- Email: [email protected]
Ab initio comparative study of C54 and C49 TiSi2 surfaces
Applied Surface Science 252 (2006) 4943–4950 www.elsevier.com/locate/apsusc
Short communication
Ab initio comparative study of C54 and C49 TiSi2 surfaces Tao Wang, Soon-Young Oh, Won-Jae Lee, Yong-Jin Kim, Hi-Deok Lee * Department of Electronics Engineering, Chungnam National University, Gung-Dong, Yusong-Gu, Daejeon 305-764, Republic of Korea Received 17 April 2005; accepted 29 July 2005 Available online 8 September 2005
Abstract A theoretical comparison of C54 and C49 TiSi2 surfaces is presented, using ab initio plane-wave ultrasoft pseudopotential method based on generalized gradient approximation (GGA). The different surface energies of TiSi2 have not only been calculated out, but the preferential formation of C49 phase in solid-state reaction could be explained by smaller surface energies and Poisson’s ratio of C49 TiSi2 as well. As for polar C54 TiSi2(1 0 0) and C49 TiSi2(0 1 0) surfaces, the Si termination surfaces are more stable. # 2005 Elsevier B.V. All rights reserved. Keywords: Ab initio; Silicide; TiSi2; Surface energy
1. Introduction TiSi2 has two phases: C54 and C49 phases. The former has the lowest resistivity (13–20 mV cm) among the silicides, thermal stability, strong adhesion with silicon substrates and process compatibilities in very large-scale integration technology so as to be used in integrated circuit as local interconnects, gate metallization and Schottky barriers. The latter is metastable phase with higher resistivity. Moreover, C49 TiSi2 is the first phase formed during the solidphase reaction between Ti and Si and then changes * Corresponding author. Tel.: +82 42 821 6868; fax: +82 42 823 9544. E-mail address: [email protected] (H.-D. Lee).
into C54 phase at the higher temperature. With the development of the IC processing, the line width shrinks further, even <100 nm, which dramatically increases the transformation temperature from C49 phase to C54 TiSi2 [1]. It is necessary to know more about TiSi2 to instruct future process by science knowledge. Besides a lot of experimental research works, TiSi2 has also been extensively studied in the theoretical views. Miglio et al. had performed tight binding (TB) molecular dynamics calculation with reasonable accuracy to investigate the structural, electronic and thermoelastic properties, intrinsic defects, diffusion kinetics and low index surfaces of TiSi2 [2–5]. The elastic constants and equilibrium structural parameters of C54 TiSi2 have been investigated by means of a full potential linear
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.07.029
4944
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
muffin-tin orbital (FP-LMTO) method using the local density approximation (LDA) and generalized gradient approximation (GGA) [6]. However, to our knowledge, there is no report about TiSi2 surface via ab initio method. The purpose of the paper is to study the most commonly observed surfaces of TiSi2 using ab initio method.
Table 1 Structural data for the TiSi2 Structure Space group
Site
Special position
C54
Ti Si
(0, 0, 0); (0.25, 0.25, 0.25) TiSi2 (0.333, 0, 0); (0.25 0.333, 0.25, 0.25) (0, 0.1022, 0.25)
Fddd
Ti C49
2. Details of the calculations
Prototype
Cmcm Si(I) (0, 0.7523, 0.25) Si(II) (0, 0.4461, 0.25)
ZrSi2
Table 2 The comparison of the equilibrium structural parameters from CASETP calculation and from experiments ˚ 3) ˚ ) b (A ˚) ˚ ) V0 (A Phases References a (A c (A
Cambridge serial total energy package (CASTEP), an ab initio pseudopotential method based on the plane-wave basis has been used in this study [7]. The density functional is treated by GGA with exchangecorrelation potential parameterized [8]. The cut-off energy (380 eV) of the plane-wave basis set was used throughout. The tolerances were set as follows: ˚ for 0.00002 eV/atom for the total energy, 0.001 A ˚ the root mean square atomic displacement, 0.05 eV/A for the root mean square atomic force, and 0.1 GPa for the root mean square stress. The SCF tolerance is set at 2.0 106 eV/atom and 13 k-points are chosen in the irreducible Brillion zone. Two a b c (a, b, c are lattice constants of C54 and C49 TiSi2) supercells were relaxed to obtain the theoretical equilibrium structures by geometry optimization and then primitive cells were used to calculate out the bulk moduli of single crystals of the two silicides. The different surfaces were formed by cleaving unit cells along ˚ ) was various lattice planes. Large vacuum space (12 A constructed above surfaces to avoid the influence between the top and bottom atoms in all slab calculations. Then the slab was relaxed by geometry optimization.
