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Analysis of the growth process of diamond films by chemical vapor deposition
Diamond and Related Materials 11 (2002) 584–588
Analysis of the growth process of diamond films by chemical vapor deposition Takashi Yanagihara* Department of Physics, College of Engineering, Nihon University, Koriyama 963-8642, Japan
Abstract Chemical reactions between gases (H, CH3 and CH2 ) and the hydrogenated (111) surface of diamond clusters during diamond growth are investigated using the semi-empirical molecular orbital method of AM1 approximation. The heat of formation at the first stage of growth has been calculated as a function of the charges given to clusters. Also, using the frontier orbital theory, chemical interactions or reactions have been analyzed based on the calculated electronic energy levels of fragments of clusters or radicals. The results explain that homoepitaxial nucleation on the diamond (111) surface proceeds easily by one of two processes, either under the influence of pulsed negative charge or alternating charge bias to the substrate. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Diamond films; Homoepitaxy; CVD; Computer simulation
1. Introduction The growth of diamond films by chemical vapor deposition (CVD) is an important undertaking for potential application in electronic and optical devices. Homoepitaxial diamond films have been synthesized on (111) surfaces using microwave-assisted plasma CVD w1,2x showing a tendency to incorporate a significant amount of hydrogen during growth. Sakaguchi et al. further asserted that a high incident microwave power was required for the growth of high-purity (111) diamond films w1x. Using semi-empirical molecular orbital methods (PM3 and AM1), Komatsu had examined the stability of an anionic vacant site (AVS) on the hydrogenated (111) surface of diamond with a 1=1 structure w3x. The author asserted that the formation of an AVS on the surface should not be ignored in the CVD diamond growth mechanism as well as the structural stability of the (100)N surface of c-BN by AM1 calculations w4x. This latter surface was suggested to be chemically inert because of the anti-bonding nature of the surface N–H bonds at the lowest unoccupied molecular orbital (LUMO). Yanagihara and Yomogita, using the AM1 calculation, suggested that the nucleation of diamond on *Fax: q81-24-956-8692. E-mail address: [email protected] (T. Yanagihara).
the (111)B surface of c-BN was influenced by charge biases to the substrate by one of three processes: an alternating charge, pulsed positive charge, and positive charge bias w5x. However, the abstraction of the ‘surface’ H atom from the (111)N surface was impeded by the high stability in the positive charge bias and neutral surface. Under the influence of the negative charge bias, a frontier orbital of the ‘surface’ H atom on the (111)N surface interacted less effectively with all the electronic energy levels of the H gas. From their results, these authors suggested that nucleation on the (111)N surface did not proceed w5x. In this paper, we consider homoepitaxial diamond growth on the diamond (111) surface using AM1 calculations. 2. Method The AM1 approximation of MOPAC 97 for semiempirical molecular orbital calculations was used for ¨ solving the Schrodinger equation at the Hartree–Fock level in the quantum chemical optimization of atomic cluster geometry w6,7x. In modeling crystal surface structure, it is appropriate to use large clusters. The diamond {111} surfaces were assumed to have a (1=1):H mono-hydride phase except for a vacant hydrogen atom site and atoms at the edges. Many energy
0925-9635/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 1 . 0 0 7 0 1 - 4
T. Yanagihara / Diamond and Related Materials 11 (2002) 584–588
levels of the clusters were calculated for the geometry optimized by AM1. Regarding diamond growth by CVD in a CH4 yH2 gas mixture, the abstraction of a ‘surface’ hydrogen atom by atomic hydrogen gas (H gas) and the chemisorption of CH3 radicals on the substrate are the most important processes w8x. Here, we assume a similar growth mechanism to that proposed by Harris for the homoepitaxial growth on a hydrogenated (100) diamond surface w9x; i.e. first, the abstraction of a ‘surface’ hydrogen atom by H gas produces a gas-phase H2 molecule and a surface with a vacant hydrogen atom site. Second, a CH3 or a CH2 radical bonds at this vacant site. Third, the hydrogen atom adjacent to the CH3 or the CH2 radical bonded to the surface is abstracted. The relative stability of the cluster structures in these models has been estimated on the basis of the heat of formation (HOF) obtained by AM1 calculations. Furthermore, a chemical interaction or reaction between the gas and the cluster surface during diamond growth by CVD has been analyzed based on the electronic energy levels of the interacting fragments of cluster and gas molecules w10,11x. The interactions between the two systems are pairwise additive over the molecular orbitals and each pair interaction is governed by the expression: 2
DEs)Hij) y ŽEiyEj.
