ABSTRACT
Total scattering cross sections suggested by Christophorou and Olthoff (2004), on the basis of measurements of Gulley et al(1998) and Cooper et al(1999) are shown in Table 122 and Figure 121 The essential features of the total scattering cross section are
1 The cross section increases toward zero energy, attributed to electron attachmentLow-energy attachment takes place most probably through p-wave attachment, unlike s-wave attachment in other species such as SF6 This explains the relatively lower cross section at low energies for Cl2 (Gulley et al 1998)
121 Selected References for Data 95 122 Total Scattering Cross Section 95 123 Elastic Scattering Cross Section 96 124 Rotational Cross Section 96 125 Vibrational Excitation Cross Section 98 126 Ionization Cross Section 98 127 Attachment Processes 99 128 Attachment Cross Section 99 129 Attachment Rate Constants 100 1210 Electron Transport 100 1211 Ionization and Attachment Coefficients 100 1212 Addendum 102
12121 Total Scattering Cross Section 102 12122 Ionization Cross Section 102
References 103
TABLE 12.1 Selected References
Parameter Range: eV, (Td) Reference
Qi 12-900 Basner and Becker (2004)
Review 0-1000 Christophorou and Olthoff (2004)
QT 08-600 Makochekanwa et al. (2003) Qa 0-9 Feketeova et al. (2003) Qa 0-02 Barsotti et al. (2002) QT 03-230 Cooper et al. (1999) QT 002-95 Gulley et al. (1998)
Qrot 001-1000 Kutz and Meyer (1995)
Qrot 10-200 Gote and Erhardt (1995) Qa 0-10 McCorkle et al. (1986) Qi 135-102 Stevie and Vasile (1981) Qi, Qa 0-100 Kurepa and Belic´ (1978) Qa 0-8 Tam and Wong (1978) ka (350) Sides et al. (1976)
α/N, η/N (210-450) Božin et al. (1967)
Note:Qa = attachment cross section; Qi: = ionization cross section; Qrot = rotational excitation; QT: = total cross section; α/N = densityreduced ionization coefficient; η/N = density-reduced attachment coefficient Bold font indicates experimental study
3 A strong peak at ~7 e
gases (see Table 122)
and Olthoff (2004) are shown in Table 123 and included in Figure 121
Rotational cross section is visualized as comprising of two com ponents: rotational scattering and rotational excitation Rotational scattering designates j = 0 → 0 and it is an elastic processRotational excitation designates j = 0 → 2, 4, 6, and it is an inelastic process (Kutz and Meyer, 1995)The essential features of rotational scattering are (Cooper et al, 1999)
1 Except for electron energies near the minimum (~04 eV), rotational scattering is the largest contribution of the total scattering cross section for energy up to ~20 eV
2 Near the peak (~8 eV) rotational excitation makes a significant contribution to the total scattering cross section
Gote and Erhardt (1995) have measured the differential rotational excitation cross sections for electrons impacting with energy from 2 to 200 eVThese results are shown in TABLE 12.2
Total Scattering Cross Sections for Cl2 Energy (eV) QT (10−20 m2) Energy (eV) QT (10−20 m2)
002 400 080 655
003 352 090 736
004 268 100 797
005 170 120 906
006 107 150 111
007 736 200 139
008 850 250 160
009 106 300 179
010 968 35 199
011 926 40 219
012 906 45 242
013 976 50 268
014 989 60 345
015 890 70 412
017 719 80 428
020 509 90 410
022 444 100 403
025 400 120 397
030 375 140 386
035 370 160 367
040 380 180 351
050 432 200 330
060 500 220 315
070 583 230 310
