 Good morning welcome back to this course on chemical engineering principles of CVD process. In the last lecture we introduced some basic principles of chemical vapor deposition and to reiterate the key point from the last lecture in chemical vapor deposition the identity and composition of the condensate that forms is different from the identities and composition of the species in the vapor phase that lead to the formation of that condensate. So for the formation of a single condensate species like silicon a variety of gas phase reactants could participate in the deposition process they can react among themselves and the transport process from the bulk of the vapor phase to the substrate will take place through the diffusion of many, many chemical species that contain the depositing element. Now the advantage the primary advantage of CVD over physical vapor deposition where the identity of the condensate exactly matches the identity of the vapor species is that it is much more energy efficient because you are essentially taking advantage of the natural tendency of gases in a high temperature system to dissociate and form a variety of species and also as species dissociate and they become lighter the diffusion rate increases because the diffusion rate of a particle as well as a species is inversely dependent on its size. So the smaller the molecules the faster they will diffuse. So the fact that in chemical vapor deposition you have extensive dissociation of the gas phase molecules into smaller precursors also results in an enhanced rate of transport of these precursors to the substrate. In addition to the advantages that we talked about last time that CVD essentially results in the in very uniform coverage over a surface it is able to follow contours much better than other types of deposition processes and the purity of the system can be maintained quite effectively. As chemical engineers we are always concerned with the design of the system. How do you design a CVD reactor? What are the key components in it? What are the factors you have to take into account when you design a CVD reactor? So let us take a look at that little bit. So a CVD reactor is in essence no different from any chemical reactor which means that you have reactants flowing into the reactor. You provide some source of energy to make the reactants come together react and form a product and then you have a mechanism by which the product can be removed and any byproducts can be exhausted from the system. And just like with any chemical reactor you have to provide appropriate controls to make sure that the reactor performs in a very consistent and repeatable and reproducible manner. So if you look at a CVD reactor in its most basic configuration you have gases essentially entering on one side of the reactor and flowing through the reactor and exiting at the other side of the reactor. There is a substrate holder or what is known as a susceptor which is fixed typically to the bottom of the reactor. It is on top of this susceptor that deposition must take place. So the deposit will actually form on top of this receptor or susceptor that is introduced essentially to make the condensate form. Now the reason that condensation will happen here and not here or here is what? You have a feel for why condensation will form will happen only at the interface between the surface and the gases. What is the difference between the rest of the reactor and the interface? Well actually there are two configurations there is something called the hot wall reactor and a cold wall reactor and by the way in CVD systems the higher the temperature the greater the chance of deposition. So actually the condensate will be maintained if anything at a temperature that is hotter than the surroundings in order for deposition to happen but that is not the primary reason. Even if you have a uniform temperature distribution in the reactor deposition is more likely to happen on the substrate rather than in the gas phase why is that, no all reactants are introduced here. So the reactants are introduced on the left side of the reactor and the products and byproducts are being taken out and the condensate is forming here. So that is not the reason. So impact only is an important phenomenon when you have large particle sizes. Fine particles and vapor molecules do not impact they just diffuse and they either stick or bounce off. So okay the primary difference is that this is a heterogeneous process versus a homogeneous process. When you look at how a CVD film is formed you do not immediately form a continuous film you initially nucleate droplets of the condensate. So it is essentially a nucleation process and the energy barrier for heterogeneous nucleation is much smaller than the energy barrier for homogeneous nucleation. So thermodynamically there is a natural tendency for chemical vapor deposition to happen on any surface that you introduce regardless of what temperature you keep it at, what surface energy it has and all that. So that helps. So because in a CVD reactor you do not want homogeneous nucleation to happen. You do not want little silicon particles forming you know here, here, here and then trying to deposit on the substrate. That would not be good because what will result is a very flaky powdery deposit rather than a continuous and belladiered film. So the entire point of a CVD reactor is to design it such that the formation of the condensed phase only occurs at the substrate on which deposition is supposed to happen and you completely suppress its formation anywhere else in the reactor. Now in essence that is actually very different from what is known as a chemical vapor synthesis reactor. In a CVD reactor you want the condensation to only happen here. In what is known as a CVS reactor or a chemical vapor synthesis reactor you actually use the reactor to make nanoparticles and the way you do that is by promoting homogeneous nucleation and getting these very, very fine particles to form in the gas phase and then providing a mechanism for them to agglomerate and form larger particles which can grow to the