 looking for implants and let us go back a little bit. We said that if the implanted energy is more than EC or less than EC then the stopping will be either nuclear or by electronics, electronic stopping and you will be able to calculate the range from that formula. Typically it is also found that the range may not be in the direction of ions where they come actually straight way. There will be somewhere randomly situated. So there is a range which is at an angle with the incident angle. So in the same direction which ion is reaching that range is called projected range or it is R cos theta. Theta we have calculated where it goes okay. So we roughly know where will be the actual projected range. Using the analysis it has been found that typical range due to electronic stopping or any this is divided by 1 plus M2 by 3 M1 and this is the range normally will be given to you in the graph sheets. If you have those graph sheets you will find there will graph for range against energy okay range against energy and this range is essentially RP projected range okay. Also we discussed last time that there will be some Gaussian distribution and since Gaussian distribution is a probability function which is a normal distribution, we will be able to calculate what is the variance or the standard deviations. Just for the sake of this data we are given to just to give an idea that phosphorus this is the atomic number this is atomic weight. Please remember these numbers are actually in atomic mass units. So you will have to convert it to gram okay or gram per mole by using the vibrator number as well as the 9.1 if the per gram you have to calculate. Okay so maybe I will give the data exactly if you wish but that is the number you should remember. So one can see from here that arsenic is very heavy so phosphorus is okay but boron is the lightest element okay boron is the lightest element. So when I am implanting boron and if I am implanting arsenic the ranges will be different okay and that is the fun part in that. That in most cases boron will be stopped by electronic stopping and in the most cases of arsenic it will be nuclear stopping okay. So we will see this this is what I thought the numbers where I wrote that the mass decides where they will go and rest okay. The probability function which all of you should know but I just I will hurriedly go through this though I am expecting you to know this. If x is a Gaussian function with a mean value m then m is equal to minus infinity to plus infinity x fx dx and the standard deviation sigma which is we calculate sigma square essentially is the expectation value of x minus m square and if I write expectation value which is essentially x minus m fx dx that I can expand this x minus m as x square plus m square minus 2 xm expectation value of x fx dx is m. So it will come minus 2m square plus m square. So it is E of x square minus 2m square plus m square learn your probability theory once again little bit of signal processing first time in our course okay. So essentially sigma square is expectation value of x square minus expectation value of x square m square is expectation value of x square. So it is expectation value of x square minus expectation value of x square. So that is the number which is called standard deviation essentially what we are saying in a profile up to where the width we will have to calculate of what sigma value 2 this is 2 sigma from the mean value each deviation is sigma. So we want to know at x is equal to sigma how much is the concentration has gone down okay that is the standard deviation and some values if you wish if this is your peak value then f at sigma is 0.606 1 upon E essentially f2 sigma is 0.135 f4 sigma is 1.81p and where peak is the peak value of this function which is essentially if I substitute here then it is 1 upon 2 pi sigma square at x is equal to m where fx is Gaussian fx is Gaussian which is 1 upon 2 pi sigma square under root exponential minus x minus m square upon 2 sigma square and this is the Gaussian profile sigma is the standard deviation and m is the mean value and this essentially gives you the Gaussian profile. So one can see when I put x is equal to m this becomes 1 so it is only 1 upon 2 pi under root 2 pi sigma is the value of f at the mean value that is the peak value what is the peak value 1 upon root 2 pi sigma is the peak value. Now why are they interested because whenever I actually push ions inside the material I like to know how many things I like to know what is the peak value what is the deviation and where is the mean value okay if I know then I know everything about the numbers which I want to calculate okay. So this is maths which I hope most of you should know or must be knowing I hope you almost everyone of you know it but in case there is a good book on probability theory in communications even in maths book one can go and verify again this is what I remember so I wrote down but just check if I may not have made any mistake because this is so trivial it will increase actually 1.81 I do not mean I think I made a mistake what I essentially means it will start increasing sigma because as you go down 4 sigma this value no no no you did not get the point if I calculate somewhere here this value will be higher than this value it is width will be higher as the as you go down and down say at infinity it is infinite very large width sigma is infinite. Now let us come to our process this maths you can verify again now let us think what we are doing since the implantation process puts ions and essentially when the charge goes away its atoms below the surface and these ions come to rest at points which leads to Gaussian distribution that is what we see because this is random numbers some ions are hitting the target or the silicon surface and they can get inside and lose their energy by number of interactions it can be either nuclear stopping or it could be either electronic stopping depend on the energy of ion you start with. So the profile which is given for Gaussian profile for the implanted system is n s upon root 2 pi delta rp delta rp is that sigma okay it is called straggle the word used for sigma here is straggle straggle of an implant. So it is delta rp exponential minus half x minus rp square rp is the mean mean value delta rp square so we have now this Gaussian profile I normally will be knowing how much dose I was putting which I can calculate otherwise so I know or I will measure actually. So I know my n s for a given energy I also know rp and delta rp which data I will have okay which means I will be able to find n x function as x what is n x against x the profile so I should be able to