 For the last, the last lecture the few, two transparencies or two faults were not shown. So first I will show them and then start the process of diffusion. As I said water is the major reagent for us in the VLSI lab and we need a very highly pure water and I already calculated the water resistivity is one of the quality marker which is around 18 mega ohms centimeter. Here is typical river osmosis system which is installed in every VLSI fab lab which creates this DIW which is called deionized water, deionized water DIW. What we do is we have a distiller in which water is first boiled and then the vapors are collected and then this water which is now after distillation the really, really pure water is available is then added some chlorine compounds and that is called chlorination and once it passes to chlorination much of the bacterias are actually killed here. Chlorine is a very strong oxidizing agent. Chlorination is a very strong process in which most of the bacterias are actually removed, at least they are killed if they are not removed. Once this slightly better bio water is available we pass it through a pre-filter which is a standard filter. It actually stops much of the high size particles maybe around 0.5 micron and above this is called pre-filter. Then there is a pump followed by a RO system. This is my RO system. Now please remember many of you might not have done a course anytime in chemistry or chemicals so seriously but we use that very often it is called reverse osmosis. Why this word reverse? Osmosis is a process which says if you have a what concentrated solution and if you have a dilute solution on the other side of the membrane then according to because of the osmotic pressures on the membrane the water from lighter side actually go towards concentrated side to dilute it actually. Water moves from lighter concentration or pure water will go to the salt which is already concentrated to dilute it out that is the process of osmosis. However what we really want the other way I want a water which is already concentrated and I want to get little lighter water or purer water so I pass through the membrane and since membrane will actually do the opposite process which is called osmosis we pump it from the other side and force reverse osmosis process. All homes these days have this RO system so it exactly is there you have to clean this membrane every three months and every one year you have to change as well. So what happens this so called good bio water clean remove many particles much of this pre-filter also have a carbon filter which is called charcoal, activated charcoals and they actually absorb some other kinds of bio impurities as well. Once this water which is concentrated here with the impurities passes through membrane you get a lighter water which is purer without impurities. This is why I say it is a reverse osmosis. Once you get a pure water out of this membrane then we actually pass through a resin a huge bunch of cylindrical tubes are there big ones through which water is pushed from below and comes from the top side and this whole container contains a resin and that resin has a property that it is cationic in nature which means it will remove sodium, potassium many of these first order compounds or elements will be actually removed as OH ions with OH ions. Once much of the NaOH or KoOH or soluble such are removed they actually are absorbed in the resins and the still pure water without those elements actually come out of cationic resin. This cationic resin water then is passed through anionic exchanger which is another resin and please remember the way it is always pushed is something like if this is your cylinder which contains resin the water is pushed from here and taken from here. So when this water enters it starts reacting with the resin and much of the hard impurities like metal impurities like copper, gold, strontium, calcium, magnesium all of them are removed in this process and the water which comes out of anionic exchange and they are retained in the resin itself and the pure water comes up and then it is passed through a mixed bed column. The mixed bed column is actually a mixture of cationic and anionic exchanges 50-50. There are two mixed bed columns kept one anionic first cationic second the second one is cationic first anion and you actually pass through both of them so that whatever traces of those other impurities would have left out of this exchange and this exchange can still be taken out in the sand or the resin and much pure water is available out of this. Please remember since we are removing ions other day I said we are looking for 18 mega ohms centimeter resistivity of a water which essentially means it is deprived of HOH ions itself and they form only H2O. There are no ions possible because ions means conductivity will actually increase and therefore resistivity will decrease. So we wish to see that pure water so the test of of course there is a electrolyte cell which I have not shown which we keep actually water can pass through it and show how or it is normally displayed these days how much resistivity water you are getting. Now further for anything bios things are still coming out or then we actually shine ultra violet light and it gives most of the bacterias. Some companies have another filter here called diarthatomic filter which actually removes biomaterials some companies do not have and after that filter we have a very fine filter 0.2 micron or lower 5 part filter which is a small membrane this what is it called polypropylene films run over which have grills grits on that and most of this all particles of larger than 0.2 or even lower are actually removed in this final filter and the water which you receive then is deionized water highly pure no contaminant because please remember why we are worried about because water is going to be used after every step what I do and therefore it should not add any ions of its choice because at that I am going to introduce very small amount of impurities of my choice. If the concentration is already changed by something else then I do not know what impurities I am adding because they will be actually sitting into many of substitution sites. So where is that water has to be highly pure. So this is a typical RO system earlier we did not have RO we have normal like aqua products also other companies have without RO systems in this there is a additional feature because purifies much more membranes are very very strong concentration gradient changer. So we use that however as I say membrane is a bio material and has to be always clean and therefore you need much more cleaner water to clean. So that is a difficulty in all this but anyway this is how the waters are actually cleaned up. In a lab there are many kinds of things which we have to work with there are tubes which carries gases sometimes water line and they are made of two materials either stainless steel or Teflon. Teflon is a very famous polymer which actually one always say nothing sticks so he is a Teflon person Teflon phase person nothing sticks or a McNaby balloon po chasar nahi that is the Teflon thing it is a normally there are both colored and non