J. Phys. Chem. 1991,95, 2471-2476 coadsorbed Au is proposed as a cause for the changed kinetic parameters for desorption and the changed selectivity of surface processes.
Acknowledgment. This research was carried out at Brookhaven
2471
National Laboratory under Contract NO. DE-AC02-75CH00016 with the U S . Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. Registry NO. Au, 7440-57-5; 02,7782-44-7; Ru, 7440-18-8.
Chemical Mechanism for p-Doping Effects on Silicon Etching Reaction by Fluorine Akitomo Tachibana,*+tSusumu Kawauchi,**fand Tokio Yamabet** Department of Hydrocarbon Chemistry, Faculty of Engineering, Kyoto University, Kyoto 606, Japan (Received: July 3, 1990)
Etching reaction of p-doped silicon by fluorine has been studied by ab initio quantum chemical calculations. Cation center as a model of hole in bulk silicon is a key motif in this study. Reaction pathways involving the cation center as a reactive site for both plasma and thermal etching have been examined. The model reactions lead to the formation of stable fluorinebridged cation center (Si-F-Si+), whose presence rationalizes the characteristic p-doping effects for the etching reaction, Le., its thick fluorinated surface layer and suppressed etch rate.
Introduction In our present study, we try to clarify the chemical mechanism of pdoping effects on the silicon etching reaction by using ab initio molecular orbital calculations. Understanding the mechanism of the silicon etching reaction by fluorine is an extremely important and challenging problem in the fabrication of semiconductor devices.'-'0 The underlying mechanism had particular implications for attaining finer resolution of the etching process. The etching proceeds involving conversion of solid silicon into the volatile main product, SiF4, with a steady-state surface layer of up to 25 A composed primarily of SiF,, and smaller contributions from SiF and SiF2.'J It is also known that the etching does not depend on the crystal-surface orientation of the silicon These experimental results indicate that fluorine penetrates into the bulk silicon before the stripping of the outermost layer and the formation of the product SiF4is rate determining. This observation is confirmed by numerical calculation in such a way that the binding energy of Si-F at the (1 11) Si surface is 7.3 eV2, and the diffusion barriers of F and F through the hexagonal interstitial site of the Si lattice are 1 eV3 and 0.7 eV2, respectively. Therefore, a t first, all of the dangling bonds at silicon surface are easily attached by F atoms, and then F atoms can diffuse into bulk silicon and react with silicon. Previously, we studied a fluorine-migration model for the thermal etching reaction of silicon by a b initio quantum chemical techniq~es.~ From these calculations, we obtained a simple picture for fluorination process in thermal etching that the adsorbed fluorine atoms tend to accumulate locally in the bulk silicon and the formation of the main etching product SiF4 is somewhat suppressed. Consequently, a fluorosilyl surface layer is formed. These results were consistent with experimental results.' An important experimental information for understanding the etching mechanism is the doping effects on the etching reaction. It is observed that the etch rate of heavily doped p-type silicon is suppressed and the etch rate of heavily doped n-type silicon is enhanced, relative to near-intrinsic substrates in the fluorocarbon-based plasma etching of ~ i l i c o n . This ~ effect was also observed in the thermal etching of silicon by XeF,.6v7 It is observed that the principal product is SiF4for the thermal etching. Houle6 observed that significant quantities of SiF3 and Si2F6were also present. Recently, Yarmoff and McFeely6 observed for the
thermal etching that the heavily doped n-type sample had a slightly thinner fluorinated layer than did the lightly doped samples, while the heavily doped p-type sample had a much thicker layer. Some mechanisms of the doping effect on the etching reaction were Winters and Haarer' proposed that field-assisted diffusion is an important effect in the reaction. This would suggest that the differences in reactivity might be due to differences in band bending. Recently from photoemission study, Yarmoff and McFeely* suggested that it is difficult to completely rely on a purely electrostatic model and at least part of the mechanism of the doping effect is a chemical mechanism. In this connection, it should be noted that the influence of doping was small or nonexistent when the dopants were not electrically This result leads to the suggestion that the origin of the pdoping effects depend on the number of holes. In spite of some theoretical studies2*3~4-9J0 for the silicon etching reaction, there seems to be no quantum chemical approaches for the important role of holes. In this paper, we report the results of a b initio quantum chemical calculations on the important role of holes to clarify the
'Also belongs to Division of Molecular Engincering, Graduate School of En ineering, Kyoto University, Kyoto 606. Japan. ?Also belongs to Institute for Fundamental Chemistry, 34-4 Nishihirakicho, Takano, Sakyo-ku, Kyoto 606, Japan. 'On leave from Kawasaki Plastics Laboratory, Showa Denko K. K.,Kawasaki, 210, Japan.
Electrochem. SOC.1986, 133, 2202. (6) Houle, F. A. J. Appl. Phys. 1986, 60, 3018. (7) Winters, H. F.; Haarer, D. Phys. Reu. B 1987, 36, 6613. (8) Yarmoff, J. A.; McFeeley, F. R. Phys. Reo. B 1988, 38, 2057. (9) Garrison, B. J.; Goddard, W.A., 111 J. Chem. Phys. 1987, 87, 1307. (10) Garrison, B. J.; Goddard, W . A., 111 Phys. Reu. B 1987, 36, 9805.