(1)
where Hij is proportional to the overlap integral and the eigenvectors (coefficients) of the atomic orbitals in the molecular orbitals, i and j, that take part in the interaction. (EiyEj) is the difference in energy of the molecular orbitals, i and j. As these can be estimated, we analyze the interactions of gases and surface atoms of clusters using Eq. (1). 3. Results and discussion 3.1. Growth process by CH3 radicals Fig. 1 shows a model of a diamond cluster M, C68H56, bound by eight hydrogenated {111} faces with optimized geometry of D3d symmetry. The large black and small gray balls represent carbon and hydrogen atoms, respectively. Sites (A), (F) and (G) are the typical sites of carbon atoms on the (111) surface. The axes x, y and z are taken along the lines w111x, w112x, and w110x, respectively. In Fig. 2, the relative energies of six clusters (P, P2, Q, S, R and T) and cluster M for HOF are shown as a function of the charge. Here, P(C68H55), Q(C68H55ØCH3), S(C68H55ØCH2), R(C68H54ØCH3), and T(C68H54ØCH2) show clusters with a vacant site of a ‘surface’ H atom at site (A) on the (111) surface, with the CH3 radical bonded to this site, with the CH2 radical bonded to this site, with the vacant H atom at site (F) adjacent to the CH3, and with this
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Fig. 1. Model of diamond cluster M, C68H56, bound by eight hydrogenated {111} faces. The large black and small gray balls represent carbon and hydrogen atoms, respectively.
site (F) adjacent to the CH2, respectively. P2(C68H54) is the cluster with a pair of vacant ‘surface’ H atoms at carbon sites (A) and (F), as shown in Fig. 1. The starting species in the growth mechanism is represented by cluster M. Here, HOFs of M(0) with a neutral charge, M(1q) with a charge of 1, M(1y) with a charge of y1, and M(2y) with a charge of y2 are 70.72, 893.90, 321.51 and 883.94 (kJymol), respectively. The reactions M™P™Q™R, M™P™S™T and M™P™P2™R (or T) on the (111) surface proceed with some barrier energies of HOF. The electronic energy levels in the clusters (M, P, P2 and Q), H gas, CH3 and CH2 are shown in Fig. 3. HO(HO9), SO, and LU represent HOMO, the singly occupied molecular orbital (SOMO), and LUMO, respectively. Also, (A), (A9), and (F) show that atoms on sites (A), (A9) and (F) have a large electric density distribution in the molecular orbital, respectively. (A9) shows a carbon atom site of CH3 bonded to the carbon site (A). When the quantum numbers, n, of the H gas are 1, 2 and 3, the energy values are y13.59, y3.40 and y1.51 eV, respectively. Also, SOMO of the CH3 and LUMO of the CH2 are y4.23 and y0.28 eV, respectively, as calculated by AM1 approximation. On the neutral surface, as indicated in Fig. 2a, the HOF of the cluster P(0) for the case of an abstracted ‘surface’ H atom from site (A) on the (111) surface is 184.3 kJymol higher than that of the starting cluster M(0), i.e. the reaction M(0)™P(0) is impeded by this high barrier energy. The ‘surface’ H atom bonding to carbon (A) of M(1y) given a negative charge of y1 has a relatively large electronic density of the eigenvector C1ssy0.172 in HOMO. A value of 0.173 in HOMO
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M(2y)™P(2y) proceed due to the gradient in the H.O.F., as shown in Fig. 2c,d. P(0), C68H55, with a vacant ‘surface’ H atom on the carbon atom (A), becomes an unstable state because the HOF of P(0) becomes higher than that of M(0) or Q(0). The SOMO of P(0), y3.88 eV, interacts more effectively with either SOMO of a CH3 radical or the levels of excited hydrogen. These interactions, involving two electrons in the two orbitals are clearly stabilized because the bonding level decreases in energy compared to the two separated levels w12x. The vacant sites (A) act as acceptors to receive the electron of the CH3 radical of large negative charge, y0.308, on the carbon. P(0) easily proceeds to Q(0) of cluster C68H55ØCH3 with a CH3 bonded to the vacant site. Although a ‘surface’ H atom bonding to carbon (F) of P(2y) has
Fig. 2. Propagation of diamond structure formation with H, CH3 and CH2, and the heat of formation (HOF) for clusters M, P, P2 , Q, S, R, and T. P, Q, S, R, T and P2 are the clusters with a vacant ‘surface’ H atom site (A), with the CH3 bonded to this site, with the CH2 to this site, with a vacant H site adjacent to the CH3, with a vacant H site adjacent to the CH2, and with a pair of vacant H at sites (A) and (F), respectively. T* has a bridge that a CH2 bonds on the two vacant H atom sites, (A) and (F). The numerical values denote the relative energies (kJymol) for HOF in each cluster compared with that of the starting species M.