know the profile of impurities inside silicon by knowing the dose of impurities I pushed in and what is the rp and delta rp or energy at which they were implanted so that is how I actually get my impurity profile inside the semiconductor. Please remember the total ions per atom square which is the dose is essentially whatever is the area under the curve for n x is the total amount of impurity per unit area is that correct nx dx minus infinity to plus infinity is the dose and if I substitute this here I can calculate the peak value of concentration is related to dose by this formulation by delta rp. So I will be able if I know n s I also know peak value what is peak value at x is equal to rp whatever is the value this value okay 1 upon root 2 pi is 0.4 so 0.4 n s by delta rp essentially is the peak concentration so I whatever I know for I need to know for a profile I roughly know everything of it and once I know the profile what is the advantage of knowing a profile I will be able to then find out for a given poisons equation how many charges are there and therefore I can calculate the current density at the end of the day I am interested in continuity equation and poisons equation solving and to do this I need to know the number of possible ions or atoms per cc or per square cc as well everywhere profile as such and only then my simulator can do normally what we assume uniform doping but it may not be actually uniform it may be a profile there and one must evaluate using every so you must have to put a grid see how much is the variation you can give final grid or if you are doing finite difference if you are looking a finite element then you have to take a triangles which you are very close so that the field does not change very much so anyone who is looking into simulation can you need to know nx value any way in your simulator and therefore this is an essential part to know what is the nx function I am going to get is that correct rp will be larger or smaller with e depending on depending on what the mass not just the energy but for the mass heavier atoms may be having a smaller rp because they will actually drive right there at the surface and may stop okay. Whereas lighter ions will have a small knockout like a ping pong ball it just goes through and can go longer okay so it is very funny system the range of a lighter ion is longer than heavier ions is that clear to you because the stopping is different in both cases okay so this is something you have to understand heavier atoms actually come rest very close to the surface whereas lighter atoms go deeper so which will go deeper in case of normal impurities boron arsenic boron so boron is a larger profile so what if I want a smaller range what should I do energy I must reduce for boron whereas for if I want the deeper implant on arsenic I must increase the energy for that is that correct but that energy should not be large enough compared to you see that it does go to electronic scattering scattering them so one has to keep worrying how much energy for which kind of species I should use to get a profile of my choice is that clear profile of my choice so in implant what are the parameters I will control the energy of implant okay and I will also amount of days how much atoms per cc I want to push into okay and what kind of profile at then I get this is the what I will look for an implant now can you see it is similar like diffusion even diffusion we got the profile what was the difference between this and diffusion in the case of diffusion what was surface concentration solid solid even error function but if the source is removed then it is as per the how much time driving you do correspondingly surface concentration will decrease okay as patterns same thing is happening but the surface here has a smaller concentration the Gaussian profile this is a silicon you are implanted from here the profile will be something like this this is my x direction so this surface is away from the peak is that clear the difference between diffusion in implant so what do I do if I want to make this peak coming to the surface okay so what I do is I will somehow manage of course I will not say how and which I will put some other material which has roughly similar sigma for both okay and see to most of it goes into the other part which is oxide or anything insulating and the peak comes closer to the silicon surface so I can tailor my profile by adjusting the thickness of the insulator between implant and silicon is that clear so this is how profiles are actually monitored where do I want peaks actually where do you think peak should be normally at the surface or away so there are two kinds of FETs we use one is called buried channels the others are called surface channels I think professor Vasiv will explain you much better and in buried channel it is better to have implant profile down okay so the surface concentration is very low the most of the concentration is much below so VT is adjusted below side and not on the surface where in surface channels I want VT to be adjusted from the surface itself so there is an issue there because if the control from the gate has to be done surface is easiest to control so if you are not looking for pure FET actions buried channel may be very good so depletion transistors are normally buried channel devices whereas normal fin FET MOSFETs are always surface channel devices is that point clear to you so this has to be understood we need such kind of profiles also the other day someone was saying and I think they were right if I want an arbitrary profile let us say NX versus X I want this very random profile I want which is absurd but maybe I need it some reason you are very great simulator people you decide I will this feed this profile and see what happens okay maybe something great may happen so if that happens I will say okay do not worry what I will do is I will do multiple Gaussian profile with energy such that it is a very sharp peaks and the depth is decided by energy as I reached this point I will increase the dutch overlapping Gaussian profiles so the envelope of all this similarly here similarly here okay if I keep doing energy and doze I will be able to create any arbitrary profile is that clear by adjusting energy and doze I and do multiple implants overlapping implants so that I get an envelope profile which is what you were actually arbitrary I want this profile okay so what is the biggest advantage implant provided that it can create a profile of your choice okay you decide from a device side suddenly I want some impurity below here like LDD we wanted to do so here is a possibility I can reduce concentration