11. Dopant Diffusion - Review Atomic Scale Models, Profile Measurement Techniques

Key Takeaways

this is um today's lecture is going to be the final lecture on chapter 7 it's not the final lecture on diffusion we're going to continue talking about diffusion once in chapter 8 once we've talked about iron implantation um but um this will finish up chapter 7 so hopefully you you're finishing reading that chapter at this point um the Fusion's uh probably the biggest topic we cover in this course in terms of sort of the overall complexity and the depth of the modeling uh so there's a lot of points I want to cover or just try to review from last time the last uh lecture was pretty dense there was a lot of material to cover so what we talked about um last time was that there are these so-called uh FY level effects um or high concentration effects and electric field effects and that both of those become important when the carrier concentration either n or P depending on how the material is doped when either of those carrier concentration ations uh is greater than ni n subi at the diffusion temperature then these high concentration effects become important the um the basic idea the model that we have is that the FY level as it moves up and down in the bank Gap in response to the doping level depending on how you have a doped it uh as it as you doped more heavily it tends to increase the point defect concentration uh as as the doping uh increases we know we've seen that in one of your homework problems you had to calculate that and the increase in point defect concentration then increases the diffusivity uh of a dopin and this leads to or it can lead to generally more box-like shaped profiles because as the dop and diffuses as you get out to the sort of the edge of that profile the concentration is dropping and as the concentration of the dopen is dropping the fmy level's moving the PO the total Point defect concentration going down so you tend to get these very steep falloffs uh in your profiles so in addition to this this is this leads to this concentration dependent diffusion um we talked about effects like oxidation enhanced diffusion which is abbreviated OED oxidation diffusion o um and the growth or shrinkage of stacking faults and these phenomenon can be explained not by not by looking at fixed law per se or whatever but by looking at atomic scale sort of diffusion models um and in fact uh what we we talked about last time is that uh based on um the uh impact on uh oxid on stacking faults that oxidation we people believe injects excess silicon interstitials into the into the bulk while thermal nitridation which again you may not be as familiar with nitridation that's basically the reaction of the Silicon surface with a gas like ammonia to create silicon nitride that process is believed to inject vacancies uh into the bulk and based on monitoring these processes people believe that Boron and phosphorus diffused primarily with interstitials so they have an F subi number um in the fraction interstitial contribution to diffusion of one and animony diffuses primarily with vacancies so its f subi is pretty close to zero maybe 02 so today I wanted to review these atomic scale mechanisms because we kind of brief through them at the end of the last lecture pretty fast and then I want to go on to uh some new material and just give you um a brief example or a brief look at one example of how um the point defect gradient we talked about this last time that not only does the dopant gradient drenic by DX but the point defect gradient for instance the interstitial gradient can actually drive diffusion in a way that actually looks like uphill diffusion so it's it's kind of a non-fickian um phenomenon and this leads to um uh a phenomenon in mosfets uh that's called the in in seos scal it's called was called the reverse short Channel effect and I'll just introduce that we'll talk about it in in in subsequent lectures in more detail and then the second half of the lecture we're going to talk about profile measurement techniques how do we measure all these complex profiles uh what's the best way to do it okay so let's review a little bit on this atomic scale mechanism and what I would encourage you in thinking about the atomic SC mechanisms rather than just looking at this particular um very static uh lattice and and imagining um how atoms might move maybe sit down with a piece of paper start out and draw yourself a simple two-dimensional lattice draw a silicon atoms everywhere except one point which you call your vacancy draw um a blue atom or or a pink or red or whatever which you call your your um arsenic dopin or whatever it happens to be and draw a couple time steps for yourself and and see if you can figure out how this Arsenic atom this dopen atom a and the vacancy together by staying in close proximity to each other uh can can move throughout the lattice give yourself a couple time shots and I think that will help understand how these uh things move together um so in this me in this vacancy assisted uh model or mechanism what we do is we say a where a is a dopen it could be Boron phosphorus arsenic animony we combine that with uh a vacancy which is pictured here uh an absence of a silicon atom and it forms a pair AV okay she said well that's fairly simple what's unique uh uh about this well here a is a substitutional dopen atom this pair AV is mobile the do substitutional dopen atom a is immobile so what we're saying is that dopin and silicon do not move they do not diffuse this is the Assumption unless they are paired with either a vacancy or interstitial but if they're just in the latus and there were no vacancies around no interstitials around the dopant won't diffuse so this is a hypothesis that we're making and we use it um to basically model all the diffusion uh of dopin and silicon so here's the example of being paired with a vacancy obviously the dopent here could hop into this vacant site the vacancy can move up here where the dopent was now what happens well the dopent can stay put for a moment the vacancy can move over here to this lattice site and a silicon atom can move there uh the vacancy can continue it can move right here and and this silicon atom would move up there now I have the vacancy at this spot