0022-3654/91/2095-2471$02.50/0
(1) (a) Winters, H. F. J. Appl. Phys. 1978, 49, 5165. (b) Donnelly, V. M.; Flamm, D. L. J. Appl. Phys. 1980,51,5273. (c) Flamm, D. L.;Donnelly, V. M.; Mucha, J. A. J . Appl. Phys. 1981, 52, 3633. (d) Winters, H. F.; Coburn, J. W. J . Vue. Sci. Technol., B 1985, 3, 1376. (e) Dagata, J. A,; Squire, D. W.; Dulcey, C. S.; Hsu, D. S. Y.; Lin, M. C. Chem. Phys. Lett. 1987, 134, 151. (f) Squire, D. W.; Dagata, J. A.; Hsu,D. S. Y.; Dulcey, C. S.; Lin, M. C. J . Phys. Chem. 1988,92,2827. (g) Chung, T. J. J. Appl. Phys. 1980, 51, 2614. (h) Winters, H. F.; Houle, F. A. J . Appl. Phys. 1983, 54, 1218. (i) Ibbotson, D. E.; Flamm, D. L.; Mucha, J. A.; Donnelly, V. M. Appl. Phys. Letf. 1984, 44, 1129. 6 ) McFeely, F. R.; Morar, J. F.; Himpel, F. J. Surf. Sci. 1986. 165. 277. (k) Houle. F. A. J . Chem. Phvs. 1987. 87. 1866. (I) Dagata, J. A.; Squire, D: W.; Dulcey, C. S.; Hsu, D. S. Y.; Lin, hi. C. J . Vuc. Sci. Technol., B 1987, 5, 1495. (2) (a) Van de Walle, C. G.; Bar-Yam, Y.; McFeely, F. R.; Pantelides, S. T. J . Vuc. Sci. Techno/., A 1988. 6, 1973. (b) Van De Walle, C. G.; McFeely, F. R.; Pantelides, S. T. Phys. Rev. Lert.'1988, 61, 1867. (3) Seel, M.; Bagus, P. S. Phys. Reu. B 1983, 28, 2023. (4) Tachibana, A.; Kurosaki, Y.; Kawauchi, S.; Yamabe, T. J . Phys. Chem., in press. ( 5 ) (a) Jinno,K.; Kinoshita, H.; Matsumoto, Y. J . Electrochem. Soc. 1978, 125,827. (b) Mogab, C. J.; Levinstein, J. J . Vuc.Sci. Technol. 1980,17,721. c) Makino, T.; Nakamura, H.; Asano, M. J . Electrochem. Soc. 1981, 128, 103. (d) Schwartz, G. C.; Schaible, P. M. J . Electrochem. SOC.1983, 130, 1898. (e) Lee, Y. H.; Chen, M.-M.; Bright, A. A. Appl. Phys. Lett. 1985, 46,260. (f) Ikawa, E.; Kurogi, Y. Nucl. Instrum. Methods B 1985, 718,820. (9) Baldi, L.; Beardo, D. J . Appl. Phys. 1985,57,2221. (h) Lee, Y. H.; Chen, M.-M. J . Vuc. Sci. Technol., B 1986, 4, 468. (i) Baldi, L.;Beardo, D. J .
Q - 1991 American Chemical Societv
2472 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
TABLE I: Ohmized Geometriesa
Tachibana et al.
