 Let us start with the new topic today. We have so far done the basic of crystal growth. We have done how a clean room is working and how do we actually go into the clean room and what are the requirements. We have also seen the incorporation of impurities through the process called solestate diffusion. Then we looked into oxidation. Then we also looked into lithography, how to print their image or the patterns. One of the possibilities of incorporation of impurities or rather the one which is now it is used is ion implantation. The word itself suggests something has to be implanted and the thing is purity ions. So we start with the little bit basic thinking on implantation. By the way implantation has nothing to do only with VLSI. This process is known to us for almost 100 years. It was late, very late in 80s that was first time used by VLSI people. Implants were known many, many years ago okay. So do not think that this is very recent or something. So the machines then where different machines now are different for semiconductors but otherwise basic idea is same ages ago. This is for us only specific. Implantation is a process where we can incorporate dopant impurities in a substrate and in our case it is mostly silicon but it can be any substrate. Dopant impurities are created in the ionic form and these are charged ions and therefore can be accelerated by electric fields. These causes increase in energy of ions. The ions are then focused into a beam and then they impinge on substrate, normal incidence. Due to high energy ions when they enter substrate they interact with the atoms of the substrate and therefore after a while lose their energy and come to rest at some distance inside the substrate or the distance up to which they can go and rest is called range. Is called range up to which they can go in and rest or lose all their energy is called range. So we are trying to see since I know ions can go inside a substrate and due to the interaction of atoms they will lose their energy and once they lose their energy they will come to rest inside the lattice. Now whether they will occupy the substitutional sites will be decided by how much further thermal process we do for them but mostly if there are vacancies are available they will like to first sit somewhere there but otherwise we may have to do something to actually force them to sit into substitutional sites so that they can contribute to conductivity. Now if you are noted down the energy loss mechanism is what we are really interested in how far they can go inside is what we want to know and if you are noted down this I will give another sheet to write down or analysis. Okay so up to where they can go they are decided by the energy loss mechanism is interaction of ions with nuclei of atoms of the substrate. They can also interact with the electrons in the lattice and therefore there are two ways of scattering one is the interaction between ions and the nuclei the other between the available electrons in the lattice. The energy range relationship therefore can be created and larger the energy obviously it will take longer before they will come to rest smaller the energy they can be they stop at much earlier depths. Time for this ions impinge on the substrate decide the total amount of how long you do this much this will decide how many impurities you are pushing inside okay. So this is something to do with the word number of atoms or number of ions per unit area are called dose. So how many atoms per centimeter square we can push in from the surface inside is the dose given for this dopant atoms. Now generally since there will be lot many number of ions and they will be impinging on substrate. The randomness in their coming and hitting the atoms because atomic positions and where they hit what angle they hit they normally will get randomized inside and this random nature of atoms coming inside a lattice essentially leads to a random distribution which is the most common distribution called Gaussian distribution. So most likely they will follow a Gaussian distribution from the in a depth that means fewer at the surface fewer at the bottom and maximum in the center okay. So there will be some kind of a Gaussian profile from the depth side okay. Now this is essentially because we do not know which atom going where so we say random numbers larger number per centimeter square are entering and therefore larger atoms they will be able and there will not be only one interaction ion hitting one atom then it moving away it may hit someone and then come down. So there is a average effect going on and therefore it will be more randomized in nature okay. Now this is where the things are very simple because once you say it is random distribution it is a Gaussian profile and what was the difference between solid state diffusion there the how the impurities were getting inside by complementary error functions. Now I do not need to have complementary because the first time itself when I will get in I will have a Gaussian profile and any thermal cycle ahead will actually will not change the distribution or the dose but will just flatten up okay. So more impurities will go ahead and ahead and we will see how many and where do they go finally okay. So this is very important that the first time itself when I push impurities in I get a Gaussian inside okay and that is something very easy for me to then operate at. What is the advantage if I put a very short in very small time as well as very small energy ions where will the rest very close to the surface for a short time I know how many small number of impurities per cc per centimeter square I am pushing in. So what is the equivalence of that in a solid state diffusion a sheet charge approximation we were trying earlier is much easier to control now because I can decide my dose as well as my time and can create surface charges okay and that is the beauty of implantation okay. So let me say something more about possible processes. The dopant incorporation in semi conductors we have seen so far solid state diffusion is the most earliest version which we have discussed a lot. We also seen during crystal growth I can add impurities and therefore incorporate impurities in a crystal. Process which we have not done is epitaxial growth. So during epitaxial growth also you can dope the wafers or dope the silicon or any other substrate. We can also do some part of what we called as during CVD using dope glass this possibility time permitting as you this is called poor man's implanter at atmospheric pressures low temperature CVD using dope glasses I can push impurities in and this process was suggested by Andy Grobe way back in 60s and we call it poor man's implanter. If you do not have an implanter which is very costly to some extent you can play with this smaller CVD system not accurately but some way and of course we can always