Ind. Eng. Chem. Res. 1999, 38, 4579-4584
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Modeling and Simulation of Photo-CVD Reactors Femi Uzuafa, Sy-Chyi Lin, Jorge Gabitto,* and K. Shukla Chemical Engineering Department, Prairie View A&M University, Prairie View, Texas 77446
Processes for deposition of thin films at low temperatures are needed in the microelectronics industry because of the increasing miniaturization of electronic devices. Laser-induced chemical vapor deposition (LICVD) has been used to deposit Si and Ge films from silane and germane. However, despite the importance of these processes, the various mechanisms that lead to the deposition are not well understood yet. In this paper we have developed a simple mathematical model to obtain better design of LICVD reactors. In the model, the active chemical species within the gas phase are selected using experimental information. Boundary layer equations are used to calculate the temperature and flow profiles, and mass balances are derived for all of the active species. A simplified surface kinetics is proposed, and a finite-difference scheme is employed to solve for the two-dimensional fluid active species concentration distributions. The model captures the main physical phenomena of LICVD. Results for silicon thin film deposition rates under different operating conditions are found to be in good agreement with experimental results. 1. Introduction The development of techniques for low-temperature semiconductor film growth is an area of intense research interest for microelectronic applications including thinfilm transistors1 and large area devices such as liquidcrystal displays and solar cells.2 Microelectronics devices consist of selective deposition of layers of solid films in conjunction with selective removal of portions of thin films. In particular, the selective thin film growth at low temperatures is important for future process technology. In recent years the role of SiHn species in the deposition of hydrogenated amorphous silicon films (a-Si:H) has become important because hydrogen saturates the dangling bonds, thereby decreasing the high density of defect states in the gap. In a comparison of the unhydrogenated material, this leads to a dramatic improvement in the electrical properties of the material. Chemical vapor deposition (CVD) is a critical process for the deposition of thin films of metals, semiconductors, and insulators on solid substrates where one or more gaseous species react on a solid surface forming solid products.3-7 The deposition species can be atoms, molecules, or a combination of both. A number of new techniques have been developed to obtain high-precision and -quality films.3,7 One of the important CVD techniques is the laserinduced chemical vapor deposition (LICVD). Using germane and silane the initial photofragments are germane photolytic products formed very near the substrate surface at low pressures.8 In this technique, the input gas is irradiated by a high-energy laser beam. After irradiation the gas phase contains neutral radicals, the presence of which enhances the growth rate and makes the in situ incorporation of dopants into the lattice feasible at low temperatures. Therefore, LICVD addresses the problems of conventional CVD while retaining the advantages that the deposition method yields primarily a-Si:H layers, which have many useful structural and electrooptical properties. A knowledge of the nature of species, which form the dominant precursors for film growth under a given set of deposition conditions, together with the mechanisms by which these species interact with the substrate and
growing film is of fundamental importance for understanding and modeling film growth. There is increasing evidence that SiH3 radicals are the primary precursors for the growth of amorphous Si films by plasmaenhanced CVD from silane. In the recent past, Fowler et al.9 have investigated the Si deposition from disilane using LICVD. They found that the predominant precursor was a “closed shell” species, H2SiSiH2. A deposition yield of Si atoms from ArF excimer laser photolysis of disilane was reported to be 20%. Their investigation suggests that the film growth results solely from the single-photon reaction mechanisms. The objective of this work is to develop a comprehensive but simple model that addresses the complex phenomena which determine the deposition of a-Si hydrogenated thin films in continuous parallel electrode LICVD reactors. This simple approach will provide a valuable knowledge on thin film technology. In section 2, we present a systematic development of our model. In section 3, we test the reliability of the model by comparing theoretical results with experimental data. Section 4 provides conclusions of the paper. 2. Model Development The study of chemical kinetics is particularly important for the understanding of a CVD process and optimization of its controlling parameters in order to obtain layers having properties required in various practical applications. A CVD deposition reaction comprises three fundamental steps: gas-phase reactions, transport toward the solid surface, and heterogeneous reaction on the substrate surface. Precursor generation in the gas phase, mass transport phenomena from the gas to the surface, and surface kinetics are the steps controlling the growth rate. The determination of the actual mechanism involves knowledge of the intermediate species formed in the gas phase and/or the substrate surface. The model proposed here rests heavily on the experimental results obtained by Fowler et al.9 They deposited Si thin films using an ArF excimer laser parallel to the substrate surface in a cylindrical reactor. They used a
10.1021/ie990155j CCC: $18.00 © 1999 American Chemical Society Published on Web 11/06/1999
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and is known as the active volume. The number N is also the number of excited Si2H6 molecules, Si2H6*, in the active volume. The photochemistry of Si2H6 is quite complex, and the predominant photoproducts of Si2H6 photolysis responsible for sustaining low-temperature deposition have to be carefully determined. The following main reactions in the gas phase are proposed based on the experimental information reported by Fowler et al.9 k1
Si2H6(g) + hν 98 SiH2*(g) + SiH4(g) k2
Si2H6(g) + hν 98 H3SiSiH*(g) + H2(g) k3
Figure 1. Schematic representation of a photoreactor for Si deposition from disilane.