the GGA error range. The theoretically obtained bulk moduli for single crystalline C49 and C54 TiSi2 are listed in Table 3 at the corresponding experimental equilibrium structural parameters. The calculated C54 TiSi2 bulk modulus (B) is in better agreement with 126.9 GPa calculated from the single elastic constants in ref. [9] than the experimental value of 146.8 GPa, which is near to values calculated from LMTO method [6,9–11]. The B of C49 TiSi2 (94 GPa) is a little <102.9 GPa which is calculated from the only obtained experimental values of Young’s modulus
3. Results and discussion
Table 3 Bulk modulus of TiSi2
This work
8.140
4.774
8.483
329.65
C54 TiSi2
Experiment [19] Experiment [20] This work
8.267 8.269 3.514
4.800 4.798 13.383
8.551 8.553 3.534
339.32 339.34 166.20
C49 TiSi2
Experiment [21] Experiment [22] Experiment [23]
3.620 3.56 3.62
13.760 13.61 13.76
3.605 3.56 3.605
179.57 172.49 170.01
Phase
C54 TiSi2 is the face-centred orthorhombic structure while C49 TiSi2 has base-centred orthorhombic structure. Their space group and atom sites are shown in Table 1. The experimental lattice constants of TiSi2 are listed in Table 2 and used as initial structural parameters for the cell optimization. The calculated equilibrium lattice constants, listed in Table 2 as well are consistently slightly smaller than the experimental ones, however, the errors are within
B (Mbar)
References
1.26 1.468
This work Experiment 23
C54 TiSi2
1.269 1.764 1.569 1.419 0.946
Experiment 9 LMTO 11 LDA 6 GGA 6 This work
C49 TiSi2
1.029 1.539
Experiment 23 LMTO 11
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
(142 GPa) and Poisson’s ratio (0.27) as the formula (B = E/(3 – 6n)) [12]. The deviations between calculated value and experimental values partly results from temperature and GGA approximation. The simulation results are close to experimental values, which demonstrates that CASTEP is feasible for two TiSi2 phases. The polycrystalline elastic properties can be considered as the aggregate of single crystals at random orientation and be calculated using Voigt and Reuss model and Hill’s approximation [13–15]. For orthorhombic lattices, the Reuss and Voigt shear (GR and GV) and the Reuss and Voigt bulk modulus (BR and BV) can be defined as 15 GR ¼ 4ðs11 þ s22 þ s33 Þ 4ðs12 þ s13 þ s23 Þ þ 3ðs44 þ s55 þ s66 Þ GV ¼
BR ¼
1 ðc11 þ c22 þ c33 c12 c13 c23 Þ 15 1 þ ðc44 þ c55 þ c66 Þ 5 1 ðs11 þ s22 þ s33 Þ þ 2ðs12 þ s13 þ s23 Þ
1 2 BV ¼ ðc11 þ c22 þ c33 Þ þ ðc12 þ c13 þ c23 Þ 9 9
(1)
(2) (3) (4)
where cij and sij are the elastic constants and elastic compliance constants, respectively. Hill proved from energy consideration that the two approximation are the upper and lower limits and recommended to arithmetic means of the extremes of the bulk and shear moduli as ref. [15] 1 GH ¼ ðGR þ GV Þ 2
(5)
1 BH ¼ ðBR þ BV Þ 2
(6)
4945
For an isotropic material, the Poisson’s ratio (n) can be calculated as n¼
3B 2G 2ð3B þ GÞ
(7)
It is worthy noting that the calculated n for C54 phase is 0.24, which is obviously larger than that of C49 TiSi2, 0.16. The ‘‘ideal surfaces’’ were investigated. The surface energy (g) is defined as the standard method g¼
1 ðEslab NEbulk Þ 2A
(8)
where Eslab is the total energy of the slab with N TiSi2 ‘‘molecular’’ and Ebulk is the bulk energy for every TiSi2 per ‘‘molecular’’. A is the surface area and the factor 1/2 means that two surfaces were present in the slab. There are two types surfaces for C54 TiSi2(1 0 0): Si-terminated as well as Ti-terminated. In order to circumvent discussion of atom potential, the layers of the slab need be carefully chosen so that the slab contains N TiSi2 molecular and the stoichiometry is not broken. As the surface energy is sensitive with the number of layers, 12 layers of atoms were used in the ˚ ) was constructed simulation. The vacuum space (12 A above surface structure to cut-off the influence between the top and bottom atoms. As shown in Fig. 1, three slabs with different surfaces were constructed with the same layer number, surface area, the number of atoms, calculation settings. The only difference is the type of the terminated atoms. The calculated surface energies in Table 4 obviously show that if the terminated atoms are Si, the surface energy is lowest among them, indicating that the Siterminated surface is most stable. The simulation result accords with the experiment [16]. Three different surfaces of C49 TiSi2(0 1 0) were constructed, as shown in Fig. 2. The calculated g are listed in Table 5. When one of surface is terminated with Ti atoms, g with Si(I) termination on opposite
Table 4 Surface energies with different termination atoms for C54 TiSi2(1 0 0) Top and bottom atoms
Top atoms
Bottom atoms
Model
˚ 2) Surface area (s) (A
Layer
Eslab (eV)
g (eV/s)
Si–Ti Si–Si Ti–Si
Si–Ti–Si– Si–Ti–Si– Ti–Si–Si–
–Si–Si–Ti –Si–Ti–Si –Ti–Si–Si
Ti5Si10 Ti5Si10 Ti5Si10
23.53 23.53 23.53
15 15 15
9116.146 9116.771 9116.158
2.768 2.455 2.762
4946
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
Fig. 1. Slabs for three kinds of atom termination surfaces of C54 TiSi2(1 0 0) ((
) Ti; ( ) Si).