put the impurities inside what is called process of ion implantations. Now why are we looking for ion implantation compared to solid state or any other process of course the second and third that is crystal growth doping and this has the biggest advantage that they are during the growth of the lattice and therefore they are uniformly distributed so if you are having a uniform doping only two process can do either during the crystal growth or during the epi growth otherwise there will be always a profile in. So advantages of ion implantation are the precise control of impurity count dose and death which I just now said I can decide my time I can decide my energy and therefore I will be able to push exact number of impurities per centimeter square and also I can decide how deep they should go depending on the energy I choose. So this is one interesting thing compared to solid state please remember solid state diffusion cannot be very accurately controlled simply because the amount of source impurities which are coming from gaseous phase to solid phase and then they react here we are not reacting but pushing in okay the impurities directly below the surface can be created we do not have to get into the silicon dioxide okay they can go below the silicon dioxide itself almost everyone can go below the layer and therefore we say called buried profile I can do a profile which is in the silicon and not in any other material above okay I can put energy which crosses that okay. Normal to diffusion normally compared to diffusion this process is low temperature process this statement need to be qualified in the present context see you need to anneal the samples afterward which is around 850 degree centigrade now it is almost all VLSI ultra large scale integrated process can go below 400 or 300. So this is still not so low as we thought but since solid state diffusion is to take 900 and to 1250 this look to be very low temperature process as of now the variance of this implantation will be used and we will see that this is that was that will be called plasma implants which will be low temperature implants okay. The biggest advantage this allows is the choice of mask material since I am pushing the irons through any layer to a depth what is in the top is not so crucial for me okay so I can have silicon dioxide I can have silicon nitride I can have even resist which can resist is very good because resist is resin large carbon hydrogen chains they are randomly distributed and therefore more likely to pass a stop implants because they will actually they will interact right there in with carbon chains and will not allow anything to really go actually but if I push energy even they can cross that energy is that clear so mask is not that crucial in my decisions. So many a times I may use resist itself with a mask because I have done a lithography so resist was there anyway I will start implanting okay so I do not need to go anything there okay that is the biggest advantage implanter provides just with this it is roughly a high energy implanter may be 300 to 400 KV implanter may cost around 10 million dollars to above so it is a very expensive system of course there are many other gadgets this is inside an implanter but apart from the gadgets the cost is very high so not everyone can buy including our CA and doesn't have an implanter okay for the same reasons our much of the money would have then gone to implanter so that is what I said that equivalence will do something okay the next or the most important reason why it was used in VLSI technology was that it allows you to create what is called as self-alloying structures we will show you this little later another very big advantage on this is that in the case of solid state diffusion think of a situation I want to make an NPN transistor and I have a N collector substrate so first I have to do base diffusion and then inside that I will do a phosphorus or arsenic emitter diffusion so first base boron and then followed by arsenic or phosphorus in implant that is not so I can first create emitter and then push the impurities down for P which will make base afterwards okay so it is the order of impurities are not very crucial of course it is not so trivial but it is not very crucial as in the case of solid state solid state you have to first create base only then you can push the emitter impurities that is not so much in the case of I can just adjust energies whichever earlier is not important they decide by the energy where they will come and rest okay this is what someone were asking may be professor Mahapatra gave you a problem arbitrary imperative profile any random profile not necessarily Gaussian or not necessarily error function or exponential or linear way you suggest a very random profile and I can create any random profile using implanter okay. Now question another why do you need a random profile well we do not need all kinds of random profiles but there is a sub junction which is called hyper abrupt junction have you heard of the word hyper abrupt junction, Virector devices which are used in micro ways for generating the sources or they are also used in the params parametric amplifiers or micro ways they actually need such high frequency reactors and you need a hyper abrupt junction hyper abrupt is some kind of inverse abrupt normally it is like this here it is afterwards okay so it is some kind of retrograde strip and we do that in main case of CV adjustments. So for any arbitrary profile possibly can only be done through implants and no the solid state will never allow because it will always through Gaussian or complementary error all good things there are some bad things to be that the disadvantage is of course there is this throughput rate word has not that small as it was earlier earlier we used to have a chap which can have at best hold 12 wafers now we have implanter which can hold 48 wafers so it is okay system is big energy is a higher kind of at least half all is a implanter so many wafers can be simultaneously implanted multiple beams can be done so many tricks have been tried at the cost of money you put money and maybe you can throughput can increase okay for a small implanter which we could not buy even in our lab which may have 12 wafers at a time for 8 inch wafers earlier we had range wafers so it much easier to put 12 now with the same time only one wafers may come so it is a very tough situation if you change technologies you change wafers size every tooling changes every tooling wafers rocks wafers everything changes so much money so no one wants to change sake of it oh now market is available buy it no no is it worth buying okay the second advantage disadvantage is like in the case of diffusions every driving cycle for is with the oxygen oxide so it will self-oxidation is done there so that next layer is on the top is oxide so it create mass