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Combined thermodynamic and mass transport modeling for material processing from the vapor phase
Thin Solid Films 365 (2000) 264±274 www.elsevier.com/locate/tsf
Combined thermodynamic and mass transport modeling for material processing from the vapor phase Michel Pons a,*, Claude Bernard a, Elisabeth Blanquet a, Roland Madar b a
Laboratoire de Thermodynamique et Physicochimie MeÂtallurgiques, UMR CNRS/INPG/UJF 5614, Institut National Polytechnique de Grenoble, 1130 rue de la Piscine, B.P. 75, 38402 Saint Martin D'Heres, France b Laboratoire de MateÂriaux et de GeÂnie Physique, UMR CNRS/INPG 5628±ENSPG, Institut National Polytechnique de Grenoble, B.P. 46, 38402 Saint Martin D'Heres, France
Abstract The computational modeling of vapor phase processes like CVD involves different routes. For complex chemical systems, thermodynamic analysis can be ®rst performed. Three examples on the CVD of refractory metal disilicides and ternary silicides show the process guidelines which can be obtained from an a priori thermodynamic analysis even in feature scale technology. However, it is a static analysis. Linking the thermodynamic approach with mass transport modeling allows the description of the dynamic chemical system in local thermochemical equilibrium (LTCE). Two examples on the deposition of titanium silicide and silicon-germanium alloys illustrate the framework provided by this approach keeping in mind the assumptions that underlie the computations. Thermodynamic and LTCE transport modeling are to be seen as an a priori computational methods based on the access of only thermodynamic and transport database. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Vapor phase process; Thermodynamic analysis; Local thermochemical equilibrium
1. Introduction The computational modeling of vapor phase processes such as CVD (chemical vapor deposition) have become valuable tools to optimize processes manufacturing to yield improved products [1±5], requiring the knowledge of accurate thermochemical, kinetic and transport data to be reactor design predictive. For complex, advanced or prospective chemical systems, thermodynamic analysis is a modeling route to obtain information on chemistry. At ®xed temperature and pressure (or volume), it is possible to obtain the equilibrium history of the gas phase and of the deposited phases for `in®nite' time or length. `CVD phase diagrams' are used to display solid equilibrium phases as a function of temperature, pressure and feed gas composition [6±12]. This a priori thermodynamic approach permits the assessment of the experimental method (choice of gas precursors, phases likely to be formed from the initial gas phase but also by reaction with the substrate and furnace walls). The predictive capability of this equilibrium analysis is illustrated for different deposition systems involving complex solid phases. To manage this modeling approach, * Corresponding author. Tel.: 1 33-4-7682-6532; fax: 1 33-4-76826677. E-mail address: [email protected] (M. Pons)
software packages solving Gibbs energy minimization and databases are needed. Generally, the data are obtained from combined experimental and theoretical studies. Nowadays, specialists of gas-phase measurements are few and a quantum chemistry approach is more and more used for thermodynamic data evaluation [14,15]. However, this method is a static approach. It is not expected to yield the equilibrium state corresponding to the temperature, the pressure and the concentrations actually established at the solid±gas interface. A dynamic approach using mass transport modeling within the entire reactor could provide considerable insight on the controlling phenomena. Whereas hydrodynamic models are generally applicable, a separate chemical model, stating the relevant homogeneous and heterogeneous reaction pathways and rate constants must be speci®ed for each CVD process. The lack of detailed kinetic data and models for complex chemical systems seems to be the most important limitation in CVD modeling. Thermodynamic and hydrodynamic phenomena in CVD systems are based on rather well-established theory and on data which are available or which can be estimated in a few cases. The linking of thermodynamic databases, local thermochemical equilibrium (LTCE) and mass transport calculations could offer a possible modeling route [10±13,16±18]. The advantages of this coupled
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(99)0105 2-4
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approach is that, for a large variety of CVD systems, reliable data are available. The main drawback is that the relevant models are restricted to local equilibrium conditions. However, although CVD is not an equilibrium process, local equilibrium analysis coupled with modeling of transport processes is of interest because it may be the only available approach for complex multicomponent chemical systems and is the most favored in a transport-limited regime. This method is able to predict the concentration ®elds and the composition of the solid ®lm from the knowledge of only databases, taking into account the geometry of the reactor and species balances. A general procedure for implementing species balances and equilibrium conditions will be shown. The thermodynamic calculations are included in the mass transport computation as source terms for the equilibrium in the gas phase and boundary conditions for the equilibrium at the gas±solid interface. The use of modeling in obtaining more realistic ¯ow and thermal ®elds inside complex reactors has provided impressive assistance to CVD equipment manufacturers. The proposed thermodynamic and local thermodynamic equilibrium coupled with mass transport approaches allow progression in the complexity of the predictive assistance, keeping in mind the assumptions that underlie the computations. The information which can be derived from this modeling approach will be illustrated. Finally, mixed kinetic and thermodynamic databases and transport computations can be processed to more closely examine the actual deposition phenomena in the light of new experimental and theoretical data. This last approach is beyond the scope of this paper, but is being used by the authors for the simulation of single crystal SiC growth for high-temperature electronics [13]. This paper gives an overview on thermodynamic modeling in Section 2 and on the LTCE linked with mass transport modeling in Section 3. For the ®rst part, we have selected three examples. The ®rst two will show the process guidelines which can be obtained in complex solid systems. The third one will show that thermodynamic modeling can help feature scale technology. For the LTCE-mass transport modeling, we have selected two examples. The ®rst one, involving complex deposited phases, will show the shifts in the phase diagrams due to transport phenomena. The second one will show, in a complex gaseous system, the in¯uence of transport phenomena on the equilibrium predictions.
2. Thermodynamic modeling 2.1. An introduction to thermodynamics and computations During recent years, CVD methods have been increasingly utilized for various applications. However, for each new application, they are in competition with other deposition processes. Ef®cient usage of CVD systems requires
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optimization of all process parameters. This leads to increasing enquiries in modeling. Historically, the ®rst modeling approach was a thermodynamic one. It was prompted by the transport approach developed by Schafer [19] in sealed tubes. Then, computer science made the method of minimization of the total Gibbs energy of the chemical system straightforward [6±8]. With this method, assuming that equilibrium is reached, it is possible to compute the composition of the gas phase and the nature of the condensed phases for a predetermined set of experimental parameters, total pressure, partial pressures of the gas precursors and temperature. This approach is based on the availability of a consistent and complete set of thermodynamic data related to all species likely to be involved in the deposition reactions. The perpetual increase of the computation power has moved the limitations of this approach. They are rather related to the availability of data than to the complexity associated with a great number of species. The thermodynamic databases, though still strongly incomplete, have been decisively updated in the last 10 years. Ab initio computations have complemented direct measurements which are unfortunately less and less determined. Parallel to the databases upgrade, software packages have been developed and linked. In terms of the leading concerns of their developers, these sets, databases and software packages, are more or less suitable for CVD problems. They are available either on-line or as packages for personal computers. In Europe, the members of the Scienti®c Group Thermodata Europe (SGTE; B.P. 166, 38402 Saint Martin D'HeÁres, France) have built a common database for substances and another for solutions. They have in their possession software packages suitable for computations of complex equilibria. For computations involving reactive gaseous phases for CVD problems, the database Coach (4200 substances) linked to the Gemini minimization code (Thermodata/INPG/CNRS, B.P. 166, 38402 Saint Martin D'HeÁres, France; http://www.cpma.u-psud.fr/therma/thermafr.html) is the most suitable. Chemsage software (G.T.T., Kaiser Strasse 100, D-52134 Herzogenrath, Germany; http://gttserv.lth.rwth-aachen.de/) is linked to the SGTE database and encloses special ®les for metastable coatings like AlON. Other software is more especially involved in phase diagram computations rather for metallurgical problems. MTDATA (N.P.L., Queens Road, Teddington, Middlesex TW11 OLW, UK; http:// www.npl.co.uk/) and Thermocalc (Royal Institute of Technology, S-10044 Stockholm, Sweden; http:// www.met.kth.se/tc/) software linked with the SGTE databank have to be mentioned. For problems involving salts or oxides, the FACT system (Centre de Recherches en Calcul Thermodynamique, Ecole Polytechnique de Montreal, Quebec, Canada H3C 3A7; http://www.crct.polymtl.ca/ fact/fact.htm) is the most suitable. The future in the CVD modeling ®eld belongs to software integrating thermodynamic databases but also transport and kinetic databases
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to meet the global complexity of the CVD process. The Chemkin software package ([20,21]; Chemkin-III: Reaction Design, 11436 Sorrento Valley Road, San Diego, CA 92121, USA; www.ReactionDesign.com, e-mail [email protected]) is one well known example of this kind of integration for combustion problems [22] and is widely used for CVD modeling [23,24]. The EGLIB library has to be quoted as a powerful tool for transport properties calculations [25]. More information on fully integrated thermodynamic databases and software packages with extensive equilibria and phase diagram capabilities, and miscellaneous links, can be found on the Web server http:// www.crct.polymtl.ca/fact/websiter.htm#Commercial Packages. 2.2. Examples Three independent examples are proposed to illustrate the use of an a priori thermodynamic analysis for the selection of the following parameters: ² Nature of the reactants, W±Si system ² Material to be deposited for a speci®c application, W±Si/ Ti±Si and MSiN systems (M is a metal) ² Range of experimental parameters, MSiN system (M is a metal) ² The effect of the nature of the substrate, selective deposition of Ti±Si The cases of blanket and selective deposition of refractory silicides were explored some years ago. 2.2.1. Low-pressure CVD of M±Si (M Ti, W) During the last decades, the improvement of the performance of integrated circuits and the trends towards higher level of integration (ULSI) have resulted in the investigation of refractory metal silicides such as TiSi2, WSi2. They have been selected for use as gates and interconnections due to their relatively low resistivity and high thermal stability. These silicides are compatible with most integrated circuit processing, offering good dry etch, adhesion, oxidation and contact properties. For the processing of silicides thin ®lms for submicronic devices, CVD techniques have been generally adopted. However, one of the main dif®culties concerns the appropriate selection of the gaseous precursors of the silicon and metal. In the case of WSi2 ®lms, while silane SiH4 is largely accepted as the most common silicon precursor, different possibilities exist to transport the tungsten in the CVD reactor. Tungsten hexa¯uoride has been commonly used since this compound is liquid at room temperature and has suf®cient vapor pressure to ¯ow directly into the reactor. But in the CVD tungsten silicide ®lm process using WF6 and SiH4, an additional annealing treatment is required to improve the ®lm stoichiometry and crystallinity. As shown in the CVD phase diagram presented in Fig. 1, the formation of pure WSi2 is thermodynamically possible only in a very narrow reactant gas-phase composi-
Fig. 1. W±Si system. CVD phase diagram calculated as a function of SiH4 and WF6 partial pressures, Pt 105 Pa, T 1000 K, PAr 9 £ 104 Pa.