Fig. 2. Slabs with three kinds of atom termination for C49 TiSi2(0 1 0) surface ((
) Ti; ( ) Si).
surface is less than g with Si(II) termination on the other surface, which means that Si(I) termination surface is more stable than Si(II) termination surface. As the same reason, the surface with Si(II) termination is more favorable than that with Ti termination. Therefore, the surface energies have the following order: g(Si(I) termination) < g(Si(II) termi-
nation) < g(Ti termination). Nevertheless, Miglio and Iannuzzi estimated the different sequence: g(Si(II) termination) < g(Ti termination) < g(Si(I) termination). They predicted that g for C49 TiSi2(0 1 0) ˚ 2, which is near to g with Si(I) and is 0.12 eV/A Ti-terminated atoms in our calculations. However, it is difficult to calculate the concrete g with only Si(I) or
Table 5 Surface energies for different termination atoms of C49 TiSi2(0 1 0) Model
Top and bottom atom
˚ 2) Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) [5] g (eV/A
C49 Ti4Si8
Si(II)–Si(II) Ti–Si(II) Si(I)–Ti
13.05 13.05 13.05
10 10 10
0.105 0.170 0.115
0.120
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
Fig. 3. Slabs for two C54 TiSi2(3 1 1) surfaces ((
) Ti; ( ) Si).
only Ti termination because of complication of atom potential. In the following discussion, g of C49 TiSi2(0 1 0) is the surface energy for Si(II)terminated surface, which is close to the value from TB simulation as well [5]. The third special surface is C54 TiSi2(3 1 1), which is cleaved into two kinds of surfaces, as shown in
4947
Fig. 3, in which the discrepancy is the distance between surface atoms to the second near surface atoms. The calculated values are listed in Table 6. g of b-type surface in Fig. 3 is evidently less than that of a type surface and is consistent with estimation using TB method [5]. Cleaving nearer atom layers to form surface in a-type slab need more energy to break stronger Ti–Si bonds than in the case of formation of b-type slab. b-type C54 TiSi2(3 1 1) surface is more stable according to our calculation (Table 7). Finally, bigger slabs have been used to investigate surfaces with balance of the surface area and the number of layers and calculation consumption. The different slabs are illustrated in Fig. 4. As for C54 ˚ 2 for (3 1 1) surface, TiSi2, the smallest g is 0.108 eV/A which is consistent with experiment that XRD always detect (3 1 1) structure in C54 TiSi2. (1 3 1)g is the minimum among C49 TiSi2 surfaces, according with Miglio estimation as well. Moreover, in general g for C49 TiSi2 are less than those of C54 TiSi2, which is in agreement with the prediction form TB method after annealing 500 K, though they fell to obtain the results at 300 K [5]. Our calculated Poisson’s ratio and surface energies can be utilized to explain of competing mechanism of the growth of thin films between Ti and Si layers,
Table 6 Surface energies for two C54 TiSi2(3 1 1) surfaces C54 TiSi2
Type
˚ 2) Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) [5] g (eV/A
Ti12Si24
a b
37.47 37.47
12 12
1.597 0.107
0.11
Table 7 Calculated surface energies of C54 and C49 TiSi2 ˚ 2) TiSi2 Model Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) at 300 K [5] g (eV/A
˚ 2) relaxed [5] g (eV/A
C54 (1 0 0) (0 1 0) (0 0 1) (3 1 1)
Ti20Si40 Ti9Si18 Ti20Si40 Ti12Si24
82.55 35.38 79.35 37.47
15 9 5 12
0.120 0.132 0.120 0.108
0.11 0.14 0.11 0.11
0.09 0.14 0.11
C49 (1 0 0) (0 1 0)
Ti20Si40 Ti16Si32
99.21 52.20
5 10
0.124 0.103
0.14 0.12
(0 0 1) (1 3 1)
Ti20Si40 Ti12Si24
99.62 39.72
5 12
0.102 0.095
0.10 0.08
0.11 0.11 {(010)-Ti} 0.15 {(010)-Si I} 0.08 {(010)-Si II} 0.07
4948
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
which is depended on an interplay between the surface strain contribution and surface energy. On one hand, the strain effects are related with film– substrate lattice constants. It is difficult for both C54 and C49 TiS2 to nucleate on crystalline silicon due to their large discrepancy of lattice constants to Si lattice constant. However, the Poisson’s ratio of C49 TiSi2 is considerably smaller than that of C54 TiSi2, which means that a larger volume change for C49 phase exists during deformation because Poisson’s ratio is associated with the volume change during uniaxial deformation. Yu et al. brought forward that C49 TiSi2/Si(0 0 1) interface is more stable than C54 TiSi2/Si(0 0 1) by comparing the total energy of the Ti film pseudomorphic body-centered tetragonal
structure on Si(0 0 1) [17]. In their paper, the lateral lattice constants of pseudomorphic C49 TiSi2 structure are 5.5% larger than those of bulk C49 TiSi2, which accords with our calculation result that C49 TiSi2 is easier to change volume so as to accelerate growth kinetics because of independent surface energies. On the other hand, the surface energies of C49 TiSi2 are generally less than that of C54 TiSi2, which means that the interface energy contribution for the C49 nucleation should be lower that that for the C54 nucleation. According to classical nucleation theory, the Gibbs free energy gain from creation of a nucleus of the new phase is the driving force, which accompanies with the formation of the surface of the nucleus. Formation of some new
Fig. 4. Structures with different surfaces of TiSi2 ((
) Ti; ( ) Si).
