 So, we are looking in detail at the various processes that are involved in your IC fabrication. So, last class we looked at an example of a layering operation where we looked at grown layers specifically oxide layers. We saw that your oxide layer can be grown on top of the silicon by consuming the silicon that is lying underneath. So, that is why it is a grown layer. We also saw different models of oxide growth. We saw that if you have a thick oxide layer, the diffusion of oxygen or the diffusing species through that oxide layer is the one that determines the growth rate. So, this we call the parabolic growth. In the case of thin films, the reaction of the diffusing species with the silicon in order to form the oxide determines the growth and this gives you the linear growth rate. So, what is true for oxidation is also true for nitridation. In case you want to form a nitride layer, a similar model can be also used for forming oxynitride layers. Today, we are going to look at one of the other processes in IC fabrication. So, today we are going to look at doping. So, doping is important because we saw that in the case of an extrinsic semiconductor where we add a specific amount of impurities or dopants to your silicon. You can precisely control the electronic properties. Similarly, in the case of devices, we always want to form junctions and these junctions are between differently doped materials. For example, the simplest thing is your PN junction that is formed between a P type and an N type material. Of course, the materials can be the same. In this case, it will be a homo junction or the materials can be different in which case you have a hetero junction. We will be mostly focusing on homo junctions when we talk about doping. So, if you think about a simple PN junction, you can start with a P type material and then you can dope a specific area to be N type. So, in that case, you have a PN junction. We also looked at junctions in terms of your transistors. So, your simple N PN transistor, once again you have a P type. You have two regions that are doped N type, there is an oxide layer and then there is the gate. So, this is your structure of your MOSFET where once again we have to dope specific regions N type. We have also seen your bipolar junction transistor in which case specific regions with depth have different dopants. So, you could have an N, P and N so that here you have an emitter, base and collector all with different dopants. In these regions again, you could have different dopant concentrations. Overall, the important point to note is that doping is an important step in your IC manufacturing because it is used to establish the different junctions that ultimately form your device. There are essentially two ways doping is carried out. We saw this briefly when we are looking at the overview of the IC fabrication process. The two ways doping is done is thermal diffusion and ion implantation. In the case of thermal diffusion, just to give you an example, we look at it in detail later. We have your wafer, usually there is some sort of mask. The mask is used if you want to dope certain portions of your sample. In the case of thermal diffusion, it is usually a high temperature process. So the mask you use is typically an oxide layer or it could even be a nitride layer. So dopants are introduced. In this particular case, your dopant could be a gas so that there is some concentrations of dopants at the surface. Now, because it is a high temperature process, you have diffusion of these dopants within the material in order to create some concentration gradient. The maximum concentration is near the surface, but there is also some diffusion of these dopants within the depth and this depends upon the time, the concentration of the surface, the type of dopant and so on. So, we will look at that in detail. This is thermal diffusion. The other way of diffusion is ion implantation. Once again, you have your surface and you have a mask. Ion implantation can be done at low temperature. In fact, it can even be done at room temperature so that you can use a mask like a conventional lithography mask. We will see that when we come to lithography, what a lithography mask is. But you could use a lithography mask and you can also dope in smaller areas. So here you have dopants in the form of ions. So you have dopants in the form of ions impinging on to your sample and these ions penetrate into the silicon wafer and lead to a certain concentration. So the concentration is maximum at a certain depth within the silicon wafer and this depth is determined by the energy or the velocity of the ions. But once again, you can get some distribution or some concentrations of dopants within the material. So let me just mark the dopants that are embedded within your wafer in both cases. So these are the two common ways by which doping is carried out. So let us look at some of the goals that we need to achieve by using doping. So we can define some process goals for doping. So the first goal is you should be able to create a specific concentration of your dopant atoms at the surface and also below the wafer surface. So we need a specific concentration of dopants at and below the surface. This idea is related to the concentration gradient of the dopants within the material. The concentration gradients are again different. If you think about thermal diffusion versus ion implantation, the gradients are different. If you have different sources for dopants in the case of thermal diffusion or if you have some sort of post diffusion annealing, so all of those processes will affect the concentration gradient. So we should be really clear on to what kind of thermal budget the wafers will see after the doping process is carried out. For example, after doping the wafers are subjected to some high temperature process later then that high temperature process can again affect the concentration of the dopants which can affect the properties. Another process goal is to create junctions. So these junctions can be PN junctions in which case you have a P type doping into an N type or an NP junction which is the other way round. So these junctions are to be created at specific