306 Epitaxy 6.11 Recommended Readings Ball, C.A.B., and J.H. Van der Merwe. 1983. "The Growth of Dislocation-Free Layers." Chap. 27 in Dislocations in Solids, v. 6, ed. F.R.N. Nabarro. North-Holland. Freund, L.B. 1992. "Dislocation Mechanisms of Relaxation in Strained Epitaxial Films " MRS Bull. July:52. Herman, M.A., and H. Sitter. 1989. Molecular Beam Epitaxy: Fundamentals and Current Status. Berlin: Springer-Verlag. Houng, Y.-M. 1992. "Chemical Beam Epitaxy." Crit. Rev. in Solid State and Mater. Sci 17:277. Hull, D., and D.J. Bacon. 1984. Introduction to Dislocations, 3rd ed. Oxford, U.K.: Per-gamon Press. Joyce, B.A. 1985. "Molecular Beam Epitaxy." Rep. Prog. Phys. 48:1637. Saloner, D. 1986. "Characterization of Surface Defects and Determination of Overlayer Nucleation and Growth by Surface-Sensitive Diffraction." Appl. Surf. Sci. 26:418. Suntola, T. 1989. "Atomic Layer Epitaxy." Materials Science Reports 4:261. Tsao, J.Y. 1992. Materials Fundamentals of Molecular Beam Epitaxy. Boston, Mass.: Academic Press. Weisbuch, C, and B. Vinter. 1991. Quantum Semiconductor Structures. Boston, Mass.: Academic Press. Chapter 7 Chemical Vapor Deposition The use of chemical vapors and gases as sources of film-forming elements was introduced in Sec. 6.5.4 in the context of epitaxy in the high-vacuum regime (Kn > 1). In this chapter, we consider the use of these sources at higher pressures in the fluid-flow regime (Kn « 1), where the process is known as chemical vapor deposition (CVD). Gaseous source materials allow process operation in this regime because they do not condense (by definition) on surrounding room-T surfaces during transport to the substrate. Therefore, the line-of-sight transport geometry from source to substrate which is required in the physical vapor-deposition (PVD) processes is not required in CVD. A monolayer or two of transporting gas may adsorb on the room-T surfaces, but this adsorption quickly saturates. On the other hand, upon reaching the heated substrate or other hot surfaces, some fraction of the adsorbing gas reacts to form the film. This fraction is expressed by the sticking coefficient, Sc, defined by Eq. (6.17). It is sometimes referred to as the "reactive" sticking coefficient, although this term seems redundant. Often, Sc « 1 at the substrate, and this makes it possible to uniformly coat substrates having convoluted surfaces, such as microcircuit patterns, or to coat large batches of substrates on all sides at once, such as tool bits. With Sc « 1, the gas can still reach remote substrate areas despite many encounters with hot surfaces along the way. This process was illustrated in contrast to PVD behavior for the filling of a trench in Fig. 5.17/". The potential for uniform coating of nonplanar substrates—that is, "conformal" coating—is a key advantage of using gaseous sources in either flow regime of Kn. Various other advantages and disadvantages were mentioned in Sec. 6.5.4. Three additional advantages apply spe- 306 Chemical Vapor Deposition cifically to the higher-pressure regime. One is that higher deposition rates can sometimes be obtained while still maintaining conformality. Another is that simultaneous etching of the depositing film can often be achieved by establishing sufficient partial pressure of a suitable chemical etchant. This technique can improve selectivity when one wants to deposit only on activated surface areas, or only on one crys-tallographic plane (anisotropic epitaxy), or only one of the possible solid phases, as in diamond versus graphitic C. The third advantage of higher process pressure is that only one stage of pumping is required ("low-pressure" or LP-CVD), or no pumping in the case of atmospheric-pressure operation (AP-CVD). However, the gas-transport problems to be discussed below are all more difficult to deal with in APCVD than in LPCVD. The basic thin-film process sequence of gas supply, transport, and deposition from Fig. 1.1 is presented in more detail for the case of CVD in Fig. 7.1. The gas-transport step is much more complex in the fluid-flow regime than in molecular flow, and therefore much of the chapter will be devoted to examining transport behaviors—mainly, free convection, homogeneous reaction, and diffusion. The discussion of the deposition step will focus on its surface processes, since most of what source-gas supply transport and homogeneous reaction forced convection free convection deposition gas-phase diffusion ,~~r~ I adsorption | rpt E surface reaction 3_ de sorption film composition I and structure 7.1 Gas Supply 309 table 7.1 Typical Overall Reactions Used in CVD pyrolysis (thermal decomposition) SiH4(g) -> Si(c) + 2H2(g) SiH2Cl2(g) -> Si(c) + 2HCl(g) oxidation hydrolysis reduction displacement CH4(g) -> Ctdiajnond or graphite) + 2H2(g) Ni(CO)4(g) -> Ni(c) + 4CCHg) SiH4(g) + 202(g) -> Si02(c) + 2H20(g) 3SiH4(g) + 4NH3(g) -> Si3N4(c) + 12H2(g) 2AlCl3(g) + 3H20(g) -*Al203(c) + GHCl(g) WF6(g) + 3H2(g) -> W(c) + 6HF(g) Ga(CH3)3(g) + AßH3(g) -> GaAs(c) + 3CH4(g) ZnCl2(g) + H2S(g) -> ZnS(c) + 2HCl(g) 2TiCl4(g) + 2NH3(g) + H2(g) -» TiN(c) + SHCKg) Figure 7,1 Sequence of process steps in CVD. has previously been said about bulk film structure and interaction in Chaps. 5 and 6 also applies to CVD films. To give a flavor of the chemistry involved in CVD, Table 7.1 lists some of the commonly used overall reactions and their chemical types; many others are listed elsewhere [1,2], We will see later that such overall reactions really consist of a series of reaction steps, some in the gas phase (homogeneous) and some on the surface (heterogeneous). Each reaction step has a rate determined by activation energy and process conditions, and any one of these rates can be the one that controls the film deposition rate. Alternatively, the gas-supply or transport step can be the one which controls deposition rate. Control by one or another of the steps in Fig. 7.1 has various advantages which will become clear below. It is important in CVD to determine the range of process conditions over which each step becomes the controlling one, and we will examine several techniques for doing so. The pyrolysis of silane (SiH4) to deposit Si will often be used as an example, because it is one of the most extensively studied reactions. It is also quite complex, despite the simple overall reaction, so it illustrates all of the reaction phenomena to be discussed. 7.1 Gas Supply Figure 7.2 illustrates typical elements of the "gas jungle" of plumbing used to supply CVD source gases and vapors to the deposition reactor. Not all of these elements will be used in a given reactor, and actual design will depend on the degree of gas hazard involved and on the operating pressures at the source and in the reactor. There are three aspects to gas-supply design: (1) protection of personnel and environ- 7.1.1 Safety 311 ||i fi sl I I ! ii i! H i> >S a> n> o.E S.B a.S S$ _ X*£^i ® ® ® B £) ment from the frequently hazardous properties of the reactants, (2) regulation of a steady and known flow of each gas, and (3) minimization of contamination in the process stream. We will discuss each of these aspects in turn below. 7.1.1 Safety Gas-supply safety starts with careful design and construction to minimize the possibility of leaks or valve-operation errors. It also provides detection of hazardous conditions such as excess pressure or leaks before they become catastrophic, coupled with automatic shutdown of the gas supply. Leak prevention is also important for process purity. Plumbing should be welded wherever possible, and metal-gasketed connecting fittings should be used elsewhere. Fittings that seal directly against the tubing instead of against a welded-on flange are not recommended, because they develop leaks more easily when stressed. Valves should have bellows or diaphragm stem seals. Wherever elastomeric seals are unavoidable, the elastomer must be chemically compatible with the reactant gas. Let us examine the safety elements in Fig. 7.2, following the gas flow path. The high-pressure gas cylinder (a) is stored in an outdoor cabinet connected to an exhaust duct, to minimize personnel exposure in the event of a leak. Gas sensors in the duct (6) as well as in the reactor-cabinet exhaust duct (c) and in the room (d) automatically shut off the pneumatically operated valves upon detecting a hazardous level. The first pneumatic valve is best installed in the gas cylinder at 1 [Eq. (3.18)]. A parabolic u profile is also obtained for flow between parallel plates (Exercise 7.2). This situation would apply to a rectangular-tube reactor of large width/height ratio. For a height of y0 and for y = 0 at the centerline, u(y) = *2 " 2n I 2 y0 4-y (7.8) and ■ - mm (7.9) The degree to which the reactor flow falls short of breaking into turbulence can be determined by calculating the Reynolds number, Re. Dimensionless numbers such as Re are very useful in characterizing transport situations in which the behavior can change with conditions from one mode to another. We have already encountered Kn, Pe [Eq. (6.23)], and the deposition purity ratio (Sec. 2.6). The importance of Re warrants a brief derivation here. Re is the ratio of the momentum (inertial) force to the viscous-drag force operating on the fluid. These forces respectively destabilize and stabilize the flow pattern, 7.2.1 Laminar flow in ducts 321 and when Re exceeds 1200 or so depending on geometry, turbulent instability begins. For flow in a tube, the momentum per length z of tube is k = (7ir02z)pma, where pm is the fluid's mass density. The force that would be required to stop this momentum within length z is k(du/dz) = ku/z = jcr02pmQ2. The viscous drag force on the fluid against the wall is (2nr0z)n|du/dr|, where |du/dr| is evaluated at r0 using Eqs. (7.5) and (7.7): |du/dr| = 4u/r0. Taking the ratio of these two forces and dropping the numerical factors, we have zq La La _ Lüf pM\ (Vpm) = v " q IrtJ (7.10) where (r02/z) has been replaced by L to represent a characteristic linear dimension of the reactor for the more general case. The "kinematic" viscosity, v (cm2/s, or Stokes) = q/pm, may be thought of as the "momentum diffusivity" and is analogous to the mass diffusivity, D (cm2/s). The last equality in Eq. (7.10) assumes ideal gas and shows that Re decreases with decreasing p at a given u, since q is independent of p by Eq. (2.28). Using q = 88 uP = 8.8X10-6 g/cms and pm = 8.2X10-5 g/cm3 for H2 at room T and 1 atm, so that v = 1.07 cm2/s, and using L = 5 cm and a = 4 cm/s, we see that the units cancel in Eq. (7.10) as they should, and that Re = 19. This is way below the onset of turbulence, and it would be even lower at lower p, so we conclude that flow is always laminar in CVD. More complicated flow patterns than the parabolic one are often encountered, however. These can be caused by abrupt changes in flow path or by steep T gradients. We will consider T gradients in Sec. 7.2.3. The flow path changes first at the point of gas injection, where the supply line expands to the reactor diameter. If the expansion is gradual and u is not too high, one obtains the nearly parallel flow pattern shown in the bottom half of Fig. 7.7. However, if the expansion is too rapid, because of an abrupt diameter change or excessive u, the flow separates from the wall and recirculates in the "Hamel-flow" vortex shown in the top half of the figure [6]. Note that this is not turbulence, because the pattern does not vary with time. Such vortices are undesirable because they increase the reactant residence time, thereby lengthening gas-composition switching time and sometimes causing excessive homogeneous reaction. Their occurrence can be detected by observing the flow patterns using tracer smoke. The flow path changes next upon encountering the susceptor, where u must drop to zero due to viscous drag along this new surface, as shown in Fig. 7.8 for the tube reactor geometry. But within only a few L lengths downstream at the low Re of CVD, the parabolic profile is re- 322 Chemical Vapor Deposition 7.2.2 Axiay m metric flow 323 Figure 7.7 Two alternative reactor-entrance geometries and flow patterns (upper and lower halves). The upper pattern is to be avoided. 2L Figure 7.8 Velocity boundary layer of width 6y forms at the susceptor leading edge in a tube reactor. stored. The initial distortion of the profile does not affect the deposition rate significantly anyway, as we will see in Sec. 7.4. This flow situation is sometimes modeled with the susceptor acting as a wing passing through a stationary fluid at velocity -u. In the wing model, the position above the wing surface at which the fluid has become accelerated by 1 percent of the way toward -u is defined as the edge of the velocity boundary layer, by. Clearly, by will expand moving downstream along the wing, but for most of the length of a typical susceptor in a CVD tube, the u profile is parabolic and does not fit this model, so the concept of by has no meaning. We will see below that there is a meaningful by in the axisymmetric flow pattern. 