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
4949
Fig. 4. (Continued ).
surface needs some energy, the hindrance force to the nucleation process. What is more, Jeon et al. proposed that C49 phase has a lower surface and interface energy to describe phase stability [18]. There is no epitaxial interface between TiSi2 and Si, or else it is more significant to investigate the interface. The intrinsical properties calculated via ab initio contribute to explain preferential formation of C49 phase in solid-phase reaction.
TiSi2(0 1 0) surfaces. b-type C54 TiSi2(3 1 1) surface should be favorable according to the calculation as well. The surface energies of C54 TiSi2(3 1 1) and C49 TiSi2(1 3 1) are the smallest among their group, respectively. Moreover, the generally smaller surface energies and less Poisson’s ratio of C49 TiSi2 help to explain the reason why C49 TiSi2 preferentially forms in solid-phase reaction.
Acknowledgment 4. Conclusions In short, ab initio has been utilized to investigate the surfaces of C49 and C54 TiSi2. The Si termination surfaces are more stable for C54 TiSi2(1 0 0) and C49
This work is supported in part by the National Program for Tera-level Nanodevices of the Ministry of Science and Technology as one of the 21st century Frontier Program.
4950
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
References [1] R.A. Roy, L.A. Clevenger, C. Cabral, K.L. Saenger, S. Brauer, J. Jordan-Sweet, J. Bucchignano, G.B. Stephenson, G. Morales, K.F. Ludwig, Appl. Phys. Lett. 66 (1995) 1732. [2] M. Iannuzi, M. Celino, L. Miglio, Phys. Rev. B 61 (2000) 14405. [3] M. Iannuzzi, P. Raiteri, M. Celino, L. Miglio, J. Phys.: Condens. Matter 14 (2002) 9535. [4] L. Miglio, M. Iannuzzi, P. Raiteri, M. Iannuzzi, A. Sabbadini, Microelectron. Eng. 55 (2001) 83. [5] M. Iannuzzi, L. Miglio, Surf. Sci. 479 (2001) 201–212. [6] P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. Wills, O. Eriksson, J. Appl. Phys. 84 (1998) 4891. [7] M.D. Sequal, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [8] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [9] M. Nakamura, Metall. Mater. Trans. A 25 (1994) 331. [10] J.F. Jongste, O.B. Loopstra, G.C.A.M. Janssen, S. Radelaar, J. Appl. Phys. 73 (1993) 2816.
[11] M. Ekman, V. Ozolin¸sˇ, Phys. Rev. B 57 (1998) 4419. [12] M.G. Grimaldi, F. Via, V. Raineri, S. Bocelli, M. Galli, F. Marabelli, F. Bonoli, M. Iannuzzi, L. Miglio, Microelectron. Eng. 37–38 (1997) 441. [13] W. Voigt, Lehrbuch der Kristallphysik, Taubner, Leipzig, 1928. [14] A. Reuss, Z. Angew. Math. Mech. 9 (1929) 55. [15] R. Hill, Proc. Phys. Soc. Lond. 65 (1952) 350. [16] A.W. Stephenson, M.E. Welland, J. Appl. Phys. 77 (1995) 653. [17] B.D. Yu, Y. Miyamoto, O. Sugino, Appl. Phys. Lett. 72 (1998) 1176. [18] H. Jeon, C.A. Sukow, J.W. Honeycutt, G.A. Rozgonyi, R.J. Nemanich, J. Appl. Phys. 71 (1992) 4269. [19] R. Rosenkranz, G. Frommeyer, Z. Metallkd. 83 (1992) 685. [20] G. Kresse, J. Futhmuller, Phys. Rev. B 54 (1996) 11169. [21] Joint Committee on Powder Diffraction Standards, File 10–255. [22] R. Beyers, R. Sinclair, J. Appl. Phys. 57 (1985) 5240. [23] W. Voigt, Lehrbuch der Kristallphysik, Taubner, Leipzig, 1928.
