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Calculation of migration barriers on hydrogenated diamond surfaces
ELSEVIER
DIAMOND RELATED MATERIALS Diamond and Related Materials 5 (1996) 613-616
Calculation of migration barriers on hydrogenated diamond surfaces A. Gali, A. MCszBros, P. Desk * Department of Atomic Physics, Technical University Budapest, H-l 521, Hungary
Abstract A very important question for modeling diamond growth is whether long-range surface migration should be taken into account as a limiting step in the growth on differently oriented surfaces. The migration of active surface sites as well as that of layerbuilding adsorbants (CH,, bridging CH,, etc.) is of interest. Calculation of migration barriers for polyatomic units is an extremely demanding computational task, especially since the surface has to be simulated appropriately. The PM3 semi-empirical method has already proven its usefulness in growth modeling studies. This method was used to calculate migration barriers in a static approximation (T = 0 K) on thin hydrogenated diamond slabs. Results are presented for C( 1ll):H as well as for 2 x 1 reconstructed C(OOl):H surfaces. Keywords: Diamond; Surface diffusion; Theory; PM3 method
1. Introduction The mechanism of CVD diamond growth is far from being understood. Experiments indicate that surface diffusion could play an important role in the growth process [ 11. It would certainly explain the necessity of a critical substrate temperature. Also, according to some reports, the growth of diamond occurs at steps or scratches [2,3]. Thus, the knowledge of the activation energies for migration is of great importance. It is difficult to measure such migration barriers but it can be calculated theoretically. The long-range migration of dangling bonds was only investigated on ( 111) and ( 110) surfaces [4] and no complete analyses of (CH,),, or (CH,),, migration on the (2 x 1) reconstructed C(OOl):H surface (the most likely growth surface in CVD) has been attempted. Most of the recent experiments (STM, AFM, RHEED, LEED) have shown that the C(OOl):H diamond surface converts into the 2 x 1 form under CVD conditions [2,3,5,f;]. For that surface the energy of single jumps has been calculated for dangling bonds and various absorbents (CH3, CHJ in the course of growth modeling [ 7,8]. Skokov et al. [7] have calculated the energy barrier for transforming an adsorbed CH2 unit into the bridging position and that of a single jump of an H atom along the dimer chain. Mehandru and Anderson [S] used calculated CH, and CH2 binding energies at different sites to estimate migration barriers; *Corresponding author. 0925-9635/96/$15.00 0 1996 Elsevier Science S.A. All rights reserved SSDZ 0925-9635(95)00398-3
however, neither the energy of the necessary H removal nor relaxation effects have been taken into account. In the present paper activation energies, calculated in static approximation (T= 0 K), are presented for the longrange migration of a dangling bond on the 2 x 1 C(OOl):H surface in both the [ 1lo] and [Ii lo] directions, as well as for the migration of the CH2 radical in the [ 1lo] direction.
2. Model and computational method For calculating migration barriers on the (001) surface a four-layer diamond slab, containing six surface dimers was used with cyclic boundary conditions in the (001) plane. The bottom layer was held fixed at lattice sites obtained for bulk diamond with the applied approximation for the Hamiltonian. Dangling bonds of this layer were saturated by two hydrogen atoms for each carbon (dihydride surface). The top two layers were allowed to relax completely into a hydrogenated (2 x 1) reconstruction (monohydride) with the atoms of the third layer only relaxing perpendicular to the surface. The resulting geometry is shown in Fig. 1. We have investigated thicker slabs, but found that four layers is sufficient to model the reconstruction of (001) diamond surface. The distance between the dimer carbon atoms is 1.65 A, in good agreement with results of Huang and Frenklach [9], Verwoerd [lo] and Yang et al. [ 111, and within 0.19 A of the results of other calculations [8,12-171.
A. Gali et al./Diamond and Related Materials 5 (1996) 613-616
614 ilo
---s
110
,
“ki6204i-i -6201.60 a-% II.
-6204.25
Fig. 1. The four-layer diamond slab (C,sH,,) used in the calculations.