nanometer size and then you suppress it. You essentially freeze it at that point but anyway that is good when you are trying to make nanoparticles but when you are trying to make a CVD film you want the exact opposite to happen. You want to design it so that thermodynamically and kinetically it is very difficult for any particles to form in the gas phase and virtually all of the condensation only occurs at the substrate that you have introduced into the reactor. So if you look at this very basic configuration you can see that what you are relying upon is that once you have this reactor you bring the reactants in, you bring it up to whatever temperature and pressure that you want to run it at, reactions happen and the condensation happens here and essentially all the byproducts are then exhausted out. The substrate is removed and the film is then inspected and used for further processing right. Now what are some of the drawbacks in this design? Let us say that you are using as we said last time silane and pyrolysis process to make silicon okay. So the silane is introduced in this direction and the temperature is designed such that it starts to form various precursors of silicon and you start condensing silicon on the substrate. Do you think you will get a uniform substrate? I mean uniform film on the substrate or will the thickness change as a function of downstream distance? Well yeah basically what will happen is that the concentration of silane here will be quite large when it first encounters a substrate but some of it will then deposit. So the precursor concentration itself will start decreasing right as the gases are flown across the substrate and therefore what you will see is that you will get a very thick deposit the leading edge but as you go towards the trading edge of the substrate you will start seeing a reduction in the thickness of the deposit which is not good. So how do you address that situation? If you are a chemical engineer and you are trying to design this process and you wanted to get a uniform film how would you do it? Increasing the velocity may reduce the severity of the problem but you will still get a non-uniform substrate. Inclining. Yeah, inclining the substrate is one way to do it and that is one of the tricks that is used in the industry to try and get a more uniform deposition. Any other ideas? Rotating the substrate can help yeah but you still have this basic problem that there is a depletion of the reactant concentration as it flows across the reactor. Ideally what you would like to see is that the reactant concentration is maintained uniform across the reactor you know wherever the substrate is. So the way to do that is to introduce a carrier gas. So instead of just flowing silane through the reactor you will essentially take a silane with for example H2 mixture and in fact the silane concentration will be kept around 10 to 20% and the H2 concentration will be kept at 80%. So the hydrogen gas in this case is used as a diluent. It lowers the concentration. Now when you do that what happens? The concentration the silicon or silane concentration can now be maintained virtually constant as the gas flows across the substrate. So use of a diluting agent helps in maintaining uniformity of the film thickness. Any other ways that you can think of? Suppose you do not have to flow the reactants left to right you know in other words parallel to the substrate. Suppose you could flow it vertical would that help? So for example if instead of this type of flow configuration supposing you were to do introduce the gas this way and essentially achieve a stagnation point flow would that be preferable? The formation of deposits on the sides that is not a big issue you know that is not a critical functional area of your substrate. And again I think that can be minimized but as far as the front you know the deposition surface will you get a more uniform substrate with vertical stagnation flow? You do in fact because essentially when you do it this way the entire layer here I mean obviously you have to design it so that the stagnation flow happens with the entirety of the deposition surface being in the stagnation zone. But if you can make that happen then you are liable to get a more uniform substrate. But are there any drawbacks to that setup what is what could be a problem with this type of flow? Or let me ask you this way when would you use this flow versus this flow? The one of the characteristics of the vertical flow is that the residence time of the vapor in the vicinity of the substrate basically becomes infinity because there is no way for it to no place for it to go. So what does that mean? Over time you are going to grow a very very thick deposit right whereas with the horizontal parallel flow you can achieve a much thinner film. So essentially the vertical stagnation flow is typically used when you need CVD films that are the order of many nanometers or even microns thick whereas if you are trying to make a very very thin and uniform CVD film then you prefer to use the parallel flow. So if you look at the components of a CVD reactor what are the critical components? So you need a good gas delivery system all the reactant gases have to be delivered to the reactor in such a way that they do not react on the way. So either you have to have multiple inlets for the reactive gases or you have to ensure that the temperature and pressure conditions during the flow into the reactor or such that chemical reactions cannot happen that result in the formation of a condensate. The second part of it would be the chamber itself and again the design of the chamber would depend very much on what mode you are going to use. You will discuss later that you can have high temperature reactors, lower temperature reactors, atmospheric pressure reactors, low pressure reactors. So depending on the operating conditions that you choose you will have to appropriately design the reactor. The third part of it is the substrate on which you are going to condense the CVD system and related to that is the loading mechanism, loading slash unloading mechanism and