5364
J. Phys. Chem. 1992, 96, 5364-5379
Kinetic Modeling of the Chemical Vapor Deposition of Tin Oxide from Tetramethyltln and Oxygen Anthony G. Zawadzki,* A T & T Bell Laboratories, Holmdel, New Jersey 07733
Carmen J. Giunta,* Department of Chemistry, LeMoyne College, Syracuse, New York I321 4
and Roy G. Gordon* Department of Chemistry, Harvard University, Cambridge, Massachusetts 021 38 (Received: August 28, 1991; In Final Form: March 19, 1992)
The gas-phase kinetics of the chemical vapor deposition of tin oxide films from tetramethyltin (TMT) and oxygen was successfully modeled by a detailed gas-phase mechanism involving hydrogen and methane oxidation submechanisms as well as alkyltin reactions. The proposed mechanism is a branched chain process, initiated by pyrolysis of TMT and sustained by a sequence of reactions propagated by both organotin radicals and OH. (CH3)$nOH is posited as a key intermediate, whose decomposition and oxidation leads to film growth, as well as releasing hydrocarbon species which are further oxidized. Model simulations were compared to experimental measurements by Borman and Gordon of tin oxide deposition rate profiles and gas-phase byproduct concentrations under conditions of varying temperature and initial reactant concentration, with generally good agreement. The proposed mechanism reproduces both the weak dependence of maximum film growth rates on input oxygen concentration and the linear dependence on input TMT, observed by Borman and Gordon. Also well predicted is the overall significantly nonequilibrium byproduct mix of both oxidized and reduced species. By supplementing the basic mechanism with initial pathways in olefin and organobromide oxidation, we were also able to model the inhibitory effects of gas-phase additives including alkenes and halogen-containingspecies. Combined with the experimental results of Borman and Gordon, our modeling strongly suggests that the rate-limiting steps in tin oxide chemical vapor deposition occur in thc gas phase and that the gas-phase oxidation of TMT which occurs proceeds through pathways fundamentally different from that of its hydrocarbon analog, neopentane.
1. Introduction Formation of thin solid films through chemical vapor deposition (CVD) from organometallic and hydride sources is an important industrial process of considerable fundamental research For example, the detailed chemistry and physics of CVD systems producing epitaxial silicon have come under both theoretical and experimental ~ c r u t i n y . ~ ~Understanding J*~ of the microscopic chemistry and physics of CVD processes may offer practical applications in optimization of process design or in the development of new deposition systems. The properties and growth rates of films formed by CVD are controlled by a complex interplay of thermodynamics, fluid dynamics, heat and mass transfer, homogeneous chemical kinetics, and heterogeneous processes. Development of comprehensive microscopic descriptions of CVD dynamics is thus a challenging problem. While quantitative reactive flow calculations may be necessary for exact analysis of commercial reactors, an appropriate initial question in many CVD systems is the relative contribution of each aspect of the overall system dynamics. Of particular chemical interest is the relative role of gas phase and surface reactions. Prior to about 1980, gas-phase chemistry was often considered either to be negligible or to have a pernicious effect on film growth due to degradation of film proper tie^.^ Recently, however, a number of studies have indicated that gas-phase chemistry plays a role in many CVD systems beyond that of supplying reactants to the film surface.6 In most CVD systems, however, the exact nature of that role is still unknown. The increasing availability of gas kinetic data should permit theoretical analysis to illuminate this issue. In addition to developing a detailed understanding of an important heterogeneous reaction type, studies of CVD systems in which gas-phase chemistry may be dominant also offer significant possibilities for practical process control through manipulation of the properties and constituents of the gas phase in the reactor. Our approach to the theoretical analysis of CVD has two major components. First, we study systems for which experimental evidence suggests gas-phase processes are likely to be both dom-