The total energy (as a function of the atomic coordinates) was calculated (and minimized) using the PM3 parametrization [ 181 of the MNDO [ 191 semi-empirical Hamiltonian. Open-shell systems were treated in a UHF and closed-shell systems in a RHF framework (no comparison was made between total energies of open- and closed-shell systems). PM3 has been checked recently with regard to heats of molecular reactions relevant in the diamond growth process [20] and force constants in hydrocarbon molecules [21]. In both cases, it was found to be superior to other semi-empirical methods. To check on its performance in a solid environment, in an earlier study we calculated the ground state properties of ideal diamond, using the cyclic cluster model (for details see Refs. [22,23]). These facts show that PM3 allows a realistic description of the problem. To check on the method of computing migration barriers we calculated the barrier for moving a dangling bond on a (111) surface from one site to the next using a four-layer (111) diamond slab with cyclic boundary conditions ((&His). The value we have found, 2.84 eV, is in excellent agreement with the 2.83 eV obtained by an ab initio LLA calculation [4]. In calculating transition states and reaction products, atoms in the top two layers of the slab were completely relaxed. In most cases (except where reasons of symmetry specified it) the transition state was located by varying one reaction coordinate in subsequent calculations, while the rest of the coordinates were changed freely in each calculation.
3. Results and discussion 3.1. Dangling bond migration The most obvious migration effect is the motion of dangling bonds created throughout the deposition process. Two feasible paths are shown in Figs. 2 and 3. The reaction coordinate was the position of the jumping H atom along the [ 1lo] and [ilO] directions, respectively. The migration barriers along [ 1lo] are 2.65 eV between
i-ii
-6201.06 ih% III.
-6204.25
Fig. 2. Energy diagram for dangling bond migration in the (110) direction. Two neighboring dimers from the (001) surface are shown, cf. Fig. 1. The numbers are the total energies of surface species in eV.
710
I.
-6204.25
-6201.31
II.
-6204.25
Fig. 3. Energy diagram for dangling bond migration in the il0) direction. Two neighboring dimers from the (001) surface are shown, rotated by 90” relative to Fig. 1. The numbers are the total energies of surface species in eV.
states I and II, and 3.17 eV between states II and III. For comparison, the barrier between II and III was calculated to be 2.88 eV by Skokov et al., also using PM3 in an embedded cluster approach [7]. The difference is due to the extent of relaxational freedom allowable in a larger cluster. For the migration in [ilO] direction, the energy barrier is 2.94 eV. 3.2. CH2 migration The generally accepted model of growth on (001) diamond [24-261 assumes the adsorption of a CH,
A. Gali et al./Diamond and Related Materials 5 (1996) 613-616
radical at a dangling bond. The methyl radical subsequently loses a H atom in a hydrogen addition/abstraction reaction and is inserted into a dimer bond. We have experimented with numerous pathways to move the CH2 unit along [ 1lo] without the mediation of a dangling bond. While most steps of this migration require activation energies bellow 1.5 eV, we were not able to find a path to move the CH2 unit from its bridging position in the absence of a dangling bond (the path with lowest energy was always dissociation). Further work is being carried out in this direction. The movement of the CH2 unit has also been investigated with mediation of a dangling bond (Fig. 4). The first step was to move oul. the CH2 unit from its bridging position. To find the migration barrier, the carbon atom of the CH, unit and the carbon atom with the dangling bond on the surface were rotated around a fixed point in the ( 110) plane by equal angles in subsequent calculations (the angle being the reaction coordinate). The fixed point was taken as the crossing of the lines of the C-CH2 bond in states I and II. ‘The migration barrier between states I and II was calculated to be 1.49 eV. The second step was to transfer a H atom from the neighboring dimer to the CH2 unit. The reaction coordinate was the position of the jumping II atom along [ 1101. We found
110 I.
-6348.99
-6354.87
IV.
-6353.81
-6353.19
'I' -6354.13
615
an energy barrier of 0.94 eV between states II and III. For comparison, this barrier was calculated to be 0.70 eV by Skokov et al. [7]. The third step was to move the CH, unit into the neighboring dimer site, as shown in Fig. 4. The reaction coordinate was the position of the carbon atom in the jumping CH3 unit along the [ 1lo] direction. The migration barrier was found to be very high - 4.82 eV (!). The fourth and fifth steps were the mirror image of the first two. It may be read from the energy diagram that the migration barrier between states IV and V was 0.62 eV, and between states V and VI it was 0.75 eV.