tion range. The substitution of tungsten chlorides for tungsten ¯uorides allows better control over the WSi2 ®lm stoichiometry [26,27]. Using WCl6 or WCl4 as tungsten source, a non-negligible domain of pure WSi2 deposition is observed in the corresponding phase diagrams (Figs.2,3). Although tungsten chlorides are solid at room temperature and therefore more dif®cult to use in a CVD process, the deposition of pure crystallized WSi2 have been obtained starting from WCl4 and SiH4 in agreement with the conditions given in the corresponding CVD diagram (point B) [28]. The shape of the CVD phase diagram is speci®c to the investigated system. For instance, it has been observed that the deposition of pure TiSi2 is much more favored than the WSi2 deposition (Fig. 4) which makes TiSi2 much more convenient to obtain by CVD.
Fig. 2. W±Si system. CVD phase diagram calculated as a function of SiH4 and WCl6 partial pressures, Pt 105 Pa, T 1000 K, PAr 9 £ 104 Pa.
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Fig. 3. W±Si system. CVD phase diagram calculated as a function of SiH4 and WCl4 partial pressures, Pt 133 Pa, T 873 K, PAr 120 Pa, A-E points correspond to simulated deposition conditions.
The data used were provided by the SGTE databank, from literature data [29] and from simultaneous optimization of experimental data and theoretical calculations for the metal silicides [30±32]. The substances included in the thermodynamic calculations and sources of thermochemical data can be found in Refs. [31,32]. 2.2.2. Low-pressure CVD of M±Si±N (M Ta, Ti, W, Re) for diffusion barriers in advanced copper metallization Since the beginning of the 1990s, ternary amorphous
Fig. 4. Ti±Si system., CVD phase diagram calculated as a function of SiH4 and TiCl4 partial pressures, Pt 330 Pa, T 1100 K.
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metallic thin ®lms made of a transition metal, one non metal (Si or B) component and nitrogen such as TaSiN, TiSiN, WSiN have been explored for use as diffusion barriers between copper overlayer and oxidized silicon substrates ([33] and references therein). The majority of the ®lms have been processed by PVD. LPCVD of ternary silicides diffusion barriers on SiO2/Si substrates, starting from silane, in situ fabricated metal chlorides, ammonia, hydrogen and argon has been investigated as potential ®lms [34]. The resulting chemical systems, M±Si±N±H±Cl±Ar, are complex. Thermodynamic investigation allowed to classify the four ternary materials into two categories according to the thermodynamic stability of the metal nitrides: the group of metals (W, Re) which do not form a stable metal nitride and the group of metals (Ti, Ta) which form stable metal nitride, in the operating temperatures and pressures ranges. The ternary phase diagram W±Si±N (Fig. 5) established at 773 K looks like the Re±Si±N one. Three equilibria between Si3N4 and M, M5Si3, MSi2 (M W, Re) are calculated. The ternary phase diagram Ti±Si±N was established considering the solubility of nitrogen in the Ti5Si3 phase (Fig. 6) [35]. In the investigated temperature and pressure ranges, the Ta±Si±N isothermal sections are similar to the Ti±Si±N ones (with the tantalum silicides in equilibrium with TaN). The simulations of metal chlorination and deposition process provided the possible range of operating conditions leading to compositions located in the different stability domains. The conditions which lead to the compositions of the highest performances PVD ®lms were taken as starting points. A correlation between the stability of the metal nitride and the thermal behaviour (crystallization temperature and nature of the crystallized phase) was found. In the W±Re group, the deposited ®lms which were `XRD amorphous' appear as nanocomposites of small grains of Re or unstable W2N and W inserted in a Si±N matrix while, in the Ti±Ta
Fig. 5. Ternary phase diagram W±Si±N calculated at 773 K with simulated deposition conditions and experimental composition.
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Fig. 6. Ternary phase diagram Ti±Si±N calculated at 773 K considering nitrogen solubility in Ti5Si3, with simulated deposition conditions and experimental composition.
group, whatever experimental conditions, the ®lms were mostly composed of crystallized TaN or TiN. When comparing the deposited phase analysis results (RBS and XRD) [34] and the simulated compositions for the same operating conditions, a rather good agreement was found for W±Si±N (Fig. 5), Ti±Si±N (Fig. 6) and Re±Si±N. For the Ta±Si±N system, even if the nature of the deposited phases is in agreement with the predicted ones, the compositions are quite different. These discrepancies can be explained by different factors such as the formation of an amorphous or nanocrystalline material while all data were determined for crystallized materials, the non-equilibrium situation and the uncertainties in some thermodynamic data (tantalum nitride compounds). It was demonstrated that WSiN and TiSiN ®lms are the most promising materials for diffusion barriers for copper metallization. Despite their difference, their morphology ensures a good compromise between resistivity and barrier performance which can be adjusted by the ®lm composition. These results show that thermodynamic modeling of the deposited phases from initial composition of the gas phase, i.e. experimental raw parameters, can give guidelines but also a preliminary range of experimental parameters to process thin ®lms of desired composition. New experimental directions and thermodynamic analysis including the interactions with copper can be proposed as well as new modeling routes involving heat and mass transfers. 2.2.3. Ti±Si system and deposition selectivity [8,36] The results reported in the previous section concern the deposition of blanket material. Silicides such as TiSi2 can be used as contact for the source and drain in addition to the gate. One solution, which is referred to as the salicide process, in which the metal deposited by evaporation or sputtering is reacted onto a Si/SiO2 patterned wafer to form the metal silicide only on the bare silicon surface. However, this process implies the consumption of the underlying silicon and thus is not compatible with the fabri-
cation of very shallow junctions. The selective deposition by CVD of TiSi2 has been implemented using TiCl4, SiH4 diluted in H2 as starting gas mixtures. This process is by itself highly selective. It is necessary to remove the native silicon oxide. Three main solutions have been used to etch it. The ®rst is the classical etching by reacting the substrate with a gas mixture of H2/HCl at 1373 K or pure H2 at 1273 K at low pressure. The second is based on the formation of volatile SiO using a low-pressure silane gas (1 mTorr) at low temperature (1073±1150 K). Thermodynamic modeling can be used to explain these results (Fig. 7). In the very lowpressure CVD process, the polysilicon ®rst deposited is simply consumed to remove the native oxide. This is why the deposition time of this polysilicon layer is so critical for the successful implementation of this selective process. The third solution is based on the in situ etching of the native oxide by an appropriate choice of partial pressure of the reactive mixture. This solution is of technological importance because it uses the same gases as for the deposition process. To obtain the possible experimental range, SiO pressures over SiO2 have been calculated at equilibrium in the Ti±Cl±Si±H±Ar±O system. The main results of these calculations concerning the oxygen-bearing molecules in the gas phase, represented in Fig. 8, indicate etching of the native oxide in the form of SiO. The etching trends re¯ect the variation in silicon activity in the condensed state, which reaches a maximum value for the TiSi2 1 Si deposition domain. This has been con®rmed experimentally in the authors' APCVD reactor by the successful deposition of TiSi2 for conditions close to those predicted by these calculations. Once the native oxide has been removed, the vapor phase reacts with an Si/SiO2 surface. Thermodynamic equilibrium
Fig. 7. Calculated SiO partial pressure as a function of total pressure at 973 K for the following conditions: excess of SiO2, initial values of SiH4 0:73 mol, H2 0:105 mol, Ar 0:165 mol.