inant and amenable to manipulation. Second, we use a hierarchical approach to modeling in which overall process dynamics are decoupled into separate types of dynamical effects and each, in turn, is decomposed into subtypes. Each of these subtypes is modeled, and the model verified with independent experimental data, before being enlarged by inclusion of further processes. Success of this approach requires integration of experimental studies with the modeling effort. For example, proper design of experimental reactors permits analysis of the relative importance of homogeneous and heterogeneous chemistry without the need to explicitly include effects due to fluid dynamics or diffusion. While our techniques are generally applicable to CVD processes, we felt it important to carry out a detailed analysis of a specific CVD system. Previous work in this laboratory has centered on those CVD processes useful for the production of photovoltaic cells, including deposition of Si? Si02,6d+7 Ti02,8and Sn02.13899Unlike many commercial CVD processes for semiconductor production, the latter three CVD systems involve oxidation, rather than simply pyrolysis, of the organometallic reactant. Although it is more complex, oxidation chemistry can offer significant opportunities for process manipulation through the use of gas-phase accelerators and inhibitors to affect film growth rates or change film composition and properties. Based on the experimental results on several such processes, we chose to model the CVD of tin oxide. A pioneering initial attempt to formulate such a model was made by Bienstock.6a In this paper, we analyze the dynamics of CVD of tin oxide films prepared by air oxidation of tetramethyltin (TMT) at atmospheric pressure and temperatures of 645-752 K. (A future publication will analyze the CVD dynamics of fluorine-doped tin oxide films, formed by co-oxidation of T M T and CF3Br.) Tin oxide CVD occurs under conditions of spatial and chemical nonequilibrium and requires consideration of chemical kinetics, fluid flow, and mass diffusion for adequate analysis. By treating a suitable reactor design and choice of operating conditions, we are able to theoretically describe the relevant fluid dynamics and mass transport using a chemical rate law formalism.
0022-365419212096-5364%03.00/0 0 1992 American Chemical Society
Kinetic Modeling of the Chemical Vapor Deposition
organotin Oxidation chain
OH
oxidation chain (CHASnOH
Figure 1. Major reaction pathways in oxidation of (CH3)$n by 02, determined by screening analysis of model simulations.
Our CVD model, schematically shown in Figure 1 and listed in Table 11, is thus implemented as a chemical reaction mechanism, containing 27 gas-phase species and 96 chemical reactions. We propose that the rate-limiting chemistry occurs in the gas phase, leading to species which diffuse to the film surface where they are adsorbed and rapidly oxidized. Model development was based on an assessment of previously studied chemical processes (such as CH, oxidation and alkyltin pyrolysis) which form subsets of the overall gas-phase reaction set. From these processes, an initial mechanism was developed independently of data on the CVD system. This hierarchical approach permitted assignment of all but four of the model parameters (rate and diffusion constants) without any comparison to experimental CVD data. Comparison to a limited set of growth rate data then permitted identification of possible additional reactions present in the CVD process and provided estimates of their rate constants. The resulting model was used, with addition of reactions describing initial oxidation of additives but without adjustment of parameters, to successfully simulate growth rate profiles in systems containing the gas-phase additives tert-butyl bromide (TBB) and various alkenes, all of which inhibit film growth. This paper is organized as follows. Section 2 briefly describes the characteristics of tin oxide and its formation through CVD and reviews the experimental data to which we compare our simulation results. Section 3 describes the model, organized by mechanistic subset. Section 4 compares model simulation results to experimental data. Section 5 discusses the successes and limitations of our model and provides a brief mechanistic analysis of the CVD process. Section 6 concludes. Throughout this paper, we will use units of kcal, cm3, mol, and s for kinetic and thermodynamic data. 2. Background Tin oxide (SnOJ is a versatile material whose optical, electrical, and mechanical properties make it a widely used industrial coating. Its reflectancttransmittance spectrum, exhibiting transparency to visible light and reflectivity to infrared radiation, gives it desirable characteristics for a heat-retaining coating on window glass. Although pure tin oxide is a wide band-gap semiconductor, conducting films can be made of fluorine-doped tin oxide (SnOSF). These transparent conducting films are well suited for use in solar cells as electrodes, which carry the cell's current without blocking sunlight. Sn02:F films can also be fabricated for the generation of resistive heating to defrost windshields of airplanes or automobiles. Tin oxide films are sufficiently sturdy, chemically inert, and adhesive on a variety of substrates to withstand the exposures typical of the above applications; in fact, tin oxide is also used as a wear-resistant coating on such objects as glass bottles. The efficient fabrication of tin oxide in thin film form has long been an area of practical research interest because of its extensive