Si2H6(g) + hν 98 2SiH3*(g)
single wafer reactor equipped with a laser beam parallel to the surface. The gas feed is also parallel to the wafer surface, but it flows perpendicular to the laser beam as shown schematically in Figure 1. Fowler et al.9 reported that the use of an excimer laser as the energy source presents distinct advantages over other photo-CVD methods. A photon energy of hν ) 6.4 eV dissociates Si2H6 by single photon absorption. This produces Sicontaining radicals that lead to film growth. Orienting the laser parallel to the surface allows reactive molecules to be created near the growth surface without an appreciable increase in the substrate temperature. To estimate the fraction of photolysis products that can reach the film by mass transport from the beamexcited region, the quantum yields (φ) for formation of the various photolysis products and the gas-phase kinetics of the individual products must be considered. The number of each photofragment produced by irradiation is given by the product of quantum yield for different species and the number of excited disilane (Si2H6*) molecules, N. The dissociated quantum yield in Si2H6 photolysis at 193 nm has been measured to be 0.7 ( 0.1. The additional 30% of Si2H6* is thought to decay radiatively or to be stabilized collisionally. Gas nucleation effects can explain observations of amorphous Si:H powder formation at high laser repetition rates.9 However, it is unlikely that a significant gasphase nucleation may occur under the operating conditions reported by Fowler et al.9 The number of Si2H6 molecules under the substrate that absorb a photon can be estimated using the photoabsorption cross section of Si2H6 at 193 nm, σ ) (3.4 ( 0.3) × 10-18 cm2, the Si2H6 concentration, n, and the path length of the beam inside the chamber, L. Fowler et al.9 derived the following equation that gives the intensity absorbed, Ia, by the Si2H6 molecules,
4 3H (g) Si2H6(g) + hν 98 H3SiSi*(g) + 2 2
Ia ) I exp(-σnL)[1 - exp(-σnL)]
(1)
where I is the measured laser intensity in J/cm2 pulse that enters into the chamber through the laser inlet window. The number of photons absorbed per pulse, N, is Ia divided by the photon energy, hν, and multiplied by the beam cross-sectional area, WH, where W is the beam width and H is the beam height. L is shown in Figure 1. Under optically thin absorption conditions, which occur at low Si2H6 partial pressures, we get
N ) IσnV/hν
(2)
where V is the volume of the beam under the substrate
(3) (4) (5)
k
k5
Si2H6(g) + hν 98 H3SiSiH2*(g) + H*(g) k6
SiH2*(g) + Si2H6(g) 98 Si3H8(g) k7
2SiH3* 98 Si2H6(g) k8
H3SiSiH* 98 H2SiSiH2
(6) (7) (8) (9) (10)
Equations 3-7 occurred through photolytic mechanisms. The quantum yields for the main Si fragments in reactions (3)-(7) are, 0.1, 0.4, 0.05, 0.1, and 0.05, respectively.9 This experimental information calls attention to the H3SiSiH* radical as the predominant precursor. This radical is also a relatively stable chemical species that reacts very slowly with silane and disilane. The radical H3SiSiH* suffers a 1,2-H isomerization to yield H2SiSiH2, which is the species transported to the substrate surface. Equations 8-10 were included to consider mechanisms for SiH2*, SiH3*, and H3SiSiH* disappearance. SiH3* is not expected to play a major role because of the fact that its quantum yield is too low compared to the H3SiSiH* radical. The participation of the radicals SiH3* and SiH2* in surface reactions is also considered. Mass transport limitations are considered by using the corresponding mass balances. We use the fact that the laser beam produces only a minimal