 Last class we looked at an overview of the patterning process, we saw that in the case of IC fabrication, we can divide the processes into 4 main kinds, we had layering, lithography or patterning, doping and heat treatment. If you think of an IC fabrication as an assembly line process, we start with a blank silicon wafer, silicon is typically the material that is used, gallium arsenide is also used. So, we start with the blank wafer which goes through these various processes and you get the finished IC circuit out. We also looked at an example of fabrication of a MOSFET, a metal oxide semiconductor field effect transistor, where we started with the blank wafer which went through this different steps could be layering, could be patterning, doping, heat treatment is included in all of this to give you the finished MOSFET. So, starting from today for the next few lectures, we look at each of these processes in detail. Today, we are going to look at layering and in layering, we are going to look particularly at grown films that is films that consume the underlying silicon. So, today we are going to focus on the oxidation of the underlying silicon film. So, the ability of silicon to form silicon dioxide or SiO2 is very important. If you remember when we talked about the introduction to integrated circuits, the first circuits were made of germanium, but later when ICs came into being, silicon was used as the material of choice. One of the reasons of course, is that silicon is abundant, so it is easy to manufacture, but more importantly silicon can also form SiO2 and SiO2 is a very good insulator. SiO2 was used as the original dielectric material for the MOSFETs, so it acts as a dielectric between the gate and the semiconductor, of course later with scaling silicon dioxide was originally replaced with oxynitrides and finally we have high-k dielectrics. When we look at silicon, silicon naturally has a native oxide on the surface. The native oxide has a thickness typically around 3 nanometers. Silicon dioxide performs a couple of functions, one it helps in passivating the surface, so this passivation can be both physical and chemical, so this is very important because surface passivation will also affect the electronic properties. So whenever we think of a surface, so it could be silicon 111 or silicon 100, there are always some dangling bonds, dangling bonds are usually defect states that lie in the middle of the band gap and they can affect the electrical properties. So silicon dioxide helps in passivating these dangling bonds, so that improves the properties, so this passivation can be physical and chemical. Silicon dioxide is also important because it is used for patterning the substrate. So it is an example of a hard mask, so silicon dioxide is a hard mask because it can basically survive at high temperatures. So in the example of MOSFET that we saw in last class, the first layer we grew was the field oxide which is nothing but silicon dioxide. So if you want to do doping at high temperatures and you want to do doping only in specific regions then usually some sort of an oxide layer is used for patterning. But the native oxide layer we saw is 3 nanometers thick is usually too thin for doing any of the patterning process. So thicker oxide layer has to be grown on silicon and this is essentially the oxidation process. We also saw briefly that there are two kinds of oxides that can be formed. The first one is dry ox, in this particular says silicon reacts with oxygen gas usually this is at high temperature to form SiO2. The other kind of oxide is called your wet ox in which case silicon reacts with steam again at high temperature to give you silicon dioxide plus hydrogen. So both of these processes require high temperature and they both consume the silicon. Now because silicon dioxide has a different density compared to that of silicon there is always some volume expansion when we have an oxide layer forming on the surface. To look at that consider a silicon substrate with an oxide layer on top. So this oxide layer is a grown oxide so that it is consumed some of the silicon. This is SiO2 so the dotted line represents the original interface of the silicon. So this much amount of silicon has been consumed in order to grow the oxide. So this is the original silicon interface, D is the amount of silicon that is consumed typically a thickness and D prime is the thickness of the oxide layer is the silicon that is consumed in forming this oxide layer. So one can find a relation between D prime and D by simply looking at the number of moles of silicon consumed and the number of moles of SiO2 formed. To do this we just need some physical properties. So first is density in grams per centimeter cube, silicon and SiO2. Silicon's density is 2.33, SiO2 is 2.65, we also need the molecular weight for silicon this will be the atomic weight. So silicon's atomic weight oxide 60.08. So if D is the thickness of the silicon consumed and A is the cross sectional area, A times D is the volume of the material. The mass is nothing but density of silicon times the volume or the number of moles. So Z of Si is nothing but the molecular weight, let me just make a notation here, this is Z. So Z of Si is the atomic weight of silicon and this is the mass of silicon that is consumed. Similarly we can write another expression for the number of moles of SiO2 formed. The thickness of the SiO2 layer is D prime. So D prime is the thickness of SiO2 and D is the thickness of the silicon that is consumed. These number of moles are essentially equal because 1 mole of silicon gives you 1 mole of SiO2. So if we equate these two area is common, we can rearrange the other terms and substitute the values from which we get D prime by D is nothing but 1.88. So if you take an example, let us say we want to grow 100 nanometers SiO2 that is the target thickness. So this will be D prime corresponding value of D is just D prime divided by 1.88. So