depths within the wafer. This will again affect the properties of the wafer. To give you an example in the case of a bipolar junction transistor, we have to dope the material twice. For example, if you have an NPN transistor, we start off with an N type, we dope with a P type in order to form the base and then dope again with N type in order to form the emitter. So you have two PN junctions there and these PN junctions have to be created at specific depths within the wafer. And then finally, we should also be able to create a distribution of dopants across the wafer surface. So we want a specific distribution of dopants at the wafer surface. This is related to patterning because in the case of a blank wafer, we are going to use to form an IC device, we will have transistors at different locations, we could have simple diodes in which case we need to form these junctions or we need to dope in specific locations on the wafer surface. This is achieved by patterning and as device dimensions shrink so that you have more and more transistors that are packed in a smaller area. So that the individual size of the transistors are lowered, we need to be able to pattern smaller and smaller regions in order to able to dope. So the three process goals are to establish a concentration gradient within your material to form junctions at specific depths and also to combine your doping process with patterning so that you can dope in really specific regions. So first we look at the thermal diffusion process. So we are going to look at thermal diffusion. Thermal diffusion can be thought of as a two-step process. In the first case, we need to introduce your dopant atoms to the surface of the wafer. So this process we call deposition where we introduce dopants to the wafer surface. We will see in a minute that there are different ways in which you can have your dopants. So these could be solid, liquid or gas but whatever be your source, some dopant atoms have to be introduced to the surface so that they can diffuse. And that is the second step which is called drive-in. So here the dopants diffuse to specific depths or I will say a better word would be to the desired depth. So if you think about a wafer and a surface with dopant atoms on the surface, diffusion not only occurs laterally into the material but diffusion is usually anisotropic or sorry diffusion is usually isotropic which means you not only have lateral diffusion into the material but you also have sideways diffusion as well. So diffusion is not only vertical but also lateral. So this is one of the greatest issues when we look at thermal diffusion. So how to avoid the lateral spread? This is one of the advantages of using the ion implantation process where the ions are implanted at low temperature so that the lateral spread can be minimized. So we can have different sources for diffusion. Your sources could be a solid source, liquid or gas. So to give an example, consider the case of silicon. We know that you can have both p-type and n-type dopants. One is a group 4 element. So your p-type dopant would be something from group 3 that has one less electron. So boron is your p-type dopant. On the other hand your n-type dopants will be elements from group 5 because group 5 elements have an extra electron. So these could be arsenic, antimony and phosphorus. These are all n-type dopants. For these elements we can have different types of sources. For example if you have antimony you can have a solid source SB203 which is a solid. For arsenic you can have a solid source AS203 or you can have RC in gas ASH3 which is a gaseous source. You can have a liquid source POCl3 which is a liquid. You can have a solid source P205 or pH3 which is a gas. For boron once again you can have BBR3 which is a liquid source B203 which is a solid source and BCL3 which is a gaseous source. So you can have your source of dopants to be either solid, liquid or gas. In all these cases they should establish a certain concentration of the atoms at the surface. So thermal diffusion is a high temperature process. Normal temperatures can be anywhere between 900 to 1200 C so that the diffusion usually takes place in a furnace. So the wafers are loaded within the furnace and the dopant atoms are delivered to the surface of the wafers. For example in the case of a gas source so this is my furnace. So usually some sort of inert gas is used. Usually argon gas is used as a source of inert gas in order to dilute your dopants to the desired concentration and then there is another bottle. So if you look at a simple gas based dopant working with a furnace you have inert gas that usually acts as a carrier. You have the dopant gas so in the case of arsenic this could be ASH3, in the case of boron this could be BCL3. So these are mixed in order to get the desired concentration of dopants and introduced into the furnace. The wafers are usually loaded onto the furnace and then preheated to the desired temperatures. The gases are introduced for the desired time in order to establish the concentration gradient that is required and then they are shut off. So this is in the case of a gas based system. You can have a similar setup in the case of a liquid based system. So once again you have a furnace so you can have the inert gas. The dopant is in the form of a liquid and then some carrier gas is bubbled into the dopant. So if in the dopant in the form of a liquid has some vapor pressure on top of it a carrier gas is used in order to draw the vapor along with the inert gas. And these are again introduced into the furnace. So the setup for both the gas faced and the liquid based is similar. The furnace setup is similar it is just that how the dopant is introduced is different. In the case of both the gas based and the liquid based dopants the concentration of dopants at the surface is essentially a constant which will in turn affect the concentration profile within the wafer. In the case of a solid state dopant for example in the form of oxides usually the oxide material is prepared in the form of a slug. So for solid dopants you have wafer size slugs. So your material is made in the form of a slug and introduced along with the wafer into the