selectively okay at a distance so this is something what you should know that why people look for implants but everything is never good so we will say why implant is not as good as everyone said so the 99% all VLSI technology uses only implants so this profile do you see what is the way it was last time I did show you or maybe I will just okay there is a figure which I want to show you this one a figure which I last time showed you that this is the kind of profile you will get isn't it this is the implant this is silicon and this thus you see the figure very carefully there is a mask material here okay and we expect no implant be possible through that okay so there is a window in which I am doing implantation and my assumption is all ions are only going vertically down okay or x axis as I said and therefore I get a profile along x axis or vertically down but in real life whenever you do a mass mask kind of implants using a mask there is a lateral profile also is possible is that clear like in diffusion the impurity is not only go down but also laterally there I probably forgot the lateral junctions are 0.8 xj whatever happens in the window this in case of diffusion so actually you see this if this is your xj this additional diffusion is 0.8 xj both sides so 1.6 xj is actually getting inside is that clear to you so it sometimes is good because if it is the channel length it reduces the lateral diffusion actually reduces the channel length good for you but there is a punch through problem so there is another issue may appear okay. So this essentially is what we keep saying to you that in diffusion is isotropic what is the isotropic word all directions it does not see which direction the since the ion energy is downward the maximum will travel on the downward side but they still can interact on the sideways because they will hit some may go okay. Now if they go through this window this is an important thing because this is real life what will happen you will actually do implantation through a profile a window mask window let us say this direction is x this direction is y and direction along the plant is z okay. Now we see let us say the window has a distance between the two lines these are mask areas could be here fully also this is 2a and this center point is a so we say 0 to minus a 0 to plus a and it is symmetric on the right side and left side is that point clear if I take 0 in the center the profile is symmetric to plus a side and minus a side and the way I look at it somewhere here I again see a Gaussian air function profile and I do not see Gaussian profile because during this source was available and source is available for a certain distance only just only. So during this this profile will also appear on the y side is that correct the earlier version where it was only on the x side this is x this is x a profile like this now I am showing you a profile which is along the y directions as well this is called transverse impurity get getting in transverse ion is coming vertically transverse where they also go okay why what is why they happen it is a isotropic process major ions will go vertically down but some may interact and go laterally transverse way and they will also give you equivalent what we call struggle the equivalent change their deviation on left and right side without going into full maths which is available in the paper which if you wish I will give you tomorrow I forgot to write down this fear is given in every book just that this is at 8 is 50% okay at the age and then it goes down okay just look at it the profile now is 2 pi to the power 3 by 2 and now my assumption is delta y and delta z are identical whatever is here is also happening on the z plane is that clear this side and this side also main is x but it goes like this and it also goes z direction and my assumption is since the window is same and unless the links are too different which may happen some case the lateral as well I mean transverse as well as orthogonal to that will be same values as assumptions so we assume delta y is delta z and the profile now is half x minus rp by delta rp square y square upon delta y square z square upon delta z square and if I write delta y by delta z is equal and that number I call transverse struggle what I call that transverse struggle so assumption is this side and this side it is same okay so if I now do this analysis this profile now I get is nxy ns by root 2 pi exponential this is my normal Gaussian profile along the x direction and y and z I equated them now so one upon root pi complementary error function y minus a root 2 times delta rt x upon 2 root dt do you recollect the error function rp x upon 2 root dt same function now this is one can see from here if y is very very larger than a far away from a what does that mean error function infinity is root pi error function complement error function of infinity is root pi root pi root pi cancels so that what is that I am trying to say away from the edge of the window very close to it has effect as long as y is less than a there is a struggle going on but far away there are no impurity transversing is that clear to you so why is a plus minus here there they will have transverse RTs okay whereas away from it we do not look for it because this function says that why larger than much larger than a there this term will become one one means normal Gaussian profile will start taking only in the x direction so initially you may find impurity like this but as you go down it is normal Gaussian profile is that clear so only at the edges there is a additional RT comes okay at near the window edge below that it does not that is what we are saying is that clear so this delta RT graph also will be given to you energy against transfer struggle energy against projected range and energy against struggle has been evaluated both experimentally and by Pearson formulas and those values graphs have been already will be available are already available on the our webpage so you can download whenever you need and one has to use them always to calculate RP delta RP and delta RT in case I actually specify you the window size okay then you must do that that means I am already asking you to take care of delta RT if I do not specify which essentially I mean neglected okay then I assume as if this is always one for you otherwise the net profile should be something this normal profile into this complemented fraction and which is only at the edge it will be effective okay other places it will not be effective so this is how actually implanted profiles are modified whenever I do mask implants I have area and I implant through top through a window then this