automatically okay so it is called passivation it does not allow other impurities to get in however in the implant since it need not be oxide there at all and therefore there is no self-passivation in the case of implant you may have to actually dump oxide if you need since ions are high energy maybe as high as 300 KV because of that this energy when it imparts to a atom the first atom it will hit with such a large energy and momentum that it will displace that atom itself it is likely that the silicon atom itself may get displaced so the near surface much of the silicon atoms will not be in their largest positions they will get damaged or amorphized at the surface however they are not so far away from their original positions and therefore what will happen that by some thermal cycle it can be retrieved back okay but there is a damage the crystal gets damaged at the surface at least because of high energy being delivered there are also a problem which are called anomalous transient enhanced diffusion suddenly we find that I change the energies for some depth change the profile should a atom should a ion should a rest somewhere here but I see a tail they are gone much deeper we never thought of it but it went in okay this called transient enhanced diffusion so there are issues which probably are for different impurities at different times different doping of substrate may create what is called as tails these are called Pearson tails and now this is not every time true for every process so one does not know how depth they are really gone okay so there is sometimes a issue which is called transient enhanced diffusion TDs since you are putting ions and if there is an SIO2 layer here and we have just now read understood the thermal oxidation process we say all SIO2 if you put charge in it gets there and that is the VT problems we have kept saying that you are putting ions anyway okay so you are charging the insulator sitting there okay which essentially means either the charge has to be removed okay all other way it will create threshold problems if the charge is not withdrawn okay so there is an issue in the case of implants that ions charges insulators because that is the way it is okay as I said already the equipments are very costly compared to solid state diffusion cost even for 12 inch papers the furnace cost right now 1 million dollar 4 stack implanter may cost smallest 8 inch 4 waifers may cost 10 million dollars minimum okay so it is a cost wise it is very exorbitant however as I say if you look at the advantages okay which solid state cannot do then there is nothing else of course I mean I cannot do so I will do whatever I had to so I will put money and will charge the customer at the end of the day okay that is the way I will yes it does it does it is difficult because oxygen is not inside oxygen is if there is oxide there is an advantage or dissonance called precipitation so one of the problem of this is some precipitation near the surface which is very bad situation because it will actually act like a recombination centers so one avoids oxygen dough papers and typically we must avoid oxygen at the surface so there is a process of what we call as ionic cleans and we actually remove the surface so that no oxygen is sitting at the surface actually heating up is not that bad as you are thinking because the chuck on which this sitting is cool chuck so the heat is immediately removed but yeah but I cannot say when they they increase they do not increase the temperature energy is given so KT is provided that the chuck on which wafers are sitting have a huge cooling trap so it removes the heat very fast relatively fast okay so I am not I am not trying to say it will not heat but it certainly will not be so high temperature that it will damage you too much see let us say it goes to 100 degree nothing happens okay but if it goes to 800 700 then I have a worry but that temperature it will not allow to reach okay yeah I am tell me is the junction may be far away then where we do not want I want junction depth of half a micron or 2000 Armstrong it may go to one micron no but the impurities will further go down if the driving will further push them out so the junction will further move away any tail if during driving will go ahead so they that issue will be even worse of course Pearson for formula suggest how it can be done and what cannot be but I think I will not go so deep for because iron implantation itself requires 20 hours to teach okay so I will not do that I will just tell you basically what we use okay so typically a machine requires what what should they should provide for VLS high process it should be able to give us uniform doping uniform does not mean not profile but uniform means once I do it I repeat it should give the same profile I should be able to put a dose of 10 to power 10 per centimeter square to as high as 10 to power 16 per centimeter square can you think what will be 10 to power 16 dose will be roughly in a thousand Armstrong depths this will be 10 to power 21 per CC so it's a huge concentration I am talking about 10 to power 16 per centimeter square is very very heavy dose okay 10 to power 10 is 10 to power 15 per centimeter cube roughly and therefore it is normal doping okay so we must be able to adjust doping from 10 to power 10 per centimeter square to 10 to power 16 at best because more than that crystal lattice will not be lattice area into depth is volume a bit thousand Armstrong is minus 5 centimeters microns so minus okay energy of ions required with typical energy required for can be in some cases very shallow implants I need then I may have implanter must have energy of ions as well as 10 KV and if I want deeper implants I may or what we will see later higher current implants at higher energies we may be able to so of course I did not say but larger the dose will require larger current implanter so implanters are classified as low current implanters medium current implanters and high current implanters depending on the dose you are really looking for similarly energies could be 10 KV as small energies and to be as high as 300 to 400 KV energies will be required for pushing ions well within the depths okay like I will show you a figure a p well or n well may require a micron or half micron now whereas the source drain may require 0.1 micron okay so I want a deeper junction also want a shallow junction so I need energies varying from very low energies to very high energies okay we should be able to incorporate all kinds of impurities whatever we could do in solid state luckily for us if I do a carbon implant or what is called as nickel complex implants on steel it becomes hardened one of the method of hardening steel is to implant either silicon or nickel complex as they call and once you implant this the tip of this why where from this there is no one from mechanical where