the substrate has to be provided a separate source of energy. The reactor itself may have its own energy source so that you can maintain the entire reactor at a certain temperature and so on. But in CVD systems typically the substrate will be maintained at a temperature that is different from the reactor itself. So you need an energy source, some kind of a typically a heater if you are going to provide thermal energy and by the way there are different ways in which you can provide the thermal energy to the system. You can have radiative energy sources, you can have RF sources you know so you can do tube furnace type of arrangements or you can use an induction heater or so and so on. So providing thermal energy is one way. The other way of course is you can also provide energy to the substrate using other means such as light, laser and so on. So you have to be able to provide some source of energy to the substrate. Similarly if the substrate can take high temperatures thermal energy is the most efficient way to achieve this energization. However there are certain substrates for example if you are trying to deposit something on aluminum you really cannot take it to a very high temperature because aluminum will oxidize and form aluminum oxide. So you have to maintain the temperature not too far above room temperature but you still need to provide energy to the substrate. Then you have to look at non-thermal means of providing energy to substrate. In any case as you design the reactor you have to keep in mind that you have to provide an energy source to the substrate which is separate from the energy source that you are providing for the entire reactor. So what are some of the other components you need? You need a vacuum system because many reactors, CVD reactors run at reduced pressures. So you have to be able to depressurize the reactor during the CVD process and then repressurize it when you are ready to open the reactor and take out the substrate. And you also need an exhaust system which takes the byproducts out of the reactor and by the way this exhaust must be done as quickly as possible because the byproducts are a potential impurity in the CVD film. So you want to minimize the time of contact between the vapor phase byproducts and the film that you are growing on the substrate. And so the exhaust system has to be extremely efficient as soon as the byproduct vapors are generated they must be taken out of the reactor. You also need an exhaust treatment system. One of the characteristics of CVD reactors is that the byproducts tend to be frequently difficult to handle. You know the byproduct could be chlorides, they could be bromides, they could be halides, they could be hydrogen itself or silane, unreacted silane. Many of these species are toxic. So there are a lot of environmental and health concerns with byproducts from CVD reactors. And therefore you have to be able to provide appropriate treatment systems to ensure that when the exhaust gases are let out into the atmosphere they do not have a harmful consequence for people and things in the vicinity. So that has to be built into the system. And finally as with any chemical reactor you need a good control system because it is especially in a CVD reactor temperature is a very, very key variable. You probably require the tightest controls on the temperature distribution in the reactor and the second most critical variable is the velocity, the velocity distribution inside the reactor because that is what really delivers the reactants to the substrate and it also takes the exhaust and gets it out of the system. So having tight controls on the transport phenomena inside the reactor is also very important. Of course pressure is important as well. Reactant concentrations that is another critical variable and again you have to have separate controls on the substrate temperature versus the reactor temperature. So you need to provide separate control systems. Many of these reactors also come with in situ inspection systems. That is as you make the CVD film you want to assess its quality. You do not want to take it offline to a lab, wait for the analysis to be done and then come back and then if you find out that it is not good and you might have made another 1000 wafers by then which you have to throw away. So preferably if you can have instrumentation that can look at the wafer and the film as it is growing and do a quick spot check whether the film is of acceptable quality then your process disruption and cost due to scrap product and so on can be minimized. And so it is important to have this in situ inspection system but if you have that obviously that needs then to be coupled to the control system because as you see things in the film that you do not like you have to tweak the control parameters so that you bring the properties of the CVD film back to where they should be. So ideally you want to provide almost an endpoint control. As you make a film you inspect it, if it looks okay, go. If something looks like it is not where it should be then you immediately provide a feedback to the system so that the appropriate parameters get adjusted and you bring the process back into line. And again more advanced manufacturers of micro electronic products where the CVD film characteristics or a very key parameter to control will provide statistical process control. So you do not look at only whether you are meeting or failing a specification but you actually look at how certain critical parameters are deviating from their process mean and as soon as the deviations exceed a certain amount even if you are not failing a spec you still try to bring it back to its nominal value. So that type of statistical process control and statistical quality control are very critical because these are very expensive operations. The substrates are expensive, the reactants are expensive and the CVD film that you are making is a very valuable thing. You know we are talking about millions of dollars worth of production on a daily basis. So the control system and the in situ inspection system are very, very key components to