7.2.2 Axisymmetric flow In this reactor geometry (Fig. 7.5a), the flow pattern is similar to one of the few two-dimensional flow situations for which an analytical solution to the Navier-Stokes equations has been found. This solution is often used in modeling CVD, but we will see below that its applica- bility is limited. The analytical solution [7] assumes that a stream of fluid of radius rs is approaching an infinite, planar, stationary surface at uniform velocity u~ in the -z direction, as shown on the left-hand half of Fig. 7.9. At some point of approach, uz begins to slow down, reaching a stagnation point of zero flow at z = 0 and r = 0. Meanwhile, radial velocity, ur, begins to increase as the fluid becomes deflected by the surface. In the "potential-flow" region, far enough above the surface so that ur is not slowed down by viscous drag against it, the functional forms u. = -2Bz and ur = Br (7.11) (7.12) are found to provide a solution [7] to the flow equations. Here, B is an unspecified constant. In this potential-flow region, the flow direction is changing while uz remains independent of r and ur remains independent of z, as shown in the figure. Closer to the surface, however, viscous drag causes u,. to decrease toward zero at z = 0, as also shown. The velocity boundary layer's edge is defined as before: it is the z value at which ur is reduced by 1 percent from its free-stream value. With this Hz l.i.-Jj L_T-f- ! ! ! r 1 ! 1 *' -i-f potential___Tlu, flow x \ \ I \ \ X \ X viscous flow stagnation point I 5vr flow model ■*—|—► actual reactor Figure 7.9 Axisymmetric flow geometry and approximate flow patterns for analytical flow model and for actual reactor. 324 Chemical Vapor Deposition definition and Eqs. (7.11) and (7.12), the thickness of the radial-velocity boundary layer is found to be 8 = 22- (7.13) where v is the kinematic viscosity [Eq. (7.10)]. Note that, according to this model, 8^ is independent of r—at least for r < r8. This is because two effects are cancelling each other: the increase in 8^ with increasing downstream distance, r, as in Fig. 7.8, and the decrease in 8^ due to the increase of ur with r. To estimate S^, we need to determine B. Since for r > r8, all of the flow has been redirected radially, it is reasonable to assume that Since kinetic energy is conserved in the potential- ur-> ur at r = r„ flow region, we also have u™ = u Eq. (7.12), we obtain B = u~/rs,rso that Using this information in (7.14) Taking v = 1.07 for H2 at room T and 1 atm and u" = 4 cm/s as in the last section, and using rs = 3 cm, we find that 6^ = 2.0 cm—a value almost as big as r„ itself. Even for the much higher-density gas Ar, we have v = 0.13 cmf/6, and 8^ = 0.70 cm. Actual CVD conditions with a heated susceptor will cause u™ to increase as the gas expands at a fixed inlet velocity, but it will also raise v, so that 6^ <* TV4. At lower reactor pressure with the same u™ , 8^ will be even higher because of the higher v (= q/pm). The fact that 8vr is not much less than rs becomes a problem for this model, because the starting assumption of an infinite planar surface is not valid in an actual CVD situation, where the susceptor radius is less than rs as shown on the right-hand half of Fig. 7.9. The flow around the susceptor edge alters the flow along the surface for several 8^ in from the edge, so that one would actually expect 8^ to decrease with increasing r in this CVD geometry as shown in the figure, rather than to be constant as in Eq. (7.13). A second problem with 8^ is that it does not directly relate to the boundary-layer edge we are really seeking, which is where the reactant transport changes from convec-tive to diffusive. The 8^ of Eq. (7.13) is defined by drag on ur, whereas reactant is transported down to the surface by uz. Thus, the z position at which uz starts to decrease could define the edge of another velocity boundary layer, 8^. From Eq. (7.11) and our estimate of B, we obtain simply 8VZ = tJ2 7.2.2 Axisymmetric flow 325 (7.15) This, too, must be considered an oversimplification on account of edge effects, but again we see that 8yZ is not much less than rs. Two main conclusions result from the above analysis of axisymmetric CVD flow with a stationary susceptor. First, the velocity boundary layers are never going to be much smaller than the susceptor radius under any reasonable flow conditions. Second, one must be careful (in any flow geometry) to select the appropriate boundary layer—the one that relates to reactant transport. Rotating the susceptor disc at an angular velocity co (rad/s) improves the above situation somewhat. The resulting flow pattern, shown in Fig. 7.10, is characterized by a boundary layer of fluid being dragged around with the disc and thrown outward by centrifugal force. This centrifugal-pumping action also sucks fluid down toward the disc along z. Thus, there are three velocity components: radial (ur), circumferential (Uo,), and axial (uz). Like the stationary disc, this special flow situation has an analytical solution [7, 8], given a disc radius much Figure 7.10 Axisymmetric flow pattern over a rotating disc. (Source: Reprinted from Ref. 7 by permission. © 1968 by McGraw-Hill Book Co.) 326 Chemical Vapor Deposition 7.2.3 Free convection 327 (0 and the velocities (F, G, H): u_ = u = ru)F(0 rcoG(0 (7.16) (7.17) (7.18) (7.19) STÄfcÖis the dimensionIess T profile" ^» e = -í— Ts-T° 1.5 -1— -'--'-1 -H 301 K 5 10 15 DimensionIess Height, ? 20 Flour. 7.11 Profiles of dimensionIess T (8) and velocity over the heated rotating disc shown in Pig. 7.10 The velocity components are radial (F), circumferential (G), and axial (H). (Source: Reprinted from Ref. 8 by permission.) An asymptotic value of H = 0.884 for axial velocity is reached at a large height above the disc, so the corresponding uz from Eq. (7.19) must be adjusted, by way of to, to match the inlet flow velocity in the reactor tube, u~, if the calculated flow pattern is to be realized in an actual CVD reactor [8], If co is too low, the beneficial effect of the rotation in reducing 5y will be lessened. If to is too high, the excess flow being pumped will recirculate up the sidewall of the tube, producing an undesirable vortex similar to the one shown in Fig. 7.7. The onset of this flow disturbance has been observed using tracer smoke [8]. Taking v = 1.07 for H2 at room T and 1 atm and u" = 4 cm/s as before, we find that the upper limit to 0) is 19 rad/s or 180 rpm. Given this, we can now determine OyZ by observing in Fig. 7.11 that H has dropped by 1 percent at about £ = 5. Combining this with Eqs. (7.16) and (7.19) to eliminate go, we have - 4.4v/u° (7.20) and for the above case of H2 at 4 cm/s, 8^ = 1.2 cm. This is not much smaller than the Oy,. or OyZ found for the stationary disc under the same conditions. However, the difference between the two 8^ values will increase with r8, since here 8^ is independent of rg; whereas, for stationary flow both 6yZ and increase with rg. Also, one must ask again whether 5^ is the relevant boundary layer for considering reac-tant transport. After all, with rotation, ur increases within that boundary layer (F in Fig. 7.11) due to the centrifugal action; whereas, without rotation, it decreases due to the viscous drag. This increase will assist reactant transport to the surface by reducing the z value at which diffusive transport must take over from convection. Empirically, it is often found that rotation does improve film-thickness uniformity. Another advantage of rotation is that the momentum induced thereby in the gas tends to dominate the flow pattern and thus avoid the free-convection problems to be discussed in the next section. 7.2.3 Free convection When the susceptor is heated in either the axisymmetric or the horizontal tube reactor of Fig. 7.5, heat transfer to the adjacent gas causes the gas to expand and therefore become less dense than the cooler gas farther away. In the absence of forced downward flow, the gas above the susceptor rises because of this buoyancy, and then falls again after being recooled. This instability develops into circulating flow patterns or "roll cells" known as "free" or "natural" convection. Free convection will not develop in the isothermal batch reactor. Calculated circulation patterns (Jensen, 1989) for a horizontal tube reactor of rectangular 328 Chemical Vapor Deposition 7.2.3 Free convection 329 cross section are shown in Fig. 7.12a, looking along the z-axis direction of forced convection through the tube. The direction of circulation depends on the T of the tube sidewalls. For a tube with cooled side-walls, the flow is downward near the sidewalls and upward near the centerline; whereas, with insulated sidewalls, the pattern is reversed. The direction and velocity of this flow affect the transport rate of reac-tant to the substrate and therefore affect the lateral uniformity profile of the deposited film. 300K , 300K (a) }"«•«■"■.......■ \..............------1 1000 K 1000 K 300 K V. 300 K (6) / / i ja 1000 K I 300 K Figure 7.12 Typical free-convection roll cells: (a) horizontal SBfcg! a,°n« -i8) «S "wo alt r nate 8ld conduions in8uIated ^ ^ er flMndownflow asymmetric reactor, showing two alternate avoTd " W-11,6 recirculati^ P-tte™ (right, isZt The degree of free-convective flow scales with the ratio of buoyancy force to viscous force and with Re. These ratios together constitute the dimensionless Grashof number [9], r Ra Pmg«TvK-T-)L3 _ gaTV(T8-T")L3 Pr gM2p2(Ts-T° R2T3r,2 (7.21) where g = gravitational acceleration = 980 cm/s2 ctrv = dV/VdT = volumetric thermal-expansion coefficient, K_1 Ts = substrate or susceptor T, K T = mean T of circulating gas, K Other notation is as used above. The last equality assumes the ideal-gas law, Eq. (2.10). Sometimes the Rayleigh number, Ra, is used instead of Gr to evaluate free convection. For gases, Ra ■ Gr, because the Prandtl number, Pr, is near unity. Pr = s? tf- - 0-8 ± 0-2 M Kp where Cp/M is the heat capacity per gram and KT is the thermal conductivity. The characteristic dimension, L in Eq. (7.21), is taken as the smaller of the two dimensions in which the roll cell lies. Using v ■ 1.07 for 1 atm H2, and taking L = 5 cm, we have Gr = 1.2xl05—high enough that free convection definitely will occur. The critical value of Gr above which free convection becomes significant cannot be stated quantitatively, because it varies with geometry and with the amount of forced convection. For example, Fig. 7.126 shows two alternate flow patterns in an axisymmetric reactor (Jensen, 1989). In the absence of forced downward flow, uz, the circulation pattern shown at the right typically develops for large Gr. However, there is always a finite uz in CVD, and a large enough uz will eliminate the circulation, producing the more parallel flow shown on the left of the figure. In addition, the flow pattern is bistable over some range of Gr and uz. That is, if the circulation pattern is allowed to develop before the uz flow is turned on, it can persist to larger uz than if flow is started before the susceptor is heated. Reactor shape and susceptor rotation will also affect the critical value of Gr. 330 Chemical Vapor Deposition Circulation against the direction of uz results in an undesirably long gas residence time in the reactor. Circulation transverse to uz, as in Fig. 7.12a, can degrade uniformity. Inspection of Eq. (7.21) shows that reducing pressure is the most effective way of reducing Gr, since pressure is the most widely adjustable among the choices of process variables there. Low Gr is one of the main advantages of LPCVD over APCVD. In the case of the axisymmetric reactor, one can also just invert it so that the hotter gas is already at the top and there is no driving force for recirculation. However, this remedy requires supporting the substrate on its front face in a way which neither disturbs the flow pattern nor contaminates the growth surface. Because of the difficulty of predicting flow patterns, it is best to examine them experimentally for the particular reactor at hand. This can be done easily using tracer smoke, but there are two problems. One is that smoke contaminates the reactor. The other is that in steep T gradients, the smoke patterns will be distorted from the actual flow pattern by the thermophoretic motion of particles down the T gradient, as will be discussed in Sec. 7.4.3. Alternatively, "schlieren" photography or interference holography [10] can be used to observe the patterns of optical interference fringes which result from refractive-index variation along the T gradient. 7.3 Reaction The source gases become heated at some point during their transport to the substrate, this point depending on the type of reactor (Fig. 7.5) and the flow pattern within it. Thus, reaction often begins in the gas phase rather than occurring entirely on the substrate surface. The products of these reactions are usually more reactive with the substrate than are the source gases themselves. Excessive gas-phase reaction can produce particles of film material within the gas phase, and these settle out as powder. It is important in CVD to understand and control both the gas-phase and the surface reactions. 