effect on the gas-phase temperature.9 Under the conditions of interest, at relatively high pressure (1 Torr), the continuum approximation is still valid. For a Newtonian fluid, the velocity field is obtained by using the boundary layer approximation. The flow consists of an infinite stream flowing past a thin film of length L. The plate is considered infinitely wide, or z-axis symmetrical, and the flow is uniform at a horizontal approximation velocity, u∞. The velocity vector has vertical and horizontal components inside the boundary layer only. An approximate solution for the flow problem has been presented by Whitaker.10 The velocity in the horizontal direction (x axis) is given by
vx ) u∞
[2δ3y - 21(δy) ] 3
(11)
where δ is the boundary layer thickness and y is the vertical coordinate. The vertical velocity at the boundary layer (y ) δ) is given by
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vy )
3u∞ dδ 8 dx
K1
(12)
H2SiSiH2(g) + 2S S S-H2SiSiH2-S K2
and the boundary layer thickness can be calculated using the condition (δ ) 0, x ) 0)
δ ) 4.64xxν/u∞
(13)
where ν is the kinematics viscosity. The gas-temperature distribution is also calculated using boundary layer approximation,10
[
T ) Tw - (Tw - T∞)
( )]
1 y 3y 2δT 2 δT
K3
SiH3*(g) S SiH3*-S ks1
S-H2SiSiH2-S 98 2SiH-S + H2(g) ks2
SiH2*-S 98 Si:H - S + H2(g) ks3
3
(14)
where T∞ is the temperature outside the boundary layer, Tw is the temperature on the wafer wall, and δT is the thermal boundary layer thickness calculated from the momentum boundary layer thickness, δ
δT ) 0.976δPr-0.333
(15)
where Pr is the Prandtl number for the gas phase (Cp µ/λ), with µ the dynamic viscosity, Cp the specific heat, and λ the thermal conductivity of the substance. Equation 15 has been derived10 for the case where δ > δT. In our case δT > δ. Following the procedure of Coulson and Richardson,11 derivation of the relation between both boundary layer thicknesses leads to results to those in eq 15. In our case, the value of Pr is less than 0.1. Because the relative high-pressure considered in this work, we assumed that free radicals dominate the deposition rate. The mass balance equations are written for the species, Si2H6, Si2H4, SiH2*, and SiH3*; however, we do not take into account the radicals SiH3Si and Si2H5. This assumption rules out the consideration of eqs 6 and 7. We neglect any multicomponent diffusion effects and use pseudo binary diffusion coefficients. These assumptions lead to the following mass balance equation:
(v‚∇ni) ) ∇‚∇ (Di,Si2H6∇ni) + Gi
(16)
Here ni is the number of molecules of species i, and Di,Si2H6 is the binary diffusivity of species i in disilane. The net generation terms for gas-phase reactions are given by
GSi2H6 ) k7[SiH3*]2 - k6[SiH2*][Si2H6] 5
kihν[Si2H6] ∑ i)1 GH2SiSiH2 ) k2hν[Si2H6] GSiH3* ) 2k3hν[Si2H6] - 2k7[SiH3*]
SiH2*(g) S SiH2*-S
(17) (18)
2
GSiH2* ) k1hν[Si2H6] - k6[SiH2*][Si2H6]
(19) (20)
where asterisks represent the free radicals. The number of moles of active [Si2H6] are computed from eq 2. Heterogeneous (surface) reactions enter in the material balance through the boundary conditions. We assume that the surface reactions for all of the neutral species follow a Langmuir-Hinselwood mechanism12
SiH3*-S 98 Si:H - S + H2(g)
(21) (22) (23) (24) (25) (26)
The controlling step is given in each case by the hydrogen desorption (eqs 24-26). Then, the boundary conditions (BC) for equations are given by
BC1: at y ) δM, for all x [Si2H6] ) [Si2H6]0
(27a)
[ni] ) 0
(27b)
where [Si2H6]0 is the initial concentration of disilane and ni represents the concentration of Si2H4, SiH2*, and SiH3*, respectively.
