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Ab initio study of aluminum chemical vapor deposition from dimethylaluminum hydride: a gas phase reaction mechanism
Journal of Molecular Structure (Theochem) 490 (1999) 155–166 www.elsevier.nl/locate/theochem
Ab initio study of aluminum chemical vapor deposition from dimethylaluminum hydride: a gas phase reaction mechanism T. Nakajima, K. Yamashita* Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan Received 7 December 1998; accepted 4 March 1999
Abstract The effect of preheating of dimethylaluminum hydride (DMAH) as a gas on the epitaxial growth in aluminum chemical vapor deposition (Al-CVD) is studied theoretically. The chemical changes of DMAH in the gas phase such as unimolecular decomposition reactions, bimolecular reactions and polymerizations are treated using ab initio molecular orbital method (MP2/631G**) and density functional theory (B3P86/LanL2DZ). The gas phase equilibrium composed of the previous reaction products under the usual experimental conditions for Al-CVD is also investigated in detail as the initial stage of the CVD process. From the energetics point of view, unimolecular decomposition reactions and bimolecular reactions hardly occur, however, polymerizations of DMAH take place readily at the low temperatures found in Al-CVD. A large amount of DMAHdimer and a small amount of DMAH-monomer and trimer coexist in the equilibrium state. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Dimethylaluminum hydride; Large scale integrated; Chemical vapor deposition
1. Introduction At present, aluminum metals are widely used as electrical wiring materials in large scale integrated (LSI) circuits. The physical vapor deposition (PVD) method, i.e. sputtering, is one of the main techniques for depositing these aluminum metallic films on surfaces of silicon or silicon dioxide. As the integration density of integrated circuits increases, however, unsatisfactory step coverage in the PVD method becomes a problem because of the difficulty in forming exceedingly fine wires in LSI circuits. On the other hand, chemical vapor deposition (CVD)
* Corresponding author. Tel./fax: 1 81-3818-5012. E-mail address: [email protected] (K. Yamashita)
methods have attracted a great deal of attention as novel techniques offering advantages in conformal step coverage and selective deposition for substrate surfaces which are required to develop very large scale integrated (VLSI) circuits. From the experimental point of view, epitaxial growth of aluminum films in the CVD technique (Al-CVD) has been extensively studied [1] using organoaluminum compound gases, such as dimethylaluminum hydride (DMAH), tri-isobutyl aluminum (TIBA), trimethylaluminum (TMA), etc. The temperature dependence of epitaxial growth of aluminum on a silicon surface was investigated by a gas-temperature-controlled CVD (GTC-CVD) method using TIBA gas [2,3]. It was found that the preheating of organoaluminum gas had much influence on the epitaxial growth. This
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00096-2
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Fig. 1. Dissociation scheme for DMAH molecule in gas phase.
suggested that the rate-determining step may not be a surface reaction such as adsorption or desorption, which is considered to be the rate-determining step in the epitaxial growth of silicon using monosilane, but rather a gas phase reaction in Al-CVD when using TIBA. DMAH has also been used by several authors [4–6] as a source gas for experimental studies of Al-CVD, which focused on selective deposition. However, these experimental studies have not yet clarified whether or not the chemical behavior of DMAH in the gas phase (e.g. unimolecular decomposition reactions, bimolecular reactions and polymerizations) as well as the surface reactions of DMAH affects the epitaxial growth in Al-CVD [7,8]. Recent developments in computers and quantum mechanical methods [9] allow accurate calculations for isolated molecules in the gas phase and largescale calculations to be carried out on systems consisting of small admolecules and a cluster representing a substrate surface [10,11]. From the viewpoint of electronic states and energetics, there are many theoretical studies on these systems which have detailed the mechanisms of chemical reactions in the gas phase, physical/chemical adsorption, desorption, and chemical reactions on the surface [12–15]. However, as the CVD of metal films should be considered as a complicated interfacial process between gas phase and surface, it is still challenging to clarify the mechanism
of epitaxial growth in CVD by using ab initio theoretical approaches. In the present paper, we predict theoretically the effect of preheating of gas on the epitaxial growth in Al-CVD prior to theoretical investigations of chemical reactions on the surface. Using DMAH as a source gas and assuming that a carrier gas is not reactive in the gas phase, we study the chemical changes of DMAH in the gas phase, such as unimolecular decomposition reactions, bimolecular reactions and polymerizations by quantum chemical methods. Reaction schemes and computational results are presented in Section 2. The calculation methods to obtain potential energies, equilibrium constants and reaction rates are also summarized. We then discuss the effect of preheating on the deposition of aluminum films using DMAH on the basis of the computational results with respect to the equilibrium-state in the gas phase. Concluding remarks are described in Section 3.
2. Reaction schemes and ab initio calculations In the present work, we considered the following possible chemical reactions in the gas phase: (i) unimolecular decomposition reactions; (ii) bimolecular reactions; and (iii) polymerizations of dimethylaluminum hydride (DMAH). Ab initio molecular orbital (MO) method and density functional theory (DFT) were employed. The basis sets adopted here were
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Table 1 Dissociation energy (kcal/mol) of DMAH using 6-31G**. (Zero point energy is included)
(CH3)AlH 1 CH3 (CH3)2Al 1 H AlH 1 2 (CH3) (CH3)Al 1 H 1 CH3 Al 1 2 (CH3) 1 H
HF
MP2
B3LYP
B3P86
B3PW91
G-2
54.51 64.86 86.18 95.08 136.11
77.56 76.53 122.68 119.42 184.56
76.42 82.88 118.39 123.07 188.29
78.85 83.85 125.57 128.62 196.63
76.32 80.41 121.64 123.75 189.36
82.75 85.63 125.13 126.50 197.47
the valence double-zeta basis set, the valence triplezeta basis set and the LanL2DZ [16–18] basis set, in which the Los Alamos effective core potential plus the double-zeta basis for the aluminum atom and Dunning/Huzinaga full double zeta basis set for the carbon and hydrogen atoms were used. These basis sets were augmented with polarization functions. The scaling factor was used only for the vibrational frequencies of the polymers of DMAH to allow comparison with the experimental ones. On the basis of thermodynamics, reaction rates of bimolecular reactions and equilibrium constants (degrees of dissociation) between monomer and polymers of DMAH were estimated from the Gibbs free energy obtained by normal mode analyses. 2.1. Unimolecular decomposition reactions of DMAH A dissociation scheme of DMAH in the gas phase is presented in Fig. 1. To examine the accuracy of our calculations, we used the following five methods to estimate dissociation energies of DMAH: (1) Hartree–Fock (HF) method; (2) second-order Moeller–Plesset perturbation theory (MP2); (3) Becke’s three parameter hybrid method using the LYP correlation functional (B3LYP) [19–21]; (4) Becke’s three-parameter hybrid method with Perdew86 (B3P86) [19,22]; and (5) three-parameter hybrid
method with Perdew/Wang91 (B3PW91). [19,23] The results from these five methods were compared with those by the Gaussian-2 (G-2) method, [24,25] which is known to give satisfactory precision. We used the 6-31G** and 6-311G** basis sets in the calculations of unimolecular decomposition reactions. The calculated results are shown in Tables 1 and 2. As we have obtained practically the same dissociation energies with respect to the 6-31G** and 6-311G** basis sets for the five different methods, we adopted the valence double-zeta class basis set with polarization functions in the following calculations. Compared with the results by the G-2 method, the HF method considerably underestimates the potential energies. In particular, there is a strong tendency to underestimate the dissociation energy of the methyl group. When we take the correlation energy into account, the results by the MP2 method and the DFT methods are in good agreement with those by the G-2 method, being within a few kcal/mol. In the results by the MP2 method, however, the dissociation energy of DMAH to (CH3)AlH and CH3 is larger than that to (CH3)2Al and H because of the underestimation of the latter. As shown in Tables 1 and 2, the B3P86 method is considered to be the best one for the present system from the energetical point of view. Thus, we chose the B3P86 method as representative of the DFT
Table 2 Dissociation energy (kcal/mol) of DMAH using 6-311G** (Zero point energy is included)
(CH3)AlH 1 CH3 (CH3)2Al 1 H AlH 1 2 (CH3) (CH3)Al 1 H 1 CH3 Al 1 2 (CH3) 1 H
HF
MP2
B3LYP
B3P86
B3PW91
G-2
54.08 64.30 85.59 94.57 135.48
79.40 77.61 125.91 121.90 189.53
76.16 82.49 117.68 122.18 187.58
78.65 83.35 125.04 127.81 195.99
76.14 79.87 121.11 122.94 188.62
82.75 85.63 125.13 126.50 197.47
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Table 3 Energies of transition states and products in bimolecular reactions with respect to those of reactant (kcal/mol) (Zero point energy is included) TS
Reaction (1) Reaction (2) Reaction (3)
concluded that the thermal dissociation of DMAH is not the main process initially for the gas phase of DMAH.
