 Okay we start with the new topic today, thermal oxidation of silicon, SiO2 is the most important material in VLSI technology and since it is very very important we like to study it little more carefully if not in that detail. So look into the structure of SiO2 and their properties and its properties. We look into kinetics of thermal growth of silicon. This is necessary for modeling of the oxidation process. We will also look into SiO2 interface. This is very important for the electrical properties of a mass transistor or a mass capacitor or a fin fate or whatever it is and therefore we will look into it, not so much detail from the fixed point of view but at least characterization and we will see what parameters we are looking into to interface circuit models. Then we will look into how some of those properties are characterized and we will finally look into how oxides are actually grown. So this is the some kind of content of this lectures or this area. I repeat this is nothing to remember this just to say. If you look at the history of mass circuits the technology of mass is used in creation of silicon ICs or most of its credit to SiO2 system. In fact when we started calling silicon ICs we should have really called silicon dioxide ICs. If there would not have been silicon dioxide pure silicon ICs would not have existed except for bipolar but certainly not mass or even bipolar making would have been impossible. So of course that is why it says SiO2 is the most important material in VLSI. We need to grow different kinds of oxides and different thicknesses for variety of steps in the interior circuit path. First is field oxide which is typically can be as low as maybe even these days maybe 2000 Armstrong's as well but typically 4000 to 1.4 micron is the field oxide. And we need to create a mass many time even for implant or even for impurities not to go through we need oxides of the kind of 600 Armstrong to 4000 Armstrong's and then we need gate oxidation if you are making mass transistors and with no high case right now then for a gate dielectric we will require a good gate oxide and typically it may be 10 Armstrong to 1000 Armstrong depending on the node of technology. For example 1000 Armstrong was useful for 1 micron technology or maybe even more whereas 1 nanometer and equivalent of that or less than that is recently going for 45 nanometer down. Then we also need to have a pad oxide and we will see what is one of the spacer technology in the case of minfin fat has some kind of padding then we also see a chemical oxide which is naturally grown all by during RCA clinic and that also is this may be very thin maybe of the order of 10 Armstrong to 50 Armstrong's but these are all kinds of oxides are grown and required in the case of making an IC these oxide thicknesses of course varies and therefore many of the process steps may vary for different oxide for example if you are doing a field oxide of very thick thickness 1 micron or so the gate oxidation is very small very thin so the same technique cannot be used for field oxide because the time taken then will be very huge okay. So we will change the technology as and when it needed and we will see how SRO2 is grown in variety of methods and here are few of the methods if you are noted down okay the word field essentially means all around okay you will see what exactly that around. Technologies which are used for creation of SRO2 are generally two kinds there is one more which I have got maybe I will add which is what current we are doing this process was actually we worked in 1984-86 and was given out now suddenly with thin oxide requirement this process has come after 25 years back in a big way okay. So when we grew in 1986-85 if we were saying that who is going to use this oxide but now it is found that that is very important process okay. So thermal oxidation of two kinds will use dry oxidation and wet oxidation, wet stand for STO, deposition techniques we will have CVDs, PVDs, PVD includes buttering and also plasma oxidation is also partly physical vapor deposition rapid thermal oxidation and sol-gel process solution gel process which is mostly used by solar cell people. Thermal oxidation is most basic oxidation and is most important step in creation of gate oxide in a MOS transistor and therefore we will look into what is the growth techniques what is the property what are the properties of this gate oxide which is needed to have a good electrical circuit electrical parameters for MOS transistors. So I repeat there are mostly two techniques in which oxide can be grown one is thermal oxidation which actually silicon converts into silicon dioxide by thermal process whereas in the other case substrate is immaterial we can deposit on any substrate including silicon okay. So the deposition techniques has advantage that it can be deposited on any surface whereas thermally grown oxide has to be out of silicon because this that is what it is oxidizing. So the property obviously one can see that thermal oxides will have better properties compared to any deposited oxide okay. So as I said we will look into variety of oxidation procedures however we will model these two and I will not model here this CVD and PVD because there is a separate chapter of separate part of the course we will discuss about CVDs, PVDs of different materials and during that time we will actually model