may occur many a time these values are not so crucial because delta RT are much smaller but if delta RP itself is small smaller energies then probably you should look for delta RT also so it is most cases I do not use RTs but if the profile is shallow then I think they will actually affect effective okay the other thing which modifies the profile is another thing after all when you do implant you are pushed some impurities per centimeter square giving a profile NX okay you are pushed some days of impurities and they distribute and they form a Gaussian profile fair enough but once I have a profile no other impurity implant is stopped now there is no additional ions coming now the wafer may still see large amount of thermal cycles because this implant may be the third step in the processing and you may have to go another 30 40 steps in which at least 8 may be thermal steps okay so what will happen these impurities is a Gaussian profile okay you keep driving it what will happen the profile will start flattening and flattening equally saying in RP what is changing delta RP will keep on increasing so I say okay I will add DT product to delta RP for any additional DT effective I use okay so here is what I do I say I had a Gaussian profile I know peak and peak concentration will not change why it will not change because once the implant has reached atoms are reached there they cannot change but as you increase thermal cycles they will start spreading okay they will start being deeper and deeper by diffusion okay that number can be taken care through this formula which is delta RP square plus 2 DT DT is effective it can be D2 T2 plus D3 T3 plus D4 any number of time temperature cycles you go through total DT product will appear here and why I made it RP square because DT is centimeter square okay so delta RP square plus 2 DT to the power half because I want actually range in 1 upon root RP so this similarly I substitute here delta RP square plus 2 DT do you recollect same thing we did in the case of Gaussian profile with driving going again and again okay same there is no difference between this so whenever I will go through thermal cycle of an implanted profile I will actually reduce what what all things will change the peak concentration will keep on reducing because the impurities are fixed they cannot be changed now area under the curve is dose which is fixed okay so if you flatten and this profile peak will go down okay however delta struggle will change or standard deviation because flatness sigma will change sigma here is delta RP was initially plus whatever thermal cycles you go through that much value will get added to this is that point clear to you so a Gaussian profile with a diffusion going through is the actual profile which you get okay is that okay so this is very important that in real life as I say the first implant will come from channel stoppers we will see you next time and after this channel stopper implant has been done maybe second mask I will go through at least 6 implants and 12 at least heating cycles okay so every time I do this the earlier profile also will keep on changing whether it is very effective change I need whether it will do lot of harm to me which I can see from my requirement but otherwise that profile will keep on modifying as I go through thermal cycles is that point clear to you so this is very very important in the case of actual that is a difference between diffusion and implant is this its surface concentration is not at the surface or sorry its peak concentration is not at the surface that can be made and I said you how by putting something else where rest of the profile is on this side and surface appears okay so I can modify position of P by my choice okay is that clear that is also doable this is particularly I am giving them those who are doing device simulation can think of actually arbitrary profile oh no I want slight dip here I want peak here I want 10 percent down make any profile implant can actually generate for you that profile okay and even if you what do you do you do not do anything you only give the variation and it one by one it will solve for you okay it may take some time to solve but it says the final difference most cases and then that takes time but that does not matter so is that point clear any implanted profile going through a thermal thermal cycles will produce additional details to that and that should be added to the initial struggle okay this is how the profile will get modified now one just now I said you something and that now I want to show if I am implanting something noted down this there is something this violet colored mask has been shown here may be oxide may be photo this may be anything through which no ions are going through is that clear but ions are very high energy particles ions okay so why are they not going through this they will go everywhere they have no such choice key this material or that material all that what we are saying that this material will have range which is much smaller than the thickness I have provided so nothing goes below that or even if it goes it is just tail goes some small amount may go but that tail goes but this itself I can use for my advantage tail okay so I can have mask of photo resist photo resist is very good mass why anyone general photo resist is made up what resins those carbon chains huge carbon links are there so when the ions come they actually will find many sides to interact is that correct so they actually go will not go deeper they will be actually stopped by resist in much thinner thickness because they will go randomly inside left and right before going deeper because they lose energy okay now this lose energy is what we are looking for so I can have a mask of photo resist I can have a mask of silicon dioxide I can also mask of silicon nitride and I can also have a mask of metals okay it can be gold tungsten platinum vanadium where vanadium is used where do you think vanadiums are used no not as a catalyst vanadium is a metal sheet now it is used I am not denying vanadium sheets are used in all space application ICs all package of ICs are actually on the top there is a thin vanadium sheet is blind why do you put that stop the ion implants ions which are the space is having a huge high energy radiations to stop that beating in we put vanadium so vanadium is excellent mask okay vanadium is excellent mask for ions much heavier ions protons it can stop most of them okay of course if the energy is too high you will require much thicker vanadium sheets typically in a mass mission 27 kilograms of vanadium sheets are used you can now think what is the issue if I have