘ゅ 4 ࠿ࡽ㸪
(2) Kr-C (Krupyon-Carbon)࣏ࢸࣥࢩࣕࣝ 14)
ᐇ㦂ᐊ⣔ࡢᩓ஘ゅ T ࡜཯㊴࢚ࢿࣝࢠ࣮T ࡣ㸪
I x Kr C
T
T
A sin 4
1 A cos 4
tan 1
4A
A 12
(8)
㐽ⶸ㛗ࡉ a ࡣᘧ㸦7㸧࡛୚࠼ࡽࡿ Firsov ࡢ㐽ⶸ㛗ࡉ
(3)
㔞 M1 ࡜ᶆⓗ⢏Ꮚࡢ㉁㔞 M2 ࡜ࡢẚ࡛㸪A
0.35e 0.3 x 0.55e 1.2 x 0.10e 6.0 x
§4·
E sin ¨ ¸
©2¹
0.1909451e 0.278544 x 0.473674e 0.63717 x
0.0.335381e 1.919249 x
(4)
(5)
(9)
(3) ࢰ࣐࣮ࣥࣇ࢙ࣝࢺ࣏ࢸࣥࢩࣕࣝ 15)
­1 x 1441 3
®
¯
I x som
࡜࡞ࡿ㸬
O ½¾¿
c
3 ࡢ㛵ಀࡀ࠶ࡾ㸪 O
ࡇࡇ࡛㸪 cO
(10)
0.8034 ࡛࠶ࡿ㸬
ཎᏊ㛫ຊ࣏ࢸࣥࢩࣕࣝ
ACAT ࢥ࣮ࢻ࡛ࡣ㸪ཎᏊ㛫࡟స⏝ࡍࡿ᩺ຊࢆホ
(4) ZBL ࣏ࢸࣥࢩࣕࣝ
౯ࡍࡿ 2 య㛫࣏ࢸࣥࢩࣕࣝ࡜ࡋ࡚㸪ࢺ࣮࣐ࢫ࣭ࣇ࢙
࣑ࣝࣔࢹࣝ࡟ࡼࡿ㐽ⶸࢡ࣮࣏ࣟࣥࢸࣥࢩࣕࣝ
10)ࢆ
᥇⏝ࡍࡿ㸬ཎᏊ␒ྕ Z1㸪Z2 ࡢ 2 ࡘࡢཎᏊ㛫࡟ാࡃ᩺
Ziegler㸪Biersak, Littmark ࡟ࡼࡗ࡚ᥦ᱌ࡉࢀࡓ
ཎᏊ㛫ຊ࣏ࢸࣥࢩ࡛ࣕࣝ㸪௨ୗ࡛ᐃ⩏ࡉࢀࡿ㸬
I x ZBL
0.028171e 0.20162 x 0.28022e 0.4029 x
0.50986e 0.94229 x 0.18175e 3.1998 x
ຊ࣏ࢸࣥࢩࣕࣝࡣ㸪
(11)
2
Z1 Z 2 e § r ·
I¨ ¸
r
©a¹
V (r )
(6)
ࡇࡇ࡛㸪㐽ⶸ㛗ࡉ a ࡣḟᘧ࡛ᐃ⩏ࡉࢀࡿ㸬
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪 I r a ࡣ㐽ⶸ㛵ᩘ࡛㸪a ࡣ
a
㐽ⶸ㛗ࡉ(Å)࡛࠶ࡾ㸪Firsov11)࡟ࡼࡗ࡚
a
0.4658
Z 11 2
23
Z 21 2
(7 )
࡜୚࠼ࡽࢀ࡚࠸ࡿ㸬ཎᏊ᰾ࡢṇ㟁Ⲵࡀ㸪࿘ࡾ࡟Ꮡᅾ
Z
0.4658
0.23
1
Z 20.23
(12)
23
࡜ᐃ⩏ࡋ࡚⏝࠸ࡿ㸬
(5) AMLJ㸦Averaged Modified Lenz-Jensen 㸧࣏ࢸࣥ
ࢩࣕࣝ 16)
ࡍࡿ㟁Ꮚࡢ㈇㟁Ⲵ࡟ࡼࡗ࡚㐽ⶸࡉࢀࡿຠᯝࢆྲྀࡾ
I x AMLJ
ධࢀࡓᙧ࡜࡞ࡗ࡚࠸ࡿ㸬ࡋࡓࡀࡗ࡚㸪ཎᏊ㛫ࡢ㊥㞳
exp D 1 x D 2 x 3 2 D 3 x 2
(13)
ࡀ㞳ࢀ࡚࠸ࡿሙྜࡣཎᏊ᰾ࡢṇ㟁Ⲵࡣ㟁Ꮚࡢ㈇㟁
Ⲵ࡟㐽ⶸࡉࢀ㸪⾪✺┦ᡭࡢཎᏊ࠿ࡽࡳࡿ࡜୰ᛶ࡟ぢ
ࡇࡇ࡛㸪 D j j 1, 2, 3 ࡣḟᘧ࡛ᐃ⩏ࡉࢀࡿ㸬
࠼㸪ẁࠎ࡜ཎᏊ㛫㊥㞳ࡀ㏆࡙ࡃ࡟ࡘࢀ㐽ⶸࡢຠᯝࡀ
ῶᑡࡋ࡚࠸ࡃ㸬
(14) (15)
D 1 1.706 Z 10.307 Z 20.307
㐽ⶸ㛵ᩘ࡟ࡘ࠸࡚ࡣ㸪ከࡃࡢ㛵ᩘᙧࡀᥦ᱌ࡉࢀ