Short communication
Ab initio comparative study of C54 and C49 TiSi2 surfaces Tao Wang, Soon-Young Oh, Won-Jae Lee, Yong-Jin Kim, Hi-Deok Lee * Department of Electronics Engineering, Chungnam National University, Gung-Dong, Yusong-Gu, Daejeon 305-764, Republic of Korea Received 17 April 2005; accepted 29 July 2005 Available online 8 September 2005
Abstract A theoretical comparison of C54 and C49 TiSi2 surfaces is presented, using ab initio plane-wave ultrasoft pseudopotential method based on generalized gradient approximation (GGA). The different surface energies of TiSi2 have not only been calculated out, but the preferential formation of C49 phase in solid-state reaction could be explained by smaller surface energies and Poisson’s ratio of C49 TiSi2 as well. As for polar C54 TiSi2(1 0 0) and C49 TiSi2(0 1 0) surfaces, the Si termination surfaces are more stable. # 2005 Elsevier B.V. All rights reserved. Keywords: Ab initio; Silicide; TiSi2; Surface energy
1. Introduction TiSi2 has two phases: C54 and C49 phases. The former has the lowest resistivity (13–20 mV cm) among the silicides, thermal stability, strong adhesion with silicon substrates and process compatibilities in very large-scale integration technology so as to be used in integrated circuit as local interconnects, gate metallization and Schottky barriers. The latter is metastable phase with higher resistivity. Moreover, C49 TiSi2 is the first phase formed during the solidphase reaction between Ti and Si and then changes * Corresponding author. Tel.: +82 42 821 6868; fax: +82 42 823 9544. E-mail address: [email protected] (H.-D. Lee).
into C54 phase at the higher temperature. With the development of the IC processing, the line width shrinks further, even <100 nm, which dramatically increases the transformation temperature from C49 phase to C54 TiSi2 [1]. It is necessary to know more about TiSi2 to instruct future process by science knowledge. Besides a lot of experimental research works, TiSi2 has also been extensively studied in the theoretical views. Miglio et al. had performed tight binding (TB) molecular dynamics calculation with reasonable accuracy to investigate the structural, electronic and thermoelastic properties, intrinsic defects, diffusion kinetics and low index surfaces of TiSi2 [2–5]. The elastic constants and equilibrium structural parameters of C54 TiSi2 have been investigated by means of a full potential linear
0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.07.029
4944
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
muffin-tin orbital (FP-LMTO) method using the local density approximation (LDA) and generalized gradient approximation (GGA) [6]. However, to our knowledge, there is no report about TiSi2 surface via ab initio method. The purpose of the paper is to study the most commonly observed surfaces of TiSi2 using ab initio method.
Table 1 Structural data for the TiSi2 Structure Space group
Site
Special position
C54
Ti Si
(0, 0, 0); (0.25, 0.25, 0.25) TiSi2 (0.333, 0, 0); (0.25 0.333, 0.25, 0.25) (0, 0.1022, 0.25)
Fddd
Ti C49
2. Details of the calculations
Prototype
Cmcm Si(I) (0, 0.7523, 0.25) Si(II) (0, 0.4461, 0.25)
ZrSi2
Table 2 The comparison of the equilibrium structural parameters from CASETP calculation and from experiments ˚ 3) ˚ ) b (A ˚) ˚ ) V0 (A Phases References a (A c (A
Cambridge serial total energy package (CASTEP), an ab initio pseudopotential method based on the plane-wave basis has been used in this study [7]. The density functional is treated by GGA with exchangecorrelation potential parameterized [8]. The cut-off energy (380 eV) of the plane-wave basis set was used throughout. The tolerances were set as follows: ˚ for 0.00002 eV/atom for the total energy, 0.001 A ˚ the root mean square atomic displacement, 0.05 eV/A for the root mean square atomic force, and 0.1 GPa for the root mean square stress. The SCF tolerance is set at 2.0 106 eV/atom and 13 k-points are chosen in the irreducible Brillion zone. Two a b c (a, b, c are lattice constants of C54 and C49 TiSi2) supercells were relaxed to obtain the theoretical equilibrium structures by geometry optimization and then primitive cells were used to calculate out the bulk moduli of single crystals of the two silicides. The different surfaces were formed by cleaving unit cells along ˚ ) was various lattice planes. Large vacuum space (12 A constructed above surfaces to avoid the influence between the top and bottom atoms in all slab calculations. Then the slab was relaxed by geometry optimization.
