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Energetics of Ti atom diffusion into diamond film
Computational Materials Science 23 (2002) 73–79 www.elsevier.com/locate/commatsci
Energetics of Ti atom diffusion into diamond film J. Wan 1, R.Q. Zhang *, H.F. Cheung Department of Physics and Materials Science, Center of Super-Diamond and Advanced Films (COSDAF), City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong Accepted 1 June 2001
Abstract Energetics of Ti atom in metallization of diamond film were studied by calculations using density functional theory (DFT) and a composite basis set. Cluster models consisting of more than 10 C atoms were chosen to simulate the diamond phase with their boundaries saturated with H atoms. When Ti atom diffuses from the surface into the bulk of diamond interstitially, the energy barriers were found to be about 40 eV. Ti was found to favor substitutional sites rather than interstitial sites in diamond crystal. Our results indicate that the high concentration of Ti in chemical vapor deposited diamond films after metallization would occupy the grain boundaries rather than the bulk of diamond grain. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: First-principle calculation; Diamond film; Titanium; Metallization
1. Introduction Diamond, the hardest material in the world, has long been investigated for its use in electronic devices such as diodes, radiation sensors, thermistors and transistors, which are expected to operate at elevated temperatures. The significant progresses of diamond hetero-epitaxy in a low-pressure chemical vapor deposition (CVD) process in the early 1990s [1,2] has fulfilled a major step to realize these applications. Further work to form low* Corresponding author. Tel.: +852-2788-7849; fax: +8522788-7830. E-mail addresses: [email protected] (R.Q. Zhang), [email protected] (H.F. Cheung). 1 On leave from State Key Laboratory of Surface Physics, Fudan University, Shanghai, China.
resistance Ohmic contacts of the devices based on diamond requires the metallization of diamond film. The metallization process normally begins with the deposition of metals such as titanium, tantalum and molybdenum [3,4] with a protective film of gold. There have been a few reports on metallization of single crystal diamond film while polycrystalline CVD diamond have been frequently used as substrates in experiments [5–7]. It has been observed that the formation of good Ohmic or rectifying contacts is not always easily accomplished on diamond films grown by CVD [8]. Contacts established with aluminum or gold on CVD films exhibit highly resistive character, although these metals can be used almost routinely to form rectifying contacts on synthetic and natural semiconducting diamond crystals. The performance of Ohmic contacts on diamond depends
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 1 ) 0 0 2 3 5 - X
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J. Wan et al. / Computational Materials Science 23 (2002) 73–79
not only on the choice of metals, but also on the doping concentration, surface pretreatments and so on. Heat treatments of metal–diamond contacts (except Au–diamond contacts) were found to induce the sequential formation of carbides which were assumed to reduce the contact resistivity. Other attempts were also reported [9,10]. To form a satisfactory contact, sufficient fundamental researches are needed. The contact property is obviously determined by the chemical reaction and interface formation in metallization. The reaction of sputter deposited layers of Ti on the (0 0 1) surface of a synthetically grown single crystal-type IIb boron-doped diamond has been studied [4]. Interfacial carbides were detected by both Auger peak shape changes and Rutherford backscattering spectroscopy (RBS) measurements for annealing temperatures as low as 500°C, and their appearance correlated with the transition to Ohmic contacts. The carbides increased in thickness to about 50 nm after 1 h annealing at 750°C. The formation of TiC at the interface of a Ti overlayer and the diamond substrate upon annealing was also confirmed in metallization on a (0 0 1) diamond single crystal surface [11]. In a study of diffusion and chemical reaction on the interface of a metal/diamond sample during the metallization of diamond particles, a Ti layer reacted with the diamond particles to form a TiC surface layer after the sample was annealed at
600°C for 4 h. The diffusion process of carbon atoms from diamond substrate into the Ti layer was regarded as the key step for the formation of a TiC surface layer [12]. In this work, we have performed theoretical calculation using density functional theory (DFT) to investigate the interaction of the transition metal Ti and diamond film so as to reveal the mechanism of carbide formation and interdiffusion in the metallization. It is expected to provide useful information to experimentalists. The study includes the energetics of Ti atom and ion diffusing from the surface to the inner of single crystal diamond in different crystallographic directions.