it is 53.2 nanometers of silicon is consumed. So there is always some volume expansion when you consume silicon and you grow a layer of silicon dioxide on the surface. Silicon dioxide growth on silicon is called a thermal oxidation process. So we can have a simple model of this thermal oxidation process. So we saw that there were two ways of growing silicon dioxide. You can either have a wet oxidation or a dry oxidation. In both cases the typical operation temperatures are somewhere between 900 to 1200. This again depends upon the thickness of the silicon dioxide layer that we want to form and also the process time and so on. So later we look at some numbers and try to compare both wet oxidation and dry oxidation. In both cases a silicon dioxide layer is formed on the surface. So for any further oxidation, the oxidizing species whether it is oxygen in the case of dry ox or steam in the case of wet ox has to diffuse through the silicon dioxide layer reach the silicon interface in order to form a further oxide. So we can look at a basic model for oxide growth. So we first consider the gas phase. So the gas phase has the species that forms the oxide. Then there is an oxide layer that forms on your silicon and then ultimately you have the silicon. So let me just write this here. So we have two interfaces. One is the interface between the gas and the oxide layer. So this oxide layer can either be a pre-existing layer or you could be somewhere at the middle of the process so that you have an oxide layer of certain thickness. Let us call this thickness D0. We have another interface between the oxide layer and the silicon. So if you look at the various steps of oxide growth, the first step is that the oxidizing species has to be transported from the bulk to the oxide gas interface. So I will use IF in future to denote an interface. So the first step is the oxidizing species has to be transported from the bulk. So let CG be the bulk composition and CS is the surface composition. So there must be some transport of the species to the interface so that it can diffuse. So let F1 be the flux corresponding to it. The next step is the diffusion species has to be transported through the oxide layer. So you need to have diffusion through the oxide layer. So this could have some flux F2. So C0 could be the concentration at the gas oxide interface. This is the concentration in the oxide layer and from here it goes to some concentration Ci which is the concentration at the interface. And then finally you can have reaction with the silicon to form a new oxide layer. This has a flux of F3. So if you look at the system in steady state F1 is equal to F2 is equal to F3. So that whatever species that diffuses from the gas phase to the gas oxide interface gets dissolved in the oxide and then diffuses to the interface where it reacts with the silicon in order to form SiO2. One of the assumptions of the model is that there is no dissociation of the species in the oxide so that whatever is in the gas phase gets directly transported or directly diffuses across the oxide to the interface. So we can actually model these various processes and using the relation between F1, F2 and F3 derive some numbers for how the oxide layer grows as a function of the diffusion coefficient and also the thickness. So let us take a look at that. So let me just redraw the diagram. So I have a gas phase, I have an oxide phase and then I have a silicon. The oxide has some thickness D0. The gas has a bulk concentration Cg and there is a surface concentration Cs. Within the oxide there is a concentration C0 at the surface and Ci at the interface. We also saw there were 3 fluxes F1, F2 and F3 and F1 equal to F2 equal to F3 in steady state. So consider the first process which is the movement of the diffusing species from the bulk of the gas phase to the surface. So this can be simply written as some constant Hg times Cs, sorry Cg-Cs. Hg is nothing but the mass transfer coefficient in the gas phase. So we can rewrite this in terms of the composition of the diffusing species within the oxide layer and if we do that F1 is H times C star-C0, C0 you have already seen is the concentration at the interface of the gas oxide layer. It is the concentration of the diffusing species in the oxide layer. C star is the equilibrium bulk concentration in the oxide. We can usually think of this as some sort of solubility limit. So in the case of dry ox, where dry oxidation, the gas species that is diffusing is O2. In the case of wet oxidation, the species that is diffusing is steam. So C star is your bulk concentration in the oxide. H is related to Hg by Henry's law. So it is Hg divided by Hk Boltzmann time temperature, where H is the Henry's law constant. So Henry's law typically relates the amount of gas that is dissolved in any solid to the partial pressure of the gas. So this by these expressions, we have written F1 which is the flux in the gas phase in terms of the concentration of the diffusion species in the oxide layer. Next we can look at diffusion within the oxide layer. So this we can usually write in terms of some diffusion coefficient F2 which is D times C0 minus Ci by D0. So D0 here is the thickness of the oxide layer and as I mentioned earlier, you can either start with an oxide layer at the surface or you look at the process at a specific time where you have a certain oxide layer that is grown. C0 and Ci are the concentrations at the two interfaces. D of course is the diffusion coefficient. C is a function of temperature and is usually written as D0 exponential minus Ea over kT which is the standard Arrhenius expression. So D0 is the constant, this is your diffusion constant and Ea is the activation energy. So the values of D0 and Ea will change depending upon the diffusing species. The last flux term is F3. F3 is related to the rate of oxide formation. So it is a rate at which silicon reacts with your diffusion species to form the oxide. And F3 is