down here at the bottom and the doin atom next to it well now they can exchange places and the doen atom has moved here so it moved from that point to that point and how it got there was just by a couple of steps of the vacancy hanging around nearby as a pair essentially uh and that's how the dopen atom moved without that vacancy it couldn't have similarly there are interstitial or interstitial C uh affected um assisted mechanisms and we write this as a chemical equation substitutional atom a dopent plus a silicon intertial forms an AI pair and it's only this AI pair that can move um and this is an example there are a couple of examples here one is called the kickout mechanism where you have a pure interstitial a silicon atom that's actually in the interstitial spaces it's an extra atom in the lattice and it can come along and it can kick out that dopen atom uh and then they they exist as a pair and then the dopen can kick out a silicon atom and so kind of Move Along can imagine them this pair always one of them either the dope or of a silicon atom being um off site uh so to speak uh that's one mechanism the other is an interstitial CA mechanism it's a little bit the distinction is a little bit different the interstial mechanism is this atom that's here in the interstitial space is presumed to be not bonded not calent bonded in any way in the interstitial C mechanism the idea is that a dopen atom and a silicon atom are kind of both bonded both sort of sharing part bonds they're sharing an um a substitutional site if you want there's an extra atom there because there's only supposed to be one atom at that site in the lattice there's two of them one of them happens to be silicon one happens to be a dopen and they can go along um sharing this this can share and then the dopen atom can then share with its neighbor and could diffuse perhaps along Bond directions so this is an interstitial or interstitial C assistant mechanism again unless it's paired with one of the point defects we assume um that a substitutional dopen atom um otherwise cannot move okay so uh last time we also talked about this picture I've showed it several times now but hopefully um you start to become comfortable with it uh what what this exemplifies is that how we use a process going on at the surface in this field to probe the atomic scale mechanism the problem is nobody can really see interstitials they diffuse too fast there's no real way of looking at them with a microscope or something like that that's a problem so what we do more often is um subject the surface to some kind of a process that we feel either injects interstitials or injects vacancies and then we see what happens somewhere somewhere at a distance in the crystal to infer uh or or to probe what we think is going on admittedly it's indirect but if you build up enough evidence uh people believe they can make a case that this is what what's probably going on so here's there are two service processes that are very commonly used first one is oxidation uh and it's usually done locally in order to do an OED experiment you typically don't put one wafer in a furnace and oxidize it put a second wafer in a furnace and have it under inert CU first of all the furnace can not may not be the exact same temperature every run we know they're not perfect Wafers May temperature may be slightly different that'll screw up your whole experiment so typically instead you start with a single wafer to do an OED experiment and you coat part of the wafer maybe one dye area one small area of the chip you coat it with silicon nitride um so it won't oxidize which is a is a good buried oxidation and you have down here um a buried layer some distance maybe half Micron or so uh could be below the surface a marker layer of some dopent that's going to diffuse and you're going to measure the extent that it diffuses so the dark green here is meant to represent the dopent when it starts out at the beginning of the oxidation the light green is sort of the edge or the junction as it appears after some time of oxidation you can see underneath the region where you were doing locost where you locally oxidizing the surface you get a large spread of the Bon layer and this green light green layer is very wide underneath the inner surface this is called inert because there is no oxidation taking place the the Bron doesn't diffuse nearly as much so this is inner diffusion this is OED oxidation enhance diffusion and also schematically in this cartoon underneath the large the area where you're oxidizing these stacking folds these defects are growing because they're adding silicon interstitials to the ends of these defects and here they're just staying put or maybe even shrinking but they're not certainly not growing so um the the key point is that people see the enhancement of BR diffusion uh the oxidation enhancement under the same conditions that cause stacking FS to grow and stacking fall growth is is interpreted to be injection of interstitials because people from materials point of view believe that the way you make the stacking fall grow is to add interstitials so that's sort of the key piece of evidence that links is sort of like a criminal case you really can never find the fingerprints but you have some circumstantial evidence and you put it all together and you convict the the person on trial it's kind of like that the circumstantial evidence and it's reasonably strong is that stacking fols are growing when you're oxidizing borin is also being enhanced aha well interstitials cause stacking false to grow therefore the interstitials are probably causing Boron to diffuse more rapidly that's kind of how the logic goes similarly people have found that nitridation so that's the reaction of silicon with ammonia the he of the opposite effect the Boron actually diffuses slower it's as we say in its diffusion and the stacky folds actually shrink relative to inert um inert uh anals so people feel that nitridation injects uh vacancies and that's how the those simple arguments go so what we say when we want to get to an atomistic level modeling and this is the type of model that that that uh when you're modeling the diffusion in Supreme we say that dopin diffuse and and uh with a fraction F subi so F subi goes from 0 to one of