2. Modeling and methods of calculation In diamond metallization using thermal evaporation, the Ti atoms may either form bond with the surface C atoms or diffuse into the bulk of diamond. For the latter case, the Ti may take a substitutional site or an interstitial site. Although Ti ion may be used in experiments, the bonding characteristics between the Ti and C of diamond may be understood by studying the neutral Ti atom interacting with the diamond, since the charge carried by the Ti ion could be neutralized when the ion approaching the diamond surface. To obtain the energetics of systems relating to
Fig. 1. Models for Ti depositing onto diamond (1 1 1) surface: (a) Ti–C4 H9 ; (b) Ti–C10 H16 . The dashed lines indicate the depositing paths of the Ti atom to the surface.
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
these processes, four cluster models were used to simulate the diamond phase. Fig. 1 represents the cluster models C4 H9 and C10 H16 which simulate the diamond (1 1 1) surface, while the cluster models of C3 H6 and C17 H24 in Fig. 2 were used to simulate the Ti interactions with diamond (1 0 0) surface. The cluster boundaries were saturated with H atoms to reduce the boundary effect so as to maintain the structure close to diamond. The geometric structures were first fully optimized and then fixed while Ti atom subsequently deposits on or diffuses into them. Hartree–Fock (HF) as well as B3LYP and B3PW91 of DFT were adopted in this work for total energy calculation. B3LYP uses Becke’s threeparameter hybrid functional [13] with the nonlocal correction provided by Lee et al. [14], while B3PW91 employs the same functional with a different non-local correction of Perdew and Wang 91 expression [15]. To obtain an accurate result from the first-principle calculation, a high-level basis set is required in general. It would be useful to select a modest basis set for calculation for the present purpose, for which the treated system is too large as compared to the systems in conventional ab initio calculations. By comparing the calculated results of DFT using STO-3G, 3-21G, 6-31G and 6-311++G , basis set of 3-21G was
75
found to be satisfactory in our previous study for systems involving both C and H atoms [16]. The 631+G , 6-31G , LanL2MB, LanL2DZ and CEP31G basis sets were respectively applied to Ti atom at the levels of all methods above. Comparing the calculated results with the data from experiments and other reports, it is concluded that the B3LYP/ 6-31G would be suitable for describing both Ti atom and ion. The total energies of Ti–diamond clusters were recorded and the energy barrier for Ti atom to diffuse into diamond was deduced. In our calculations the relaxation of diamond structure was omitted while Ti atom diffuses into the cluster. It is estimated that the relaxation of diamond structures may slightly decrease the energies calculated. All the calculations were carried out using the Gaussian 94 package [17].
3. Results and discussion 3.1. Ti on diamond (1 1 1) surface For Ti depositing onto diamond (1 1 1) surface, the possibility of the Ti atom forming bonds with the surface C atoms was examined at first using the cluster C4 H9 shown in Fig. 1(a). When Ti atom moving close to the carbon atom which is
Fig. 2. Models for Ti depositing on diamond (0 0 1): (a) Ti–C3 H6 ; (b) Ti–C17 H24 . The dashed lines indicate the depositing paths of the Ti atom to the surface.
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J. Wan et al. / Computational Materials Science 23 (2002) 73–79
supposed to be the surface atom, the potential energy change is illustrated in Fig. 3(a). It is shown that there is a bond formation at the Ti–C distance . The bond energy is about 1.82 eV. at about 2.1 A Another possibility for Ti deposited on the surface is that the Ti atom comes to the surface along the symmetrical line of the model shown in Fig. 1(b). The corresponding potential energy curve is shown in Fig. 3(b), where there is an energy barrier of about 39.73 eV for the Ti when crossing the surface layer. After that, there is a slight decrease in energy when the Ti approaching to the bulk. The stabilization energy is about 10.48 eV. Therefore, the reaction is endothermic and the energy involved is about 29.25 eV. Fig. 3(c) shows the energetics of the Ti atom in a similar diffusion process however on an unpassivated surface. It is shown that the energy required to overcome the energy barrier is slightly lower (33.93 eV) as compared with the hydrogen saturated surface. In addition, the stabilization energy when the Ti enters the bulk of the diamond drops to 5.58 eV, while the energy required in the whole process is about 28.35 eV. 3.2. Ti on diamond (0 0 1)
Fig. 3. Potential energy curves for Ti depositing onto diamond (1 1 1) surface using the models in Fig. 1: (a) Bonding with surface carbon (with the model in Fig. 1(a)); (b) diffusion into diamond through a hydrogenated diamond surface (with the model in Fig. 1(b)); (c) diffusion into diamond through a clean diamond surface (with the model in Fig. 1(b), however with the surface hydrogen atoms being removed).