do you use such things the high speed tools which are used with lathes have actually tip which is high speed steels okay with such hardness in that but they should be able to cut the steel itself so their tip should be even harder and that is how it is done okay so that is what I say implants are not new implants are of ages old process we want to have a dose once I fixed a dose it should be stopped after that I don't want oh watching oh nothing like this it should happen that's the end of it it should show a mark okay everything should shut off so it should be automated we also should be able to tilt the beams to a certain angle if I need I don't want always normal incidence I want 3 degrees 7 degrees can I do that so it should be able to do an even angular implants in many processes of LDD's structure of a MOSFET we do 7 degree implants okay so that one side there is no impurity the other side they you understood this is a mask if I do implants like this this side I won't get impurities but this side I can so I can reduce my doping on one side this is called asymmetric MOSFETs they are used using a symmetric implants okay or in angular implants of course one will expect all implanters should go at least moderate throughput or high throughput if it is possible this is requirement may or may not be meant depends on the money you have this will be meant for the technologies like CMOS double double gate FET or FinFET or all kinds of structures normally require following press following areas are made there p well n well I have a figure I will show you then we need challenge stopper depletion implant for depletion transistors source and drain impurity implant with higher doses but smaller energies threshold corrections all these are requirement in a MOS technology I will just show you a figure after you write down this why are we trying to learn all this because when I go into the lab I should be able to know where I am going to use what kind of implants okay at the end maybe after this implantation is done we will before we do before we do epitaxial or CVDs I assume you can deposit by some technique then and we will show you actual IC fabrication 16 mass process triplomers process or many other I will give modification to FinFET what should be done what processes are changed to make a FinFET okay. So first thing we will do is we will finish implant because without implant it is not proper to do for the full processing though we also need lot of CVDs but right now that time we will assume I can deposit okay by some technique you could I said you could I also said here anything could be no I think implant is more important and therefore I thought I will first finish implants and then start looking for actual IC wafer fab our course is asking you to actually know how a fabrication process steps goes through 16 mass process will how many real life processes as I keep saying typical processing sequence require 450 steps even for 16 mass what is worst in this all processing there are no retrace paths is that word clear to you if I make a mistake on 3 36 the whole wafer is wafer lot is through a so there is no hope said okay I can make an error you cannot if you can make error you will be out so all the papers so no mistakes so much why so much automation the reason is this because they should not be any possible mistake of course all seven done nature does not believe all that it does make mistake itself okay and then you are happy about I have not done it the term which we are going to use soon our terms rather but one of the major two terms which are there one is doze and I say number of ions per centimeter square if a is the area then if the ions constitute a current what is current charge per unit time so current divided by charges ions numbers this number in a given time t dash if I integrate over a given time divided by area is the dose is that clear current is charged per unit time so current by charge is time is this so for a given time whatever is the integral of total this multiple divided by number divided by area is essentially the dose so what is the method I am now suggesting monitor the current okay and through which how I monitor with what kind of system an integrator so if I use an integrator and see that after given time how much is the dose I can actually calibrate and say okay here is the dose okay this is what circuit will be allowing you to monitor it and also therefore control it as soon as you compare it with the given value of a particular voltage drop it will shut off the source itself okay this is what automation will be done but let us see this whole figure whole of this may be understood through this figure this is taken from Rochester Institute of Technology professor Kirch Herschman's lectures available on website I was looking for a good photograph so I got one okay I wanted also color photographs so I was looking many sites in which good color photograph is there okay so here is the typical CMOS process okay in this only one of the channel is was being used either N channel or P channel one can see from here this is a STI it is a trench isolation silicon trench isolations this is a new process last 10 years earlier we used to do only channel fox kind of this birds be called birds crest now we will do STI then for we have a source drain here we have this LDDI we are just saying load low doping density is somewhere here low dope drains so we can use this okay then we have a gate which may be any insulator and there will be separation from the drain to this is the spacer okay then there is a contact to the gate either it can be metal poly or can be molybden or any other material which can form silicides why silicides it should replicate metal okay what is the advantage of metal it is a conductive very highly conductive material so any silicide should be as high conductivity as possible and should also be able to stick to the gate insulator okay so silicides moly silicide titanium silicide tungsten silicide all can be done moly is the most popular one which we use for work function engineering 5ms can be changed through this then there is a something called points through implants which actually does not allow this channel to be connected to elsewhere okay and this well itself is a retrograde retrograde means the doping normally how do you put an implant doping profile higher doping ahead earlier ahead and then diffusion down what is retrograde lower above and higher below it is retrograde okay so you need a retrograde well so how do implants allow you to do this so these are the processes for typical one of the device it is either n or p equivalently there will be other device so when you do this you will block that when you do this you will block this and you will do processing for both n channel and p channels so yes in normal solid state diffusion either the source if you are