TABLE II: Vibrational Freuueacies“ lad Zero-Point Enemled ~~
species
sYm
-
SiH, SiH? SiF, SiH, SiH4+ FSi H
,
FSiH,’ SiF, H3SiSiH, H,SiSiH,+ F,SiSiH3
FISiSiH3+
H,Si-F-SiH, staggered
r(SiF) = 1.855, r(SiH) = 1.467, B(FSiH) = 107.70 r(SiF) = 1.855, r(SiH) = 1.467, B(FSiH) = 107.70
eclipsed H,Si-F-SiH,+ staggered eclipsed
-
H3Si-F-SiH3+. SiH, complex staggered
eclipsed
geometrical parameters r(SiH) = 1.475. NHSiH) = 110.90 r(SiHj = 1.452, eiHsiHj = 120.00 r(SiF) = 1.575, B(FSiF) = 107.19 r(SiH) = 1.475, B(HSiH) = 109.47 r(SiHt) = 2.280, r(SiH,/H,/Hd) -. _. . = 1.452, B(H‘,SiHZ) = 91 -70 r(SiF) = 1.593, r(SiH) = 1.469, B(FSiH) = 109.05 r(SiF) = 1.547, r(SiHI) = 2.398, r(SiH,/H,) = 1.444, B(FSiHI) = 97.29, B(H2SiH,) = 127.37 r(SiF) = 1.557, B(FSiF) = 109.47 r(SiSi) = 2.342, r(SiH) = 1.478, B(SiSiH) = 110.29, B(HSiH) = 108.64 r(SiSi) = 2.720, r(SiH) = 1.458, B(SiSiH) = 98.15, B(HSiH) = 118.03 r(SiSi) = 2.032, r(SiF) = 1.576, r(SiH) = 1.473, B(SiSiF) = 112.42, B(SiSiH) = 108.96, B(FSiF) = 106.37, B(HSiH) = 109.98 r(SiSi) = 2.599, r(SiF) = 1.545, r(SiH) = 1.457, O(SiSiF) = 102.96, B(SiSiH) = 96.45, B(FSiF) = 115.12, B(HSiH) = 118.76
r(SiF) = 1.753, r(SiH) = 1.453, B(FSiH) = 101.64 r(SiF) = 1.753, r(SiH) = 1.453, B(FS1H) = 101.62 r(SilF) = 1.732, r(Si2F) = 1.788, r(SizSil) = 3.404, r(SilH) = 1.454, r(SizH) = 1.452, r(SilH) = 1.467, 6(HSilF) = 102.36, B(FSi2H) = 98.89, O(Si2Si3H)= 104.01 r(SilF) = 1.732, r(SizF) = 1.788, r(SizSi3) = 3.404, r(SilH) = 1.454, r(Si2H) = 1.452, r(Si3H) = 1.467, 6(HSilF) = 102.36, B(FSizH) = 98.89, .9(Si2Si3H)= 104.01
“At the HF/3-21G(*) level. Bond lengths (r) in A, bond angles (e) in degrees. The subscripts for the atoms in parentheses are in order to distinguish each other.
chemical mechanism for etching reaction of pdoped silicon. For pdoped silicon, it is considered that a hole is situated with a center in bulk silicon, which we hereafter call “cation center”. The local environment of the cation center is simulated by a positively charged small finite cluster of silicon, with H atoms used to saturate the remaining valences, as would occur in the solid. A specific reaction mechanism is proposed to explain all the salient aspects on the experimental results of pdoped silicon. Our mechanism suggests that fluorine bridged structure (Si-F-Si+) at the cation center may be seen as a reaction intermediate and plays an important role in etching reaction of p-doped silicon. Methods and Calculation
Molecular orbital calculations were performed with the GAUASSIAN 82 program.” The geometries of all the compounds were optimized with the analytical energy gradient method12 at the Hartree-Fock level by using the 3-21G(*)basis (HF/ (11) Binkley, J. S.;Frisch, M.; DeFrees, D. J.; Raghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E.M.; Pople. J. A. GAUSSIAN 82, Release A version (Sep. 1983), An Ab Initio Molecular Orbital Program; Carnegic-Mcllon University, Pittsburgh, PA. (12) Pulay, P. In Modern Theoretical Chemistry; Schaefer, H. F., I11 Ed.; Plenum: New York, 1977; Vol. 4, Chapter 4.
species SiHI SiH? SiF, SiH4 SiH4+ FSiH, FSiH,+
SiF, H,SiSiH,
HlSiSiH3+ H,Si-F-SiH,+ staggered
eclipsed
HISi-F-SiH, staggered
eclipsed
harmonic vibrational frequencies 877 (a,). I020 (e), 2380 (a,), 2396 (e) 913 (a?), 1028(e’), 2506 (al’), 2575‘(e’) 319 (e), 443 (al), 954 (al), 1112 (e) 1021 (t2). 1057 (e), 2397 (tJ, 2406 (al) 389 (e), 411 (al), 907 (al), 1020 (e), 2504 (al), 2569 (e) 824 (e), 996 (al), 1037 (e), 1160 (al), 2436 (e), 2448 (al) 226 (a’), 356 (a”), 357 (a’), 773 (a”), 841 (a’), 1033 (a’), 1160 (a’), 2571 (a’), 2632 (a”) 283 (e), 41 1 (t2), 887 (al), 1184 (t2) 131 (a,,,), 418 (e,,), 466 (alg), 701 (e ), 951 (a2,,), 1030 (e,), 1033 (alg), 1045 !e,,), 2373 (azu), 2374 (eg), 2382 (e,,), 2389 (a1g) 118 (a,”), 205 (alg), 310 (e,,), 459 (e ), 814 ( a d 911 ( q g L 993 (eg), 1009 ,!,e(, 2464 ( a d , 2469 (alg),2516 (eg), 2521 (e,)
ZPE 12.84 13.52 5.42 18.79 14.99 16.79 12.66 7.93 29.57
28.75
29i (al,,), 103 (e,,), 436 (alg), 713 (eg), 713 (az,,), 754 (e,,), 1028 (eg). 1034 (e,,), 1037 ( a d , 1076 (alg),2516 ( a d , 2518 (al8), 2552 (eg), 2554 (e,,) 26 (al”), 102 (e’), 436 (al’), 710 (e”), 714 (a2)1), 758 (e’), 1025 (e”), 1037 (e’), 1037 2518 (al’), (a;), 1076 (al’), 2516 (a;), 2552 (e”), 2554 (e’)
32.79
1168i (azu), 11 (alu), 66 (e,,), 192 (e,,), 201 (e8), 309 (alg),797 (az,), 810 (als), 1029 (e,,), 1029 (e,), 2420 (az,,), 2425 (alg), 2438 (e ), 2442 (e,) 1168i (ai?, 14 (al”), 66 (e’), 195 (e”), 198 (e’), 369 (al’), 797 (a;). 810 (al’), 1026 (e”), 1033 (e’), 2420 ( a r ) , 2425 (al’), 2438 (e”), 2443 (e’)
27.44
32.82
27.45
‘At the HF/3-31G(*) level; in cm-l. bScaled by 0.89; in kcal/mol.