Source:Adapted from Christophorou, LGand JKOlthoff, Fundamental Electron Interactions with Plasma Processing Gases, Kluwer Academic/Plenum Publishers, New York, NY, 2004
Note:See Table 1211 also
TABLE 12.3 Elastic Scattering Cross Sections for Cl2 Energy (eV) Qel (10−20 m2) Energy (eV) Qel (10−20 m2)
020 150 70 271
022 164 80 288
025 182 90 302
030 211 100 313
035 238 120 327
040 266 140 331
050 330 160 329
060 410 180 321
070 498 20 309
080 599 22 295
090 689 23 288
10 777 25 273
12 934 30 240
15 114 40 194
20 146 50 161
25 169 60 136
30 186 70 116
35 199 80 101
40 211 90 887
45 221 100 799
50 232 150 631
60 252 200 616
Source:Adapted from Christophorou, LGand JKOlthoff, Fundamental Electron Interactions with Plasma Processing Gases, Kluwer Academic/Plenum Publishers, New York, NY, 2004
Cl2
Total scattering Elastic scattering
1 Energy (eV)
0.10.01 1
Cr os
ss ec
tio n
(1 0-
2 )
30 eV
Rotational excitation
Scattering angle (°) 0
0 10
20 30
20 eV
16012080400 0
10 eV
Differential scattering
Di ffe
re nt
ial cr
os ss
ec tio
n (1
m 2 /s
r)
2 eV 5 eV Cl2
400 0
Excitation SCl2 in Units of 10−20 m2/sr
Energy (eV)
Angle (°) 2 5 10 20 30 50 70 100 150 200
10 1591 5819 21283 31605 31838 28722 22238 15695 14123 12915
20 1129 4584 14387 19320 15896 8607 5434 3498 2397 2518
30 0856 3349 7491 9406 5860 2409 1457 0912 0778 0831
40 1017 2984 4615 3970 2263 1012 0592 0415 0345 0357
50 1318 2542 1740 1834 1180 0505 0262 0188 0185 0230
60 1528 2023 1411 1316 0687 0196 0131 0133 0154 0190
70 1615 1720 1082 0961 0406 0158 0152 0148 0154 0132
80 1577 1506 0963 0754 0431 0304 0219 0201 0126 0094
90 1453 1381 0843 0799 0621 0440 0295 0192 0086 0064
100 1291 1177 0858 0886 0712 0485 0320 0148 0054 0035
110 1029 1115 0874 0893 0593 0435 0237 0076 0026 0026
120 0723 1196 0977 0831 0393 0288 0117 0036 0030 0048
130 0540 1146 1080 0651 0218 0179 0093 0073 0084 0110
140 0510 1156 1569 0548 0111 0154 0177 0153 0154 0239
150 0600 1225 2058 0571 0107 0327 0435 0590 0328 0339
160 0744 1294 3124 0886 0198 0688 1049 0909 0547 0580
Source: Adapted from Gote, M and H Erhardt, J. Phys. B: At. Mol. Opt. Phys, 28, 3957, 1995
200 eV
0 40 80 Scattering angle (°)
Rotational excitation
Differential scattering
120 0
16 12
8 4
1600 40 80 120 0
16 12
8 4
1600 40 80 120 0
1600 40 80 120 0
10 20 30
100 eV
70 eV
50 eV Cl2
Di ffe
re nt
ial cr
os ss
ec tio
n (1
m 2 /
sr )
125Theoretical cross sections up to 1000 eV are given by Kutz and Meyer (1995)
The vibrational excitation energy for Cl2 is 694 meV (Christophorou and Olthoff, 2004) Further experimental data on vibrational cross sections are not available Theoretical or derived values are given by Christophorou and Olthoff (2004)
Total ionization cross sections for Cl2 are shown in Table 126 and Figure 124Partial ionization cross sections have been measured by Calandra et al (2000)
TABLE 12.5 Cross Sections for Rotational Excitation for Cl2 Energy (eV) Qrot (10−20 m2) Energy (eV) Qrot (10−20 m2)
2 1422 50 1557 5 2261 70 1141 10 3125 100 789 20 320 150 641 30 2312 200 634
Source:Adapted from Integrated by Gorur Govinda Raju, unpublished data, 2007
TABLE 12.6 Total Ionization Cross Sections for Cl2
Total Ionization Cross Section (10−20 m2)
Energy (eV) Stevie and Vasile
(1981) Kurepa and Belic´
(1978)
110 0
112 0016
114 0028
116 0050
118 0068
120 00927
122 0122
124 0146
126 0158
128 0192
130 0231
132 0283
134 0317
135 017
136 0371
138 0414
