Chemical vapour deposition of silicon films in capillary layers

Chemical vapour deposition of silicon films in capillary layers


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Thin Solid Films, 91 (1982) 211-216



CHEMICAL VAPOUR DEPOSITION OF SILICON FILMS IN C A P I L L A R Y LAYERS* M. JANAI Department of Physics and Solid-State Institute, Technion, Haifa 32000 (Israel) (Received October 15, 1981 ; accepted October 21, 1981)

A simple experimental method for the direct derivation in chemical vapour deposition (CVD) of the decomposition probability of a reactant molecule per surface collision is described. The method is based on the analysis of the thickness profile of a thin film deposited onto the internal walls of a two-dimensional capillary cavity. It is shown that for a unimolecular decomposition reaction the thickness profile decays exponentially with the depth in the cavity. F r o m the decay constant and from the time it takes to reach a given thickness profile, both the decomposition probability and the diffusion coefficient of the reactant molecules are obtained. The method is demonstrated for the CVD of silicon from silane diluted in helium at atmospheric pressure. At 600°C a decomposition probability of 2 x 10 - 6 is obtained.

1. INTRODUCTION Chemical vapour deposition (CVD) has become in recent years an established method of thin film deposition in the microelectronics, optics and protective coating industries 1. In the most c o m m o n variant of the C V D process, cold gas (e.g. Sill4 diluted in helium) flows into a reactor where it decomposes pyrolytically upon contact with a hot substrate. As a result a thin solid film (e.g. silicon) is deposited onto the surface. In the process the gas molecules pass through temperature and concentration gradients in the system, partly by mass flow and convection and partly by diffusion 2. On striking the hot surface most of the molecules bounce off; only a small fraction of the reactant molecules acquire sufficient energy to undergo decomposition. The average decomposition probability of a reactant molecule per collision with the surface is usually of the order of 10 3_10-6 only and is strongly temperature dependent. The deposition rate in a CVD process depends on this thermal decomposition probability as well as on the reactor geometry, the gas flow rate, the temperature profiles in the reactor, the local partial pressures of the reactant and the carrier gas, the diffusion coefficients of the gaseous constituents and * Paper presented at the Fifth International Thin Films Congress, Herzlia-on-Sea, Israel, September 21-25, 1981. 0040-6090/82/0000-0000/$02.75

© ElsevierSequoia/Printed in The Netherlands



gravitational effects. The deposition rate may be affected also by extrinsic factors such as gas or surface impurities and surface morphology. Because of the complexity of the CVD process it is usually difficult to obtain direct and unambiguous information about the values and the temperature dependences of basic CVD parameters such as the net decomposition probability of a reactant molecule per surface collision or the molecular diffusion coefficient of the reacting gas in the deposition environment. In this paper we describe a simple experimental method by which the values of the molecular decomposition probability and the diffusion coefficient can be directly derived. The method is based on the analysis of the thickness profile of a film deposited onto the internal wall of a two-dimensional capillary cavity. Such a cavity can easily be formed in any CVD reactor by placing two parallel substrate plates in the reactor with a narrow gap between them. The method to be described is insensitive to the particular CVD reactor geometry, to the gas flow rate or to local variations in the reactant partial pressure in the CVD reactor. The validity of the method depends only on the prevalence of steady state conditions in the reactor during the deposition experiment. 2. THEORY OF CHEMICAL VAPOUR DEPOSITION IN CAPILLARY LAYERS

Let us suppose that a two-dimensional capillary cavity of width g is formed in a CVD reactor. We assume that the cavity walls maintain an equal and uniform temperature T so that no convection takes place in the cavity; the only mass transport mechanism in the cavity is assumed to be gas diffusion. We further assume that at time t = 0 the reacting gas is introduced into the system and it reaches its steady state partial pressure value at the entrance to the cavity at a time much shorter than the total time of the deposition experiment. Thus at time t = 0 the reactant molecules start to diffuse into the cavity. For a two-dimensional semiinfinite cavity the net diffusion current will be in the x direction (Fig. 1). (In the general case where a fast surface reaction takes place the concentration gradient has also a z component, as does the diffusion current. However, for a capillary cavity where ~ < 8D/~g the concentration gradient in the z direction and the corresponding component of the diffusion current are negligible relative to the respective components in the x direction. In the following experimental example ct = 1.5 × 10-4D/bg (~ is the decomposition probability, D is the diffusion coefficient and ~ is the average thermal velocity).) The propagating reactant molecules strike the internal walls of the cavity at a rate

q W y~/" g-J" i' x



Fig. 1. The diffusion geometry in a two-dimensional semi-infinite capillary cavity.