creating error function it will start with solid solubility so it will be always higher so as you go down that is in the depth it will always redistribute and smaller values will come ahead okay I want this area to be higher dope and the upper area lighter dope because that is going to decide my implants I mean my thresholds so I want to retrograde yeah so you can do implants that is why what is the biggest advantage implants allows okay implant allows you to do any kind of that's what I say any profile give me any profile and I will say you how it can be done okay that is the biggest advantage implants allow there is something we are doing through spacer firstly you can think of it this source drain somehow are not getting something which is related to silicites but there is a possibility what is we called as boron depletion so I am trying to avoid it okay so I will see why I need a spacer boron oil all the way through oxide it has a distribution coefficient will go in boron has a very high segregation coefficient this is here but no no when I do this implants I do not want that to be seen by this as much so I am isolating it with source drains by implants okay so that spacer is the one which stops that let us wait okay I will give a actual in pin pad or everywhere why the major result of a process actually on a pin pad current on current is a slightly spacer thickness which is very funny people never realized that the spacer is really causing so much so it is the spacer which is deciding the currents fringe of course it depends on high k if it is a low k it is not that that worrisome you are right high k of course because thickness are high there is a huge fringe but otherwise it is not so serious okay so this figure was not to discuss on CMOS right now this is only to show you how many places I may require implants okay I will do source drain I will do retrograde I will do points through implant I may do for silicide I may do sidewalls I do everywhere everything through number of implant processes and which each will have something different profiles and different depths and different uses okay that is the game we want to play okay from where all these are coming from my IV characteristics of a transistor I figured out this is what I should get if I have to get it I went back and looked into structure so that is how this is the DOS programs or center us allow you to know which areas need some control okay that is all you do in a simulation because we want to see how what will actually affect the performance once I know that then I will say you will come to tell this technology man I want this he said are you kidding then he said no I want it he said okay I will create a new technology for you okay that is how the process is build up okay okay I said first two things I said about okay I forgot this two things which I said first is DOS and second the most important thing is a range and associated word which will lose is a projected range okay we will see what is that the after these two we have a imperative profile I want to know profile how many how the impurities are inside the silicon since it is a Gaussian system it will always have some variance or what we call a standard deviation and an implant that word is called struggle the standard deviation is called struggle so I want to know what is the struggle I want to know at what energy this is to be done so I need to know energy then I also have two terms of my interest how do energies are lost inside a lattice of ions so we say either they will interact with ion atoms or they will interact with electrons so there are two ways energy can be lost one is through interaction with atoms or nuclei the other through electrons so if they interact more with nuclei then we say nuclear stopping if they interact also with electrons then they will call electronic stopping we will see this this is our research I mean this is what we want to learn we also figured out that when we do implant through a window apart from this side vertically down it also goes partly in lateral way is that clear if impurities are coming like this they also go laterally this is called transverse struggle this is one direction and normal to that is transverse to this so any any variation now on the side also it may vary so this range is has a profile okay but laterally profile that standard deviation is called transfer strategy we will show you that that is our research then there are two terms which we often use annealing because crystal is going to be implanted with high energy ions they may damage a crystal so we must recover it back and also by during this thermal process or additional process afterwards we may push the profile impurities to a known depth where we want okay so we must push this by process of drive in okay there is also a word which will come later we will say channeling something which we did not want happened okay and we say why it happened and of course we will write to know which mask materials be used during implant now this is another figure taken from the same people you want to still write on that there is nothing there as I said these are all known when you do a maths you will see all these terms I will discuss almost everything when I actually do the maths for that okay because for example if I am passing an implant through nitride how much thickness of nitride should keep or if I am passing through resist how much resist thickness should be if I am passing through oxide how much oxide thick I will figure it out how much okay so I will actually evaluate that value how much okay so it is not really random though process is random we still can get some but how do you get from very random process something by method which is called mean value theorems okay Gaussian Raphael can always generate a mean and so we can average out many of the effects and say okay here is the way we can average is this okay as soon as you have a normal distribution much game can be easily X FX DX one upon something is average effect so you can always figure out a very straight forward averaging effect okay do some maths here again the figure from same Mr. Herschman this is how it looks to be and since it looked very random I thought this figure was brought specially for this ions are getting in they are moving here and there okay interacting with ions interacting with electrons and these are the positions at which they will come to rest okay and equivalently if we say there will be a profile in the depth a number of a per CC profile in the this maximum is available here so that is the peak value minimum somewhere beyond this and the this distance as we call is the struggle or standard deviation is to delta RP and we will discuss how much delta RP so we have a graph which will give you RP against energy and delta RP against energy and also delta RT against energy what is RT transfer