colored Teflons are used but the best Teflon are white colored which means no other impurities other than Teflon itself and therefore Teflon tubes are normally white and of Teflon everything which we actually use in the lab are either Teflon or at best sometime polypropylene ones or mostly the gases pass through stainless steel please remember stainless steel is also a different quality is 304, 306, 316 if you are really a hardcore engineer in a lab you will have to know which tube to buy 316 is very costly it is it does not have chromium inside but it has a chromium coating outside which is why it is becomes stainless and it does not affect much of the grease much of the other things and it is a highly pure steel it has much less carbon content because we are not looking for hardness so this 316 stainless steel tubes are used and of different sizes quarter inch, half inch, one inch, two inch depending on the flow you are looking for then we have equipments which are used along with in the process are quartzware everything has to be quartzware and even including tweezers and many many things which we use there are either quartz material to racks, tubes everything are made of quartz or sometime Teflon okay either of them no other species are allowed in sometimes if the initial cleaning is to be done or removal of grease or something it can be done in normal polypropylene which is also highly pure we use tweezers of course this one now is almost gone earlier we used to ask wafer size of 3 inch maybe 4 inch so a tweezer I could hold it because mass was not very high with 12 inch wafers we need probably 200 tweezers and even then you do not know it may break okay so one nowadays we just replace it with a gongs they say and then you put it in the rack immediately or rack to rack transfer from one rack you put it to the other rack but if you are using SS I mean tweezers then they should be SS or Teflon SS are not used with any acids because they will be attacked okay only water or some such material where we can use stainless steel highest quality stainless steel is 316 the chrome carbon combination is very good okay some other day metallurgy if you are looking to see what is SS chemicals we use both kinds of organic and inorganic chemicals often in the cleaning process as well as during the other processes for example if you see organic we use trichloroethylene trichloroethane acetone benzene and all kinds of resist photoresist e-beam resist and these are all organic materials then we also use inorganic acids and bases for example we use chloric hydrochloric acid hydrofluoric acid hydro sulphuric acid nitrate nitric acid ammonium hydroxide H2O2 H3 orthophosphoric acid and ammonium fluoride all these are inorganic materials and they are used one important thing which I wrote just below that all these chemicals should be mass electronic grade this is essentially minimum electronic grade material should have 6 9 purity that is 99.99999 purity percentage whereas the mass grade is not only it is better than normal electronic it is 8 9 purity plus it has some way no sodium inside mass is most affected by sodium I have shown you other day and therefore it does not have any alkaline is particularly sodium or potassium. So therefore these are called mass grade unfortunately in India no one makes mass grade chemicals so if you go by the lab everything looks to be imported okay that is the worst part in all this technology because there is no firehouse here big ones and therefore there is no cell here to make such things so we all import of course please as I told you the electronic import in 2025 may exceed oil export so please oil import so please think of it any small amount you say today is at least one person saving in 25 gases we use all kinds of gases oxygen ozone nitrogen hydrogen hydrochloric acid gas TCA gas N2, NH3, argon, phosphine, arsine, diborine, silane, silicon tetrachloride gas of course you have to boil it and silicon trichlorosilane, monochlorosilane, dichlorosilane, fluorine, CF4 and sulfur fluoride S2F6 all these gases are required for some things some of them are for cleaning some for etching some for reactions and some for putting better oxide growths so all these gases are required and many most of them are again as I say better than electronic grade there should be very very ultra ultra high pure gases some of them are very poisonous extremely poisonous for example phosphine, arsine they are extremely poisonous silicon tetrachloride fumes are poisonous CF4 is free on is very poisonous do you know why where does where was this used earlier and now we stopped it in air air air conditioners or fridges we have changed this CF4 from there we use S2F6 sometimes or some other we also removed dichlorosilane from there they are very toxic ones also some of them are flammables like silane is extremely flammable like hydrogen just at room temperature under pressure it just blast okay so we have to be worried about the tubing which you keep the exhaust you keep all these have to be taken care when you are working in a lab when the cylinders are there where the gases are stored no leak should occur there there should be leak detectors there should be scrubbers which immediately removes those gas into non-toxic material converts them all these are required when you actually enter this so then why do I enter it not a problem but that is the fun part I make devices or I make circuits as I say so clean room making is a tough job and maintaining it is even worse because humans will be there and they will never care but the system doesn't believe that way so it spoils so devices yield was anyway 1 out of 100 it will be 0 out of 100 so that is where you should start looking for that your cleanliness has to be there okay of course there is a fire extinguisher there are gases there are some mask everything is available when you are working with the toxic and flammable gases now we start with the new this was all about the last lecture these two slide I could not finish yesterday so I start with now the new topic which is diffusion okay the diffusion process is the most important process in semiconductor device fabrication or IC fabrication all semiconductor devices use multiple impurity regions for diode as to regions PNN transistor bipolar is 3 PNP mass has substrate source drain plus thin oxide plus gate so we can see there are different kinds of areas have different kinds of doping and different kinds of concentrations of impurities that is the major part like source drain are really heavily doped materials areas so most of the time we start with the wafer which is from the crystal grown and we can add impurities directly when the crystal is grown so at that time we can make substrate either P type or N type whichever way you whichever impurities I add during crystal goes so wafers are available P type N type for given dopant concentration so it is called that as substrate so wafer is we call substrate and as I say thickness can be as large as 1 millimeter or may be more now with 16 inch papers and we will use only thick or large better the technology we are doing smaller is the surface area we are using okay