N(x, t) = ¼n(x, t)~(T)


where N(x,t) is the number of surface collisions per unit time per unit area at point x at time t, n is the reactant concentration and the average thermal velocity = (8kT/rcm)l/2 3. With the assumption of a unimolecular CVD reaction the deposition rate is given by

dLfx, t) _ ¼n(x, t)~(T)c~ V (2) dt where L(x, t) is the thickness in centimetres of the deposited film on the cavity wall, c~ is the net decomposition probability of a reactant molecule per surface collision and V is the specific molecular volume of the solid film in cubic centimetres. The reactant molecules which diffuse into the cavity are gradually lost by collisions with the walls. The net flow density J of the reactant molecules in the x direction is thus governed by the equation

~J(x,t) ~3x

o~2n(x,t) 8x 2

~n(x,t) 8t

~bn(x,t) 2g


where D is the diffusion coefficient (cm z s - 1) of the reactant molecules. Solving for n(x, t) we obtain 4

n(x,t) n~




= ~ e x p ( - X ) e r f c L 2- l-~- -l / 2


1/2'~ 1




W llz)



X = x(k/D) x/2


W= tk


k = ~(T)c~/2g



This solution has the following properties. (1) At x = 0 n(x,t) has a constant value. Thus, according to eqn. (2) at x = 0 the deposited film thickness is linear with time. (2) F o r W ~ 1 (i.e. for t >>2g/fJ~) a steady state concentration profile is reached so that

, ( x , t ) = n ( O ) e x p - - x ~ 5/ky/27 ) ;


F r o m eqns. (2) and (5) we obtain that for a sufficiently long deposition time the thickness of the deposited layer attains an exponential profile with a decay constant

xl/e,wo~ = (2Dg/b~) vz


The thickness profile of the deposited layer at any time t is given by


1 F' n(x,t)


t Jo



This function is plotted in Fig. 2 on a semilogarithmic scale for various values of W.



We see from the figure that the thickness profile is subexponential for W = 0.50 (i.e. for t = g/c~f) and drops to 1/e of its entrance value at x = 0.50Xl/e.W~. Thus by recording the thickness profile for various deposition times and monitoring the X~/e positions as a function of time we obtain (2Dg/#~) ~/2 and g/~c~ and hence ~ and D. In principle it is possible to obtain these two values from a single deposition experiment in a given cavity by real-time monitoring of the thickness profile on the cavity wall. However, for experimental simplicity and for better accuracy we can take advantage of the dependence of W and X on the cavity width g. By performing the deposition experiment with various deposition times and cavity gaps we can obtain the whole spectrum of curves shown in Fig. 2, from which c~ and D can be derived. For a preliminary analysis a slightly tapered (wedge-like) cavity may be used so that a wide range of g values (from zero to any desirable value) are obtained in a single experiment. The cavity width, however, should not exceed the limit where convection or streamline flow become significant nor should it exceed the value O/:~. l









Fig. 2. Plot of the normalized thickness profile (eqn. (7)) for various values of W (W = (:w;2g)t).