a geostationary satellite for TV transmissions or other wireless applications if I have my satellite takes 27 kilograms one transponder I do not know whether you know exactly between transmitter transponder think of it one transponder transponder weighs roughly around 6 kg to 8 kgs okay now if I say this 27 kilograms of sheet of which I put I make it thinner than half okay but my circuit below is such that it does not change its characteristic even with the dose it receives now that is called rad hot circuits okay for the remainder 13 kilograms I will put another transponder 400 million dollars annual fees a transponder hire okay so rad hot circuits are made because I want to remove the vanadium sheets as much as I can of course full I will never because I do not trust my technology will stand so at least 50 percent chance I will take that is what rad hot circuits let us say how do I know how much is the thickness for a resistor should have so that below that whatever goes into silicon is smaller I decide how much I want this is called blocking capability so how the blocking numbers are given if the total dose is NS and 69 blocking I want what does that 69 means 99.99 99 percentage that is the amount of impurity which has gone in divided by the total impurities per centimeter square I pushed in that ratio is the percentage how much I can block is that clear smaller gone in the right total out of how much gone that is the percentage I declare so I may block 96 9's I may lock 4 9's I may decide how much I can tolerate okay if you want 8 9's it will be even more problem because then you let that this has to be adjust thickness should be proportional okay so why we needed it we want to know how much blocking I have how do I calculate I will calculate those which goes into silicon okay I know how much how many impurities integrate I can always I will tell you how to get that once I get this NS I anyway know because that I started with I said okay I want so many percentage of blocking so I know Q if the Q is the dose gone in and NS is the total dose Q by NS percentage I know is that correct if I know this by my implant profiles I will be able to tell you how much D I should have so that this much blocking is possible is that clear to you what I am saying so many irons per centimeter square pushed in I put thickness of some material where most of it stay and very small amount both into silicon the ratio which I allow decided by my blocking capability I want I want this mass should have 6 9 blocking or it has 8 9 blocking okay so if I adjust my blocking then I know how much is the thickness of that material I should have in terms of energy in terms of blocking capability and species which you are implanted for each species it will be different because the ranges are different so we will have to figure out for each material for silicon you may have another material and you may have another irons so again you will have to figure out how much for that okay so essentially I am now saying I can decide the thickness of the mass clear by deciding the blocking percentile I want is that clear so here is the maths I do is that clear what I am doing I am pushing irons I put some layer in I right now should I say but can be any other material which any among them and then the rest which is good go in this because it is a Gaussian profile so part is called tail so tail is going into silicon let us say q is the residual residual means whatever has gone in the silicon out of total is the residual then I know the profile of Gaussian profile how do I calculate q X now doesn't start with 0 X starts with D so D to infinity this is in silicon D to infinity this is in silicon q is the dose available in silicon silicon start from X is equal to D and not X is equal to minus infinity X it starts from X is equal to D just check this figure from D to it goes in so I said D to infinity NS root 2 pi RP delta RP X minus RP square upon delta RP square DX I integrate that this is a profile NX DX is the dose is that clear integral NX DX is the dose but those were from D to infinity not minus infinity to plus infinity but from D to infinity for people who want to know much I saw the number though you do like this this is how I do it I substitute Y is equal to X minus RP upon root 2 delta RP then I differentiate it so delta Y is one upon root 2 delta RP DX at X is equal to D YD is D minus RP upon root 2 delta RP which is I call Y 0 and at X is equal to infinity Y is infinity is that okay I want to know this in terms of new parameters you have changed X to Y now so when X is equal to D how much is Y and when X is infinity Y how much is Y okay so we calculated the limits Y 0 to infinity NS root 2 pi or delta RP now this 2 root delta RP exponential minus Y square dy is that correct so I just change from X minus RP square into Y term Y terms okay so if I do this NS is constant is a root 2 will cancel so I delta RP will cancel so NS upon root pi Y 0 to infinity e to the power minus Y square dy or essentially this but any finite value to infinity can be written as what 0 to infinity minus 0 to D 0 to infinity minus 0 to D the rest is that clear so I now break this Y 0 to infinity as 0 to infinity e to the power minus Y square minus this minus 0 to Y 0 is minus Y square dy is that okay I could have directly written from here but I thought maybe I will show you how it is done okay so Q is that okay everyone has noted down so Q is equal to NS upon root pi but 0 to infinity e to the power minus Y square dy has integral which is root pi by 2 the other one 0 to Y 0 e to the power minus Y square dy is an integral which is root pi by 2 error function Y 0 okay it is a error function Y that is how error functions are defined so I write root 2 I will take up NS by 2 1 minus error function Y 0 which is NS by 2 complementary error function Y 0 okay complementary error function Y 0 okay maybe we should put like this not to get confused okay but what is Y 0 D minus R p upon root 2 delta R p so substitute back Y 0 so 2 Q or Q is equal to NS by 2 complementary error function D minus R p upon root 2 delta R p then I do little maths I take 2 in this side NS back this so 2 Q by NS is complementary error D minus R p upon root 2 delta R p is that clear just all to say D why are we doing all this I want to know the D for what values Q by NS value I will decide which is blocking so for that how much D I should have for a given energy which will decide R p and delta R p so I write re-adjust the terms so I get D plus root 2 delta R p complementary function inverse 2 Q by NS is D complementary function inverse of 2 Q by is D minus R p upon this which is