a smaller is the depth we are using in 5 micron processes we at least have junction depth of around 1.5 to 2 microns now with 14 nanometer that concentration layer of source and then is even around 15 nanometers so the everything is getting other way so what are happening the wafer is thickening but the volume which you are using of silicon is very thin very small so rest is only physical support okay as I say of course silicon is far better than others material which is very popular in other areas called 3, 5 compound materials gallium arsenide, indium phosphide, indium arsenide and host of them said in gallium arsenide that if you see it may break so how do I work that is the fun okay so gallium arsenide is extremely fragile the silicon is not that fragile as gallium arsenide but it is fragile is that okay so we want to control impurities let us say we started with this so during the crystal goes we are controlling one kind of impurities but when I make a diode I will introduce the other kind of impurities for given concentration to a certain depth and that will make my diode okay that controllability is essentially what is most important in making any semiconductor device so impurities in silicon right now I say if I do not say anything material is silicon for us we are only looking for silicon ICs so unless said otherwise 3, 5, 2, 6, no other semiconductor will be thought of in this for this the gallium arsenide technology is maturing and it is a technology of future and as I said future never comes 50 years it has not come however Moon himself is suggesting that yeah it will come so maybe it will come during CZ crystal goes we had fixed amount of desired impurities in the melt so one method is this the other is during float zone we can add a dope crystal and actually give a number of passes to give uniform doping from that dope crystal to the undoped crystal that is called zone leveling so we are shown in the float zone we can actually uniformly dope from a given standard silicon which is dope known value and you keep passing the float zone and it all impurities will get distributed along axis and therefore this in absent absent is using zone leveling but it is uniform doping what is important in crystal growth the doping is fixed or at least uniform I will not say fixed okay of course number can be decided by amount of impurities you add an amount of increase of zone leveling how many passes you give and what is the in a concentration in the crystal you start with there is another process which will look into is called epitaxial growth okay now this epitaxial world epitaxial growth impurities gets uniformly distributed during the growth process itself okay it is more like crystal growth but it is slightly different okay solid state diffusion is the major source of impurity in corporation how from a solid source like in the case of phosphorus it is phosphorus pentoxide P2O5 in case of arsenic it is AS2O3 arsenic oxide in case of boron it is B2O3 which is diboridin so we have solid sources which contains impurities and from solid into silicon solid we pass the impurities okay so therefore this diffusion is called solid state diffusion okay however nothing can move unless heat temperature is increased we will see how much it will be this is the major post way impurities are earlier used to be incorporated flat we don't but this is but there are some we will have to learn this much more because even after any process I do impurity motion is decided by process of diffusion so we will see that again the most important process of incorporating impurity these days is ion implantation and we will have a full 3-4 hours of talk on the implants but these are the major we at least have to go through 6 to 8 implants processes steps before we make an IC okay so implants is a major process of incorporation of impurities basically what we are doing is whichever impurity I want to introduce I somehow get a purified form of that by some method and then by electromagnet I only get that element getting into particular tube because it will follow certain Lawrence law and it will bend only in one particular angle so I pick it out and I put a lot of electrostatic field on that so that it picks energy and this high energy ions of impurities actually go and bombard the silicon okay so this is wafer and the busy beam it just bombards so if I want everywhere I just scan it like this okay so I actually push the impurities by force I am having lot of kinetic energy and I am bombarding static silicon so they will hit the silicon atom and get in okay by force robbery okay just get in however you need huge energy 300 keV or something like that you will see in implants however these are the this is the major step in which we can incorporate impurities there is a version of this which is more like a CVD which we call is called plasma implants so when I teach implantation though it is not part of implantation specifically I will tell you what is the difference we did the reason why we went to plasma was low temperature process compared to normal implants process so we will see we will do on plasma implants of course there is a energy see energetic ions is created therefore it is still plasma still ions but created out of plasma therefore it is plasma implants we will see this when we come to that the epitaxial growth is like a growth on any substrate it can be silicon or any other substrate can be glass quartzware or even gallium arsenide any any substrate gallium nitride any material you can put and the top of this I will create silicon by vapour depositions okay and during this vapour deposition I can make N or P this is called epitaxial word essentially starts come from the growth as below so whatever crystalline part is below is replicated above okay it is called epitaxy as it is grown okay so epitaxial is a process where we want a very thin silicon layer on and silicon dioxide itself I do not want on silicon then I will have to deposit it on any other surface and that is called epitaxy okay so that process is slightly different from normal crystal growth this so the silicon is brought in the contact it will heat it it will sit there all this process will be discussed in epi growths okay. However more important issue then all that I said so far is to know how these impurity transport in crystalline silicon or material this process of transport is known as diffusion any time temperature cycle to a silicon or any substrate or vapour which may have any other process done earlier whenever it sees time temperature cycle what does that mean vapour sees certain temperature for a given time is called time temperature cycle and if we if vapour sees any of this larger time small temperature larger temperature smaller time larger temperature larger time whatever it is then the impurities which are already inside will get energised and will start moving okay these impurities will start moving this process is called diffusion we will see this this is what will next hour of whatever time we will do so what is the definition we will say diffusion is the process by which atoms move in crystal lattice the motion of impurity atom in a lattice