An integrated framework for the neutral flux calculation inside trenches and holes during plasma etching is described, and a comparison between the two types of structure in a number of applications is presented. First, a detailed and functional set of equations for the neutral and ion flux calculations inside long trenches and holes with cylindrical symmetry is explicitly formulated. This set is based on early works [T. S. Cale and G. B. Raupp, J. Vac. Sci. Technol. B8, 1242 (1990); V. K. Singh et al, J. Vac. Sci. Technol. B10, 1091 (1992)], and includes new equations for the case of holes with cylindrical symmetry. Second, a method for the solution of the respective numerical task, i.e., one or a set of linear or nonlinear integral equations, is described. This method includes a coupling algorithm with a surface chemistry model and resolves the singularity problem of the integral equations. Third, the fluxes inside trenches and holes are compared. The flux from reemission is the major portion of the local flux at the bottom of both types of structure. The framework is applied in SiO2 etching by fluorocarbon plasmas to predict the increased intensity of reactive ion etching lag in SiO2 holes compared to trenches. It is also applied in deep Si etching: By calculating the flux of F atoms at the bottom of very high aspect ratio (up to 150) Si trenches and holes during the gas chopping process, the aspect ratio at which the flux of F atoms is eliminated and etching practically stops is estimated.

1.
R. A.
Gottscho
,
C. W.
Jurgensen
, and
D. J.
Vitkavage
,
J. Vac. Sci. Technol. B
10
,
2133
(
1992
).
2.
J. C.
Arnold
and
H. H.
Sawin
,
J. Appl. Phys.
70
,
5314
(
1991
).
3.
M.
Boufnichel
,
S.
Aachboun
,
P.
Lefaucheux
, and
P.
Ranson
,
J. Vac. Sci. Technol. B
21
,
267
(
2003
).
4.
T. J.
Dalton
,
J. C.
Arnold
,
H. H.
Sawin
,
S.
Swan
, and
D.
Corliss
,
J. Electrochem. Soc.
140
,
2395
(
1993
).
5.
G. S.
Hwang
and
K. P.
Giapis
,
J. Vac. Sci. Technol. B
15
,
70
(
1997
).
6.
J. T.
Drotar
,
Y. P.
Zhao
,
T. M.
Lu
, and
G. C.
Wang
,
Phys. Rev. B
61
,
3012
(
2000
).
7.
A. P.
Mahorowala
and
H. H.
Sawin
,
J. Vac. Sci. Technol. B
20
,
1064
(
2002
).
8.
H. C.
Wulu
,
K. C.
Saraswat
, and
J. P.
McVittie
,
J. Electrochem. Soc.
138
,
1831
(
1991
).
9.
T. S.
Cale
,
J. Vac. Sci. Technol. B
9
,
2551
(
1991
).
10.
M. K.
Abachev
,
Y. P.
Baryshev
,
V. F.
Lukichev
,
A. A.
Orlikovsky
, and
K. A.
Valiev
,
Vacuum
42
,
129
(
1991
).
11.
V. K.
Singh
,
E. S. G.
Shaqfeh
, and
J. P.
McVittie
,
J. Vac. Sci. Technol. B
10
,
1091
(
1992
).
12.
J. C.
Arnold
,
D. C.
Gray
, and
H. H.
Sawin
,
J. Vac. Sci. Technol. B
11
,
2071
(
1993
).
13.
A.
Misaka
and
K.
Harafuji
,
IEEE Trans. Electron Devices
44
,
751
(
1997
).
14.
J. A.
Levinson
,
E. S. G.
Shaqfeh
,
M.
Balooch
, and
A. V.
Hamza
,
J. Vac. Sci. Technol. A
15
,
1902
(
1997
).
15.
M.
Tuda
,
K.
Nishikawa
, and
K.
Ono
,
J. Appl. Phys.
81
,
960
(
1997
).
16.
V. F.
Lukichev
and
V. A.
Yunkin
,
Microelectron. Eng.
46
,
315
(
1999
).
17.
T. S.
Cale
,
T. H.
Gandy
, and
G. B.
Raupp
,
J. Vac. Sci. Technol. A
9
,
524
(
1991
).
18.
S.
Hamaguchi
, in
Thin Films
,
Modeling of film deposition for microelectronic applications
, edited by
S.
Rossnagel
and
A.
Ulman
(
Academic Press
,
1996
), Vol.
22
, p.
81
.
19.
T. S.
Cale
and
V.
Mahadev
, in
Thin Films
,
Modeling of film deposition for microelectronic applications
, edited by
S.
Rossnagel
and
A.
Ulman
(
Academic Press
,
1996
), Vol.