3. EXPERIMENTAL METHOD AND RESULTS We applied this method to the derivation of the value ofe for the CVD of silicon from silane diluted in helium. The deposition was done in a radiatively heated horizontal reactor at atmospheric pressure. The cavity was formed by placing two fused silica plates in proximity on the substrate holder with nichrome wires as spacers. Figure 3 shows the deposited film profile on a 1 in square silica plate for t = 7 min, g = 2.5 x 10-3 cm and T = 600 °C. The photograph was taken through an interference filter at wavelength 2 = 6500 ~. The dark fringes are destructive interference fringes which indicate the L = (m + qS)2/2n thickness levels of the thin film (m is an integer, 4) is the phase constant and n is the refractive index of silicon). The inset in Fig. 3 shows a plot of the interference order m versus x on a semilogarithmic scale. At high values of x the curve becomes subexponential; the reason for this is not yet known. At low values o f x the measured thickness appears higher than the extrapolated value of the curve, probably because of edge effects at the entrance to the cavity. From this experiment we obtained xl/e = 0.29 cm. With D ~ 2 cmZs 1, g = 2.5 x 10-3 cm, b(600 °C) = 7.6 x 104 cm s-1 and assuming that steady state conditions were achieved we obtain from eqn. (6) that ~(600'~C)




= 1.6 × 10 - 6 . Substituting this value in eqns. (4c) and 4(b) with t = 7 min we obtain W = 1.0 × 104, which confirms our previous assumption that steady state conditions have long been achieved in the cavity. In all our experiments we found identical deposition profiles on the upper and the lower fused silica plates of the cavity. This supports the validity of the assumption made in Section 2 that there is no temperature gradient in the z direction in the cavity.

Fig. 3. Photograph of a thin silicon film deposited onto a 1 in square fused silica plate. The plate was the upper part of a 25 pm cavity. The traces of the nichrome wires which were used as spacers can be seen as two horizontal scratches at the top and bottom of the plate. The inset shows the thickness profile of the photograph plotted on a semilogarithmic scale. The left-hand scale gives the interference order and the right-hand scale gives the absolute thickness, based on refractive index measurements by Janai e t al. 5 In this deposition the film thickness outside the cavity was 2.2 + 0.3 pm, the deposition time was 7 min, [SiH4]/[He] ~ 20~ and T = 600 °C.

It is quite interesting to calculate, on the basis of a simple Arrhenius model, the activation energy E a of the silane decomposition reaction if only a fraction ~ of the molecules are assumed to have sufficient kinetic energy to undergo decomposition on striking the surface< We obtain this value by solving the equation ~(T) = exp(-- Ea/RT )


where R -- 1.987 cal mol-x K - 1 is the universal gas constant. From our data we o b t a i n E a = 23 kcal m o l - 1. Values of 19 ___2, 20 ± 5 and 17 _+2 kcal m o l - l have been reported by others 6-8. We obtained results consistent with eqn. (8) from other measurements at temperatures in the range 550 °C ~< T ~< 700 °C. Our values of e disagree with those extrapolated from the measurements of Farrow 8 by some two orders of magnitude. However, his measurements were performed at higher temperatures and at far lower pressures than our measurements were. Also, the method of molecular beam sampling that he used seems to be a less direct way to determine e than the method proposed by us since it requires a careful calibration of the mass spectrometer in order to obtain quantitative pressure readings for different gases. In contrast, the method described here requires only time and distance measurements.




This research was supported in part by the Aviac foundation and by the U.S.Israel Educational Foundation (Fulbright program). I would like to thank Dr. H. Gurev for help in sample preparation, Professor B. O. Seraphin for helpful discussions and Mrs. M. Janai for typing the manuscript. REFERENCES

I 2 3 4 5 6 7 8

B.E. Barry, Thin Solid Films, 39 (t976) 35. F . C . Eversteyn, P. J. W. Severin, C. H. J. van den Brekel and H. L. Peek, J. Electrochem. Soc., 117 (1970) 925. W . J . Moore, Physical Chemisto,, Prentice-Hall, Englewood Cliffs, NJ, 4th edn., 1962, Chaps. 7,8. J. Crank, 771eMathematics of Diffusion, Oxford University Press, Oxford, 1957, p. 129. M. Janai, D. D. Allred, D. C. Booth and B. O. Seraphin, Sol. Energy Mater., 1 (1979) 11. B.A. Joyce, R. R. Bradley and G. R. Booker, Philos. Mag., 15 (1967) 1167. R . C . Henderson and R. F. Helm, SutJi Sci., 30 (1972) 310. R . F . C . Farrow, J. Electrochem. Sot., 121 (1974) 899.