essentially R p plus root 2 delta R p complementary function of this now this is so what should we do now if I say I want 9 6 9 blocking what does 6 9 means 99.9999 this is the blocking I want so Q by NS is how much 10 to power minus 6 but I want 2 Q by NS and this is the catch the error function term has to be evaluated for 2 Q by NS and not Q by NS this is the only catch in all that analysis so 2 Q by NS is 0.0002 this is complementary error function inverse so how do I calculate the this value 1 minus error function inverse of that is this so what do I do I subtract this from 1 so I get 0.999998 okay and for which I will go on the error function table and find the value of X there which will be inverse of complementary of 2 Q by NS is that clear this is 2 Q by NS this is complementary while going on so 1 minus this will be error functions so you subtract 1 out of 1 this from 1 so you get 0.999998 look for a function table the error function value against X and see for this value how much is X so this value I can obtain if I obtain this value for again our energy RP and delta RP's are known to me okay so I know how much is thickness of the material I wish the only catch I did something can you tell me what is the catch word in this maybe I will show you this later so is that point clear to you how to calculate D okay so I will give you a blocking I say okay 4 9's then how much it will be 99.99 so 10 to power minus 4 but into 2 okay subtract from 1 then 0.9998 only will come go on error function table for this error function value how much is X that will be this value then the for a given energy from the graph I know RP and delta RP so I know the thickness whatever I said I did it again just to show you as I keep saying I keep writing myself so that is the value of course I did not go on the table to check this but you can see what is the value this will be around 3. something 0.98 is roughly 3 3 or 3. something so this will be root 2 4 into so this will be roughly 4 this into root 2 will be roughly 4 4 something of that kind okay so RP plus 4 times delta RP is roughly the thick graph I am not saying because that exact value you can take from the table I can just tell you from 0.98 the error function is roughly of 4 error function 4 is roughly this value sorry 3 so 3 into 1.41 is roughly 4.2 or 4 roughly you can say now so 4 into delta RP plus RP is the D thickness for what value is blocking 6 9 blocking if I want to do I will be able to find the D. The problem assumption the problem which is creating is that I am assuming RP and delta RP in the material of mass material same as that of silicon which is not true okay so what we do is some rough estimate we did and which is not accurate but sufficiently good if you find out RP of the mass layer and this I may give you RP of the mass layer whichever is the material RP is the silicon then the ratio will be also ratio of their thicknesses so D actual is RP in the mass layer upon RP in silicon into D obtained from here is that word correct assumption if both are same RPs then you get D and this D should be multiplied by ratio of RP to the mass layer divided by RP to the silicon this is rough estimate which gives reasonably good results if they are equal then what was happening if I assume both are equal then it is 1 D obtained is same as D actual okay but in real life it will be different okay will be smaller or larger normally mass RP will be smaller so this is the ratio smaller than 1 so actual obtained will be by into fraction will be actual thickness will be even smaller to actually mask typically 6000 Amstrons of photoresist can block 300 KV of implants 0.6 6000 Amstrons is 0.6 microns of resist can block 300 KV of any ions so it is a very powerful mask is that clear so in the implant what mass I should use normally resist why should I go put another layer I am anyway doing lithography I have resist sitting there I use that itself as a mask resist was sitting is not it so instead of removing and doing implant later I will do implant right there is that correct keeping resist there okay so what will happen then I do not need additional state also to go through okay is that okay so this resist is one of the major mask which is used in all implantations okay is that clear to you so please take it normally RP in silicon is same as SiO2 nitride so one normally whatever you obtain is true but for metals or for resist RPs are different and therefore this number must be specified if not specified do not do all this you just write D whatever it is but if specified you will have to take a ratio and figure out how much is the ratio and then multiplied with this value to get the actual values is that okay so this somehow we are now figured out what are the things we are done we implanted we say how are they coming how much days I can put so much I know the profile now I also know if I want to profile moving I can adjust profile moving I can do any arbitrary profile do through multiple implants of different doses and different energies so I can create any arbitrary profiles okay we also see where the actual RPs and delta RP can come because of the scattering whether it is nuclear or it is electronic so this much we have done so far okay. Some question was last time raised after the class that how is this impurities which are ions actually get activated means unless they sit where substitutional sites how are they going to actually contribute to conductivities okay so obviously there must be some process must be happening either directly or indirectly that they will actually get into the substitutional site the impurities are coming inside in ion forms okay and they are resting randomly they are not going to necessarily substitutional sites is that clear so if they are not reaching substitutional site they will not contribute to conductivities is that only when they replace silicon only then they are activated so I must do some process now in which these so called ions which are coming inside and due to the scattering rest somewhere they actually occupy the substitutional site. For when I say if they are heavier ions then I also figure out the damage is very high I will show you how okay so now that means the surface of silicon is not silicon then crystalline silicon it is actually amorphous okay so now these two are two different things but they can be taken together in one go a modification helps substitutions okay that is the purpose typically what we do is to recover the damage which is caused we anneal the sample after implants okay at temperature from 600 to 1000 okay now it is we do RTP rapid thermal RTOS RTPs but even if old time furnace will used