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This example clearly shows that thermodynamic modeling can help feature scale technology. 2.2.4. Conclusions From these examples, it should be emphasized that thermodynamic analysis of deposited solid phases is a possible modeling route. The CVD phase diagrams map the experimental parameters that will produce equilibrium deposition of a phase or phases of interest. They provide a broad overview of the experimental parameter space in which the desired phase(s) can be deposited. However, possible deviations between calculated and experimental deposition are to be expected. Even if the resulting predictions may be qualitative in nature, they can give guidelines to limit the range of conditions for deposition, or correctly give the trends in deposition behaviour with changing experimental parameters. Fig. 8. Calculated SiO partial pressure as a function of the partial pressure of SiH4 in the Ti±Cl±Si±Ar±H±O system for the following conditions; T 1200 K, total pressure 10 5 Pa, partial pressure of Ar 9 £ 104 Pa, partial pressure of TiCl4 2 £ 102 Pa, partial pressure of H2 98 £ 102 Pa.
calculations performed in the TiSi2 domain show that the introduction of the silicon substrate induces competition between the silicon from the gas phase (SiH4) and the substrate for the formation of TiSi2 and the gaseous silicon-bearing molecules (Fig. 9). This result indicates that, in the deposition domain, the silicon substrate participates in the formation of the TiSi2 layer, while there is almost no chemical interaction with the SiO2 parts of the substrate. This implies automatically some silicon consumption during the growth process which is almost independent of the etching procedure. This statement is in agreement with the ®ndings of most of the works reported on this subject.
Fig. 9. Partial pressure of gaseous silicon bearing molecules as a function of the nature of the substrate at equilibrium: T 1200 K, total pressure 10 5 Pa, partial pressure of Ar 9 £ 104 Pa, partial pressure of TiCl4 2 £ 102 Pa, partial pressure of SiH4 4 £ 102 Pa, partial pressure of H2 94 £ 102 Pa.
3. Combined thermodynamics (LTCE) and mass transport When the thermodynamic analysis is completed, it is possible to move toward reactor design by linking thermodynamic modeling and databases with mass transport modeling [10±13]. This method is used to predict the composition of the solid ®lm from the knowledge of the gas-phase composition taking into account the geometry of the reactor and species balances. Zhu and coworkers [17] have already employed the local equilibrium concept together with the ¯ux balance principle to determine the concentration of the species on the substrate and the rate of deposition of silicon from SiCl4 and H2. They have used thermochemical calculations to obtain the boundary conditions on the substrate, i.e., the partial pressures of various species in local equilibrium at the substrate. A general procedure for implementing species balances and equilibrium conditions may be different. As will be shown, the thermodynamic calculations are included in the mass transport computation as source terms for the equilibrium in the gas-phase and boundary conditions for the equilibrium at the gas-solid interface. Rosner and coworkers [18] have built `transport-shifted' CVD phase diagrams which are generated by using both feed gas and mass-transfercorrected wall element fractions. They have shown that chemical segregation in mass-transfer-controlled CVD systems can produce important shifts in phase boundaries of equilibrium deposits in CVD phase diagrams. Gokoglu [16] has shown the implications of the predictions of local thermodynamic equilibrium coupled with mass transport in boundary layers for Na2SO4 deposition from combustion product gases on turbine blades. 3.1. The local thermochemical equilibrium (LTCE) concept Table 1 describes the transport equations. More details can be found in Refs. [1±4].
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Table 1 Multicomponent transport equations 7: JCi 1 JFi 1 JTi Si ; i 1¼N 1
Transport Eq. (1): Si is the source term of species i
JCi rvvi ; i 1¼N
Convection Eq. (2): r; v; vi are density, velocity and mass fraction of i Fickian diffusion Eq. (3): Dij are the multicomponent diffusion coef®cients
JFi 2
N X j1
JTi 2DTi
2
rDij 7vj ; i 1¼N
3
7T ; I 1¼N T
4
Thermo-diffusion Eq. (4): DTi is the thermodiffusion coef®cient of species i
The multicomponent diffusion (Eq. (3)) is de®ned by generalizing the binary diffusion to a N-component system. The relations between multicomponent diffusion coef®cients Dij and the binary values come from matrix calculations [25]. The last term of Eq. (1), Si , represents the rate of creation or depletion of i species by homogeneous chemical reaction and must be calculated by the near LTCE concept. From a guessed concentration ®eld (vi , i 1¼N), Gibbs energy minimization at each grid point of the reactor gives a new set of vieq ; the near-equilibrium sources terms Sieq can be obtained from 0
Sieq
1 7T A 7@rvvieq 2 rDij 7vjeq 2 DTi T j1 N X
5
i 1¼N. The sources terms Sieq cannot be directly inserted to continue the iterative modeling and to compute a new set of vi from Sieq guessed ®eld. The constraints associated with LTCE and mass transport analysis are different. LTCE calculations assume elements and mass conservation in a closed chemical system (the stoichiometry of the reactions is respected). Mass transport calculation only assumes mass conservation in an open chemical system. It is necessary, to import the data of LTCE calculation into Eq. (1), to ®nd the intersection between the two spaces of solutions. Projective methods are used to calculate Si for iteration n 1 1 from Sieq calculated by Eq. (5) from vi and vieq calculated at iteration n (PROJ is the projection operator) h i Si iter:n 1 1 PROJ Sieq iter:n
6
The vector S must be orthogonal to the matrix A of the stoichiometric coef®cients de®ned by E rows and N columns; E is the number of element and N the number of gaseous species. The mass transport-LTCE model that is to be solved is 0 Si 7:@rvvi 2
N X j1
rDij 7vj 2
DTi
1 7T A T
7
where i 1¼N; minimization of G(P,T,v i,v N) at each grid point S [ h Ai' . The iterative procedure for homogeneous phenomena is stopped when vi 7 ! vieq , e.g. when near LTCE is reached at each grid point of the reactor. The common rules were used to calculate the transport properties of the gas mixture as a function of pressure, temperature and concentrations [3]. The boundary conditions on the substrate, the mass ¯uxes, Rgi , are linked with thermodynamic heterogeneous equilibrium. This boundary condition leads to a complex situation. Unlike the model allowing the calculation of source terms by minimization and subsequent transformation, there is not conservation of the mass on the reactive substrate but M 2 1 relations between gas and associated solid ¯uxes due to the conservation of the elements (M is the number of solids which could appear). The matrix A is now de®ned by E rows and N 1 M columns. If B is the matrix de®ned by the conservation of the ®lm composition, the boundary condition on the substrate is Rgi n: JCi 1 JFi 1 JTi
8
i 1¼N; minimization of G(P,T,v i,v N) at each grid point Rg [ h Ai' >hBi.The Rg vector at iteration n 1 1 is obtained by projection of the Rgeq vector on the h Ai' >hBi space. The Rgeq vector is computed from a guessed equilibrium concentration ®eld on the substrate at iteration n. The Eqs. (1)±(4) associated with boundary conditions and constraints described in Eqs. (5)±(8) are iteratively solved by ®nite element and minimization methods. Flux-Expert (Simulog, 1 rue James Joule, 78286 Guyancourt, France) and Melange (LTPCM, B.P. 75, 38402 Saint Martin D'HeÁres, France) software packages were customized. Two examples are presented to illustrate the LTCE concept. They will show the effects of transport phenomena on the predicted deposition products. 3.2. Ti±Si system [10,37] For the deposition of TiSi2 on silicon in horizontal reactors, experimental results have shown that the consumption of the substrate is directly related to the SiH4/TiCl4 ratio. However, for high SiH4/TiCl4 ratios, the silicon provided by SiH4 pyrolysis is in excess and codeposition of TiSi2 1 Si occurs, with a subsequent loss of selectivity. The overall consumption, leading to gas-phase depletion along the substrate, may induce the deposition of different silicides. In addition, when large substrates are used, the thickness and the composition of the coating are not uniform and are largely in¯uenced by the gas distributors [7,38±40]. A typical Ti±Si CVD phase diagram starting from TiCl4 and SiH4 is given in Fig. 4. Fig. 10 represents a horizontal reactor which is widely used in CVD research and development. Gas enters through a distributor or diffuser and ¯ows over the substrate. The opposing wall is water-cooled to provide a more uniform
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Fig. 10. Schematic representation of the cold-wall horizontal reactor (dimensions are in meters); and the calculated velocity ®eld: (Q 2 SLM of H2±4 vol.% SiH4±1 vol.% TiCl4).
pro®le in the reactor. Horizontal reactors have been thoroughly analyzed by analytical and numerical models ([2] and references therein). Details on the velocity and thermal ®elds can be found in a previous work [11]. Assumptions have been made for the reactive mass transport model. In the gas phase, no dissociation of inlet reactive species has been assumed. From homogeneous thermochemical equilibrium calculations, the intermediate and product species in small amounts have been neglected. With these assumptions, the mass transport modeling involves ®ve species, SiH4, TiCl4, SiCl4, HCl and H2. It was checked that these simpli®cations are reasonable simulations of the more complex system resulting from a complete data set. In addition, the substrate has been assumed chemically inactive, i.e., silicon diffusion from the bulk and subsequent enrichment of the coating is neglected. Particular attention must be paid to the diffusion ¯ux boundary conditions on the reactive substrate because they de®ne the coupled mass transport/local thermodynamic equilibrium (LTCE) approach considering the gas-phase simpli®cations. The boundary conditions at the substrate are prescribed by the LTCE. LTCE iteratively modi®es the species ¯uxes at the substrate to obtain `equilibrium ¯uxes'. The iterative procedure is stopped when diffusion ¯uxes at the substrate remains constant (about 20 iterations in standard cases) i.e., the overall system has reached thermodynamic equilibrium. The `elemental' ¯uxes obtained after convergence are consistent with LTCE predicted deposit composition. As we have pointed out previously, the general trend revealed by experimental results is the in¯uence of the SiH4/TiCl4 ratio on the properties, selectivity, uniformity and composition of the coating. So, ®ve compositions have been selected (Fig. 11). The thermodynamic equilibrium calculations performed from inlet gas-phase compositions determine the chemical nature of the deposit assuming ®xed temperature and pressure. The modi®cations
due to reactive transport are now shown. Fig. 8 shows the actual molar fractions of Si-containing and Ti-containing gaseous species over the substrate leading to equilibrium deposition; they are inserted in the CVD phase diagram. Along the substrate, the coupled approach clearly shows that it is possible to cross phase boundary lines due to the overall depletion, the transport of reactive species, the variations of the mass ¯uxes on the substrate and the presence of product gases. From the leading edge of the substrate the Sicontaining and Ti-containing gaseous species concentrations decrease, then the Si-containing gaseous species depletion increases more rapidly than that of the Ti-containing gaseous species. Near the trailing edge both concentra-
Fig. 11. (a) Actual composition of Si- and Ti-containing gaseous species over the substrate inserted in the CVD phase diagram; (b) zoom of the 4:1 composition showing the phase change along the substrate. These results are only valid for the studied geometry.