࡚࠾ࡾ㸪ACAT ࢥ࣮ࢻ࡛ࡣ㸪௨ୗࡢ 5 ࡘࡢ㐽ⶸ㛵ᩘ
ࢆ᥇⏝ࡍࡿࡇ࡜ࡀ࡛ࡁࡿ㸬ᮏ◊✲࡟࠾࠸࡚ࡣ㸪
60 ）
（ D2
0.916 Z 10.169 Z 20.169
23
少数回衝突機構によるスパッタリング現象への寄与
D3
0.244 Z 10.0418 Z 20.0418
ࡇࡇ࡛㸪 x { r a B ࡛࠶ࡾ㸪 a B
2
61
㜼Ṇ᩿㠃✚ࢆ s ZBL (E ) ࡜ࡍࡿ࡜㸪ධᑕ⢏Ꮚࡀࢱ࣮ࢤ
(16)
ࢵࢺ୰ࢆ 'x ࡔࡅ㐍ࡴ㛫࡟ኻ࠺㟁Ꮚⓗ࢚ࢿࣝࢠ࣮ᦆ
0.529 Å㸦࣮࣎࢔
ኻ 'E ࡣ㸪
'E
༙ᚄ㸧ࢆ⏝࠸ࡿ㸬
Ns ZBL ( E )'x
(19)
࡜⾲ࡉࢀࡿ㸬
࢚ࢿࣝࢠ࣮ᦆኻ
㐠ືࡋ࡚࠸ࡿ⢏Ꮚࡀ㟼Ṇࡋ࡚࠸ࡿࢱ࣮ࢤࢵࢺ
ࢫࣃࢵࢱࣜࣥࢢ཰㔞ࡢホ౯ᘧ
ཎᏊ࡜⾪✺ࡍࡿࡇ࡜࡟ࡼࡿ㐠ື࢚ࢿࣝࢠ࣮ࡢᦆኻ
ACAT ࢥ࣮ࢻ࡛ィ⟬ࡉࢀࡓࢫࣃࢵࢱࣜࣥࢢ཰
ࡣ㸪⾪✺ࡢ๓ᚋ࡛㐠ື࢚ࢿࣝࢠ࣮࡜㐠ື㔞ࡀಖᏑࡉ
㔞ࡢጇᙜᛶࢆ᳨ドࡍࡿࡓࡵ㸪⤖ᯝࢆᐇ㦂ࢹ࣮ࢱ㸪ཬ
ࢀࡿᙎᛶ⾪✺࡟ࡼࡿࡶࡢ࡜㸪㐠ື㔞ࡀಖᏑࡉࢀ࡞࠸
ࡧᐇ㦂ࢹ࣮ࢱࢆࡼࡃ෌⌧ࡍࡿࡇ࡜࡛▱ࡽࢀࡿ
㠀ᙎᛶ⾪✺࡜ࡀ࠶ࡿ㸬ᙎᛶ⾪✺࡟ࡼࡗ࡚㸪ࢱ࣮ࢤࢵ
Yamamura ➼࡟ࡼࡗ࡚ᥦ᱌ࡉࢀࡓබᘧ
ࢺཎᏊ࡟୚࠼ࡿ࢚ࢿࣝࢠ࣮ࡣᘧ㸦5㸧࡛୚࠼ࡽࢀࡿ㸬
㍑ࡋࡓ㸬ࡇࡢࢫࣃࢵࢱࣜࣥࢢබᘧࡣ㸪ᆶ┤ධᑕࡢࢫ
㠀ᙎᛶ⾪✺ࡣ㸪㟁Ꮚⓗ࢚ࢿࣝࢠ࣮ᦆኻ࡜ࡶゝࢃࢀ㸪
ࣃࢵࢱࣜࣥࢢ཰㔞ࢆホ౯ࡋ㸪⥺ᙧ࢝ࢫࢣ࣮ࢻ⌮ㄽ 5)
ධᑕ࢚ࢿࣝࢠ࣮ࡀ኱ࡁࡃ࡞ࡿ࡟ࡘࢀ࡚ࢱ࣮ࢤࢵࢺ
࠿ࡽᑟ࠿ࢀࡿ㛵ᩘᙧ࡟㸪ᐇ㦂ࢹ࣮ࢱࢆᇶ࡟Ỵࡵࡽࢀ
ཎᏊࡢཎᏊ᰾ࡢࡲࢃࡾ࡟Ꮡᅾࡍࡿ㟁Ꮚ⣔࡟㸪ບ㉳࣭
ࡓࣇ࢕ࢵࢸ࢕ࣥࢢࣃ࣓࣮ࣛࢱࢆྵࡴ༙⌮ㄽ༙ᐇ㦂
㟁㞳࡜࠸࠺㐣⛬ࢆ⤒࡚࢚ࢿࣝࢠ࣮ࡀ௜୚ࡉࢀࡿࡼ
ᘧ࡛࠶ࡿ㸬ࡇࡢࣇ࢕ࢵࢸ࢕ࣥࢢࣃ࣓࣮ࣛࢱ࡟㛵ࡋ࡚
࠺࡟࡞ࡿ㸬㟁Ꮚ⣔࡟࢚ࢿࣝࢠ࣮ࡀ௜୚ࡉࢀࡿሙྜࡣ㸪
ࡣ㸪ཧ⪃ᩥ⊩ 6)࡟ᩘ್⾲ࡀ࠶ࡾ㸪ࢱ࣮ࢤࢵࢺẖ࡟᭱
㟁Ꮚࡢ㉁㔞ࡀධᑕ⢏Ꮚ࡟ẚ࡭࡚ᅽಽⓗ࡟ᑠࡉ࠸ࡓ
㐺್ࡀ♧ࡉࢀ࡚࠸ࡿ㸬 Yamamura බᘧ࡛୚࠼ࡽࢀ
ࡵ࡟㸪ධᑕ⢏Ꮚࡣ┤㐍ࡍࡿ࡜⪃࠼࡚ࡼ࠸㸬
ࡿࢫࣃࢵࢱࣜࣥࢢ཰㔞ࡣᘧ㸦20㸧࡛୚࠼ࡽࢀࡿ㸬
ධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ୰ࢆ༢఩㛗ࡉᙜࡓࡾ㐍
ࡴࡢ࡟ኻ࠺࢚ࢿࣝࢠ࣮ࢆ㜼Ṇ⬟࡜࠸࠸㸪
³
dE
dx
N T ( p) ˜ 2Spdp
Ns ( E )
Y (E)
(17)
6)ࡢ⤖ᯝ࡜ẚ
§ QD ·­° S n ( E ) ½°­ § E th ·½
¸®
1 ¨¨
0.042¨¨
¸¸¾
¸
0.3 ¾®
© U s ¹°̄1 *k e H °¿¯ © E ¹¿
s
(20)
ࡇࡇ࡛㸪Y(E) [atoms/ion]ࡣධᑕ࢚ࢿࣝࢠ࣮E [eV]ࡢ
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪x ࡣධᑕ⢏Ꮚࡀࢱ࣮ࢤࢵࢺ
࡜ࡁࡢࢫࣃࢵࢱࣜࣥࢢ཰㔞㸪Q㸪s ࡣࢱ࣮ࢤࢵࢺཎ
