high temperature silicon carbide chemical vapor ...

European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate, J. Périaux (Eds) © TU Delft, The Netherlands, 2006

HIGH TEMPERATURE SILICON CARBIDE CHEMICAL VAPOR DEPOSITION PROCESSES: FROM PURE THERMODYNAMIC TO MASS TRANSPORT MODELING Elisabeth Blanquet*, Didier Chaussendea, Shin-ichi Nishizawab and Michel Ponsc *LTPCM, INPG, CNRS, UJF 1130 rue de la piscine, BP 75, 38402 Saint Martin D’Hères France e-mail: [email protected] Web page: http://ltpcm.inpg.fr/ a

LMGP, INPG, CNRS 961 rue de la houille blanche, BP 46, 38402 Saint Martin D’Hères France e-mail: [email protected] b

National institute of Advanced Industrial Science and technology (AIST) 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 Japan e-mail: [email protected] c

LTPCM, INPG, CNRS, UJF 1130 rue de la piscine, BP 75, 38402 Saint Martin D’Hères France e-mail: [email protected]

Key words: Chemical Vapor Deposition, Modeling, Simulation, Silicon carbide growth Abstract. Over the last twenty years, processes which lead to materials synthesis from a gaseous phase constitute an important technology in many applications fields such as microelectronics or protective coating industry. Due to the complexity of the involved phenomena, computational modeling had been required to improve technological processes and help in designing new equipment. Predictive modeling approaches of transport phenomena and chemistry have been developed with increasing levels of complexity, from pure thermodynamic, kinetic descriptions of the chemistry to mass transport models. The example of SiC epitaxial thin films deposited by a high temperature chemical vapor deposition process illustrates the framework provided by these modeling approaches. This paper reviews some of the recent modeling studies from the authors’ research groups.

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

1 INTRODUCTION The objective of computational modeling for gaseous phase processes like CVD (Chemical Vapor Deposition) is to correlate the as-grown material quality (uniformity, growth rate, cristallinity, composition, …) to general parameters such as growth conditions, reactor geometry, as well as local parameters that are actual flow, thermal fields and chemical kinetics at the solid/gas interface. Modeling should shed lights into the underlying physicochemical processes of the system, that might not be available from experimental information. Gas phase synthesis involves a variety of interconnected phenomena: flow, turbulence, heat transfer, multicomponent mass transport, chemical phenomena (homogeneous and heterogeneous) and solid material growth 1, 2. Over the last twenty years, many studies 3-7 in the field of gaseous phase growth processes modeling have been carried out. These studies are based on one or several approaches among: fluid mechanics calculations associated to convective, conductive and radiative heat transfer, electromagnetic, thermodynamic equilibrium computations, kinetic computations, mass transport calculations linked with chemical kinetic data and/or local thermodynamic equilibrium. The modeling results (limiting phenomena, growth rates, uniformity, composition, doping are conditioned to the availability and accuracy of the corresponding databases (thermochemical properties, kinetic data, transport data). This article gives an overview on simulation of reactive flows in Chemical Vapor Deposition processes, illustrated with the example, from our groups’ research studies, of the high temperature growth of epitaxial silicon carbide films. 2 CVD MODELING AND SIMULATION 2.1 Thermodynamic Modeling Thermodynamic analysis is considered as the first step in any material science modeling methodology8. With the recent upgrade of thermodynamic databases, it could be the only rational route to obtain information on chemistry for a complex chemical system. At fixed pressure or volume and temperature, the equilibrium composition in the gaseous phase (homogeneous calculations) or at the solid/gas interface (heterogeneous calculations) can be obtained from the Free Energy minimization of the complex system. This a priori thermodynamic approach is a valuable tool for help in the experimental method: stability of the fabricated material, phases likely to be formed from the initial gas phase and from the reactions with the reactor walls and the substrate, composition of the gas phase, contribution of each gaseous species precursor to the deposition.