was determined for an H atom bonding to carbon (A) of M(2y). These interact effectively with the electron energy level at ns2 of H gas because the corresponding EiyEj values in Eq. (1) become 2.67 and 0.33 eV, respectively, as shown in Fig. 3. Each ‘surface’ H atom is removed from carbon (A), and consequently, a gaseous H2 molecule and a radical site at the surface are produced. Thus, the reactions M(1y)™P(1y) and
Fig. 3. Orbital energy diagram for H, CH3, CH2, M(0), P(0), P2(0), M(1y), Q(1y), M(2y), P(2y) and Q(2y). HO (HO9), SO, and LU represent HOMO, SOMO and LUMO, respectively. (A), (A9) and (F) show that atoms on sites (A), (A9) and (F) have a large electric density distribution in the molecular orbital. (A9) shows the carbon atom site of CH3 bonded to the carbon site (A).
T. Yanagihara / Diamond and Related Materials 11 (2002) 584–588
a relatively small electronic density of the eigenvector C1ssy0.105 in the HOMO (y3.38 eV), the reaction P(2y)™P2(2y) will proceed due to the small EiyEj value and the gradient in the HOF. Here, P2(2y) is the cluster with a pair of vacant ‘surface’ H atoms at carbon sites (A) and (F), as indicated in Fig. 1. However, the reaction P2(2y)™P3 (2y) is impeded by a high barrier energy of 251.8 kJymol. Here, P3(2y) is the cluster with a triangular vacancy of the ‘surface’ H atoms at carbon sites (A), (F) and (G) in Fig. 1. The ‘surface’ H atom on the site (F) adjacent to (A) of Q(1y) has the large eigenvector C1s in HOMO of y6.12 eV and in Q(2y) the same large C1s in HOMO, y3.05 eV. These frontier orbitals interact more effectively with the levels of excited H gas. The reactions Q(1y)™R(1y ) and Q(2y)™R(2y) proceed easily due to the gradient in the HOF, as shown in Fig. 2. Furthermore, R(0) proceeds to the cluster with two neighboring CH3 groups on the (111) surface. Using MINDOy3 calculations, Tsuda et al. showed that the diamond structure is formed when a CH3 radical approaches one of the three neighboring CH3 groups on the positively charged diamond (111) surface w13x. From the above results, the nucleation of diamond by CH3 proceeds easily via one of four processes, under the influence of three pulsed negative charges (Reactions 2–4) or an alternating charge (Reaction 5); M(1y)™P(1y)™P(0)™Q(0)™Q(1y) ™R(1y)
(2)
M(2y)™P(2y)™P(0)™Q(0)™Q(2y) ™R(2y)
(3)
M(2y)™P(2y)™P2(2y)™P2(0)™R(0)
(4)
and M(2y)™P(2y)™P2(2y)™P2(1q)™R(1q)
(5)
3.2. Growth process by CH2 radicals Compared to the growth process based on the CH3 addition, LUMO (y0.28 eV) of a CH2 radical interacts more effectively with HOMO of P(2y) with an anionic vacant H site (AVS), as shown in Fig. 3. Thus, the reactions P(2y)™S(2y) will proceed although this process has a slight positive HOF. In the nucleation by CH2, the cluster S (C68H54ØCH2) with the various charge states except S(2y) does not proceed to T, with the vacant ‘surface’ H atom at site (F) adjacent to CH2, as shown in Fig. 2. Also, the ‘surface’ H atom on (F) of the cluster S(2y) has a very small eigenvector with HOMO and is not abstracted by reaction with the hydrogen atom. Thus, the reaction S(2y)™T(2y) is impeded. Also, P2(0)™T*(0) shown in Fig. 2 readily proceeds, but T*(0) produces a bridge comprised of CH2 bonds on the two vacant H atom sites, (A) and
587