Considering the unsaturated feature of the diamond (0 0 1) surface, we believe that the most possible deposited sites are: (1) ontop site and (2) the bridge site. In the first case, the Ti atom may form bond with one surface C atom. The bond formation is examined by using model C3 H9 shown in Fig. 2(a). The corresponding potential energy curve when the Ti atom approaching the surface C atom is shown in Fig. 4(a). It is shown that the bond energy of Ti–C bond here (4.59 eV) is much higher than that on (1 1 1) surface (1.82 eV). For the case that the Ti depositing to the bridge site, the cluster model C17 H24 in Fig. 2(b) was adopted. The potential energy contour obtained is shown in Fig. 4(b). It indicates that the Ti atom requires 24.62 eV energy to overcome the barrier in order to enter the bulk. Since there is 10.31 eV of stabilization energy, the reaction is endothermic and the energy in the reaction is about 14.31 eV. When compared to the result on (1 1 1) surface, the diffusion of the Ti atom into the bulk of the dia-
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
77
Fig. 4. Potential energy curves for Ti depositing onto diamond (0 0 1) surface using the models in Fig. 2: (a) Bonding with surface carbon (with the model in Fig. 2(a)); (b) diffusion into diamond through a hydrogenated diamond surface (with the model in Fig. 2(b)); (c) diffusion into diamond through a clean diamond surface (with the model in Fig. 2(b), however with the surface hydrogen atoms being removed).
mond through the (0 0 1) surface is found much easier. On the other hand, further calculations of
the potential energy of the above process with an unsaturated (0 0 1) surface is presented in Fig. 4(c).
78
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
It shows that the barrier feature disappears and the Ti atom can easily go into the space between the first and the second surface layer. Further diffusion of the Ti atom into the deeper of the diamond bulk could be understood using the result of Ti diffusion on (1 1 1) surface, since the Ti diffusion path as indicated by arrow in Fig. 2(b) would be similar as that for the case on (1 1 1) surface. 3.3. Energetics of Ti atom substituting C atom in diamond When using high-energy Ti atom in the metallization with sputtering or ion implantation, the Ti atom can probably take a substitution site. On the other hand, it is also possible that the Ti atom fill in the vacancies left by some carbon after the activation of them in thermal treatment. The energetics in these processes could be understood using the following study. As shown in Fig. 5, a cluster model C29 H36 is used to simulate the diamond phase. The cluster and the one with one Ti atom substituting the central carbon atom were fully optimized at the level of B3LYP/6-31G. It was found the endothermic energy was about 7.8 eV
for Ti atom to substitute one of C atoms in diamond. 3.4. A general discussion In view of the various energetics of the Ti on the diamond surfaces, it is difficult for Ti to diffuse into the bulk interstitially in a pure thermal process like annealing. This indicates that a thermally evaporated Ti deposition may not cause Ti diffusion into the single diamond. It is estimated that the thermally evaporated Ti to the surface may favor bond formation with the surface C, which may still adherent even at a high temperature. For a CVD diamond film which is always polycrystalline, the Ti atom may go to the boundary. However, if higher energy Ti atom was used, Ti may go into the bulk of the diamond and form TiC. Comparing the energetics of Ti diffusion into diamond and taking a substitution site, highenergy Ti atom is found to favor substitutional rather than interstitial in single crystal diamond, indicating the facilitation of Ti–C formation. This might explain why the contacts established with metal on CVD films exhibit highly resistive Ohmic behavior while these metals like Ti can be used almost routinely to form rectifying contacts on synthetic and natural semiconducting diamond crystals. Moreover, the deposited Ti atom may play a role of catalyst so that the graphitization may be enhanced in the thermally treated Ti/diamond interface, leading to the increase of conductivity and poor adhesion.
4. Conclusion
Fig. 5. Cluster model C29 H36 simulating bulk diamond. The central C atom is the site for Ti substitution.