CVD process and a PVD process. PVD is essentially sputtering evaporation and that kind we will see in molecular beam taxi all these are PVDs. So we will look into models for them in general and not necessary for oxide it can be nitride it can be metals it can be anything. So deposition can be if any material on any material other material. So we will see there but we will certainly look into the models which are related to thermally grown oxides typically by two processes dry oxidation and wet oxidations. So I said okay this is what we are really looking for before we start let us look into basic properties of SiO2 why it became so popular actually. So let us look at this first thing we want to see a bond bonding situation the natural bond for SiO2 is SiOSI okay the natural bond for SiO2 is SiOSI and typically the figure which is shown here if this is your silicon atom it is surrounded by four oxygen atoms okay slightly shown better way same figure the distance bond length as it is called oxygen to oxygen bond has a length of 2.62 Armstrong's silicon to oxygen has a bond length of 1.62 Armstrong's and silicon to any other next silicon is a bond length around around 3 Armstrong's. If you see SiO bond the silicon lattice oxide lattice may look SiOSI, SiOSI, SiOSI, SiOSI and if you keep doing this OSI and so on and so forth. So this is how silicon dioxide lattice is created. So one can see from here which is most important thing we will see oxygen is not free it is bonded on both sides by silicon atoms okay and this is a very strong bond okay this is a very of course it is not stronger than silicon to silicon which is the strongest but at least it is still quite a strong bond. So if I want to take oxygen I will have to break this and I must apply energy to break this bond actually. We will see this is most important in actually growth models. If you have seen this links are just for the sake of it I mean just to give an idea what kind of lattice structures one has okay. If you have noted down then we will start ahead. While we are using SiO2 in a MOS technology please forget material in specific or otherwise because it is a excellent dielectric material and since it is a very good dielectric material it is used in the field effect transistors because it does not allow DC current to flow through it okay it is excellent dielectric material. It is available in two phases amorphous phase and crystalline phase. We are already I have told you the crystalline phase of SiO2 is quartz whereas the oxide which we use in all VLSR technology is always in amorphous phase as I just now said thermally grown oxides are amorphous in nature and typical atomic structure of SiO2 with some impurities or ions are shown below the lattice is random this is say for example SiOO this but this oxygen around is also connected to another say silicon atom then it is called bridging bond whereas this silicon atom and if I create another oxygen on this this is free to it and it is called non bridging it does not have another silicon on the other side then it is called non bridging. So to break a non bridging bond is easier compared to a bridge bond because bridge bond means two silicon will hold it and if one oxygen is free other side that oxygen probably can be taken away okay. There can be possibility of some kind of impurities inside the lattice which is at interstitial sites these are called network modifier and network formers and we will look into it. There is also a possibility between silicon atoms or oxygen atom there may be a formation of OH ions or OH bonding and this is very important in many cases at least for weight oxides. This silicon is going to oxygen and there is no silicon ahead so the oxygen is dangling right now the other bond. So it is free to cut out very fast it is not bonded other side okay so non bridged like this OH has nothing here OH is also non bridged okay anything connected other side it bridged. So based on this lattice there are some observations we can make and of course as I said these are not the way book writes a bit but I think I will give simple observations out of all this structure. If you have drawn this this is given in a book Plummer's book and any other book okay. There is a book by Kalk laser micro electronics technology or something old book but has new addition has come I am told Kalk laser I am not sure whether we have one but many of the old technology models and everything are well given in Kalk laser's book. From the some observations about the lattice from the lattice structure of SiO2 we observe that if silicon has to leave SiO2 lattice it must break force oxygen bonds SiO bonds responded on the force side so it must leave all 4 of them while if oxygen atom has to leave it needs only one bond if it is non bridging and 2 bonds if it is bridging okay. SiO2 with no impurities like diffusing impurities or sodium lead or borium is called intrinsic silica. If there are no impurities in oxide then it is called intrinsic silica or intrinsic SiO2 while if there are impurities then we call it as extrinsic silica. So these are few this there are few more if you note down I repeat the SiO when silicon leaves the SiO2 bond it needs it is very difficult because it needs 4 bonds to be broken okay whereas oxygen is only 2 or in non bridging it is only 1 so it just goes away okay. This property has been used during