(F). T*(0) that impedes homoepitaxial growth of diamond, rises in P2(2y) grown on the surface given the negative charge of y2. However, T(1y), T(2y) and T(1q) have two activation sites of the CH2 radical residing on the site (A) and the vacant ‘surface’ H site on the (F); T(1y) and T(2y) have large negative charges, y0.37 to y0.84, at the two carbons of the CH2 and the site (F), and T(1q) has the same small positive charges of about 0.06 at these sites. On these clusters, the bridge has not grown from repulsive forces by poles of the same charge although the carbon sites of T(1y) and T(1q) possess the frontier orbitals of the same phase. The CH2 radicals of S(0) and S(1q) interact more effectively with H gas because these have very large eigenvectors with the frontier orbitals. Thus, the reactions S(0)™Q(0) and S(1q)™Q(1q) proceed due to the gradient in the HOF, as shown in Fig. 2a,b. The nucleation of diamond by CH2 proceeds easily via one of two processes under the influence of a pulsed negative charge (Reaction 6) and an alternating charge (Reaction 7); M(1y)™P(1y)™P(0)™S(0)™Q(0)™ Q(1y)™R(1y)
(6)
and M(1y)™P(1y)™P(0)™S(0)™S(1q)™Q(1q)™ Q(1y)™R(1y) (7) On the other hand, Sakaguchi et al. had asserted that high incident microwave power was required for the growth of high-purity (111) diamond films w1x. The calculated results are consistent in their assertion that the plasma during the microwave discharge might be thought to give negative charge (y1) and positive charge (q1) bias to the substrate w14x. 4. Conclusions The mechanism for diamond growth on the hydrogenated diamond (111) surface has been investigated by AM1 calculations. The heat of formations at the first stage of the growth have been described as a function of the electric charge to the substrate. Furthermore, the electronic energy levels of fragments of clusters have been discussed by chemical interactions with gases, H, CH3 and CH2. From these results, the reaction of the CH3 radical on the (111) surface proceeds by one of two processes, either under the influence of a pulsed negative charge or an alternating charge bias to the substrate. The homoepitaxial growth of diamond is impeded due to the CH2 on the neutral (111) surface forming a bridge bonded on a pair of vacant H atom sites. However, the CH2 adsorbed on a vacant H site exerts positive influence on homoepitaxial growth by a pulsed negative charge (y1) or an alternating charge (y1 and q1) bias to the substrate.
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Acknowledgments The author wishes to express his sincere thanks to Emeritus Professor K. Yomogita of the Nihon University for his helpful discussions. References w1x I. Sakaguchi, M.N. Gamo, K.P. Loh, H. Haneda, T. Ando, J. Appl. Phys. 86 (1999) 1306. w2x M.N. Gamo, I. Sakaguchi, T. Takami, K. Suzuki, I. Kusunoki, T. Ando, J. Mater. Res. 9 (1999) 3518. w3x S. Komatsu, J. Appl. Phys. 80 (1996) 3319. w4x S. Komatsu, J. Mater. Res. 12 (1997) 1675. w5x T. Yanagihara, K. Yomogita, Jpn. J. Appl. Phys. 39 (2000) 5229.
w6x M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. w7x J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. w8x T. Nishimori, H. Sakamoto, Y. Takakuwa, S. Kono, Diamond Relat. Mater. 6 (1997) 463. w9x S.J. Harris, Appl. Phys. Lett. 56 (1990) 2298. w10x R. Hoffmann, Solids and Surfaces: A Chemist’s View of Bonding in Extended Structures, VCH Publishers, New York, 1988, p. 108. w11x K. Fukui, Bull. Chem. Soc. Jpn. 39 (1966) 498. w12x T.A. Albright, J.K. Burdett, M.H. Whangbo, Orbital Interactions in Chemistry Chap. 20, Wiley-Interscience, New York, 1985. w13x M. Tsuda, M. Nakajima, S. Oikawa, Jpn. J. Appl. Phys. 26 (1987) L527. w14x O. Matsumoto, H. Toshima, Y. Kanzaki, Thin Solid Films 128 (1985) 341.