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

This approach which provides an upper limit (infinitely fast kinetics) of what is to be expected, should be used being aware of the underlying assumptions (static equilibrium conditions). 2.2 Kinetic Modeling The kinetic approach is based on the statement of the relevant homogeneous and heterogeneous reaction pathways and associated rate constants. In a closed system, for a given temperature, pressure and initial conditions, solving a set of reaction pathways equations gives the evolution of the species mole fractions as a function of time. Consequently, it allows to quantify each species reactivity as well as each reaction time. For “infinite” residence time, kinetics results should lead to the values obtained with thermodynamic equilibrium calculations. When the residence time in the reactor is low (low pressure processes for instance), the results obtained with the kinetic approach are closer to actual values than thermodynamic predictions. Unfortunately, for many systems, the lack of detailed kinetic schemes and associated rate constants is definitely an important limitation in process modeling. Few systems, such as deposition of Si from silane6, 9, have been extensively studied. In that case, the number of simultaneous gas phase and surface reactions that have to be taken into account, in a large range of typical CVD conditions, is close to 100. The use of mathematically reduced models10 or tractable global models11 in dynamic modeling is an alternative which had been successful in predicting growth rate under certain conditions. It is usual to separate the expressions of kinetic pathways and related kinetic constants in homogeneous and surface reactions. If k reversible reactions and N species are taken into account, the general form of the homogeneous reactions is : N

∑

k

ν ik' Ai ↔ −k

i =1

N

∑ν

'' ik

Ai

i=1, N

(1)

i =1

Ai represents here the different gaseous species, kk and k-k are the forward and reverse reaction of the kth reaction in the gas phase, ν ik' and ν ik'' are the stoechiometric coefficients for the specie i in the reaction k. The rate of production of the specie i is: K

ri = ∑ν ik ℜ k

i=1, N

(2)

k =1

with ν ik = ν ik'' −ν ik' and ℜ k is the reaction rate of the reaction k that may be obtained from:

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

N

ℜk = kk

∏ i =1

ν ik'

P ⎞ ⎛ ⎜ xi ⎟ ⎝ RT ⎠

N

−k − k

∏ i =1

ν ik' '

P ⎞ ⎛ ⎜ xi ⎟ ⎝ RT ⎠

(3)

The rate constants of forward reactions kk follow generally the Arrhenius law: ⎛ E ⎞ k k = Ak .T β exp⎜⎜ − k ⎟⎟ ⎝ RT ⎠ k

(4)

where Ak, βk and Ek are constants, specific to each reaction. The equilibrium constants K c are used to calculate the rate constants of reverse reactions. They can be found in classical thermodynamic databases, for instance 12, 13. k

k −k =

kk Kc

(5) k

Surface reactions are characterized by complicated reaction mechanisms including adsorption, dissociation, diffusion, island formation and desorption. To model the heterogeneous phenomena, the simplest approach is to calculate adsorption rates from the sticking probability of the gaseous species involved in the growth. In a more general form, using surface species, the molar production rate of the k-th specie, S& k , due to chemical reaction at the surface, is a complex non-linear function of the species mass-fractions. We consider a multi-step (with Nsteps steps) surface reaction of the following general form: Ng

Ns

Ng

Nb

Ns

Nb

∑ a′ A + ∑ b′ B (s) + ∑ c′ C (b) = ∑ a′′ A + ∑ b′′B (s) + ∑ c′′C (b) i =1

ij

i

i =1

ij

i

i =1

ij

i

i =1

ij

i

i =1

ij

i

i =1

ij

i

j = 1,2,..., N steps

(6)

where aij, bij, and cij are stoichiometric coefficients of gas, adsorbed, and solid bulk species, respectively. Ng, Ns, Nb are total numbers of gas-phase, adsorbed, and solid bulk species, respectively. For this kind of reaction, the surface reaction rate may be expressed as it can be found in the CFDACE user manual14 (equation 7). Ng N steps Ns Ns ⎡ Ng b′′ ⎤ aij′ bij′ a′′ & S k = ∑ σ kj ⎢k fj ∏ [A i ] w ∏ [B i (s)] − k rj ∏ [A i ] wij ∏ [B i (s)] ij ⎥ j =1 i =1 i =1 i =1 ⎣⎢ i =1 ⎦⎥

The different coefficients for each surface reaction should be estimated.