B3P86/6-31G**
B3P86/LanL2DZ** a
2.2. Bimolecular reactions of DMAH
Product
TS
Product
28.1 57.2 22.1
2 0.6 9.3 4.0
29.3 59.9 23.7
We have considered the following three bimolecular reactions:
0.2 13.0 4.7
a
LanL2DZ** represents the basis set which consists of LanL2DZ and polarization d-functions for aluminum and carbon atoms and p-functions for hydrogen atoms.
methods and use it in the following calculations of bimolecular reactions and polymerizations of DMAH. As shown in Table 1, DMAH is a comparatively stable molecule, therefore, dissociations of the hydrogen atom and the methyl group from DMAH need 78.9 and 83.9 kcal/mol by the B3P86 method, respectively. The dissociation of (CH3)2Al and (CH3)AlH to (CH3)Al and AlH also require about 40 kcal/mol. Since the calculated dissociation energies are too high (more than about 80 kcal/mol by the B3P86 method) for thermal dissociation to occur at the usual process temperature for Al-CVD using DMAH, which is about 2008C (473.15 K), it may be
CH3 2 AlH 1 CH3 2 AlH
1
! CH3 2 Al 2 Al CH3 H 1 CH4 CH3 2 AlH 1 CH3 2 AlH ! CH3 HAl 2 Al CH3 H 1 C2 H6 CH3 2 AlH 1 CH3 2 AlH ! CH3 2 Al 2 Al CH3 2 1 H2
2
3
Potential energies, geometries and normal mode frequencies were calculated using the B3P86 method with respect to the reactants, products, and transition states of the bimolecular reactions. The basis sets employed here were 6-31G** and LanL2DZ supplemented p functions on the hydrogen atoms and d functions on the carbon and aluminum atoms (hereafter,
Fig. 2. Transition states of bimolecular reactions of DMAH in gas phase. (a) 2DMAH ! (CH3)2Al–Al (CH3)H 1 CH4, (b) 2DMAH ! H ˚ ), activation energies (in kcal/mol (CH3)Al–Al (CH3)H 1 C2H6, and (c) 2DMAH ! (CH3)2Al–Al (CH3)2 1 H2. Geometries (bond lengths in A relative to the reactant) and imaginary vibrational frequencies (cm 21) by B3P86/LanL2DZ**.
T. Nakajima, K. Yamashita / Journal of Molecular Structure (Theochem) 490 (1999) 155–166 Table 4 Reaction rates of bimolecular reactions (The rate constants (m 3s 21mol 21) at 1.0 Torr using the B3P86/LanL2DZ** method) 273.15 (K) Reaction (1) Reaction (2) Reaction (3)
222
1.37 × 10 3.49 × 10 248 1.65 × 10 218
473.15 (K) 212
8.89 × 10 2.20 × 10 227 1.10 × 10 29
673.15 (K) 4.06 × 10 27 1.09 × 10 218 7.65 × 10 26
this basis set is denoted as LanL2DZ**). As, in future we intend to study the reaction of DMAH on the aluminum substrate surface using a cluster model to elucidate the mechanism of the epitaxial growth of aluminum films, in the following LanL2DZ** was utilized to assess the quality. We obtained only one imaginary frequency for all the transition states by normal mode analyses. As shown in Table 3, the basis set dependence of the energetics is not so significant in the results by the B3P86 method. The transition state in reaction (2) has the highest activation energy among the three bimolecular reactions mentioned above, 57.2 and 59.9 kcal/mol for 6-31G** and LanL2DZ**, respectively. In contrast the activation energies of reactions (1) and (3) are remarkably low, 29.3 and 28.1 kcal/ mol for reaction (1), and 23.7 and 22.1 kcal/mol for reaction (3). Fig. 2 shows the optimized structures of the transition states, the activation energies with zero point corrections and the imaginary frequencies along the reaction coordinate using B3P86/LanL2DZ**. The most distinctive feature of transition states in reactions (1) and (3) is found in the bond formation
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of two aluminum atoms mediated by the hydrogen atom which was directly bonded to an aluminum atom in the reactant. In other words these bimolecular reactions proceed as follows: (i) the hydrogen atom which is directly bonded to the aluminum atom on one side of the DMAH approaches the aluminum atom on the other side of the DMAH in the course of forming a new bond between these aluminum atoms; (ii) two aluminum atoms directly form a new bond; and (iii) the exclusion of a methane or a hydrogen molecule occurs in reactions (1) or (3). However, the direct formation of a new chemical bond between aluminum atoms without the mediation of the hydrogen atom causes an increase in the activation energy in reaction (2). At a temperature of 2008C (473.15 K) and pressure of 1 Torr, the calculated rate constants are 8.89 × 10 212, 2.20 × 10 227 and 1.10 × 10 29 m 3 s 21 mol 21 for reactions (1)– (3), respectively, as presented in Table 4. As a result of the low reaction rate constants, these bimolecular reactions are also considered to occur scarcely under the usual process conditions of Al-CVD. 2.3. Polymerizations of DMAH From several experimental [26–28] and theoretical [26,28–30] studies, it has been suggested that DMAH molecules form the DMAH-dimer or the DMAHtrimer at process temperatures of Al-CVD (hereafter, DMAH-monomer, -dimer and -trimer are abbreviated to monomer, dimer and trimer, respectively). In the
˚ ) of: (a) DMAH-monomer: (b) -dimer; and (c) -trimer by B3P86/LanL2DZ (with polarization Fig. 3. Optimized geometries (bond lengths in A functions).