the reactor to make sure that we do not waste product that virtually every product we make is certified to be usable, okay. Alright so these are some of the key parts of the CVD system. So what are the key steps in the CVD process? How would you actually run a CVD process? Well the first thing that you will do is you have a reactor so you will first take the substrate on which you are trying to put a film down, mount it on to the load and load mechanism and you will load it into the reactor, you will close the reactor. By the way most CVD systems are run as batch reactors primarily because the environment of the reactor has to be very tightly controlled. Now there are atmospheric pressure CVD reactors that can potentially be run as flow through reactors but that is very rarely done. We will talk about a few cases where that is done but you know the two requirements to run it as a flow through process or a continuous process is that the temperatures must not be too far from atmospheric temperature and the pressure must also not be too far from atmospheric pressure. But under atmospheric conditions it is not easy to grow thin film in a controlled manner on a substrate. So it is very rare that we have CVD reactors that are entirely open to the environment that typically operated as closed systems with very tight controls on the operating parameters. So as soon as the substrate is mounted into the reactor using your load and load mechanism the reactor is sealed and it is then brought to operating conditions. So if the temperature needs to be maintained at a certain value, the temperature is increased and you wait until you reach a steady state on the temperature distribution. If the pressure has to be modified again you pull the appropriate vacuum and again usually CVD reactors do not run at pressures that are higher than atmospheric pressure but they are frequently run at pressures that are lower than atmospheric pressure. Can you imagine why? I mean why just intuitively why would you not want to run a CVD reactor at elevated pressures? The primary reason is that you will see later that especially at high temperatures the CVD the deposition process itself is transport controlled and the predominant transport mechanism that is happening in a CVD reactor would be diffusion. It is the diffusion across the boundary layer that leads to the formation of the film and what effect does pressure have on diffusion? It is essentially diffusion goes as one over pressure right. So if you go to a high pressure essentially you will slow down the diffusion process almost entirely and therefore typically CVD reactors are run at atmospheric pressure or lower. So you have mounted the substrate, you have brought the temperature and the pressure and all the other conditions to the operating conditions then you introduce the reactants into the system and run it for a sufficient amount of time for achieving a certain thickness of the film. The obviously when you are trying to make any film on a surface the number one metric that you measure is the thickness right. So when I was talking about the in situ inspection systems they what they typically measure is the thickness distribution. We essentially make the assumption that as long as the thickness on the surface of the film on the surface remains constant the reactor is working the way it should. Obviously offline analysis would still be needed to monitor things like impurity levels and characteristics you know the metallurgical characteristics of the film and so on but that is not possible to do in situ or online. So a simple online measurement must be as quantitative as possible and just give you a number that you can use as an indicator of whether your process is running properly or not and so the film thickness is typically taken as that variable. So as you run the reactor essentially that is what you will do. Once you have brought the reactor to operating conditions you run it for a sufficient amount of time use your inspection system to see whether it has reached the thickness that it is supposed to reach check for the uniformity of the film and then turn off the reaction. So the way you do that is you cut off the reactant gases and you bring the temperature and pressure back to nominal values and you exhaust the product gases as quickly from the system as possible. So that is typically done using your exhausting system which may simply be again a vacuum pulling of all the species there or it may be a high velocity convective pushing of the product gases out. So to some extent that depends on the design of the reactor itself and after the reactants the unreacted materials have been purged from the system then you remove the wafer from the system and then subject it to further processing or for further analysis and so on. So that is roughly how you would operate a CVD reactor but if you look at the deposition process itself you know what we talked about just now was the various steps in just operating a CVD reactor but when you look at the formation of a film on the surface what are the critical steps involved in that you know how does it happen if you look at the CVD process and you break it down into sequential steps what are the different steps that are involved. Now from a transport viewpoint once the gases are introduced into the reactor the first step is essentially the convective transport of reactants plus carrier gas into the reactor. So again this needs to stabilize you need to have the convective flow established in such a way that far from the substrate we are not talking about flow near the substrate but in the bulk of the reactor we want to establish a stable flow. By the way in a CVD reactor one thing you must try to avoid at all cost is turbulence all CVD reactors are designed in order to have laminar conditions of flow inside the reactor why is that why would turbulence not be desirable. Turbulence has some good properties right for one thing it enhances transport rates whether you are talking about mass transfer or heat transfer or momentum transfer they are all enhanced when turbulence happens. So