BC2: at x ) L, for all y ∂[Si2H6] )0 ∂x
(28a)
∂ni )0 ∂y
(28b)
BC3: at x ) 0, for all y [Si2H6] ) [Si2H6]0
(29a)
ni ) 0
(29b)
∂[Si2H6] )0 ∂y
(30a)
BC4: at y ) 0, for all x
-Dni,Si2H6
∂ni ) ksiβ(i)ni ∂y
(30b)
where β(i) is the sticking coefficient onto the substrate surface. To calculate the deposition rate using eqs 2325, we need to estimate the hydrogen desorption rate constants (ksi). They are calculated using the formula presented by Matsui et al.13
ksi ) β(i)
x
107RT 2πMi
(31)
where R, Mi, and T are the gas constant, molecular weight, and gas temperature, respectively. [i] is the mole concentration of the ith species at the surface. This formula was derived assuming collisions between neutral species and the surface and involves the definition of a reactive sticking coefficient. It can be concluded from work by Buss et al.14 that both models are equivalent. The reactive sticking coefficient for radicals is considered to be 1.9 The sticking coefficient for
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Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 Table 2. Typical Operating Conditions of the LICVD System* property
value
gas velocity (m/s) substrate temperature (K) light flux (J/m2‚s) Gas pressure (Pa) viscosity (10-4 Pa‚s) specific heat (kJ/kg‚K) thermal conductivity (w/m‚K) Prandtl number (Pr) path length of the laser beam (L, cm) substrate diameter (cm)
1 523 200 133 8.8 14.44 0.256 0.05 18 10
a Values for viscosity, specific heat, and thermal conductivity are taken from ref 18.
Figure 2. Schematic representation of the domain of integration. Table 1. Rate Constants for the Reactions15-17 reaction k1
Si2H6 + hν 98 SiH2* + SiH4 k2
Si2H6 + hν 98 H3SiSiH* + H2 k3
Si2H6 + hν 98 2SiH3*
k (cm3 molecule-1 s-1) 1.01 × 10-6 2.1 × 10-8 8.0 × 10-11
k4
Si2H6 + hν 98 H3SiSi* + 1.5H2
N.A.
k5
Si2H6 + hν 98 H3SiSiH2* + H* k6
SiH2* + Si2H6 98 Si3H8 k7
2SiH3* 98 Si2H6
N.A. 3.0 × 10-10 7.7 × 10-11
k8
H3SiSiH* 98 H2SiSiH2
N.A.
H2SiSiH2 is taken to be unity. The values of rate constants used in our calculations were obtained from the literature,15-17 and they are reported in Table 1. 3. Results and Discussion To implement the model described above, a computer code was developed. Equation 16 describes a set of nonlinear coupled elliptical differential equations. An iterative overrelaxation finite difference scheme was used to solve eq 16 subject to boundary conditions of eqs 27-30 within the integration domain as depicted in Figure 2. The numerical procedure calculates the concentration values using a five-point scheme. Two different solution procedures were tried. In the first procedure, a scheme that sequentially computed the whole concentration profile for each of the radicals and disilane was used. The coupled terms were calculated using the previous iteration value. When two consecutive concentration profiles for every species differed by more than a set norm value, a new iteration was performed. This procedure involved individual calculation of all of the concentration profiles and iteration until convergence was achieved. The second procedure involved simultaneous solution of the set of differential equations for each grid point before moving to the next point. The calculated values were then used to determine the concentration values for other species. The
Figure 3. (a) Temperature contour between the gas input temperature and wafer temperature. (b) Velocity contour for the set of operating conditions of Table 2.
second numerical scheme was found to be more efficient than the first scheme by a factor of 2. However, both numerical schemes were found to exhibit the same accuracy. Typical values for operating parameters are shown in Table 2. They were selected from Fowler et al.9 and were used in our calculations presented below. The velocity and temperature boundary layers are functions of the approximation velocity (u∞) and the temperature outside the boundary layer (T∞). Our calculations show that the temperature boundary layer is about 1 order of magnitude thicker than the velocity boundary layer. This fact is illustrated in Figure 3. Significant temperature effects on the rate of thermal reactions can be expected because the gas temperature is significantly
Ind. Eng. Chem. Res., Vol. 38, No. 12, 1999 4583
Figure 4. Dimensionless Si2H4 concentration profile.