The Journal of Physical Chemistry, Vol. 96, NO.13, I992 5365 ~ t i l i t y . ~ In , ~ this J ~ laboratory, such research has focused on CVD from the reaction of organotin compounds with oxygen. A comprehensive study of the kinetics of such precesses, carried out by Borman and Gordon (BG),l forms the experimental basis for the present modeling work. This section will review the pertinent experimental data of Borman and Gordon. 2.1. Summary of Borman and Gordon's Observatiorrs. BG, in their investigation of the deposition of SnO, from T M T and 02, used a horizontal laminar-flow reactor consisting of a borosilicate glass (Pyrex) tube enclosed in a tube furnace and connected to gas handling systems for input of reactants and capture of gasphase byproducts. The replaceable Pyrex tubes served as both reactor and substrate. Narrow tubes (2-7 mm i.d.) were used, in order to minimize effects of diffusion in the gas phase. (The majority of kinetic data referred to in this paper was obtained with reactors of 7-mm i.d.). Laminar flow in the reactor allowed direct conversion of distance along the flow direction to gas residence time within the reactor. External heating by a tube furnace resulted in an approximately uniform temperature ( f 2 K) measured both axially and radially within the heated zone of the reactor, including the reactor walls. These spatially isothermal conditions allowed kinetic analysis to be carried out without the complication of temperature-sensitive rate coefficients varying within the reactor. BG investigated depositions in the temperature range of 645-752 K, with 741 K a typical temperature. In this range, BG observed widespread homogeneous nucleation for peak film growth rates of 15-20 A s-l or higher. Such nucleation tended to depress the maximum observable film growth growth rate. In order to keep deposits free from particulate contamination, BG kept initial T M T concentration low enough (usually less than 0.2 mol %) to preclude homogeneous nucleation. Initial oxygen concentration, however, was varied over a wide range. BG's kinetic studies included gas chromatographic characterization of the reactor effluent, as well as measurement of the growth profile of the film product. BG measured complete profiles of film differential growth rate (DGR) against gas-phase reactor residence time for varying initial concentrations of both T M T and 02. Typical growth profiles are shown in Figures 2a and 3. (Initial gas concentrations are reported in the figure in the notation '% TMT/% 0,";the remainder of the carrier gas was N2. For example, "0.1/21" means 0.1% T M T and 21% Oz.) Measured DGR profiles show a definite induction period, rise to a maximum value (G-), and then decline. Figure 2b illustrates the variation of film growth rates with initial O2concentration, [O2lO,with [TMTIokept constant. BG report a half-order dependence of G,,, on [OJO for [02]o/[TMT]o < 65, in agreement with Ghostagore.'& This variation leveled off for values of this ratio above 200 (Figure 2b). (We emphasize the sometimes sizable error bars in Figure 2b because the peak deposition rates were derived from growth profiles measured by use of interference fringes; in general, no fringes fall precisely at the growth rate peak.) Figure 3 illustrates film growth rates for several values of [TMTJo,with [02],, held constant at about 20 mol %. For [TMTIo < 0.2%, BG report that measured values of G,,, were proportional to [TMT],,. Figure 4 shows the temperature dependence observed by BG for peak deposition rates. Although the absolute growth rate varied with reactor size and reactant concentration, the activation energy for G,,, under several sets of conditions was reported to be 39.6 f 2.9 kcal mol-'. This value is in line with previous reports of the activation energy,lobVcdespite differences in reactor design. BG report signs of a lower activation energy at the high end of their temperature range, possibly indicating the onset of diffusion-limited growth. Typical analysis results of the effluent of BG's reactor are presented in Figure 5 . Both oxidized and reduced byproducts were detected. The most plentiful products include water, carbon dioxide, and methane. Some independently oxidized carbon compounds (such as carbon monoxide and formaldehyde) as well as traces of two-carbon hydrocarbons are also present. The detected byproducts account essentially quantitatively for input
5366 The Journal of Physical Chemistry, Vol 96, No. 13, 1992
Zawadzki et al.
1
Expt
Model
I
A 0.1110.5
I
two cab ron-
I
!
ethane oxidized carbon carbon oxides carbon dloxide
0.0
0.5
1.0
1.5
2.0
carbon monoxide
time (s)
formaldehyde water -7
Y:
i
obsewed
"6
-5
-6
-3
-4
-2
log (mole fraction)
Figure 5. Gas-phase byproducts from 0.1% T M T + 21% 0,at 741 K and 3 . 5 s reactor residence time. Experimental observations are due to BG.