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Table 5 Vibrational frequencies (cm 21) of DMAH-monomer, -dimer and -trimer Monomer Unscaled b,c
783[b] 813[b] 839[b]
1337[c]
Dimer Scaled d
738[s] 766[s] 791[s]
1260[m]
Unscaled b,c
Expt. a
Trimer Scaled d
696[b] 769[b] 789[b]
656[m] 725[m] 744[s]
916[a]
863[s]
1315[d] 1339[c]
1234[s] 1263[m]
1519[d] 1533[d]
1432[s] 1446[s]
1960[d]
1848[s]
3031[e]
2857[m]
3035[e]
2861[m]
3109[e] 3139[e]
2930[m] 2959[m]
3121[e] 3130[e] 3132[e]
2942[m] 2951[m] 2953[m]
Unscaled b,c
Scaled d
697[a]
657[m]
786[b] 816[a]
741[s] 770[m]
877[a]
826[s]
960[a] 1090[a] 1337[c] 1343[c]
905[s] 1027[m] 1260[m] 1266[m]
2002[d] 3030[e]
1887[s] 2857[m]
3118[e] 3120[e] 3121[e] 3123[e] 3125[e]
2939[m] 2941[m] 2942[m] 2944[m] 2945[m]
Freq. e
Assign. f
571[w] 692[s] 709[s]
D1T D D1T
792[w] 851[s] 934[w]
T D T
1206[s] – 1353[s] 1424[s] 1460[s]
D1T – D D D
1789[s] 2840[w] 2905[w] 2955[m] – – – –
T D1T D1T D1T – – – –
a
Ref. [26]. Calculated frequencies using the MP2/6-31G† method. c Calculated mode assignment; [a] H–Al–H bending, [b] C–Al–C bending, [c] Al–C stretching, [d] Al–H stretching, [e] C–H stretching. d Scaled values of frequencies using the scale factor 0.9427 for the MP2/6-31G** method. Calculated infrared intensity; [s] strong, [m] medium. e [s] strong, [m] medium, [w] weak. f Intensity of infrared spectrum; D dimer, T trimer. b
present study, equilibrium structures, energies and frequencies of monomer, dimer and trimer were obtained using MP2 and B3P86 methods. Here, the basis sets used were: (1) 6-31G**; and (2) 6-31G supplemented by d functions (exponent 0.325) [31] on the aluminum atoms and p functions (exponent 1.100) [31] only on the hydrogen atoms directly bonding to the aluminum atoms (basis set (2) is denoted by 6-31G† in the following). The optimized geometries of the monomer, dimer and trimer are shown in Fig. 3 along with the characteristic values of bond length. With respect to the structures of the dimer and trimer, the aluminum atoms and the hydrogen atoms, which bond directly to the aluminum atoms, produce 4- and 6-membered
rings, respectively. In the dimer molecule, the ˚, distance between two aluminum atoms is 2.627 A which is almost the same as that of the products of ˚ ). However, the the bimolecular reactions (2.616 A bond length between the aluminum and the hydrogen ˚ , becomes considerably large atoms, 1.740 A ˚ ). These compared to that of the monomer (1.590 A bond lengths agree closely with those suggested by Hiraoka and Mashita [30] calculated using the HF/6˚ for the former and 1.757 A ˚ for the 31G** (2.656 A latter). In the trimer molecule, the distance between ˚ , is remarkably larger two aluminum atoms, 3.199 A than that of the dimer. However, the distance between the aluminum and the hydrogen atoms is smaller than that of the dimer. The cyclic part of the trimer is also
T. Nakajima, K. Yamashita / Journal of Molecular Structure (Theochem) 490 (1999) 155–166 Table 6 Stabilization energies (kcal/mol) of DMAH-dimer and -trimer (Zero point energy is included)
2M ! D c 3M ! T c
MP2/6-31G†a
B3P86/6-31G† a
B3P86/6-31G** b
32.15 55.81
31.22 52.47
31.40 52.76
a d-functions for the aluminum atoms and p-functions only for the hydrogen atoms, which directly bond to the aluminum atoms, are augmented as polarization functions in the present basis set. b The standard 6-31G** basis set including all d-functions for aluminum and carbon atoms and all p-functions for hydrogen atoms. c M, D and T represent DMAH-monomer, -dimer and -trimer, respectively.
due to the bonding between the aluminum atoms and the hydrogen atoms. No other striking geometric changes are found in other parts of the dimer and trimer. In Table 5, calculated vibrational frequencies and infrared intensities of the monomer, dimer and trimer are shown along with the experimental data [26] and assignments for dimer and trimer. These values were calculated by using the MP2/6-31G† method and the optimal scaling factor 0.9427 recommended to correct calculated frequencies by the MP2/6-31G** method [32]. Although calculated frequencies are evidently overestimated, the scaled values agree fairly well with the experimental ones [26] except at 1353 and 2905 cm 21. Calculated stabilization energies are given in Table 6. There are no significant differences among the results using the three listed calculation methods.
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The estimated stabilization energies are 31–32 kcal/ mol for dimerization and 52–56 kcal/mol for trimerization. In particular, the stabilization energy of dimerization is in good accordance with that estimated by Hiraoka and Mashita [30] by using MP2/ 6-31G** and HF/6-31G**. From these results, the polymerizations of DMAH seem to occur easily at low temperatures in the gas phase because of large stabilization energy. In Fig. 4, the bonding molecular orbitals in the dimer are schematically represented to elucidate this large stabilization energy. In these molecular orbitals, two p-type atomic orbitals of aluminum atoms form s- and p -bonding orbitals causing a strong bonding between two aluminum atoms while s -bonding and s -anti-bonding orbitals are formed from two s-type atomic orbitals of hydrogen atoms. To investigate the temperature and pressure dependence of the existence ratios of monomer and polymers, we also estimated equilibrium constants and degrees of dissociation. The total energies and the molecular data to calculate the enthalpies, entropies and free energies were obtained by using MP2/631G†. Calculated thermal energies, thermal enthalpies, entropies and thermal free energies for each temperature at a standard pressure (1.0 Torr) are listed in Table 7. Using these values, we carried out the equilibrium constants and degrees of dissociation for the two-component systems between monomers, dimers and trimers. Plots of equilibrium constants for these two-component systems are represented in Fig. 5. The most notable feature is the rapid increase
Fig. 4. Schematic bonding molecular orbitals of DMAH-dimer. Showing only the cyclic part (Al–H–Al–H).
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Table 7 Thermal energies (E), Thermal enthalpies (H), Entropies (S) and Thermal free energies (F.E.) of DMAH-monomer, -dimer and -trimer using MP2/6-31G† at 1.0 Torr as a standard pressure. (d-functions for the aluminum atoms and p-functions only for the hydrogen atoms, which directly bond to the aluminum atoms, are augmented as polarization functions in the present basis set) Species of DMAH
Temperature (K)
E a (a.u.)
Monomer
273.15 298.15 373.15 473.15 573.15 673.15 273.15 298.15 373.15 473.15 573.15 673.15 273.15 298.15 373.15 473.15 573.15 673.15
2 321.856987 2 321.856218 2 321.853660 2 321.849717 2 321.845245 2 321.840316 2 643.765427 2 643.763811 2 643.758426 2 643.750075 2 643.740547 2 643.730011 2 965.659298 2 965.656712 2 965.648131 2 965.634947 2 965.620043 2 965.603677
Dimer
Trimer
H a (a.u.) 2 321.856122 2 321.855274 2 321.852479 2 321.848219 2 321.843430 2 321.838184 2 643.764562 2 643.762867 2 643.757244 2 643.748576 2 643.738731 2 643.727880 2 965.658433 2 965.655768 2 965.646950 2 965.633448 2 965.618228 2 965.601545
S (cal/mol K)
F.E. a (a.u.)
90.33 92.19 97.43 103.76 109.51 114.80 120.41 124.14 134.66 147.54 159.37 170.30 156.95 162.80 179.32 199.38 217.66 234.48
2 321.895441 2 321.899077 2 321.910413 2 321.926452 2 321.943452 2 321.961330 2 643.816976 2 643.821848 2 643.837323 2 643.859824 2 643.884291 2 643.910570 2 965.726750 2 965.733121 2 965.753580 2 965.783780 2 965.817031 2 965.853075
a In these energies (thermal energies, thermal enthalpies and thermal free energies), the electronic energies (2321.941817, 2643.940745 and 2965.923085 a.u. for monomer, dimer and trimer, respectively) and zero-point energies (49.71, 103.10 and 154.60 kcal/mol for monomer, dimer and trimer, respectively) are also included.
of monomer as the temperature rises. The temperature and pressure dependence of degrees of dissociation for these two-component systems is represented in Fig. 6. At room temperature, hardly any monomer can exist in the gas phase and the equilibrium is realized between the dimer and the trimer. However, the rise of temperature results in a decrease of the amount of trimer and a shift of the equilibrium between the monomer and the dimer. Finally, almost all molecules dissociate to monomers at high temperatures. Based on these equilibrium constants and degrees of dissociation for the two-component systems, the mole fractions among the monomer, dimer and trimer was calculated for each partial pressure of DMAH 0.01, 0.1, 1.0 and 10.0 Torr using the relations between the partial pressures of DMAH and a total pressure (The total pressure of a carrier gas and DMAH is 10.0 Torr.) The results are shown in Fig. 7. When the partial pressures of DMAH are 0.1, 1.0 and 10.0 Torr at 2008C (473.15 K), the main component of gas is a dimer as shown in Fig. 7 (b)– (d), respectively. Nevertheless, the existence ratios of the monomer are still about 26, 8 and 3% of all molecules
at pressures, 0.1, 1.0 and 10.0 Torr at 2008C (473.15 K), respectively. At low partial pressures, the monomer appears to predominate at low temperatures as shown in Fig. 7 (a). Our results show that the existence ratios of the monomer are quite low as compared with those found by Willis and Jensen [28] they indicated that the main ingredient is the monomer when the DMAH pressure is 2.0 Torr at 2008C (473.15 K) and all DMAH molecules are monomers at the partial pressure of 1 × 10 23 Torr at 2008C. These discrepancies are considered to be attributed to the calculation methods and the basis sets adopted in their work. Though Al-CVD using DMAH as a gas is usually done near 2008C (473.15 K), this discrepancy is expected to affect the reaction rate, i.e. the growth rate of Al film assuming that monomer is the most reactive species as suggested by Willis and Jensen [28]. However, the temperature and pressure dependence of existence ratios are in good agreement between both results. The mole fractions also show an increase of the existence ratio of trimer when the temperature is near 1508C, as shown in Fig. 7 (c). This is because of the rapid
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163
Fig. 5. Calculated equilibrium constants (dimensionless) with respect to temperature: (a) between monomer and dimer; (b) between monomer and trimer; and (c) between dimer and trimer.