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tions increase due to axial diffusion of reactant gas against the ¯ow. Experimentally, similar variations of the Si/Ti ratio have been observed by resistivity measurements. Unfortunately and contrary to CVD phase diagrams, these results are only valid for the geometry studied. The observed shifts are weaker for axisymmetric and vertical reactors. It is well known that, for this reactor con®guration, the reactive ¯ux variations are of less importance and lead to ®lms more uniform in composition and thickness [1±3]. Generally, it should be noted that the predicted deposition rate are too high compared with experiments. This is mainly due to the fact that the process is controlled by kinetics rather than by reactive transport. The coupled approach is limited to equilibrium conditions but gives information on the relations between reactor geometry and coating nature and uniformity as well as on the complex chemical heterogeneous and homogeneous reactions based on well established theory and reliable data. 3.3. Si±Ge system [11,12] Though the processing of silicon-germanium alloys Si12xGex at high temperature is somewhat removed from the microelectronics industry, this example is presented to show the potential of the coupled approach to manage the stoichiometry of the deposited ®lm. The thermodynamic equilibrium study in the Si±Ge±H± Cl system showed that the germanium fraction in the deposit, XGe (XGe nGe/(nGe 1 nSi)) decreases as the temperature or the chlorine quantity increases. The thermodynamic analysis gave the guidelines for the variations of the stoichiometry of the deposit. The coupled approach re®ned it by taking into account transport phenomena. The reactor is vertical, inverted and axisymmetric. The gas is admitted at the bottom of the reactor. The model predicts the ¯ow and temperature ®elds of the mixture and the concentration ®elds of the gaseous species. It also predicts the deposition rate and the stoichiometry of the deposited ®lm. Fig. 12 shows the calculated velocity and temperature ®elds inside the reactor when the substrate was set at 1300 K, the inlet mixture was Ar (89%)±H2 (10%)± SiH4(0.5%)±GeCl4(0.5%), e.g. YGe, which is the germanium fraction in the gas phase, equal to 0.5, the total ¯ow rate was 2 l/min and the pressure 315 Pa. The most important gaseous species contributing to the ®lm growth are, in equilibrium conditions, GeCl, GeH, Ge1, Si3, Si2, Si1 and SiH when argon is the carrier gas (Fig. 13). These results revealed strong dependence of gas-phase equilibrium composition with the distance to the substrate. Fig. 14 shows the deposition rate and the stoichiometry of the ®lm as a function of the radial position along the substrate for the experimental conditions described above. The ®lm stoichiometry, XGe, is uniform and is about 0.18 (Y Ge 0:5). Simple previous equilibrium calculations predicted a minor depletion in germanium, X Ge 0:25, for Y Ge 0:5. These results show that the high thermody-
Fig. 12. Velocity and temperature ®elds: T 1300 K; ¯ow rate 2 l/min.
namic stability of germanium chlorides, compared to that of silicon hydrides and chlorides, associated with the mass transport phenomena deplete the ®lm in germanium
Fig. 13. Gaseous mass fraction along the center line above the substrate. (1: H2; 2: GeH4; 3: SiH2Cl2; 4: SiHCl3; 5: SiH3Cl; 6: SiH4; 7: SiCl4; 8: GeH3; 9: GeH3Cl; 10: GeCl3; 11: Si2H6; 12: GeCl; 13: SiCl2; 14: Si3; 15: HCl; 16: GeH; 17: Ge(g); 18: SiH; 19: SiCl3; 20: SiH4).
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4. Conclusions When implementing a new CVD process, the wide range of parameters, geometry, gas precursors, temperature, etc., could discourage any modeling attempts. Despite the inherent dif®culties and the speci®c complexities of each CVD process, it seems that the thermodynamic approach could be ®rst performed to determine the engineering interest of the selected chemical system. Then, by assuming the absence of kinetics barriers, the use of near-local thermochemical equilibrium within the ¯owing system could provide useful information. This modeling route could provide an assessment of the experimental method and a framework into which a kinetic-mass transport model could ®t. It would narrow the range of variables which may be involved in causing undesirable effects (recirculation, inadequate gas ¯ow¼) and indicate the weak and strong dependencies between the different non-linear phenomena leading to deposition. Thermodynamic and LTCE-transport modeling are to be seen as a priori approaches. The deposition process is generally controlled by kinetic phenomena, so that the model gives the trends but not absolute engineering values. Once kinetic information is available, this already built framework can be updated and more realistic simulations can be performed. Acknowledgements The authors acknowledge the Centre National de la Recherche Scienti®que for the long-lasting ®nancial support and Eric Ramberg for reviewing the manuscript.
Fig. 14. Deposition rate (a) and stoichiometry (b) along the radius of the substrate.
compared to the inlet germanium content. Thermodiffusion plays an important role for the germanium containing species depletion of the gas phase near the substrate. Thermodiffusion causes heavier molecular weight species to be driven along a temperature gradient away from hot surfaces towards cold surfaces. The concentration of GeCl, the most important gaseous species containing germanium, near the substrate is ®ve times higher when thermodiffusion is neglected. The thermal diffusion rates can be modi®ed by changing the diluting gas. These results, assuming equilibrium conditions in a ¯owing system match the experimental measured ones at 1300 K. They should therefore be used for the identi®cation of the reaction pathways and the in¯uence of geometry, ¯ow rate and temperature gradients but perhaps not for predicting the chemical composition of the ®lm under actual operational conditions. It is well known that the residence time required for the system to reach its equilibrium composition is much larger than the residence time typically met in LPCVD.
References [1] K.F. Jensen, in: D.W. Hess, K.F. Jensen (Eds.), Microelectronics Processing: Chemical Engineering Aspects, Advances in Chemistry Series, 221, American Chemical Society, Washington, DC, 1989, p. 199. [2] S.A. Gokoglu, in: T.M. Besmann, B.M. Gallois, J.W. Warren (Eds.), Chemical Vapor Deposition of Refractory Metals and Ceramics II, MRS Symp. Vol. 250, 1992, p. 17. [3] C.R. Kleijn, C. Werner, Modeling of Chemical Vapor Deposition of Tungsten Films, BirkhauÈser, 1993. [4] C.R. Kleijn, in: M. Meyappan (Ed.), Computational Modeling in Semiconductor Processing, Artech House, London, 1995, p. 97. [5] J.P. Couderc, in: M.D. Allendorf, C. Bernard (Eds.), Chemical Vapor Deposition, Proc. 14th Int. Conf., Vol. 97-25, The Electrochemical Society, Pennington, NJ, 1997, p. 202. [6] C. Bernard, in: J.M. Blocher Jr., G.E. Vuillard, G. Wahl (Eds.), Proc. 8th Int.l Conf. CVD, The Electrochemical Society, Pennington, NJ, 1981, p. 3. [7] R. Madar, C. Bernard, Appl. Surf. Sci. 53 (1991) 1. [8] C. Bernard, R. Madar, MRS Symp. 168 (1990) 3. [9] K.E. Spear, R.R. Dirkx, High Temp, Sci. 27 (1990) 107. [10] M. Pons, C. Bernard, R. Madar, Surf. Coat. Technol. 61 (1993) 274. [11] M. Pons, C. Bernard, H. Rouch, R. Madar, Appl. Surf. Sci. 91 (1995) 34. [12] H. Rouch, M. Pons, A. Benezech, C. Bernard, R. Madar, Thin Solid Films 281±282 (1996) 64.
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[13] M. Pons, E. Blanquet, J.M. Dedulle, I. Garcon, R. Madar, C. Bernard, J. Electrochem. Soc. 143 (1996) 3727. [14] M.D. Allendorf, J. Electrochem. Soc. 140 (3) (1993) 747. [15] C.F. Melius, M.D. Allendorf, M.E. Covin, in: M.D. Allendorf, C. Bernard (Eds.), Chemical Vapor Deposition, Proc. 14th Int. Conf., Vol. 97-25, The Electrochemical Society, Pennington, NJ, 1997. [16] S.A. Gokuglu, J. Electrochem. Soc. 135 (6) (1988) 1562. [17] D. Zhu, Y. Sahai, Met. Trans. 22B (1991) 309. [18] D.E. Rosner, J. Collins, MRS Symp. Proc. 168 (1990) 43. [19] H. Schafer, in: J.M. Blocher Jr., H.E. Hintermann, L.H. Hall (Eds.), Proc. 5th Int. Conf. CVD, The Electrochemical Society, Pennington, NJ, 1975. [20] R.J. Kee, F.M. Rupley, E. Meeks, J.A. Miller, Chemkin-III: a Fortran Chemical Kinetics Package for the Analysis of Gas Phase and Plasma, Sandia Report SAND96-8216, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, 1996. [21] M.E. Coltrin, R.J. Kee, F.M. Rupley, E. Meeks, Surface Chemkin-III: a Fortran Package for Analysing Heterogeneous Chemical Kinetics at a Solid Surface-Gas Phase Interface, Sandia Report SAND96-8217, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, 1996. [22] R.J. Kee, J.A. Miller, A Structured Approach to the Computational Modeling of Kinetic and Molecular Transport in Flowing Systems, Sandia Report 88-41, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, 1988. [23] M.E. Coltrin, R.J. Kee, F.M. Rupley, Inst. J. Chem. Kin. 23 (1991) 1111. [24] M.D. Allendorf, R.J. Kee, J. Electrochem. Soc. 138 (1991) 841. [25] A. Ern, V. Giovangigli, EGLIB, a Multicomponent Transport Software for Fast and Accurate Evaluation Algorithm, CERMICS-ENPC, 93167 Noisy-le-Grand cedex, France, 1999 http://blanche.polytechnique.fr/www.eglib.