takes place in series of random chance now this word is important because diffusion process is a random jump process or random walk as it is called what is random walk it is a statistical process random word itself says is statistical so a person is standing here maybe our CR is standing here and he has probability that let us say one X is he decides he can either come to my side or he can go the other side so there is a 50% chance this person may come this side 50% chance you may go back side so maybe 50% chance you may go to left 50 maybe right maybe any angle so there is a 50% probability across left or right right or whichever it is so it is a random process however after long time this he is not found there which means he has moved from his original position even in random jumps so the distance which it travels is essentially because of process of diffusion the simplest example of diffusion given in many elementary books is if you have a water add a ink drop on the top there is a bluish surface and suddenly it becomes blue all around so the ink atoms actually diffuse through to equalize that this word is most important the diffusion wants to equalize so let us say I smoke which I do not and I hope none of you should so for example if I start so the smoke particles are largest concentration here where I start or incense like Agarbati you just burn it so for a while only it is particles are around but after sometime everyone smells it means these have gone forth back and forth back and forth but at the end equalize everywhere this is the process of diffusion however in case of silicon I do not want impurities to go everywhere I want in a particular direction and that is the game we are trying to play how impurities get in where I want okay if they go randomly it is called isotropic system everywhere then I am under not control so I want to see they actually channelized they come to where I want to a depth I want number I want this is something what we will do in the technique how to control everything but process wise it is a random walk system okay so as I said you hence for control and specific impurity motion one must study some physics of the diffusion because we have to finally control all my life I have been preaching you all that every subject has some influence on others while I am physics learn because if I had to do something at the end to control then I cannot say I someone should have written a software relatively yeah these days many softwares are available so let us sit please note that even silicon the interesting part is very important in this not only the impurities the silicon itself can move okay atoms during temperature cycles can move from one position to the other it is called self diffusion however as I see this will be much smaller than impurity transport but there is a self diffusion also possible so anything you heat cycle you will see some kind of motion and that is essentially process of diffusion have you noted down anyone of course these are given in every book not necessarily in the language not necessarily in the order but given in most book because these are nothing to do with any specific person this is processing I may state in a one way you may state in another way but you have to state the same okay at the end okay. So please remember this most important part this self diffusion because now I am sooner I will come to this how much is self diffusion and how much impurities because in real life both can happen so how much I will be tolerating the other ones or will that add or will that obstruct we will see that how do impurities influence electrical behavior in semiconductor devices and circuits they are essentially concentration decides the majority how much types of majority carriers use but on a p type or n type that will decide the property how much numbers carrier concentration you have is also going to decide the property of semiconductor or circuit rather carrier concentration gradients decide how fast or how distant they will go okay. Then carrier lifetime how long they can survive okay that is called lifetime most devices are affected by this word lifetime BJTs are maximally affected the minority carrier lifetime in the base decides the gain of a transistor so lifetime is very crucial in most processes. So in many technologies if I am working for power rectifier industry or I am working for micro industry where they use what called pion diode I have to control the lifetime in the eye region very strongly for a faster or slower whatever I want I will have to control the lifetime. So this process is very important in deciding the property of a device and which is technologically has to be controlled actually. Then of course there are internal electric fields you are looking as charge any charge is essentially affecting each other because this is there is a space charge and there will be always a Poisson's equation sitting right there so there will be electric field and therefore voltage drops okay so any charge system will always be associated with this is essentially statement of Gauss's law okay. So one of the Maxwell's equation and please I do not know if any one of you appeared in I do not take these days M Tech or period entries often but once I will if I said I ask such trivial why should charge should be electric field that is I am asking Maxwell equation so you also start thinking Maxwell's equation is the crux of all electrical engineering if you do not know four at least learn two by heart and know about other two otherwise is that okay majority number type, concentration, gradient, lifetime and internal fields decide the device property okay. Impurities used in semiconductor devices show energy levels or level in semiconductor band gap n type show energy level very close to the conduction band and p type show energy level close to the balance band. If an impurity gives a level at the mid gap that is easy by true what are those called recombination centers both hole and electron can come and recombine these are called recombination. They are away from the edges that means they call traps any impurity will give energy level in the band gap if it is near conduction band it is n type near balance band p type this in the center recombination center and anywhere else it is essentially a electron or hole trap okay and that also is a very important way of controlling device property. Yesterday I said leakage Karane mass transistor is essentially governed by short choclary all recombination theory, theory is not relevant actually we see it so theory is only because choclary did it everyone has to say choclary did it okay so we also should say. The another example of electrical behavior is shown here this is a mass transistor n channel kind of course this statement is always made of n channel MOSFETs are better than p channel this is little false statement in a CMOS both are required so why do you say this is better or worse and p has its own advantage and has its own advantage but let us so because mobility of electrons is some numbers higher than the holes we keep believing n MOS is the best device okay but at least do not go by that crack statement in every