to do at 600 to 1000 and the way we used to do it some for a while we will do 600 then we will go to 800 then we will go to 1000 time wise we will adjust because some impurities may be activated at 1000 some may get activated at 600 depending on the base I have okay or initial impurities where they were so there is a catch going on that you have to learn your own anneal cycles this is called annealing okay now this recovery of silicon from amorphous to this itself helps you to create substitution sites that is the fun is that clear recurring of the damage which is amorphization when you start recovering to crystallize crystalline this which is called EP growths there are substitution sites automatically easily available to them and here is some maths which we can do please remember ion energies could be as low as 10 K may be 100 I wrote but may be as low as 10 KV or 30 KV at least maybe I should write so lowest energy normally will be 30 KV so 30 KV to 300 KV implants are done larger energy means what deeper implant smaller energy means shallow implants okay but if you are doing a new nuclear stopping in particular case what will happen they will push their enough energy okay they will push silicon atom from their original sites okay when they actually know so silicon crystalline it is broken because silicon is not in periodic structure in the surface so at least some 100 planes okay now that happens that the you know please remember that is the area where you are in FET that is the channel area is that point clear to you this with the worst case will be where the silicon this inversion channel is going to come you are actually implanting something to adjust VT there and you are creating all damage there so its recovery should be extremely good because I am adjusting threshold there actually okay so this recovery is a very tricky game okay so that the VT VT is exactly adjusted by I will show you this when I go through full process okay. Now the surface layers of silicon this could be of the major disadvantage of an implant that means every time I must recover it because there is a damage going on okay so what we now say we have done some crystal about crystals thinking about we did something it requires certain energy to create a frankel pair if the silicon atoms moves what it will do left behind a vacancy so it is called frankel pair so if a frankel pair has to be created and it moves away from the surface where now impurity can come and rest it needs certain amount of activation energy is that point clear after hitting ions the energy absorbed by silicon atom should be sufficient enough that it displaces itself moves down along with a vacancy pair with it and that is called frankel pairs okay. So basically what we are doing is trying to create frankel pair movement from surface to away and as impurities will come they will occupy vacancy sides and this silicon will keep moving this is called first silicon because a single atom it moves it is called first silicon blocks okay and but it moves itself okay. So silicon diffusion is very important in the case of recovery some other day more details it is made infinite things material means up to get married or say okay please remember the three major problems implantation is the disadvantage of implantation is damage the other is very cost very large amount of cost per wafer is created if I do implants and not hundreds of wafers can be implanted simultaneously so there is a lower throughput rate or lower throughput because I may put 24, 40, 80 but in further how many I can push 250, 400 wafer in one run okay. So that is something which implants, implantors do not allow okay you can put 200 wafers implant also is there but then the cost of implant itself is exorbitant okay. So whatever I was saying if ED is the activation energy for creation of frankel pair and not just creation but moving away okay the silicon during the energy transfer from ion to silicon it is possible that SI, SI bond may break and frankel pair can be created and it can move away from the amorphous area and that typical energy one observes by calculation and by measure equivalent measurements is 15 electron volt okay. Separated frankel pair means moving away it requires roughly 15 eV of energies. If energetic ions are heavier like arsenic or phosphorous atomic mass is 78 and 30 or something of course phosphorous is in between boron is 11, 10.8, boron is very light it is just 11 okay 10.8 to mmu okay. So how the boron will lose this energy most likely electron and the higher will always lose with nuclear. So most likely arsenic phosphorous stopping will be nuclear and boron stopping will be by electron stopping. So if you see the damage you are not you wanted that lighter will always be mostly electronic okay because they will not be able to transfer the energy to silicon to move it out because they are lighter ions they do not have half mv square enough. Is that clear what is the kinetic energy is very small with them okay. So they cannot push too much. So most of the energy they will lose through scattering of electron they will exchange energy. But heavier ions half mv square is high m is high so it actually move the silicon is that clear is it okay. I repeat if energetic ions are normally heavy and they normally are lose their energy through nuclear stopping lighter ions do not able to move silicon so they lose most of their energy through electronic scattering. So if you have a lighter ions or a heavier ions the kind of damage shown here is the following for a lighter ions you know there is small displacement may be very small I have shown you larger just for this but the range is very high long. The lighter ions can keep going because it is not losing too much energy with the lighter lattice is not moving. So lattice does not get enough energy out of it but electrons do. So they keep moving in and that creates something called dislocation chain which is small displacements they do not move too much okay. So this is called small dislocation chain is created but the range is sufficiently long okay lighter ions so it is funny is not it lighter is actually creating damage deeper but it is a smaller damage. Whereas if you have a heavier ions of course this looks to be same but this is much smaller this is a shorter range but the damage this is where silicon atoms actually move away because of energy transferred to them okay and they create triangle pair which are moving away from the original sides. So only in the case of heavier atoms we should really look for what is the kind of damage it is creating. Lighter since it is a dislocation even a normal 600 degree anneal they