oxidation that this oxygen is available I can break it okay is it okay? Our ultimate aim today is to actually go through the model but let us see how fast we go okay so that I can ask tomorrow some question on models. I keep telling you our interest in the course is manifold one is to understand the material property so that at least 1 out of 100 are people here let us say giant technology and also thinks 20 years ahead what he can do to become an entrepreneur of his own technology pad house in India somewhere okay. The boron phosphorus or arsenic or such such impurities is in silicon and hence create bond between oxygen and them such impurities are called network formers because oxygen will also get bonded to them however if impurities sit in the interstitial site and then they modify the net see example these impurities can sit on a silicon. So you have instead of silicon you have impurity in 4 oxygen bonds similar I mean similar as SiO bond it would be impurity OSI bond whereas if the impurity sitting in interstitial site it still will form a bond with oxygen and they will modify the structure of network such materials which do that is called is because of Na2O barium oxide then there is a lead oxide PBO Pb2O3 then comes to another phase of Pb which is PbO there is a tin oxide which I forgot these are called network formers or modifiers whereas the impurities when they replace silicon these are called network formers okay. Please remember these impurities are only present in some traces 1 part per billion or lower but it is not that they are 0 because due to the processing we pass gases we have heated materials around so some impurities will be always there how small we make them is most important. If we have a SiO2 is put into water it is very interesting thing that this SiO Si bond reacts with HOH which is water to form SiOH SiOH bond okay this is very important silicon hydroxyl bonds this is silicon hydroxyl two such molecules actually gets bonded and this is the most important thing why great oxides can be grown okay. One more interesting feature of SiO2 is that it is a strong hydrophilic water attracts to the surface of SiO2 and bonds and actually create this hydroxyl bonds okay. So one test that we have a silicon surface or oxide surface is just dip it into water if water sticks that means there is SiO2 layer if water does not stick it is a silicon layer okay. So these are some properties of this and we also know when Na2O kind of structure gets into silicon dioxide lattice we call soda glass okay these are very bad kind of glasses very impure large amount of potassium sodium first group elements actually forms oxides there and they are not very good as far as the properties of mass structures are concerned. So we must avoid sodium potassium, barium in the lab as much as possible probably 0 but nothing is 0 so something lower than 0. So these material this what I said the other one we of course said that if there is an impurity oxides along with the silicon dioxide these are called silicate glasses if you have boron then it is called borosilicate glass if it is phosphorus it is called phosphosilicate glass if it is arsenic then it is arsenic silicate glass. So these glasses are good sometimes they are used as the impurity sources because they have the impurity in them but the mixture is called glasses okay silicate glasses Pyrex is essentially borosilicate glass borosil is the company in India which manufacture Pyrex okay there are certain properties of SiO2 which are very relevant for at least some electrical properties are relevant for us even these days optical properties because silicon has been used in opto devices not necessarily for electrical behavior for optical gratings many of the communication people are now looking for optical communication and gratings are one of the most important element in optical communication. So you need to know gratings index so how do I change the index okay. So okay the typical resistivity of SiO2 is very high 10 to power 16 ohm centimeter our conductivity should be less than 10 to power minus 16 mahos per centimeter the band gap of SiO2 actually this is slightly misnomer why I say misnomer the band gaps are only available for crystalline materials because there is a periodicity there is no periodicity in amorphous materials so there is this is only a matter of conjecture that there is a band gap in a small crystallite and that band gap is typical if the order of 9 electron volts okay. What essentially what is the silicon band gap 1.1 electron volt so it is much easier even at room temperature to create whole electron pairs because the band gap energy is very small germanium it is 0.6 so even more easy so the intrinsic carrier concentration of germanium is higher than silicon because its band gap is lower if the band gap of 9 electron volts so at room temperature it would be almost impossible for whole electron pair to form and therefore no conduction therefore large resistivity okay. A typical refractive index for SiO2 is 1.45 density is 2.22 the number of you should write grams per cc normally this definition has slightly I did not write specifically because there is something in the case of molecular density there is a vibrato number appears so think of it why I did not write the full density units the number of atoms per cc is 2.3 into power 22 per cc. Directly constant