struggle so 3 graphs which are provided to you with your initial this you can see there are 3 graphs given to you one is giving the projected range versus energy this is only for SI system with known impurities okay then we have given it for struggle which is delta RP which the value has been given and we also have given a graph which is struggle delta RT versus energy for all impurities okay so these graphs so what is why we are given you graph solving every time this equations and getting the value may be not easy because it is a non-linear equation though we average out so it is fine but this graphs are monitored graph what do you mean the monitored are actually did implants number of times measured actual ranges projected range as well as struggles on profiles this is done by actual physical measurement technique called sims some other day okay second year on mass spectroscopy we do sims and we can do exact profiles atom by atom I would not say atom by atom but large number you can say but much more accurate profiling can be done there are also processes of measurement technique called ESCA but sims is better than ESCA sims can be used in almost all cases ESCA is only in certain cases only okay then we can do XFS we can do many technology many measurement techniques which can give you actual profiles so XPS is same XO photo lumensants so they are same some call ESCA some call XPS so there are number of instrumentation techniques available also in IIT Bombay there is a center which is now called nano center or something is that okay so what is the way it is why is that now clear random word is how random so you can see that actually that is why as I say last one hour last night one hour I was trying to see various figures so that I can explain you what exactly I am I was saying random what random now you can see what random so I was trying to make a video visual experience for you so if I can do it for you do not have time you can claim that you may have time from any other thing but for this so okay so I will do for you before we we start now the little bit of modeling though we will not go into too deep because this model which I am suggesting is credited to three people called linhard sharp and short or called LSS theory of this energy loss mechanisms LSS was very popular theory till may be 95 98 till that time this theory was used very heavily by everyone okay by 90 ends we have learned a better technique of doing this of course it was known even earlier but we started using in all electrical engineering vigorously which is called Monte Carlo technique so once we have Monte Carlo we can have a pseudo pseudo random generator program then it became very easy to do a Monte Carlo system this and much easier way to do this however Monte Carlo does not give any physics it just simulates something LSS at least we will tell you what is the mechanism going on okay what is the even modern version of Monte Carlo another algorithm CSS CS people have come out and gave a good name you know because we are very fond of our linear line age so genetic algorithms okay they are modified versions of Monte Carlo genetic algorithms okay so there are many more now you come out with something else and you say okay here is another algorithm basic idea is randomize the process and take an average out of it okay so do whatever it is you must be aware not aware but all these techniques we learned ourselves because there was no other background with us okay now there are books there are journals everything in our time but that was fun okay maybe this is also a fun one let us say m1 is the maybe I will this is also m1 m1 is the ion and small m1 is the mass of the atom or ion which is traveling normal and say this is our substrate surface where it impinges okay now as it starts traveling with a velocity v0 so we may say it has a kinetic energy half m1 v0 square and it has an energy equivalent of e0 which is kinetic energy ions are accelerated so they are a kinetic energy which is half m1 v0 square equivalent to e0 okay before it impinges on m2 m2 is the substrate atom okay which is at what what is m2 status it is at rest okay now our first assumption in this all kinds of this is I think way back in in our schools or maybe in first take no schools only these days it may be on fourth standard also in my term it was in 12th or something we used to have the theory of elastic collisions and non elastic collisions okay so all our assumption is the they are all elastic collisions and which essentially means there is any reflection of this does not lose extra energy on that otherwise that e restitution coefficient has to be added to that so all our elastic collisions so as soon as it hits stationary atom m2 which has a mass small m2 for example I just casually either capital M1 or capital M2 also has a mass so don't I said what capital L has the same as soon as it hits it due to a recoil depending on this it may go into one direction at an angle theta to the direction in which it was appearing and by saying this this will give you a recoil now and this m2 will also move on the other side is that clear so I want to know this is called the theta which is called cosine theta is what I want to know how much is the angle through which atom moves away okay is that clear it is impinging at 0 degrees okay and then bifurcates one atom the this may still have an energy which is e1 which is mass m1 and velocity v1 it may v1 will be less than v0 because it had lost some energy but m2 has gained some energy e2 which therefore creates a velocity v2 and this please remember this also is now moving so is that clear why random because this atom itself is not at its original position so when the next something here it may hit somewhere else now so there will be a random process going on okay is that okay stationary atoms have kinetic energy 0 moving atoms are kinetic energy mv square half mv square whatever I said we can write need not write I can just say this is a projectile m1 moves along the projectile with an angle theta from the direction of m1 before impinging and the stationary atom m2 moves in a direction theta opposite side let us say p is defined as a separation between the two spheres atoms are assumed as spheres okay when the collision will occur the dia is 2 r0 r0 let us say radii so if 2 r0 if p is greater than 2 r0 then they will be separated will go away they won't hit but if they are p is separation is less than 2 r0 dia then only they will hit it is that there are two planes one this and one this if they are like this they will not hit but they are there then they will hit okay so condition of impact is that p should be less than 2 r0 and manage p is equal to 0 means head on collision of course our assumption is elastic collisions and therefore we can apply laws of conservation of energy and momentum two equations energy is conserved