why would not you want it I mean it will speed up the process right yeah I mean turbulence by definition is very hard to control if you can achieve controlled turbulence then perhaps it is a good thing but I mean it is just not possible. So while turbulence may offer certain advantages in terms of localized increases in transport rates it is not something you want to have in your system and have to deal with it is kind of the reverse of stagnation flows right why do not you want stagnation flow again stagnation essentially implies that there is more time for deposition to happen the reactants stay in contact with the substrate for a longer period of time so it is all goodness but then how do you cannot control it once stagnation happens you cannot break it essentially. So you cannot have a sharp cut off and say that here is where I want to stop you know as soon as my thickness reaches this number I want to stop here so you really do not want the two extremes you do not want the prevailing Reynolds numbers to be so low that you are essentially in creep flow conditions or stagnation conditions you do not want it to be so high that you are in turbulent conditions. So you want to operate somewhere in the middle where your Reynolds numbers are reasonably high to ensure that you know the convective transport is happening at a sufficiently high rate but at the same time the Reynolds number should not be so high that you kind of slip over into the turbulent regime the other problem with turbulence of course is the eddies you know once you have these turbulent eddies forming the transport of material is no more by diffusion it is essentially whole chunks of fluid are getting thrown around and so again if you look at a CVD film that has been formed under turbulent conditions it will look very similar to a CVD film that has been formed under homogeneous nucleation conditions. You will essentially have a very very uneven powdery deposit where certain locations will have essentially boulders of material and certain locations will have virtually no deposit. So two things you want to avoid in CVD reactor turbulence and homogeneous nucleation okay. So the second step is obviously the chemical reactions to happen and these must happen in the bulk phase when I talk about the bulk what I am talking about is the locations in the gas stream that are very far from the substrate where the deposition is taking place we can also call it mainstream we can call it free stream or we can call it bulk fluid but whatever term I use I am basically referring to a location in the gas stream that is sufficiently far away from the substrate. So chemical reactions will continue to happen as long as you have appropriate temperature and pressure conditions but in addition we want that chemical reactions must also happen near the substrate and these reactions will be qualitatively different from the reactions in the bulk primarily because of the temperature gradient because the substrate temperature is different from the bulk temperature you will form a set of molecules or compounds which are different from the set of compounds that are formed in the bulk fluid. The concentrations will be different for example if SiOH is one of the compounds that is forming the concentration of that particular compound would be very different in the mainstream condition compared to the near the vicinity of the substrate it is this concentration gradient that will then drive the transport process okay. So because you have chemical reactions happening in the bulk and chemical reactions happening at near the substrate but under very different temperature and pressure conditions concentration gradients develop which drives diffusion. So the diffusion will happen from bulk fluid to the interface with the substrate but we are still talking about outside the boundary layer. However as you know when flow happens past a plate you develop a boundary layer right so if the flow is happening in this direction you will essentially form a boundary layer that looks like that and convective flow will essentially stop when it encounters the boundary layer the velocities will rapidly decrease. So you still have to transport the reactant molecules from just outside the boundary layer to the surface itself and that has to happen by diffusion across the boundary layer and that as I said earlier is frequently the rate limiting step in a CVD reactor by the way the diffusion from bulk to the outside the boundary layer is what we call convective diffusion. So the convection process itself is aiding the diffusion process. So it is essentially enhanced diffusion process but the diffusion inside the boundary layer is happening in the absence of any convective phenomena. So it is a purely molecular diffusion process which is also aided by something called thermal diffusion. The existence of a temperature gradient actually induces mass diffusion. We will talk about this later in the course but the combination of thermal diffusion and thick diffusion actually provides the driving force for transporting the reactant molecules from just outside the boundary layer to the substrate itself. So that is the next step. So the sixth step would be actual heterogeneous chemical reactions taking place at the substrate which leads to the formation of the film right. So this is a step where you actually start seeing the appearance of a CVD film on the substrate. So that is the sixth step in the process. Now as the film forms it has to bond to the surface. So the adhesion of the film to the substrate is also a very critical step. So in some cases it happens simply by molecular adsorption or molecular attachment. In some cases physical adsorption happens, in some cases chemisorption happens and obviously the bonding force increases as you go from simple van der Waals forces of adhesion to adsorption to chemisorption and depending on how tightly you want the film to adhere to the substrate you will design the conditions again such that the sticking of the film to the substrate happens by one of these mechanisms. In any case film adhesion to the