Numerical simulation of chemical vapour deposition process in electric field

Suppl.,pp. S755-S758, 1998 0 1998 Elsevier Science Ltd. All rights reserved

Computers them. Engng Vol. 22.

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Numerical simulation of chemical vapour deposition process in electric field L. Rudniak Department of Chemical and Process Engineering, Warsaw University of Technology, ul. Warynskiego l, OO-645 Warsaw, Poland. Abstract The deposition of thin solid films in CVD processes is determined by hydrodynamics, the chemical kinetics of the process and transport phenomena (heat transfer, species diffusion) in the reactor. The electric field must also be taken into account in simulation of some type CVD reactors (PECVD and RPCVD reactors). The paper deals with the modelling of CVD process in electric field. The purpose of this study was to estimate influence of electric field on deposition rate. 0 1998 Elsevier Science Ltd. All rights reserved. Keywords: computational fluid dynamics, chemical vapour deposition, electric field. Introduction Fundamental models of CVD should employ detailed descriptions of fluid flow, mass transfer, heat transfer and chemical kinetics. In the presented paper the mathematical model of CVD is based on steady-state mass, momentum and energy balances in a horizontal reactor (Fig. 1). In two-dimensional Cartesian coordinates, these equations are as follows:

Chemical Vapour Deposition (CVD) processes are applied to deposit thin solid films. Such thin films are used as coating in mechanical (e.g. TiN) and in micro-electronic manufacturing (e.g. &As, Si), Carlsson (1985) and Badgwell et al. (1995). In general, the growth rate, the structure and mechanical properties of the deposited layer vary with deposition conditions such as the temperature, the type of the reactant gas, the flow rate, the total pressure of the system, the partial pressures of the reactant gases and the geometry of the deposition chamber. In many CVD processes a high deposition rate can only be achieved at a relatively high substrate temperature (about 1273 [K]). The deposition temperature can be reduced considerably by using various activated processes (e.g. plasma activation), Carlsson (1985). Plasma or glow discharges are generated by applying an external electric field to process gases. The resulting plasma consists of high-energy or ,,hot” electrons and ,,cold” ions and neutral species (300 [K]). The high electron energy relative to the low temperature of neutral species makes discharges useful in driving CVD reactions. The created ions, electrons, and neutral fragments participate in complex surface reactions that form the basis of the film growth. Another useful variant of PECVD is remote plasma-enhanced CVD (RPCVD), Kamins et al. (1982) and Badgwell et al. (1995). In this process the glow discharge is maintained in an upstream discharge region and the radicals are transported to the deposition region. This remote plasma configuration eliminates ion bombardment, which can cause negative effects on substrates and allows the selective activation of reactants by regulating the species that flow through or bypass the discharge region.

Continuity

d(pu)+WV) =. ax ay

(1)

Conservation of momentum: x component

(2) Conservation of momentum: y component

Conservation of energy

Pc,(u~+vg) +(a$$ +$(a$) (4) Conservation of mass of reactant species

In the above equation, X, n, E are particle density, mobility, and electric field, respectively.

Mathematical model. S755

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European Symposium on Computer Aided Process Engineering-8

Y

I

T,-973[K]

Fig. 1 Schematic of horizontal CVD reactor. Additionally in order to find distribution of electric field it is necessary to solve Poisson equation which relates divergence of the local electric fields to the charge density [2]:

inflow temperature was 293 [K], and the susceptor temperature was 973 [K]. The carrier gas was a hydrogen. The properties (p, p, ii) of gas mixture was taken as for pure hydrogen. The top wall temperature in the susceptor region was assumed to be 400 [Kj. The dimension of the reactor was : height h=O.OlS [ml, entrance region 1=0.2 [ml, susceptor length s z 0.2 [ml. The set of partial differential equations (l)-(5) was numerically solved by applying commercial software Fidap based on finite element formulation. The results from the numerical simulations were compared with the experimental data of GaAs deposition obtained by van de Ven et al. (1986). On the Fig. 2 it is shown a good agreement with the experimental data. Influence of electric field on deDosition rate.