(7)

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

2.3 CVD Mass/Heat Transport Modeling

To access the dynamic nature of the gaseous deposition processes, further model refinement requires the incorporation of flow and thermal fields inside the reactor. Modeling these fields requires accurate descriptions of the interactions between radiation, conduction and convection both within and between the various phases. CVD reactor models consist of nonlinear, partial differential equations that represent the conservation of momentum, energy and individual species in the gas phase. The general derivation and form of these equations is given in standard references on transport phenomena. The gas flow is essentially subsonic and laminar. By neglecting compressibility, turbulence effects, the conservation equations for the transport of Nth species can be presented in the following vector form14: r r ∂ ( ρv ) = −∇.( ρv ²) + ∇τ − ∇p + ρg ∂t

r

r

2 3

(8)

r

τ = µ (∇v + (∇v ) t ) − µ (∇v ).I

(9)

r

Where I is the stress tensor, p, v are the pressure and the velocity vector of the gas mixture, respectively, ρ is the density, µ is the viscosity and g is the acceleration of gravity. ρ and µ properties are dependent on temperature. So equations (8) and (9) are strongly coupled to the energy balance (equation 10).

Cp

⎛ N DiT ∇xi r = −C p .∇.(ρvT ) + ∇.(λ∇T ) + ∇.(q rad ) + ∇.⎜ RT ∑ ⎜ i=1 M i xi ∂t ⎝

∂ρT

⎞ N Hi r N K g g ⎟+ ∑ ∇.J i − ∑ ∑ H iν ik ℜ k − ℜ −k ⎟ i=1M i i =1k =1 ⎠

(

)

(10)

In this equation, T is the temperature, Cp is the heat capacity and λ the thermal conductivity of the gas. For the specie i, xi is the molar fraction, Mi is the molar mass, DiT is r the thermal diffusion coefficient and Hi is the molar enthalpy. The diffusion flux J i , the stoichiometric coefficient, ν ik , and the homogeneous reaction rates, ℜ kg and ℜ −g k , are discussed below. Heat transfer by radiation (qrad) should not be neglected at high temperatures. The balance over the ith chemical species (i= 1..N) consists of contributions from diffusion, convection and loss/production of the species in K gas phase reactions.

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

v ∂ ( ρω i ) r = −∇.( ρω i v ) − ∇.J i + M i ∂t

∑ν (ℜ K

ik

g k

− ℜ −g k

)

k =1

i=1..N

(11)

where ωi and Mi represent the mass fraction and molecular weight of species i, respectively. r r The diffusion fluxes come from concentration ( J ic ) and temperature ( J iT ) gradients. r r r J i = J ic + J iT

i=1..N (12)

r ∇T J iT = − DiT T

i=1..N

N rc J i = −∑ ( ρDij )∇ω j

i=1..N

j =1

(13)

(14)

Dij is the matrix of multicomponent diffusion coefficients and DiT the multicomponent thermodiffusion coefficient. When there is an important dilution of species in the carrier gas, the diffusion flow can be described with a simpler law: r J ic = − ρDim ∇ω i

i=1..N

(15)

With

Dim

⎛ ⎜ = (1 − x i )⎜ ⎜ ⎜ ⎝

⎞ xi ⎟ ⎟ Dij ⎟ ⎟ ⎠

N

∑ j =1 j ≠i

i=1..N

(16)

Dim is the diffusion coefficient of the specie i in the gas mixture. Finally the description is completed by the ideal gas law. ρ=

PM RT

(17)

N

M =

∑x M i

i =1

i

(18)