of silicon dioxide is 3.9 this is much of the major parameter in decision of the mass transition performance epsilon and we know we are trying to go for higher epsilon oxides high k materials because of some reasons we will see that later. Another problem which most of the oxides particularly gate oxide you are applying a VGS across the gate and thickness is very thin because you are scaling down so the and voltage is not scaling down so voltage divided by the thickness of oxide is the field across the oxide which is increasing as the technology node is reducing now this field which you are getting should be less than 10 to the power 7 because at 10 to the power 7 all bonds can be broken and we say dielectric ionization will start so any anything voltage you can apply is as much as that the field is at least a order of half of 10 to the power 4, 5, 10 to the power 6 or 4 into 10 to the power 6 should be the best of old per centimeter should be the applied fields. So safety then you do not actually most of the oxide even do not reach 10 to the power 7 most oxide in our lab you may get strength of 4 into power 6, 5 into power 6 so safe oxide fields are only 10 to the power 6 volt per centimeter. So your thickness if you decide then your voltage is essentially decide that it should reduce the field below 10 to the power 6 okay. This is a compulsory requirement that is a otherwise in a circuit I may go we need your 5 volt for the 10 ohm strong circuit also how was the bad thing in that I will push it but by then oxide will puncture okay. So this is an important property which SiO2 has not most materials are this high strengths okay even a half name oxide is lower than this. So the major problem with many other high KEs their direct strength is as is not as good as SiO2 and therefore SiO2 is taking for last 50 years do what they do okay. Of course now we have to change for some reasons we will see later SiO2 has strong utility of IC processing why we want to use SiO2 firstly of course its electrical properties are great and everything is fine but it is much easier to create as well as to H you know a silicon dioxide HSN2 for example SiO2 plus let us say HF so I want 4 it can give me as 4SIF which is plus H2O SiF silicon fluoride is soluble in water so if I put my silicon dioxide doing wafer into HF then it will get removed all of the HF in the HF forming silicon fluorides and water inside the water so it is very easy to H and therefore of course Florian has his own advantage and this advantage is some other day okay. So please remember that SiO2 has is much easier to grow much easier to H much easier to control in every sense best dialectic strengths very good EGs very good insulator okay and refractive index is also very good for many optical circuits okay. So all in all glass is very good okay glass is very good and glass of something is even better okay. The other properties which you see in the case of most impurities in silicon have poor diffusion coefficient in SiO2 like silicon arsenic antimony phosphate all these impurities or boron everything has a very pure diffusivity in SiO2 compared to silicon so they act like a mask no impurity can easily pass through oxide compared to what it will go into silicon. Another important feature of SiO2 is extremely stable what do you mean by stable its structure does not change easily and it remains for all full processing SiO2 properties do not change okay. So essentially it is stable with temperature with everything it is very very stable material and therefore extremely useful in all IC because ICs have to last tens of years or at least these three to four years so why the life is not now ten years which earlier we used to say because companies will collapse if things work out for ten years what will they do then so they will finish three years it must go. Another advantage of silicon is silicon dioxide is the interface between Si and SiO2 is ideal if not it is very good if not ideal and it is extremely reproducible many number of times in any IC processing any number of times you go you can have control on this interface that is why it is very good when silicon is oxidized there is a volume expansion this is very important when silicon is oxidized there is a volume expansion total here is a shown here the dark one is silicon which you have and I started putting oxygen ambient and oxidizes so what it does is it consumes certain amount of silicon to convert into SiO2 but the volume of that is larger than the silicon volume which you consume this is essentially because of the law of mass action NS XS must be equal to NOX ES XOX and since the NS NOX has a ratio on silicon and SiO2 concentration is given this typical ratio of this number of atoms per CC is 5 and 2.3 ratio is actually appearing in the ratio of silicon to oxide ratio and so one can see 0.46 of silicon 4.46 of micron of silicon will grow how much oxide 1 micron of oxide is that clear to you 0.46 and strong so microns of silicon will consume to create one so oxide will grow above 0.46 will glow inside and 0.54 will go above and this is the figure which shows this 0.46 inside and so its volume expansion and essentially because of the density ratio or because of the concentration ratio essentially so that is important if someone says I have only this much surface of silicon so please remember when you oxidize it its volume