usually written as some rate constant Ks times the concentration at the interface. So Ks is the rate constant for the silicon dioxide reaction. So by equating F1 equal to F2 equal to F3, it is possible to get the expressions for both C0 which is the concentration at the surface and Ci and also how the thickness of the oxide layer changes as a function of temperature. There are usually two extreme cases when we look at oxide growth on the surface. So if you look at oxide growth on the silicon surface, there are usually two limiting cases. Now diffusion in the gas phase is usually fast so that that is usually not a rate limiting step but one kind of process is where your rate limiting step is the diffusion of the species within the oxide layer. This is called a diffusion controlled case or simply diffusion controlled growth. In here, the rate limiting step is the diffusion of the species through the oxide layer to the silicon interface. So the supply of the oxidizing species to the silicon SiO2 interface controls the overall rate of the process. So this is usually the case when we have a thick oxide layer at high temperatures where the rate of reaction is fast. The other extreme case is called reaction controlled. So in this case, the conversion of silicon to silicon dioxide that is the rate of the process is the limiting step. So Si to SiO2 is limiting. Usually this is the case when we have a thin oxide layer and may be not a sufficient temperature for the reaction to happen. So in this case, both are essentially extreme conditions and they can actually be obtained by solving the general equation by equating the three fluxes. So we can actually write a general equation that relates the thickness of the oxide layer to the time. So this is obtained by solving for F1 equal to F2 equal to F3. The assumption is there is a starting oxide layer of a certain thickness on the silicon before we start oxidation. So the final solution, I will just write the general equation, will not go through the steps, relates the thickness D0 to the time A, B and tau are some constants. So D0 here is the oxide thickness at time t, A is equal to 2D. So D is your diffusion coefficient, Ks is the rate of reaction and H is the mass transfer coefficient which is related through the mass transfer coefficient in the gas phase by Henry's law. B is also a constant, B is 2D, C star over N1. So D again is the diffusion coefficient, C star is the bulk concentration of the diffusing species in the oxide and N1 is the number of oxide molecules incorporated, number of molecules incorporated in the oxide layer. So this is again the diffusion species, so let me just write diffusing molecules. So this will be different whether you have oxygen as the diffusion species or water as the diffusion species. Tau is nothing but Di square plus A Di by B and Di is the oxide thickness at time t equal to 0. So this is the initial oxide thickness. So this is a general expression that relates the thickness of the oxide layers to the various parameters in these rate equations. So we saw there are two extreme cases, one is the diffusion control case, the other is the reaction control case. If we can take this expression and simplify it to obtain various relations or different relations for these two cases. In the case of diffusion control, so here the diffusion of the oxide species through the oxide layer is what that matters. So this is usually for a thick oxide, in this particular case T is much larger than tau and T is much larger than A square over 4B. If we use those assumptions in the general equation, so let me write the general equation down. If we use those assumptions in the general equation, this essentially simplifies to D naught square equal to BT. This is called a parabolic rate law because if you look at this, this equation resembles the equation of a parabola. To see how we get this from the general equation, we can rearrange the general equation to write this as D naught A over 2 is equal to 1 T plus tau A square over 4B whole power half minus 1. So this is just a rearrangement of this equation. So if T is much larger than A square over 4B and T is much larger than tau, this equation will essentially simplify, can ignore this one and the other one and you are left with this D square equal to BT for a parabolic rate law. On the other hand, when you have a reaction control case, so here the diffusion is fast but the reaction with the silicon is slow. So in this particular case, T plus tau is much smaller than A square over 4B, so the final expression is D naught equal to B over A T plus tau which is a linear rate law. So based upon these equations, conclusion is as you have a thicker oxide layer, it takes more time to grow. So let us put some numbers in. So consider the case of dry ox. So in dry ox, the oxygen is a species that is diffusing. So at a typical temperature of 1,100 degrees centigrade, the constant B is 0.0117 micrometer square per hour. So these values are usually tabulated for different concentrations and different pressures and so on. So to grow an oxide layer D naught of 100 nanometers thickness, the time that is required just by using the parabolic rate law equation is D naught square over B which is approximately 51 minutes. Now instead of 100 nanometers, if I want to grow 200 nanometers, so D naught is 200. The time is not just doubled, so it is not just 2 times 51 but because of this parabolic rate law, the time if you calculate will be actually 3 hours and 25 minutes or it is more than 3 times. On the other hand, instead of dry ox, if you had wet oxidation, B naught is higher. So if you have wet ox, B is higher, B is usually 0.287. So that the time to grow 100 nanometers is just 2 minutes. So comparing these two numbers, 51 minutes for dry ox and just 2 minutes for wet ox shows you that wet oxidation is usually much faster than dry oxidation because the diffusing species and the reactions that are involved are