book everywhere they write this is a Milman's thinking this has to be like this he was in 1800 times so he still thinks it is in 2000s correct for example we used to teach in 87 CMOS process is the low power process in 2012 it is no low power process it is as much consuming as that would have thought earlier we did not think that time so all statements have to be modified as years come here is a oxide which is called for this is essentially where I am going to fabricate okay so all the process some way are shown here not every one of them many of them so this is a p substrate n regions are created which are source and drain there is a metal contact to source and drain this cross ones are metals just about this source drain area area please take it area this is two dimensional but in actual device transistors are three dimensional device WL and thickness is third dimension so this thin oxide sitting here can be insulator of any other or late was a site one even now many devices use a site or two but now the new name lanthanum oxide half neumoxide half neumoxinide all tantalum oxide titanium oxide zirconium oxide all are trying to replace silicon dioxide the top of this can be either metal or polysilicon and this if it is poly it has to be doped because met poly doped can be have will have concentration around very close to metal not anyway very close but close to metal so I want a metal like structure there so I use dope poly it is always covered by oxides these are called spacers we have problem there so if you see there are different materials here n is why n plus doping is here source drain p is doping in the substrate then there is a poly doping there is a metals here which make a contact with silicon please metal into semiconductor is called short key contact that is a rectifying contact it can be made omic by doping heavily below but it is still rectifying rectifying contact what is the difference between omic and rectifying what is the difference the resistance in the other case is 0 okay in a omic in rectifying there will be finite resistance of the contact it is called contact resistance so you can see there is a contact resistance due to this metal to cement then there is a semiconductor sitting here source and drain the themselves will have source drain resistances then there will be a channel the some part will be depleted out in the below so there will be some contact here as well there is a junction resistance here there is a junction here below is a depletion layer so there is a pure channel resistance some external additional resistance extra resistances on the edges and there is a as I say poly is not as good as metal so it has some resistivity and therefore it will have some resistance so it is called gate resistance okay many people believe that gate resistance does not play a huge role because there is an oxide setting no DC current pass but AC we are passing stepping RC time constant is there that means the input clock will lower go with the same frequency if R is larger it will get attenuated right there okay so please remember gate thickness gate resistance many people do not even think it but as I increase frequencies I did realize that that time constant is also very relevant so in 2000 onwards we are going back from poly silicon gate to metal gates so then question another 70s metal get up tap cune is abit continue cune we will come to this technology of course we are not using same metal there we use aluminum earlier now using molybden titanium tungsten many other materials and their silicites as word goes okay so that means there are parasitics which are RS, RD, R external, RSC, RDC and they will adjust let us look at current going from source to drain simple one calculation if there is a very small R here okay or sigma is very large the current is essentially called drift current field added current so J sigma E if sigma is large current is large at smaller E okay sigma is large if there is a resistance there I will have a drop on this parasitics so the I may apply VD but actual VDS may not be exactly what VD I apply because there will be a drop in the this parasitic essentially means I require additional current to come either by increasing power supply voltage or by increasing the size of the transistor because otherwise the speed will go down because your R is getting current will reduce which is called IDSAT current the current of a transistor is defined in IDSAT that current drive current will go down because the simply drops in the parasitics resistance we shall see soon is a function of rule by A so some way if you are thinning something your resistance will increase in a newer technologies we thought it will be decreasing actually it will increase so more worries started when you scale down the new technologies new technologies 4 day nanometers are worst problem so we are now saying why do we will make short key content metal metal no in between okay there are issues with that we will see that technology later if you scale down the technologies from say 1 micron 90 nanometer 45 65 45 32 this is the channel start reducing and it gives lot many effects Professor Vasi is the best person to explain them short channel effects it deteriorates the performance of transistor if I would have been teaching that but let since he is the best person around so you learn from him this is very important worry for all designers short channel effects and of course they are decided by doping size so around source and drain the fields you create therefore they are very crucial leakage currents as I just said used they are substrate doping decide the leakage current so is the because of the junction formed so all this you can say technology is some way controlling the circuit performance or device performance larger current means higher speeds okay but larger current means higher power keep matching what do you want okay so what is our ideal thinking we must make a chip or device which has 0 power consumption infinite speed and 0 area that is the ultimate but that is only 0 so please do not believe it will happen but that is the ultimate we are looking for typically the things which I will use in my theory my measurements as well as theories the resistance of any bar of a semiconductor N or P is given by rho L by A L is the length T is the thickness W is the width so if I replace it L A by W into T then I can rewrite it is rho by T into L by W one can see from here rho by T if rho is constant when rho will be constant when the doping is constant rho will be constant but if the doping is varying rho will also be a function of X or Y or Z whatever okay so rho by T if it is constant and even if rho is a function of X or Y that term is called sheet resistivity or sheet resistance RS so we define R as RS into L by W now you can see this L by W is also called aspect ratio if you see this semiconductor bar and if you say L by W is equal to smaller than L so you have say three parts this is also 1W WW so one can see one cube of L L and W same so one cube two cube three cube L by W is three three cubes okay or length is three times the width so it is L by W is three so it is called aspect ratio