Analysis of the growth process of diamond films by chemical vapor deposition Takashi Yanagihara* Department of Physics, College of Engineering, Nihon University, Koriyama 963-8642, Japan
Abstract Chemical reactions between gases (H, CH3 and CH2 ) and the hydrogenated (111) surface of diamond clusters during diamond growth are investigated using the semi-empirical molecular orbital method of AM1 approximation. The heat of formation at the first stage of growth has been calculated as a function of the charges given to clusters. Also, using the frontier orbital theory, chemical interactions or reactions have been analyzed based on the calculated electronic energy levels of fragments of clusters or radicals. The results explain that homoepitaxial nucleation on the diamond (111) surface proceeds easily by one of two processes, either under the influence of pulsed negative charge or alternating charge bias to the substrate. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Diamond films; Homoepitaxy; CVD; Computer simulation
1. Introduction The growth of diamond films by chemical vapor deposition (CVD) is an important undertaking for potential application in electronic and optical devices. Homoepitaxial diamond films have been synthesized on (111) surfaces using microwave-assisted plasma CVD w1,2x showing a tendency to incorporate a significant amount of hydrogen during growth. Sakaguchi et al. further asserted that a high incident microwave power was required for the growth of high-purity (111) diamond films w1x. Using semi-empirical molecular orbital methods (PM3 and AM1), Komatsu had examined the stability of an anionic vacant site (AVS) on the hydrogenated (111) surface of diamond with a 1=1 structure w3x. The author asserted that the formation of an AVS on the surface should not be ignored in the CVD diamond growth mechanism as well as the structural stability of the (100)N surface of c-BN by AM1 calculations w4x. This latter surface was suggested to be chemically inert because of the anti-bonding nature of the surface N–H bonds at the lowest unoccupied molecular orbital (LUMO). Yanagihara and Yomogita, using the AM1 calculation, suggested that the nucleation of diamond on *Fax: q81-24-956-8692. E-mail address: [email protected] (T. Yanagihara).
the (111)B surface of c-BN was influenced by charge biases to the substrate by one of three processes: an alternating charge, pulsed positive charge, and positive charge bias w5x. However, the abstraction of the ‘surface’ H atom from the (111)N surface was impeded by the high stability in the positive charge bias and neutral surface. Under the influence of the negative charge bias, a frontier orbital of the ‘surface’ H atom on the (111)N surface interacted less effectively with all the electronic energy levels of the H gas. From their results, these authors suggested that nucleation on the (111)N surface did not proceed w5x. In this paper, we consider homoepitaxial diamond growth on the diamond (111) surface using AM1 calculations. 2. Method The AM1 approximation of MOPAC 97 for semiempirical molecular orbital calculations was used for ¨ solving the Schrodinger equation at the Hartree–Fock level in the quantum chemical optimization of atomic cluster geometry w6,7x. In modeling crystal surface structure, it is appropriate to use large clusters. The diamond {111} surfaces were assumed to have a (1=1):H mono-hydride phase except for a vacant hydrogen atom site and atoms at the edges. Many energy
0925-9635/02/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 1 . 0 0 7 0 1 - 4
T. Yanagihara / Diamond and Related Materials 11 (2002) 584–588
levels of the clusters were calculated for the geometry optimized by AM1. Regarding diamond growth by CVD in a CH4 yH2 gas mixture, the abstraction of a ‘surface’ hydrogen atom by atomic hydrogen gas (H gas) and the chemisorption of CH3 radicals on the substrate are the most important processes w8x. Here, we assume a similar growth mechanism to that proposed by Harris for the homoepitaxial growth on a hydrogenated (100) diamond surface w9x; i.e. first, the abstraction of a ‘surface’ hydrogen atom by H gas produces a gas-phase H2 molecule and a surface with a vacant hydrogen atom site. Second, a CH3 or a CH2 radical bonds at this vacant site. Third, the hydrogen atom adjacent to the CH3 or the CH2 radical bonded to the surface is abstracted. The relative stability of the cluster structures in these models has been estimated on the basis of the heat of formation (HOF) obtained by AM1 calculations. Furthermore, a chemical interaction or reaction between the gas and the cluster surface during diamond growth by CVD has been analyzed based on the electronic energy levels of the interacting fragments of cluster and gas molecules w10,11x. The interactions between the two systems are pairwise additive over the molecular orbitals and each pair interaction is governed by the expression: 2
DEs)Hij) y ŽEiyEj.