will increase at least 50 percent above and 50 percent below and accordingly oxide will be available. So you can see from here there is an oxide layer see let us say I have to select you maybe and that is very important if you have noted down I will just show you a figure which is called local oxidation. So silicon thickness is roughly 0.46 or for simplicity you may say 50 50 50 percent as I will convert it to 100 percent as I have to what value of no no the ratio is 0.46 if it is one micron of this then it is 0.46 micron the ratio is 0.46. So if I want an oxide thickness of one micron you must be this that 0.46 micron silicon must be made available to grow that much silicon dioxide. That is what I say I will just show you a figure if this is my silicon surface and I restrictively do oxidation only here okay. So what will happen? I will get oxide something like this the rest places is surfaces here but the selective oxidation process part of the oxide is above and in fact there will be some something called taper down. So now you can see this is how the oxides are actually protecting the rest of area this much is their field oxide as we shall see this process this selective this is called local we will do this process later oxidation of silicon and it is called low-cost. So in actual IC making wherever you do not want impurities to go the field oxide is generally grown by process of low-cost only those areas oxidized but the silicon surface is retained wherever your actual device is going to come is that correct. So that is very important that oxide thickness is roughly double that of silicon thickness consumed okay okay. So this this roughly tells about the properties and some comments on SiO2 some observations. Now we start today our basic modeling issue we have discussed earlier that properties we look into so we looked into properties we now start looking into the models or how oxide is actually grown is it okay everyone. The process of growth is essentially thermally related in thermal oxidation and the process is essentially whenever it is related to thermodynamics we say it is kinetics there is some species moving and reacting reaction any reaction is has a kinetic model okay. So we look into kinetics a thermal oxidation of silicon as I say silicon dioxide is generally grown by oxidation of silicon at higher temperatures typical temperatures could be 800 degree to 1200 degree obviously one can think very simply that lower the temperature thickness will be smaller larger the temperature oxidation will continue at higher temperatures will have higher thickness oxidation rates okay and generally done in an oxygen ambient typically ambience used are either oxygen pure oxygen or pure water okay. Of course there is a mixture of water and oxygen which is called partial pressures of oxygen in H2O or a steam partial pressure in this ambient these are called polygenic systems we will discuss this later. So the wet oxide when I say tomorrow next time the wet oxidation is essentially not a steam oxidation is that part clear when the steam will come out when the water is heated at what temperature steam comes 100 degree wet oxides are not steam oxides so we do 95 degree heating so only water vapours come which are bubbling I mean you see the bubbler system and they are used in the this but there is no full steam so there is some oxygen content in the way steam part and that is why it is called wet oxidation it is not called steam oxidation okay. The typical reactions which are very simple Si plus O2 at high temperatures of 800 to 1200 converts into SiO2 and if the only oxygen is the ambient then it is called dry oxidation. This is the most common oxide thickness oxide growing procedure when you want thin oxides okay dry oxidations. SiO2 is also formed by oxidation, silicon and water vapours. Actually the process is quite complicated maybe I will show you quickly something. However overall one may say Si plus 2 H2O is SiO2 plus 2 H2O this is overall reaction this is called wet oxidation okay. Those who are little more interested in models of chemistry or chemical engineering or material science here is what can happen high temperatures 800 to 1200 is a high temperature room temperature is 27 degree okay. Oxides cannot be grown below 800 is not correct statement any temperature it will grow but the required thicknesses cannot be attained at lower than 800. But water vapor oxidation is performed on the silicon which is heated to 800 to 1200 we will see the technology. The water vapours are coming and reacting with the silicon vapours which are held at 800 to 1200 degree centigrade okay that is why it is high temperature. Water vapour is at 95. Here is something what chemistry can do an H2O can react with SiOSI bond and form SiOH, SiOH hydroxyl bonds. This hydroxyl bonds can react with silicon silicon bond and may form SiOSI SiOSI plus what is hydrogen. This hydrogen may react with unfinished unbridged bonds or non-bridged bonds OSI and may convert into OHSI and this OHSI is essentially going back SiOH and again it will react with silicon to form SiO2. So this is a ring mineral system and it keeps doing itself to get SiOSI bonds okay. So if you really see a chemistry at a given temperature some may dominate some may not so some thickness may not be correct. So those who are really looking for very thin oxide models these equations