୰ࢆ㐍ࢇࡔ㛗ࡉ㸪N [atoms/cm ]ࡣࢱ࣮ࢤࢵࢺࡢᩘᐦ
Ꮚ࡟౫Ꮡࡍࡿࣃ࣓࣮ࣛࢱ࡛࠶ࡿ㸬ࡲࡓ㸪Us [eV]ࡣࢱ
ᗘ࡛㸪T(p)ࡣ⾪✺ಀᩘ p ࡟࠾ࡅࡿ཯㊴࢚ࢿࣝࢠ࣮㸪
࣮ࢤࢵࢺཎᏊࡢ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮࡛㸪㏻ᖖࡣ᪼⳹
s(E) [eV ˜ cm ]ࡣ㜼Ṇ᩿㠃✚࡜࿧ࡤࢀࡿ㸬ᘧ㸦17㸧࡟
࢚ࢿࣝࢠ࣮ࡀ⏝࠸ࡽࢀࡿ㸬Eth [eV]ࡣࢫࣃࢵࢱࣜࣥࢢ
ࡣ㸪ᙎᛶ⾪✺࡟ࡼࡿ࢚ࢿࣝࢠ࣮ᦆኻ࡜㸪㠀ᙎᛶ⾪✺
ࡢࡋࡁ࠸್࢚ࢿࣝࢠ࣮࡛㸪
3
2
࡟ࡼࡿ࢚ࢿࣝࢠ࣮ᦆኻࡀྵࡲࢀ࡚࠾ࡾ㸪๓⪅ࢆ᱁ⓗ
㜼Ṇ⬟ dE dx n 㸪ᚋ⪅ࢆ㟁Ꮚⓗ㜼Ṇ⬟ dE dx e ࡜࿧
E th
ࡪ㸬㜼Ṇ⬟ࢆࡇࢀࡽ஧ࡘࡢせ⣲࡟ศ๭ࡋ࡚⾲ࡍ࡜㸪
dE
dx
§ dE · § dE ·
¸
¸ ¨
¨
© dx ¹ n © dx ¹ e
N s n ( E ) s e E (18)
E th
ª1 5.7M 1 M 2 º
«
» uU s
J
¬
¼
for
6.7
J
M1 d M 2
(21)
M1 t M 2
(22)
uU s
for
࡜࡞ࡿ㸬
㟁 Ꮚ ⓗ 㜼 Ṇ ⬟ ࡢ ⌮ ㄽ ࡜ ࡋ ࡚ 㸪 Lindhard 㸪
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪Jࡣᙎᛶ⾪✺࡟࠾ࡅࡿ࢚ࢿ
Scharff㸪Schiøtt ࡟ࡼࡗ࡚ᥦ᱌ࡉࢀࡓ LSS ࡢ㜼Ṇ⬟
ࣝࢠ࣮⛣⾜ᅉᏊ࡛㸪
7)
බᘧ ࡀ᭷ྡ࡛࠶ࡿࡀ㸪ACAT ࢥ࣮ࢻ࡟࠾࠸࡚ࡣ㸪
J
Ziegler㸪Biersak, Littmark (ZBL)࡟ࡼࡗ࡚୚࠼ࡽࢀࡓ
ᗈ࠸࢚ࢿࣝࢠ࣮⠊ᅖ࡟ரࡗ࡚㐺⏝࡛ࡁࡿᐇ㦂ࢹ࣮
ࢱࢆᇶ࡟ࡋࡓබᘧ
4M 1 M 2
M 1 M 2 2
(23)
࠶ࡿ㸬ࡑࡢ௚ࡢࣃ࣓࣮ࣛࢱࡣḟࡢࡼ࠺࡟ᐃ⩏ࡉࢀࡿ㸬
17)
ࢆ᥇⏝ࡋ࡚࠸ࡿ㸬ࡇࡢᐇ㦂ᘧࡢ
61 ）
（ 剣持貴弘
62
D
D
§M
0.249¨¨ 2
© M1
§M
0.088¨¨ 2
© M1
·
¸¸
¹
·
¸¸
¹
0.56
࣮ࡢ Ar+࢖࢜ࣥ, H+࢖࢜ࣥ࡜ࡋ㸪ࢱ࣮ࢤࢵࢺࡣ㖡ࢆ
0.15
§M ·
0.0035¨¨ 2 ¸¸
© M1 ¹
for M 1 d M 2
0.15
§M ·
0.165¨¨ 2 ¸¸
© M1 ¹
for M 1 t M 2
㑅ࢇࡔ㸬
(24)
㸬 $U㸫&X ࢫࣃࢵࢱࣜࣥࢢ
Fig. 3 ࡟㸪Ar+࢖࢜ࣥࢆ㖡ࢱ࣮ࢤࢵࢺ⾲㠃࡟ᑐ
ࡋ࡚ᆶ┤࡟ධᑕࡉࡏࡓሙྜࡢ㖡ཎᏊࡢࢫࣃࢵࢱࣜ
ࣥࢢ཰㔞ࡢᐇ㦂ࢹ࣮ࢱ
(25)
18-20)
㸪 ACAT ࢹ ࣮ ࢱ 㸪
Yamamura බᘧ࡟ࡼࡾᚓࡽࢀࡓ⤖ᯝࢆ♧ࡍ㸬Fig. 3
ࡇࡇ࡛㸪M1㸪M2 [a.m.u]ࡣධᑕ⢏Ꮚ࡜ࢱ࣮ࢤࢵࢺཎ
ࡼࡾ㸪ACAT ࢹ࣮ࢱ㸪Yamamura බᘧ࡜ࡶ㸪ⱝᖸ
Ꮚࡢ㉁㔞࡛࠶ࡿ㸬᰾ⓗ㜼Ṇ᩿㠃✚ Sn(E) [eV·Å/cm2]