substrate is also a critical step which again needs to be kept separate from the deposition of the film. When you talk about the heterogeneous reactions of the substrate which lead to film formation what you have to keep in mind is that this is a dynamic process. Just because for example silicon substrate, silicon solid is forming on the substrate does not mean that the silicon is going to stick to the substrate. You still have to provide a mechanism by which the silicon atoms that are forming will get attached to the surface. So that is a separate step and in fact you can play with the adhesion force by doing things like baking and aligning and so forth. So the initial deposit that forms is actually quite loose on the surface but as you increase the temperature, as you increase the pressure you can start essentially making it stick much harder. Sintering is another process that is used to bake the film onto the substrate so that it virtually becomes an irreversible process. Once you have sintered a CVD film on a substrate there is really no chemical means to take it off. You will have to destroy it in order to remove it from the surface. So what is the other step then? Starting with the CVD film that has adsorbed on the substrate, you may have some of the by-product gases which have also adsorbed on the substrate but these are impurities. So you have to desorb the adsorbed impurities. So desorption of impurities is also an important step, desorption of adsorbed impurities. So this ensures the purity of the CVD film that you have deposited. Now once the adsorbed species that you do not want have been desorbed, first they have to be removed out of the boundary layer. So you have to kind of reverse the diffusion process, you have to provide an appropriate concentration gradient so that the desorbed species as soon as they leave the substrate will quickly diffuse to the outer edge of the boundary layer. So the exiting of these desorbed impurities from the boundary layer to the outside is another important step otherwise again they will stick around and keep getting re-absorbed onto the substrate. So as soon as possible you get them out of the boundary layer and then the last step of course is exhaust. So all the unreacted gases, all the gaseous byproducts and all the desorbed impurities from the surface all then have to be exhausted from the reactor so that again they do not stick around and recontaminate your film, okay. So if you look at these various steps that are involved in the CVD process, you get a feel for why you know chemical engineering is such an important discipline to apply to the design and operation of a CVD reactor. Each of these steps involves again either equilibrium thermodynamics or chemical reactions and kinetics or transport phenomena of various kind, various control mechanisms. So in order to achieve a CVD film on a surface which sounds you know simple enough in principle you have to pay attention to many of these mechanisms. Each one has a bearing on the next so it is not that you can kind of design the reactor in sequence even though we have broken out the steps in some sequential fashion I am sure you understand that these are going on simultaneously. So these are highly coupled mechanisms, anything you do at a substrate level can affect even the bulk of the reactor and vice versa. And so whether you are trying to do modeling of CVD reactor or the actual operation control and optimization of a CVD reactor, you not only have to pay attention to the individual steps that are involved in the formation of the film but you also have to take a close look at how each step in your mechanism is coupled to the next step and try to obtain a system wide solution that works for you. One of the things that I mentioned that somewhat helps us both in terms of modeling as well as operation is the fact that the conditions are typically such that flow is uniform and laminar. And as you know the system becomes much more predictable under those conditions. So you have the potential to be able to develop a predictive model for a CVD reactor and actually achieve the same results when you actually operate the reactor. You cannot say that about many reactors in real life you know if you go to the chemical industry and you look at the various chemical reacting equipment that are being used, modeling is not first principles based. It is more empirical data driven. So people collect a lot of data on what is coming in, what is going out and establish correlations because really that is the best you can do. But in a CVD reactor because the conditions are so well controlled you actually have at least the potential to develop virtually a first principles model and use that for the design of the reactor and the control and optimization of the reactor. So in subsequent classes we will look at how to develop a good model for a CVD reactor incorporating all these various steps. How do you model the thermodynamic behavior of your reactor? When can you assume that equilibrium prevails and when do you have to allow for kinetic limitations to kick in? How do you model diffusion processes when there are multiple species that are diffusing? How do you handle the case where they are all dilute species versus the case where some of them are not? How do you take into account the various types of reactor designs? We still have not talked about the hot wall, cold wall reactor or the atmospheric pressure, low pressure reactor. There are very, very significant differences in the design and operation of the CVD reactors depending on which particular configuration you go with. So it is an interesting and challenging problem to deal with CVD reactors but keep in mind that compared to traditional chemical reactors, CVD reactors are run under much more tightly controlled conditions. So you have the ability to apply some of your knowledge about various mechanisms that are prevailing and actually have a practical influence on how the process is run. So we will take up some of these aspects in the next few lectures. Any questions on what we have talked about today? See you then.