different. The trade off of course is that if you are looking for a very uniform process control, 2 minutes is usually too less a time to get good process control. So here you might either go for a lower temperature in order to increase the time or you might go for a dry oxidation in case of wet oxidation. So there are always trade offs involved in choosing the appropriate temperature, the appropriate diffusing species depending upon the oxide thickness that is required. So the oxidation also depends upon the orientation of the silicon wafer. So this is because for example, if you look at silicon 111, usually the planar density is higher because there is more packing, so there is actually a faster growth rate. Just to compare at 900 degree C for wet oxidation, the value of B which is related to your diffusion coefficient is 0.151 micrometers per hour for the 111 plane, for the 100 plane it is lower, 0.143. So again with increase in temperature, this difference becomes smaller but at lower temperature there is always a significant difference in the growth depending upon the plane that is exposed to the surface. The presence of the oxide layer will also have an effect on the concentration of dopants. If you have n type dopants as the oxide layer is being formed, these n type dopants have a lower solubility in the oxide and they get rejected. So if you have an n type silicon, the oxide layer will lead to a pile up of the dopants in the silicon. This is usually near the silicon-silicon dioxide interface. Remember the oxide layer is consuming the silicon as it grows, so that any dopants there are, if they are n type they basically get rejected. On the other hand, if you have p type silicon, the oxide as layer as it grows will tend to consume the dopants, so that there is a depletion. This is significant because we know that the dopants affect the electrical properties of silicon. So by growing an oxide layer, you can actually change the concentration of the dopants and affect the local electrical properties of the silicon. Usually oxide layers that are grown especially for patterning are thick. So there are a few 100 nanometers in thickness. Thin oxide layers are grown these days especially when we have device scaling. So we have smaller and smaller dimensions. So these thin oxides can also be grown at low temperatures. So thin oxides usually they have a thickness, so let me just say thickness less than 30 nanometers or 300 angstroms. So one example is the case of an oxide layer that is used for the gate oxide. Usually a high gate dielectric is used for the gate, but during the patterning process an initial oxide layer is grown which is then replaced by the high gate dielectric. This is a thin oxide layer usually has a thickness of a few tens of nanometers. Thin oxides can be grown by chemical reactions at temperatures close to room temperature. For example an ultra-thin oxide layer, so the thickness is less than 20 nanometers can be grown by silicon reacting with nitric acid at temperatures of around 100 degrees. So this is much lower than the conventional thermal oxide layers where the temperature is usually around 1000 degrees, so 10 orders of magnitude higher. The advantage of growing thin oxides in these low temperatures is that these can be used with the regular patterning process so that we can grow oxide layers at really small areas. So thermal oxides are usually grown in a furnace. It is a batch process so that multiple wafers are grown at the same time. So you can usually have either a horizontal furnace which is used for small wafers, typically 3 or 4 inch wafers, you can have a horizontal furnace or a vertical furnace. So horizontal furnaces are usually for 3 inch or 4 inch wafers, they are usually present in say research labs where work is done on the small wafers. Typical furnaces are usually used for large wafers, so almost always in all production kind of fabs you will find vertical diffusion furnaces. If you look at a typical profile of a furnace you would have some, you can divide it into 3 zones, there is a source zone, so the source zone is where you have your gas source, there is a center zone where usually the wafers are loaded and then there is a load zone, the load zone is the one that is facing outermost. If you look at the temperature profile across the furnace, there is usually a fat profile in the center zone, so this is temperature, so the wafers that need to be processed are usually loaded in the center zone. In the case of furnace growth for thermal oxide, there is usually a boat, the boat contains the wafers, for example in the case of a vertical diffusion furnace, your boat could be having something like say 100 to 125 wafers, the wafers that need to be processed, so these are called the product wafers are loaded in the center. So the product wafers are in the center and then a bunch of blank wafers are usually loaded at the ends, so these are loaded in order to ensure temperature uniformity and also usually gas uniformity. So these are called blank wafers, they are also called baffles, sometimes baffles are made of other materials are well and these are usually loaded at the edges. So the boat is loaded and then fed into the furnace and then there is a whole programming cycle that goes about, so the initial temperature is at room temperature, so these are heated to the process temperature exposed to the gases and after the oxidation process is done they are cooled and the boat is taken out and the wafers are unloaded. We have only looked at the oxidation process so far, another example of a grown layer is the nitradation layer or the nitride layer that forms on silicon. So the processes for forming the nitride layer is similar, so we can also think of it as a grown layer where you have a nitride layer at the surface, so we can think of similar models for diffusion and growth. We also have oxynitride layers where we have a layer with both oxygen and nitrogen in them.