7.3.1 Chemical equilibrium The simplest analysis of a reacting system assumes that all species reach chemical equilibrium with each other. Since CVD reactors are continuously producing a net change of reactant to product, they cannot be operating at equilibrium, which by definition entails no net change. Moreover, it is often necessary to operate far from equilibrium in order to avoid powder formation or to achieve deposition-rate uniformity over large areas, because these objectives are accomplished by flowing gas through the reactor much faster than it can react. Never- 7.3.1 Chemical equilibrium 331 theless, the calculation of equilibrium composition is a convenient and useful starting point for the analysis of a CVD process. At least it tells us what reactions are possible and how far they can proceed in the equilibrium limit. How far they actually proceed is determined by reaction rate and by gas-phase diffusion, which we will discuss later. It was shown in Eqs. (4.4) through (4.6) that a reacting "system" operating at constant pressure, p, reaches equilibrium when its total Gibbs free energy, G, is minimized. [A system operating instead at constant V would reach equilibrium when the Helmholtz free energy, (G - pV), was minimized, but CVD always operates at constant p.] Here, G is in units of kJ for the total system, not in kJ/mol. The "system" under consideration starts as some fixed number of moles of the feed gas (supply gas) mixture, which then reacts to various gaseous and solid products as it moves through the reactor at constant p. For this mixture of reactant and product species, the total free energy is G(kJ) =£Nmip, (7.22) where is the number of moles of the ith species, and m is its chemical potential. Recall from Eq. (4.7) that m (kJ/mol) is the incremental Gibbs free energy per mole of i added to the mixture. We repeat here Eq. (5.28) for u, which was derived for ideal gases. u; = Ui°(T) +RT In^i (7.23) This gives Uj versus the partial pressure of i, p;, in the reactor at temperature T, relative to m°(T), which is the Pj at the standard reference pressure, p° = 105 Pa = 1 atm, and at the same T. Since the ^ of an ideal gas at a given p, is not influenced by the presence of other species, m°(T) is identical to the molar free energy of formation of that species from its elements in their standard states, AfG,0 (kJ/mol). The standard state of an element is its common phase (solid, liquid, or gas) at 105 Pa and 298 K, and that phase is assigned G = 0 at 105 Pa and all T. Most AfG° values can be found in handbooks [11,12] or in various on-line data bases [13]. Note that AjG° tends to be a slowly varying and often linear function of T, some examples are shown in Fig. 7.13. For a gas-phase species, Pj can be found from ArG° and Pj using Eq. (7.23). For condensed phases such as the depositing film, the p dependence of p is negligible. When the film is a solid solution (an alloy) rather than a pure element or compound, the p of each species in the solution is reduced by the mole fraction Xj to which it is diluted. For "ideal" solutions, 332 Chemical Vapor Deposition 7.3.1 Chemical equilibrium 333 400 -1800 Figure 7.13 Gibbs free energies of formation for selected (c) compounds at 105 Pa [12]. selected Mi = m°(T) + RTIn Xj gaseous and solid (7.24) This dilution effect is closely related to the reduction of a species' vapor pressure by dilution [Eq. (4.21)]. However, for the present, we will deal only with pure solid phases. Once the p.j equations for the species in a reacting system have been written, the system's equilibrium composition can be determined numerically by minimizing system G in Eq. (7.22), subject to the following constraints: non-negative Nm values, fixed total p (=Xpj), and conservation of the total amount of each element as it becomes distributed among the various product species (that is, conservation of mass). Programs such as SOLGASMIX [14] and BELLTHERM [15] are available for calculating the thermodynamics of complex systems that are undergoing multiple simultaneous reactions. However, to obtain more insight into equilibrium behavior, we consider instead a single generalized reaction between molecules A and B to form products C and D: vAA + vBB vcC + vDD (7.25) Here, the V; values are the stoichiometric coefficients that satisfy the mass balance for all chemical elements in the reaction. The double arrow indicates that the reaction is reversible and proceeds in both directions. Some typical deposition (heterogeneous) reactions were listed in Table 7.1. Gas-phase (homogeneous) reactions can also be important, such as SiH4 <^ SiH2 + H2 and BC13 + H2 *j HBC12 + HC1. (Note that all the V; values happen to be unity in these two reactions.) Assume for now that Eq. (7.25) is the only significant reaction of A and B, that some fraction, of A has reacted away, and that there is present an excess fraction, y, of B above the stoichiometric amount vB. Then, for vA moles of A at the start of reaction, Eq. (7.22) becomes G = (1 - £)vaPA + (!-£ + y)vBuB + ^(vcpc + vDpD) (7.26) and at equilibrium, dG/d^ = 0 = -vApA - vBpB + vcPc + vDpD <7-27) where both t, and y have vanished. Inserting Eq. (7.23) for m gives -ArG°(T) = -(vcpc° + vDpD0-vApA0-vBpB°) = RT In (pv)c(pvJd UV)a(pv = RT InK b (p°) Av (7.28) where A,.G0 is the free energy of reaction calculated from p° data at the T of interest, and K is known as the equilibrium constant of the reaction. The net change in molarity, Av = \q + Vrj - vA - vB, drops out of Eq. (7.28) if the p, values are given in units of 105 Pa (= atm), since then the reference pressure p° = 1. Equation (7.28) is the general form of the expression arrived at in Eq. (5.31), which applied to the first-order reaction of an adsorbed spe- 334 Chemical Vapor Deposition cies into a transition state. It is the central equation of chemical equilibrium. If there are multiple simultaneous reactions occurring, their equilibria must all be satisfied simultaneously, again subject to the constraint that p = Zpj- This p; sum includes nonreacting species as well, so the result will vary with dilution if Av * 0 (see Exercise 7.8). The mass-balance constraint in Eq. (7.28) is contained in the Vj values, since they come from the balanced Eq. (7.25). Further discussion of equilibrium calculations is given by Smith (1980). Equation (7.28) can provide various types of information useful in CVD. It predicts the upper limit of reactant conversion to gaseous products (Exercises 7.7 and 7.8). It also tells whether deposition can occur and what solid phases are likely to form, and we give several examples of such prediction in the remainder of this section. In integrated-circuit fabrication, the deposition of W from WF6 vapor is sometimes used for Si contact metallization. Usually, selective deposition is desired, meaning deposition on the exposed Si areas but not on the surrounding Si02. The following reaction is the most favorable one on Si02; that is, it has the lowest Aj-G": WF6(g) +2si02(c) W(c) +|SiF4(g) +3-02 (g) (7.29) where (g) and (c) denote gaseous and condensed (liquid or solid) phases. From the data of Fig. 7.13, it is found that at a typical deposi- Znit >K ' Ar = +42° ^ f°r thlS ^tion. ^us, using kq. (7.28) with p; in atm, 6 K = p3/2(SiF4)p3/2(0,) P(WF,) p (SiF4) ^ -A,.G0/RT P(WF,) = 6 , „-420/2.3 x 0.0083 x 700 , „-31 = 10 -10 (7 30) Note that there are no p; terms here for the condensed-phase species, in accordance with the discussion following Eq. (7.23). The above result says that even for a high WFg P; of 1 atm, the product-species Pi values would have to kept below 10~10 atm for the W deposition reaction to reach equilibrium. For higher product pj values, the driving force toward equilibrium is in the reverse direction, that is, etching of W in an attempt to increase the p; of WF6. Since keeping the product pj values this low would require a ridiculously high flow rate of WF6, W cannot be deposited on Si02 from WF6 alone. On the other hand, the reaction of WF6 with elemental Si to form W and SiF4 has a 7.3.1 Chemical equilibrium 335 much lower ArG° of -707 kJ/mol at 700 K, and in fact this reaction occurs readily up to a limiting W thickness of = 20 nm which is imposed by the need for Si to diffuse through the W film [16]. Thicker W films are deposited using the reaction WFfi + 3H2 «- W(c) + 6HF(g) (7.31) or the reaction of WF6 with SiH4 gas to form W, HF, and SiF4. Both of these reactions can be found from the data of Fig. 7.13 to be very favorable (large negative AyG0). Manipulation of the pj values which make up K can be used to drive a reaction in the desired direction. For example, C contamination in GaAs deposited from (CH3)3Ga occurs due to CH3 decomposition on the surface at high substrate T. Without knowing the details of the surface reaction mechanisms, one can assume an overall reaction, C(a) + 2H2(g) (7.33) (7.34) Here, subscript (+) denotes the forward direction in a reversible reaction such as Eq. (7.25), and nA B are the reactant concentrations in mc/ m3. The conversion to partial pressures p^B assumes the ideal-gas law [Eq. (2.10)]. Note that the units of the rate constant, k+, will depend on the reaction order, and that kB must be in J/mc • K. It is important to recognize that the order of a reaction is not just the sum of the reactant coefficients, v,, in the stoichiometric equation [such as Eq. (7.25)]. This is because such an equation represents an overall reaction, which generally involves more than one reaction step. For example, Fig. 7.15 maps the reactions believed to be important in the deposition of Si from silane by the overall reaction SiH4(g) -> Si(c) + H2(g) In general, the rate of an overall reaction is the rate of the slowest step in the fastest of various parallel reaction pathways. The fastest path- SiH. k, SiH2+H2 L- +SiH M Si2H6 D, nH2 D, !-+Si f ^SinH2n+1-^ Powder kP . |Scl k SiH4(a) Si + 2nH-*i2SiH3(a) ,M *° thaTwe a+ B -) /RT (7.36) and K = -ArG°/RT ArS°/R -a HVRT = e e (7.37) where subscript (-) denotes the reverse reaction direction. The definition of G in Eq. (4.5) has been used to obtain the last equality in Eq. (7.37), and AyH0 is known as the heat of reaction. Neglecting the small dependencies of ArS° and AjH0 on T, we obtain the same T dependence of K in these two equations when \H° = Ea+ - Ea_. This fundamental relationship is illustrated in the familiar activation-energy diagram of Fig. 7.16. Note that a thermodynamically favorable reaction (negative Aj.G°) may have a AjH0 of either sign, depending on the entropy change, AyS0. Reactions having positive AjH0 absorb heat (they are "endothermic"), and their K increases with T. "Exothermic" reactions behave just the opposite. ArH° may be calculated from H° U reactants ^ products Figure 7.16 Activation-energy diagram for an exothermic reaction. The (t) at the top of the hill represents the energy level of the activated complex, and U is the internal energy of Iv; moles in Eq. (7.25). values found in handbooks [11, 12] or in various on-line data bases [13]. By the way, since only relative heat content can be measured, the H° of all species is specified to be zero at 298 K. Relating Ea+ and Ea_ to thermodynamics in the above way only tells us their difference, AyH0, unfortunately. Thus, we encounter the first difficulty of reaction kinetics: finding Ea. The slope of an experimental Arrhenius plot, logi0R+ versus 1/T (K), is frequently used to calculate an Ea using Eqs. (7.33) through (7.35) or the equivalent equations for surface reactions. In thin-film work, the R+ measured is generally the deposition rate (mc/cm2 s). The significance of such an apparent Ea must be viewed with some caution. Often, it is not known which reaction step is the rate-limiting one, nor even what are the elementary reaction steps. If two steps have similar rates, the Ea will be an average of the two and is likely to change with T. Often, something other than a reaction rate is controlling the film deposition rate, such as diffusion of reactants to the surface (Sec. 7.4) or the supply of activated species from a plasma (Sec. 9.6). In both of these cases, a very low and physically meaningless Ea will be obtained from the Arrhenius plot, and then the value of the plot becomes simply the revelation that something other than a thermally activated process is controlling the deposition rate. Reaction kinetics is largely an empirical science, because it is not reliable to calculate either B+ or Ea in Eq. (7.35) from first principles. Nevertheless, it is useful to examine how B+ is likely to vary with reaction conditions, and we do so below for the cases of unimolecular and bimolecular reactions. The bimolecular gas-phase reaction [Eq. (7.34)] involves the two reactant molecules colliding with enough total translational kinetic energy, Et, along the direction of their mutual approach to surmount the Ea "hill" of Fig. 7.16. We saw in Sec. 2.2 that the probability of a molecule having energy et in a given direction is proportional to expi-e^/ kpT), and this is the origin of the exponential factor in the Arrhenius equation. The top of the Ea hill represents the "activated complex" in 340 Chemical Vapor Deposition which the bonds of the reactant molecules have become excited enough vibrationally by the collision so that those of the product molecules can begin to form. The probability of the products actually forming instead of the reactants re-forming when the activated complex decomposes depends both on the orientation of the molecules to each other upon collision (the "steric" factor) and on the entropy change of the reaction. In cases where there is only one product molecule, a third probability factor appears, because conservation of momentum prevents the activated complex from transferring its excess