furnace. So that these slugs are placed in close proximity with the wafers so that at high temperature material diffuses from the dopant into the wafer they are packed in the furnace. The other way of introducing a solid dopant is to actually a spin a layer of the dopant on to the wafer so you can also spin. So the dopant is usually dissolved in a specific solvent and this solvent is just spun on to the wafer. The similar wave photo resist is spun on a wafer during lithography. Again this wafer is then taken into the furnace and heated at high temperature so that diffusion of the dopant materials take place. In the case of a solid dopant the initial concentration of the dopant is a constant but there is no external source in the case of a liquid or a gas based. As the material diffuses within the wafer the surface concentration will essentially drop. This again will affect how the concentration gradient within the wafer looks like at the end. So we can have different concentration profiles for the wafers. So to understand how the concentration profile of the wafers look we need to look at the mechanism of diffusion. So diffusion in the case can easily take place either by a vacancy diffusion mechanism or an interstitial diffusion this in turn depends upon the size of your dopant atoms. So boron and phosphorus are essentially small atoms so they can diffuse by interstitial mechanism are small so they can diffuse by interstitial or by vacancy. So this is some sort of a dual mechanism on the other hand arsenic and antimony are big the atomic size is comparable to that of silicon. So the diffusion takes place predominantly by vacancy diffusion. If you look at diffusion then the first thing that comes to mind is of course fixed law. Fixed law can be used in order to understand how the concentration at a particular depth changes as a function of time. So there are two fixed laws one is your fixed first law which says that the flux is proportional to the concentration gradient. So dou c over dou x your fixed second law relates how the concentration changes as a function of time to the rate of change of flux with distance. If d is assumed to be a constant so we have the two fixed laws so the first law and the second law and these can be used to get c as a function of both x and t. So we saw that doping can be done either by a solid source liquid or a gas source. In the case of a liquid and a gas source we found that the concentration of dopants at the surface is a constant. So if your diffusion length is much smaller than the thickness of the wafer and a typical wafer thickness is around 500 to 700 micrometers so slightly less than a millimeter and typical diffusion distances are of the order of a few micrometers. So for a liquid or a gas based source we can consider diffusion from a constant surface concentration. So this is a very standard problem in the case of metallurgy this is something we use when you look at say carburizing or nitriding of a steel sample. So here your solution is given in the form of an error function so that c of x, t is c s error function x divided by square root of dt. This is your error function solution c s is the surface concentration which is a constant. So this could be from a liquid source or a gas source. On the other hand in the case of a solid source either we have a wafer slug or the material is spun on to the wafer. In this case the concentration is not a constant you have a starting initial concentration and as the material diffuses within your wafer the concentration drops. So here if you have a constant total dopant the solution is an exponential solution q t over square root of pi dt exponential minus x square over 4 dt. q t is the total dopant concentration per unit area. So the assumption in both of these is that d is a constant and it is not a function of concentration. This is not completely true for example there could be some cases where the diffusion coefficient will also change with concentration or in other words it will change with depth so that the equations are modified. But here we are assuming that d is a constant and all of these processes are at constant temperature. So that d can be written as a simple d naught exponential minus e a over k t. So d naught is the pre activation factor and e a is the activation energy. So in the case of thermal diffusion we can write d as d naught exponential minus e a over k t. So these values can be tabulated for the different dopant materials. Unit of d naught the same as d so centimeter square per second or meter square per second e a is electron volts. So you have boron phosphorus arsenic antimony 0.76 3.46 is e a 3.85 3.66 24 4.1 214 3.65. So these are some typical values for e a and d naught for the different dopant atoms in the case of silicon. So let us look at an example in the case of doping with silicon. So consider an n type silicon wafer. So you have arsenic concentration of 10 to the 16 per centimeter cube. So we now want to form a P n junction in this by adding boron. Boron is P type and we are going to use a solid source something like say B 2 O 3. We are going to do this at a constant temperature. So temperature is equal to 1000 k. So the first thing we need to do is to calculate the diffusion coefficient of boron. So we have the values for d naught and e a. So for boron it is 0.76 e a is 3.46. So the diffusion coefficient d can be calculated using this expression. The value for d is 2.875 times 10 to the minus 18 centimeter square per second. So again here we have a solid source so that we have a constant concentration of dopants on the surface or we have a constant initial concentration of dopants. So the expression is c of x is nothing but qt square root of pi dt exponential minus x square over 4 dt. So this term 4 dt or square root of 4 dt is usually called a diffusion length. It is an estimate of how far the dopant atoms have moved within a given time t. Higher the temperature, higher the diffusion coefficient d because temperature is higher correspondingly the diffusion length will also be higher. So in this particular case let me take a constant value for qt. So we are looking at solid state diffusion of boron into an n type