(1)
where Hij is proportional to the overlap integral and the eigenvectors (coefficients) of the atomic orbitals in the molecular orbitals, i and j, that take part in the interaction. (EiyEj) is the difference in energy of the molecular orbitals, i and j. As these can be estimated, we analyze the interactions of gases and surface atoms of clusters using Eq. (1). 3. Results and discussion 3.1. Growth process by CH3 radicals Fig. 1 shows a model of a diamond cluster M, C68H56, bound by eight hydrogenated {111} faces with optimized geometry of D3d symmetry. The large black and small gray balls represent carbon and hydrogen atoms, respectively. Sites (A), (F) and (G) are the typical sites of carbon atoms on the (111) surface. The axes x, y and z are taken along the lines w111x, w112x, and w110x, respectively. In Fig. 2, the relative energies of six clusters (P, P2, Q, S, R and T) and cluster M for HOF are shown as a function of the charge. Here, P(C68H55), Q(C68H55ØCH3), S(C68H55ØCH2), R(C68H54ØCH3), and T(C68H54ØCH2) show clusters with a vacant site of a ‘surface’ H atom at site (A) on the (111) surface, with the CH3 radical bonded to this site, with the CH2 radical bonded to this site, with the vacant H atom at site (F) adjacent to the CH3, and with this
585
Fig. 1. Model of diamond cluster M, C68H56, bound by eight hydrogenated {111} faces. The large black and small gray balls represent carbon and hydrogen atoms, respectively.
site (F) adjacent to the CH2, respectively. P2(C68H54) is the cluster with a pair of vacant ‘surface’ H atoms at carbon sites (A) and (F), as shown in Fig. 1. The starting species in the growth mechanism is represented by cluster M. Here, HOFs of M(0) with a neutral charge, M(1q) with a charge of 1, M(1y) with a charge of y1, and M(2y) with a charge of y2 are 70.72, 893.90, 321.51 and 883.94 (kJymol), respectively. The reactions M™P™Q™R, M™P™S™T and M™P™P2™R (or T) on the (111) surface proceed with some barrier energies of HOF. The electronic energy levels in the clusters (M, P, P2 and Q), H gas, CH3 and CH2 are shown in Fig. 3. HO(HO9), SO, and LU represent HOMO, the singly occupied molecular orbital (SOMO), and LUMO, respectively. Also, (A), (A9), and (F) show that atoms on sites (A), (A9) and (F) have a large electric density distribution in the molecular orbital, respectively. (A9) shows a carbon atom site of CH3 bonded to the carbon site (A). When the quantum numbers, n, of the H gas are 1, 2 and 3, the energy values are y13.59, y3.40 and y1.51 eV, respectively. Also, SOMO of the CH3 and LUMO of the CH2 are y4.23 and y0.28 eV, respectively, as calculated by AM1 approximation. On the neutral surface, as indicated in Fig. 2a, the HOF of the cluster P(0) for the case of an abstracted ‘surface’ H atom from site (A) on the (111) surface is 184.3 kJymol higher than that of the starting cluster M(0), i.e. the reaction M(0)™P(0) is impeded by this high barrier energy. The ‘surface’ H atom bonding to carbon (A) of M(1y) given a negative charge of y1 has a relatively large electronic density of the eigenvector C1ssy0.172 in HOMO. A value of 0.173 in HOMO
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M(2y)™P(2y) proceed due to the gradient in the H.O.F., as shown in Fig. 2c,d. P(0), C68H55, with a vacant ‘surface’ H atom on the carbon atom (A), becomes an unstable state because the HOF of P(0) becomes higher than that of M(0) or Q(0). The SOMO of P(0), y3.88 eV, interacts more effectively with either SOMO of a CH3 radical or the levels of excited hydrogen. These interactions, involving two electrons in the two orbitals are clearly stabilized because the bonding level decreases in energy compared to the two separated levels w12x. The vacant sites (A) act as acceptors to receive the electron of the CH3 radical of large negative charge, y0.308, on the carbon. P(0) easily proceeds to Q(0) of cluster C68H55ØCH3 with a CH3 bonded to the vacant site. Although a ‘surface’ H atom bonding to carbon (F) of P(2y) has