4. Conclusion The activation energies for dangling bond migration have been calculated on a C(OOl):H surface with (2 x 1) reconstruction both in [llO] and [ilO] directions. The calculated values, 3.17 and 2.94 eV, seem to be too big for this kind of motion to take place at 600-800 “C. It has to be noted, however, that our values are about 10% too high owing to neglection of dynamic effects. It is also known that semi-empirical Hartree-Fock-based methods overestimate the energy of transition states by another lo%-15% [27]. Assuming the Harris mechanism [24,25], i.e. that an adsorbed CH, radical is reduced instantly to CH2, we have investigated the motion of a CH2 unit on the C(OOl):H surface in the [ 1101 direction. No migration was found to be possible without dangling bond assistance. With the assistance of a dangling bond the activation energy of the limiting step was found to be above 4 eV. Even regarding the possible sources of error in our calculation, we are inclined to disregard long-range hydrocarbon diffusion on the (2 x 1) reconstructed C(OOl):H surface as a likely process.
k-ifk
i-c
k
h&--i III.
Acknowledgments
-6354.13
-6353.19
-6353.38
-6353.81
2-i VI.
fr
The authors are indebted to H. Ehrhardt for fruitful discussions. The support of the OTKA grant No. T14334 is gratefully acknowledged.
References
-6354.67
Cl1 W.J.P. van Enckevort et al., Diamond Relat. Mater., 2 (1993) 997. PI L.F. Sutcu, C.J. Chu, MS. Thompson, R.H. Hauge, J.L. Fig. 4. Energy diagram for CHI migration with assistance of a dangling bond in the (110) direction. Two neighboring dimers from the (001) surface are shown, c.f. Fig. 1. The numbers are the total energies of surface species in eV.
Margrave and M.P. D’Evelyn, J. Appl. Phys., 71 (1992) 5930 c31 T. Tsuno, T. Imai, Y. Nishibayashi, K. Hamada and N. Fujimoti, Jpn. J. Appl. Phys., 30 (1991) 1063. c41 MI. Heggie, CD. Latham, R. Jones and P.R. Briddon, 187th Meet. of The Electrotechnical Society, Reno, ND, May 21-26, 1995.
A. Gali et al./Diarnond and Related Materials 5 (1996) 613-616
616
[S] T. Ando, T. Aizawa, K. Yamamoto, Y. Sato and M. Kamo, Diamond Relat. Mater., 3 (1994) 975. [6] [7]
H. Kawarada, M. Aoki, H. Sasaki and K. Tsugawa, Diamond Relat. Mater., 3 (1994) 961. S. Skokov, B. Weiner and M. Frenklach, J. Phys. Chem., 98
(1994) 7073. S.P. Mehandru and A.B. Anderson, Surf. Sci., 248 (1991) 369. D. Huang and M. Frenklach, J. Phys. Chem., 96 (1992) 1868. W.S. Verwoerd, Surf Sci., IO8 (1981) 153. S.H. Yang, D.A. Drabold and J.B. Adams, Phys. Rev. B., 48 (1993) 5261. [ 121 Y.L. Yang and M.P. D’Evelyn, J. Am. Chem. SOL, 114 [ 81 [9] [lo] [ll]
(1992) 2796. [13]
D.W. Brenner, Phys. Rev. B, 42 (1990) 9458. [ 141 B.J. Garrison, E.J. Dawnkaski, D. Srivastava and D.W. Brenner, Science, 255 (1992) 835. [15] Th. Frauenheim, U. Stephan, P. Blaudeck, D. Porezag, H.-G. Busman, W. Zimmerman-Edling and S. Lauer, Phys. Reo. B, 48 (1993) 18189.
X.M. Zheng and P.V. Smith, Surf. Sci., 256 (1991) 1. Z. Jing and J.L. Whitten, Phys. Rev. B, 50 (1994) 2598. J.J.P. Stewart, J. Comput. Chem., 2 (1989) 209. M.J.S. Dewar and W.J. Thiel, J. Am. Chem. SOL, 99 (1977) 4899. B.H. Besler, W.L. Hase and K.C.J. Hass, Phys. Chem., 96 (1992) 9369. [21] D.M. Seeger, C. Korzeniewski and W. Kowalchyk, J. Phys. Chem., 95 (1991) 6871. [22] P. De&k, L.C. Snyder and J.W. Corbett, Phys. Reo. B, 45 (1992) 11612. [23] P. Desk, A. Gali, G. Sczigel and H. Ehrhardt, Diamond Relat.
[ 161 [17] [18] [19] [20]
Mater., 4 (1995) 706. [24]
S.J. Harris, Appl. Phys. Lett., 56 (1990) 2298. S.J. Harris and D.G. Goodwin, J. Phys. Chem., 97 (1993) 23. [26] B.J. Garrison, E.J. Dawnkaski, D. Srivastava and D.W. Brenner, Science, 255 (1992) 835. [27] W. Thiel, Tetrahedron, 44 (1988) 7393.