ࡢᕪࡣぢࡽࢀࡿࡀ㸪ᐇ㦂ࢹ࣮ࢱࡢㄗᕪ࡞࡝ࢆ⪃៖ࡍ
ࡣ㸪
ࡿ࡜㸪ᐇ㦂ࢹ࣮ࢱ࡜ࡼࡃ୍⮴ࡋ࡚࠸ࡿ㸬ࡇࡢሙྜ࡟
S n E Z
84.78Z 1 Z 2
23
1
Z 22 3
M1
s n (H )
M1 M 2
12
⏝࠸ࡓ Yamamura බᘧࡢࣇ࢕ࢵࢸ࢕ࣥࢢࣃ࣓࣮ࣛ
(26)
ࢱࡢ್ࡣ㸪Q=1.0㸪W=0.73㸪s=2.5 ࡛࠶ࡿ㸬ࡲࡓ㸪
ACAT ࢥ࣮ࢻ࡜ Yamamura බᘧ࡟ࡘ࠸࡚ࡶ㸪ࡼࡃ
࡛ᐃ⩏ࡉࢀࡿ㸬ࡇࡇ࡛㸪Z1㸪Z2 ࡣධᑕ⢏Ꮚ࡜ࢱ࣮ࢤ
୍⮴ࡋ࡚࠾ࡾ㸪ࢫࣃࢵࢱࣜࣥࢢ཰㔞ࡢゎᯒ࡟㛵ࡋ࡚㸪
ࢵࢺཎᏊࡢཎᏊ␒ྕ࡛࠶ࡿ㸬ࡲࡓ㸪᥮⟬᰾ⓗ㜼Ṇ᩿
ACAT ࢥ࣮ࢻ㸪Yamamura බᘧ࡜ࡶ᭷⏝࡛࠶ࡿ࡜
㠃✚ s n (H ) ࡣ㸪
⪃࠼ࡽࢀࡿ㸬
s n H 3.441 H ln H 2.718
1 6.355 H H 6.882 H 1.708
M1
u
s n (H )
M1 M 2
(27)
࡛୚࠼ࡽࢀࡿ㸬ࡇࡇ࡛㸪᥮⟬࢚ࢿࣝࢠ࣮ H ࡣ
H
0.03255
Z 1 Z 2 Z 12 3
12
Z 22 3
M1
E
M1 M 2
(28)
࡛࠶ࡿ㸬ࡲࡓ㸪
*
W
(29)
1 M 1 7 3
࡛୚࠼ࡽࢀ㸪ࣇ࢕ࢵࢸ࢕ࣥࢢࣃ࣓࣮ࣛࢱ W ࡣࢱ࣮
ࢤࢵࢺཎᏊ࡟౫Ꮡࡍࡿ㸬ke ࡣ Lindhard ࡢ㟁Ꮚⓗ㜼Ṇ
⬟ಀᩘ࡛࠶ࡾ㸪
ke
0.079
M 1 M 2 3 2
M 13 2 M 21 2
Z
Z 12 3 Z 21 2
23
1
Z 22 3
Fig. 3. Sputtering yields of Cu bombarded by Ar+
34
(30)
ions at 0°.
ḟ࡟㸪100 eV㸪5 keV ࡢ Ar+࢖࢜ࣥࢆ㖡ࢱ࣮ࢤ
࡛࠶ࡿ㸬
4㸬ゎᯒ⤖ᯝ
ࢵࢺ࡟ᆶ┤࡟ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉࢀࡓ
ACAT ࢥ࣮ࢻࢆ⏝࠸࡚㸪⾪✺࢝ࢫࢣ࣮ࢻࡀ༑ศ
㖡ཎᏊࡢゅᗘศᕸࢆ ACAT ࢥ࣮ࢻ࡛ゎᯒࡋࡓ⤖ᯝ
Ⓨ㐩ࡋ࡞࠸ሙྜ࡟࠾࠸࡚㸪ࢫࣃࢵࢱࣜࣥࢢࡀ⌮ㄽ࡜
ࢆ Fig. 4㸪5 ࡟♧ࡍ㸬ࡲࡓ㸪༑ศⓎ㐩ࡋࡓ⾪✺࢝ࢫ
࡝ࡢࡼ࠺࡟␗࡞ࡿ࠿ࢆゎᯒࡋࡓ㸬⾪✺࢝ࢫࢣ࣮ࢻࡀ
ࢣ࣮ࢻ࡟ࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉࢀࡓࢫࣃࢵࢱ࣮⢏Ꮚ
༑ศⓎ㐩ࡋ࡞࠸ሙྜ࡜ࡋ࡚㸪ධᑕ⢏Ꮚࢆప࢚ࢿࣝࢠ
ࡢゅᗘศᕸࢆ෌⌧ࡍࡿ࡜ࡋ࡚⌮ㄽⓗ࡟ᑟ࠿ࢀࡿࢥ
62 ）
（ 少数回衝突機構によるスパッタリング現象への寄与
ࢧ࢖ࣥศᕸ
12)
ࡶేࡏ࡚♧ࡍ㸬ࢥࢧ࢖ࣥศᕸࡣᴟゅ
63
Us ࡣࢱ࣮ࢤࢵࢺཎᏊࡢ⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮࡛࠶ࡿ㸬
T㹼T dT 㸪᪉఩ゅ I㹼I dI ୰࡟ᨺฟࡉࢀࡿ⢏Ꮚ
࡟ᑐࡍࡿࢫࣃࢵࢱ⋡ࢆ Y T , I ࡜ࡋ࡚㸪
Y (T , I )dTdI v cos TdTdI