energy into translational kinetic energy of the products. To prevent this energetic product molecule from decomposing, its energy must instead be transferred in a collision with a nonreacting "third body" before the decomposition has time to occur. The third body can be either a nonreacting gas-phase molecule/atom or a surface. When it is a molecule or atom, the rate constant increases with total pressure as well as with the reactant concentrations nA and nB, so that the reaction exhibits "pseudo-third-order" kinetics. None of the above three probabilities can be predicted accurately, so they are accounted for together by a "fudge" factor, s, in the rate expression: RIT mc/cm' s = se -E./RT -E „/RT s e kcnAnB - kIInAnB (7.38) where subscript II denotes a bimolecular reaction; Rc is the collision rate per unit volume between the two reactants, A and B; and k^ is the collision rate constant. The upper limit of the gas-phase bimolecular reaction rate occurs when s is unity and Ea « RT. In that case, kjj -» k,,, and the reaction is said to be proceeding at "collision rate." This rate, at least, can be calculated easily from the gas kinetic theory of Chap. 2. The collision frequency (collisions/s) of some individual molecule with any other molecule is C //, where the mean speed, C, and the mean free path, /, were given by Eqs. (2.3) and (2.24). This frequency times nA is the collision rate of species A with any other molecule, per unit volume, and this rate times the fraction of B in the gas mixture, ng/n, is the A-B collision rate, Rc (mc/cm_3s_1). Combining all of this, we have '8RT nanb (7.39) a i*V«t,mean;8quare collision diameter of the A-B pair, and i H SfAh ^ X I XB) iS ltS "reduced" Comparison with Eq. (7.38) shows that the term in brackets is the k, that we seek For where a' 7.3.2 Gas-phase rate 341 typical values of a = 3X10-8 cm and C = 4xl04 cm/s (for Ar at 298 K from Fig. 2.4), we find k<. = 1.6xl0-10 cm3/mcs, a very useful number to keep in mind as the upper limit of bimolecular reaction rate. When an A-B reaction is occurring at collision rate, the deficient reactant becomes half consumed within the travel time between A-B collisions. Reactions occurring at this rate may be considered to be instantaneous in CVD. We now turn to unimolecular gas-phase reactions such as the silane decomposition shown as ki in Fig. 7.15. Although the term unimolecular implies spontaneous decomposition, the rate is governed by collisions with nonreactive neighbors, because that is how a gas molecule gains enough internal energy to dissociate—at least in a thermally controlled reaction. Having gained enough energy to reach the top of the Ea hill of Fig. 7.16, the molecule then dwells for some time, te, in that activated state until the internal energy, in its statistical ramblings, happens to concentrate itself into the vibrational mode(s) leading to dissociation. If te is less than the mean time between collisions, which is tc = lit (mean free path/mean speed), then the molecule is likely to dissociate before the next collision. Thus, when te < tc, the unimolecular dissociation rate per unit volume, RIt increases not only with concentration nA, but also with collision frequency and, therefore, with total pressure. That is, Rt « pnA (7.40) By comparison with Eq. (7.34), we can see that this reaction is behaving as a first-order reaction with ki « p, or as a "pseudo-second-order" reaction. More complex molecules have longer te due to their larger number of internal-energy modes. Also, tc <* 1/p, so at high enough p, tc becomes less than te. Then, the activated molecule is just as likely to lose energy as to gain it in the second collision, so further increase in p does not increase the rate at which reactant molecules achieve dissociation energy. This is the "high-pressure limit," where kj becomes independent of p, and the unimolecular dissociation reaction exhibits true first-order kinetics. It should now be clear why it is not possible to predict gas-phase kj values from first principles. Similar complications arise for surface reactions, as we discovered in Sec. 5.2 by examining the simplest possible surface "reaction"—the hopping of an adsorbed molecule from one bonding site to another. Therefore, the kinetically favored pathways in a CVD reaction map such as that of Fig. 7.15 must be determined experimentally. The kinetic modeling approach to this problem is often used in CVD process studies. This involves proposing a likely reaction pathway and then fitting its kj values to data for deposition rate ver- 342 Chemical Vapor Deposition 7.3.2 Gas-phase rate 343 sus pj, p, and T. However, Fig. 7.15 shows that even for a simple overall CVD reaction having only one reactant and one gaseous product, there are many k; terms, including also the sticking coefficients, Scj, of the depositing precursors. Even the diffusivities, Dj, of the precursors may limit deposition rate at high p. Fitting CVD data by adjusting many k; values is like fitting a wavy line to a polynomial: it is always possible, but there is no chemistry involved. That is to say, the achievement of a fit does not mean that one has correctly identified the reaction pathway or correctly calculated the kj values of the individual reaction steps. The second and more fruitful approach to the kj values is to actually measure them individually. This difficult and tedious task has not been carried out for most CVD reactions, but it must be done to fully understand a chemical process. One way is to generate a burst of a single reactive-intermediate species by flash photolysis (light-induced dissociation) and then track its disappearance transient using some species-selective probe such as laser-induced fluorescence. For example, it has been found using this approach [18, 19] that the insertion reactions of silylene (SiH2) into SiH4 and Si2H6 shown in Fig. 7.15 by k2 and kp proceed at collision rates. The first reaction requires a third body (denoted by M), but k2 was found to reach kc by the time p reached only 130 Pa using He diluent. Significantly, these kj values are orders of magnitude higher than previous estimates made by kinetic modeling. This result establishes that the gas-phase reaction rate in silane pyrolysis is governed by kj, the unimolecular dissociation of silane. Under Si CVD conditions where ^ was believed to be controlling deposition rate [20], rate analysis yielded kj = 0.35 s-1. A certain amount of gas-phase reaction is sometimes required to partially decompose the feed gases and thereby render them sufficiently reactive when they arrive at the film surface, as in the case of the (CH3)3Ga and ASH3 used in GaAs deposition. However, if the sticking coefficients, Sc, of these gas-phase products are too high, they will adsorb before they can diffuse between the stacked substrates of the batch reactor (Fig. 7.6c) or down into the crevices of rough substrates. This results in poor uniformity of film coverage, as we will see in the next section. Excessive gas-phase reaction also usually leads to gas-phase nucleation of film material as powder which can contaminate the film surface and which depletes the reactant supply ("parasitic" reaction). In Si deposition from silane, powder formation occurs by the successive insertion of SiH2 into SinH2n+2 as shown by the polymerization rate constant kp in Fig. 7.15. The rate of each step is second-order in concentration [Eq. (7.34)] and also increases with the dissociation rate of SiH4 into SiH2, which increases with both p(SiH4) and total p [Eq. (7.40)]. The resulting strong p dependence of powder formation leads to the observation of a critical p(SiH4), above which it becomes noticeable. In one study [21] at T8 = 1000 K and with a l-s residence time of undiluted SiH4 in the reactor, the critical p(SiH4) was found to be about 130 Pa. The extent of any gas-phase reaction occurring within a CVD reactor is proportional to residence time and rate. Residence time, t,., in the entire reactor volume, Vr, is given by r w (Q/p)(T/273) (7.41) where W (cm3/s) = total volume flow rate of gas Q (sees) = total mass flow rate of gas p (atm) = reactor pressure T (K) = volume-average T in reactor Except in isothermal reactors, only some smaller volume, Vn, is heated enough that reaction proceeds at a significant rate. Then, the fraction of t, which the reactant spends in that volume is Vh/Vr when diffu-sional mixing is fast (low p). When mixing is slow (high p), Vn/Vr instead roughly represents the fraction of reactant that passes through Vn rather than passing around it. In either case, the fractional exposure of reactant to the "hot zone" is roughly the same. When, in addition, the fractional consumption of reactant, ^, is small enough so that one does not need to use integration to follow the kinetics, and when the reacted composition is far enough from equilibrium so that the reverse reaction is negligible, then the amount of reactant A consumed in the controlling gas-phase reaction of rate Rg is simply AnA = RgtrfvyVr) (7.42) Assuming further, for simplicity, that the kinetics are first-order in A, we then obtain from Eqs. (7.33), (7.41), and (7.42) a very useful qualitative expression for fractional reactant consumption in the gas phase: AnA kIVh p. 273 Q P° T (7.43) Note that another p factor due to residence time has been added to the one already incorporated into k|. The above two equations suggest other ways to reduce ^ besides decreasing p. One way is to decrease t,. by increasing Q. However, if t,. is made too small, reactant will not have time to diffuse to the surface or to encounter enough collisions there to react before being swept down- 344 Chemical Vapor Deposition stream. The other way is to decrease the hot-zone volume, Vh. The size of varies considerably with reactor design and flow pattern. Clearly, the worst case is the isothermal batch reactor of Fig. 7.5c. Nevertheless, particles can be avoided in this reactor if p is sufficiently low, and the good substrate-T control of the isothermal reactor makes it useful for deposition-rate uniformity. In cold-wall reactors, the roll cells which can occur in the flow pattern (Figs. 7.7 and 7.12) cause V^ to increase toward Vr by convec-tively carrying heat away from the substrate region. When these cells are avoided, Vh is instead restricted to the region of steep T gradient adjacent to the substrate surface, which is shown by 0 for the rotat-ing-disc situation in Fig. 7.11. This steep T gradient not only minimizes Vj,, but also greatly simplifies process modeling by allowing the use of the "chemical-boundary-layer" concept [22]. There, the reaction zone is approximated as a layer of uniform T = Ts and of thickness 8C against the substrate surface. The value of 5C is adjusted so that the same amount of reaction occurs as that which would occur integrated over the actual T gradient. This concept conveniently separates the gas-phase-reaction step of the process from the convective-transport step, whereas the treatment of these two steps together amidst T gradients is a formidable problem. For the case of parabolic flow in a horizontal-tube reactor of height y0, 8C can be approximated by the following equation [22] when the activation energy, Ea, for the rate-limiting gas-phase reaction is >100 kJ/mol: 5C (l + BXT/T )!+P RT 16 (T/T )'+P-l Ea ~Ea(kJ/mol) (7.44) Here, P comes from K-p « Tp, where Kj is the gas thermal conductivity. When heat capacity Cy * flT), P = 0.5 by Table 2.1. For a more typical value of p = 0.7, for Ta = 1000 K, and for T^ = 300 K, we obtain the last equality in Eq. (7.44). This is a useful way of making a rough estimate of hot-zone volume and therefore of the extent of gas-phase reaction. 