[25]
DIAMOND RELATED MATERIALS Diamond and Related Materials 5 (1996) 613-616
Calculation of migration barriers on hydrogenated diamond surfaces A. Gali, A. MCszBros, P. Desk * Department of Atomic Physics, Technical University Budapest, H-l 521, Hungary
Abstract A very important question for modeling diamond growth is whether long-range surface migration should be taken into account as a limiting step in the growth on differently oriented surfaces. The migration of active surface sites as well as that of layerbuilding adsorbants (CH,, bridging CH,, etc.) is of interest. Calculation of migration barriers for polyatomic units is an extremely demanding computational task, especially since the surface has to be simulated appropriately. The PM3 semi-empirical method has already proven its usefulness in growth modeling studies. This method was used to calculate migration barriers in a static approximation (T = 0 K) on thin hydrogenated diamond slabs. Results are presented for C( 1ll):H as well as for 2 x 1 reconstructed C(OOl):H surfaces. Keywords: Diamond; Surface diffusion; Theory; PM3 method
1. Introduction The mechanism of CVD diamond growth is far from being understood. Experiments indicate that surface diffusion could play an important role in the growth process [ 11. It would certainly explain the necessity of a critical substrate temperature. Also, according to some reports, the growth of diamond occurs at steps or scratches [2,3]. Thus, the knowledge of the activation energies for migration is of great importance. It is difficult to measure such migration barriers but it can be calculated theoretically. The long-range migration of dangling bonds was only investigated on ( 111) and ( 110) surfaces [4] and no complete analyses of (CH,),, or (CH,),, migration on the (2 x 1) reconstructed C(OOl):H surface (the most likely growth surface in CVD) has been attempted. Most of the recent experiments (STM, AFM, RHEED, LEED) have shown that the C(OOl):H diamond surface converts into the 2 x 1 form under CVD conditions [2,3,5,f;]. For that surface the energy of single jumps has been calculated for dangling bonds and various absorbents (CH3, CHJ in the course of growth modeling [ 7,8]. Skokov et al. [7] have calculated the energy barrier for transforming an adsorbed CH2 unit into the bridging position and that of a single jump of an H atom along the dimer chain. Mehandru and Anderson [S] used calculated CH, and CH2 binding energies at different sites to estimate migration barriers; *Corresponding author. 0925-9635/96/$15.00 0 1996 Elsevier Science S.A. All rights reserved SSDZ 0925-9635(95)00398-3
however, neither the energy of the necessary H removal nor relaxation effects have been taken into account. In the present paper activation energies, calculated in static approximation (T= 0 K), are presented for the longrange migration of a dangling bond on the 2 x 1 C(OOl):H surface in both the [ 1lo] and [Ii lo] directions, as well as for the migration of the CH2 radical in the [ 1lo] direction.
2. Model and computational method For calculating migration barriers on the (001) surface a four-layer diamond slab, containing six surface dimers was used with cyclic boundary conditions in the (001) plane. The bottom layer was held fixed at lattice sites obtained for bulk diamond with the applied approximation for the Hamiltonian. Dangling bonds of this layer were saturated by two hydrogen atoms for each carbon (dihydride surface). The top two layers were allowed to relax completely into a hydrogenated (2 x 1) reconstruction (monohydride) with the atoms of the third layer only relaxing perpendicular to the surface. The resulting geometry is shown in Fig. 1. We have investigated thicker slabs, but found that four layers is sufficient to model the reconstruction of (001) diamond surface. The distance between the dimer carbon atoms is 1.65 A, in good agreement with results of Huang and Frenklach [9], Verwoerd [lo] and Yang et al. [ 111, and within 0.19 A of the results of other calculations [8,12-171.
A. Gali et al./Diamond and Related Materials 5 (1996) 613-616
614 ilo
---s
110
,
“ki6204i-i -6201.60 a-% II.
-6204.25
Fig. 1. The four-layer diamond slab (C,sH,,) used in the calculations.