According to our calculations, Ti atom thermally deposited onto the diamond surfaces may form Ti–C bond with the surface carbon atom. High-energy deposition using sputtering or ion implantation may result in Ti atom diffusion from the surface to the bulk of diamond and substitution of carbon atom in single crystal diamond. The high concentration of Ti in CVD diamond films after metallization would occupy the grain boundaries rather than the bulk of diamond grain.
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
Acknowledgements The work described in this paper was fully supported by a grant from City University of Hong Kong (Project No. 7000764).
References [1] X. Jiang, C.P. Klages, R. Zachai, M. Hartweg, H.-J. F€ usser, Appl. Phys. Lett. 62 (1993) 3438. [2] S.D. Wolter, B.R. Stoner, J.T. Glass, P.L. Ellis, D.S. Buhaenko, C.E. Jenkins, P. Southworth, Appl. Phys. Lett. 62 (1993) 1215. [3] Y. Zhu, B. Zheng, W. Yao, L. Cao, Diamond Relat. Mater. 8 (1999) 1073. [4] P.E. Viljoen, E.S. Lambers, P.H. Holloway, J. Vac. Sci. Technol. B 12 (1994) 2997. [5] N.B. Wong, G.Q. Li, S.M. Zhu, S.C. Tjong, S.T. Lee, Phys. Stat. Sol. A 169 (1998) 5. [6] O.R. Monterio, M.C. Salvadori, M. Cattani, V. Mammana, I.G. Brown, Thin Solid Films 308 (1997) 215.
79
[7] W.J. Meng, T.J. Curtis, L.E. Rehn, P.M. Baldo, J. Appl. Phys. 83 (1998) 6076. [8] K. Das, V. Venkatesan, K. Miyata, D.L. Dreifus, J.T. Glass, Thin Solid Films 212 (1992) 19. [9] M. Werner, O. Dorsch, H.U. Baerwind, A. Ersoy, E. Obermeier, C. Johnston, S. Romadi, P.R. Chalker, V. Moore, I.M. Buckley-Golder, Diamond Relat. Mater. 3 (1994) 983. [10] M. Werner, R. Job, A. Denisenko, A. Zaitsev, W.R. Fahrner, C. Johnston, P.R. Chalker, I.M. Buckley-Golder, Diamond Relat. Mater. 5 (1996) 723. [11] P.E. Viljoen, W.D. Roos, H.C. Swart, P.H. Holloway, Appl. Surf. Sci. 100/101 (1996) 612. [12] Y.F. Zhu, W.Q. Yao, B. Zheng, L.L. Cao, Surf. Interf. Anal. 28 (1999) 254. [13] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [14] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [15] J.P. Perdew, Electronic Structure of Solids’91, Akademie Verlag, Berlin, 1991. [16] R.Q. Zhang, E. Bertran, S.-T. Lee, Diamond Relat. Mater. 6 (1998) 1663. [17] M.J. Frisch et al., Gaussian 94, Revision E.3, Gaussian, Pittsburgh, PA, 1995.
Energetics of Ti atom diffusion into diamond film J. Wan 1, R.Q. Zhang *, H.F. Cheung Department of Physics and Materials Science, Center of Super-Diamond and Advanced Films (COSDAF), City University of Hong Kong, 83 Tat Chee Avenue, Hong Kong Accepted 1 June 2001
Abstract Energetics of Ti atom in metallization of diamond film were studied by calculations using density functional theory (DFT) and a composite basis set. Cluster models consisting of more than 10 C atoms were chosen to simulate the diamond phase with their boundaries saturated with H atoms. When Ti atom diffuses from the surface into the bulk of diamond interstitially, the energy barriers were found to be about 40 eV. Ti was found to favor substitutional sites rather than interstitial sites in diamond crystal. Our results indicate that the high concentration of Ti in chemical vapor deposited diamond films after metallization would occupy the grain boundaries rather than the bulk of diamond grain. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: First-principle calculation; Diamond film; Titanium; Metallization
1. Introduction Diamond, the hardest material in the world, has long been investigated for its use in electronic devices such as diodes, radiation sensors, thermistors and transistors, which are expected to operate at elevated temperatures. The significant progresses of diamond hetero-epitaxy in a low-pressure chemical vapor deposition (CVD) process in the early 1990s [1,2] has fulfilled a major step to realize these applications. Further work to form low* Corresponding author. Tel.: +852-2788-7849; fax: +8522788-7830. E-mail addresses: [email protected] (R.Q. Zhang), [email protected] (H.F. Cheung). 1 On leave from State Key Laboratory of Surface Physics, Fudan University, Shanghai, China.