so if I want to increase or decrease resistance one of the method is adjust sheet resistance or adjust aspect ratio okay this has in a design this is important how much this is you want you must decide whether I should use aspect ratio as if the doping are fixed which you cannot modify and the only way R can be varied is by different L by W's if you are allowed to vary doping's different regions what is the problem if I dope different regions differently so many mass will be every small process I will have to bomb mass rest of this and dope only that part the mass numbers will increase but only more accurate I can control row much better and therefore resistance in a circuit is normally avoided in most circuits because this R control is very difficult larger the R means larger the aspect ratio who will put if one chip contains only one resistance what do I put out therefore bipolar technology lost race many a time simply because without R it cannot work easily or very better way and R's are there there is emitter resistance collector every resistance resistance now I cannot put too many R C such things in on a chip instead I put mass transistor itself everywhere okay so I have better way of doing however as I say bipolar still could be faster could be mass are getting on okay so please remember R is this RS word is very crucial called sheet resistance we will actually monitor in a lab whenever I do diffusion the first thing I monitor is the sheet resistance how much heat resistance I got okay and that gives me an idea how much doping I have done okay so this is my major parameter which I control or which I monitor actually extending same thing we know conductivities Q mu n plus Q mu p p if it is n type then it is n is larger than p so we can either Q mu n or Q mu p or if it is p type the current from say x direction where the voltages are applied for example let us say this is x direction along L then the electric field is voltage divided by the length applied voltage divided by the length is the electric field along the x direction and the current and sigma is given by the carrier concentrations you have so j into sigma e is the current which is called drift current density if you want current multiplied by area so you get current density j r by a is j so i is a times sigma e in the dope resistance if I have a junction maybe I will show you here this is let us say p and n so the impurities have only gone to a distance and where junction is formed between p and n this depth up to from where the junction lies is called junction depth okay that means impurities from the surface are introduced and they go up to xj and the material is n type only till then below this there is a p type and what happens at the junction how many impurities 0 because they must that is why junction is made they are compensating each other okay this is what essentially I say rs is rho by xj in case of diffuse regions and rho of course is 1 upon q mu nn q mu pp is a specific resistivity so rho is by t instead xj is in real diffuse regions it is instead of t we write xj let us say if n is not uniform in the doping normally the diffusion process does not give uniform doping only crystal growth if it goes gives it but diffusion process is gradient based please diffusion processes are gradient based so the concentration is not uniform everywhere so they give some profile nx down side and surface concentration is the maximum and impurities start diffusing down due to the gradient and some way down where this impurity concentration same as p type it will form a junction okay we will show you this is what all that process will work into so if I use this as my junction depth I can then write sigma average sigma that is called universal averaging what is averaging some of all terms divided by the distance you take or integral of that so sigma is 1 upon xj 0 to xj q nx minus nb nb is the base concentration because these impurities minus these impurities are only available in this so nx minus nb into mu nx mu n also is a function of x because mobilities are also function of the doping larger the doping mobilities are smaller okay so if you really want this needs to be solved numerically not easy to solve analytically however we define RS as rho by xj are 1 upon sigma xj so this 1 upon this integral is essentially sheet resistance so I will tell you later I can if I monitor number of RS at different points in xj then I can find RS nx actually that is how the profiling is done I repeat if I RS 1 I find nx 1 RS 2 I h out something measure again then this the next point next point next point so actually I can plot n versus x as I keep etching and measuring RS values that is the one process we will see later otherwise you can do secondary on spectroscopy and can sense as the word goes we can always get a profile but even there we etch all that we do is etch okay so basically any diffuse profile the monitoring is only by sheet resistance this is the whole crux of all that was that whether it is uniformly doped or radian doped this will always be RS can be always monitored okay at the surface so at x is equal to 0 at the surface we know the concentration which we start with which is essentially called the word we shall use later is called solid solubility what is the word solid solubility we are always talked of solutions the maximum number of atoms which can introduce into other material without dislocating it without disturbing its lattice structure is called solid solubility okay at a given temperature solubility the function of temperature largest number of like in silicon we have 5 into 10 to the power 22 atoms per cc is the concentration of pure silicon so obviously no impurity can be 5 into 10 to the power 22 per cc why if they replace all of them then there is no silicon okay so obviously silicon concentration will be higher than impurities so the best of doping can be done with arsenic which is around 4 into 10 to the power 21 per cc one order less okay 10 atoms of silicon one arsenic that itself will put some value of sheet resistance because larger the even larger if I reduce the resistance so I want to see how much higher I can go okay is that clear RS can figure out even in the dope regions as well as universe uniform ones so it is not that only uniform doping I should I can have profiling and I can find what is the way impurity is getting in impurities can contribute to resistivity only and only if this occupies substitutional sites if they are an interstitial sites they do not bond itself to any silicon okay there okay here is an example this is a silicon lattice these are atoms and there is a vacancy here there is a vacancy a no atom and as I already discussed with you vacancies are naturally created because of the crystal growth when we do okay some atoms just do not go there where they should okay but when we say it is a defect we thought it is a defect but if it is not there there is no doping okay. So it is good that there are defects these are also first found by Schottky and therefore they were given name Schottky defect now if you have vacancy it can be also created by something you have a lattice good lattice and during this