3-21G(*)). Some of the optimized geometries are already published,I4 but all of them are given in Table I for comparison under same condition. The spin-restricted Hartree-Fock (RHF) method and the spin-unrestricted HartreeFock (UHF) method were used for closed-shell singlet states and open-shell doublet states, respectively. The computed expectation values of the spin-squared operator (Sz) before spin annihilation were within the range of 0.750-0.761 for all doublet species considered here. The largest values (0.761) were for staggered and eclipsed H3Si-F-SiH3. However, these are all close to 0.750, the correct value for pure doublets. Theoretical harmonic vibrational frequencies were obtained from analytical second derivative^'^ calculated at the HF/3-21G(*) level. Zero-point vibrational energies (ZPE) were then computed with a scaling factor of 0.89 to correct for known deficiencies of frequencies obtained by using Hartree-Fock theory.16 Calculated vibrational frequencies and ZPE are summarized in Table 11. Electron correlation energies were estimated by single and double substituted configuration interaction1’ (CISD) with the frozen-core approximation and the 6-3 1G** basis at the HF/3-21G(*) optimized geometries. Unlinked cluster quadruple corrections1*(QC) were added to allow for the size (13) (a) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrtes, D. J.; Pople, J. A.; Binkley, J. S. J . Am. Chem. Soc. 1982,101,5039. (b) Francl, M.M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S.;DeFrecs, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77. 3654. (14) For a r w n t review, see: Apeloig, Y. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z. Eds.; Wiley: New York, 1989; Vol. 1, Chapter 2. (15) Pople, J. A.; Krishnan, R.; Schlegel. H. B.; Binkley, J. S. Inr. J . Quantum Chem. Symp. 1979, 13, 325. (16) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrecs, D. J.; Binkley, J. S.;Frisch, M. J.; Whiteside, R. A. Inr. J . Quantum Chem. Symp. 1981,
IS, 269. (17) Pople, J. A.; Binkley, J. S.;Seegcr, R. Inr. J. Quantum Chem. Symp. 1916, 10, 1.
The Journal of Physical Chemistry, Vol. 95, No. 6,1991 2473
Silicon Etching by Fluorine TABLE III: Total Energies' HF/ species 3-21G(*) H -0.496 20 F -98.84501 SiH, -289.166 16 SiH3+ -288.881 29 Si F3 -584.393 93 SiH4 -289.184 26 SiH4+ -289.390 32 FSiH, -388.19334 FSiH3+ -381.19085 SiF, -683.452 81 H3SiSiH3 -518.421 52 H3SiSiH3+ -518.102 21 F,SiSiH, -813.61960 F3SiSiH3+ -813.305 40 H3Si-F-SiH3+ staggered -611.11901 eclipsed -611.11914 H3Si-F-SiH3 staggered -611.28996 eclipsed -611.28996 H3Si-F-SiH3+. SiH3 complex staggered -966.351 82 eclipsed -966.351 90
HF/ 6-31G** -0.498 23 -99.36496 -290.61058 -290.333 98 -581.381 16 -291.230 84 -290.831 51 -390.15282 -389.14948 -686.94984 -581.31354 -580.993 02 -878.100 12
CISD+QC/ 6-31G**
-680.55829 -680.55831
-680.95591 -680.95596
-99.491 85 -290.12201 -290.435 54 -581.965 81 -291.366 33 -290.931 12 -390.44481 -390.01544 -681.115 98 -581.559 I5 -581.214 49 -818.81586
TABLE Iv: Relative Energies0 for Diapofition of Si&+, HfiiSiHS', and HfiiSiH3 HF/3-21 G(*)HF/6-3 1G** CISD+QC/6-3 1G** SiH4+ 0 0 0 SiH3+ + H 2.8 1.9 1 .O H3SiSiH3+ 0 0 0 SiH, + 8.2 28.9 33.3 SiH3+ H3SiSiH3 0 0 0 ZSiH, 55.9 54.1 68.3
-
a With ZPE corrections at the HF/3-21G(*) optimized geometries; in kcal/mol.