.
5
10 15 20 25 oxygen (mol O h ) Figure 2. Deposition rates of SnO, from 0.1% T M T and various 0, concentrations at 741 K. (a) Deposition profiles as a function of reactor residence time; curves are results of model simulations, points are experimental results of BG. (b) Maximum deposition rate (GmaX)as a function of initial 0,concentration. Low-0, point used 0.08% T M T rather than 0.1%.
0.0
0.5
1.o
1.5
time (s) Figure 6. Effects of alkene additives on growth rates of SnO, films from 0.1 1% TMT 20% 0,at 752 K. Curves represent simulation results, and points the experimental data of BG.
+
time (s)
Figure 3. Deposition rate profiles of SnO, at 741 K as a function of reactor residence time for various initial concentrations of T M T + 20% 0,.Curves represent simulations, and points are experimental data of BG.
0.39:3.8circular 0.39: 6square
40.4 kcalhol
1.3
1.4
1.5
1.6
1OOO/T(K)
Figure 4. Arrhenius plot of maximum deposition rates of SnO, from T M T 21% 0,.Line through "+" symbols represents simulations of 0.1% TMT in a 7-mm-diameter cylindrical reactor. Other symbols show experimental data from BG, labeled with initial T M T concentration and reactor type and size (width or diameter).
+
carbon and for over 95% of the input hydrogen. (H2 was not detected by the flame-ionization detector used in the analysis and is therefore not included in this figure.) Input TMT is more than
99.9% consumed during the gas residence time in the reactor (about 3.5 s). A notable feature of the films produced by BG is lack of carbon incorporation, as determined by Auger analysis with a threshold of 0.1 atomic %.I1 BG carried out depositions with various additives introduced into the gas stream (Table I and Figure 6). Species such as Br2 and tert-butyl bromide were found to severely inhibit film deposition, by increasing the induction period for film growth and greatly decreasing the rate of film formation. Interestingly, CF,Br, whose addition leads to fluorine-doped film, actually increased deposition rates under most conditions. The alkenes ethene, propene, cis-butene, trans-butene, and isobutene produced less inhibition (Figure 6). These alkenes had little effect on the induction period and reduced film growth rates by amounts varying from less than 10%for ethene, to approximately 35% for isobutene (Table I). The observed inhibition increased with both the size and initial concentration of the added alkene. Reduction in film growth was not uniform but occurred primarily downstream of the point of maximum growth rate. The additives methane, formaldehyde, carbon monoxide, and krypton had little or no observable effect on film deposition. BG studied several organotin and halotin species besides TMT as starting materials for CVD of tin oxide. The two relevant to this study were (CH3),SnOH and (CH,),SnBr. BG observed that the former was oxidized to tin oxide film even more readily than T M T itself. In contrast, (CH,)$nBr reacted more slowly than T M T under CVD conditions, producing growth rates approximately 70% lower. Due to the low vapor pressure of (CH,),SnOH, which is a solid at room temperature, BG did not obtain detailed data on the oxidation kinetics of this material. They did, however, find a considerable temperature dependence, observing no measurable deposit at 623 K, and a significant deposition rate, about 3 A SS', at 673 K. Evidence from the work of BG for the importance of gas-phase chemistry in the CVD oxidation of TMT includes observation of
Kinetic Modeling of the Chemical Vapor Deposition
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5367
TABLE I: Kinetic Effects of Cas-Phase Additive on Tin Oxide CVD additive
initial concn (mol %) additive TMT 0
Gin,,
T (K +2)
15.0 f 1
0.68 3 3 2.9 2.5
0.11 0.11 0.1 1 0.1 1 0.11 0.1 1
752 152 152 152 752 752
0 5 0,l
0.1 0,l 0.1
743 143 743
b
TBB
0 0.6 1 0.86
TBB
0.1
TBB none
0.6 1
0.63 0.63 0.63 0.1 0.1
0.06d 0,06d
none HZ
co
CJ-4 C3HO i-C4H8
none ' 3 4
CH2O none
TBB
Bri
0 11
(A s-')
expt (BG) a a a
14.0 f 0.3 9.5 f 0.3
tm,,
model 13.5 13.3 13.2 12.8 11.3 9.4
expt
(BG)
0,2t 0,05 a a a
0.2 f 0.05 0.15 f 0.05
a
8.6
a
743 743 743 143 743
127 f 10 47 f 3 23 f 3 b b
C
0,9 0,6 1 3 h 0.25 1.45 f 0.1 b b
723 723
5 e
4.1 1.1
c
1.0 x 10-3 3.0 x 10-4
a
*
b e
model 0,16 0.18 0.18 0.2 0.24 0.28 0.20 0.30 0.24
9.2 7.9
b
a
C
(8)
C
c C
4.2 3.0 0.32 0.18
"BG report that the additive had *no effect". bExperimentalvalue unavailable. E Model not directly applicable. dInitial O2concentration was 8-9 mol %. 'BG report that they observed no film growth and collected (CH&3nBr downstream of the heated zone.