(31)
࡛⾲ࡉࢀࡿ㸬ࡇࡇ࡛㸪ゅᗘ T ࡣᅛయ⾲㠃࡟ᑐࡋ࡚ᆶ
┤᪉ྥࢆ 0r࡜ࡋ㸪ྑഃࢆ 0r㹼90r㸪ᕥഃࢆ 0r
㹼㸫90r࡜ࡍࡿ㸬ᅗ୰࡟♧ࡉࢀࡿࢥࢧ࢖ࣥศᕸࡣ㸪
ゅᗘศᕸࡢᆶ┤ᡂศ࡜୍⮴ࡍࡿࡼ࠺࡟つ᱁໬ࡋ࡚
࠶ࡿ㸬ᅗ࡟♧ࡉࢀࡿࡼ࠺࡟㸪
ධᑕ࢚ࢿࣝࢠ࣮ࡀ 1 keV
ࡢሙྜࡣ㸪࡯ࡰࢥࢧ࢖ࣥศᕸ࡜୍⮴ࡋ࡚࠸ࡿࡢ࡟ᑐ
ࡋ࡚㸪100 eV ࡢሙྜࡣ㸪ゅᗘศᕸࡢᆶ┤ᡂศࡀᢚ
Fig. 5. Calculated angular distributions of sputtered Cu
࠼ࡽࢀࡓ࢔ࣥࢲ࣮࣭ࢥࢧ࢖ࣥศᕸࢆ♧ࡋ࡚࠸ࡿ㸬ࡇ
atoms bombarded by 1 keV Ar+ ions at 0°.
ࢀࡣධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ࡓࡵ࡟㸪ᅛయෆ࡛⾪✺࢝
ࡲࡓ㸪ࢺࣥࣉࢯࣥࡢබᘧ࡛୚࠼ࡽࢀࡿ࢚ࢿࣝࢠ࣮
ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡏࡎ㸪ධᑕ᪉ྥࡢ㐠ື㔞ᡂศࡀ
ศᕸࡢࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧࢆ࢚
ከࡃṧࡗ࡚࠸ࡿࡓࡵ࡛࠶ࡿ㸬
ࢿࣝࢠ࣮࡟㛵ࡋ࡚ᚤศࡋ࡚ᴟ್ࢆồࡵࡿࡇ࡜࡛ᚓ
ࡽࢀ㸪ࡑࡢ್ࡣ U s 2 ࡜࡞ࡿ㸬ࢱ࣮ࢤࢵࢺࡀ㖡ࡢሙ
ྜ㸪⾲㠃⤖ྜ࢚ࢿࣝࢠ࣮ࡣ 3.49 eV ࡛࠶ࡾ㸪⌮ㄽⓗ
࡟ண ࡉࢀࡿࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ 1.75 eV ࡛࠶ࡿ㸬
Fig. 6 ࡟♧ࡉࢀࡿࡼ࠺࡟㸪ධᑕ࢚ࢿࣝࢠ࣮1 keV ࡢ
ሙྜࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧ࡟ࡼࡃྜ⮴ࡋ࡚࠸ࡿࡇ࡜
ࡀศ࠿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࡞࠸ࡇ࡜ࡢᙳ㡪ࡣ㸪ࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚
ࢿࣝࢠ࣮ศᕸ࡟ࡶ⌧ࢀࡿ㸬ゅᗘศᕸ࡜ྠᵝ࡟ධᑕ࢚
ࢿࣝࢠ࣮100 eV ࡜ 1 keV ࡢ Ar+࢖࢜ࣥࢆ㖡ࢱ࣮ࢤ
ࢵࢺ࡟ᆶ┤࡟ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉࢀࡓ
㖡ཎᏊࡢ࢚ࢿࣝࢠ࣮ศᕸࢆ ACAT ࢥ࣮ࢻ࡛ゎᯒࡋ
ࡓ⤖ᯝࢆ Fig. 6㸪7 ࡟♧ࡍ㸬༑ศⓎ㐩ࡋࡓ⾪✺࢝ࢫ
Fig. 6. Calculated energy distributions of sputtered Cu
ࢣ࣮ࢻ࡟ࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉࢀࡓ⢏Ꮚࡣ⌮ㄽⓗ࡟
atoms bombarded by 1 k eV Ar+ ions at 0°.