TABLE V: Relative Energies' for Reaction 1 and Related Reactions HF/ HF/ CISD+QC/ 3-21G(*) 6-31G** 6-31G** F HaSiSiHa' 0 0 0 -103.9 -82.2 -19.3 FSiH, + &HI+ -4.6 -12.5 FSiH3+ SiH3 -9.4 -121.6 -148.8 eclipsed H3Si-F-SiHIt -141.4 eclipsed H3Si-F-SiH3+ 0 0 0 staggered H3Si-F-SiH3+ 0.0 0.0 0.0
--+ -
+
0 With ZPE corrections at the HF/3-21G(*) optimized geometries; in kcal/mol.
F
'At the HF/3-21G(*) optimized geometries; in au. *,.*.
\I
,Si\
,....--... + --...*
/Si\
\I
/Si,
H
\I
'I
Si
Si
I
H
H
H
H
Figure 2. (a) Back-side attack and (b) front-side attack of F to H3SiSiH3+. U
H
Model Figure 1. Model for cation center in p-doped bulk silicon.
consistency. Total energies (ClSD+QC/6-3 1G**//HF/3-21G(*)) are given in Table Ill.
Results and Discussion A. Cation Center. The cation center defined in the Introduction is simulated by XSiH3+ (X = H, SiH,) as shown in Figure 1. SiH4+itself has been studied theoretically by many workers because of its Jahn-Teller distortion^.'^ Although the most stable structure is controversial, we treat the C,, structure of SiH4+ throughout our present study. C,, SiH4+is known as a complex between H radical and planar SiH3+.1".b The optimized geometry (18) (a) Langhoff, S. R.; Davidson, E. R. Inr. 1.Quantum Chem. 1974. 8,61. (b) Davidson, E. R.; Silver, D. W. Chem. Phys. I r r r . 1978, 52,403. (c) Pople, J. A.; mer,R.;Krishnan. R.Inr. J. Quantum Chem. Symp. 1977, 11, 149. (19) (a) Gordon, M. S. Chem. Phys. I r r r . 1978,59.410. (b) Power, D.; Brint, P.PpaMing, T. J. Mol. Srmr. 1984,108,81. (c) Caballol, R.; Catala, J. A.; Problet, J. M. Chem. Phys. Leu. 1986, 130, 278. (d) Pople, J. A.; Curtiss, L. A. J . Phys. Chem. 1987, 91. 155. (e) Curtiss, L. A.; Pople, J. A. Chem. Phys. Lett. 1988,144,38. (0 Kudo, T.; Nagase, S. Chem. Phys. 1988, 122, 233. (g) Frey, R. F.;Davidson, E. R. J. Chem. Phys. 1988,89, 4227.
at HF/3-21G(*) level can be separated into two parts. SiH4+has one long (2.280 A) and three equivalent Si-H bond length (1.452 A) which is consistent with that of SiH3+(1.452 A). Additionally, a singly occupied MO (SOMO) of C,, SiH4+is localized on only one H atom. Moreover, the binding energy of SiH4+is only about 1 kcal/mol (CISD+QC/6-31G**//HF/3-21G(*) with ZPE corrections, Table IV). H3SiSiH3+is known as a complex between SiH, and SiH3+.m This is not apparently from its structure and molecular orbitals. However, its rotation barrier is only 1 kcal/mol at the MP2/631G* leveLz0 The dissociation energy of H3SiSiH3+into SiH, and SiH3+,33.3 kcal/mol, is smaller than that of H3SiSiH3into 2SiH3, 68.3 kcal/mol (CISD+QC/6-3lG**//HF/3-21G(*) with ZPE corrections, Table IV). As a result, Si-Si bond of cation center in pdoped silicon may be somewhat longer and weaker than that of intrinsic silicon. B. Reaction between F Radical and Cation Center. In this subsection, we treat the reaction between F radical and cation center as a model for p-doped Si plasma etching reaction. Garrison and Goddard'O have recently calculated for the reaction between F and neutral H3SiSiH3 as an undoped silicon etching model in which a F radical attacks the Si-Si bond from the back side (see (a) in Figure 2), yielding FSiH, and SiH3 with exothermicity of 82.6 kcal/mol without ZPE corrections.10 Therefore, at first, back-side F attack reaction between F and H3SiSiH3+is considered as a model reaction between F radical and cation center. Calculated relative energies are shown in Table
V. The back-side F attack reaction between F and H3SiSiH3+leads to decomposition into FSiH, and SiH3+ with exothermicity of 103.9 kcal/mol (CISD+QC/6-31G**//HF/3-21G(*) with ZPE corrections, 105.4 kcal/mol without ZPE corrections), together (20) Clark, T. J. Am. Chem. Sm. 1988, 110, 1672.
2414 The Journal of Physical Chemistry, Vol. 95, No. 6,1991
Tachibana et al.
TABLE VI: Geometrical Panmeter@ for Erlipsed H$i-F-SiH,+
HF/3-21Gb 1.767 1.463
r(SiF) r(SiH) B(FSiH)
HF/3-21G(*) 1.753
0
1.779
1.454
1.453 101.62
101.9
0
HF/6-31G*' 101.0
"Bond lengths ( r ) in A, bond angles (e) in degrees. bReference21. 'Present work.