22
, p.
176
.
20.
T. S.
Cale
and
G. B.
Raupp
,
J. Vac. Sci. Technol. B
8
,
1242
(
1990
).
21.
M.
Sato
,
S.
Kato
, and
Y.
Arita
,
Jpn. J. Appl. Phys., Part 1
30
,
1549
(
1991
).
22.
B.
Abraham-Shrauner
and
C. D.
Wang
,
J. Electrochem. Soc.
143
,
672
(
1996
).
23.
S.
Abdollahi-Alibeik
,
J. P.
McVittie
,
K. C.
Saraswat
,
V.
Sukharev
, and
P.
Schoenborn
,
J. Vac. Sci. Technol. A
17
,
2485
(
1999
).
24.
J. S.
Han
,
J. P.
McVittie
, and
J.
Zheng
,
J. Vac. Sci. Technol. B
13
,
1893
(
1995
).
25.
M. O.
Bloomfield
,
D. F.
Richards
, and
T. S.
Cale
,
Philos. Mag.
83
,
3549
(
2003
).
26.
L. C.
Musson
,
P.
Ho
,
S. J.
Plimpton
, and
R. C.
Schmidt
,
Microsyst. Technol.
12
,
137
(
2005
).
27.
H. H.
Hwang
,
T. R.
Govindan
, and
M.
Meyyappan
,
J. Electrochem. Soc.
146
,
1889
(
1999
).
28.
Y. H.
Im
,
Y. B.
Hahn
, and
S. J.
Pearton
,
J. Vac. Sci. Technol. B
19
,
701
(
2001
).
29.
A.
La Magna
and
G.
Garozzo
,
J. Electrochem. Soc.
150
,
F178
(
2003
).
30.
D.
Adalsteinsson
and
J. A.
Sethian
,
J. Comput. Phys.
138
,
193
(
1997
).
31.
G.
Kokkoris
,
A.
Tserepi
,
A. G.
Boudouvis
, and
E.
Gogolides
,
J. Vac. Sci. Technol. A
22
,
1896
(
2004
).
32.
B.
Abraham-Shrauner
and
W. J.
Chen
,
J. Vac. Sci. Technol. B
14
,
3492
(
1996
).
33.
E.
Gogolides
,
P.
Vauvert
,
G.
Kokkoris
,
G.
Turban
, and
A. G.
Boudouvis
,
J. Appl. Phys.
88
,
5570
(
2000
).
34.
B. E.
Volland
,
T.
Ivanov
, and
I. W.
Rangelow
,
J. Vac. Sci. Technol. B
20
,
3111
(
2002
).
35.
I. W.
Rangelow
,
J. Vac. Sci. Technol. A
21
,
1550
(
2003
).
36.
T.
Pandhumsoporn
,
L.
Wang
,
M.
Feldbaum
,
P.
Gadgil
,
M.
Puech
, and
P.
Maquin
,
Vide: Sci., Tech. Appl.
56
,
673
(
2001
).
37.
F.
Laermer
and
A.
Urban
,
Microelectron. Eng.
67/68
,
349
(
2003
).
38.
G.
Kokkoris
,
E.
Gogolides
, and
A. G.
Boudouvis
,
J. Appl. Phys.
91
,
2697
(
2002
).
39.
H.
Liao
and
T. S.
Cale
,
Thin Solid Films
236
,
352
(
1993
).
40.
T. S.
Cale
,
B. R.
Rogers
,
T. P.
Merchant
, and
L. J.
Borucki
,
Comput. Mater. Sci.
12
,
333
(
1998
).
41.
M. O.
Bloomfield
and
T. S.
Cale
,
Microelectron. Eng.
76
,
195
(
2004
).
42.
J. W.
Coburn
and
H. F.
Winters
,
Appl. Phys. Lett.
55
,
2730
(
1989
).
43.
R. D.
Present
,
Kinetic Theory of Gases
(
McGraw-Hill
,
New York
,
1958
), pp.
56
57
.
44.
J. L.
Ryans
and
D. L.
Roper
,
Process Vacuum System Design and Operation
(
McGraw-Hill
,
New York
,
1986
), pp.
22
24
.
45.
J.
Jeans
,
An Introduction to Kinetic Theory of Gases
(
Cambridge University Press
,
London
,
1962
), p.
53
.
46.
K.
Atkinson
and
G.
Chandler
,
J. Integral Equ. Appl.
10
,
253
(
1998
).
47.
B.
Abraham-Shrauner
,
J. Vac. Sci. Technol. B
19
,
711
(
2001
).
48.
H. H.
Hwang
,
M.
Meyyappan
,
G. S.
Mathad
, and
R.