7.3.3 Surface processes The surface processes of CVD are adsorption of the source gases, surface diffusion, heterogeneous reaction of the adsorbates with each other and with the surface, and desorption of gaseous by-products, as shown for Si deposition in Fig. 7.15. Four quantities are used to describe the fractional consumption of reactant impinging with flux Jj on the surface, as discussed in Sec. 5.1 and Fig. 5.1. These quantities must be carefully distinguished in describing CVD, but there is some 7.3.3 Surface processes 345 discrepancy in the literature. Here, we define them as follows, in order of increasing amount of interaction with the surface. The trapping probability, 8, is the fraction of J; that physisorbs into the precursor state instead of being immediately reflected from a clean surface, a clean surface being one whose bonding sites are all free of adsorbate. The vapor may subsequently desorb from the precursor state without reacting. The chemisorption-reaction probability, is the fraction of J, that does react into a chemisorbed state with the clean surface. It may subsequently react back into a precursor state and desorb, or it may remain and become part of the film. The sticking coefficient, Sc, is the fraction of J; that remains adsorbed long enough to become buried and thus permanently incorporated into the depositing film. Its value is averaged over the whole surface, both clean and adsorbate-occupied portions. The Sc will be less than £ when some of the chemisorbed reactant is desorbing or when part of the surface is passivated against adsorption by being already occupied with adsorbate. Finally, the utilization fraction, q, is that fraction of the vapor entering the reactor that becomes incorporated into the film instead of being carried downstream and pumped away. Since there are many encounters of a vapor molecule with the surface, q can be high even when the other fractions are low. Adsorption and reaction of a single species were considered in Sec. 5.1, where Eq. (5.7) for £ was derived for conditions of vanishingly small and steady-state precursor surface concentration and irreversible chemisorption reaction. For that case, £ ■ Sc. Studies on clean, hot Si under ultra-high vacuum [18, 23] approximate these conditions and have shown that the Sc of Si2H6 is much higher than that of SiH4. This points up the importance of knowing the extent of gas-phase reaction (here SiH4 -» Si2H6) in analyzing CVD kinetics. Thus, the deposition rate of Si from SiH4 is found [24] to increase with total pressure, p, and residence time, tr [Eq. (7.41)], at fixed p(SiH4) due to an increasing amount of gas-phase reaction with increasing p and tr as discussed prior to Eq. (7.41). In general, the surface concentrations of precursors and reaction by-products in CVD cannot be neglected as they were for Eq. (5.7). They can inhibit further adsorption or drive surface-reaction equilibrium one way or the other. Regarding by-product buildup, for example, H bonds very strongly to the Si surface and passivates it against any adsorption, as pointed out in Sec. 6.3, so that Sc is much lower on an H-covered Si surface than on a clean one. In fact, the H desorption reaction, 2H(a) -» H2(g), is believed to be the rate-limiting surface step in Si CVD [18] at low pressure where the gas-phase decomposition of SiH4 is small. A plot of deposition rate versus 1/T under these 346 Chemical Vapor Deposition 7.3.3 Surface processes 347 conditions then measures the Ea of H2 desorption and gives Ea ~ 200 kJ/mol. As in the gas phase, surface-reaction rates are determined by the surface concentrations of the reactants, n„ (mc/cm2), in accordance with the rate equations, Eqs. (7.33) and (7.34) (written there for the gas phase). We now consider the steady-state ng of a single reactant A as a function of its partial pressure, pA, at some fixed surface T, assuming for the moment a negligible loss rate by film-forming reaction. Such a function is known as an "adsorption isotherm" and is analogous to the n-p behavior at fixed T for a gas, either ideal [Eq. (2.10)] or nonideal (Fig. 2.1). To derive a typical isotherm, we start with the Langmuir adsorption model of Sec. 6.5.5, in which adsorption is assumed to occur only on unoccupied surface sites. In Sec. 6.5.5, we also assumed a fast chemisorption reaction (that is, £ -» S) that was irreversible (no desorption), and this resulted in an asymptotic approach of na to monolayer coverage: 0 = njn80 - 1. Those assumptions were appropriate for the adsorption of a reactant upon a surface with which it bonds strongly. Here, we instead want to examine precursor reactions on less reactive surfaces, so we neglect the chemisorption reaction and add to the Langmuir model a finite desorption rate obeying first-order kinetics with a rate constant kj. The steady-state mass balance on the surface thus becomes Ji6(l-e) = kdns = kdnBOe (7.45) which is also the limiting form of the Eq. (5.3) mass balance as the chemisorption rate constant, kr, vanishes. From the Knudsen equation [Eq. [2.18)], we know that J, « pA, so adsorption on the clean surface may be thought of as a first-order reaction with J,8 = kapA. Here, the 1/kgT factor from Eq. (7.33) has been incorporated into ka. Solving Eq. (7.45) for 0 and using this expression for J,8 gives the equation for the Langmuir isotherm: 0 = _■ = n__ Pa k ,n „ d so Pa (7.46) Inspection of this equation and its plot in Fig. 7.17 shows a linear region where 0 « pA at low pA, and a saturation region where 0 is independent of pA at high pA. These limiting regions are observed for all isotherms, not just for the Langmuir model, provided that pA < pv so that bulk condensation does not occur. For CVD, the limiting behaviors are more important than the exact shape of the curve in between. Figure 7.17 Typical adsorption isotherms: 0 = n,/nM = fractional monolayer surface coverage. Two common variations from Langmuir behavior are also shown in Fig. 7.17. Observation of the mobile-adsorbate effect shown was cited after Eq. (6.20). The other variation involves adsorption beyond 1 ML, as embodied in the BET (Brunauer-Emmett-Teller) and other isotherms developed in the study of heterogeneous catalysis. Now that we have established a formalism for describing adsorption and surface coverage in CVD, we will examine five effects of adsorbate concentration, n8, on film deposition behavior, namely: pressure dependence of deposition rate, competitive adsorption, film conformality over topography, roughening, and selective deposition. The behavior of n8 versus pA, as embodied in the adsorption isotherm, is reflected in film deposition rate versus pA in cases where the surface reaction is controlling the rate rather than another step in the Fig. 7.1 sequence. That is, the rate typically increases with pA and then saturates at high pA. For high 8 and low in Eq. (7.45) corresponding to strong adsorption, coupled with a low rate of the film-forming reaction [kr in Eq. (5.5)], this saturation can occur at very low pA even into the Kn > 1 regime (see Exercise 7.10). The nonlinear behavior of nB versus pA also points up a problem with extrapolating high-vacuum studies of surface-reaction kinetics to CVD behavior at higher pressure. High vacuum with Kn » 1 is required for such studies, since they typically involve modulated-molecular-beam techniques (Fig. 6.9) or surface analysis by electron spectroscopy (Sec. 6.4.1). Un- 348 Chemical Vapor Deposition fortunately, nB is much lower under high vacuum than under typical CVD conditions, and the extrapolation from one pressure regime to the other is not straightforward. In addition, the rate-limiting step may change with pressure. Alternatively, optical techniques of surface analysis, such as ellipsometry (Sec. 4.8.2) and infrared absorption, can be used at any pressure, and the latter technique has the advantage of being able to monitor individual adsorbates by their bond vibrational frequencies. Multiple internal reflection of the probe beam in an infrared-transparent substrate can be used to obtain sufficient infrared absorption for submonolayer sensitivity. However, a single external reflection at grazing incidence also enhances surface sensitivity [25] and is easier to implement. There is much to be done in using these techniques to understand CVD reactions under actual film-deposition conditions. When more than one surface species is involved in a CVD reaction, competitive adsorption must be taken into account. For example, the deposition rate of Si is greatly reduced when a small amount of PH3 or AsH3 is added to the reactant feed to n-dope the Si, because the adsorption of these reactants passivates the surface against SiH4 adsorption (see references cited in Ref. 20), The curious and troublesome phenomenon of multiple steady states of reaction behavior [26] has also been explained by competitive adsorption in the case of TiCl4 and C3H8 reacting in the adsorbed state (Langmuir-Hinshelwood mechanism) to form TiC film and HC1 gas. As the partial pressure of TiCl4, p(TiCl4), is raised, deposition rate and p(HCl) at first increase due to increasing nB(TiCl4). At some level of p(TiCl4), however, deposition rate and p(HCl) suddenly drop to a much lower level, because excessive n8(TiCl4) is preventing adsorption of the other reactant, C3H8. When p(TiCl4) is then decreased, hysteresis is observed: that is, rate and p(HCl) remain low and then finally jump up at some lower p(TiCl4). Clearly, these situations must be understood to achieve good process control. Good film conformality over surface topography is one of the principal features of CVD, but it does not always occur. Conformality becomes harder to achieve when the recessed regions into which one wants the deposit to penetrate have a lateral dimension less than that needed for convective transport into them. Then, penetration can occur only by diffusive transport through the stagnant gas, as will be discussed in Sec. 7.4. This is the situation, for example, for the spaces between the stacked wafers of the batch reactor of Fig. 7.5c. When the lateral dimension of the recess is still smaller—less than the gas mean free path, diffusion no longer slows down the penetration, but still the reactant becomes progressively depleted by deposition onto the side-walls of the recess as it penetrates deeper by molecular flow, bouncing 7.3.3 Surface processes 349 off the sidewalls as illustrated in Fig. 5.17/". At 1 atm, molecular flow prevails in channels <100 nm wide Eq. (2.24)], and it prevails in much larger channels at LPCVD pressures. Surface diffusion (Sec. 5.2) also contributes to penetration, but conformality behavior of a wide variety of CVD films suggests that it is not a factor for penetration distances > 100 nm or so. Conformality versus film thickness, within recesses deep enough to safely neglect surface diffusion and narrow enough to be operating in molecular flow, has been analytically modeled by assuming first-order kinetics [Eq. (7.33)] for the film-forming surface reaction and for precursor desorption, and by assuming a cosine distribution [Eq. (4.30)] for molecules scattered or desorbed from the sidewalls [27]. Results were computed for trenches of different aspect ratios (height/width), as shown in Fig. 7.18. The reactant supply becomes depleted with increasing depth into a trench because of deposition further up the side-walls and also because of "necking" of the trench mouth, which narrows the solid angle from which deeper regions can receive deposition flux. Clearly, for good conformality one wants a low sticking coefficient, Sc, for the reactant so that most of it can bounce down to the bottom of the trench. When deposition conditions are such that the fractional surface coverage, 0, of precursor is low, then Sc ■ £, where £ is the reaction probability of a molecule impinging on bare surface as defined in Eq. (5.7). Figure 7.18a shows trench coverage computed for 0 = 0 and £ = 0.10 (although the notation and terminology are different in the referenced work). The poor coverage for the deeper trenches shows that £ needs to be still lower to obtain good coverage under conditions of low 0, which is the "adsorption-limited" regime of deposition rate. Lower £ can be achieved by reducing surface T. When 0 is higher, on the other hand, Sc becomes low even if £ is high, since precursor is (a) 8 = 0, r = 0.10 Figure T.1B Calculated film-con-formality profiles in trenches. (Source: Reprinted from Ref. 27 by permission.) (6)8 = 0.01 at top of trench, £ = 1 350 Chemical Vapor Deposition assumed not to adsorb on surface already covered. Figure 7.186 shows trench coverage for 0 = 0.91 at the mouth of the trench and for ( ■ .1. [0 becomes lower inside the trench due to depletion of reactant incident flux and partial pressure, p^, in accordance with Eq. (7.46).] The figure shows that 0 needs to be still higher to obtain good coverage. This can be achieved by operating at higher pA, further into the adsorption-saturation regime of the Eq. (7.46) isotherm. This is the "surface-reaction-limited" regime of deposition rate. However, if high pA causes gas-phase reactions to form powder or high-Sc precursors, this remedy becomes less workable. The trench conformality problem is often encountered in integrated-circuit manufacture. It also occurs when coating the internal surface area of porous materials (see Exercise 7.15). Deposition into trenches or into cavity structures such as that of Fig. 9.35 is a good way to determine the Sc of film precursors. Reactant depletion in recessed areas due to high Sc also aggravates film roughening, a topic discussed at length in Sec. 5.4.1. To summarize that discussion, substrate roughness and statistical roughening initiate the process, which is then amplified by "self-shadowing" for high Sc or by "nutrient (reactant) depletion" for low Sc. These are actually two names for the same phenomenon in different Sc ranges, that phenomenon being removal of reactant from the vapor phase by deposition. In either case, it is inherently destabilizing to surface smoothness, because the deeper the roughness features become, the more depletion there is, the slower the deposition rate is at the bottom relative to the top, and thus the faster the roughness develops. Surface diffusion is the counteracting phenomenon which stabilizes the smooth surface, and the final amplitude and scale of the roughness represent the balance between depletion and diffusion [28]. The achievement of selective deposition is largely determined by control of adsorbate surface coverage, n8. The wide range of adjustability in nB and the presence of large activation energies for the reaction of source gases together make selectivity much easier to achieve in CVD than in physical vapor deposition (PVD), where the sticking coefficients of most vapors are near unity, regardless of surface conditions. Selectivity can mean deposition on substrate areas of one