and momentum is also conserved if I have hit Kia is that okay one atom ion is hitting to the next it moves away with some velocities so the output velocities are output energies are half m1 v1 square plus half kinetic energy is half m2 v2 square must be equal to how much half m1 v0 square because that's the net energy energy is conserved okay is that okay whatever I stated I just wrote down also so that for your sake this is also given in plumber's book of course this is their nomenclature my nomenclature may not they may have angle there is another angle five will not go into too much detail they are very interesting theories of lss okay but some other day those who are into maybe three hours I can give what is the implant theory okay we are never said it so far we are never said it so what I started there is a mass m1 I never said charge there is an atom with mass m1 so kinetic energy is half mv square so no p may not change that's the whole fun okay we will have some distribution okay so there just wait for it from the law of energy conservation of collisions half m1 v0 square is half m1 v1 square cos square theta half m2 v2 cos square theta v cos theta is the in the direction okay so this clearly the kinetic energy of incident ion was or incident atom was half m1 v0 square and therefore initial velocity is 2 by m1 is 0 to the power half by same argument v1 is 2 by m1 e to the power half e1 to the power half p2 is 2 by m1 e to the power half okay so I can I know the mass and there and I know the energy at which this or I know the velocities I they are related so I know energy is root of e1 root of velocity root of e1 on each okay from equation 1 we can find out cos square theta we write cos square cos theta is root m1 v0 upon this then replace v0 from here so I got e0 to the power half upon even square plus e2 square so cos theta is energy dependent is it okay cos theta minus is minus cos theta so it is same angle the opposite see here this is incident if you are going this side is still cos theta this angle is still theta it requires that is why elastic whatever goes up the same angle this will go down okay so I have a cos theta which I was looking for I can get one more relationship of velocity with cos theta by which theory what is being conserved here energy but now we can also conserve momentum is that okay to all of you I repeat given in plumber's book no no no that is the e if I say 1 then it will always be it will always split that is why I kept saying I am using my theory well okay if you have written down this then I can also conserve momentum so I have m1 v0 is equal to m2 v2 cos theta plus m1 v1 cos theta and from there again I can get a cos theta term and using the last two equations I can write cos theta in terms of energy and mass I just copied it maybe check this maybe some e v1 e2 may have gone wrong but 99% they may be correct 1% error stands because I did not I did not substitute myself and verify but hopefully it is right okay so in case now I know in case of ion implantation the kinetic energy I buy up due to momentum gained by atoms of m1 and m2 this is what we are saying change in momentum is essentially force so we are really looking for conservation of energy and momentum and we know the angle through which it will get deflected will be essentially related to incident ion energy the energy associated with incident deflected ion as well as deflected stationary atom and energy so mass associated with them so this relationship is not really used very often this is just to show you that if I know my cos theta I am not interested in exactly the position where they are I will show you what we are interested but this theta I know there so I have figured out how much is the cos theta okay now your answer you are saying now what you are saying that after all you are not having a neutral atoms okay so when you interact with neutral mass this conservation of m1, m2, m3 is fine momentum energy but you are now looking for ions okay ions are charged species and therefore they will also have some kind of potential associated with essentially they will follow Coulomb's law they will follow Coulomb's law is that okay expression this potential due to electric nature of ions essentially it will modify the actual transverse motions okay it is called screening screen means weighing something okay so if you are passing through a screen some may go some may not as it is trying to weigh the initial push change the input okay so what this VR potential associated with ions is it will actually modify the theta what you are saying however due to the charged nature of ions they all experience Coulomb's force this lead to a potential VR which is by Coulomb's force z1, z2 by r exponential minus r by a this is solving the Poisson's equation in this case radially okay r is the position taken r theta is any coordinate polar coordinate where z1, z2 atomic number of atoms m1, m2 are respect to their masses and we define a parameter a which is called screening parameter which as I say I will not solve but it is related to this calculation using VR it is little long because you have to first then figure out how much they diversify then this diversify due to electric field is how much it affect the mechanical energy so really complication the final answer is this this 0.885 a0 upon z1 to the power 2 by 3 plus z2 to the power 2 by 3 half where a0 is called Bohr's radius which is typically some number of m strongs 5, 3.2 for different material. So basically what we are saying that the screening potential VR is integrated along the path of ions to get the scattering angle and that modifies the conservation of momentum and energy paths so both together modify and depending on how strong is your VR it will actually modify larger or smaller. This is what LSS theory is all about. How do we now do it? I have a number of atoms with random energies and I will put a charge with them and we will expect I will allow them random ions to move inside a lattice with random number atoms available and I will say whenever this average energy goes to 0 find out for each of them. Number of such permutations hitings. So some will stop somewhere some will stop and I will see whether it still give Gaussian. If it gives all these theories is not needed because then I will find they have given me Gaussian profiles. So Monte Carlo technique is much faster programs are available you should need you need to have a pseudo random generator which most program these days available. The randomness should be at least thousands or above. If you are only doing 10 or 20 do not do say it is a random. So if your random numbers are very high then certainly you can do as much correctness as LSS theory wants. So is that to some extent I answered you. Before we quit we will just show you some important things to happen. As we have said there are two ways of