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

M is the average molar mass of the mixture gas. The transport properties λ, µ, Dij, DiT , Cp are computed by the kinetic theory of gases. Special treatment of heat transfer in the solid phase has to be applied depending on the nature (resistive or inductive) of heating method. The case of inductive heating which is typically used for high temperature SiC CVD is described in15. 3 HIGH TEMPERATURE CVD GROWTH OF SILICON CARBIDE FILMS

Silicon carbide (SiC) possesses many favorable properties such as excellent physicochemical and electronic properties. Among them, a wide band gap and a high breakdown field make it interesting for a multitude of applications, from high temperature to high frequency and high power device16, 17. SiC device processing is conditioned to the fabrication of large area single crystal wafers with the lowest defect density associated to the deposition of epitaxial thin films which present good structural quality and controlled doping level18. The most common processes used to develop SiC thin films are the High Temperature Chemical Vapor Deposition (HTCVD) techniques from propane and silane, diluted in hydrogen, performed at high temperature (1600-2000°C) and reduced pressure (100 to 500 mbar) on off-axis single crystals19-21. Operations are separated in two steps, first an in situ etching step to prevent epitaxy-induced defects, then the deposition step. Different reactors configurations (hot-wall, cold-wall, vertical or horizontal) have been proposed by CVD equipment manufacturers. However, hot-wall reactors (figure 1) have proved their superiority with the addition of a rotating substrate to achieve reproducible processing of high quality homoepitaxial layers. Macroscopic modeling has given valuable information to understand the impact of some growth parameters and improve growth rate, thickness homogeneity and doping level (see for instance 15, 20, 22-29).

susceptor Inlet H2 SiH4 C3H8

Outlet

wafer

susceptor Figure 1: Schematic representation of the simplified geometry. The dimension of the wafer is around 50 mm, the length of the susceptor is 270 mm.

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

Recently, some work has been focused on the choice of the most appropriate chemical system, with deposition criteria such as the deposition yield, the C/Si ratio in the deposit, and technological criteria such as the ability to work at high temperature and simplicity to handle30. Another parameter which has been found to be one of the main parameters in this process for growth and doping features is the effective gas phase C/Si ratio on the growing SiC crystal surface29. Chlorine additions via chlorinated precursors (tetramethylsilane TMS (Si(CH3)4), methyltrichlorosilane MTS (H3SiCl3) and propane/silicon tetrachloride (C3H8/SiCl4)) are investigated to modify the chemistry31, 32. The further paragraphs present some modeling trends combined with experimental results obtained on HTCVD processes. Special emphasis is given to chemical related results. To carry out modeling, we have followed the different levels of complexity procedure described in the earlier paragraphs. 3.1 Chemical databases and kinetic model development

For thermodynamic data, we have used a coherent set of data from SGTE database12 and optimized data from mass spectrometry measurements for the gaseous species Si2C, SiC2, SiC and the condensed SiC phase33, 34. For kinetic data in the Si-C-H system, a great body of literature dealing with both theoretical and experimental kinetic results has been devoted to understanding chemistries relevant to the separate Si-H and C-H systems. From our previous work15, the chemistry set finally adopted for SiC deposition is a simplified version of the models reported in the literature23, completed with few reactions containing the species H3SiCH, H3SiCH3, SiCH2 and Si2C. These latter species have been found important in thermodynamic calculations and since they are likely to present higher surface reactivity than saturated species such as SiH4 and CH4, they may contribute significantly to the limiting surface reactivity mechanisms35. The homogeneous and heterogeneous chemical pathways shown in Tables 1 and 2 were proposed 15,29 with 17 gaseous species, 17 gas phase reactions and 15 surface reactions. Since experiments have demonstrated the occurrence of SiC etching by H2 during deposition36, two reactions (1,2) which correspond to this etching are included in the surface mechanism. More precisely, in order to describe the SiC surface polarity, two sets of surface data which separate the deposition on Si- terminated and C-terminated surfaces have also been proposed29.