[26] C. Vahlas, G. Baret, J.F. Million- Brodaz, C. Bernard, R. Madar, in: R. Porat (Ed.), Proc. 6th Euro. Conf. CVD, 1987, p. 255. [27] S.L. Zhang, R. Buchta, Y.F. Wang, E. Niemi, J.T. Wange, C.S. Peterson, in: G.W. Cullen (Ed.), 10th Int. Conf. Chemical Vapor Deposition, Vol. 87-8, The Electrochemical Society, Pennington, NJ, 1987, p. 135. [28] N. Thomas, P. Suryanarayana, E. Blanquet, C. Vahlas, R. Madar, C. Bernard, J. Electrochem. Soc. 140 (1993) 475. [29] M.E. Coltrin, R.J. Kee, J.A. Miller, J. Electrochem. Soc. 133 (1986) 206. [30] C. Vahlas, P.Y. Chevalier, E. Blanquet, Calphad 13 (1989) 273. [31] E. Blanquet, Ph.D Thesis, Institut National Polytechnique de Grenoble, France, 1990. [32] E. Mastromatteo, Ph.D Thesis, Institut National Polytechnique de Grenoble, France, 1991. [33] M.-A. Nicolet, Appl. Surf. Sci. 91 (1995) 112. [34] E. Blanquet, A.M. Dutron, V. Ghetta, C. Bernard, R. Madar, Microelec. Eng. 37/38 (1997) 189. [35] E. Blanquet, A.M. Dutron, C. Bernard, G. Llauro, R. Hillel, in: M.D. Allendorf, C. Bernard (Eds.), Chemical Vapor Deposition, Proc. 14th Int. Conf., Vol. 97-25, The Electrochemical Society, Pennington, NJ, 1997, p. 23. [36] R. Madar, C. Bernard, J. Vac. Sci. Technol. A 8 (1990) 1413. [37] M. Pons, J.N. Barbier, C. Bernard, R. Madar, Appl. Surf. Sci. 73 (1993) 71. [38] A. Bouteville, J.C. Remy, C. Attuyt, J. Electrochem. Soc. 138 (8) (1992) 2260. [39] J. Mercier, J.L. Regolini, D. Bensahel, J. Electron. Mater. 19 (1990) 253. [40] J.L. Regolini, E. Mastromatteo, M. Gauneau, et al., Appl. Surf. Sci. 53 (1991) 18.
Combined thermodynamic and mass transport modeling for material processing from the vapor phase Michel Pons a,*, Claude Bernard a, Elisabeth Blanquet a, Roland Madar b a
Laboratoire de Thermodynamique et Physicochimie MeÂtallurgiques, UMR CNRS/INPG/UJF 5614, Institut National Polytechnique de Grenoble, 1130 rue de la Piscine, B.P. 75, 38402 Saint Martin D'Heres, France b Laboratoire de MateÂriaux et de GeÂnie Physique, UMR CNRS/INPG 5628±ENSPG, Institut National Polytechnique de Grenoble, B.P. 46, 38402 Saint Martin D'Heres, France
Abstract The computational modeling of vapor phase processes like CVD involves different routes. For complex chemical systems, thermodynamic analysis can be ®rst performed. Three examples on the CVD of refractory metal disilicides and ternary silicides show the process guidelines which can be obtained from an a priori thermodynamic analysis even in feature scale technology. However, it is a static analysis. Linking the thermodynamic approach with mass transport modeling allows the description of the dynamic chemical system in local thermochemical equilibrium (LTCE). Two examples on the deposition of titanium silicide and silicon-germanium alloys illustrate the framework provided by this approach keeping in mind the assumptions that underlie the computations. Thermodynamic and LTCE transport modeling are to be seen as an a priori computational methods based on the access of only thermodynamic and transport database. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Vapor phase process; Thermodynamic analysis; Local thermochemical equilibrium
1. Introduction The computational modeling of vapor phase processes such as CVD (chemical vapor deposition) have become valuable tools to optimize processes manufacturing to yield improved products [1±5], requiring the knowledge of accurate thermochemical, kinetic and transport data to be reactor design predictive. For complex, advanced or prospective chemical systems, thermodynamic analysis is a modeling route to obtain information on chemistry. At ®xed temperature and pressure (or volume), it is possible to obtain the equilibrium history of the gas phase and of the deposited phases for `in®nite' time or length. `CVD phase diagrams' are used to display solid equilibrium phases as a function of temperature, pressure and feed gas composition [6±12]. This a priori thermodynamic approach permits the assessment of the experimental method (choice of gas precursors, phases likely to be formed from the initial gas phase but also by reaction with the substrate and furnace walls). The predictive capability of this equilibrium analysis is illustrated for different deposition systems involving complex solid phases. To manage this modeling approach, * Corresponding author. Tel.: 1 33-4-7682-6532; fax: 1 33-4-76826677. E-mail address: [email protected] (M. Pons)
software packages solving Gibbs energy minimization and databases are needed. Generally, the data are obtained from combined experimental and theoretical studies. Nowadays, specialists of gas-phase measurements are few and a quantum chemistry approach is more and more used for thermodynamic data evaluation [14,15]. However, this method is a static approach. It is not expected to yield the equilibrium state corresponding to the temperature, the pressure and the concentrations actually established at the solid±gas interface. A dynamic approach using mass transport modeling within the entire reactor could provide considerable insight on the controlling phenomena. Whereas hydrodynamic models are generally applicable, a separate chemical model, stating the relevant homogeneous and heterogeneous reaction pathways and rate constants must be speci®ed for each CVD process. The lack of detailed kinetic data and models for complex chemical systems seems to be the most important limitation in CVD modeling. Thermodynamic and hydrodynamic phenomena in CVD systems are based on rather well-established theory and on data which are available or which can be estimated in a few cases. The linking of thermodynamic databases, local thermochemical equilibrium (LTCE) and mass transport calculations could offer a possible modeling route [10±13,16±18]. The advantages of this coupled
0040-6090/00/$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S00 40-6090(99)0105 2-4
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approach is that, for a large variety of CVD systems, reliable data are available. The main drawback is that the relevant models are restricted to local equilibrium conditions. However, although CVD is not an equilibrium process, local equilibrium analysis coupled with modeling of transport processes is of interest because it may be the only available approach for complex multicomponent chemical systems and is the most favored in a transport-limited regime. This method is able to predict the concentration ®elds and the composition of the solid ®lm from the knowledge of only databases, taking into account the geometry of the reactor and species balances. A general procedure for implementing species balances and equilibrium conditions will be shown. The thermodynamic calculations are included in the mass transport computation as source terms for the equilibrium in the gas phase and boundary conditions for the equilibrium at the gas±solid interface. The use of modeling in obtaining more realistic ¯ow and thermal ®elds inside complex reactors has provided impressive assistance to CVD equipment manufacturers. The proposed thermodynamic and local thermodynamic equilibrium coupled with mass transport approaches allow progression in the complexity of the predictive assistance, keeping in mind the assumptions that underlie the computations. The information which can be derived from this modeling approach will be illustrated. Finally, mixed kinetic and thermodynamic databases and transport computations can be processed to more closely examine the actual deposition phenomena in the light of new experimental and theoretical data. This last approach is beyond the scope of this paper, but is being used by the authors for the simulation of single crystal SiC growth for high-temperature electronics [13]. This paper gives an overview on thermodynamic modeling in Section 2 and on the LTCE linked with mass transport modeling in Section 3. For the ®rst part, we have selected three examples. The ®rst two will show the process guidelines which can be obtained in complex solid systems. The third one will show that thermodynamic modeling can help feature scale technology. For the LTCE-mass transport modeling, we have selected two examples. The ®rst one, involving complex deposited phases, will show the shifts in the phase diagrams due to transport phenomena. The second one will show, in a complex gaseous system, the in¯uence of transport phenomena on the equilibrium predictions.