relaxation of energy or scattering or losing an energy. One is we say one is we say nuclear stopping power and the other we call it electronics stopping power. The rate d by dx which is the gradient of energy loss okay as it moves from the surface x is the direction in the lattice. Okay. Energy is that the x is equal to 0 and then it goes in atoms are going in. So one says if n is the number of atoms per cc involved from the substrate then d by dx is minus n times sne into se where sne is called nuclear stopping power and se is called electronics stopping power. Okay. The nuclear stopping power has been derived and then its equivalents have been found to a great I mean to first approximation the nuclear stopping power is more decided by the charges and the masses and not so much by energies and therefore sne is equal to sn0 and this function has been derived 2.8 into 10 to the power minus 15 z1 z2 upon z1 to the power 2 by 3 plus z2 to the power 2 by 3 to the power half m1 upon m1 plus m2 and the units are ev centimeter square energy centimeter square where I repeat m1 z1 are the incident ionic masses and charge atomic numbers are charge associated and m2 z2 are substrate atoms with mass and atomic number z2 substrate ions. So sn0 what is the approximation we made sne is independent of e so sne is sn0 which is constant okay which is constant. Why are we doing this? There is some reason for doing this is the following is that okay this is first approximation which is called Pearson's approximations Pearson 4 formula as it is called okay. This is LSS Pearson is actually worked with LSS theory so this VR term was actually brought more by Pearson rather than LSS. LSS is a universal theory for any mass Pearson is the man who actually worked for implants by similar argument it has been found that if I look for electronic stopping power then it is proportional to the e to the power half and proportionally constant is related to substrate which is called k and for silicon it is 0.2 or rather 200 to the power minus 16 root of e v centimeter square. Why root? This is e to the power half okay so root of e that is why it will give e v then e v c also should have unit of e v centimeter square. So this is root e v this is root e v so e v ho jai la multiply karenge to e v ho jai la. So this is for silicon for different materials this k values will be different okay. So if I now plot energy versus stopping power exactly what do I plot energy versus stopping power what is Sn0 we said it is a nuclear stopping power independent of energy first approximation so I have plotted Sn0 which is independent of energy. However electronic stopping power is root of e which is parabolic in nature so I draw a parabolic nature for A C E and I figure out somewhere at E is equal to EC Sn0 is equal to A C E is that okay I plot A C E I have Sn0 here when they intersect at that energy Sn0 is same as A C E okay. Now can I find EC then because if I equate A C E equal to Sn0 at E equal to EC I will get the value of EC itself okay is that okay to you Sn0 is independent of E A C at EC is k EC to the power half equate the two terms and get the value for EC okay. Before we come to this figure let me show you this is it okay so if I what I said just now equate Sn0 to at E equal to A C it is k root to power EC is equal to Sn0 so if I do this analysis finally I get EC is 1 upon k square this this this M 1 upon M 2. Now one interesting feature about this is if you see that graph what is it trying to say from the graph can you think of that I have already written if E is less than EC E is less than EC which value is higher Sn0 or SnE Sn0 because that is higher if E is less than EC just a minute if E is less than EC Sn0 dominates higher value if E is greater than EC S E E dominates so if E is oh sorry I am very sorry if E is greater than EC electronic stop power stopping dominates if E is less than EC nuclear stopping dominates I have done some calculation for you for arsenic impinging on silicon at 250 keV if you wish you can call that E0 initial energy I am implanting arsenic atoms ions with 250 keV energy on silicon. These values are known to me M1 mass for arsenic is grams per atom it is called gram molecular weight is 1.243310 to power minus 22 if I want actual grams what do I do divide by number okay. Z arsenic is 33 Z for the atomic number for arsenic is 33 mass for silicon is 4.662810 to power minus 23 gram per atom and Z2 for silicon is 14. So I now know M1 M2 Z1 Z2 and K for silicon is also known to me how much 2 into 10 to power minus 16 e to eV to the power half centimeter square so that K is known to me this is known to me this is known to me this is known to me this is known to me all quantities are known to me so what can I calculate EC is that okay I know EC I have all the values for arsenic implanting at this okay so if I do this what is the EC I got I got 13750 keV kilo electron volt how much energy I got critical energy of this EC 13750 keV how much was my implanting energy E0 was how much 250 keV so what is the condition we have is much less than EC so what will dominate nuclear stopping power will take care of actual energy loss mechanisms so in D by DX what should I put the term now only minus N into SN0 because SE is much smaller compared to SN0 is that clear what is D by DX the energy loss is minus N time SNE plus SE if SE is much smaller compared to SN0 then I would say it is minus N SN0 then I can integrate this and find X at that where it will stop okay that is the my purpose I am doing all this just for the before we come to end here is a you have noted down so what is the way you have to do it given an energy given the species which is bombarding given the lattice mostly this data will be given by me okay then figure out what is its EC then compare that EC with implanting ion energy if E is larger than EC then you have electronic stopping if it is less than EC then it is nuclear stopping so the D by DX relaxation term will have either SE or SNE not both but may happen that at E equal to EC both terms are equals of multiplied by 2 and use it okay last figure for the day last show this again from the same Rochester University slide one can see from here this is exactly what I wanted to show you this is a nuclear stopping and this is electronic stopping so you can have either nuclear stopping or you may have electronic stopping and since we know either of them will be we know the expressions for either of them I can always find the energy loss at other distance okay that is my purpose of finding out so what how will I calculate where is the end where E will become 0 when the energy of ion becomes 0 the distance traveled is range so we will calculate next time range D by DX is known so I have no slope so when the energy becomes 0 I will say it has stopped okay so distance traveled is range okay we will come back to it tomorrow