crystal growth freezing because of energy released one atom may leave the space and can sit other places okay may go to interstitial also but then creating a vacancy there if this atom moves from here to here it will create a vacancy so vacancies can move is that word clear atom jump self diffusion atom jump create vacancies from here something else will come vacancy will move somewhere else so we say vacancy also can move okay this is important. This is the other diffusion we can see if silicon any impurity atom sits between this lattice points not bonded to anything please remember silicon is essentially tetravalent bonded so every silicon is a has one silicon on all sides this is how silicon lattice works okay four sides each similarly for this 4 4 4 but there is a place in between and those in this essentially is called primitive lattice 3 this is called primitive lattice not in itself this is called primitive lattice so I have figured out if I take a surface picture of this primitive lattice these are 4 atoms there is a void in between which is actually larger do you think so even if whatever is their size this space diagonal space is larger and because of that voids are very easy to be available for us so actually impurities will like to go where to the voids first because they are they have enough number everywhere available and they will try to go there okay. So interstitial diffusion as such looks to be much more dominant but if all atoms impurities sit into interstitial side they do not get bonded to silicon atom and therefore no change in resistivity at where they may give defects okay so but it can also form something else as I just now talked about this a vacancy you know from here an atom can move from a good lattice to interstitial side and create a vacancy some of this will come here occupy this so this pair itself will move ahead okay so we say Frankel pair interstitial substitutional pair is called Frankel pair unlikely event but can occur together jumping unlikely event but can occur okay so there are three major defects which we see in crystal vacancies interstitials and Frankel okay sorry interstitial and Frankel so the diffusion can happen to either at vacancy sites this or vacancy this pair itself can move we will see this is also important actually is that okay so this is something how impurities diffuse inside a silicon crystal okay please remember the point defect density is a function of substrate concentration number of atoms of silicon for example per cc the activation is because if they are to move they need some energy so it is called activation energy and of course at a given temperature only that much additional energy it is a thermodynamic process so thermal part will actually enhance the kinetic energy so let us calculate at least this how much how many defects per cc we create if ns is the number of defects per cc created in a crystal of concentration and atoms per cc if ns is the number of defects per cc created in a crystal of concentration and atoms per cc by thermodynamic principle the defect density due to availability of them in n atoms at a given temperature e can be given mathematically this is a possible combination permutation and combination towards one out of so much can go okay so ns is the defect and the number of how many ways actually they can have possible moving there can be given by c and ns which can be given by n factorial ns factorial n minus this is I suppose you know this much maths anyway however thermodynamic system say the entropy of this system can be written as k k is bowman's constant 1.23 10 to power minus 23 joule per second okay please remember number of course I will give you data wherever I need do not have to remember 30 odd here 40 odd here I am doing so much of that I remember all numbers but you need not you will give you the data data is from our side all that I am asking is this and hand work so s is k ln this probability c ns to n this is how it is defined then I I multiply both side t so t dot s is k t ln n by upon ns this the binding energy of atom which is also called enthalpy h as it is called can be written as activation energy into multiplied by this is per unit volume into numbers so how many defects this is for creation this what is yes if the energy required to create a defect if the ns defect the entropy total enthalpy is E s times ns if defects have to be created there is a thermodynamics law which says maybe I should say somewhere below g is equal to or maybe delta g but right now I may say g is enthalpy minus T s where s is the entropy T is the temperature h is the enthalpy if h is larger than T s gives energy is positive if h is smaller than T s the gives energy is negative in any reaction a plus b equal to c plus d a forward reaction is to be held g should be positive if reverse reaction is to be there c plus d is coming back to a plus b minus g should dissociation and formation this process thermodynamics says life is not simple it forms this forms come keep cutting all the time and the equilibrium something is available to you okay so if I write g then g is ns e s minus T s okay I have already I have written sorry then I substitute T s from here and h from here so g is ns dot s minus kT bracketed ln n bar and factorial factorial these are this some people write this I am writing this factorial okay is that okay I just put this T s here and h here so h minus T s is g so g is ns e s minus kT ln n factorial minus ln n minus n factorial minus ln this is log so ln a minus ln b so this is the function is that okay we must first evaluate the Gibbs energy which is h minus T s in fact the way it is it is written delta g is equal to delta h minus T delta s is the change in from the room temperature but I am right now did not want to take you too much in thermodynamics so I directly wrote is to create a defect how much energy is required there is a for any process there is a activation energy so to create one interstitial defect or a vacancy defect you need an e s energy if there are n such atoms defects to be created I need n times e s the net energy okay each KLA e s n KLA e s because we are asking is why should we multiply the multiplied part is something each defect will require that much energy it is sum of e s plus 2 s this is n e s each atom will require that much energy same energy cannot be used that is will spend that much energy from the thermal area okay so each will require e s energy to create one defect a n s will require n times e s defects energy for totally n s defects okay if I write expand this via maths formula which is well known ln x factorial is x ln x minus x this is a very important maths formula given in every book maths book tables Google go anywhere and the books of this silicon wheels as well this is a formula ln x factorial is x ln x minus x this is known maths okay so I use this to remove this factorial solve this c terms which are going for example this n and my minus n plus n will go in s n s will go something I have done this this n this n will go this n s this n s will go so I get this as my g okay you can write down I am just saying the thermal area principle says the maximum defects