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Fig. 6. Calculated degrees of dissociation (a e) with respect to temperature and pressure: (a) between monomer and dimer; (b) between monomer and trimer; and (c) between dimer and trimer.
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Fig. 7. Calculated mole fractions between DMAH-monomer, -dimer, and -trimer at the following pressures (Torr) of DMAH: (a) 0.01; (b) 0.1; (c) 1.0; and (d) 10.0.
change of equilibrium constants between monomer and trimer with respect to the pressure. Although dimer amounts decrease and monomer amounts increase in the range from 100 to 2008C, monomers consequently form trimer owing to the equilibrium between the monomer and the trimer at high pressures.
3. Conclusions To understand the epitaxial growth in CVD, we should take account of the various physical and chemical processes such as reactions of source materials in gas phase, physical/chemical adsorptions, diffusions and reactions on substrate surface, desorptions of reactants and products, etc. In particular, the situation of source
materials in the gas phase should be well known since this is the initial step in CVD. However, the chemical changes of DMAH molecules in the gas phase are not clear in the case of Al-CVD using DMAH, as well as other organoaluminum source gases. In the present study, three kinds of gas phase chemical reactions were considered using ab initio molecular orbital method and density functional theory. From the results of our calculations, we concluded that hardly any dissociation and bimolecular reactions of DMAH occurred at the low temperatures found in Al-CVD. Even abstraction of methyl radical from DMAH molecule, the easiest process among the dissociation processes, needed almost 80 kcal/mol. Bimolecular reaction (2) had a high activation barrier of about 60 kcal/mol. However, the
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activation barriers of bimolecular reactions (1) and (3) were low (25–30 kcal/mol) so that these reactions may contribute to the CVD process in the gas phase at high temperatures. The stabilization energies were calculated as 31–32 and 52–56 kcal/mol in dimerization and trimerization reactions, respectively. Regarding the equilibrium between the monomer, the dimer and the trimer of DMAH, the monomer was the dominant molecule above 4008C (673.15 K) and the DMAH molecules formed mostly dimer and trimer below 08C (273.15 K) and in the range of 0.01– 10.0 Torr. However, the equilibrium composition changed remarkably with respect to the temperature and pressure, especially between 08C (273.15 K) and 4008C (673.15 K) at the same range of pressures. Above 2008C (473.15 K), the trimer disappeared and the equilibrium between the monomer and the dimer was realized at low pressures. In this equilibrium condition, the monomer amounts decreased and the dimer amounts increased with the increasing pressure of DMAH. Although it has been pointed out that the equilibrium between the dimer and the trimer is realized over the temperature range of 85–1678C and all the DMAH molecules become dimers at 1708C [26,33,34] our results showed that it was a mixture including a small amount of monomer and trimer, and a large amount of dimer under the same condition. However, the dimer is considered to be a stable molecule and it possesses low reactivity. We therefore expect that the information about the reactions of monomer with the substrate surface (e.g. adsorptions, reactions and desorptions on the surface) are essential to elucidate the mechanism of the epitaxial growth in Al-CVD using DMAH [35]. Ab initio calculations of reactions on the aluminum surface will be undertaken in subsequent papers. Acknowledgements This work was partially supported by the Semiconductor Technology Academic Research Center (STARC). We are grateful to Profs. H. Komiyama, Y. Shimogaki and Y. Egashira for their valuable comments and discussions. We also thank Drs T. Yoshimi, H. Ito, J. Aoyama and J. Ueda for their useful discussions. References [1] M. Hanabusa, A. Komatsu, Appl. Phys. Lett. 65 (1994) 1826 and references cited therein.
[2] T. Kobayashi, A. Sekiguchi, N. Hosokawa, T. Asamaki, Jpn. J. Appl. Phys. 27 (1988) L1775. [3] A. Sekiguchi, T. Kobayashi, N. Hosokawa, T. Asamaki, Extended Abstracts of the 21st Conference on Solid State Devices and Materials, Tokyo, 1989, p. 29. [4] N. Zhu, T. Cacouris, R. Scarmozzino, R.M. Osgood Jr, J. Vac. Sci. Technol. B 10 (1992) 1167. [5] N. Takeyasu, Y. Kawano, E. Kondoh, T. Katagiri, H. Yamamoto, H. Shinriki, T. Ohta, Jpn. J. Appl. Phys. 33 (1994) 424. [6] M. Hanabusa, A. Oikawa, P.Y. Cai, J. Appl. Phys. 66 (1989) 3268. [7] K. Masu, M. Yokoyama, H. Matsuhashi, K. Tsubouchi, Appl. Surf. Sci. 79/80 (1994) 237. [8] K. Tsubouchi, K. Masu, J. Vac. Sci. Technol. A 10 (1992) 856. [9] W. Kohn, A.D. Becke, R.G. Parr, J. Phys. Chem. 100 (1996) 12974. [10] J.L. Whitten, Chem. Phys. 177 (1993) 387. [11] Z. Jing, J.L. Whitten, Phys. Rev. B 48 (1993) 17 296. [12] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 98 (1993) 8810. [13] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 101 (1994) 11 012. [14] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 103 (1995) 6562. [15] G. Valerio, H. Toulhoat, J. Phys. Chem. A 101 (1997) 1969. [16] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 270. [17] W.R. Wadt, P.J. Hay, J. Chem. Phys. 82 (1985) 284. [18] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 299. [19] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [20] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [21] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 157 (1989) 200. [22] J.P. Perdew, Phys. Rev. B 33 (1986) 8822. [23] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13 244. [24] J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari, L.A. Curtiss, J. Chem. Phys. 90 (1989) 5622. [25] L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94 (1991) 7221. [26] A.S. Grady, S.G. Puntambekar, D.K. Russell, Spectrochim Acta, A 47 (1991) 47. [27] E. Kondoh, T.J. Ohta, Vac. Sci. Technol. A 13 (1995) 2863. [28] B.G. Willis, K.F. Jensen, Conference Proceedings ULSI XII, p. (1997) 29. [29] M. Pelissier, J.P. Malrieu, Theoret. Chim. Acta 56 (1980) 175. [30] Y.S. Hiraoka, M.J. Mashita, Crystal Growth 145 (1994) 473. [31] P.C. Hariharan, J.A. Pople, Theoret. Chim. Acta 28 (1973) 213. [32] J.A. Pople, A.P. Scott, M.W. Wong, L. Radom, Israel J. Chem. 33 (1993) 345. [33] T. Wartik, H.I. Schlesinger, J. Am. Chem. Soc. 75 (1953) 835. [34] A. Almenningen, G.A. Anderson, F.R. Forgaard, A. Haaland, Acta Chem Scand. 26 (1972) 2315. [35] T. Takahashi, Y. Shimogaki, T. Yoshimi, H. Ito, J. Aoyama, J. Ueda, H. Komiyama, Proceedings of the 14th International VLSI Multilevel Interconnection Conference (VMIC), 1997, p. 369.