Ranade
,
J. Vac. Sci. Technol. B
20
,
2199
(
2002
).
49.
R. J.
Hoekstra
,
M. J.
Kushner
,
V.
Sukharev
, and
P.
Schoenborn
,
J. Vac. Sci. Technol. B
16
,
2102
(
1998
).
50.
B. A.
Helmer
and
D. B.
Graves
,
J. Vac. Sci. Technol. A
16
,
3502
(
1998
).
51.
M.
Schaepkens
and
G. S.
Oehrlein
,
J. Electrochem. Soc.
148
,
C211
(
2001
).
52.
M. J.
Kushner
,
J. Appl. Phys.
58
,
4024
(
1985
).
53.
L. L.
Raja
and
M.
Linne
,
J. Appl. Phys.
92
,
7032
(
2002
).
54.
B. E.
Thompson
,
H. H.
Sawin
, and
D. A.
Fisher
,
J. Appl. Phys.
63
,
2241
(
1988
).
55.
J. I.
Ulacia
and
J. P.
McVittie
,
J. Appl. Phys.
65
,
1484
(
1989
).
56.
Z. L.
Dai
and
Y. N.
Wang
,
Phys. Rev. E
69
,
036403
(
2004
).
57.
C. W.
Jurgensen
,
J. Appl. Phys.
64
,
590
(
1988
).
58.
M.
Kratzer
,
R. P.
Brinkmann
,
W.
Sabisch
, and
H.
Schmidt
,
J. Appl. Phys.
90
,
2169
(
2001
).
59.
W. J.
Chen
and
B.
Abraham-Shrauner
,
J. Appl. Phys.
81
,
2547
(
1997
).
60.
O.
Joubert
,
G. S.
Oehrlein
, and
M.
Surendra
,
J. Vac. Sci. Technol. A
12
,
665
(
1994
).
61.
Y. J. T.
Lii
and
J.
Jorne
,
J. Electrochem. Soc.
137
,
2837
(
1990
).
62.
J. I.
Ulacia
,
C. J.
Petti
, and
J. P.
McVittie
,
J. Electrochem. Soc.
135
,
1521
(
1988
).
63.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in C: The Art of Scientific Computing
, 2nd ed. (
Cambridge University Press
,
Cambridge, England
,
1997
), pp.
791
794
,
797
798
.
64.
G. S.
Oehrlein
,
Y.
Zhang
,
D.
Vender
, and
O.
Joubert
,
J. Vac. Sci. Technol. A
12
,
333
(
1994
).
65.
O.
Joubert
,
G. S.
Oehrlein
, and
Y.
Zhang
,
J. Vac. Sci. Technol. A
12
,
658
(
1994
).
66.
L.
Rolland
,
M. C.
Peignon
,
C.
Cardinaud
, and
G.
Turban
,
Microelectron. Eng.
53
,
375
(
2000
).
67.
J.
Matsui
,
N.
Nakano
,
Z. L.
Petrovic
, and
T.
Makabe
,
Appl. Phys. Lett.
78
,
883
(
2001
).
68.
C.
Liu
and
B.
Abraham-Shrauner
,
IEEE Trans. Plasma Sci.
30
,
1579
(
2002
).
69.
S.
Aachboun
,
P.
Ranson
,
C.
Hilbert
, and
M.
Boufnichel
,
J. Vac. Sci. Technol. A
18
,
1848
(
2000
).
70.
G.
Craciun
,
M. A.
Blauw
,
E.
van der Drift
,
P. M.
Sarro
, and
P. J.
French
,
J. Micromech. Microeng.
12
,
390
(
2002
).
71.
F.
Marty
,
L.
Rousseau
,
B.
Saadany
,
B.
Mercier
,
O.
Francais
,
Y.
Mita
, and
T.
Bourouina
,
Microelectron. J.
36
,
673
(
2005
).
72.
J.
Kiihamaki
and
S.
Franssila
,
J. Vac. Sci. Technol. A
17
,
2280
(
1999
).
73.
J.
Kiihamaki
,
J. Vac. Sci. Technol. A
18
,
1385
(
2000
).
74.
B. E.
Volland
and
I. W.
Rangelow
,
Microelectron. Eng.
67/68
,
338
(
2003
).
75.
T.
Lill
,
M.
Grimbergen
, and
D.
Mui
,
J. Vac. Sci. Technol. B
19
,
2123
(
2001
).
76.
M. A.
Blauw
,
G.
Craciun
,
W. G.
Sloof
,
P. J.
French
, and
E.
van der Drift
,
J. Vac. Sci. Technol. B
20
,
3106
(
2002
).
You do not currently have access to this content.