2. Thermodynamic modeling 2.1. An introduction to thermodynamics and computations During recent years, CVD methods have been increasingly utilized for various applications. However, for each new application, they are in competition with other deposition processes. Ef®cient usage of CVD systems requires
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optimization of all process parameters. This leads to increasing enquiries in modeling. Historically, the ®rst modeling approach was a thermodynamic one. It was prompted by the transport approach developed by Schafer [19] in sealed tubes. Then, computer science made the method of minimization of the total Gibbs energy of the chemical system straightforward [6±8]. With this method, assuming that equilibrium is reached, it is possible to compute the composition of the gas phase and the nature of the condensed phases for a predetermined set of experimental parameters, total pressure, partial pressures of the gas precursors and temperature. This approach is based on the availability of a consistent and complete set of thermodynamic data related to all species likely to be involved in the deposition reactions. The perpetual increase of the computation power has moved the limitations of this approach. They are rather related to the availability of data than to the complexity associated with a great number of species. The thermodynamic databases, though still strongly incomplete, have been decisively updated in the last 10 years. Ab initio computations have complemented direct measurements which are unfortunately less and less determined. Parallel to the databases upgrade, software packages have been developed and linked. In terms of the leading concerns of their developers, these sets, databases and software packages, are more or less suitable for CVD problems. They are available either on-line or as packages for personal computers. In Europe, the members of the Scienti®c Group Thermodata Europe (SGTE; B.P. 166, 38402 Saint Martin D'HeÁres, France) have built a common database for substances and another for solutions. They have in their possession software packages suitable for computations of complex equilibria. For computations involving reactive gaseous phases for CVD problems, the database Coach (4200 substances) linked to the Gemini minimization code (Thermodata/INPG/CNRS, B.P. 166, 38402 Saint Martin D'HeÁres, France; http://www.cpma.u-psud.fr/therma/thermafr.html) is the most suitable. Chemsage software (G.T.T., Kaiser Strasse 100, D-52134 Herzogenrath, Germany; http://gttserv.lth.rwth-aachen.de/) is linked to the SGTE database and encloses special ®les for metastable coatings like AlON. Other software is more especially involved in phase diagram computations rather for metallurgical problems. MTDATA (N.P.L., Queens Road, Teddington, Middlesex TW11 OLW, UK; http:// www.npl.co.uk/) and Thermocalc (Royal Institute of Technology, S-10044 Stockholm, Sweden; http:// www.met.kth.se/tc/) software linked with the SGTE databank have to be mentioned. For problems involving salts or oxides, the FACT system (Centre de Recherches en Calcul Thermodynamique, Ecole Polytechnique de Montreal, Quebec, Canada H3C 3A7; http://www.crct.polymtl.ca/ fact/fact.htm) is the most suitable. The future in the CVD modeling ®eld belongs to software integrating thermodynamic databases but also transport and kinetic databases
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to meet the global complexity of the CVD process. The Chemkin software package ([20,21]; Chemkin-III: Reaction Design, 11436 Sorrento Valley Road, San Diego, CA 92121, USA; www.ReactionDesign.com, e-mail [email protected]) is one well known example of this kind of integration for combustion problems [22] and is widely used for CVD modeling [23,24]. The EGLIB library has to be quoted as a powerful tool for transport properties calculations [25]. More information on fully integrated thermodynamic databases and software packages with extensive equilibria and phase diagram capabilities, and miscellaneous links, can be found on the Web server http:// www.crct.polymtl.ca/fact/websiter.htm#Commercial Packages. 2.2. Examples Three independent examples are proposed to illustrate the use of an a priori thermodynamic analysis for the selection of the following parameters: ² Nature of the reactants, W±Si system ² Material to be deposited for a speci®c application, W±Si/ Ti±Si and MSiN systems (M is a metal) ² Range of experimental parameters, MSiN system (M is a metal) ² The effect of the nature of the substrate, selective deposition of Ti±Si The cases of blanket and selective deposition of refractory silicides were explored some years ago. 2.2.1. Low-pressure CVD of M±Si (M Ti, W) During the last decades, the improvement of the performance of integrated circuits and the trends towards higher level of integration (ULSI) have resulted in the investigation of refractory metal silicides such as TiSi2, WSi2. They have been selected for use as gates and interconnections due to their relatively low resistivity and high thermal stability. These silicides are compatible with most integrated circuit processing, offering good dry etch, adhesion, oxidation and contact properties. For the processing of silicides thin ®lms for submicronic devices, CVD techniques have been generally adopted. However, one of the main dif®culties concerns the appropriate selection of the gaseous precursors of the silicon and metal. In the case of WSi2 ®lms, while silane SiH4 is largely accepted as the most common silicon precursor, different possibilities exist to transport the tungsten in the CVD reactor. Tungsten hexa¯uoride has been commonly used since this compound is liquid at room temperature and has suf®cient vapor pressure to ¯ow directly into the reactor. But in the CVD tungsten silicide ®lm process using WF6 and SiH4, an additional annealing treatment is required to improve the ®lm stoichiometry and crystallinity. As shown in the CVD phase diagram presented in Fig. 1, the formation of pure WSi2 is thermodynamically possible only in a very narrow reactant gas-phase composi-
Fig. 1. W±Si system. CVD phase diagram calculated as a function of SiH4 and WF6 partial pressures, Pt 105 Pa, T 1000 K, PAr 9 £ 104 Pa.
tion range. The substitution of tungsten chlorides for tungsten ¯uorides allows better control over the WSi2 ®lm stoichiometry [26,27]. Using WCl6 or WCl4 as tungsten source, a non-negligible domain of pure WSi2 deposition is observed in the corresponding phase diagrams (Figs.2,3). Although tungsten chlorides are solid at room temperature and therefore more dif®cult to use in a CVD process, the deposition of pure crystallized WSi2 have been obtained starting from WCl4 and SiH4 in agreement with the conditions given in the corresponding CVD diagram (point B) [28]. The shape of the CVD phase diagram is speci®c to the investigated system. For instance, it has been observed that the deposition of pure TiSi2 is much more favored than the WSi2 deposition (Fig. 4) which makes TiSi2 much more convenient to obtain by CVD.
Fig. 2. W±Si system. CVD phase diagram calculated as a function of SiH4 and WCl6 partial pressures, Pt 105 Pa, T 1000 K, PAr 9 £ 104 Pa.
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Fig. 3. W±Si system. CVD phase diagram calculated as a function of SiH4 and WCl4 partial pressures, Pt 133 Pa, T 873 K, PAr 120 Pa, A-E points correspond to simulated deposition conditions.
The data used were provided by the SGTE databank, from literature data [29] and from simultaneous optimization of experimental data and theoretical calculations for the metal silicides [30±32]. The substances included in the thermodynamic calculations and sources of thermochemical data can be found in Refs. [31,32]. 2.2.2. Low-pressure CVD of M±Si±N (M Ta, Ti, W, Re) for diffusion barriers in advanced copper metallization Since the beginning of the 1990s, ternary amorphous
Fig. 4. Ti±Si system., CVD phase diagram calculated as a function of SiH4 and TiCl4 partial pressures, Pt 330 Pa, T 1100 K.
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metallic thin ®lms made of a transition metal, one non metal (Si or B) component and nitrogen such as TaSiN, TiSiN, WSiN have been explored for use as diffusion barriers between copper overlayer and oxidized silicon substrates ([33] and references therein). The majority of the ®lms have been processed by PVD. LPCVD of ternary silicides diffusion barriers on SiO2/Si substrates, starting from silane, in situ fabricated metal chlorides, ammonia, hydrogen and argon has been investigated as potential ®lms [34]. The resulting chemical systems, M±Si±N±H±Cl±Ar, are complex. Thermodynamic investigation allowed to classify the four ternary materials into two categories according to the thermodynamic stability of the metal nitrides: the group of metals (W, Re) which do not form a stable metal nitride and the group of metals (Ti, Ta) which form stable metal nitride, in the operating temperatures and pressures ranges. The ternary phase diagram W±Si±N (Fig. 5) established at 773 K looks like the Re±Si±N one. Three equilibria between Si3N4 and M, M5Si3, MSi2 (M W, Re) are calculated. The ternary phase diagram Ti±Si±N was established considering the solubility of nitrogen in the Ti5Si3 phase (Fig. 6) [35]. In the investigated temperature and pressure ranges, the Ta±Si±N isothermal sections are similar to the Ti±Si±N ones (with the tantalum silicides in equilibrium with TaN). The simulations of metal chlorination and deposition process provided the possible range of operating conditions leading to compositions located in the different stability domains. The conditions which lead to the compositions of the highest performances PVD ®lms were taken as starting points. A correlation between the stability of the metal nitride and the thermal behaviour (crystallization temperature and nature of the crystallized phase) was found. In the W±Re group, the deposited ®lms which were `XRD amorphous' appear as nanocomposites of small grains of Re or unstable W2N and W inserted in a Si±N matrix while, in the Ti±Ta
Fig. 5. Ternary phase diagram W±Si±N calculated at 773 K with simulated deposition conditions and experimental composition.