an induction period in the tin oxide growth profiles, the identification of byproducts of gas-phase free-radical reactions, and the kinetic effects of gaseous additives on film deposition rates and byproduct compositions. The observation that the growth rate of tin oxide does not peak at the gas inlet indicates that the species which stick to the growth surface were not present in the input gas stream. In B G s flow experiments, the spatial position of the onset of film growth, and of the peak in film growth rate, varied in proportion to the flow velocity, supporting the hypothesis that the rate-limiting steps leading to the immediate film precursor occurred in the gas phase. This hypothesis is also supported by the fact that the inhibitory additives used by BG are known to act as free-radical chain inhibitors in the gas phase. Moreover, "pulsed" inhibition experiments performed by BG indicate there was no poisoning of the substrate surface by gas-phase additives to retard film growth." 3. Model 3.1. Oveniew. A fully detailed model of a CVD system includes gas-phase and surface chemical reactions, gas-phase fluid dynamics, and gas-phase and surface diffusion. Simulation of such a multidimensional model coupling chemical reactions and fluid dynamics requires solution of a potentially large set of coupled partial differential equations-at great computational expense. l2 Gas-phase kinetic mechanisms have often been simplified, or omitted in favor of quasi-equilibrium assumptions, in studies which attempt to accurately model fluid dynamics and diffusion,13 To treat nonequilibrium chemistry in detail, we model a system in which the fluid dynamics and diffusion can be essentially described analytically. Our model is thus implemented as a homogeneous chemical reaction mechanism, with chemical species concentrations calculated as a function of gas residence time in the heated reactor zone. The velocity profile in the cylindrical reactor is approximated by a plug flow, while gas-phase radial diffusion and wall loss are cast in an approximate form identical to that of a first-order homogeneous reaction. Axial diffusion is neglected. Model chemistry is based on the oxidation of T M T through a gas-phase free-radical process forming oxygen-containing tin species such as (CH3)3SnOH,which react further in the gas-phase to form film precursors. Based on known organotin chemistry, and the lack of carbon incorporation into tin oxide films observed by BG, we hypothesize that the film precursors are SnO and SnOz. These species diffuse to the growth surface, where they are adsorbed, further oxidized (in the case of SnO), and incorporated into the deposit. Organic byproducts of T M T oxidation in our model include CHzO, CH3, and CH,, whose further oxidation adds to the pool of gas-phase free radicals. Gas-phase additives such as Brz, TBB, or alkenes act as free-radical scavengers to disrupt
the oxidation chain and ultimately retard film growth. In the interest of treating chemical reactions in detail, we do not include homogeneous nucleation in our model. As noted above, BG observed significant quantities of homogeneously nucleated powder in depositions with initial concentrations of TMT of more than approximately 0.2-0.3%. This powder formation decreases observed growth rates below those which would be predicted from the same chemical mechanism in the absence of nucleation. Our model in its present form is thus quantitatively applicable only to deposition processes with initial TMT Concentrations less than 0.2%. 