4\
4\ Bulk Silicon
a
\'/F
2
4 5 r(Si,-F) ( A ) Figure 4. Potential energy profiles for reaction 2 along the reaction coordinate as a function of r(Sil-F) at the HF/3-21G(*) level.
\
L
Si
4\
a
3
TABLE VII: Relative Energies" for Reaction 2 and Related Reactions HF/ HF/ CISD+QC/
Si
4- -\
3-21G(*) 6-31G** SiH,+ t FSiH3 0 0 eclipsed H,Si-F-SiH3+ + H -61.9 -45.8 H3SiSiH3++ FSiH3 0 0 eclipsed complex -35.46 eclipsed H3Si-F-SiH3+ + SiH3 -31.2b -14.4b
--
,......... 1? -.
,
6-31G** 0
-49.3 0
-11.6
" With ZPE corrections at the HF/3-21G(*)optimized geometries; in kcal/mol. Without ZPE corrections. Figure 3. Reaction between F and cation center.
with minor decomposition into FSiH,+ and SiH, with exothermicity of 12.5 kcal/mol. Consequently, Si-Si bond cleavage for pdoped silicon etching may occur more easily than that for undoped silicon etching. This result seems to be contrary to experimental results for pdoped silicon, Le., its suppressed etch rate. However, this is explained consistently by H3Si-F-SiH3+ complex formation. As shown in Table V, FSiH3 and SiH3+ can further react together to form H3Si-F-SiH3+ complex with exothermicity of 44.9 kcal/mol (CISD+QC/6-3lG**//HF/3-2lG(*) with ZPE corrections). The optimized geometries of staggered and eclipsed H3Si-F-SiH3+ are both linear. The two equivalent interacting Si-F bond lengths are 1.753 8, in both staggered and ecli sed forms, and longer than the normal Si-F distance (1.593 in FSiH3, Table I). Staggered H3Si-F-SiH3+ has one small imaginary frequency, but the eclipsed form has none (see Table 11). Nevertheless, there is no energy difference between staggered and eclipsed H3Si-F-SiH3+ as shown in Table V. The SiH, groups in H3Si-F-SiH3+ are free rotators. The H3Si-F-SiH3+ itself has been studied by Ignacio and Schlegel for the reaction product between F+ and H3SiSiHp.21 As shown in Table VI, our results using HF/3-21G(*) geometry are consistent with their HF/6-31G* geometry. The other reaction, front-side F attack reaction (see (b) in Figure 2), between F and H3SiSiH3+ leads directly to H,Si-FSiH3+ formation with exothermicity of 148.8 kcal/mol (CISD+QC/6-31G**//HF/3-21G(*) with ZPE corrections in Table V). Therefore, both reactions, (a) and (b) in Figure 2, lead to the same product as follows:
8:
+
H3SiSiH3+ F -.H3Si-F-SiH3+
(1) From these results, we can obtain the following picture for the p-doped effect on plasma etching. As shown in Figure 3, at the initial stage for the pdoped silicon etching, Si-Si bond cleavage (21) Ignacio. E. W.; Schlegel, H.
B. Chem. Phys. Leff. 1986, 127, 367.
by fluorine radical occurs more easily than that for undoped silicon etching but subsequently the products, F-attached Si and tricoordinated Si cation, may be recombined to form fluorine-bridged cation center (Si-F-Si+). As a consequence, fluorine radical is trapped at cation center and the etch rate for heavily p-doped silicon is suppressed. C. Reaction between FSiH3 and the Cation Center. Fluorine-attached silicon (FSiH3) can attack the cation center (XSiH,+) as well as tricoordinated Si cation (SiH,+). Previously, we investigated the analogous reaction for thermal etching of undoped ~ilicon.~ For thermal etching of pdoped silicon, pdoping effects are not only the suppression of etch rate?' as for plasma etching, but also a thicker fluorinated silicon layer.* After various reactions were considered, we found the novel reaction between cation center, XSiH: (X = H, SiH,), and FSiH3 proceeds with no barrier as follows:
-
XSiH,+ + FSiH3 X' + eclipsed H3Si-F-SiH3+ (2) In this reaction, the fluorine-bridged cation center (same as the product of reaction 1) and the radical X are produced. This reaction is different from the previous F-migration model for undoped silicon4in which fluorine migrates from fluorineattached silicon to another silicon. We describe here only eclipsed attack reaction between XSiH3+and FSiH3 as shown in Figure 4, because the results of staggered attack reaction are almost the same (energetics, charge distribution, and other geometrical parameters). Figure 4 shows potential energy profiles for reaction 2 along the reaction coordinate. We assumed the linearity for X-Si,-F-Si2 in this figure. We chose the SiI-F distance between Si atom of XSiH3+ and F atom of FSiH3 as a reaction coordinate and optimized the other geometrical parameters along the change of the reaction coordinate (see Figure 4). Reaction 2 is exothermic either for X = H or SiH3. Calculated relative energies are shown in Table VII. Exothermicity for X = H, 49.3 kcal/mol, is larger than that for X = SiH,, 11.6 kcal/mol (CISD+QC/6-31G**/ /HF/3-21G(*) with ZFE corrections, Table VII). Only for X = SiH,, complex (H3Si-.H3Si-F-SiH3+) can be seen with binding energy of 4.2 kcal/mol at the HF/3-21G(*) level (see Table VI1 and Figure 4).