may be of relevance okay. Water attacks O2 bond and creates non-bridging bond this because the network first part SiOSI to interface OH group react with silicon to form SiO bond which is the structure for SiO2 and hydrogen also actually diffuses through SiO2 layer and react with bridging oxygen and it loses the network as it shows okay. The basic idea how much oxygen can go inside is there must be some structure in which oxygen can flow ahead. This is how a network can loosen and can allow oxygen to move in okay that is what the chemistry is about okay. Anyway if you forget it is fine but if you those who are very keen should know that there is lot of chemistry goes, lot of thermodynamics associated. For example say rest of the time I did not show error but in this case this is both side reaction and I must maintain certain temperatures to actually have a forward reaction on the reverse backward reactions. Particularly in CVD we will come back and look into forward and reverse reaction very seriously because what is reverse etching forward depositions. So if you are depositing it may etch, if you are etching it may deposit. So we will have to see when I deposit or deposit, when I etch it does not deposit okay. So that time we will come back and do lot of thermodynamics to see when the reaction is favored on one side or the other. Okay way back in 1965 two scientists from Intel actually first time suggested the kinetic model for oxidation, thermal oxidation and these names are very famous in mass technology. This is called Bruce Deel and Andy Grove. Deel is still around so is Andy. Deel is still working on SIO2 after 60 years okay. Great man 50 plus years. Andy of course was the chief of Intel few years ago and he is not well these days but still on the board of Intel. He is the founder member of Intel. Is that okay? In 1965 they suggested the model and till very late as may be around 95 to 2000 this Grove Deel model or Deel Grove model remained as the only model available when the oxide thickness started reducing further and further modifications to Grove Deel model started coming in but these are the words modification that means the basic tenets of Deel Grove model remain even now sufficiently valid though there are ways of saying that they are not correct in every case okay. What actually Deel Grove model is suggesting or what are the assumption it starts with? It actually what why we are looking into I want to grow SIO2 of thickness XOR XOX and I want to see how it is related to temperature and time. I have silicon wafers pushed into a furnace of higher temperature I pass oxygen ambient and I expect thickness of my choice by deciding the temperature and time okay. Now this model should do that it should be able to be if XO must be proportional to temperature and time if it shows that means I can decide how much oxide thickness I will get at a given temperature after how much time of oxidation okay or given a time of oxidation fixed if I change the temperature I can change the thickness okay. This is what my aim and therefore I like to see what the model is so that I will be able to derive that part or other than when I was showing you some graphs I have oxide thickness versus time at different temperatures 1111100 wafers okay. Those graphs have been derived out of this model okay. So for our quick calculations we can use those graphs directly time versus thickness at different temperature at different concentrations of wafers. One can immediately read out how much oxide thickness okay okay. So the model assumes there is a finite layer of thin oxide layer present at on the silicon at T is equal to 0 minus before that means before the oxidation start already there a very thin layer of oxide exist. Now this is an issue which is challenging at times so if someone actually H is the silicon pure and push it you mean to say oxide will not start oxidation it does but the model expects that there is a finite thickness of oxide at T is equal to 0 minus and 0 plus means oxidation starts just before there is a thin oxide a very very thin oxide. The next it says that the oxidant gas species impinges on this SiO2 layer and not silicon oxide so here is before I write this do not write I will just show you figure and then you may write. This is the physics physical model of picture of that. This is the gas ambient this is the gas ambient this is the thin oxide and this is silicon okay. So got gas on oxidant come here and actually impinges on this SiO2 layer surface okay. Now we are saying how much it will reach here then how much it will reach to the silicon interface to please remember oxide can be grown only when there is a reaction with silicon. So how much oxidant from the gas will actually reach to the interface to oxidize further silicon that is the model we are looking for. You start with huge amount of gases there is a silicon wafer thin oxide partly it does not allow all of it to go or how much it goes and reacts with silicon to form new SiO2 is that clear. If SiO2 is grown further the flux which is going through may be further reduced because now oxide thickness will be increasing. So we will see what is the model of growth of XO okay. This is the figure please note down this figure then I will come back to those ABCs again so that you know what I am talking about. If you have drawn the figure a few names I have suggested