silicon. We found that the concentration gradient c of x, t pi dt exponential minus x square over 4 dt. So let me take the value of qt to be 1 times 10 to the 13 atoms per centimeter square. So this is the total dopant concentration which is a constant when you start the experiment. So if you want to know how the surface concentration changes x is equal to 0. So this is just qt over square root of pi dt. This is 0. So this term is 1. You substitute the numbers 3.31 times 10 to the 21 square root of t per centimeter cube. So as the material constantly diffuses within the silicon the surface concentration drops and it goes as the square root of the time. So we want to know at what depth the P n junction is formed. In this particular example where you already have arsenic with concentration of 10 to the 16th. So Nd is 10 to the 16th. So I want to know at what depth my P n junction is formed. So to simplify matters I will assume that Nd is a constant throughout the material and does not change during my doping. Let me also take time to be pretty long. So I will take 2 hours which in seconds is just 7200 seconds. So t is something that we know we want to calculate x all the other terms in the expression is known d we have already calculated to be 2.875 times 10 to the minus 18. So we want to calculate the depth at which the concentration of my P dopants which is boron is equal to Nd which is 10 to the 16th per centimeter cube. Substituting the numbers and simplifying we can get time or we can get the distance x time is 2 hours to be around 8.3 nanometers. So at around 1000 Kelvin which is roughly around 700 degree C we find that your P n junction is established at a depth of just 8 nanometers below the surface. In order to increase the depth the simplest way is to increase the temperature you can also increase the concentration of dopants at the surface. If you do the same calculation with temperature equal to 1200 K so that the increase is by 200 degree centigrade x is now 180 nanometers. So same calculation for the temperature is at 1200 K. So far we have looked at thermal diffusion where you have a concentration gradient that is established by a diffusion of dopants within the material. We will next look briefly at the ion implantation process. So one of the drawbacks of thermal diffusion is that you not only have diffusion vertically within the material but you also have lateral diffusion so that you always have a spread of the dopants within the material. So this can be avoided by using ion implantation which is a low temperature process. So let me draw a schematic of the ion implantation process typically there is an ion source. The ion source is the source of the dopants. Ions are produced by bombarding the dopants with electrons so these in turn create ions. These ions are accelerated to a magnet it is called a 90 degree magnet. This is used in order to select ions of the specific mass which relates again to ions of a specific charge. So these ions are extracted they are typically accelerated through a specific voltage and then they pass through a whole bunch of beam traps and gates. These ions are then finally deflected and then fall on the wafer. So the dopant atoms are ionized. So typically dopant sources are gas based sources so they could be gases like Arsene or Ph3 or Bf3. Sometimes the element can also be used so elemental boron or elemental phosphorous is used. So these dopants form the ion source. They are produced by bombardment with electrons in order to form the ions. These ions are selected using the magnet. The magnet is also called a mass analyzer because it separates the material based upon the mass. They are then accelerated and then using specific lenses are focused on to the wafer. So the advantages of ion implantation are that the wafer is at room temperature or it is very close to room temperature which means that we do not have to worry about lateral diffusion from the mask which is an issue when we look at thermal diffusion. Also because the wafer is at room temperature you can use conventional lithography to pattern the surface. So in the case of thermal diffusion because of the high temperature of the process typically an oxide or a nitride layer has to be used for patterning but in the case of ion implantation conventional lithography can be used. Ion implantation also produces wafers with a concentration gradient. If you look at dopant concentration versus depth here the wafers here the dopants impinge on the wafers with some velocity and are implanted into the material. So that there is a higher concentration at some depth and this is called the range. In the case of thermal diffusion the maximum concentration is usually at the surface and then it drops as you go within the material. Here the maximum concentration is somewhere within the material. The range depends upon the energy of the impinging ions. So that by increasing the energy the ions can be implanted at a greater depth. The concentration depends upon the current or the beam current of the ions. So that by having more ions you can increase the concentration. It is also possible to combine ion implantation with some sort of a rastering or a scanning procedure so that the ion beam can essentially scan the wafer surface. Usually ion implantation leads to some sort of a thermal damage to the crystal. This is because you are impinging the crystal surface with high energy ions. So it leads to damage of the wafer surface. The ion implantation is always followed by some post annealing. This can again be done in a furnace with typical temperature of around 600 degrees or you could do some sort of rapid thermal annealing where you can go to a higher temperature but the annealing time is very short. So today we have looked at doping which is one of the steps in your IC fabrication. We saw that there were two techniques thermal diffusion and ion implantation. Thermal diffusion is usually used at the beginning of the process in order to define large doped areas. As the process gets refined and we need to dope in smaller regions we typically go for ion implantation. In the next class we will look at another IC fabrication technique which is lithography.