can occur when dg by dns is all g is minimum all thermal area system wants to go to the minimum energy state so g has to be dg by ds has to be minimum if that happens I differentiate this equate it to 0 and I remove the term whichever can go where go cut the amen n factorial minus n okay n log n minus n minus n minus n s ln n minus n s plus n minus n s minus n n s ln n s plus n s minus n n s ln n s plus n s okay so if I differentiate this and then equate it to 0 I get e s minus k t ln n minus n s minus ln n s the other terms this is minus 1 this is plus 1 so that goes away only these two terms remained so these are the two terms what is that I am trying to do so far what is this relation is going to look at you I want to find n s as a function of e s and t I want to know how many defects I can create at a given temperature that is the relation I am trying I could have written day 1 this is how it but I have told you how do we really do in thermodynamics this is the way I do it this is the way books do not want to do it I just want to show you how interesting it is to see how actually happened okay maybe some for them someone maybe I am wasting my time and theirs maybe more theirs than mine since I do not have this solution from anywhere or maybe it is there I do not see I solve myself so I have to write all steps you can write this and maybe this for me to know what is this last I will have to do substitution sub cutting putting equal to 0 and then see which term goes I get this expression after some maths you need not do it you can assume that this is done okay but to prove tomorrow if I would have written directly this is equal to 0 you have asked me how come it has so I just thought okay this is how it comes of course these are available in many old books okay so if I reorganize e s by k t is ln n minus n s I assume that the number of silicon atoms are atoms in which this defects are going to be larger than the defects I am creating if I am more defect than as I said there will not be silicon at all so I assume n is larger than n s so if I expand this n by n s minus 1 I neglect 1 because n by n s is larger than 1 so it is close to n by n s so I write n s is n e to the power minus e s by k t so defect is one can see from this expression available atoms n in silicon it is 5 into 10 to power 22 for example e s is the activation energy of I can see all substitution I mean interstitial or Frankel okay whatever is e s required to do that so one can see what is the crux of all this n s will be larger if temperature is larger e to the power minus 0 is 0 and therefore sorry e to the power 1 and therefore n all of them are as if replaced so at t is equal to infinity this is e to the power 0 which is 1 so at very large temperature silicon will be replaced by impurities which is what we do not go to that much temperature okay so obviously larger the temperature incorporation will be larger vacancies or interstitial will be available at least impurity interstitial vacancies will be larger larger the vacancy what does that mean I can replace with so many impurity atoms so I can dope so is that now clear why high temperature process required because I need atoms space to replace so I must create that is how I decide I will learn oh thermodynamically it must be happening clearly I must increase the increase of temperature since crystal goes outside at very high temperatures there is a very large probability of creation of vacancies and interstitials and because of that there is an impurity incorporation possible so one question always ask that how can how do you know it they will get in so much so at a given temperature only those many amount of impurities can be introduced so is that that clear to you so why you have to increase temperatures if I want higher doping I must push higher temperature lower the temperature lower will be doping but I do not want that I want lower temperature all control so I search for non-diffusive non-solicited diffusion process where temperatures are not necessarily thermal temperatures thermal temperature is how much energy KT is the energy associated so I say okay I will give you KT energy in some other form why why do I want only from heating which is the method plasmas okay so I can clear plasmas which are as much energy okay which is equivalently high electron temperature but not system temperature system may be 200 degree okay but the electron the ion will have high energy and therefore higher temperature I use the same mass later and say okay all that you wanted I did it at low temperature okay so there are processes which are trying to use this theory anyway because this is the only theory how impurities can get inside okay whichever way you are providing temperature it is yours okay this is last maybe few minutes a last slide number the Khaze family in general MS for interstitial sites is called N I 0 I to the power 0 is different from NS for vacancies which is NV to the power 0 this 0 is intentionally put it is starting vacancy concentration starting interstitial concentrations and there is something will later learn there is no just v 0 but v minus v minus minus v plus v plus plus so some game has going to play so I right now put 0 some books write X so the interstitial concentration to N silicon at that temperature e to the power Si 0 by KT NV 0 or NV to the power 0 vacancies as they be called NS I to the power SV 0 by KT and if for a silicon if I substitute this N numbers and activation energies I get N I 0 is 10 to the power 27 exponential minus 3.8 EV per KT NV 0 is N into 10 to the power 23 exponential minus 2.6 EV by KT so what which number seems to be larger so interstitial sites are always larger than vacancy sites okay so is that clear to you so for a given crystal or given concentration silicon of course are used but any other species any other impurity the defect and interstitials can be found if you know the activation energy for those impurities in that material and a given temperature I can find number of defects both interstitial and vacancies if I know the number I know how many I can push in for given concentration value I am looking for someone want 10 to the power 20 if we do process a 700 nothing will go there so I must increase to 1100 so that those impurities can go there so why process has to be have temperature strong dependence is decided by availability is that okay is that okay because the activation energies are not same for both they will not be same this number is not very clear this is a fit function as I called okay I adjusted this number to suit some equal other this value will be smaller and this value will be correspondingly adjusted so what I did is I readjusted to fit to occur so this is not mine means many others have done it so this is a fitting curve please remember most modeling people what do they do they only do this see occur and put a a 0 plus a 1 x plus a 2 x square polynomial which is may fit 100th order all surface volume anything can be fitted randomness everything can be taken care large amount of program running you have to do it but it will fit finally okay shorter term may fit cannot put strict that's the way it is okay