composition while not on other areas, or it can mean selective deposition of one solid phase and not others, such as diamond but not graphite. (Diamond deposition uses plasma activation, which will be discussed in Chap. 9.) Area selectivity is a very important goal in integrated-circuit manufacture, as in the selective deposition of W contact metal into vias etched through SiC*2 film down to underlying Si transistors. In general, selectivity may be obtained by controlling either equilibrium or kinetics. Selective W deposition from WF6 on Si, but not on SiC^, was mentioned after Eq. (7.30) and is an example of equilibrium con- 7.3.3 Surface processes 351 trol, since there is no favorable W-deposition reaction on Si02. But since the reaction on Si consumes the Si, it is self-limiting, and thick deposits thus require the addition of H2 or SiH4 to chemically reduce the WFg. There, deposition on Si02 can still be avoided, but now it is due to a kinetic limitation. Let us assume that the film-forming reaction is second-order in reactant surface coverage, ns, with a rate given by By ■ krnB(WF6)ng(H2). In the absence of chemisorption reaction with the Si02, these molecules will only physisorb and will thus both have low n8 because of a high kj and possibly also a low ka in Eq. (7.46) for surface coverage. Nevertheless, R,. is not zero, so W nuclei will eventually form after some "incubation time." Subsequent deposition on these nuclei is much faster, probably due to a lowering of the reaction's Ea by dissociative adsorption [16] of H2 on W. Thus, selectivity is quickly lost once nuclei form. The surface W is acting here as a catalyst to activate the H2. Nucleation behavior was discussed at length in Sec. 5.3. Deposition on undesired areas or deposition of unwanted phases can also be avoided by raising the surface coverage of a deposition-reaction by-product and thus driving the reaction in the reverse direction in accordance with equilibrium behavior [Eq. (7.28)]. For example, addition of HC1 product improves selectivity in the deposition of Si from SIH2CI2. Presumably, the ArG° is less negative on Si02 than on Si because of weaker bonding of Si to Si02 than to itself; in other words, AfG°[Si(a)] > AfG°[Si(c)] because of excess surface energy, Yi, at the Si(a)/Si02 interface. Thus, with proper partial-pressure adjustment, a balance can be achieved where deposition is occurring on the Si while etching of Si nuclei by HC1 is occurring on the Si02. H2 plasma can also be used [29] instead of HC1 to supply active etchant. The achievement of such an equilibrium balance is more reliable than kinetic control of selective deposition, because kinetic control breaks down at nuclei formed after the incubation time or formed at spurious active surface sites such as contamination islands or scratches. In another selectivity example, a shift in ArG° with surface energy can even cause large variations in deposition rate from crystallo-graphic plane to plane in a CVD process that is operating near equilibrium, because of variations in surface energy, 7, with surface structure. This appears to be the cause of the dramatic crystallo-graphic selectivity of deposition rate shown in Fig. 7.19 for the GaAs "chloride" CVD process [30]. There, GaCl, AsCl3, and H2 react to deposit GaAs, and at the same time the HCl(g) by-product etches the GaAs. The lllll planes in the upper hemisphere are the Ga-rich ones, and the lower ones are As-rich. (GaAs polarity was discussed at the end of Sec. 6.5.6.) The deposition-rate anisotropy between these polar faces is more than 15/1. 352 Chemical Vapor Deposition «i^-r^ 100 7.4 Diffusion 353 Ga-rich faces As-rich faces Figure 7.19 Polar diagram of GaAs deposition rate by the chloride process vs. crystal-lographic plane. (Source: Reprinted from Ref. 30 by permission.) The final aspect of surface chemistry to discuss is the steep exponential Ts dependence of deposition rate which is induced when a surface reaction is the rate-controlling step of the CVD process. There are both advantages and disadvantages to this behavior. To obtain uniformity over large areas, the furnace-enclosed reactor of Fig. 7.5c is usually needed in order to obtain sufficient substrate-T control under such conditions. To compensate for the reactant depletion which occurs at substrates toward the downstream end of this reactor, an increasing T profile can be imposed along the furnace (Exercise 7.11). In other reactors, the steep T dependence can be used to start and stop the deposition reaction abruptly by changing surface T. This feature has been exploited in a technique known as "limited-reaction" or "rapid thermal" processing, in which the substrate is rapidly heated by irradiation from a quartz-halogen lamp focussed through a quartz reactor wall. The substrate is then somewhat less rapidly cooled by thermal radiation when the desired film thickness has been reached [311. This procedure minimizes the time at high T needed to deposit a given thickness, and it thus minimizes the amount of interdiffusion occurring between layers in a heterostructure. A surface-T increase can also be obtained on selected areas of a substrate by directing there the focussed beam from a high-power laser, so that deposition occurs only in the irradiated areas. This is done in conjunction with conventional substrate heating to just below the deposition T, to minimize laser power and thermal shock. The laser can be programmed to scan and write arbitrary patterns of deposition for the generation of three-dimensional thin-film structures. When a short wavelength is used, there is also the possibility that photochemical activation is occurring [32] in addition to local heating; that is, direct breaking of a reactant bond due to absorption of photon energy in electron excitation. One way to identify a photoc/iemica/ versus a photo-thermal effect is to see if it still occurs at cryogenic T [33]. The above discussion of chemical reactions in CVD has presented the basic principles of equilibrium and kinetics for gas-phase and surface reactions. However, it has stopped short of attempting overall kinetic modeling, because good data on rate constants are usually unavailable. Even in the much-studied SiH4 pyrolysis reaction, the important rates are known only for the gas phase. Nevertheless, understanding how reaction equilibria and rates vary with pressure and T is valuable in designing and optimizing CVD processes. 7.4 Diffusion We now consider the final transport step in the CVD process sequence of Fig. 7.1: gas-phase diffusion of reactants to the substrate surface. Forced and free convection have carried the gases to the vicinity of the substrate, and sometimes there also has been some homogeneous reaction along the way. However, viscous friction requires that the convection velocity drop to zero at the surface whatever the flow profile, so the final transport of reactants to the surface has to occur by diffusion through a relatively stagnant boundary layer of gas. The transition from convection to diffusion is gradual upon approaching the surface, but it is convenient to model this situation as two distinct regions: a convectively supplied reservoir of reactant, and a diffusive boundary layer between this reservoir and the surface. The surface on which film is depositing is a sink for the reactant, so the reactant concentration, n^, just over the surface is always lower than that in the reservoir, n„. That concentration gradient drives the reactant diffusion flux, J^, as shown in Fig. 7.20, and the edge of the concentration boundary layer in which this diffusion is occurring, 8n, is arbitrarily but conventionally defined as the plane at which nA has dropped by 1 percent from n„. We shall see that 6n behaves very differently from 8V, the velocity boundary layer, which was discussed in Sec. 7.2.2. Below, we will apply the boundary-layer model to the three reac- 354 Chemical Vapor Deposition 7.4.1 Diffusion-limited deposition 355 flowstream . um reservoir — h—8n-reaction "y3 'l^ control diffusion / control — y 0 Figure 7.20 Quantities relevant to the diffusion of a single reactant, A, through the concentration boundary layer, 5,,, to the depositing-film surface at y = 0. tors of Fig. 7.5. But first, we need to write the equations that describe diffusive transport. In Sec. 2.8.1, we showed that the diffusion flux of species A in an A-B mixture is proportional to the concentration gradient by the binary diffusivity, D^b, m accordance with Fick's Law, Eq. (2.27). When the total amount of gas remains constant, the countercurrent flux of B due to the displacement of B by A has to be equal and opposite to JA, so Jg + JA = 0. However, there is a complication in film deposition due to molarity changes upon reaction, such as SiH4(g) -» Si(c) + 2H2(g). There, for every mole of SiH4 diffusing to the surface and depositing Si, two moles of H2 must diffuse away from the surface. This net flux of gas away from the surface, Jg + Ja * 0. is known as Stefan flow, and it sweeps A away from the surface in proportion to the mole fraction (or molecular fraction) of A in the mixture, xA = ^A^nA + nb^ = n^/n. Thus, the net flux of A toward the surface is the sum of the Stefan-flow and Fick's-law components: ja = xa 0). By contrast, consider conditions leading to large Stefan flow; that is, vp = 2, no dilution, and all reactant being deposited (xA = 0 at y = 0). Then, we may take the average xA across the xA gradient as 1/3, so that the denominator becomes 4/3. Thus, we see that this flow effect is noticeable but not enormous, and it may be neglected for rough calculations. 7.4.1 Diffusion-limited deposition We wish to determine the degree to which the concentration gradient required for diffusion depletes the reactant over the surface and thereby limits the film-forming surface-reaction rate. We will assume that only one reactant is diffusion-limited, and we will thus will drop some of the A subscripts from above for simplicity. Using the boundary-layer model just introduced and referring to Fig. 7.20, consider a flowstream reservoir in which the concentration of this one reactant is maintained at a level nz by its mass flow, QA, into the reactor. In general, nz will decrease with axial position, z (perpendicular to the plane of the figure), from its reactor-inlet value of n„ at z = 0 as it becomes depleted by the film deposition. Just over the film surface at y = 0, the reactant concentration has dropped to some lower level, n0. For steady-state deposition and negligible film re-evaporation, the diffusion flux toward the surface, JA atoms/cm2 s, will be equal to the film deposition flux, Jr. Approximating dnA/dy in Fick's law by the nA difference across the boundary layer, 8n, we obtain Jr = JA = -D z o (7.51) When generalized to three-dimensional diffusion of multicomponent mixtures, this becomes the Stefan-Maxwell equations [34]: or for the fractional depletion of reactant at the surface, 356 Chemical Vapor Deposition n - n f — Dn /& z n (7.52) There are two limiting cases of Eq. (7.52), and it is important to know which one applies to the CVD process being run: 1. reaction control: f0 -> 0, n0 = nz, and Jr « Dn;j/8n 2. diffusion control: f0 —> 1, n^, -» 0, and Jr = DnJ5n These cases are illustrated in Fig. 7.20, along with an intermediate case. The intermediate case is more difficult to analyze, but since it is also more difficult to control, it should be avoided in CVD practice anyway. Reactors in which the uniformity of reactant flow over the substrate is poor, such as the batch reactor of Fig. 7.5c, need to operate under reaction control to achieve uniformity. On the other hand, when surface-T uniformity is hard to achieve, as in the axisymmetric reactor of Fig. 7.5a, the exponential dependence of reaction rate on T means that better uniformity is obtainable under diffusion control. One way to determine whether a process is controlled by reaction or diffusion is to estimate the quantities in Eq. (7.52). The linear deposition rate, dh/dt (nm/s), is easily measured either by thickness deposited in a given time or continuously by ellipsometry or interferometry (Sec. 4.8.2), and it is easily converted to Jr by Eq. (2.21). D often can be found in handbooks or estimated from the formula in Table 2.1. The amount by which nz is less than the inlet value, n„, can be found from the value of J,Ar (mc/s) compared to QA (in mc/s). Here, A,, is the total deposition area upstream of the z position being considered; this includes all of the area heated to deposition T, not just the substrate area (see Exercise 7.12). Note that the depletion at z is less than the total fractional utilization of reactant, n, which is determined from nz at the outlet. In the case of the axisymmetric reactor, n may be large, but the depletion in the flowstream over the substrate is still small, since that region is upstream of the deposition region. For the other reactors in Fig. 7.5, n must be kept small to ensure deposition uniformity, as we shall see below. Consequently, for present purposes we may take nz = n^,. The most uncertain quantity in Eq. (7.52) is 5n. For the axisymmetric reactor with stationary substrate, it might be taken as 8VZ from Eq. (7.15), since that is where the flowstream begins to stagnate. However, if the substrate is rotating, 8n is