resistance Ohmic contacts of the devices based on diamond requires the metallization of diamond film. The metallization process normally begins with the deposition of metals such as titanium, tantalum and molybdenum [3,4] with a protective film of gold. There have been a few reports on metallization of single crystal diamond film while polycrystalline CVD diamond have been frequently used as substrates in experiments [5–7]. It has been observed that the formation of good Ohmic or rectifying contacts is not always easily accomplished on diamond films grown by CVD [8]. Contacts established with aluminum or gold on CVD films exhibit highly resistive character, although these metals can be used almost routinely to form rectifying contacts on synthetic and natural semiconducting diamond crystals. The performance of Ohmic contacts on diamond depends
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 1 ) 0 0 2 3 5 - X
74
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
not only on the choice of metals, but also on the doping concentration, surface pretreatments and so on. Heat treatments of metal–diamond contacts (except Au–diamond contacts) were found to induce the sequential formation of carbides which were assumed to reduce the contact resistivity. Other attempts were also reported [9,10]. To form a satisfactory contact, sufficient fundamental researches are needed. The contact property is obviously determined by the chemical reaction and interface formation in metallization. The reaction of sputter deposited layers of Ti on the (0 0 1) surface of a synthetically grown single crystal-type IIb boron-doped diamond has been studied [4]. Interfacial carbides were detected by both Auger peak shape changes and Rutherford backscattering spectroscopy (RBS) measurements for annealing temperatures as low as 500°C, and their appearance correlated with the transition to Ohmic contacts. The carbides increased in thickness to about 50 nm after 1 h annealing at 750°C. The formation of TiC at the interface of a Ti overlayer and the diamond substrate upon annealing was also confirmed in metallization on a (0 0 1) diamond single crystal surface [11]. In a study of diffusion and chemical reaction on the interface of a metal/diamond sample during the metallization of diamond particles, a Ti layer reacted with the diamond particles to form a TiC surface layer after the sample was annealed at
600°C for 4 h. The diffusion process of carbon atoms from diamond substrate into the Ti layer was regarded as the key step for the formation of a TiC surface layer [12]. In this work, we have performed theoretical calculation using density functional theory (DFT) to investigate the interaction of the transition metal Ti and diamond film so as to reveal the mechanism of carbide formation and interdiffusion in the metallization. It is expected to provide useful information to experimentalists. The study includes the energetics of Ti atom and ion diffusing from the surface to the inner of single crystal diamond in different crystallographic directions.
2. Modeling and methods of calculation In diamond metallization using thermal evaporation, the Ti atoms may either form bond with the surface C atoms or diffuse into the bulk of diamond. For the latter case, the Ti may take a substitutional site or an interstitial site. Although Ti ion may be used in experiments, the bonding characteristics between the Ti and C of diamond may be understood by studying the neutral Ti atom interacting with the diamond, since the charge carried by the Ti ion could be neutralized when the ion approaching the diamond surface. To obtain the energetics of systems relating to
Fig. 1. Models for Ti depositing onto diamond (1 1 1) surface: (a) Ti–C4 H9 ; (b) Ti–C10 H16 . The dashed lines indicate the depositing paths of the Ti atom to the surface.