Ab initio study of aluminum chemical vapor deposition from dimethylaluminum hydride: a gas phase reaction mechanism T. Nakajima, K. Yamashita* Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan Received 7 December 1998; accepted 4 March 1999
Abstract The effect of preheating of dimethylaluminum hydride (DMAH) as a gas on the epitaxial growth in aluminum chemical vapor deposition (Al-CVD) is studied theoretically. The chemical changes of DMAH in the gas phase such as unimolecular decomposition reactions, bimolecular reactions and polymerizations are treated using ab initio molecular orbital method (MP2/631G**) and density functional theory (B3P86/LanL2DZ). The gas phase equilibrium composed of the previous reaction products under the usual experimental conditions for Al-CVD is also investigated in detail as the initial stage of the CVD process. From the energetics point of view, unimolecular decomposition reactions and bimolecular reactions hardly occur, however, polymerizations of DMAH take place readily at the low temperatures found in Al-CVD. A large amount of DMAHdimer and a small amount of DMAH-monomer and trimer coexist in the equilibrium state. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Dimethylaluminum hydride; Large scale integrated; Chemical vapor deposition
1. Introduction At present, aluminum metals are widely used as electrical wiring materials in large scale integrated (LSI) circuits. The physical vapor deposition (PVD) method, i.e. sputtering, is one of the main techniques for depositing these aluminum metallic films on surfaces of silicon or silicon dioxide. As the integration density of integrated circuits increases, however, unsatisfactory step coverage in the PVD method becomes a problem because of the difficulty in forming exceedingly fine wires in LSI circuits. On the other hand, chemical vapor deposition (CVD)
* Corresponding author. Tel./fax: 1 81-3818-5012. E-mail address: [email protected] (K. Yamashita)
methods have attracted a great deal of attention as novel techniques offering advantages in conformal step coverage and selective deposition for substrate surfaces which are required to develop very large scale integrated (VLSI) circuits. From the experimental point of view, epitaxial growth of aluminum films in the CVD technique (Al-CVD) has been extensively studied [1] using organoaluminum compound gases, such as dimethylaluminum hydride (DMAH), tri-isobutyl aluminum (TIBA), trimethylaluminum (TMA), etc. The temperature dependence of epitaxial growth of aluminum on a silicon surface was investigated by a gas-temperature-controlled CVD (GTC-CVD) method using TIBA gas [2,3]. It was found that the preheating of organoaluminum gas had much influence on the epitaxial growth. This
0166-1280/99/$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(99)00096-2
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Fig. 1. Dissociation scheme for DMAH molecule in gas phase.
suggested that the rate-determining step may not be a surface reaction such as adsorption or desorption, which is considered to be the rate-determining step in the epitaxial growth of silicon using monosilane, but rather a gas phase reaction in Al-CVD when using TIBA. DMAH has also been used by several authors [4–6] as a source gas for experimental studies of Al-CVD, which focused on selective deposition. However, these experimental studies have not yet clarified whether or not the chemical behavior of DMAH in the gas phase (e.g. unimolecular decomposition reactions, bimolecular reactions and polymerizations) as well as the surface reactions of DMAH affects the epitaxial growth in Al-CVD [7,8]. Recent developments in computers and quantum mechanical methods [9] allow accurate calculations for isolated molecules in the gas phase and largescale calculations to be carried out on systems consisting of small admolecules and a cluster representing a substrate surface [10,11]. From the viewpoint of electronic states and energetics, there are many theoretical studies on these systems which have detailed the mechanisms of chemical reactions in the gas phase, physical/chemical adsorption, desorption, and chemical reactions on the surface [12–15]. However, as the CVD of metal films should be considered as a complicated interfacial process between gas phase and surface, it is still challenging to clarify the mechanism
of epitaxial growth in CVD by using ab initio theoretical approaches. In the present paper, we predict theoretically the effect of preheating of gas on the epitaxial growth in Al-CVD prior to theoretical investigations of chemical reactions on the surface. Using DMAH as a source gas and assuming that a carrier gas is not reactive in the gas phase, we study the chemical changes of DMAH in the gas phase, such as unimolecular decomposition reactions, bimolecular reactions and polymerizations by quantum chemical methods. Reaction schemes and computational results are presented in Section 2. The calculation methods to obtain potential energies, equilibrium constants and reaction rates are also summarized. We then discuss the effect of preheating on the deposition of aluminum films using DMAH on the basis of the computational results with respect to the equilibrium-state in the gas phase. Concluding remarks are described in Section 3.
2. Reaction schemes and ab initio calculations In the present work, we considered the following possible chemical reactions in the gas phase: (i) unimolecular decomposition reactions; (ii) bimolecular reactions; and (iii) polymerizations of dimethylaluminum hydride (DMAH). Ab initio molecular orbital (MO) method and density functional theory (DFT) were employed. The basis sets adopted here were
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Table 1 Dissociation energy (kcal/mol) of DMAH using 6-31G**. (Zero point energy is included)
(CH3)AlH 1 CH3 (CH3)2Al 1 H AlH 1 2 (CH3) (CH3)Al 1 H 1 CH3 Al 1 2 (CH3) 1 H
HF
MP2
B3LYP
B3P86
B3PW91
G-2
54.51 64.86 86.18 95.08 136.11
77.56 76.53 122.68 119.42 184.56
76.42 82.88 118.39 123.07 188.29
78.85 83.85 125.57 128.62 196.63
76.32 80.41 121.64 123.75 189.36
82.75 85.63 125.13 126.50 197.47
the valence double-zeta basis set, the valence triplezeta basis set and the LanL2DZ [16–18] basis set, in which the Los Alamos effective core potential plus the double-zeta basis for the aluminum atom and Dunning/Huzinaga full double zeta basis set for the carbon and hydrogen atoms were used. These basis sets were augmented with polarization functions. The scaling factor was used only for the vibrational frequencies of the polymers of DMAH to allow comparison with the experimental ones. On the basis of thermodynamics, reaction rates of bimolecular reactions and equilibrium constants (degrees of dissociation) between monomer and polymers of DMAH were estimated from the Gibbs free energy obtained by normal mode analyses. 2.1. Unimolecular decomposition reactions of DMAH A dissociation scheme of DMAH in the gas phase is presented in Fig. 1. To examine the accuracy of our calculations, we used the following five methods to estimate dissociation energies of DMAH: (1) Hartree–Fock (HF) method; (2) second-order Moeller–Plesset perturbation theory (MP2); (3) Becke’s three parameter hybrid method using the LYP correlation functional (B3LYP) [19–21]; (4) Becke’s three-parameter hybrid method with Perdew86 (B3P86) [19,22]; and (5) three-parameter hybrid
method with Perdew/Wang91 (B3PW91). [19,23] The results from these five methods were compared with those by the Gaussian-2 (G-2) method, [24,25] which is known to give satisfactory precision. We used the 6-31G** and 6-311G** basis sets in the calculations of unimolecular decomposition reactions. The calculated results are shown in Tables 1 and 2. As we have obtained practically the same dissociation energies with respect to the 6-31G** and 6-311G** basis sets for the five different methods, we adopted the valence double-zeta class basis set with polarization functions in the following calculations. Compared with the results by the G-2 method, the HF method considerably underestimates the potential energies. In particular, there is a strong tendency to underestimate the dissociation energy of the methyl group. When we take the correlation energy into account, the results by the MP2 method and the DFT methods are in good agreement with those by the G-2 method, being within a few kcal/mol. In the results by the MP2 method, however, the dissociation energy of DMAH to (CH3)AlH and CH3 is larger than that to (CH3)2Al and H because of the underestimation of the latter. As shown in Tables 1 and 2, the B3P86 method is considered to be the best one for the present system from the energetical point of view. Thus, we chose the B3P86 method as representative of the DFT
Table 2 Dissociation energy (kcal/mol) of DMAH using 6-311G** (Zero point energy is included)
(CH3)AlH 1 CH3 (CH3)2Al 1 H AlH 1 2 (CH3) (CH3)Al 1 H 1 CH3 Al 1 2 (CH3) 1 H
HF
MP2
B3LYP
B3P86
B3PW91
G-2
54.08 64.30 85.59 94.57 135.48
79.40 77.61 125.91 121.90 189.53
76.16 82.49 117.68 122.18 187.58
78.65 83.35 125.04 127.81 195.99
76.14 79.87 121.11 122.94 188.62
82.75 85.63 125.13 126.50 197.47
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Table 3 Energies of transition states and products in bimolecular reactions with respect to those of reactant (kcal/mol) (Zero point energy is included) TS
Reaction (1) Reaction (2) Reaction (3)
concluded that the thermal dissociation of DMAH is not the main process initially for the gas phase of DMAH.