Cross Sections for Cl2
Total Ionization Cross Section (10−20 m2)
Energy (eV) Stevie and Vasile
(1981) Kurepa and Belic´
(1978)
140 034 0463
142 0521
144 0581
146 0631
148 0682
150 068 0747
152 0797
154 0859
156 0913
158 0979
160 085 103
162 109
164 115
166 121
168 126
170 124 132
172 138
174 143
176 148
178 154
180 175 159
182 164
184 170
186 175
188 180
190 220 186
192 191
194 195
196 200
198 207
20 265 212
21 344 238
22 400 256
23 428 279
24 297
25 318
26 490 330
27 351
28 535 366
29 379
30 390
31 580
32 409
34 427
36 625 442
38 453
40 461
42 631 468
44 480
46 487
47 654
continuted
Cl2 + e → Cl + Cl− (121)
and attachment
Cl2 + e → Cl2 (122)
In addition, at energies >10 eV, ion pair production is possibleThe threshold energy for Cl+ ion appearance by this process is 1187 eV (Kurepa and Belic´, 1978)The potential energy diagram of the Cl2 molecule and the lowest of the four states of negative ion Cl2− are shown in Figure 125 (Barsotti et al, 2002)
Appearance potentials of negative ions and positions of peaks from electron attachment to the Cl2 molecule are shown in Table 127
The total attachment cross sections for Cl2 molecule are shown in Table 128 and Figure 126 (Kurepa and Belic´, 1978)
TABLE 12.7 Appearance Potentials and Peak Positions
Process Appearance
Potential (eV) Peak (eV) Reference
Cl2 + e → Cl2−* 00 00 Kurepa and Belic´ (1978)
Cl2 + e → Cl + Cl− 10 25 34 575
82 97
Cl2 + e → Cl + Cl− 003 Tam and Wong (1978) 25
55
654 Internuclear distance (10-10 m)
–2
–1
Po te
nt ia
le ne
rg y(
eV )
Total Ionization Cross SCl2
Total Ionization Cross Section (10−20 m2)
Energy (eV) Stevie and Vasile
(1981) Kurepa and Belic´
(1978)
48 498
50 506
52 513
53 671
54 520
56 526
58 687 532
60 539
62 543
64 687 5468
66 548
68 552
69 710
70 553
72 554
74 556
76 557
78 558
80 117 558
82 558
84 558
86 558
88 5572
90 5568
91 682
92 556
94 555
96 554
98 5535
100 5524
102 682
Note: Also see Table 1212
Kurepa (1978) Stevie (1981) Christophorou (2004)
6040200 0
10 Ionization (Cl2)
Energy (eV)
Cr os
ss ec
tio n
(1 0-
2 )
More recent measurements have confirmed that the cross section at zero energy peak is 25 × 10−20 m2 (see Barsotti et al, 2002) Figure 127 shows the details at low energy The total cross section at zero energy is much higher at 40 × 10−20 m2 (see Gulley et al, 1998) and the discrepancy has not been satisfactorily resolved
Christophorou and Olthoff (2004) summarize the data on attachment rates at various temperatures, reduced electric field E/N, and derived mean energy of the swarmTable 129 shows the rates at various temperatures obtained by several researchers
Figure 128 (Bailey and Healy, 1935) shows the drift velocity and characteristic energy (D/µ) at low values of E/NBoth sets are the only data available
Table 1210 and Figure 129 show the density-reduced ionization coefficients (α/N), density-reduced attachment coefficients (η/N), and density-reduced effective ionization
Total Attachment Cross SCl2 Energy (eV)
Qatt (10−22 m2)
Energy (eV)
Qatt (10−22 m2)
Energy (eV)
Qatt (10−22 m2)
00 2016 68 355 28 135
01 800 70 301 30 108
02 245 72 231 32 089
03 62 74 178 34 074
04 20 76 138 36 065
05 098 78 100 38 062
06 068 80 0699 40 060
07 063 82 051 42 040
08 050 84 045 44 062
09 044 86 041 46 064
10 042 88 0395 48 069
12 048 90 0395 50 076
14 059 92 0380 52 088
16 084 94 0386 54 105
18 132 96 0392 56 128