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

Homogeneous Model Reactions 1. SiH4 ⇔ SiH2 + H2 2. Si2H6 ⇔ SiH2 + SiH4 3. SiH2 ⇔ Si + H2 4. 2H + H2 ⇔ 2H2 5. C3H8 ⇔ CH3 + C2H5 6. CH4 + H ⇔ CH3 + H2 7. C2H5 + H ⇔ 2CH3 8. 2CH3 ⇔ C2H6 9. C2H4 + H ⇔ C2H5 10. C2H4 ⇔ C2H2 + H2 11. H3SiCH3 ⇔ SiH2 + H2 12. H3SiCH3 ⇔ HSiCH3 + H2 13. Si2 ⇔ 2Si 14. Si2 + CH4 ⇔ Si2C + 2H2 15. SiH2 + Si ⇔ Si2 + H2 16. CH3 + Si ⇔ SiCH2 + H 17. SiCH2 + SiH2 ⇔ Si2C + 2H2

A 6.671x1029 3.240x1029 1.060x1014 9.200x1016 1.698x1016 2.200x104 1.000x1014 9.030x1016 2.210x1013 1.500x1015 2.000x1014 1.000x1014 1.000x1015 3.011x1015 1.500x1014 1.390x1012 1.000x1015

β -4.795 -4.24 -0.88 -0.6 0 3 0 -1.18 0 0 0 0 0 0 0 0.5 0

E/R 31946 29202 22657 0 42715 4406 13350 330 1040 41467 36413 32033 37460 10000 0 0 0

Table 1 : Gas-phase reactions and rate constants for reaction k (k = 1, 17)

⎛ E ⎞ k k = Ak .T β k exp⎜ − k ⎟ ; Units are cm, s, mol, K14. ⎝ RT ⎠ Heterogeneous Model Reactions 1. Cvol + Sisurf + H2 → SiH2 + Csurf 2. 2Sivol + 2Csurf + H2 → C2H2 + 2Sisurf 3. SiH4 + Csurf → SiH2surf + H2 + Cvol 4. SiH2surf → H2 + Sisurf 5. SiH2 + Csurf → SiH2surf + Cvol 6. Si + Csurf → Sisurf + Cvol 7. C2H2 + Sisurf → 2Csurf + H2 + 2Sivol 8. C2H4 + 2Sisurf → 2Csurf + 2H2 + 2Sivol 9. CH4 + Sisurf → Csurf +2H2 + Sivol 10. HSiCH3 + Csurf → Sisurf + H + CH3 + Cvol 11. CH3 + Sisurf → Csurf + 1.5H2 + Sivol 12. Si2 + 2Csurf → 2Sisurf + 2Cvol 13. Si2C + Sisurf → Si2 + Csurf + Sivol 14. SiCH2 + Csurf → Sisurf + CH2 +Cvol 15. CH2 + Sisurf → Csurf + H2 + Sivol

A 2.200x1018 2.200x1032 1.592x1010 2.912x1014 3.060x1011 3.167x1011 3.040x1018 2.342x1016 2.098x105 2.490x1011 4.270x1011 1.000x1020 1.000x1011 2.550x1011 4.419x1011

β 0 0 0 0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

E/R 52786 52786 9401 4527 0 0 0 0 0 0 0 0 0 0 0

Table 2 : Surface reactions and rate constants of Si-terminated surface for reaction k (k = 1, 15)

⎛ E ⎞ k k = Ak .T β k exp⎜ − k ⎟ ; Units are cm, s, mol, K14. ⎝ RT ⎠

Elisabeth Blanquet, Didier Chaussende, Shin-ichi Nishizawa and Michel Pons.

3.2 Thermodynamic results

Thermodynamics has been used to evaluate systematically the effects of additional hydrogen and chlorine injected in the gas phase on the nature of the deposited phase and of the specie contributing to the deposition. The software Factsage37 has been adopted to carry out thermodynamic calculations. Composition of the initial gas phase is discussed in terms of atomic ratios taken in the following range: 0.01