likely to be less than the 5VZ of Eq. (7.20), since the radial flow carrying fresh reactant is actually increasing as it approachs the substrate, as shown by curve F in Fig. 7.11. For the tube reactor (Fig. 7.5o), the solution for 8n versus z will be pre- 7.4.1 Diffusion-limited deposition 357 sented below. For the batch reactor (Fig. 7.5c), 8n is the entire distance from substrate edge to center, since there is negligible convective flow between substrates. Another way to distinguish the reaction- and diffusion-controlled regimes is to measure deposition flux, Jr, versus T. The behavior of this function can be seen by considering the simple case of an irreversible first-order film-forming reaction and a surface coverage n8 « 1 ML in the linear portion of the adsorption isotherm [Eq. (7.46)] where ns « n0, n0 being the gas-phase reactant concentration just over the surface. Then, Jr - ksns = kan0 (7.53) where the rate constant ka here has units of cm/s. Setting this Jr equal to Eq. (7.51), solving for n0, and substituting back into Eq. (7.53), we have a z (7.54) 1 + D/5, which has the following limiting values: 1. reaction control: ka « D/8n and Jr -ka » D/Sn and Jr 2. diffusion control kanz * Dnz/8n Since log ka ~ 1/T8 with a slope of-Ea/R by Eq. (7.35), where T8 is the surface T in K, such an "Arrhenius plot" for a reaction-controlled process yields a steep straight line as shown for segment (1) of Fig. 7.21. As ka becomes larger with increasing Ts, diffusion control eventually takes over in segment (2). There, the much smaller slope is determined by the relatively small combined T dependencies of D, nz, and 8n. Sometimes, the slope in the reaction-controlled region changes Figure 7.21 Arrhenius-plot behavior of deposition rate. Segments (1) and (3) are reaction-rate controlled with two different Ea values, whereas segments (2) and (5) are diffusion controlled at two different pressures. UT.fK") r 358 Chemical Vapor Deposition with T as shown by segment (3), and this indicates a change in the rate-limiting reaction step to one with a higher Ea. In the special case of a reaction which has marginally negative ATG° and which is also endothermic, the steep slope may instead represent the equilibrium constant shift toward product [30] with increasing T [Eq. (7.37)]. The slope reversal at high T in segment (4) may indicate either the onset of an equilibrium limit for an exothermic reaction, or the onset of film re-evaporation [Eq. (5.8)]. In general, one must be cautious in the interpretation of Arrhenius plots when thermodynamic and kinetic backup data are unavailable. The effect of reactor total pressure, p, on deposition flux, Jr, depends on the extent of diffusion or reaction control and on whether it is the reactant's mole fraction, xA (= nA/n = pA/p), or its concentration, nA (« pA), which is held constant as p is varied. The value of xA can be held constant by increasing p with a fixed gas-flow ratio, using pump throttling at valve b' in Fig. 7.2. Then nA (=nz) increases, and in the reaction-controlled regime, Jr increases per Eq. (7.54). In the diffusion-controlled regime, on the other hand, the 1/p dependence of D cancels out the nA increase and leaves Jr independent of p. However, it is difficult to keep xA constant over a wide range of p, because at low p, nA becomes too low for reasonable deposition rate, and at high p it becomes so high that homogeneous reaction to powder can occur, as discussed prior to Eq. (7.41). Therefore, it is more common to keep nA constant by increasing reactant dilution with increasing p. In that case, Jr is independent of p in the re action-controlled regime, but it increases with decreasing p in the diffusion-controlled regime because of the increase in D, as shown by segment (5) in Fig. 7.21. This increase in the D-limited Jr is the main reason to operate CVD at reduced p, because it allows reaction-controlled deposition at higher Jr so as to maintain uniformity with reasonable deposition rate in batch reactors. 7.4.2 Reactor models Having now outlined diffusion behavior in general terms, we proceed to model specific reactors, namely the tube and batch types of Figs. 7.56 and c. Tube reactors can operate either in diffusion or reaction control. If f„ in Eq. (7.52) is still small even when 8n is taken to be as large as the entire tube diameter, then reaction control applies, and nz may be assumed constant across the tube, as shown by the horizontal line in Fig. 7.20. If f„ is very small (< 10"2), then considerable axial diffusion will also occur, and nz will become independent of z as well. More commonly though, axial diffusion is still small under reaction control. Then, reactant transport may be described using an Eq. (3.1) mass balance on an axially differential (dz) volume element of uniform 7.4.2 Reactor models 359 nz across the reactor's cross section, as shown in Fig. 7.22a for a rectangular cross-sectional area, A,,, and for deposition occurring on area Az per unit length in z. Since the lateral diffusional mixing is fast, the velocity profile across At does not matter, and we may use the "plug-flow" assumption of uniform velocity at the mean value, u , as we did for the oil backstreaming problem in Eq. (3.14) and Fig. 3.46. For first-order reaction kinetics and low surface coverage, where the reactant sticking coefficient, Sc, is independent of nz, it can be shown (Exercise 7.14) that the reactant depletes exponentially with increasing z according to — = exp n„ (7.55) for units of g, cm and s. Under these conditions, the fraction xij/r^ and thus the reactant utilization fraction, q, must be kept small to obtain deposition-rate uniformity over the length of the reactor, unless a compensating TB(z) gradient is imposed to increase Sc along z. This transport situation may be thought of equivalents as a volume element of unit length in z moving through the reactor at velocity u and depositing material out at the periphery as it proceeds. Then, nz depletes exponentially in time (and thus in z) within the volume element. This behavior is analogous to the exponential pumpout situation of Eq. (3.11). When diffusion is too slow to maintain reactant concentration at a uniform level nz across the tube reactor, the volume element shown in Fig. 7.226 must be used instead for the mass balance. This element is differential in both y and z, so the u profile in y must now be consid- Sc=l A^dz; SC<1 (6) Figure 7.22 Mass-balance volume elements for determining reactant depletion in axial-flow tube reactors: (a) reaction control and (b) diffusion control. 360 Chemical Vapor Deposition ered. The net convective flow of reactant A into the element in the z direction, per unit width in x, is -uOnA/dz)dzdy. The net diffusive flow into the element in the y direction is ( d(dnA/dy)\ l-DHi—Jay*- In steady state, nA is constant in the volume element, so u(y) dnA (y. z) 1i = D d n. (y. z) (7.56) This illustrates the general procedure for modeling multidimensional flow in CVD reactors. In some cases, gradients in x must also be considered. Such a mass balance must be satisfied for every species in every dxdydz volume element. When homogeneous reactions are occurring, the balance must also include the rates of generation and consumption of every reacting species. Usually, solutions can only be obtained numerically. However, an analytical solution can be obtained for the Fig. 7.226 geometry when the u(y) profile is assumed to be either flat or linear [35], and these solutions are shown in Fig. 7.23 using normalized coordinates. The assumed linear u(y) profile approximately tracks the actual parabolic one where the nA gradient is steep (y < 0.3yo), as shown by the inset. The boundary conditions assumed are: uniform nA = n„ for z = 0, nA = 0 at y = 0, and no deposition at the top of the reactor (dnA/dy = 0 at y = y0) or on the sides (no flux in the x direction). Figure 7.23 provides valuable insight into diffusion-limited CVD behavior. Surprisingly, the nA profile is only slightly affected by the choice of u(y) profile, so the simplest assumption of plug flow is satisfactory even when lateral diffusion is limiting. With that assumption, by the way, we may equivalently model the problem as a Fig. 7.22a volume element moving at Q and depositing material at the bottom, as we did for the Eq. (7.55) case. This is now identical to the classic one-dimensional diffusion or heat-transfer problem involving a block of uniform semi-infinite material suddenly subjected to an nA or T drop at y = 0, for which the solution is [36] — = erf ~_ n- 2jDt 2 7Dz/u (7.57) Note that the denominator of the error-function (erf) argument is equivalent to the diffusion length, A, from Eq. (5.25). Returning now r 7.4.2 Reactor models 361 1.00 it 0.75 t 0.25 * 0.75 2VDz7a £ 0.50 0.25 8n at 1/4 1.00 Figure 7.23 Diffusion-limited reactant concentration profiles for four successive normalized axial positions in a tube reactor: solid line = plug flow, long dashes = linear u profile, and short dashes in inset = parabolic profile. (Source: Reprinted from Ref. 35 by permission; curve labeling changed to conform to text.) to Fig. 7.23, note that as z increases [or t in the Eq. (7.57) model], the nA-gradient region spreads upward in y; that is, the concentration boundary layer, 8n, expands. At a z value such that 2 VDz/u/y0 = 1/2, 5n reaches the top wall, because that is when nA(y0) drops by 1 percent from n„, this drop defining the edge of 8n. At this point, the fractional reactant utilization averaged across y happens to be n, = 21 percent. For still larger z, the semi-infinite assumption breaks down and Eq. (7.57) no longer holds, because 8n has now spread across the reactor (throughout the reservoir). Then, nA begins to deplete exponentially in z as in the case of fast lateral diffusion which we previously considered. For smaller z, where 8n < y0, the deposition flux, Jr, still decreases with increasing z, because the expansion of 8n reduces the nA gradient at the substrate, as seen in Fig. 7.23. It can be shown [35] that for the linear u(y) profile and for nA = 0 at y = 0, 362 Chemical Vapor Deposition J = d ay 0.89Dn y = o (Dyz/tl) 1/3 (7.58) This is slightly different from the solution that would be obtained from Eq. (7.57), due to the presence of the u profile here. Using Eq. (7.57), we would have Jr z~ instead. In any case, this dropoff of film deposition rate through the tube can be counteracted by tilting the susceptor as shown in Fig. 7.56. This constricts the flow cross section with increasing z, thus decreasing y0 and increasing Q. The right amount of tilt can cancel out the increase in (Dy0z/u) with z and thus maintain uniform deposition rate, at least until 8n —> y0. Further downstream where 8n > y0, or equivalently, where n > 21 percent, the exponential dropoff of n^ cannot be compensated out. The last diffusion situation to be examined is the batch reactor of Fig. 7.5c. There, essentially no convective flow occurs between the substrates, so diffusion must carry the reactant all the way from the peripheral flowstream radially inward to the centers of the substrates. It is not possible to counteract a decrease in n^ along this path by the constriction or T-gradient techniques used above for the tube reactor, so the batch reactor must be operated in reaction control to obtain uniformity. We need to determine how high the deposition rate can be before nA depletion causes an unacceptable drop in deposition rate at the substrate center. The exact solution to this problem involves integration over radially differential volume elements within which both diffusion and deposition are occurring. However, a considerable simplification which is nevertheless quite accurate enough for present purposes can be made by using only two volume elements and by considering the diffusion to be one-dimensional rather than radial, as shown in Fig. 7.24 by the two dashed rectangles. It is supposed that only diffusion occurs in the outer (left-hand) element, and only n, T 1 cm IV2 1 IV2 Figure 7.24 Batch-reactor model for diffusion and deposition between stacked substrates of half-width L and arbitrary y dimension; view looking down on a substrate and along the axis of the reactor tube, z. 7.4.3 Temperature gradients 363 deposition in the inner (shaded) one. The same concept of judicious separation of coupled phenomena was used to similar advantage in prior sections in the concepts of the concentration and chemical boundary layers. In the Fig. 7.24 model, each volume element has unit size in y, a size in x of one-half the distance L from substrate edge to center, and a height in z equal to the gap, b, between substrates in the batch. For the steady-state mass balance, we set diffusive mass flow (mc/s) equal to deposition flow, noting that deposition occurs on both faces of each substrate. We omit reactant dilution to maximize diffusive flow, and use Eq. (7.50) for a typical case of vp = 2. Then, using the notation of Fig. 7.24, we have bD(nz-nL)/(l/2)L 4/3 = LJ. (7.59) For uniform deposition, the fractional reactant depletion at the center, fL = (nz - nLVnz, needs to be no more than, say, 1 percent if its surface coverage is low. Then, rearranging Eq. (7.59), we have 0.015bDn, (7.60) Note that the upper limit of Jr is strongly dependent on substrate size, L, but is independent of pressure, p, since nz « p but D <* 1/p. Of course, p must usually be «1 atm when operating undiluted, to avoid powder formation. Taking typical conditions of b = 1 cm, L = 10 cm, T = 800 K, and D = 0.7 cm2/s at room T and 1 atm, scaled to 800 K by the Table 2.1 formula, we find that Jr <, 5xl015 atoms/cm2s or 1 nm/s, a respectable deposition rate. This is a simple procedure for roughly estimating the range of conditions suitable for operating a batch reactor. 7.4.3 Temperature gradients Two significant perturbations to diffusion behavior occur in T gradients such as that over the substrate surface. One is "thermal diffusion," which causes the heavier and/or larger of the two molecular species in an A-B mixture to become depleted from the hot region. (In liquids but not in gases, this is known as Soret diffusion.) This behavior is described by the following equation [37], whose derivation is too involved to give here: dx^ dy r dt^ D AB I 41 T dy dT T dy (7.61) 364 Chemical Vapor Deposition where D-r- is the thermal-diffusion coefficient, and kj is the thermal-diffusion ratio for the mixture. Measured values of kj are ~0.2, give or take a factor of five for various mixtures [34, 37], but kj is not easily predicted. It increases with the M differences and diameter differences of the molecules in the mixture, and decreases with increasing molecular interaction. It vanishes for M differences of <10 percent and for xAor Xr < 0.1. A qualitative picture of the thermal-diffusion effect can be developed using an argument similar to that used to derive the thermal-transpiration effect, Eq. (3.18). Consider the molecular flux of each species along the T gradient as it crosses some plane in space that is perpendicular to the gradient. The flux in each direction arrives at the plane from about one mean free path away toward the hot (Tj,) or cold (Tc) end, and the flux is proportional to p;/^MjT in accordance with the Knudsen equation [Eq. (2.19)], where i = A or B. If the initial composition is uniform along the gradient (pjn = p;c with total p constant), then Eq. (2.19) results in a net flux, AJj, for each species toward the hot end. The ratio of these net fluxes is 7.5 Conclusion 365 aj, aX JAh'JAc JBh" JBc PAh PAc PBh PBc (7.62) If this flux ratio were equal to the pj ratio, the situation would amount simply to an initial bulk motion of the mixture toward the hot end as in thermal transpiration. However, the flux ratio is seen to be smaller than the pj ratio when MA > Mr, so that the heavier species has an insufficient net flux and begins to segregate toward the cold end until a steady state is achieved. This segregation can significantly change reactant fluxes to the surface in CVD [38]. The second T-gradient effect is "thermophoresis," which causes small particles suspended in gas to be driven from the hot end [39], just as large molecules are. When the molecular fluxes have reached steady state and when the particle is small enough so that these fluxes can communicate with each other around it (Kn > 1 based on the particle diameter), we must have equal opposing fluxes (J^ = Jc) along the gradient. Again, application of the Knudsen equation leads to Ph (7.63) That is, p is higher against the hot face of the particle than against the cold face, and the particle is thus pushed toward the cold end. This is identical to the thermal-transpiration equation, Eq. (3.18). Thermophoresis is a very valuable though generally unappreciated phenomenon in CVD. It is extremely effective in preventing particles homogeneously nucleated within the chemical boundary layer from settling on the film surface. They instead remain suspended within the boundary layer above the substrate and are eventually swept away in the flowstream. Scattering of laser light can be used to dramatically reveal this suspended layer. Particle rejection from the surface is so effective that I have seen quantum-well laser structures (Sec. 6.2.1) successfully grown on a routine basis under MOCVD conditions where such particles were present in abundance. Excessive homogeneous nucleation still causes other problems, however, such as parasitic consumption of source gas and contamination of the reactor with dust. 7.5 Conclusion CVD is the most complex deposition process which we have examined, due to the many phenomena occurring simultaneously and nonuni-formly in the gas phase, namely, forced convection, free convection, homogeneous reaction, and diffusion. Nevertheless, by proper reactor design and operation, it is possible to control each of these phenomena and also to separate their spatial regimes for modeling purposes. Such control provides the surface-chemistry and deposition-rate stability needed to exploit the potential advantages of working with gaseous source materials in the fluid-flow regime. The low sticking coefficient characteristic of gaseous reactants facilitates the coating of convoluted or even porous substrates, or large batches of odd shapes. It also assists selective deposition. The higher pressure of the fluid-flow regime simplifies or eliminates pumping, increases chemistry control latitude because of the higher reactant concentrations, and permits operation under diffusion control for improved film uniformity in the presence of substrate-T nonuniformity. The high T required for activation of most CVD reactions can exceed the tolerance of some substrates, but then one can turn to plasma-enhanced CVD to activate the reactions at lower T, as we will see in Sec. 9.6. 7.6 Exercises 7.1 Reactant gas is flowing into a 1500 cm3 room-T reactor at 200 seem as measured on a mass flow controller calibrated for Ar. With the reactor valved off at the outlet, the rate of pressure 366 Chemical Vapor Deposition rise is 1 torr/s. (a) What is the actual flow rate of the reactant gas in seem? (b) What is the c^, of the reactant gas? 7.2 For steady-state, one-dimensional laminar flow between parallel plates positioned in the x-z plane at +y0 and -y0, show that the fluid's velocity profile, u(y), is given by Eq. (7.8) and that the mean velocity, u, is given by Eq. (7.9). 7.3 Show that the thickness of the velocity boundary layer in axisym-metric flow scales as (T/p2)1/4 for a fixed flow velocity at the room-T inlet of the reactor. 7.4 Show that the last equality in Eq. (7.21) for Gr holds assuming the ideal-gas law, and show that it is dimensionless. 7.5 Name at least six ways of suppressing recirculating roll cells in the CVD-reactor gas-flow pattern. 7.6 Show how the chemical-equilibrium equation, Eq. (7.28), is obtained from the G minimization of Eq. (7.27). 7.7 bci3 at a partial pressure of 103 Pa in 1 atm of H2 is supplied to an APCVD reactor for the deposition of B at 1400 K. If the only significant gas-phase reaction produces hbci2 and hc1 and reaches equilibrium, what is the fractional conversion of bci3? (Use the data of Fig. 7.13) 7.8 The two common forms of arsenic vapor, As4 and As2, are in equilibrium with each other in an Ar diluent, (a) Derive the expression for the As2 partial pressure (in atm) in terms of K, total pressure p, and initial p^.. At the T for which A,.G° = 0 and for p = 1 atm, what is the As2/As4 partial-pressure ratio for (b) no dilution and (c) for a feed composition of 1 at.% As4 in Ar? 7.9 A particular deposition reaction operating at 100 Pa and 900 K in a 2-liter isothermal reactor is limited by the unimolecular dissociation, with kj = 0.1 s-1, of the reactant vapor, which is supplied undiluted at 100 seem. What fraction, n, of reactant is utilized in the deposition? 7.10 A particular adsorbate, A, of M = 40 is known to have a surface residence time of 1 ms at 1000 K; in other words, the time constant for its desorption when pA = 0 is 1 ms. (a) For a monolayer coverage of nso = 1015 mc/cm2, what is the desorption rate constant in s_1? (b) Assuming Langmuir adsorption kinetics and 8 = 1, what pa is required to sustain a steady-state surface coverage of 90 percent of a monolayer? 7.11 If the Si deposition rate from SiH4 at 1000 K is being controlled by H2 desorption at © = 0.9 in a furnace-type batch reactor, how much of a T increase is needed from the first to the last substrate along the gas flow path to maintain deposition rate uniformity if the SiH4 utilization is 20 percent? (See data in Sec. 7.3.3.) 7.7 References 367 7.12 Si is being deposited at 10 nm/min in an isothermal reactor of 2 m total internal-surface area. If SiH4 is supplied at 200 seem, what is its fractional utilization, n? 7.13 An axisymmetric cold-wall reactor operating at 1 atm in a flow of 10 seem B2He and 5 slm Ar is depositing B onto a stationary 10-cm-diameter, 1400-K substrate. What is the maximum deposition rate in nm/s determined by diffusion limitations? 7.14 (a) Derive Eq. (7.55) using the stationary mass-balance volume element of Fig. 7.22a, Eq. (2.18) for the impingement rate of reactant, the ideal-gas law, and the other assumptions stated for Eq. (7.55). (b) Show that the same result is obtained using a volume element moving at the axial flow velocity, (c) For pyrolytic-graphite deposition from methane flowing at 600 seem and 1300 Pa through a 1-cm-inside-diameter, 1400-K, isothermal tube, what is the length of tube at which the methane will be 20 percent depleted if Sc = lO-^? 7.15 It is desired to coat the internal-surface area of porous ceramic catalyst pellets with Pt for application in crude-oil hydrogena-tion. Assume that this is to be done by CVD from Pt(CO)2Cl2 at 800 K, and that the pores can be modeled as cylinders 20 nm in diameter and 1 mm long. Using a model similar to that of Fig. 7.24 and the molecular-flow-conductance equation [Eq. [3.6)] adjusted for T and M, determine the maximum Sc to obtain 10 percent coating uniformity from pellet surface to center. 7.16 The units of a reaction rate constant depend on the units of the reactant and the order of the reaction, and one must be careful to use consistent units. What are the SI units of ka in Eq. (7.46)? 7.7 References 1. Pierson, H.O. 1992. Handbook of Chemical Vapor Deposition. Park Ridge, New Jersey: Noyes Publications. 2. Galasso, F.S. 1991. Chemical Vapor Deposited Materials. Boca Raton, Fla.: CRC Press. 3. Hinkle, L.D., and C.F. Mariano. 1991. "Toward Understanding the Fundamental Mechanisms and Properties of the Thermal Mass Flow Controller." J. Vac. Sei. Tech-nol. A9:2043. 4. Houng, Y.-M. 1992. "Chemical Beam Epitaxy," Crit. 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"Chemical Etching of GaAs and InP by Chlorine: The Thenno-dynamically Predicted Dependence on Cl2 Pressure and Temperature." J. Vac. Sci. Technol. B4:1216. 16. Skelly, D.W., T.-M. Lu, and D.W. Woodruff. 1987. "Metallization Techniques," Chap. 3 in VLSI Metallization, vol. 15 of VLSI Electronics and Microstructure Science, ed. N.G. Einspruch, S.S. Cohen, and G. Sh. Gildenblat. Orlando, Fla.: Academic Press. Spear, K.E., and R.R. Dirkx. 1990. "Predicting the Chemistry in CVTJ Systems." In Proc. Chemical Vapor Deposition of Refractory Metals and Ceramics Symp. 168:19. Pittsburgh, Pa.: Materials Research Society. Jasinski, J.M., and S.M. Gates. 1991. "Silicon Chemical Vapor Deposition One Step at a Time: Fundamental Studies of Silicon Hydride Chemistry." Accts. Chem. Res., 24:9. Jasinski, J.M. 1994. "Gas Phase and Gas Surface Kinetics of Transient Silicon Hydride Species." In Gas-Phase and Surface Chemistry in Electronic Materials Processing. Pittsburgh, Pa.: Materials Research Society. 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Rosner, K Nauka, J. Turner, and T.I. Kamins. 1990. "Limited Reaction Processing: Growth of Sii.xGe,/Si for Heterojunction Bipolar Transistor Applications." Thin Solid Films 184:93. 32. Houle, FA. 1989. "Surface Photoprocesses in Laser-Assisted Etching and Film Growth.",/. Vac. Sci. Technol. B7:1149. 33. Isobe, C, H.C. Cho, and J.E. Crowell. 1993. "Photochemical vs. Thermal Deposition of Group IV Semiconductors." Paper presented at annual Am. Vacuum Soc. Meeting, Chicago, November 1993. Bird, R. B., W.E. Stewart, and E.N. Lightfoot. 1960. Transport Phenomena. New York: John Wiley & Sons, 570. Van de Ven, J., G.M.J. Rutten, J.J. Raarjmakers, and L.J. Giling. 1986. "Gas Phase Depletion and Flow Dynamics in Horizontal MOCVD Reactor." J. Crystal Growth 76:352. Crank, J. 1975. The Mathematics of Diffusion. Oxford, U.K: Oxford University Press. Grew, KE., and T.L. Ibbs. 1952. "Thermal Diffusion in Gases." Cambridge, U.K.: Cambridge University Press. van Sark, W.G.J.H.M., M.H.J.M. de Croon, G.G. Janssen, and L.J. Giling. 1990. "Analytical Models for Growth by Metal Organic Vapour Phase Epitaxy: II. Influence of Temperature Gradient." Semicond. Sci. Technol. 5:36. Talbot, L., R.K. Cheng, R.W. Schefer, and D.R. Willis. 1980. Thermophoresis of Particles in a Heated Boundary Layer." J. Fluid Mech. 101:737. 34. 35. 36. 37. 38. 39. 7.8 Recommended Readings Benson, S.W. 1968. Thermochemical Kinetics. New York: John Wiley & Sons. Jensen, KF. 1989. "Transport Phenomena and Chemical Reaction Issues in OMVPE (Organometallic Vapor Phase Epitaxy) of Compound Semiconductors." J. Crystal Growth 98:148. Smith, W.R. 1980. "The Computation of Chemical Equilibria in Complex Systems." Indust. and Engineering Chem. Fundamentals 19:1. Stringfellow, G.B. 1989. Organometallic Vapor-Phase Epitaxy: Theory and Practice. Boston, Mass.: Academic Press.