will come back okay. So lighter ions, anneals, implants are annealed at lower temperatures why because damage is much lower. Higher ions heavier ions damage will be larger this so you must anneal it at higher temperature is that your range of temperatures okay so you have to do this differently. Now there is one interesting thing which book has given and which I thought is interesting many Frankel pairs can be formed as heavier ion traverses number of planes in the lattice. Now in the lattice we have already seen I hope you have not forgotten your Miller indices there are number of planes okay identical planes 1 0 0 may have n such planes parallel to each other that is why it is shown in triangle 1 0 0 or bigger this. So if you have number of planes ions are hitting so it is trying to go deeper by actually going through number of planes where atoms are actually situated, silicon atoms. So what we say typical distance between the two planes of silicon is around 2.5 amstrongs or 25 maximum 2.5 nanometers okay or 25 maximum distance in this cases. So let us say the range whatever is the range of ions gone in divided by number of distance between a plane is the number of planes through which and ions are going through. So I divide range divided by the distance between the planes okay this is the arbitrary number this can be 1.25 2.5 amstrong and then the number will be even larger planes thousand planes will be involved. So as I start actually putting the ion in it interacts with number of planes and then come to rest. So in a given range and distance between plane is known so I know how many planes it has actually crossed okay is that okay. If this is my range and these are my planes so I know in this range if the spacing is known I know how many planes it is actually interacting. I want to know for every plane interaction how much energy it loses, ion loses. If I know one per plane is so much and I know so many planes then I look at total energy should be same as which I started with okay. So let us see what it is. Okay ion number of planes ions are entering and interacting losing energy and going through and through okay because all energy cannot be given to one single plane atoms so it keeps moving okay. This is particularly true for heavier ions lighter ions are very small amount of damage and required at 600 degree itself so we do not care too much though it may be deeper but we do not care very much okay is that okay. Now energy loss per plane is the implanted energy divided by number of planes. Let us say I have a 30 keV implant or 300 keV implant divided by number of planes is the actual energy loss per plane okay 300 keV has to go range means what the energy goes to 0. So if 100 planes required to reach this much range that means per plane is divided by 100 energy. The assumption is every plane actually loses only that much energy which is not very valid assumption but greatly okay. So initial implantation energy divided by number of planes is the energy loss per plane. Let us say number of atoms involved in interaction is n then actually number of planes into energy loss per plane please what do you mean by atoms involved in creation of Frankel pair okay creation of Frankel pairs. So it is number of planes multiplied by energy loss per plane into twice ed is the displacement energy required okay and twice because one on this side probability wise both side it can move so it is called degeneracy factor so 2 okay. So 2 ed so if I say number of planes 1 upon 2 ed initial implant any number of planes so this this cancels. So essentially I could have said directly but I just showed you how game goes. The number of atoms involved to create Frankel pairs is initial implant energy divided by 2 ed or 2 for creation of Frankel pairs. An example is a 50 kV implant of a heavy atom arsenic or anyone will displace silicon Frankel pairs 15 to the power 3 divided by 2 into 15 so roughly 1700 atoms will be displaced Frankel pairs. Is that correct Frankel pair means one silicon moving is creating a vacancy is that clear. So a Frankel pair 1700 atoms will be required to lose 50 kV of heavy ions in a silicon is that clear. So this number is not very small but in the 10 to power something this number is very small so the damage is always localized okay damage is always localized. So I can now find that whenever I will do this anneal 600, 800,000 for each of this ed correspondingly Frankel pairs will be varying and as the Frankel pair is moved impurity ion which was hitting that may actually occupy the vacancy and releasing the silicon. So it is substitutional itself during the Frankel pair motion so how the ions activate during anneal the pairs are moving and number of pairs I just now 1700 for example example I showed. So there impurity ions will keep on these are apart from what this is at the surface only the rest is anyway silicon available okay. At the surface whatever is the damage the recovery of damage also allows me to ionize that part okay so I get substitutional impurity actually getting into sites okay. So damage and activation is together so it is good we do not have to twice anything we do anneal once and all that recovery as well as substitutional thing is done in one go. Only thing is if it is 10 to power 12 dose I may have to do different temperature 10 to power 15 dose which is very heavy dose I may have to do much higher temperatures is that clear. Higher the dose the number of atoms which are impinging are very high so the damage will also be high so you will have to anneal at much higher temperature. They are not given but book has given typically it requires 1.1 picosecond to generate one triangle pair. You know the kinetic energy you know velocity by that you can evaluate typically 0.1 picosecond is required to create a pair okay so you can see how fast this process takes place okay. So we only are left with now the machine which we will start next time that is Friday which is not big one and after that we will start with the actual please do come on Friday and Saturday. We are actually going to show you how silicon IC is going through 16 mass process and chip is actually fabricated okay. There are 2 processes I need which is etching as well as metallurgy and depositions right now assume we can we say we can do that and we will continue doing the full because I want to first show you how IC is made okay. That is given in plumbers book so I will actually follow it but I have already shown you diode I can show you a transistor so now I will show you how a normal MOSFET is created CMOS okay. So is that okay implants now only thing left is implant machine which is very interesting