Fig. 2. Propagation of diamond structure formation with H, CH3 and CH2, and the heat of formation (HOF) for clusters M, P, P2 , Q, S, R, and T. P, Q, S, R, T and P2 are the clusters with a vacant ‘surface’ H atom site (A), with the CH3 bonded to this site, with the CH2 to this site, with a vacant H site adjacent to the CH3, with a vacant H site adjacent to the CH2, and with a pair of vacant H at sites (A) and (F), respectively. T* has a bridge that a CH2 bonds on the two vacant H atom sites, (A) and (F). The numerical values denote the relative energies (kJymol) for HOF in each cluster compared with that of the starting species M.
was determined for an H atom bonding to carbon (A) of M(2y). These interact effectively with the electron energy level at ns2 of H gas because the corresponding EiyEj values in Eq. (1) become 2.67 and 0.33 eV, respectively, as shown in Fig. 3. Each ‘surface’ H atom is removed from carbon (A), and consequently, a gaseous H2 molecule and a radical site at the surface are produced. Thus, the reactions M(1y)™P(1y) and
Fig. 3. Orbital energy diagram for H, CH3, CH2, M(0), P(0), P2(0), M(1y), Q(1y), M(2y), P(2y) and Q(2y). HO (HO9), SO, and LU represent HOMO, SOMO and LUMO, respectively. (A), (A9) and (F) show that atoms on sites (A), (A9) and (F) have a large electric density distribution in the molecular orbital. (A9) shows the carbon atom site of CH3 bonded to the carbon site (A).
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a relatively small electronic density of the eigenvector C1ssy0.105 in the HOMO (y3.38 eV), the reaction P(2y)™P2(2y) will proceed due to the small EiyEj value and the gradient in the HOF. Here, P2(2y) is the cluster with a pair of vacant ‘surface’ H atoms at carbon sites (A) and (F), as indicated in Fig. 1. However, the reaction P2(2y)™P3 (2y) is impeded by a high barrier energy of 251.8 kJymol. Here, P3(2y) is the cluster with a triangular vacancy of the ‘surface’ H atoms at carbon sites (A), (F) and (G) in Fig. 1. The ‘surface’ H atom on the site (F) adjacent to (A) of Q(1y) has the large eigenvector C1s in HOMO of y6.12 eV and in Q(2y) the same large C1s in HOMO, y3.05 eV. These frontier orbitals interact more effectively with the levels of excited H gas. The reactions Q(1y)™R(1y ) and Q(2y)™R(2y) proceed easily due to the gradient in the HOF, as shown in Fig. 2. Furthermore, R(0) proceeds to the cluster with two neighboring CH3 groups on the (111) surface. Using MINDOy3 calculations, Tsuda et al. showed that the diamond structure is formed when a CH3 radical approaches one of the three neighboring CH3 groups on the positively charged diamond (111) surface w13x. From the above results, the nucleation of diamond by CH3 proceeds easily via one of four processes, under the influence of three pulsed negative charges (Reactions 2–4) or an alternating charge (Reaction 5); M(1y)™P(1y)™P(0)™Q(0)™Q(1y) ™R(1y)
(2)
M(2y)™P(2y)™P(0)™Q(0)™Q(2y) ™R(2y)
(3)
M(2y)™P(2y)™P2(2y)™P2(0)™R(0)
(4)
and M(2y)™P(2y)™P2(2y)™P2(1q)™R(1q)
(5)