different from the temperature outside the boundary layer at positions far away from the wafer. This result raises the issue of what temperature should be used to evaluate gas-phase reactions. Traditionally, in cold wall reactors two different temperatures are referred to, the gas input temperature (T∞) and the wafer temperature (Tw). The results shown in Figure 3 demonstrate the existence of a whole range of temperatures between these two values. Temperature is in Kelvin and velocity is in meters per second. This fact is not significant for relatively low temperatures because, under these conditions, photolytic and free-radical reactions determine the rate of deposition. The temperature effect becomes important for higher temperatures than the ones used in this work. Figure 3 also depicts the velocity boundary layer for the set of operating conditions shown in Table 2. Solution of eq 17 allows us to determine concentration profiles for the different intermediates considered in this model. We investigated the concentration profiles for disilane, SiH3*, SiH2, and Si2H4 species. For example, Figure 4 shows the dimensionless concentration profile for Si2H4. The disilane initial concentration was used to calculate the dimensionless concentration in all cases. We found that only a small amount of disilane was lost in gas-phase reactions. For all practical purposes the disilane concentration could be considered constant. Comparison of concentration profiles of the above species shows that SiH3* concentrations are lower than those of SiH2 and Si2H4 species. This result shows that SiH3* makes only a small contribution to the total rate of deposition. SiH2 and Si2H4 concentrations exhibit the same order of magnitude. Our results show that the contribution of SiH2 to the total rate of deposition cannot be neglected despite the fact that SiH2 concentrations are approximately 4 times lower than Si2H4 concentrations. This is in contrast to the assumptions made by Fowler et al.9 Similar results were obtained using operating conditions different from the ones shown in Table 2. Figure 5 shows a radical concentration profile along the wafer for two different positions of the laser beam. In Figure 5b the location of the velocity boundary layer is also depicted. A more uniform rate of deposition is achieved when the laser beam is closer to the wafer. The total rate of deposition was calculated by combining
Figure 5. (a) Radical concentration profile (dimensionless × 100 000). (b) Radical concentration profile (dimensionless × 100 000)
Figure 6. Comparison of deposition rates caused by radicals and disilane at T ) 523 K.
the individual rates of deposition of all of the active species generated in the gas phase. Consideration was also given to the deposition mechanism involving direct deposition of disilane by collision against the wafer surface. A disilane reactive sticking coefficient was calculated by using the procedure reported by Buss et al.14 The average value for this sticking coefficient (β) was approximately 10-13. This value is too low to allow consideration of any significant contribution of this direct deposition mechanism. Figure 6 shows the rate of deposition profile calculated for the set of conditions contained in Table 2. Significant nonuniformity can be appreciated. Results corresponding to the direct disilane deposition rate mechanism are also presented. It can be concluded that for the temperature used in these calculations (523 K) this mechanism makes a negligible contribution to the total rate of deposition. Comparisons of theoretical results with experimental
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has been found for the rate of deposition of disilane. The model can be used reliably to calculate the total rate of deposition as a function of wafer position and operating conditions.
Figure 7. Comparison of calculated results with experimental data for deposition rates of disilane.