ᑟ࠿ࢀࡿࢺࣥࣉࢯࣥࡢබᘧ
12)
࡟ᚑ࠺ࡇ࡜ࡀ▱ࡽࢀ
୍᪉㸪100 eV ࡢሙྜࡣ㸪ࢫࣃࢵࢱ࣮⢏Ꮚࡢ㧗࢚
࡚࠾ࡾ㸪ࢺࣥࣉࢯࣥࡢබᘧࡣ
Y ( E )dE v
E
E U s 3
(32)
ࢿࣝࢠ࣮㒊ศࡢ཰㔞ࡀ㸪ࢺࣥࣉࢯࣥࡢබᘧ࠿ࡽண ࡉࢀࡿࡶࡢ࡟ẚ࡭࡚ᑡ࡞࠸㸬ࡇࡢ㐪࠸ࡣ㸪ゅᗘศᕸ
࡜࡞ࡿ㸬
ࡇࡇ࡛㸪E ࡣࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚ࢿࣝࢠ࣮㸪
࡜ྠᵝ࡟⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡚࠸࡞࠸ࡇ࡜࡟
63 ）
（ 剣持貴弘
64
㉳ᅉࡍࡿ㸬ࡲࡓ㸪࢚ࢿࣝࢠ࣮ศᕸࡢࣆ࣮ࢡ࢚ࢿࣝࢠ
ゅࡀ␗࡞ࡿ㸬⤖ᯝ࡜ࡋ࡚㸪ᚋ᪉ᩓ஘ࡉࢀࡿ㍍࢖࢜ࣥ
࣮ࡣ㸪100 eV㸪1 keV ࡢධᑕ࢚ࢿࣝࢠ࣮ඹ㸪ࢺࣥࣉ
ࡢ᪉ྥࡣࣛࣥࢲ࣒࡟࡞ࡾ㸪➼᪉ⓗ࡟࡞ࡿ࡜⪃࠼ࡽࢀ
ࢯࣥࡢබᘧ࠿ࡽண ࡉࢀࡿ 1.75 eV ࡟㏆࠸್ࢆ♧ࡍ㸬
ࡿ㸬ࡋࡓࡀࡗ࡚㸪ᚋ᪉ᩓ஘ࡉࢀࡓ㍍࢖࢜ࣥ࡟ࡼࡗ࡚
ࡋࡓࡀࡗ࡚㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞࠸ࡇ࡜࡟ࡼ
ࢫࣃࢵࢱ࣮ࡉࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡣప࢚ࢿࣝࢠ࣮
ࡿ࢚ࢿࣝࢠ࣮ศᕸࡢᙳ㡪ࡣ㸪㧗࢚ࢿࣝࢠ࣮㒊ศࡢ཰
࡛࠶ࡗ࡚ࡶ㸪ゅᗘศᕸࡢᆶ┤᪉ྥᡂศࡢῶᑡࡣぢࡽ
㔞࡟⌧ࢀࡿ㸬
ࢀ࡞࠸㸬ࡇࡢഴྥࡣධᑕ࢖࢜ࣥ࡜ࢱ࣮ࢤࢵࢺཎᏊࡢ
㉁㔞ᕪࡀ኱ࡁ࠸ሙྜࡸ㸪ධᑕ࢚ࢿࣝࢠ࣮ࡀప࠸ሙྜ
࡟㢧ⴭ࡟࡞ࡿ㸬
Fig. 8. Calculated angular distributions of sputtered Cu
Fig. 7. Calculated energy distributions of sputtered Cu
atoms bombarded by 100 eV H+ ions at 0°.
atoms bombarded by 1 00eV Ar+ ions at 0°.
㸬+㸫&X ࢫࣃࢵࢱࣜࣥࢢ
⾪✺࢝ࢫࢣ࣮ࢻࡀᮍⓎ㐩࡜࡞ࡿࡢࡣ㸪Ỉ⣲࢖࢜
ࣥ࡞࡝ࡢ㍍࢖࢜ࣥ࡟ࡼࡿࢫࣃࢵࢱࣜࣥࢢࡢሙྜࡶ
ྠᵝ࡛࠶ࡿ㸬Fig. 8㸪9 ࡟ 100 eV H+࢖࢜ࣥࢆ㖡ࢱ
࣮ࢤࢵࢺ࡟ᆶ┤࡟ධᑕࡉࡏࡓሙྜࡢࢫࣃࢵࢱ࣮ࡉ
ࢀࡓ㖡ཎᏊࡢゅᗘศᕸ࡜࢚ࢿࣝࢠ࣮ศᕸࢆ♧ࡍ㸬
Fig. 8 ࡛♧ࡉࢀࡿࡼ࠺࡟㸪㍍࢖࡛࢜ࣥࢫࣃࢵࢱ࣮ࡉ
ࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡢゅᗘศᕸࡣ㸪100 eV ࡢప࢚
ࢿࣝࢠ࣮࡟ࡶ㛵ࢃࡽࡎࢥࢧ࢖ࣥ࡟㏆࠸ศᕸࢆ♧ࡍ㸬
ࡇࡢゎᯒ⤖ᯝࡣ㸪Ar+࢖࢜ࣥධᑕࡢሙྜ࡜␗࡞ࡿഴ
ྥ࡛࠶ࡿ㸬ࡇࢀࡣ Fig. 10 ࡟♧ࡉࢀࡿࡼ࠺࡟㸪㍍࢖
Fig. 9. Calculated energy distributions of sputtered Cu ࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢ࣓࢝ࢽࢬ࣒ࡀᑡᩘᅇ⾪✺࡟
atoms bombarded by 100 eV H+ ions at 0°.