3.2. Growth process by CH2 radicals Compared to the growth process based on the CH3 addition, LUMO (y0.28 eV) of a CH2 radical interacts more effectively with HOMO of P(2y) with an anionic vacant H site (AVS), as shown in Fig. 3. Thus, the reactions P(2y)™S(2y) will proceed although this process has a slight positive HOF. In the nucleation by CH2, the cluster S (C68H54ØCH2) with the various charge states except S(2y) does not proceed to T, with the vacant ‘surface’ H atom at site (F) adjacent to CH2, as shown in Fig. 2. Also, the ‘surface’ H atom on (F) of the cluster S(2y) has a very small eigenvector with HOMO and is not abstracted by reaction with the hydrogen atom. Thus, the reaction S(2y)™T(2y) is impeded. Also, P2(0)™T*(0) shown in Fig. 2 readily proceeds, but T*(0) produces a bridge comprised of CH2 bonds on the two vacant H atom sites, (A) and
587
(F). T*(0) that impedes homoepitaxial growth of diamond, rises in P2(2y) grown on the surface given the negative charge of y2. However, T(1y), T(2y) and T(1q) have two activation sites of the CH2 radical residing on the site (A) and the vacant ‘surface’ H site on the (F); T(1y) and T(2y) have large negative charges, y0.37 to y0.84, at the two carbons of the CH2 and the site (F), and T(1q) has the same small positive charges of about 0.06 at these sites. On these clusters, the bridge has not grown from repulsive forces by poles of the same charge although the carbon sites of T(1y) and T(1q) possess the frontier orbitals of the same phase. The CH2 radicals of S(0) and S(1q) interact more effectively with H gas because these have very large eigenvectors with the frontier orbitals. Thus, the reactions S(0)™Q(0) and S(1q)™Q(1q) proceed due to the gradient in the HOF, as shown in Fig. 2a,b. The nucleation of diamond by CH2 proceeds easily via one of two processes under the influence of a pulsed negative charge (Reaction 6) and an alternating charge (Reaction 7); M(1y)™P(1y)™P(0)™S(0)™Q(0)™ Q(1y)™R(1y)
(6)
and M(1y)™P(1y)™P(0)™S(0)™S(1q)™Q(1q)™ Q(1y)™R(1y) (7) On the other hand, Sakaguchi et al. had asserted that high incident microwave power was required for the growth of high-purity (111) diamond films w1x. The calculated results are consistent in their assertion that the plasma during the microwave discharge might be thought to give negative charge (y1) and positive charge (q1) bias to the substrate w14x. 4. Conclusions The mechanism for diamond growth on the hydrogenated diamond (111) surface has been investigated by AM1 calculations. The heat of formations at the first stage of the growth have been described as a function of the electric charge to the substrate. Furthermore, the electronic energy levels of fragments of clusters have been discussed by chemical interactions with gases, H, CH3 and CH2. From these results, the reaction of the CH3 radical on the (111) surface proceeds by one of two processes, either under the influence of a pulsed negative charge or an alternating charge bias to the substrate. The homoepitaxial growth of diamond is impeded due to the CH2 on the neutral (111) surface forming a bridge bonded on a pair of vacant H atom sites. However, the CH2 adsorbed on a vacant H site exerts positive influence on homoepitaxial growth by a pulsed negative charge (y1) or an alternating charge (y1 and q1) bias to the substrate.
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Acknowledgments The author wishes to express his sincere thanks to Emeritus Professor K. Yomogita of the Nihon University for his helpful discussions. References w1x I. Sakaguchi, M.N. Gamo, K.P. Loh, H. Haneda, T. Ando, J. Appl. Phys. 86 (1999) 1306. w2x M.N. Gamo, I. Sakaguchi, T. Takami, K. Suzuki, I. Kusunoki, T. Ando, J. Mater. Res. 9 (1999) 3518. w3x S. Komatsu, J. Appl. Phys. 80 (1996) 3319. w4x S. Komatsu, J. Mater. Res. 12 (1997) 1675. w5x T. Yanagihara, K. Yomogita, Jpn. J. Appl. Phys. 39 (2000) 5229.
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