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Fig. 6. Ternary phase diagram Ti±Si±N calculated at 773 K considering nitrogen solubility in Ti5Si3, with simulated deposition conditions and experimental composition.
group, whatever experimental conditions, the ®lms were mostly composed of crystallized TaN or TiN. When comparing the deposited phase analysis results (RBS and XRD) [34] and the simulated compositions for the same operating conditions, a rather good agreement was found for W±Si±N (Fig. 5), Ti±Si±N (Fig. 6) and Re±Si±N. For the Ta±Si±N system, even if the nature of the deposited phases is in agreement with the predicted ones, the compositions are quite different. These discrepancies can be explained by different factors such as the formation of an amorphous or nanocrystalline material while all data were determined for crystallized materials, the non-equilibrium situation and the uncertainties in some thermodynamic data (tantalum nitride compounds). It was demonstrated that WSiN and TiSiN ®lms are the most promising materials for diffusion barriers for copper metallization. Despite their difference, their morphology ensures a good compromise between resistivity and barrier performance which can be adjusted by the ®lm composition. These results show that thermodynamic modeling of the deposited phases from initial composition of the gas phase, i.e. experimental raw parameters, can give guidelines but also a preliminary range of experimental parameters to process thin ®lms of desired composition. New experimental directions and thermodynamic analysis including the interactions with copper can be proposed as well as new modeling routes involving heat and mass transfers. 2.2.3. Ti±Si system and deposition selectivity [8,36] The results reported in the previous section concern the deposition of blanket material. Silicides such as TiSi2 can be used as contact for the source and drain in addition to the gate. One solution, which is referred to as the salicide process, in which the metal deposited by evaporation or sputtering is reacted onto a Si/SiO2 patterned wafer to form the metal silicide only on the bare silicon surface. However, this process implies the consumption of the underlying silicon and thus is not compatible with the fabri-
cation of very shallow junctions. The selective deposition by CVD of TiSi2 has been implemented using TiCl4, SiH4 diluted in H2 as starting gas mixtures. This process is by itself highly selective. It is necessary to remove the native silicon oxide. Three main solutions have been used to etch it. The ®rst is the classical etching by reacting the substrate with a gas mixture of H2/HCl at 1373 K or pure H2 at 1273 K at low pressure. The second is based on the formation of volatile SiO using a low-pressure silane gas (1 mTorr) at low temperature (1073±1150 K). Thermodynamic modeling can be used to explain these results (Fig. 7). In the very lowpressure CVD process, the polysilicon ®rst deposited is simply consumed to remove the native oxide. This is why the deposition time of this polysilicon layer is so critical for the successful implementation of this selective process. The third solution is based on the in situ etching of the native oxide by an appropriate choice of partial pressure of the reactive mixture. This solution is of technological importance because it uses the same gases as for the deposition process. To obtain the possible experimental range, SiO pressures over SiO2 have been calculated at equilibrium in the Ti±Cl±Si±H±Ar±O system. The main results of these calculations concerning the oxygen-bearing molecules in the gas phase, represented in Fig. 8, indicate etching of the native oxide in the form of SiO. The etching trends re¯ect the variation in silicon activity in the condensed state, which reaches a maximum value for the TiSi2 1 Si deposition domain. This has been con®rmed experimentally in the authors' APCVD reactor by the successful deposition of TiSi2 for conditions close to those predicted by these calculations. Once the native oxide has been removed, the vapor phase reacts with an Si/SiO2 surface. Thermodynamic equilibrium
Fig. 7. Calculated SiO partial pressure as a function of total pressure at 973 K for the following conditions: excess of SiO2, initial values of SiH4 0:73 mol, H2 0:105 mol, Ar 0:165 mol.
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This example clearly shows that thermodynamic modeling can help feature scale technology. 2.2.4. Conclusions From these examples, it should be emphasized that thermodynamic analysis of deposited solid phases is a possible modeling route. The CVD phase diagrams map the experimental parameters that will produce equilibrium deposition of a phase or phases of interest. They provide a broad overview of the experimental parameter space in which the desired phase(s) can be deposited. However, possible deviations between calculated and experimental deposition are to be expected. Even if the resulting predictions may be qualitative in nature, they can give guidelines to limit the range of conditions for deposition, or correctly give the trends in deposition behaviour with changing experimental parameters. Fig. 8. Calculated SiO partial pressure as a function of the partial pressure of SiH4 in the Ti±Cl±Si±Ar±H±O system for the following conditions; T 1200 K, total pressure 10 5 Pa, partial pressure of Ar 9 £ 104 Pa, partial pressure of TiCl4 2 £ 102 Pa, partial pressure of H2 98 £ 102 Pa.
calculations performed in the TiSi2 domain show that the introduction of the silicon substrate induces competition between the silicon from the gas phase (SiH4) and the substrate for the formation of TiSi2 and the gaseous silicon-bearing molecules (Fig. 9). This result indicates that, in the deposition domain, the silicon substrate participates in the formation of the TiSi2 layer, while there is almost no chemical interaction with the SiO2 parts of the substrate. This implies automatically some silicon consumption during the growth process which is almost independent of the etching procedure. This statement is in agreement with the ®ndings of most of the works reported on this subject.
Fig. 9. Partial pressure of gaseous silicon bearing molecules as a function of the nature of the substrate at equilibrium: T 1200 K, total pressure 10 5 Pa, partial pressure of Ar 9 £ 104 Pa, partial pressure of TiCl4 2 £ 102 Pa, partial pressure of SiH4 4 £ 102 Pa, partial pressure of H2 94 £ 102 Pa.
3. Combined thermodynamics (LTCE) and mass transport When the thermodynamic analysis is completed, it is possible to move toward reactor design by linking thermodynamic modeling and databases with mass transport modeling [10±13]. This method is used to predict the composition of the solid ®lm from the knowledge of the gas-phase composition taking into account the geometry of the reactor and species balances. Zhu and coworkers [17] have already employed the local equilibrium concept together with the ¯ux balance principle to determine the concentration of the species on the substrate and the rate of deposition of silicon from SiCl4 and H2. They have used thermochemical calculations to obtain the boundary conditions on the substrate, i.e., the partial pressures of various species in local equilibrium at the substrate. A general procedure for implementing species balances and equilibrium conditions may be different. As will be shown, the thermodynamic calculations are included in the mass transport computation as source terms for the equilibrium in the gas-phase and boundary conditions for the equilibrium at the gas-solid interface. Rosner and coworkers [18] have built `transport-shifted' CVD phase diagrams which are generated by using both feed gas and mass-transfercorrected wall element fractions. They have shown that chemical segregation in mass-transfer-controlled CVD systems can produce important shifts in phase boundaries of equilibrium deposits in CVD phase diagrams. Gokoglu [16] has shown the implications of the predictions of local thermodynamic equilibrium coupled with mass transport in boundary layers for Na2SO4 deposition from combustion product gases on turbine blades. 3.1. The local thermochemical equilibrium (LTCE) concept Table 1 describes the transport equations. More details can be found in Refs. [1±4].
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Table 1 Multicomponent transport equations 7: JCi 1 JFi 1 JTi Si ; i 1¼N 1
Transport Eq. (1): Si is the source term of species i
JCi rvvi ; i 1¼N
Convection Eq. (2): r; v; vi are density, velocity and mass fraction of i Fickian diffusion Eq. (3): Dij are the multicomponent diffusion coef®cients
JFi 2
N X j1
JTi 2DTi
2
rDij 7vj ; i 1¼N
3
7T ; I 1¼N T
4
Thermo-diffusion Eq. (4): DTi is the thermodiffusion coef®cient of species i
The multicomponent diffusion (Eq. (3)) is de®ned by generalizing the binary diffusion to a N-component system. The relations between multicomponent diffusion coef®cients Dij and the binary values come from matrix calculations [25]. The last term of Eq. (1), Si , represents the rate of creation or depletion of i species by homogeneous chemical reaction and must be calculated by the near LTCE concept. From a guessed concentration ®eld (vi , i 1¼N), Gibbs energy minimization at each grid point of the reactor gives a new set of vieq ; the near-equilibrium sources terms Sieq can be obtained from 0
Sieq
1 7T A 7@rvvieq 2 rDij 7vjeq 2 DTi T j1 N X
5
i 1¼N. The sources terms Sieq cannot be directly inserted to continue the iterative modeling and to compute a new set of vi from Sieq guessed ®eld. The constraints associated with LTCE and mass transport analysis are different. LTCE calculations assume elements and mass conservation in a closed chemical system (the stoichiometry of the reactions is respected). Mass transport calculation only assumes mass conservation in an open chemical system. It is necessary, to import the data of LTCE calculation into Eq. (1), to ®nd the intersection between the two spaces of solutions. Projective methods are used to calculate Si for iteration n 1 1 from Sieq calculated by Eq. (5) from vi and vieq calculated at iteration n (PROJ is the projection operator) h i Si iter:n 1 1 PROJ Sieq iter:n
6
The vector S must be orthogonal to the matrix A of the stoichiometric coef®cients de®ned by E rows and N columns; E is the number of element and N the number of gaseous species. The mass transport-LTCE model that is to be solved is 0 Si 7:@rvvi 2
N X j1
rDij 7vj 2
DTi
1 7T A T
7
where i 1¼N; minimization of G(P,T,v i,v N) at each grid point S [ h Ai' . The iterative procedure for homogeneous phenomena is stopped when vi 7 ! vieq , e.g. when near LTCE is reached at each grid point of the reactor. The common rules were used to calculate the transport properties of the gas mixture as a function of pressure, temperature and concentrations [3]. The boundary conditions on the substrate, the mass ¯uxes, Rgi , are linked with thermodynamic heterogeneous equilibrium. This boundary condition leads to a complex situation. Unlike the model allowing the calculation of source terms by minimization and subsequent transformation, there is not conservation of the mass on the reactive substrate but M 2 1 relations between gas and associated solid ¯uxes due to the conservation of the elements (M is the number of solids which could appear). The matrix A is now de®ned by E rows and N 1 M columns. If B is the matrix de®ned by the conservation of the ®lm composition, the boundary condition on the substrate is Rgi n: JCi 1 JFi 1 JTi
8
i 1¼N; minimization of G(P,T,v i,v N) at each grid point Rg [ h Ai' >hBi.The Rg vector at iteration n 1 1 is obtained by projection of the Rgeq vector on the h Ai' >hBi space. The Rgeq vector is computed from a guessed equilibrium concentration ®eld on the substrate at iteration n. The Eqs. (1)±(4) associated with boundary conditions and constraints described in Eqs. (5)±(8) are iteratively solved by ®nite element and minimization methods. Flux-Expert (Simulog, 1 rue James Joule, 78286 Guyancourt, France) and Melange (LTPCM, B.P. 75, 38402 Saint Martin D'HeÁres, France) software packages were customized. Two examples are presented to illustrate the LTCE concept. They will show the effects of transport phenomena on the predicted deposition products. 3.2. Ti±Si system [10,37] For the deposition of TiSi2 on silicon in horizontal reactors, experimental results have shown that the consumption of the substrate is directly related to the SiH4/TiCl4 ratio. However, for high SiH4/TiCl4 ratios, the silicon provided by SiH4 pyrolysis is in excess and codeposition of TiSi2 1 Si occurs, with a subsequent loss of selectivity. The overall consumption, leading to gas-phase depletion along the substrate, may induce the deposition of different silicides. In addition, when large substrates are used, the thickness and the composition of the coating are not uniform and are largely in¯uenced by the gas distributors [7,38±40]. A typical Ti±Si CVD phase diagram starting from TiCl4 and SiH4 is given in Fig. 4. Fig. 10 represents a horizontal reactor which is widely used in CVD research and development. Gas enters through a distributor or diffuser and ¯ows over the substrate. The opposing wall is water-cooled to provide a more uniform
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Fig. 10. Schematic representation of the cold-wall horizontal reactor (dimensions are in meters); and the calculated velocity ®eld: (Q 2 SLM of H2±4 vol.% SiH4±1 vol.% TiCl4).