the GGA error range. The theoretically obtained bulk moduli for single crystalline C49 and C54 TiSi2 are listed in Table 3 at the corresponding experimental equilibrium structural parameters. The calculated C54 TiSi2 bulk modulus (B) is in better agreement with 126.9 GPa calculated from the single elastic constants in ref. [9] than the experimental value of 146.8 GPa, which is near to values calculated from LMTO method [6,9–11]. The B of C49 TiSi2 (94 GPa) is a little <102.9 GPa which is calculated from the only obtained experimental values of Young’s modulus
3. Results and discussion
Table 3 Bulk modulus of TiSi2
This work
8.140
4.774
8.483
329.65
C54 TiSi2
Experiment [19] Experiment [20] This work
8.267 8.269 3.514
4.800 4.798 13.383
8.551 8.553 3.534
339.32 339.34 166.20
C49 TiSi2
Experiment [21] Experiment [22] Experiment [23]
3.620 3.56 3.62
13.760 13.61 13.76
3.605 3.56 3.605
179.57 172.49 170.01
Phase
C54 TiSi2 is the face-centred orthorhombic structure while C49 TiSi2 has base-centred orthorhombic structure. Their space group and atom sites are shown in Table 1. The experimental lattice constants of TiSi2 are listed in Table 2 and used as initial structural parameters for the cell optimization. The calculated equilibrium lattice constants, listed in Table 2 as well are consistently slightly smaller than the experimental ones, however, the errors are within
B (Mbar)
References
1.26 1.468
This work Experiment 23
C54 TiSi2
1.269 1.764 1.569 1.419 0.946
Experiment 9 LMTO 11 LDA 6 GGA 6 This work
C49 TiSi2
1.029 1.539
Experiment 23 LMTO 11
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
(142 GPa) and Poisson’s ratio (0.27) as the formula (B = E/(3 – 6n)) [12]. The deviations between calculated value and experimental values partly results from temperature and GGA approximation. The simulation results are close to experimental values, which demonstrates that CASTEP is feasible for two TiSi2 phases. The polycrystalline elastic properties can be considered as the aggregate of single crystals at random orientation and be calculated using Voigt and Reuss model and Hill’s approximation [13–15]. For orthorhombic lattices, the Reuss and Voigt shear (GR and GV) and the Reuss and Voigt bulk modulus (BR and BV) can be defined as 15 GR ¼ 4ðs11 þ s22 þ s33 Þ 4ðs12 þ s13 þ s23 Þ þ 3ðs44 þ s55 þ s66 Þ GV ¼
BR ¼
1 ðc11 þ c22 þ c33 c12 c13 c23 Þ 15 1 þ ðc44 þ c55 þ c66 Þ 5 1 ðs11 þ s22 þ s33 Þ þ 2ðs12 þ s13 þ s23 Þ
1 2 BV ¼ ðc11 þ c22 þ c33 Þ þ ðc12 þ c13 þ c23 Þ 9 9
(1)
(2) (3) (4)
where cij and sij are the elastic constants and elastic compliance constants, respectively. Hill proved from energy consideration that the two approximation are the upper and lower limits and recommended to arithmetic means of the extremes of the bulk and shear moduli as ref. [15] 1 GH ¼ ðGR þ GV Þ 2
(5)
1 BH ¼ ðBR þ BV Þ 2
(6)
4945
For an isotropic material, the Poisson’s ratio (n) can be calculated as n¼
3B 2G 2ð3B þ GÞ
(7)
It is worthy noting that the calculated n for C54 phase is 0.24, which is obviously larger than that of C49 TiSi2, 0.16. The ‘‘ideal surfaces’’ were investigated. The surface energy (g) is defined as the standard method g¼
1 ðEslab NEbulk Þ 2A
(8)
where Eslab is the total energy of the slab with N TiSi2 ‘‘molecular’’ and Ebulk is the bulk energy for every TiSi2 per ‘‘molecular’’. A is the surface area and the factor 1/2 means that two surfaces were present in the slab. There are two types surfaces for C54 TiSi2(1 0 0): Si-terminated as well as Ti-terminated. In order to circumvent discussion of atom potential, the layers of the slab need be carefully chosen so that the slab contains N TiSi2 molecular and the stoichiometry is not broken. As the surface energy is sensitive with the number of layers, 12 layers of atoms were used in the ˚ ) was constructed simulation. The vacuum space (12 A above surface structure to cut-off the influence between the top and bottom atoms. As shown in Fig. 1, three slabs with different surfaces were constructed with the same layer number, surface area, the number of atoms, calculation settings. The only difference is the type of the terminated atoms. The calculated surface energies in Table 4 obviously show that if the terminated atoms are Si, the surface energy is lowest among them, indicating that the Siterminated surface is most stable. The simulation result accords with the experiment [16]. Three different surfaces of C49 TiSi2(0 1 0) were constructed, as shown in Fig. 2. The calculated g are listed in Table 5. When one of surface is terminated with Ti atoms, g with Si(I) termination on opposite
Table 4 Surface energies with different termination atoms for C54 TiSi2(1 0 0) Top and bottom atoms
Top atoms
Bottom atoms
Model
˚ 2) Surface area (s) (A
Layer
Eslab (eV)
g (eV/s)
Si–Ti Si–Si Ti–Si
Si–Ti–Si– Si–Ti–Si– Ti–Si–Si–
–Si–Si–Ti –Si–Ti–Si –Ti–Si–Si
Ti5Si10 Ti5Si10 Ti5Si10
23.53 23.53 23.53
15 15 15
9116.146 9116.771 9116.158
2.768 2.455 2.762
4946
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
Fig. 1. Slabs for three kinds of atom termination surfaces of C54 TiSi2(1 0 0) ((
) Ti; ( ) Si).