B3P86/6-31G**
B3P86/LanL2DZ** a
2.2. Bimolecular reactions of DMAH
Product
TS
Product
28.1 57.2 22.1
2 0.6 9.3 4.0
29.3 59.9 23.7
We have considered the following three bimolecular reactions:
0.2 13.0 4.7
a
LanL2DZ** represents the basis set which consists of LanL2DZ and polarization d-functions for aluminum and carbon atoms and p-functions for hydrogen atoms.
methods and use it in the following calculations of bimolecular reactions and polymerizations of DMAH. As shown in Table 1, DMAH is a comparatively stable molecule, therefore, dissociations of the hydrogen atom and the methyl group from DMAH need 78.9 and 83.9 kcal/mol by the B3P86 method, respectively. The dissociation of (CH3)2Al and (CH3)AlH to (CH3)Al and AlH also require about 40 kcal/mol. Since the calculated dissociation energies are too high (more than about 80 kcal/mol by the B3P86 method) for thermal dissociation to occur at the usual process temperature for Al-CVD using DMAH, which is about 2008C (473.15 K), it may be
CH3 2 AlH 1 CH3 2 AlH
1
! CH3 2 Al 2 Al CH3 H 1 CH4 CH3 2 AlH 1 CH3 2 AlH ! CH3 HAl 2 Al CH3 H 1 C2 H6 CH3 2 AlH 1 CH3 2 AlH ! CH3 2 Al 2 Al CH3 2 1 H2
2
3
Potential energies, geometries and normal mode frequencies were calculated using the B3P86 method with respect to the reactants, products, and transition states of the bimolecular reactions. The basis sets employed here were 6-31G** and LanL2DZ supplemented p functions on the hydrogen atoms and d functions on the carbon and aluminum atoms (hereafter,
Fig. 2. Transition states of bimolecular reactions of DMAH in gas phase. (a) 2DMAH ! (CH3)2Al–Al (CH3)H 1 CH4, (b) 2DMAH ! H ˚ ), activation energies (in kcal/mol (CH3)Al–Al (CH3)H 1 C2H6, and (c) 2DMAH ! (CH3)2Al–Al (CH3)2 1 H2. Geometries (bond lengths in A relative to the reactant) and imaginary vibrational frequencies (cm 21) by B3P86/LanL2DZ**.
T. Nakajima, K. Yamashita / Journal of Molecular Structure (Theochem) 490 (1999) 155–166 Table 4 Reaction rates of bimolecular reactions (The rate constants (m 3s 21mol 21) at 1.0 Torr using the B3P86/LanL2DZ** method) 273.15 (K) Reaction (1) Reaction (2) Reaction (3)
222
1.37 × 10 3.49 × 10 248 1.65 × 10 218
473.15 (K) 212
8.89 × 10 2.20 × 10 227 1.10 × 10 29
673.15 (K) 4.06 × 10 27 1.09 × 10 218 7.65 × 10 26
this basis set is denoted as LanL2DZ**). As, in future we intend to study the reaction of DMAH on the aluminum substrate surface using a cluster model to elucidate the mechanism of the epitaxial growth of aluminum films, in the following LanL2DZ** was utilized to assess the quality. We obtained only one imaginary frequency for all the transition states by normal mode analyses. As shown in Table 3, the basis set dependence of the energetics is not so significant in the results by the B3P86 method. The transition state in reaction (2) has the highest activation energy among the three bimolecular reactions mentioned above, 57.2 and 59.9 kcal/mol for 6-31G** and LanL2DZ**, respectively. In contrast the activation energies of reactions (1) and (3) are remarkably low, 29.3 and 28.1 kcal/ mol for reaction (1), and 23.7 and 22.1 kcal/mol for reaction (3). Fig. 2 shows the optimized structures of the transition states, the activation energies with zero point corrections and the imaginary frequencies along the reaction coordinate using B3P86/LanL2DZ**. The most distinctive feature of transition states in reactions (1) and (3) is found in the bond formation
159
of two aluminum atoms mediated by the hydrogen atom which was directly bonded to an aluminum atom in the reactant. In other words these bimolecular reactions proceed as follows: (i) the hydrogen atom which is directly bonded to the aluminum atom on one side of the DMAH approaches the aluminum atom on the other side of the DMAH in the course of forming a new bond between these aluminum atoms; (ii) two aluminum atoms directly form a new bond; and (iii) the exclusion of a methane or a hydrogen molecule occurs in reactions (1) or (3). However, the direct formation of a new chemical bond between aluminum atoms without the mediation of the hydrogen atom causes an increase in the activation energy in reaction (2). At a temperature of 2008C (473.15 K) and pressure of 1 Torr, the calculated rate constants are 8.89 × 10 212, 2.20 × 10 227 and 1.10 × 10 29 m 3 s 21 mol 21 for reactions (1)– (3), respectively, as presented in Table 4. As a result of the low reaction rate constants, these bimolecular reactions are also considered to occur scarcely under the usual process conditions of Al-CVD. 2.3. Polymerizations of DMAH From several experimental [26–28] and theoretical [26,28–30] studies, it has been suggested that DMAH molecules form the DMAH-dimer or the DMAHtrimer at process temperatures of Al-CVD (hereafter, DMAH-monomer, -dimer and -trimer are abbreviated to monomer, dimer and trimer, respectively). In the
˚ ) of: (a) DMAH-monomer: (b) -dimer; and (c) -trimer by B3P86/LanL2DZ (with polarization Fig. 3. Optimized geometries (bond lengths in A functions).