data9 for the mean deposition rates of disilane are shown in Figure 7 as a function of temperature. It should be noted that the rate constants used in computing the deposition rates were calculated from first principles without any adjustable parameters. Considering the simplicity and approximations involved in the model, the agreement between theoretical and experimental results is seen to be very good. The model prediction is still 50% away from the experimental data because we have simplified the complicated kinetics in the photo-CVD system. Nevertheless, the comparison between model and experimental results can be improved by adjusting the rate constant, sticking coefficient, and other parameters with further effort. We have also performed calculations to investigate the effect of temperature on the deposition mechanism. Temperature variation can change the whole deposition mechanism. A detailed study on the temperature effect will be published separately. 4. Conclusions We have developed a simple model which can predict silicon thin film deposition rates as a function of operating conditions with certain confidence. The model accounts for gas-phase phenomena, convective transport effects, and reaction rates on the solid wafer. One critical stage is the modeling of velocity and temperature profiles in the proximity of wafer. Boundary layer theory allowed us the direct computation of velocity and temperature profiles. The velocity and temperature profiles were used to calculate the concentration profiles of all of the important intermediate species. Mechanisms to explain the gas-phase and solid surface reactions have been proposed. Despite their simplicity, those mechanisms captured the main physical phenomena in LICVD. Our results show that the temperature effect is significant even at locations far away from the wafer. While Si2H4 makes the largest contribution to the rate of deposition, the contribution of other species cannot be neglected. Contribution of direct disilane deposition is found to be insignificant. In general, good agreement between the model predictions and experimental results
Acknowledgment The work was supported by National Science Foundation through a subgrant from the Science and Technology Center at the University of Texas at Austin (STCUT Austin). Support from the NASA Center for Applied Radiation Research at Prairie View A&M University (CARR-PVAMU) is also acknowledged. We are grateful to Dr. Thomas N. Fogarty (CARR-PVAMU) and Dr. John G. Ekerdt (STC-UT Austin) for their advice and support. Literature Cited (1) Sherman, A. Chemical Vapor Deposition for Microelectronics; Noyes Publications: Park Ridge, NJ, 1987. (2) Reinberg, A. R. J. Electrochem. Soc., Ext. Abstr. 1974, 1, 24. (3) Badgwell, T. A.; Bushman, S. G.; Butler, S. W.; Chatterjee, S.; Edgar, T. F.; Toprac, A. J.; Trachtenberg, I. Modeling and Control of Microelectronics Materials Processing. Comput. Chem. Eng. 1995, 19, 1. (4) Hough, O. P. Handbook of Chemical Vapor Deposition (CVD), Principles, Technologies and Applications; Noyes Publications: Park Ridge, NJ, 1992. (5) Oxley, P. J. H.; Blocher, J. M., Jr. Chemical Vapor Deposition in Vapor Deposition; John Wiley and Sons: New York, 1996. (6) Blocher, J. M. Chemical Vapor Deposition. J. Electrochem. Soc. 1960, 107, 177c. (7) Lee, H. K. Fundamentals of Microelectronics Processing; McGraw-Hill: New York, 1990. (8) Motooka, T.; Greene, J. E. J. Appl. Phys. 1986, 59, 15. (9) Fowler, B.; Lian, S.; Krishnan, S.; Jung, L.; Li, C.; Samara, D.; Manna, I.; Banerjee, S. J. Appl. Phys. 1992, 72, 1137. (10) Whitaker, S. Introduction to Fluid Mechanics; R. E. Krieger Pub. Co.: Melbourne, FL, 1981. (11) Coulson, R. Chemical Engineering; Pergamon Press Pub. Co.: London, 1974; Vol. 1. (12) Fogler, S. Introduction to Chemical Reactor Design; Prenttice-Hall Pub. Co.: New York, 1994. (13) Matsui, Y.; Yuuki, A.; Morita, N.; Tachibana, K. Jpn. J. Appl. Phys. 1987, 9, 1575. (14) Buss, R. J.; Ho, P.; Breiland, W. G.; Coltrin, M. E. Reactive Sticking Coefficients for Silane and Disilane on Polycrystaline Silicon. J. Appl. Phys. 1988, 63, 2808. (15) Yuuki, A.; Matsui, Y.; Tachibana, K. A Numerical Study on Gaseous Reactions in Silane Pyrolysis. Jpn. J. Appl. Phys. 1987, 26, 747. (16) Coltrin, M. E.; Kee, R. J.; Evans, G. H. A Mathematical Model of the Fluid Mechanics and Gas-Phase Chemistry in a Rotating Disk Chemical Vapor Deposition Reactor. J. Electrochem. Soc. 1989, 136, 819. (17) Coltrin, M. E.; Kee, R. J.; Miller, J. A. A Mathematical Model of Silicon Chemical Vapor Deposition. J. Electrochem. Soc. 1986, 133, 1206. (18) Perry, R.; Green, D. Perry’s Chemical Engineering Handbook, 6th ed.; McGraw-Hill: New York, 1984.
Received for review March 1, 1999 Revised manuscript received September 14, 1999 Accepted September 20, 1999 IE990155J