pro®le in the reactor. Horizontal reactors have been thoroughly analyzed by analytical and numerical models ([2] and references therein). Details on the velocity and thermal ®elds can be found in a previous work [11]. Assumptions have been made for the reactive mass transport model. In the gas phase, no dissociation of inlet reactive species has been assumed. From homogeneous thermochemical equilibrium calculations, the intermediate and product species in small amounts have been neglected. With these assumptions, the mass transport modeling involves ®ve species, SiH4, TiCl4, SiCl4, HCl and H2. It was checked that these simpli®cations are reasonable simulations of the more complex system resulting from a complete data set. In addition, the substrate has been assumed chemically inactive, i.e., silicon diffusion from the bulk and subsequent enrichment of the coating is neglected. Particular attention must be paid to the diffusion ¯ux boundary conditions on the reactive substrate because they de®ne the coupled mass transport/local thermodynamic equilibrium (LTCE) approach considering the gas-phase simpli®cations. The boundary conditions at the substrate are prescribed by the LTCE. LTCE iteratively modi®es the species ¯uxes at the substrate to obtain `equilibrium ¯uxes'. The iterative procedure is stopped when diffusion ¯uxes at the substrate remains constant (about 20 iterations in standard cases) i.e., the overall system has reached thermodynamic equilibrium. The `elemental' ¯uxes obtained after convergence are consistent with LTCE predicted deposit composition. As we have pointed out previously, the general trend revealed by experimental results is the in¯uence of the SiH4/TiCl4 ratio on the properties, selectivity, uniformity and composition of the coating. So, ®ve compositions have been selected (Fig. 11). The thermodynamic equilibrium calculations performed from inlet gas-phase compositions determine the chemical nature of the deposit assuming ®xed temperature and pressure. The modi®cations
due to reactive transport are now shown. Fig. 8 shows the actual molar fractions of Si-containing and Ti-containing gaseous species over the substrate leading to equilibrium deposition; they are inserted in the CVD phase diagram. Along the substrate, the coupled approach clearly shows that it is possible to cross phase boundary lines due to the overall depletion, the transport of reactive species, the variations of the mass ¯uxes on the substrate and the presence of product gases. From the leading edge of the substrate the Sicontaining and Ti-containing gaseous species concentrations decrease, then the Si-containing gaseous species depletion increases more rapidly than that of the Ti-containing gaseous species. Near the trailing edge both concentra-
Fig. 11. (a) Actual composition of Si- and Ti-containing gaseous species over the substrate inserted in the CVD phase diagram; (b) zoom of the 4:1 composition showing the phase change along the substrate. These results are only valid for the studied geometry.
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tions increase due to axial diffusion of reactant gas against the ¯ow. Experimentally, similar variations of the Si/Ti ratio have been observed by resistivity measurements. Unfortunately and contrary to CVD phase diagrams, these results are only valid for the geometry studied. The observed shifts are weaker for axisymmetric and vertical reactors. It is well known that, for this reactor con®guration, the reactive ¯ux variations are of less importance and lead to ®lms more uniform in composition and thickness [1±3]. Generally, it should be noted that the predicted deposition rate are too high compared with experiments. This is mainly due to the fact that the process is controlled by kinetics rather than by reactive transport. The coupled approach is limited to equilibrium conditions but gives information on the relations between reactor geometry and coating nature and uniformity as well as on the complex chemical heterogeneous and homogeneous reactions based on well established theory and reliable data. 3.3. Si±Ge system [11,12] Though the processing of silicon-germanium alloys Si12xGex at high temperature is somewhat removed from the microelectronics industry, this example is presented to show the potential of the coupled approach to manage the stoichiometry of the deposited ®lm. The thermodynamic equilibrium study in the Si±Ge±H± Cl system showed that the germanium fraction in the deposit, XGe (XGe nGe/(nGe 1 nSi)) decreases as the temperature or the chlorine quantity increases. The thermodynamic analysis gave the guidelines for the variations of the stoichiometry of the deposit. The coupled approach re®ned it by taking into account transport phenomena. The reactor is vertical, inverted and axisymmetric. The gas is admitted at the bottom of the reactor. The model predicts the ¯ow and temperature ®elds of the mixture and the concentration ®elds of the gaseous species. It also predicts the deposition rate and the stoichiometry of the deposited ®lm. Fig. 12 shows the calculated velocity and temperature ®elds inside the reactor when the substrate was set at 1300 K, the inlet mixture was Ar (89%)±H2 (10%)± SiH4(0.5%)±GeCl4(0.5%), e.g. YGe, which is the germanium fraction in the gas phase, equal to 0.5, the total ¯ow rate was 2 l/min and the pressure 315 Pa. The most important gaseous species contributing to the ®lm growth are, in equilibrium conditions, GeCl, GeH, Ge1, Si3, Si2, Si1 and SiH when argon is the carrier gas (Fig. 13). These results revealed strong dependence of gas-phase equilibrium composition with the distance to the substrate. Fig. 14 shows the deposition rate and the stoichiometry of the ®lm as a function of the radial position along the substrate for the experimental conditions described above. The ®lm stoichiometry, XGe, is uniform and is about 0.18 (Y Ge 0:5). Simple previous equilibrium calculations predicted a minor depletion in germanium, X Ge 0:25, for Y Ge 0:5. These results show that the high thermody-
Fig. 12. Velocity and temperature ®elds: T 1300 K; ¯ow rate 2 l/min.
namic stability of germanium chlorides, compared to that of silicon hydrides and chlorides, associated with the mass transport phenomena deplete the ®lm in germanium
Fig. 13. Gaseous mass fraction along the center line above the substrate. (1: H2; 2: GeH4; 3: SiH2Cl2; 4: SiHCl3; 5: SiH3Cl; 6: SiH4; 7: SiCl4; 8: GeH3; 9: GeH3Cl; 10: GeCl3; 11: Si2H6; 12: GeCl; 13: SiCl2; 14: Si3; 15: HCl; 16: GeH; 17: Ge(g); 18: SiH; 19: SiCl3; 20: SiH4).
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4. Conclusions When implementing a new CVD process, the wide range of parameters, geometry, gas precursors, temperature, etc., could discourage any modeling attempts. Despite the inherent dif®culties and the speci®c complexities of each CVD process, it seems that the thermodynamic approach could be ®rst performed to determine the engineering interest of the selected chemical system. Then, by assuming the absence of kinetics barriers, the use of near-local thermochemical equilibrium within the ¯owing system could provide useful information. This modeling route could provide an assessment of the experimental method and a framework into which a kinetic-mass transport model could ®t. It would narrow the range of variables which may be involved in causing undesirable effects (recirculation, inadequate gas ¯ow¼) and indicate the weak and strong dependencies between the different non-linear phenomena leading to deposition. Thermodynamic and LTCE-transport modeling are to be seen as a priori approaches. The deposition process is generally controlled by kinetic phenomena, so that the model gives the trends but not absolute engineering values. Once kinetic information is available, this already built framework can be updated and more realistic simulations can be performed. Acknowledgements The authors acknowledge the Centre National de la Recherche Scienti®que for the long-lasting ®nancial support and Eric Ramberg for reviewing the manuscript.
Fig. 14. Deposition rate (a) and stoichiometry (b) along the radius of the substrate.
compared to the inlet germanium content. Thermodiffusion plays an important role for the germanium containing species depletion of the gas phase near the substrate. Thermodiffusion causes heavier molecular weight species to be driven along a temperature gradient away from hot surfaces towards cold surfaces. The concentration of GeCl, the most important gaseous species containing germanium, near the substrate is ®ve times higher when thermodiffusion is neglected. The thermal diffusion rates can be modi®ed by changing the diluting gas. These results, assuming equilibrium conditions in a ¯owing system match the experimental measured ones at 1300 K. They should therefore be used for the identi®cation of the reaction pathways and the in¯uence of geometry, ¯ow rate and temperature gradients but perhaps not for predicting the chemical composition of the ®lm under actual operational conditions. It is well known that the residence time required for the system to reach its equilibrium composition is much larger than the residence time typically met in LPCVD.
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