interstitial type mechanism uh and a fraction F subv so which is one minus fi um a vacancy type mechanism so we break down its diffusion coefficient into separate terms there's uh one term which is proportional to f subi * CI over CI star so again F subi goes from 0 to one if you believe the dopen only diffuses with interstitials and vacancies are insignificant you would make ep equal to one like the case of boron or phosphorus um there's and then this term becomes negligible if you believe that it only diffuses with vacancies like animony you'd make F subv close to one if you think it's both well then you propor you proportion it accordingly and how do you figure out F subi and F subv those proportions well you subject the dopen in the Silicon to different uh circumstances of injecting vacancies or injecting interstitials and seeing whether the how much the diffusivity goes up or down uh under those conditions and that's what people have done over the years to try to nail down EPs subi and EP subv um so the da here is the effective diffusivity now it's being measured under any condition but particularly under conditions where the point defect populations are Disturbed or perturbed so this would be during oxidation or nitridation da star what does that mean that's the normal equilibrium diffusivity of the dopen um measured under inert conditions so again when we're talking about diffusion and we're talk about inert what we mean is no oxidation no nitridation inert means nothing that injects excess uh Point defects uh into the into the bulk so by using this equation you can understand how to model OED what happens in OED is that this term CI over CI star the inter the interstitial equilib the interstitial um population uh relative to what it is in equilibrium goes up by some fraction some some amount could be 5 10 times higher that causes the diffusivity to be enhanced by 5 to 10 times um in addition because of recombination interstitials and vacancies can recombine if you pump up the interstitials the vacancy is going to go down so this term can actually go down to a certain extent uh and that's how the model accounts for OED or for nitridation um diffusion because nitritation does just the opposite it enhances the CV over CV star and and suppresses this term and depending on your dope your fi and your FV values it will have more or less of an effect on diffusivity and and that gets modeled in the simulations I actually pulled out of the data out of the literature some data just to show you um some of the classic experiments that took place quite some time ago on uh people trying to determine fi um and f&v and this is a paper by it's a review article it's quite long it's many pages by F Griffin and plumber it's uh it's getting older it was written back published back in 1989 but still that was sort of at the height of people really coalescing all this data on these atomic scale mechanisms so it's a good review article if you want to understand in more detail than it's given in your text about this since that time of course there have been new discoveries and we'll talk about that those newer discoveries when we talk about teed but what people did was this this is particular data I took from fa's article uh this is an experiment on nitr so you're flowing ammonia at very high temperatures ammonia doesn't react as as as at as low a temperatures as O oxygen does with the surface so you kind of have to go to pretty high temperatures that's at one disadvantage of nitridation but uh so you typically see nitridation experiments 900 1, 1100 you know in in order to get reasonable injection so under nitronation 1100° C and there're three different dopin studied here phosphorus Arsenic and anodi and this axis here shows uh the time averaged uh because they do diffusion experiments for a certain amount of time here you could do it for half an hour or 5 hours 10 hours 20 hours and you take the the time average enhancement or time average diffusivity that you get averaged over that time interval and you divide it by um da star so the um the equilibrium the diffusion coefficient measured right next to it in the stripe right next to it uh on the in the near Inner case so if I go um a couple slides back to slide three so the da star they measured right over here by measuring the amount of diffusion in in underneath this region inner region and the da time average they measured over here under either oxidation or nitridation this particular one is nitridation and so if you look at these um uh dopant look at antimony here uh what you see uh at pretty much at all times da over da star is enhanced under nitridation so animon has a strong uh dep on the excess vacancy population uh that's how people came to give eventually give animony um uh F subv number that's close to one arsenic has some effect but not very much uh what happens in the case of phosphorous actually as we inject as we do nitridation we inject vacancies phosphorus diffusion over time is actually it's actually slowing down it's actually now how can that be well let's say phosphorus doesn't diffuse by vacancy mechanism but it diffuses almost entirely by interstitials as I inject vacancies you say well then it shouldn't have any effect but it does via recombination excess vacancies recombine and they reduce the um interstitial population lower than it would be in in equilibrium and that lower interstitial population lowers the diffusion coefficient and so for for uh phosphorus this gives us a hint that fi is probably pretty close to one then you can do the analogous experiment with these same dopin uh with oxidation and see how it it per it uh it reacts during uh injection of interstitials and between those two experiments you try to get an estimate of what this F subi and F subv value um could be so those are some classic experiments people have done and in fact also on the next slide um slide six I've taken a table from that paper that just summarizes at that time uh what was known at the state-of-the-art of the interface processes at the surface and how they affect um the diffusion of different dopant under different conditions and also how they affect stacking faults there three colums here the first and the last we've already talked about oxidation injects