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Table 5 Vibrational frequencies (cm 21) of DMAH-monomer, -dimer and -trimer Monomer Unscaled b,c
783[b] 813[b] 839[b]
1337[c]
Dimer Scaled d
738[s] 766[s] 791[s]
1260[m]
Unscaled b,c
Expt. a
Trimer Scaled d
696[b] 769[b] 789[b]
656[m] 725[m] 744[s]
916[a]
863[s]
1315[d] 1339[c]
1234[s] 1263[m]
1519[d] 1533[d]
1432[s] 1446[s]
1960[d]
1848[s]
3031[e]
2857[m]
3035[e]
2861[m]
3109[e] 3139[e]
2930[m] 2959[m]
3121[e] 3130[e] 3132[e]
2942[m] 2951[m] 2953[m]
Unscaled b,c
Scaled d
697[a]
657[m]
786[b] 816[a]
741[s] 770[m]
877[a]
826[s]
960[a] 1090[a] 1337[c] 1343[c]
905[s] 1027[m] 1260[m] 1266[m]
2002[d] 3030[e]
1887[s] 2857[m]
3118[e] 3120[e] 3121[e] 3123[e] 3125[e]
2939[m] 2941[m] 2942[m] 2944[m] 2945[m]
Freq. e
Assign. f
571[w] 692[s] 709[s]
D1T D D1T
792[w] 851[s] 934[w]
T D T
1206[s] – 1353[s] 1424[s] 1460[s]
D1T – D D D
1789[s] 2840[w] 2905[w] 2955[m] – – – –
T D1T D1T D1T – – – –
a
Ref. [26]. Calculated frequencies using the MP2/6-31G† method. c Calculated mode assignment; [a] H–Al–H bending, [b] C–Al–C bending, [c] Al–C stretching, [d] Al–H stretching, [e] C–H stretching. d Scaled values of frequencies using the scale factor 0.9427 for the MP2/6-31G** method. Calculated infrared intensity; [s] strong, [m] medium. e [s] strong, [m] medium, [w] weak. f Intensity of infrared spectrum; D dimer, T trimer. b
present study, equilibrium structures, energies and frequencies of monomer, dimer and trimer were obtained using MP2 and B3P86 methods. Here, the basis sets used were: (1) 6-31G**; and (2) 6-31G supplemented by d functions (exponent 0.325) [31] on the aluminum atoms and p functions (exponent 1.100) [31] only on the hydrogen atoms directly bonding to the aluminum atoms (basis set (2) is denoted by 6-31G† in the following). The optimized geometries of the monomer, dimer and trimer are shown in Fig. 3 along with the characteristic values of bond length. With respect to the structures of the dimer and trimer, the aluminum atoms and the hydrogen atoms, which bond directly to the aluminum atoms, produce 4- and 6-membered
rings, respectively. In the dimer molecule, the ˚, distance between two aluminum atoms is 2.627 A which is almost the same as that of the products of ˚ ). However, the the bimolecular reactions (2.616 A bond length between the aluminum and the hydrogen ˚ , becomes considerably large atoms, 1.740 A ˚ ). These compared to that of the monomer (1.590 A bond lengths agree closely with those suggested by Hiraoka and Mashita [30] calculated using the HF/6˚ for the former and 1.757 A ˚ for the 31G** (2.656 A latter). In the trimer molecule, the distance between ˚ , is remarkably larger two aluminum atoms, 3.199 A than that of the dimer. However, the distance between the aluminum and the hydrogen atoms is smaller than that of the dimer. The cyclic part of the trimer is also
T. Nakajima, K. Yamashita / Journal of Molecular Structure (Theochem) 490 (1999) 155–166 Table 6 Stabilization energies (kcal/mol) of DMAH-dimer and -trimer (Zero point energy is included)
2M ! D c 3M ! T c
MP2/6-31G†a
B3P86/6-31G† a
B3P86/6-31G** b
32.15 55.81
31.22 52.47
31.40 52.76
a d-functions for the aluminum atoms and p-functions only for the hydrogen atoms, which directly bond to the aluminum atoms, are augmented as polarization functions in the present basis set. b The standard 6-31G** basis set including all d-functions for aluminum and carbon atoms and all p-functions for hydrogen atoms. c M, D and T represent DMAH-monomer, -dimer and -trimer, respectively.
due to the bonding between the aluminum atoms and the hydrogen atoms. No other striking geometric changes are found in other parts of the dimer and trimer. In Table 5, calculated vibrational frequencies and infrared intensities of the monomer, dimer and trimer are shown along with the experimental data [26] and assignments for dimer and trimer. These values were calculated by using the MP2/6-31G† method and the optimal scaling factor 0.9427 recommended to correct calculated frequencies by the MP2/6-31G** method [32]. Although calculated frequencies are evidently overestimated, the scaled values agree fairly well with the experimental ones [26] except at 1353 and 2905 cm 21. Calculated stabilization energies are given in Table 6. There are no significant differences among the results using the three listed calculation methods.
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The estimated stabilization energies are 31–32 kcal/ mol for dimerization and 52–56 kcal/mol for trimerization. In particular, the stabilization energy of dimerization is in good accordance with that estimated by Hiraoka and Mashita [30] by using MP2/ 6-31G** and HF/6-31G**. From these results, the polymerizations of DMAH seem to occur easily at low temperatures in the gas phase because of large stabilization energy. In Fig. 4, the bonding molecular orbitals in the dimer are schematically represented to elucidate this large stabilization energy. In these molecular orbitals, two p-type atomic orbitals of aluminum atoms form s- and p -bonding orbitals causing a strong bonding between two aluminum atoms while s -bonding and s -anti-bonding orbitals are formed from two s-type atomic orbitals of hydrogen atoms. To investigate the temperature and pressure dependence of the existence ratios of monomer and polymers, we also estimated equilibrium constants and degrees of dissociation. The total energies and the molecular data to calculate the enthalpies, entropies and free energies were obtained by using MP2/631G†. Calculated thermal energies, thermal enthalpies, entropies and thermal free energies for each temperature at a standard pressure (1.0 Torr) are listed in Table 7. Using these values, we carried out the equilibrium constants and degrees of dissociation for the two-component systems between monomers, dimers and trimers. Plots of equilibrium constants for these two-component systems are represented in Fig. 5. The most notable feature is the rapid increase
Fig. 4. Schematic bonding molecular orbitals of DMAH-dimer. Showing only the cyclic part (Al–H–Al–H).
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Table 7 Thermal energies (E), Thermal enthalpies (H), Entropies (S) and Thermal free energies (F.E.) of DMAH-monomer, -dimer and -trimer using MP2/6-31G† at 1.0 Torr as a standard pressure. (d-functions for the aluminum atoms and p-functions only for the hydrogen atoms, which directly bond to the aluminum atoms, are augmented as polarization functions in the present basis set) Species of DMAH
Temperature (K)
E a (a.u.)
Monomer
273.15 298.15 373.15 473.15 573.15 673.15 273.15 298.15 373.15 473.15 573.15 673.15 273.15 298.15 373.15 473.15 573.15 673.15
2 321.856987 2 321.856218 2 321.853660 2 321.849717 2 321.845245 2 321.840316 2 643.765427 2 643.763811 2 643.758426 2 643.750075 2 643.740547 2 643.730011 2 965.659298 2 965.656712 2 965.648131 2 965.634947 2 965.620043 2 965.603677
Dimer
Trimer
H a (a.u.) 2 321.856122 2 321.855274 2 321.852479 2 321.848219 2 321.843430 2 321.838184 2 643.764562 2 643.762867 2 643.757244 2 643.748576 2 643.738731 2 643.727880 2 965.658433 2 965.655768 2 965.646950 2 965.633448 2 965.618228 2 965.601545
S (cal/mol K)
F.E. a (a.u.)
90.33 92.19 97.43 103.76 109.51 114.80 120.41 124.14 134.66 147.54 159.37 170.30 156.95 162.80 179.32 199.38 217.66 234.48
2 321.895441 2 321.899077 2 321.910413 2 321.926452 2 321.943452 2 321.961330 2 643.816976 2 643.821848 2 643.837323 2 643.859824 2 643.884291 2 643.910570 2 965.726750 2 965.733121 2 965.753580 2 965.783780 2 965.817031 2 965.853075
a In these energies (thermal energies, thermal enthalpies and thermal free energies), the electronic energies (2321.941817, 2643.940745 and 2965.923085 a.u. for monomer, dimer and trimer, respectively) and zero-point energies (49.71, 103.10 and 154.60 kcal/mol for monomer, dimer and trimer, respectively) are also included.
of monomer as the temperature rises. The temperature and pressure dependence of degrees of dissociation for these two-component systems is represented in Fig. 6. At room temperature, hardly any monomer can exist in the gas phase and the equilibrium is realized between the dimer and the trimer. However, the rise of temperature results in a decrease of the amount of trimer and a shift of the equilibrium between the monomer and the dimer. Finally, almost all molecules dissociate to monomers at high temperatures. Based on these equilibrium constants and degrees of dissociation for the two-component systems, the mole fractions among the monomer, dimer and trimer was calculated for each partial pressure of DMAH 0.01, 0.1, 1.0 and 10.0 Torr using the relations between the partial pressures of DMAH and a total pressure (The total pressure of a carrier gas and DMAH is 10.0 Torr.) The results are shown in Fig. 7. When the partial pressures of DMAH are 0.1, 1.0 and 10.0 Torr at 2008C (473.15 K), the main component of gas is a dimer as shown in Fig. 7 (b)– (d), respectively. Nevertheless, the existence ratios of the monomer are still about 26, 8 and 3% of all molecules
at pressures, 0.1, 1.0 and 10.0 Torr at 2008C (473.15 K), respectively. At low partial pressures, the monomer appears to predominate at low temperatures as shown in Fig. 7 (a). Our results show that the existence ratios of the monomer are quite low as compared with those found by Willis and Jensen [28] they indicated that the main ingredient is the monomer when the DMAH pressure is 2.0 Torr at 2008C (473.15 K) and all DMAH molecules are monomers at the partial pressure of 1 × 10 23 Torr at 2008C. These discrepancies are considered to be attributed to the calculation methods and the basis sets adopted in their work. Though Al-CVD using DMAH as a gas is usually done near 2008C (473.15 K), this discrepancy is expected to affect the reaction rate, i.e. the growth rate of Al film assuming that monomer is the most reactive species as suggested by Willis and Jensen [28]. However, the temperature and pressure dependence of existence ratios are in good agreement between both results. The mole fractions also show an increase of the existence ratio of trimer when the temperature is near 1508C, as shown in Fig. 7 (c). This is because of the rapid
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Fig. 5. Calculated equilibrium constants (dimensionless) with respect to temperature: (a) between monomer and dimer; (b) between monomer and trimer; and (c) between dimer and trimer.