here this is Cg capital G this at the surface is C small capital S there is just below that there is a C star just below that there is a C0 at the silicon silicon dioxide where concentration is Ci which has a gradient and there are three fluxes associated one in the gas phase other in the oxide and third entering the silicon three fluxes. Flux means amount of oxidant per unit area per unit time okay flux okay. So there are three fluxes F1 is the oxidant flux in a gas phase F2 in the oxide phase F3 is what is reaching at the silicon okay. Now this figure is the model figure for Bruce Deel and Andy Groves model which is most important model in thermal oxidations. This the text part I will now explain once you have drawn the figure and maybe if you wish this fluxes I have written okay. The ABC I will repeat again. This figure I will redraw again but since if you have drawn now it will be you do not have to redraw it again okay. So is that model clear what we are saying there is a thin oxide present from the gas stream some oxidant arrive at the surface of SiO2 then it goes through oxide with some flux reaches silicon and oxidizes this is the model okay. Have you drawn the figure? So I will come back to this. So as I just now said initially there is a finite thickness yes initially there is a finite thickness. Oxidant gas species impinges on SiO2 layer okay and now the oxidant species then reacts with silicon as much as it goes through the oxide and creates near oxide layer. This is the model we have suggested not be Deel and Groves okay. This process continues as long as your oxidant is available and oxides keep growing assumption is temperature is held constant at a given temperature the gas flows are also constant but gas is flowing all the time and as long as that flows silicon dioxide will keep increasing in its thickness this is the model. Now we must see that therefore one thing we are clear that as the time increases oxide thickness will grow. So one requirement I said I want to know what is the oxide thickness at the end of my oxidation cycle. Further I have temperature this right now I get one temperature if I change the temperature I will see how much additionally oxide will be grow is that okay. So there are three fluxes which we have talked about three process so what are three requirement for oxidation is transport of oxidant from the furnace please remember the way we will discuss the technology later but maybe I will show you the furnace and this is the rack all the thing is in quads okay these are my wafers sitting on a rack this temperature could be adjusted to 800 degree to 1200 degree sometimes 1250 people have done nothing very serious and oxygen is entering. So this is the gas ambient okay at least between this so this is called the mid zone so mid zone temperature the gas is heated to this mid zone temperature but the gas is everywhere this is the concentration flux which is entering from here is everywhere okay then it actually reaches to the surface of silicon okay it impinges on silicon this flux which actually impinges on silicon surface or silicon dioxide surface because we assume there is oxide is essentially flux F1 okay the oxidant species then before we this word it has already impinged here then it gets inside SiO2 by the process of diffusion okay because there is no oxidant here there is an oxidant here there is a gradient creation so oxidant species diffuses in the SiO2 to reach silicon-silicon dioxide interface. So the second flux is diffuses through SiO2 with a flux F2 and the third before I come back again it reaches silicon surface or silicon-silicon interface and reacts with silicon to form near oxide. So oxidant reacts with silicon to with flux F3 however in there are two things we say in devices as well as in any process for that matter thermodynamic process there are two terms which we use thermal equilibrium and steady state what does that say in the case of thermal equilibrium as there is no external force applied okay the system is only by thermonunically adjusting its energy to the minima okay this is the entropy this relationship. So first law of thermodynamics says that it should remain valid for any temperature you fix okay it is a equilibrium with the ambient however what we are saying now is we are passing gases so there is a force going on so there is not a equilibrium thermal equilibrium situation however the gas is constant okay if the gas is constant some oxidant is getting in some is impinging some is reacting so system is time invariant that is called steady state so we are looking of a case when it is steady state okay yes. No it does not because there is no SiO SiO bond oxygen it will actually break it so it does not help us but SiO SiO bond does not break at 800 degree so as I say it is one of the strongest bond SiO SiO bond is even stronger SiO SiO break state at 1412 that is even higher temperature but 812 that is why 1200 I said I will say 1400 is that okay so it does not happen so that is why we say it impinges diffuses and reacts okay and even if I mean of course not true but even if I take your word this is not deal go model this is what deal is suggesting okay firstly it is not true but even if it is true you may say modify whatever your good name put say modified deal go model by so and so publish it. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .