Arthur Sherman - Chemical Vapor Deposition for Microelectronics (779637), страница 4
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There are a numberof numerical techniques for the solution of this minimization problem, 7,8 butrather than review the details, we will simply describe some of the results ofsuch calculations.12Chemical Vapor Deposition for MicroelectronicsAs noted earlier, the great value of the free energy minimization techniqueis that one can consider completely new systems and not exclude any species.In this way, one identifies all potentially important species. As an illustration,we can consider the very complex Nb-Ge-CI-H system for which equilibriumcalculations have been made.
9 The motivation for the study was to determineconditions suitable to the deposition of Nb 3 Ge, which has a high superconducting transition temperature. The initial gaseous reactants were NbCl s , GeCI 4and H2 . Gaseous and condensed species that were considered are shown in Table2.
Clearly, a system with 17 gaseous species and 11 condensed species is toocomplex to approach by any other technique.Table 2: Chemical Species and Data Used in the Thermodynamic9Calculations for Nb-Ge-CI-H System, After WanGaseous Species~Ho f1200Kso 1200K( kca 1/mo 1e)(ca1/mo1e-deg)Nb117.6553.80Ge89.8849.64H2C12HC1041.03065.38-22.6554.65C129.8046.9334.31H53.38GeC131.4371.97GeC1-41.2590.67-117.95117.53GeC124GeH4GeH C13GeH C12 2GeHC13Ge C12 6NbC14NbC1518.7474.69-15.0088.29-52.00102.5-86.05109.92-135.0161.8-131.2126.48-164.0150.89Condensed Speci es *NbC1 2 • 33-108.7661.7NbC1 2 . 67NbC13NbC1 3 • 13-123.7364.54-133.5569.85-137.6872.33- 12.022.9NbGe O• 54- 14.626.6NbGe O.
67NbGe2Nb- 15.428.5- 20.849.9NbGe O. 33GeNbH O. 67*Each017.51015.91- 10.018.71fonnu1a is written to contain one niobium. except for pure Ge.Fundamentals of Thermal CVD13The phase diagram for condensed phases in this system is shown in Figure4. Apparently, there is a fairly narrow regime where Nb 3 Ge can be obtainedwithout contamination from other solid species. In Figure 5, the gas composition is shown as a function of temperature, pressure, and source gas composition.Other systems can be treated in a similar manner such as the Ti-B-CI-Hsystem/o and of course the Si-H-CI system has been exhaustively studied because of the commercial importance of silicon epitaxial films used for integrated circuit fabrication.!!T(K)1573H/(H+Cn·O.eTotal pressure 0.1 atm14731 - NbClz.332 - Nb13733 - NbGeo."4 - NbGeo.S45 - NbGe O.
1 112736 - NbGez1173461073.9.8.7.6Nbl ( Nb.5.4+Ge ) Mole Fraction.3.2.1oFigure 4: Equilibrium CVD phase diagram for the Nb-Ge-H-CI system. Thediagram was constructed from thermodynamic calculation results and depictsthe condensed phases which form as a function of experimental variables. TheNb/{Nb+Ge) values are reactant gas concentrations. After Wan. 91.3 MODELING OF FLOW AND CHEMICAL KINETICSAs noted earl ier, our principal interest will be in an open, flowing CVDsystem. In order to correctly interpret the phenomena occurring in such systems, it will be necessary to study chemically reacting gas flows with nonuniform flow and temperature fields. And, of course, we will have to understandthe surface reactions that lead to the solid film formation.
Within the reactinggas, we will consider homogeneous gas phase reactions. At the surface, we have14Chemical Vapor Deposition for MicroelectronicsEo10731173Temperatule (K)1313.86.4.2Nb I(Nb+ Gel Mole F,actlon(a)o(b)1.0 _ _.......__......---.,--y-o--,.-.,----r--r---=1.1.2.3.4.~67.8H/(H+CI) Mole Fraction(e)(d)Figure 5: Equil ibrium gas compositions as functions of (a) temperature, (b)total pressure, (c) Nb/(Nb+Ge) mole fraction, and (d) H/(H+CI) mole fraction9in the reactant gas. After Wan.to work with heterogeneous surface reactions. In special situations, we maymake use of chemical equilibrium arguments to evaluate deposition phenomena,but in general, an accurate representation of the process will require consideration of chemical kinetics.1.3.1 Diffusion vs. Surface Controlled DepositionBefore considering the full problem in all its complexity, it will be usefulllto understand the concept of "surface" or "diffusion controlled CVD.
Atone extreme, with very low pressures (large diffusion coefficients) and low surface temperatures, there is a large flux of reactants to the surface where theyreact slowly so that there is an oversupply of reactants waiting to be consumed.This would be considered the IIsurfacell controlled regime where the rate ofFundamentals of Thermal CVD15deposition is more controlled by the surface temperature than by the detailsof what is occurring in the bulk gas.At the other extreme, we have higher pressures (smaller diffusion coefficients) and high surface temperatures. Now, any molecule that can make it tothe surface will react rapidly, so that the deposition rate will be more limitedby diffusion through the gas adjacent to the surface.
Si nce diffusion is weaklydependent on temperature, this type of "diffusion" controlled regime tendsto be relatively insensitive to surface temperature.It will be instructive to quantify this phenomena by approximate arguments, although actual predictions will depend on more comprehensive models. 12,13 Initially, we recognize that an understanding of fluid dynamic behavioris essential to any attempt to describe these phenomena. In particular, we havethe concept of a boundary layer. When a fluid (gas or liquid) flows adjacent toa solid surface, the velocity of the fluid at the surface must be zero.
The regionin which the fluid velocity changes from its normal value to the zero value onthe surface is referred to as a boundary layer (see Figure 6). For high velocityflows, the thickness of this transition region, 8, can be quite small and is approximately proportional to the inverse of the square root of the Reynold'snumber. Or,~e(25)where:puxRe----p:-pumass densityflow velocitydistance in flow directionviscosityxSimilar boundary layers (transition regions) exist for temperature as well asspecies concentrations.uuTFigure 6: Fluid dynamic boundary layer.Assume we have a mixture of ideal reacting gases, and a concentrationboundary layer.
Then the diffusion of species i from the body of the gas tothe sol id surface is governed by Fick's Law!16Chemical Vapor Deposition for MicroelectronicsJ(26)= D~where D is the diffusion coefficient for diffusion of species i in the mixture,p is the local density of species i, and J is the mass flux. Alternately, we canexpress J in terms of a pressure gradient from the perfect gas law, p = p/RT.(27)J_-s!£0RTdyor assuming p varies linearly across the boundary layer,(28)where:JPbPs=oDRTT ~1?6yRTpartial pressure of i in gaspartial pressure of i at surfaceWhen deposition is controlled by diffusion, Equation (28) shows that variations in boundary layer thickness, 0, influence the mass flux due to diffusionand thereby, the deposition rate. In practical CVD reactors, boundary layerthicknesses can vary so that thickness uniformity of deposition can be poorunless this phenomena is recognized and corrected.For example, when diffusion-controlled deposition is done in a tube suchas that shown in Figure 7, the boundary layer grows and there is an exponentialdecrease in deposition thickness as x increases.
14 To correct for this phenomena,the susceptor is tilted up, as shown in Figure 8. As the susceptor is tilted up,the velocity above it increases due to the constriction in the channel. The increased velocity increases the Reynold's number, which thins the boundarylayer so that the deposition rate goes up. The net effect is to maintain a relatively uniform deposition along x...uu~\ \ S \e.x~ ~ SUSCEPTORFigure 7: Axial flow reactor.Fundanlentals of Thermal CVD17xFigure 8: Reactor with tilted susceptor.Turning our attention to surface phenomena rather than diffusion, werecognize that species will transit across the boundary layer and may be createdor destroyed in this passage due to chemical reactions which will proceed atfinite rates (homogeneous gas phase reactions).
Upon impacting the surface,they may adsorb and then decompose, leaving a solid thin film. This will be aheterogeneous surface reaction which will have a characteristic chemical reaction rate. One way to describe th is phenomena is in terms of a Il mass transfer" coefficient. The mass flux can be expressed in terms of this coefficient,as follows:(29)Jwhere Peq refers to the partial pressure of species i that would exist underequil ibrium at the surface temperature, and k o is the mass transfer coefficient.For diffusion-controlled situations, Equation (28) shows that the drivingforce for mass flux to the surface is the pressure difference of species i betweenthe main gas flow and the wall.
For surface-controlled reactions, the drivingforce instead is the supersaturation at the surface. In other words, Ps > Peq,and there are more gas molecules available at the surface than can be reactedthere.1.3.2 Effects of Gas Phase KineticsTo properly describe chemical vapor deposition, one must develop a systemof equations that encompasses all phenomena involved. This includes a properrepresentation of reactions in the gas phase, a suitable description of the surfacekinetics, and the gas dynamics of a reacting gas mixture. Because the full governing equations are extremely complex and difficult to solve, most authors haveexamined only limited regimes.
For example, we can ignore the gas dynamics18Chemical Vapor Deposition for Microelectronicscompletely and only study the kinetics of the gas phase reactions. Or, we couldlook at the kinetics of the heterogeneous surface reactions. If we also wish toignore gas phase kinetics, we can study the thermodynamic description of thereaction.Unfortunately, chemical vapor deposition is a field which is, basically,interdisciplinary. Essential understanding can be gained by including all ofthe phenomena involved. To do this in full generality would require the solution of many coupled, nonlinear, partial differential equations. Such a formulation is clearly beyond the scope of this text.We will, therefore, choose to look at a particular simplified physical problem, but attempt to formulate the problem from first principles. This shouldlead to a problem, which although complex and involving nonlinear equations,can at least be described by ordinary differential equations.Let us consider laminar flow through a two-dimensional channel, theso-called Poisseulle flow.
The geometry is shown in Figure 9.Figure 9: Channel flow.As in the classical Poisseulle flow, the channel is assumed to be two-dimensional (nothing varies in the z direction) and doubly infinite in the x direction. We will impose a constant temperature, T, on each wall and assume that Twill not vary with x. An axial pressure gradient will have to exist in order forthere to be an axial flow, and we recognize that it should be constant so that pwill vary linearly with x.In a typical CVD reactor, mass flow is small so the pressure gradient will besmall.
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