Fig. 2. Slabs with three kinds of atom termination for C49 TiSi2(0 1 0) surface ((
) Ti; ( ) Si).
surface is less than g with Si(II) termination on the other surface, which means that Si(I) termination surface is more stable than Si(II) termination surface. As the same reason, the surface with Si(II) termination is more favorable than that with Ti termination. Therefore, the surface energies have the following order: g(Si(I) termination) < g(Si(II) termi-
nation) < g(Ti termination). Nevertheless, Miglio and Iannuzzi estimated the different sequence: g(Si(II) termination) < g(Ti termination) < g(Si(I) termination). They predicted that g for C49 TiSi2(0 1 0) ˚ 2, which is near to g with Si(I) and is 0.12 eV/A Ti-terminated atoms in our calculations. However, it is difficult to calculate the concrete g with only Si(I) or
Table 5 Surface energies for different termination atoms of C49 TiSi2(0 1 0) Model
Top and bottom atom
˚ 2) Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) [5] g (eV/A
C49 Ti4Si8
Si(II)–Si(II) Ti–Si(II) Si(I)–Ti
13.05 13.05 13.05
10 10 10
0.105 0.170 0.115
0.120
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
Fig. 3. Slabs for two C54 TiSi2(3 1 1) surfaces ((
) Ti; ( ) Si).
only Ti termination because of complication of atom potential. In the following discussion, g of C49 TiSi2(0 1 0) is the surface energy for Si(II)terminated surface, which is close to the value from TB simulation as well [5]. The third special surface is C54 TiSi2(3 1 1), which is cleaved into two kinds of surfaces, as shown in
4947
Fig. 3, in which the discrepancy is the distance between surface atoms to the second near surface atoms. The calculated values are listed in Table 6. g of b-type surface in Fig. 3 is evidently less than that of a type surface and is consistent with estimation using TB method [5]. Cleaving nearer atom layers to form surface in a-type slab need more energy to break stronger Ti–Si bonds than in the case of formation of b-type slab. b-type C54 TiSi2(3 1 1) surface is more stable according to our calculation (Table 7). Finally, bigger slabs have been used to investigate surfaces with balance of the surface area and the number of layers and calculation consumption. The different slabs are illustrated in Fig. 4. As for C54 ˚ 2 for (3 1 1) surface, TiSi2, the smallest g is 0.108 eV/A which is consistent with experiment that XRD always detect (3 1 1) structure in C54 TiSi2. (1 3 1)g is the minimum among C49 TiSi2 surfaces, according with Miglio estimation as well. Moreover, in general g for C49 TiSi2 are less than those of C54 TiSi2, which is in agreement with the prediction form TB method after annealing 500 K, though they fell to obtain the results at 300 K [5]. Our calculated Poisson’s ratio and surface energies can be utilized to explain of competing mechanism of the growth of thin films between Ti and Si layers,
Table 6 Surface energies for two C54 TiSi2(3 1 1) surfaces C54 TiSi2
Type
˚ 2) Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) [5] g (eV/A
Ti12Si24
a b
37.47 37.47
12 12
1.597 0.107
0.11
Table 7 Calculated surface energies of C54 and C49 TiSi2 ˚ 2) TiSi2 Model Surface area (A
Layer
˚ 2) g (eV/A
˚ 2) at 300 K [5] g (eV/A
˚ 2) relaxed [5] g (eV/A
C54 (1 0 0) (0 1 0) (0 0 1) (3 1 1)
Ti20Si40 Ti9Si18 Ti20Si40 Ti12Si24
82.55 35.38 79.35 37.47
15 9 5 12
0.120 0.132 0.120 0.108
0.11 0.14 0.11 0.11
0.09 0.14 0.11
C49 (1 0 0) (0 1 0)
Ti20Si40 Ti16Si32
99.21 52.20
5 10
0.124 0.103
0.14 0.12
(0 0 1) (1 3 1)
Ti20Si40 Ti12Si24
99.62 39.72
5 12
0.102 0.095
0.10 0.08
0.11 0.11 {(010)-Ti} 0.15 {(010)-Si I} 0.08 {(010)-Si II} 0.07
4948
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
which is depended on an interplay between the surface strain contribution and surface energy. On one hand, the strain effects are related with film– substrate lattice constants. It is difficult for both C54 and C49 TiS2 to nucleate on crystalline silicon due to their large discrepancy of lattice constants to Si lattice constant. However, the Poisson’s ratio of C49 TiSi2 is considerably smaller than that of C54 TiSi2, which means that a larger volume change for C49 phase exists during deformation because Poisson’s ratio is associated with the volume change during uniaxial deformation. Yu et al. brought forward that C49 TiSi2/Si(0 0 1) interface is more stable than C54 TiSi2/Si(0 0 1) by comparing the total energy of the Ti film pseudomorphic body-centered tetragonal
structure on Si(0 0 1) [17]. In their paper, the lateral lattice constants of pseudomorphic C49 TiSi2 structure are 5.5% larger than those of bulk C49 TiSi2, which accords with our calculation result that C49 TiSi2 is easier to change volume so as to accelerate growth kinetics because of independent surface energies. On the other hand, the surface energies of C49 TiSi2 are generally less than that of C54 TiSi2, which means that the interface energy contribution for the C49 nucleation should be lower that that for the C54 nucleation. According to classical nucleation theory, the Gibbs free energy gain from creation of a nucleus of the new phase is the driving force, which accompanies with the formation of the surface of the nucleus. Formation of some new
Fig. 4. Structures with different surfaces of TiSi2 ((
) Ti; ( ) Si).