The total energy (as a function of the atomic coordinates) was calculated (and minimized) using the PM3 parametrization [ 181 of the MNDO [ 191 semi-empirical Hamiltonian. Open-shell systems were treated in a UHF and closed-shell systems in a RHF framework (no comparison was made between total energies of open- and closed-shell systems). PM3 has been checked recently with regard to heats of molecular reactions relevant in the diamond growth process [20] and force constants in hydrocarbon molecules [21]. In both cases, it was found to be superior to other semi-empirical methods. To check on its performance in a solid environment, in an earlier study we calculated the ground state properties of ideal diamond, using the cyclic cluster model (for details see Refs. [22,23]). These facts show that PM3 allows a realistic description of the problem. To check on the method of computing migration barriers we calculated the barrier for moving a dangling bond on a (111) surface from one site to the next using a four-layer (111) diamond slab with cyclic boundary conditions ((&His). The value we have found, 2.84 eV, is in excellent agreement with the 2.83 eV obtained by an ab initio LLA calculation [4]. In calculating transition states and reaction products, atoms in the top two layers of the slab were completely relaxed. In most cases (except where reasons of symmetry specified it) the transition state was located by varying one reaction coordinate in subsequent calculations, while the rest of the coordinates were changed freely in each calculation.
3. Results and discussion 3.1. Dangling bond migration The most obvious migration effect is the motion of dangling bonds created throughout the deposition process. Two feasible paths are shown in Figs. 2 and 3. The reaction coordinate was the position of the jumping H atom along the [ 1lo] and [ilO] directions, respectively. The migration barriers along [ 1lo] are 2.65 eV between
i-ii
-6201.06 ih% III.
-6204.25
Fig. 2. Energy diagram for dangling bond migration in the (110) direction. Two neighboring dimers from the (001) surface are shown, cf. Fig. 1. The numbers are the total energies of surface species in eV.
710
I.
-6204.25
-6201.31
II.
-6204.25
Fig. 3. Energy diagram for dangling bond migration in the il0) direction. Two neighboring dimers from the (001) surface are shown, rotated by 90” relative to Fig. 1. The numbers are the total energies of surface species in eV.
states I and II, and 3.17 eV between states II and III. For comparison, the barrier between II and III was calculated to be 2.88 eV by Skokov et al., also using PM3 in an embedded cluster approach [7]. The difference is due to the extent of relaxational freedom allowable in a larger cluster. For the migration in [ilO] direction, the energy barrier is 2.94 eV. 3.2. CH2 migration The generally accepted model of growth on (001) diamond [24-261 assumes the adsorption of a CH,
A. Gali et al./Diamond and Related Materials 5 (1996) 613-616
radical at a dangling bond. The methyl radical subsequently loses a H atom in a hydrogen addition/abstraction reaction and is inserted into a dimer bond. We have experimented with numerous pathways to move the CH2 unit along [ 1lo] without the mediation of a dangling bond. While most steps of this migration require activation energies bellow 1.5 eV, we were not able to find a path to move the CH2 unit from its bridging position in the absence of a dangling bond (the path with lowest energy was always dissociation). Further work is being carried out in this direction. The movement of the CH2 unit has also been investigated with mediation of a dangling bond (Fig. 4). The first step was to move oul. the CH2 unit from its bridging position. To find the migration barrier, the carbon atom of the CH, unit and the carbon atom with the dangling bond on the surface were rotated around a fixed point in the ( 110) plane by equal angles in subsequent calculations (the angle being the reaction coordinate). The fixed point was taken as the crossing of the lines of the C-CH2 bond in states I and II. ‘The migration barrier between states I and II was calculated to be 1.49 eV. The second step was to transfer a H atom from the neighboring dimer to the CH2 unit. The reaction coordinate was the position of the jumping II atom along [ 1101. We found
110 I.
-6348.99
-6354.87
IV.
-6353.81
-6353.19
'I' -6354.13
615
an energy barrier of 0.94 eV between states II and III. For comparison, this barrier was calculated to be 0.70 eV by Skokov et al. [7]. The third step was to move the CH, unit into the neighboring dimer site, as shown in Fig. 4. The reaction coordinate was the position of the carbon atom in the jumping CH3 unit along the [ 1lo] direction. The migration barrier was found to be very high - 4.82 eV (!). The fourth and fifth steps were the mirror image of the first two. It may be read from the energy diagram that the migration barrier between states IV and V was 0.62 eV, and between states V and VI it was 0.75 eV.