3.2. Spatial Dynamics. We treat CVD in a tubular reactor in which a premixed reactant gas stream flows under fully developed laminar flow conditions. To reduce its mathematical description to a one-dimensional problem, we assume plug-flow behavior for the mixture. This leads to constant radial concentration profiles for species which do not react at the tube surface. The concentration profiles of such species thus vary only as a function of axial distance from the entrance to the heated zone. This distance may be expressed as a residence time, x / 8 , where x is the distance and the linear (plug) flow velocity. With this definition of residence time, the usual temporal ordinary differential equations of mass action kinetics may be applied. Species which undergo surface reactions have nonuniform radial concentration profiles even in plug flow. If their loss to the surface is completely efficient (i.e,, unit sticking probability), then an approximate equation for the rate of change of the radially averaged gas-phase species concentration, { P ) ~ caused , by loss to the walls, is given by6b*14
where], is the first positive node of the Bessel function Jo (Le. the first positive root of Jo(x) = O;j,= 2.404 ...), D is the diffusivity, and R is the tube radius. This diffusive loss term has the form of a first-order kinetic loss process with rate constant k = j,2D/R2.The temperature dependence of such rate constants arises from that of the diffusivities. Diffusive wall loss was included for H, 0, OH, H 0 2 , H202, SnO, and S n 0 2 in all reported simulations, by incorporation of reactions H1, H20, H22, H28, H32, T18, and T19 in the oxidation mechanism (Table 11). The rate constants listed for these processes in Table I1 are based on the species diffusivities listed in Table 111, combined with a reactor diameter of 7 mm. Species diffusivities were calculated using standard gas kinetic methods, including corrections for species polarity.I5 Molecular force parameters for simple carbon-, hydrogen-, and oxygen-containing species were taken from the literature,I6 while those for SnO were
Zawadzki et al.
5368 The Journal of Physical Chemistry, Vol. 96, No. 13, 1992
TABLE II: TMT Oxidation Mechanism" labcl H1 H21 H3 H4
HS H6' H7 H8l H9 H10 Hll H12 H13t H14 H1S H16 HI7 HI8 H19 H20 H21t H22 H23 H24' H25 H26' H27 H28 H293 H30 H31 H32 H33* H34 H35 H36
c1 c2 c3 c4
c5 C6 c7 C8 c9 c10 ClI c12 C13 C14 c15 C16 C17 C18 C19' c20 c21 C22' C23 C24 C25 C26 C27 C28 C29 C30 C3 1 C32 c33 C341 c35 C36r c37 C38
rcactants H H+H H + H20 H + Hi01 H H@2 H + O H+OH H+OH H HO, H HO, H HO,
+
+ + +
H + 0, € + 0, i
H2 + 0 Hi OH Hi HOz Hi 0 2 HzO 0 HzO HO2 0
+ + +
+
+ 0+0
OH
OH+O QH+O OH OH OH OH OH HOZ HO2 HO2
+ + +
+0 H02 + HOI HO,
Hi02 Hi02 H202 HzOz HZOZ
+0 +0 + OH
CH, + H CHI + 0 CH4 O H CHI H 0 1 2 CH4 0 CH4 C H 3 0 CH, CH,O, CH, + H CH; + HI
+
+ + + +
+0 CHI + OH CH,
CHj CHI CHI CH, CH,
+ H02 + H202 + 02
+ 0,
+ CH, CH,+ CHiOZ CHI + CH2O CH30 CH,O + O2 CH,O + CH2O CH302 CH302 + H CH302 + H2 C H 3 0 2+ H 0 2 CH302 + CH302 CH302 + CH20 CHJOIH CH20 + H CH20 + 0 CH20 + OH CH2O + H 0 2
+
CH2O 0 2 CHO CHO + 0 2
co+o CO CO
+ OH + HO2
-
products A* Hydrogen - - Oxidation Reactions -L wall 1,41 (-2) H, 5.4 (18) *H,+OH 6.2 (7) ---L HI + H02 4.82 (13) 2.4 (13) H I 0 + OH OH 4.7 (18) 4.9 (3) -Hz+O HZO 2.2 (22) H, 0, 6.62 (1 3) --c HZO 0 1.8 (12) -OH+OH 1,69 (14) -OH+O 1,68 (17) 4 H02 6.42 (18) a H + O H 4.33 (13) 6.3 (6) H + H20 3.0 (13) H Ha02 -H+HO, 1.8 (14) -OH+OH 4.6 (9) H 2 0 , + OH 1.8 (13) wall 3