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
these processes, four cluster models were used to simulate the diamond phase. Fig. 1 represents the cluster models C4 H9 and C10 H16 which simulate the diamond (1 1 1) surface, while the cluster models of C3 H6 and C17 H24 in Fig. 2 were used to simulate the Ti interactions with diamond (1 0 0) surface. The cluster boundaries were saturated with H atoms to reduce the boundary effect so as to maintain the structure close to diamond. The geometric structures were first fully optimized and then fixed while Ti atom subsequently deposits on or diffuses into them. Hartree–Fock (HF) as well as B3LYP and B3PW91 of DFT were adopted in this work for total energy calculation. B3LYP uses Becke’s threeparameter hybrid functional [13] with the nonlocal correction provided by Lee et al. [14], while B3PW91 employs the same functional with a different non-local correction of Perdew and Wang 91 expression [15]. To obtain an accurate result from the first-principle calculation, a high-level basis set is required in general. It would be useful to select a modest basis set for calculation for the present purpose, for which the treated system is too large as compared to the systems in conventional ab initio calculations. By comparing the calculated results of DFT using STO-3G, 3-21G, 6-31G and 6-311++G , basis set of 3-21G was
75
found to be satisfactory in our previous study for systems involving both C and H atoms [16]. The 631+G , 6-31G , LanL2MB, LanL2DZ and CEP31G basis sets were respectively applied to Ti atom at the levels of all methods above. Comparing the calculated results with the data from experiments and other reports, it is concluded that the B3LYP/ 6-31G would be suitable for describing both Ti atom and ion. The total energies of Ti–diamond clusters were recorded and the energy barrier for Ti atom to diffuse into diamond was deduced. In our calculations the relaxation of diamond structure was omitted while Ti atom diffuses into the cluster. It is estimated that the relaxation of diamond structures may slightly decrease the energies calculated. All the calculations were carried out using the Gaussian 94 package [17].
3. Results and discussion 3.1. Ti on diamond (1 1 1) surface For Ti depositing onto diamond (1 1 1) surface, the possibility of the Ti atom forming bonds with the surface C atoms was examined at first using the cluster C4 H9 shown in Fig. 1(a). When Ti atom moving close to the carbon atom which is
Fig. 2. Models for Ti depositing on diamond (0 0 1): (a) Ti–C3 H6 ; (b) Ti–C17 H24 . The dashed lines indicate the depositing paths of the Ti atom to the surface.
76
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
supposed to be the surface atom, the potential energy change is illustrated in Fig. 3(a). It is shown that there is a bond formation at the Ti–C distance . The bond energy is about 1.82 eV. at about 2.1 A Another possibility for Ti deposited on the surface is that the Ti atom comes to the surface along the symmetrical line of the model shown in Fig. 1(b). The corresponding potential energy curve is shown in Fig. 3(b), where there is an energy barrier of about 39.73 eV for the Ti when crossing the surface layer. After that, there is a slight decrease in energy when the Ti approaching to the bulk. The stabilization energy is about 10.48 eV. Therefore, the reaction is endothermic and the energy involved is about 29.25 eV. Fig. 3(c) shows the energetics of the Ti atom in a similar diffusion process however on an unpassivated surface. It is shown that the energy required to overcome the energy barrier is slightly lower (33.93 eV) as compared with the hydrogen saturated surface. In addition, the stabilization energy when the Ti enters the bulk of the diamond drops to 5.58 eV, while the energy required in the whole process is about 28.35 eV. 3.2. Ti on diamond (0 0 1)
Fig. 3. Potential energy curves for Ti depositing onto diamond (1 1 1) surface using the models in Fig. 1: (a) Bonding with surface carbon (with the model in Fig. 1(a)); (b) diffusion into diamond through a hydrogenated diamond surface (with the model in Fig. 1(b)); (c) diffusion into diamond through a clean diamond surface (with the model in Fig. 1(b), however with the surface hydrogen atoms being removed).
Considering the unsaturated feature of the diamond (0 0 1) surface, we believe that the most possible deposited sites are: (1) ontop site and (2) the bridge site. In the first case, the Ti atom may form bond with one surface C atom. The bond formation is examined by using model C3 H9 shown in Fig. 2(a). The corresponding potential energy curve when the Ti atom approaching the surface C atom is shown in Fig. 4(a). It is shown that the bond energy of Ti–C bond here (4.59 eV) is much higher than that on (1 1 1) surface (1.82 eV). For the case that the Ti depositing to the bridge site, the cluster model C17 H24 in Fig. 2(b) was adopted. The potential energy contour obtained is shown in Fig. 4(b). It indicates that the Ti atom requires 24.62 eV energy to overcome the barrier in order to enter the bulk. Since there is 10.31 eV of stabilization energy, the reaction is endothermic and the energy in the reaction is about 14.31 eV. When compared to the result on (1 1 1) surface, the diffusion of the Ti atom into the bulk of the dia-
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
77
Fig. 4. Potential energy curves for Ti depositing onto diamond (0 0 1) surface using the models in Fig. 2: (a) Bonding with surface carbon (with the model in Fig. 2(a)); (b) diffusion into diamond through a hydrogenated diamond surface (with the model in Fig. 2(b)); (c) diffusion into diamond through a clean diamond surface (with the model in Fig. 2(b), however with the surface hydrogen atoms being removed).
mond through the (0 0 1) surface is found much easier. On the other hand, further calculations of
the potential energy of the above process with an unsaturated (0 0 1) surface is presented in Fig. 4(c).