4. Conclusion The activation energies for dangling bond migration have been calculated on a C(OOl):H surface with (2 x 1) reconstruction both in [llO] and [ilO] directions. The calculated values, 3.17 and 2.94 eV, seem to be too big for this kind of motion to take place at 600-800 “C. It has to be noted, however, that our values are about 10% too high owing to neglection of dynamic effects. It is also known that semi-empirical Hartree-Fock-based methods overestimate the energy of transition states by another lo%-15% [27]. Assuming the Harris mechanism [24,25], i.e. that an adsorbed CH, radical is reduced instantly to CH2, we have investigated the motion of a CH2 unit on the C(OOl):H surface in the [ 1101 direction. No migration was found to be possible without dangling bond assistance. With the assistance of a dangling bond the activation energy of the limiting step was found to be above 4 eV. Even regarding the possible sources of error in our calculation, we are inclined to disregard long-range hydrocarbon diffusion on the (2 x 1) reconstructed C(OOl):H surface as a likely process.
k-ifk
i-c
k
h&--i III.
Acknowledgments
-6354.13
-6353.19
-6353.38
-6353.81
2-i VI.
fr
The authors are indebted to H. Ehrhardt for fruitful discussions. The support of the OTKA grant No. T14334 is gratefully acknowledged.
References
-6354.67
Cl1 W.J.P. van Enckevort et al., Diamond Relat. Mater., 2 (1993) 997. PI L.F. Sutcu, C.J. Chu, MS. Thompson, R.H. Hauge, J.L. Fig. 4. Energy diagram for CHI migration with assistance of a dangling bond in the (110) direction. Two neighboring dimers from the (001) surface are shown, c.f. Fig. 1. The numbers are the total energies of surface species in eV.
Margrave and M.P. D’Evelyn, J. Appl. Phys., 71 (1992) 5930 c31 T. Tsuno, T. Imai, Y. Nishibayashi, K. Hamada and N. Fujimoti, Jpn. J. Appl. Phys., 30 (1991) 1063. c41 MI. Heggie, CD. Latham, R. Jones and P.R. Briddon, 187th Meet. of The Electrotechnical Society, Reno, ND, May 21-26, 1995.
A. Gali et al./Diarnond and Related Materials 5 (1996) 613-616
616
[S] T. Ando, T. Aizawa, K. Yamamoto, Y. Sato and M. Kamo, Diamond Relat. Mater., 3 (1994) 975. [6] [7]
H. Kawarada, M. Aoki, H. Sasaki and K. Tsugawa, Diamond Relat. Mater., 3 (1994) 961. S. Skokov, B. Weiner and M. Frenklach, J. Phys. Chem., 98
(1994) 7073. S.P. Mehandru and A.B. Anderson, Surf. Sci., 248 (1991) 369. D. Huang and M. Frenklach, J. Phys. Chem., 96 (1992) 1868. W.S. Verwoerd, Surf Sci., IO8 (1981) 153. S.H. Yang, D.A. Drabold and J.B. Adams, Phys. Rev. B., 48 (1993) 5261. [ 121 Y.L. Yang and M.P. D’Evelyn, J. Am. Chem. SOL, 114 [ 81 [9] [lo] [ll]
(1992) 2796. [13]
D.W. Brenner, Phys. Rev. B, 42 (1990) 9458. [ 141 B.J. Garrison, E.J. Dawnkaski, D. Srivastava and D.W. Brenner, Science, 255 (1992) 835. [15] Th. Frauenheim, U. Stephan, P. Blaudeck, D. Porezag, H.-G. Busman, W. Zimmerman-Edling and S. Lauer, Phys. Reo. B, 48 (1993) 18189.
X.M. Zheng and P.V. Smith, Surf. Sci., 256 (1991) 1. Z. Jing and J.L. Whitten, Phys. Rev. B, 50 (1994) 2598. J.J.P. Stewart, J. Comput. Chem., 2 (1989) 209. M.J.S. Dewar and W.J. Thiel, J. Am. Chem. SOL, 99 (1977) 4899. B.H. Besler, W.L. Hase and K.C.J. Hass, Phys. Chem., 96 (1992) 9369. [21] D.M. Seeger, C. Korzeniewski and W. Kowalchyk, J. Phys. Chem., 95 (1991) 6871. [22] P. De&k, L.C. Snyder and J.W. Corbett, Phys. Reo. B, 45 (1992) 11612. [23] P. Desk, A. Gali, G. Sczigel and H. Ehrhardt, Diamond Relat.
[ 161 [17] [18] [19] [20]
Mater., 4 (1995) 706. [24]
S.J. Harris, Appl. Phys. Lett., 56 (1990) 2298. S.J. Harris and D.G. Goodwin, J. Phys. Chem., 97 (1993) 23. [26] B.J. Garrison, E.J. Dawnkaski, D. Srivastava and D.W. Brenner, Science, 255 (1992) 835. [27] W. Thiel, Tetrahedron, 44 (1988) 7393.
[25]