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Fig. 6. Calculated degrees of dissociation (a e) with respect to temperature and pressure: (a) between monomer and dimer; (b) between monomer and trimer; and (c) between dimer and trimer.
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Fig. 7. Calculated mole fractions between DMAH-monomer, -dimer, and -trimer at the following pressures (Torr) of DMAH: (a) 0.01; (b) 0.1; (c) 1.0; and (d) 10.0.
change of equilibrium constants between monomer and trimer with respect to the pressure. Although dimer amounts decrease and monomer amounts increase in the range from 100 to 2008C, monomers consequently form trimer owing to the equilibrium between the monomer and the trimer at high pressures.
3. Conclusions To understand the epitaxial growth in CVD, we should take account of the various physical and chemical processes such as reactions of source materials in gas phase, physical/chemical adsorptions, diffusions and reactions on substrate surface, desorptions of reactants and products, etc. In particular, the situation of source
materials in the gas phase should be well known since this is the initial step in CVD. However, the chemical changes of DMAH molecules in the gas phase are not clear in the case of Al-CVD using DMAH, as well as other organoaluminum source gases. In the present study, three kinds of gas phase chemical reactions were considered using ab initio molecular orbital method and density functional theory. From the results of our calculations, we concluded that hardly any dissociation and bimolecular reactions of DMAH occurred at the low temperatures found in Al-CVD. Even abstraction of methyl radical from DMAH molecule, the easiest process among the dissociation processes, needed almost 80 kcal/mol. Bimolecular reaction (2) had a high activation barrier of about 60 kcal/mol. However, the
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activation barriers of bimolecular reactions (1) and (3) were low (25–30 kcal/mol) so that these reactions may contribute to the CVD process in the gas phase at high temperatures. The stabilization energies were calculated as 31–32 and 52–56 kcal/mol in dimerization and trimerization reactions, respectively. Regarding the equilibrium between the monomer, the dimer and the trimer of DMAH, the monomer was the dominant molecule above 4008C (673.15 K) and the DMAH molecules formed mostly dimer and trimer below 08C (273.15 K) and in the range of 0.01– 10.0 Torr. However, the equilibrium composition changed remarkably with respect to the temperature and pressure, especially between 08C (273.15 K) and 4008C (673.15 K) at the same range of pressures. Above 2008C (473.15 K), the trimer disappeared and the equilibrium between the monomer and the dimer was realized at low pressures. In this equilibrium condition, the monomer amounts decreased and the dimer amounts increased with the increasing pressure of DMAH. Although it has been pointed out that the equilibrium between the dimer and the trimer is realized over the temperature range of 85–1678C and all the DMAH molecules become dimers at 1708C [26,33,34] our results showed that it was a mixture including a small amount of monomer and trimer, and a large amount of dimer under the same condition. However, the dimer is considered to be a stable molecule and it possesses low reactivity. We therefore expect that the information about the reactions of monomer with the substrate surface (e.g. adsorptions, reactions and desorptions on the surface) are essential to elucidate the mechanism of the epitaxial growth in Al-CVD using DMAH [35]. Ab initio calculations of reactions on the aluminum surface will be undertaken in subsequent papers. Acknowledgements This work was partially supported by the Semiconductor Technology Academic Research Center (STARC). We are grateful to Profs. H. Komiyama, Y. Shimogaki and Y. Egashira for their valuable comments and discussions. We also thank Drs T. Yoshimi, H. Ito, J. Aoyama and J. Ueda for their useful discussions. References [1] M. Hanabusa, A. Komatsu, Appl. Phys. Lett. 65 (1994) 1826 and references cited therein.
[2] T. Kobayashi, A. Sekiguchi, N. Hosokawa, T. Asamaki, Jpn. J. Appl. Phys. 27 (1988) L1775. [3] A. Sekiguchi, T. Kobayashi, N. Hosokawa, T. Asamaki, Extended Abstracts of the 21st Conference on Solid State Devices and Materials, Tokyo, 1989, p. 29. [4] N. Zhu, T. Cacouris, R. Scarmozzino, R.M. Osgood Jr, J. Vac. Sci. Technol. B 10 (1992) 1167. [5] N. Takeyasu, Y. Kawano, E. Kondoh, T. Katagiri, H. Yamamoto, H. Shinriki, T. Ohta, Jpn. J. Appl. Phys. 33 (1994) 424. [6] M. Hanabusa, A. Oikawa, P.Y. Cai, J. Appl. Phys. 66 (1989) 3268. [7] K. Masu, M. Yokoyama, H. Matsuhashi, K. Tsubouchi, Appl. Surf. Sci. 79/80 (1994) 237. [8] K. Tsubouchi, K. Masu, J. Vac. Sci. Technol. A 10 (1992) 856. [9] W. Kohn, A.D. Becke, R.G. Parr, J. Phys. Chem. 100 (1996) 12974. [10] J.L. Whitten, Chem. Phys. 177 (1993) 387. [11] Z. Jing, J.L. Whitten, Phys. Rev. B 48 (1993) 17 296. [12] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 98 (1993) 8810. [13] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 101 (1994) 11 012. [14] H. Burghgraef, A.P.J. Jansen, R.A. van Santen, J. Chem. Phys. 103 (1995) 6562. [15] G. Valerio, H. Toulhoat, J. Phys. Chem. A 101 (1997) 1969. [16] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 270. [17] W.R. Wadt, P.J. Hay, J. Chem. Phys. 82 (1985) 284. [18] P.J. Hay, W.R. Wadt, J. Chem. Phys. 82 (1985) 299. [19] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [20] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [21] B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 157 (1989) 200. [22] J.P. Perdew, Phys. Rev. B 33 (1986) 8822. [23] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13 244. [24] J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari, L.A. Curtiss, J. Chem. Phys. 90 (1989) 5622. [25] L.A. Curtiss, K. Raghavachari, G.W. Trucks, J.A. Pople, J. Chem. Phys. 94 (1991) 7221. [26] A.S. Grady, S.G. Puntambekar, D.K. Russell, Spectrochim Acta, A 47 (1991) 47. [27] E. Kondoh, T.J. Ohta, Vac. Sci. Technol. A 13 (1995) 2863. [28] B.G. Willis, K.F. Jensen, Conference Proceedings ULSI XII, p. (1997) 29. [29] M. Pelissier, J.P. Malrieu, Theoret. Chim. Acta 56 (1980) 175. [30] Y.S. Hiraoka, M.J. Mashita, Crystal Growth 145 (1994) 473. [31] P.C. Hariharan, J.A. Pople, Theoret. Chim. Acta 28 (1973) 213. [32] J.A. Pople, A.P. Scott, M.W. Wong, L. Radom, Israel J. Chem. 33 (1993) 345. [33] T. Wartik, H.I. Schlesinger, J. Am. Chem. Soc. 75 (1953) 835. [34] A. Almenningen, G.A. Anderson, F.R. Forgaard, A. Haaland, Acta Chem Scand. 26 (1972) 2315. [35] T. Takahashi, Y. Shimogaki, T. Yoshimi, H. Ito, J. Aoyama, J. Ueda, H. Komiyama, Proceedings of the 14th International VLSI Multilevel Interconnection Conference (VMIC), 1997, p. 369.