V.E,eX

(6)

EO where e - an elementary charge , E, permitivity of gas mixture. An overall model for RPCVD reactors could be very complicated. In this model, several assumptions were taken into account in order to simplify their implementation: - the reacting species is charged with positive charge (positive ions) at the entrance of the reactor, - the positive ions are transported about reactor by convection, species gradient and an electric field. The species flux may be written as: J =-D.VX+q.X.E+u.X

In the simulation of mass transfer of charged species, there was necessary to include additional terms (see equation (5) and (7)) due to existence of electric field. The Poisson equation (6) relating the divergence of the local electric field to the charge density enabled to find the values of E. The side walls of the reactor were assumed to be insulators and susceptor a ground electrode (the potential V was equal zero). The total pressure in the reactor was 1300 [Pa]. The gas inlet condition were: ui= 0.07 [m/s], mass f?action of the species 1O-8,

(7)

- the plasma chemistry in the reactor has been neglected.

h = 0.018 [m],T,=973 [Kj 12000

Model prediction Model prediction (electric field absence) In order to estimate the influence of electric field on deposition rate on susceptor, the equations (l)-(5) were numerically solved and the last term on the right side of equations (5) was not included (no existence of electric field). The boundary conditions for the case without electric field were: Inlet Outlet

U = Uij V =

;=o,v=o,

0,

T=Ti

X=X;

z bl Fig. 2 Comparison between model predictions for growth rates and experimental results by Van de Ven at al. (1986)

$o,$o Model orediction (electric field existence)

Susceptor Wall

u,v = 0, T = T,, X = 0 u,v = 0, T = T,,

g =0 ax At the susceptor surface a very high chemical reaction was assumed, leading to transport limited growth. The total pressure in the reactor was lo5 [Pa], the

The results are shown as the velocity field in Fig. 3, streamlines in Fig. 4, temperature field in Fig. 5, species concentrations in Fig. 6. Figure 7 shows the potential field generated by positive charged species. It is seen a gradient of a potential along the reactor

European Symposium on Computer Aided Process Engineering-8 (non zero electric field E which’has an influence on species flux, see eq. (7) ).

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average flux species on the susceptor was 0.59*1@12 mg/s]. It is seen that the flux charged species is grater 74 % than in a case of neutral species. Conclusion

Fig. 3 Calculated velocity vector field. As seen in Fig. 4 and Fig. 5, the gas mixture are cold over most the entrance region and start heating up as they flow over the susceptor.

susceptor Fig. 4 Streamlines in the reactor. Due to heat convection, gas being heated by the susceptor tends to rise. In this case the gas velocity is enough high, so there is no recirculation zone.

The modeling of CVD reactor in electric field has been presented. This mathematical model of the reactor is a first step into modeling of plasma reactors. An overall plasma reactor model should account the following phenomena, Lymberopoulos et al. (1994) and Caquineau et al. (1997): - continuum models for time-averaged solution of electron, ion, electron energy transport, magnetic and electric field, - plasma enhanced chemical reactions including ionisation, attachment, detachment, recombination, metatastable excitation, - momentum and charge exchange, - heat transport. Due to a strong interaction of the phenomena above mentioned, simulation of plasma reactor is a very challenging task. The autor is presently working on numerical implementation of plasma reactor model Acknowledgments.

This work was supported by the State Committee for Scientific Research (KBN, Poland), grant No. 3T09C007 1 I.

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Notation CP

susceptor Fig. 5 Temperature field in the reactor. The calculated average flux species on the susceptor was 0.103*10~” [kg/s].

D E e hg J P ; U

susceptor

; X

Fig. 6 Calculated mass fractions of charged species (*lo*) in the reactor.

9 susceptor

Greek symbols = permitivity of gas mixture [F/m], c0 = ion mobility [m*/s] 11 = conductivity [W/mK], h = viscosity [Pas], p = density [kg/m3], P References Kamins,

Fig. 7 Calculated potential field in Volts. The numerical simulation for the same boundary condition and for neutral species has been performed in order to compare depositions rates. The calculated

heat capacity [J/&K], = difftusion coeficient [m2/s], = electric field [V/m], = electron charge [As], = gravity constant [m/Z], = reactor height [ml, = species flux = pressure [Pa], = susceptor length [ml, = temperature in the reactor [K], = x velocity component [m/s], = y velocity component [m/s], = potential [VI, = particle density [mm’],

=

T.I.

and

Chiang,

K.L.,

(1982)

J.

Electrochem. Sot., 129,2326.

Ven, J. Van de, Rutten, G.J.M., Raaymakers, M.J. and Giling, L.J., (1986), .I Cryst. Growth, 76,352. Carlsson, J., (1985) Thin Solid Films, 130,261. Lymberopoulos, D.P. and Economu, D.J., (1994) J. Vat. Sci. Technol., 12(4), 1229.

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Caquineau,

H., and Despax, B., (1997), Chem.

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