20 181 98 0390 58 152
22 242 100 0380 60 176
24 277 102 0372 62 196
26 279 104 0365 64 218
28 249 106 0355 66 234
30 192 108 0348 68 252
32 136 110 0344 70 272
34 106 112 0325 72 318
36 095 114 0316 74 373
38 105 116 0318 76 406
40 129 118 0328 78 424
42 169 120 0365 79 428
44 209 122 0440 80 425
46 257 124 0530 82 420
48 308 126 0625 84 413
50 363 128 0720 86 404
52 408 130 0510 88 394
54 446 14 0900 90 382
56 474 16 180 92 370
58 484 18 240 94 357
60 478 20 258 96 340
62 462 22 240 98 322
64 438 24 207 100 307
66 399 26 166
Note: For electron energy ≥14 eV, cross section for ion pair production is also included
100101 Energy (eV)
0.1 0.1
(Cl2)
Cr os
ss ec
tio n
(1 0-
161161 0
5 Attachment
(Cl2)
Energy (eV)
Cr os
ss ec
tio n
(1 0-
2 )
(1967) on pressure, unlike for Br2 (see Razzak and Goodyear (1969)) (Table 1210)
0 7
W (1
06 cm
s1 )
Cl2
14(a)
50 100 150 200 250
0 1.0
D T /μ
/( V)
Cl2
2.5
2.0
1.5
(b)
50 100 E/N (10-17 V cm2)
150 200 250
TABLE 12.9 Attachment Rate Constants
Temperature (K) Rate (10−16 m3/s) Method Reference
213 122 Swarm McCorkle et al (1984)
233 135
253 151
273 167
298 186
323 214
203 <10 FA/LP Smith et al (1984) 300 20
455 33
590 48
350 37 FA/ECR Sides et al (1976)
293 31 Swarm Christodoulides et al (1975)
Note:ECR = electron cyclotron resonance; FA = flowing afterglow; LP = Langmuir probe
(Cl2)
400 E/N (Td)
(a)
(c) Ionization (a) Attachment (b) Effective ioniz. (c)
(b)
200 –20
30Co effi
cie nt
s( 10
2 )
TABLE 12.10 Ionization and Attachment Coefficients for Cl2 E/N (Td) α/N (10−22 m2) η/N (10−22 m2) (α-η)/N (10−22 m2)
213 645
215 253 −185 220 734
225 244
240 982
250 223 −107 260 124
275 200
280 155
300 192 176 213
320 234
325 156
340 282
350 137 180
360 334
375 119
380 390
400 447 100 337
420 504
425 814
440 562
450 591 626 509
500 691
550 868
600 1037
650 1203
700 1369
750 1534
Makochekanwa et al (2003) have measured the total scattering cross sections as shown in Table 1211 and Figure 1210
See Table 1212
Total scattering
10.1 1
Energy (eV)
Cr os
ss ec
tio n
(1 0-
2 )
(Cl2)
TABLE 12.12 Total Ionization Cross Sections for Cl2 Energy (eV)
Qi (10-20 m2)
Energy (eV)
Qi (10-20 m2)
Energy (eV)
Qi (10-20 m2)
Energy (eV)
Qi (10-20 m2)
12 0100 28 634 525 856 180 756
13 0346 30 675 55 867 200 718
14 0778 32 726 575 876 300 573
15 119 34 747 60 886 400 484
16 166 36 758 65 900 500 414
17 213 38 768 70 911 600 359
18 260 40 775 80 920 700 326
19 302 42 789 90 908 800 292
20 357 44 799 100 903 900 267
22 437 46 810 120 873
24 508 48 826 140 812
26 573 50 840 160 789
Source:Adapted from R Basner and K Becker, New J. Phys., 6, 118, 2004 Note:For partial ionization cross sections (Cl2
+ ions), see original paper
Total Scattering Cross SCl2 Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
Energy (eV)
QT (10−20 m2)
08 545 65 2584 280 2239
10 496 71 2799 300 2155
12 595 73 3033 350 2019
14 677 77 3212 400 1990
16 738 81 3128 450 1926
18 797 85 3071 500 1820
20 758 90 3071 600 1649
22 1004 95 3060 700 1604
25 1217 100 2929 800 1464
29 1337 110 2966 900 1385
32 1381 120 3020 100 1267
35 1450 140 3046 150 1042
38 1532 160 2834 200 896
41 1637 180 2681 300 659
47 1818 200 2656 400 624
51 1993 220 2410 500 550
56 2222 240 2309 600 457
59 2389 260 2298
Source: Digitized and interpolated from CMakochekanwa et al J. Phys. B: At. Mol. Opt. Phys, 36, 1673, 2003
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