78
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
It shows that the barrier feature disappears and the Ti atom can easily go into the space between the first and the second surface layer. Further diffusion of the Ti atom into the deeper of the diamond bulk could be understood using the result of Ti diffusion on (1 1 1) surface, since the Ti diffusion path as indicated by arrow in Fig. 2(b) would be similar as that for the case on (1 1 1) surface. 3.3. Energetics of Ti atom substituting C atom in diamond When using high-energy Ti atom in the metallization with sputtering or ion implantation, the Ti atom can probably take a substitution site. On the other hand, it is also possible that the Ti atom fill in the vacancies left by some carbon after the activation of them in thermal treatment. The energetics in these processes could be understood using the following study. As shown in Fig. 5, a cluster model C29 H36 is used to simulate the diamond phase. The cluster and the one with one Ti atom substituting the central carbon atom were fully optimized at the level of B3LYP/6-31G. It was found the endothermic energy was about 7.8 eV
for Ti atom to substitute one of C atoms in diamond. 3.4. A general discussion In view of the various energetics of the Ti on the diamond surfaces, it is difficult for Ti to diffuse into the bulk interstitially in a pure thermal process like annealing. This indicates that a thermally evaporated Ti deposition may not cause Ti diffusion into the single diamond. It is estimated that the thermally evaporated Ti to the surface may favor bond formation with the surface C, which may still adherent even at a high temperature. For a CVD diamond film which is always polycrystalline, the Ti atom may go to the boundary. However, if higher energy Ti atom was used, Ti may go into the bulk of the diamond and form TiC. Comparing the energetics of Ti diffusion into diamond and taking a substitution site, highenergy Ti atom is found to favor substitutional rather than interstitial in single crystal diamond, indicating the facilitation of Ti–C formation. This might explain why the contacts established with metal on CVD films exhibit highly resistive Ohmic behavior while these metals like Ti can be used almost routinely to form rectifying contacts on synthetic and natural semiconducting diamond crystals. Moreover, the deposited Ti atom may play a role of catalyst so that the graphitization may be enhanced in the thermally treated Ti/diamond interface, leading to the increase of conductivity and poor adhesion.
4. Conclusion
Fig. 5. Cluster model C29 H36 simulating bulk diamond. The central C atom is the site for Ti substitution.
According to our calculations, Ti atom thermally deposited onto the diamond surfaces may form Ti–C bond with the surface carbon atom. High-energy deposition using sputtering or ion implantation may result in Ti atom diffusion from the surface to the bulk of diamond and substitution of carbon atom in single crystal diamond. The high concentration of Ti in CVD diamond films after metallization would occupy the grain boundaries rather than the bulk of diamond grain.
J. Wan et al. / Computational Materials Science 23 (2002) 73–79
Acknowledgements The work described in this paper was fully supported by a grant from City University of Hong Kong (Project No. 7000764).
References [1] X. Jiang, C.P. Klages, R. Zachai, M. Hartweg, H.-J. F€ usser, Appl. Phys. Lett. 62 (1993) 3438. [2] S.D. Wolter, B.R. Stoner, J.T. Glass, P.L. Ellis, D.S. Buhaenko, C.E. Jenkins, P. Southworth, Appl. Phys. Lett. 62 (1993) 1215. [3] Y. Zhu, B. Zheng, W. Yao, L. Cao, Diamond Relat. Mater. 8 (1999) 1073. [4] P.E. Viljoen, E.S. Lambers, P.H. Holloway, J. Vac. Sci. Technol. B 12 (1994) 2997. [5] N.B. Wong, G.Q. Li, S.M. Zhu, S.C. Tjong, S.T. Lee, Phys. Stat. Sol. A 169 (1998) 5. [6] O.R. Monterio, M.C. Salvadori, M. Cattani, V. Mammana, I.G. Brown, Thin Solid Films 308 (1997) 215.
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