The Journal of Physical Chemistry, Vol. 95, No. 6. 1991 2415
Silicon Etching by Fluorine
1 : \ ..--.._
\
8o
t
i 2
3
4
r(Sil-F)
(A)
5
Figure 5. Bond angle (FSiIHI)changes along the reaction coordinate as a function of r(Sil-F) at the HF/3-21G(*) level.
1.0
-
.Go5 tn al E
0 al
P
0
s V
0-
I
.....................................
-0.5
2
3
4
r(Sil-F)
(A)
5
Figure 6. Mulliken atomic charge density changes for reaction 2 along the reaction coordinate as a function of r(Sil-F) at the HF/3-2IG(*)level (X = H (-) and X = SiH, (---)).
Figure 5 shows FSiH bond angle (B(FSi,H,)) changes for the reaction 2 along the reaction coordinate. For either X = H or SiH3, the bond angle increases monotonously from reactants to products along the reaction coordinate. The bond angle for X = SiH, is larger than that for R = H throughout the reaction. Garrison and Goddard'O reported that B(FSilHI) at the transition state is 75' for the reaction of F with H3SiSiH3from the backside of the Si-Si bond ((b) in Figure 2). At the initial stage of the reaction between FSiH3 and H3SiSiH3+(reaction 2), B(FSilHI) (88.6O,82.1O for X = H, SiH, at r(SilF) = 5 A, respectively) is already beyond that of the transition state for the reaction between F and H3SiSiH3.This is the reason why reaction 2 has no barrier. Reaction 2 resembles SN2nucleophilic substitution reaction. Figure 6 shows Mulliken atomic charge density changes along the reaction coordinate. All of the Si atoms are always positively charged throughout the reaction. Fluorine is known as a high electronegative element. As a result, fluorine, even though bonded, may attack another silicon. The charge density of F atom is almost constant throughout the reaction. The charge density of Si in FSiH3 is also constant. Charge transfer from H in FSiH3 and Si in XSiH3+to X and H in XSiH3+occurs. The degree of charge transfer of Si to X in XSiH3+ is larger for X = SiH, than that for X = H. From these results, we can obtain the following picture for the pdoped effect on plasma and thermal etching of silicon as shown
Figure 7. Reaction between adsorbed F and cation center.
TABLE VIII: Relative Energieso for Reaction 3 and Related Reactions HF/3-21G(*) F3SiSiH3' + FSiH, 0 eclipsed H3Si-F-SiH3+ + SiF3 -46.6 F,SiSiH, 0 SiF3 + SiH3 75.0 F3SiSiH3' 0 SiF3 + SiH3+ 15.2 Without ZPE corrections at the HF/3-21G(*) optimized geometries; in kcal/mol.
-
in Figure 7. Adsorbed F atoms react with the cation center to form the stable fluorine-bridged cation center (Si-F-Si+) and a dangling bond. Then the dangling bond may serve as reactive center for further attack by F atom. As a result, a thick fluorinated layer is formed and the etch rate is suppressed. D. Side Reaction. Houle6 has observed that significant amounts of SiF, and Si2F6are also present for p-doped silicon etching, more than those for n-doped silicon etching. This is considered to be a side reaction. The dissociation energy of F3SiSiH3+into SiF3 and SiH3+(1 5.2 kcal/mol) is smaller than that for F3SiSiH3 into SiF3 and SiH3 (75.0 kcal/mol at the HF/3-2 1G(*) level, Table VIII). Consequently, SiF3 formation for pdoped silicon etching may be easier than for undoped silicon. Moreover, SiF3 formation may be accelerated by the following reaction analogous to reaction 2. F3Si-SiH3+
+ FSiH3
-
H3Si-F-SiH3+
+ SiF3
(3)
This reaction has an exothermicity of 46.6 kcal/mol (HF/3-21G(*) level in Table VIII). Si2F6can be explained as a product from the recombination reaction of two SiF3. These results support that the formation of fluorine-bridged cation center (Si-F-Si+) plays an important role in p-doped silicon etching. E. Explanationfor Stability of H3Si-F-SiH3+. The stability of eclipsed H3Si-F-SiH3+ contrary to neutral H3Si-F-SiH, can be understood from Bader-Pearson's perturbation theory (second-order Jahn-Teller effect).22 Figure 8 shows the MO energy level diagram of eclipsed H3Si-F-SiH3+ (RHF) and eclipsed H3Si-F-SiH3 (UHF). The lowest energy transition of neutral H3Si-F-SiH3 is from singly occupied MO (SOMO) 3al' to lowest unoccupied MO (LUMO) 3a2". This gives a transition density of A T symmetry. The SOMO and LUMO for neutral H3SiF-SiH3 are shown in Figure 9. The A; transition density corresponds to decomposition into SiH3and SiH4. This is consistent with the result of vibrational analysis from which neutral H3Si-F-SiH3 has one imaginary A; frequency (1 1681'cm-I, see Table 11). The A; normal mode is shown in figure 9. For H3Si-F-SiH3+, the corresponding A21) transition energy is not the lowest as shown in Figure 8. Furthermore, this is supported by their structural difference. The two equivalent Si-F bonds (22) Pearson, R. G . Symmerry Rules for Chemical Reacrions; Wiley: New York, 1976.