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
4949
Fig. 4. (Continued ).
surface needs some energy, the hindrance force to the nucleation process. What is more, Jeon et al. proposed that C49 phase has a lower surface and interface energy to describe phase stability [18]. There is no epitaxial interface between TiSi2 and Si, or else it is more significant to investigate the interface. The intrinsical properties calculated via ab initio contribute to explain preferential formation of C49 phase in solid-phase reaction.
TiSi2(0 1 0) surfaces. b-type C54 TiSi2(3 1 1) surface should be favorable according to the calculation as well. The surface energies of C54 TiSi2(3 1 1) and C49 TiSi2(1 3 1) are the smallest among their group, respectively. Moreover, the generally smaller surface energies and less Poisson’s ratio of C49 TiSi2 help to explain the reason why C49 TiSi2 preferentially forms in solid-phase reaction.
Acknowledgment 4. Conclusions In short, ab initio has been utilized to investigate the surfaces of C49 and C54 TiSi2. The Si termination surfaces are more stable for C54 TiSi2(1 0 0) and C49
This work is supported in part by the National Program for Tera-level Nanodevices of the Ministry of Science and Technology as one of the 21st century Frontier Program.
4950
T. Wang et al. / Applied Surface Science 252 (2006) 4943–4950
References [1] R.A. Roy, L.A. Clevenger, C. Cabral, K.L. Saenger, S. Brauer, J. Jordan-Sweet, J. Bucchignano, G.B. Stephenson, G. Morales, K.F. Ludwig, Appl. Phys. Lett. 66 (1995) 1732. [2] M. Iannuzi, M. Celino, L. Miglio, Phys. Rev. B 61 (2000) 14405. [3] M. Iannuzzi, P. Raiteri, M. Celino, L. Miglio, J. Phys.: Condens. Matter 14 (2002) 9535. [4] L. Miglio, M. Iannuzzi, P. Raiteri, M. Iannuzzi, A. Sabbadini, Microelectron. Eng. 55 (2001) 83. [5] M. Iannuzzi, L. Miglio, Surf. Sci. 479 (2001) 201–212. [6] P. Ravindran, L. Fast, P.A. Korzhavyi, B. Johansson, J. Wills, O. Eriksson, J. Appl. Phys. 84 (1998) 4891. [7] M.D. Sequal, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717. [8] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [9] M. Nakamura, Metall. Mater. Trans. A 25 (1994) 331. [10] J.F. Jongste, O.B. Loopstra, G.C.A.M. Janssen, S. Radelaar, J. Appl. Phys. 73 (1993) 2816.
[11] M. Ekman, V. Ozolin¸sˇ, Phys. Rev. B 57 (1998) 4419. [12] M.G. Grimaldi, F. Via, V. Raineri, S. Bocelli, M. Galli, F. Marabelli, F. Bonoli, M. Iannuzzi, L. Miglio, Microelectron. Eng. 37–38 (1997) 441. [13] W. Voigt, Lehrbuch der Kristallphysik, Taubner, Leipzig, 1928. [14] A. Reuss, Z. Angew. Math. Mech. 9 (1929) 55. [15] R. Hill, Proc. Phys. Soc. Lond. 65 (1952) 350. [16] A.W. Stephenson, M.E. Welland, J. Appl. Phys. 77 (1995) 653. [17] B.D. Yu, Y. Miyamoto, O. Sugino, Appl. Phys. Lett. 72 (1998) 1176. [18] H. Jeon, C.A. Sukow, J.W. Honeycutt, G.A. Rozgonyi, R.J. Nemanich, J. Appl. Phys. 71 (1992) 4269. [19] R. Rosenkranz, G. Frommeyer, Z. Metallkd. 83 (1992) 685. [20] G. Kresse, J. Futhmuller, Phys. Rev. B 54 (1996) 11169. [21] Joint Committee on Powder Diffraction Standards, File 10–255. [22] R. Beyers, R. Sinclair, J. Appl. Phys. 57 (1985) 5240. [23] W. Voigt, Lehrbuch der Kristallphysik, Taubner, Leipzig, 1928.