ࡼࡿࡶࡢ࡛࠶ࡿࡇ࡜࡟㉳ᅉࡍࡿ㸬
㍍࢖࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢሙྜ㸪ධᑕ⢏Ꮚࡢ㉁
㔞ࡀࢱ࣮ࢤࢵࢺཎᏊ࡟ẚ࡭࡚㍍࠸ࡓࡵ࡟ࢱ࣮ࢤࢵ
㍍࢖࢜ࣥࢫࣃࢵࢱࣜࣥࢢࡢሙྜࡢ࢚ࢿࣝࢠ࣮
ࢺཎᏊ࡜⾪✺ࡋࡓ㝿࡟ᚋ᪉࡟ᩓ஘ࡉࢀࡿ⋡ࡀ㧗ࡃ
ศᕸࡣࢺࣥࣉࢯࣥࡢබᘧ࡜኱ࡁࡃ␗࡞ࡿ㸬࢚ࢿࣝࢠ
࡞ࡿ㸬ࡇࡢᚋ᪉࡟ᩓ஘ࡉࢀࡓ㍍࢖࢜ࣥࡢ᪉ྥࡣ㸪ࢱ
࣮ศᕸࡢࣆ࣮ࢡࢆ୚࠼ࡿ࢚ࢿࣝࢠ࣮ࡣࢺࣥࣉࢯࣥ
࣮ࢤࢵࢺཎᏊ࡜ࡢ⾪✺఩⨨ࡼࡗ࡚኱ࡁࡃᙳ㡪ࡉࢀ
ࡢබᘧ࡛ࡣ 1.75 eV ࡛࠶ࡿࡢ࡟ᑐࡋ࡚㸪ACAT ࡢ⤖
ࡿࡓࡵ࡟㸪ഹ࠿࡞⾪✺఩⨨ࡢ㐪࠸࡟࠾࠸࡚ࡶ㸪ᩓ஘
ᯝࡣప࢚ࢿࣝࢠ࣮ഃ࡟ࢩࣇࢺࡋ࡚࠾ࡾ㸪0.5 eV ㏆ഐ
64 ）
（ 少数回衝突機構によるスパッタリング現象への寄与
࡛࠶ࡿ㸬ࡲࡓ㸪࢚ࢿࣝࢠ࣮ศᕸࡢ㧗࢚ࢿࣝࢠ࣮㒊ศ
65
࣮ࡶ㸪⌮ㄽⓗ࡟ண ࡉࢀࡿ್ࡢ༙ศ௨ୗ࡜࡞ࡿ㸬
࡟ࡘ࠸࡚ࡶ㸪ACAT ࢥ࣮ࢻࡢゎᯒ࠿ࡽᚓࡽࢀࡿศᕸ
㍍࢖࢜ࣥධᑕ᫬ࡢࢫࣃࢵࢱ࣮⢏Ꮚࡢゅᗘศᕸ
ࡣ㸪ࢺࣥࣉࢯࣥࡢබᘧࡀ⦆ࡸ࠿࡟ῶᑡࡍࡿࡢ࡟ᑐࡋ㸪
࡟ࡘ࠸࡚ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞ࡃ࡚ࡶ㸪ᚋ
ᛴ⃭࡟ 0 ࡬࡜཰᮰ࡍࡿ㸬
᪉ᩓ஘ࡉࢀࡿධᑕ⢏Ꮚࡢ㐠ື㔞ࡀ༑ศ࡟ࣛࣥࢲ࣐
࢖ࢬࡉࢀࡿࡇ࡜࡟ࡼࡗ࡚Ⓨ㐩ࡋࡓ⾪✺࢝ࢫࢣ࣮ࢻ
࡜ྠࡌ⤖ᯝࢆ♧ࡍ㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪࢚ࢿࣝࢠ࣮ศᕸ
࡟ᑐࡋ࡚ࡣ㸪⾪✺࢝ࢫࢣ࣮ࢻࡀⓎ㐩ࡋ࡞࠸ᙳ㡪ࡀ㢧
ⴭ࡟⌧ࢀ㸪⌮ㄽⓗ࡟ண ࡉࢀࡿࢺࣥࣉࢯࣥࡢබᘧ࠿
ࡽ኱ࡁࡃእࢀࡓࡶࡢ࡟࡞ࡿ㸬
ᮏ◊✲ࡢ୍㒊ࡣࠕ2008 ᖺᗘྠᚿ♫኱Ꮫ⌮ᕤᏛ◊✲
ᡤ◊✲ຓᡂ㔠㸦ಶே㸧ࠖࡢᨭ᥼ࢆཷࡅࡓ㸬ࡇࡇ࡟㸪
グࡋ࡚ㅰពࢆ⾲ࡍࡿ㸬
Fig. 10. Undeveloped collision cascade.
ཧ⪃ᩥ⊩
1) ᑠᯘ᫓ὒ㸪ⷧ⭷㸦ᇶ♏ࡢࡁࡑ㸧
㸪
㸦᪥หᕤᴗ᪂⪺♫㸪ᮾ
⤖
⤖ㄽ
ி㸪2006㸧
㸪p. 51.
ࢫࣃࢵࢱࣜࣥࢢゎᯒࢥ࣮ࢻ ACAT ࢆ⏝࠸࡚㸪
⾪
✺࢝ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸ሙྜ㸪ࡍ࡞ࢃࡕᑡᩘ
ᅇ⾪✺࡛⏕ࡌࡿࢫࣃࢵࢱࣜࣥࢢᐤ୚ࡀ኱ࡁ࠸ሙྜ
2)
R. F. K. Herzog and F. P. Viehböck, “Ion Source for Mass
Spectrography”, Phys. Rev. 76, 855-856 (1949).
3)
R.
Behrisch,
B.
M.
U.
Scherzer,
“He
wall
ࡢゎᯒࢆ⾜ࡗࡓ㸬ලయⓗ࡟ࡣ㸪పධᑕ࢚ࢿࣝࢠ࣮㸪
bombardment and wall erosion in fusion devices”,
ཬࡧ㍍࢖࢜ࣥධᑕ᫬ࢫࣃࢵࢱࣜࣥࢢ⌧㇟ࢆᑐ㇟࡜
Radiat. Eff. 78, 393-403 (1988).
ࡋࡓ㸬ࡲࡎ⾪✺࢝ࢫࢣ࣮ࢻࢆࡶ࡜࡟ࡋࡓ⌮ㄽ࡜ࡢ㐪
࠸ࢆゎᯒࡋࡓ㸬ࢫࣃࢵࢱ࣮⢏Ꮚࡢゅᗘศᕸ࡟ᑐࡋ࡚
4) ᑠᯘ᫓ὒ㸪ⷧ⭷㸦ᇶ♏ࡢࡁࡑ㸧
㸪
㸦᪥หᕤᴗ᪂⪺♫㸪ᮾ
ி㸪2006㸧
㸪p. 52.
5) P. Sigmund, “Theory of Sputtering . I. Sputtering Yield of
ࡣ㸪Ⓨ㐩ࡋࡓ⾪✺࢝ࢫࢣ࣮ࢻ࡟ࡼࡗ࡚ࢫࣃࢵࢱ࣮ࡉ
Amorphous and Polycrystalline Targets”, Phys. Rev., 184,
ࢀࡓࢱ࣮ࢤࢵࢺཎᏊࡢゅᗘศᕸࡣࢥࢧ࢖ࣥศᕸ࡜
࡞ࡿࡇ࡜ࡀ⌮ㄽⓗ࡟ண ࡉࢀࡿࡀ㸪ప࢚ࢿࣝࢠ࣮
384-416 (1969).