Tachibana et a].
2476 The Journal of Physical Chemistry, Vol. 95, No. 6,1991
-
5.;
-E; -10
0
-*
z-20
-33r 30;
---
3.4
2v
+e*+=
4=
-
0,
t
W
-30-
t-50t 1
&Si-F-SiY+
- + a i - +
4 YSi-F -SiH3
Figure 8. MO energy level diagram of eclipsed H3Si-F-SiH3+ and eclipsed H3Si-F-SiH, at the HF/3-2IG(*) level.
n
n
I
\ n4 n
h un LUMO (a?)
X
B
B SOMO
A$ mode
h')
Figure 9. SOMO and LUMO,and A? vibrational mode of H3Si-F-
SiH3. (1.855 A) of eclipsed H3Si-F-SiH3 are longer than those of H3Si-F-SiH3+ (1.753 A). As mentioned earlier, H3Si-F-SiH3+ has been studied by Ignacio and Schlegel for the reaction product between F+ and H3SiSiH3.21The reaction between F+ and H3SiSiH3was a model of Fc implantation reaction into amorphous silicon. From measurement of the infrared (IR) spectra, the F+-implanted silicon shows the metastable "B band" (750 cm-I), interpreted as arising from metastable bridging F configurations such as Si-F*-Si.23 (23) Azarbayejani, G. H.; Tsu,R.;Lucovsky, G. Nucl. fmrrum. Methods 1985, BIO/II,522.
This interpretation is supported by force field consideration^.^^ Ignacio and Schlege12' identified the metastable B band with a strongly infrared active antisymmetric Si-F stretch mode from the model calculations for H3Si-F-SiH3+ (740 an-'at HF/3-21G level). Our results at HF/3-21G(*) level of calculation is 714 cm-I as shown in Table 11. Although H3Si-F-SiH3+ is so small and calculated in the gas phase, these results may imply the following suggestion. If one can measure the IR spectra of the silicon surface under etching reaction, one may observe a specific band correspond to stable fluorine-bridged cation center (Si-F-Si+) for p-doped silicon as seen in F+-implanted silicon.
Conclusion In order to clarify the chemical mechanism of etching reaction of pdoped silicon by ab initio quantum chemical calculations, the cation center, i.e., distributed hole, in p-doped bulk silicon is simulated by a positively charged small finite cluster of silicon. Reaction pathways involving the cation center as a reactive site for plasma and thermal etching have been examined. The following conclusion can be drawn for the etching reaction of heavily p-doped silicon by fluorine. 1. For plasma etching of pdoping silicon, fluorine radical reacts with cation center to cleavage Si-Si bond more easily than that for undoped silicon etching but subsequently the products, Fattached Si and tricoordinated Si cation, may be recombined to form fluorine-bridged cation center (Si-F-Si+). As a consequence, the fluorine radical is trapped at the cation center and the etch rate for heavily p-doped silicon is suppressed. 2. For thermal and plasma etching, the adsorbed F atom can react with the cation center to form a stable fluorinebridged cation center (Si-F-Si+) and a dangling bond. Then the dangling bond may serve as the reactive center for further attack by the F atom. As a result, a thick fluorinated layer is formed and the etch rate is suppressed. 3. The side reaction, SiF3formation, for pdoped silicon etching can be also explained by the formation of fluorine-bridged cation center (Si-F-Si+). 4. The stability of eclipsed H3Si-F-SiH3+ can be understood from Bader-Pearson's perturbation theory (second-order JahnTeller effect). 5. By measurement of the IR spectra of the silicon surface under etching reaction, one may observe a specific band correspond to stable fluorine-bridged structure (Si-F-Si+) for pdoped silicon as seen in F+-implanted silicon. SiH4+and H3SiSiH3+may be so small as the cation center model of p-doped tetracoordinated silicon that a further sophisticated approach should be addressed to the more detailed understanding of the chemical mechanism. Our approach is considered a preliminary model for the chemistry of pdoping effects on the silicon etching reaction by fluorine. We are planning now to study another important doping effect, Le., n-doping effect, on the silicon etching reaction. Acknowledgment. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan. The molecular orbital calculations were carried out at the Data Processing Center of Kyoto University and the Computer Center of the Institute for Molecular Science (IMS) and we thank them for their generous permission to use FACOM M-780 and VP-400, and HITAC M-680H and S-820 computer systems, respectively. (24) Mosley, L.E.;Paesler, M.A.; Lucovsky, G.; Waltner, A.; Wortman,
J. J. Solid Store Commun. 1985, 53, 513.