6)
Y. Yamamura and H. Tawara, “Energy Dependence of
Ion-Induced Sputtering Yields from Monoatomic Solids at
Ar+࢖࢜ࣥࡢ㖡ࢱ࣮ࢤࢵࢺᆶ┤ධᑕࡢሙྜࡣ⾪✺࢝
Normal Incidence”, Atomic Data and Nuclear Data Tables,
ࢫࢣ࣮ࢻࡀ༑ศⓎ㐩ࡋ࡞࠸ࡓࡵ࡟㸪ධᑕ᪉ྥࡢ㐠ື
62, 149-253 (1996).
㔞ᡂศࡀከࡃṧࡿ㸬ࡑࡢ⤖ᯝ㸪⾲㠃ᆶ┤ᡂศࡢ཰㔞
7) Y. Yamamura and Y. Mizuno, “Low-Energy Sputterings
ࡀᑡ࡞࠸࢔ࣥࢲ࣮ࢥࢧ࢖ࣥศᕸࢆ♧ࡍ㸬୍᪉㸪H+
with the Monte Carlo Program ACAT, IIPJ-AM-40, Inst.
࢖࢜ࣥࡢప࢚ࢿࣝࢠ࣮㖡ࢱ࣮ࢤࢵࢺᆶ┤ධᑕࡢሙ
Plasma Physics, Nagoya Univ., 1985.
ྜࡣ㸪ᑡᩘᅇ⾪✺ᶵᵓࡀᨭ㓄ⓗ࡟࡞ࡾ㸪⤖ᯝⓗ࡟ゅ
8) J. P. Biersack and L. G. Haggmark, “A Monte Carlo
Computer Program for the Transport of Energetic Ions in
ᗘศᕸࡣࢥࢧ࢖ࣥศᕸ࡟㏆࠸ศᕸࢆ♧ࡍ㸬
Amorphous Targets”, Nucl. Instr. and Meth., 174,
ࢫࣃࢵࢱ࣮⢏Ꮚࡢ࢚ࢿࣝࢠ࣮ศᕸ࡟ࡘ࠸࡚ࡣ㸪
ప࢚ࢿࣝࢠ࣮Ar+࢖࢜ࣥࡢሙྜࡣ㸪࢚ࢿࣝࢠ࣮ศᕸ
257-269 (1980).
9)
ࡢࣆ࣮ࢡ࢚ࢿࣝࢠ࣮ࡣ⌮ㄽⓗ࡟ண ࡉࢀࡿࢺࣥࣉ
ࢯࣥࡢබᘧ࡜ࡼࡃ୍⮴ࡍࡿࡀ㸪㧗࢚ࢿࣝࢠ࣮㒊ศࡢ
཰㔞ࡀࢺࣥࣉࢯࣥࡢබᘧ࡟ẚ࡭࡚ᑡ࡞࠸㸬ࡇࡢഴྥ
Eckstein,
“Computer
Simulation
of
Ion-Solid
10) W. Eckstein, “Computer Simulation of Ion-Solid
Interaction”, (Springer-Verlag, Berlin, 1991), p. 40.
11) O. B. Firsov, ”Calculation of the interaction potential of
ࡣ㍍࢖࢜ࣥప࢚ࢿࣝࢠ࣮ධᑕࡢሙྜ࡛≉࡟㢧ⴭ࡛㸪
㍍࢖࢜ࣥࡢሙྜࡣ㸪ศᕸࡢࣆ࣮ࢡࢆ୚࠼ࡿ࢚ࢿࣝࢠ
W.
Interaction”, (Springer-Verlag, Berlin, 1991), p. 17.
atoms” , Sov. Phys. JETP 6, 534-537 (1958).
12)
65 ）
（ G.. Molière, “Therorie der Streuung schneller
剣持貴弘
66
geladener
Teilchen
I.
Einzelstreuung
am
abgeschirmten Coulomb-Feld “, Z. Naturforsch. A2,
133-145 (1947).
13)
J. F. Ziegler, J. P. Biersack, U. Littmark, “The Stopping
and Range of Ion in Solids: The Stopping and Range of
Ions in Matter”, Vol.1, ed. by J. F. Ziegler (Pergamon, New
York, 1985).
14) W. D. Wilson, L. G. Haggmark, J. P. Biersac, “Calculations
of nuclear stopping, ranges, and straggling in the
low-energy region”, Phys. Rev. 15, p. 2458 (1977).
15)
A.
Sommerfeld,
“Asymptotische
Integration
der
Differentialgleichung des Thomas-Fermischen Atoms,” Z.
Phys. 78, 283 (1932).
16) S. T. Nakagawa and Y. Yamamura, “Interatomic potential
in solids and its applications to range calculations”, Radiat.
Eff. 105, 239-256 (1988) .
17) J. Lindhard, M. Scharff and H. E. Schiott, “ Range
Concepts and Heavy Ion Ranges”, K. Dan. Vidensk. Selsk.
Mat. Fyz. Medd., 33 No. 14, 1-41 (1963).
18) H. H. Andersen and J. F. Ziegler, “Hydrogen Stopping
Powers and Ranges in All Elements”, (Pergamon, New
York, 1977), pp. 1-16.
19) F. Keywell, “Measurements and Collision—Radiation
Damage Theory of High-Vacuum Sputtering”, Phys. Rev.,
97, 1611-1619 (1955).
20) M. Bader, F. C. Winterborn and T. W. Snouse, NASA Tech.
Report R105 (1961).
11) N. Laegreid and G. K. Wehner, “Sputtering Yields of
Metals for Ar+ and Ne+ Ions with Energies from 50 to 600
eV”, J. Appl. Phys., 32, 365-369 (1961).
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Atoms”, Appl. Phys., 25, 307-310 (1981).
66 ）
（