interstitials causes vacancies population to go down stacking Falls grow the right column nitridation uh interstitial population goes down vacancies go up and stacking folds shrink um and for either one of these columns you can see what happens say to phosphorus and Boron diffusion now he's he's sort of broken this out to Intrinsic diffusion when n is less than or equal to ni or extrinsic when it's higher in either case when you do oxidation uh phosphorus and Brawn are enhanced um animon is a little um little tricky um actually there's a little bit of enhancement initially but overall the effect is is be believed to be or slowed down um arsonic is a tough one because again its F subi value is going to be close to half it turns out it it can be enhanced uh uh to a certain extent depending on if it's intrinsic or extrinsic it can be so it's a little bit tricky under oxidation um uh arsenic also is enhanced under nitridation so it's it's it's tough that's why we believe that F subi and F subv are somewhat equally weighted depending on the amount of enhancement it's enhanced in both cases um Bon's easier to understand because it's pure it's it's enhanced under ox ation but it's under nitridation so people have um concluded based on a lot of data that the FI is close to one now there's one other column in the middle that uh we didn't talk about in this class and I don't think it's mentioned much in your text but but Fey talks about it in this article it's called oxy nitridation it's a little bit trickier um oxy nitridation refers to the fact that if you start with a thin oxide so you have a thin oxide on the surface and then you nitride that you you subject it the uh to a high temperature ammonia um you are um doing something called oxy you're growing something called oxy nitride it's not pure nitride it's not pure uh silicon dioxide it's kind of got both silicon oxygen and nitrogen and so people believe because stacking faults grow people believe the interstitials are injected and it vacancy population goes down but it's it's uh another marker uh another process people use it's a little bit harder in some ways to interpret so that's the of some of their classic data um if I go on to slide seven now I want to talk about some what I think are some very clever experiments what we've talked about so far when I've been showing this cartoon I've been showing talking about onedimensional so I've I've been assuming I'm very far from the interface between the neutral or or the inner ambient and the uh reactive surface so so far I haven't talked about what happens in the the interface but you know as you're injecting the interstitials here due to the oxidation they don't just diffuse straight down they diffuse out in in a two-dimensional fashion right they diffuse down sideways over to the edge so they're they're actually diffusing in in different directions now if you're far from this Edge You Don't See Much effect uh of the inner s they primarily go uh down but if you're near the edge here you're going to see some Edge effects the and in fact um depending on how far from this stripe you know the enhancement of the oxidation occurs give you some idea of how rapidly the interstitials are diffusing in this lateral Direction but there's another process besides just the fact that the interstitials are diffusing around so they're going vertically and horizont and laterally one other process is recombination that we have to consider so in fact the interstitial flux into the surface is is the difference between the generation rate there's a certain number of interstitials being generated per unit time that's G there's a certain number of interstitials being recombined at the surface period of time that's R the net Flux Of intials injected is is you can think of it the net fluxes if G and R are fluxes is G minus r okay now the the problem and we we know that the generation rate here is proportional to the oxidation rate but the question is in your mind the recombination rate at this point here at this interface is not necessarily the same at the Active oxidizing interface is not necessarily the same as the recombination rate at the innert interface for one thing this interface is changing it's continuously reacting and oxidizing so it's not clear that R should be the same here as it is here in the inner and in fact um it's not necessarily the same depending on the reaction it can be quite different so when we uh in Supreme you'll see that various parameters there'll be a diffusivity for the so interstitial you need to know that there'll also be a recombination rate sometimes they call it K Subs there'll be a recombination constant associated with this oxidizing interface and there'll be another recombination constant uh associated with the inner um uh interface and there'll also be bulky combination we need to know those three parameters if we're really going to understand what this lateral extent of the oxidation enhanced diffusion looks like because after all if I'm getting a lot of surface recombination over here uh interstitials injected basically they're all get sucked into that surface and recombined so the net exis interstitial population will fall off more rapidly um and here's an example on the right of a test structure that um people came up with to try to study two-dimensional effects and I I I think it's it's kind of a neat um test structure what they what this is in cross-section now so it's a little tricky but I'm looking at three different cross-sections so this is the surface of the sample this is a phosphorus uh Junction that's been that's being uh that was initially diffused in so it has a starting Junction depth say of half a micron whatever phosphorus diffused into lightly dope boron and they put stripes on the sample and the stripes are masks such that the open region where they cut away the nitri these open regions uh these open stripes are getting smaller and smaller as we go from left to right so here's a a pretty wide open region narrower narrower until it gets to the point where it's a very narrow open region um so the nice thing is what you're doing is you're you're sort of um changing you know the region over which you inject these Point defects and then they did the oxidation they did the oxidation of phosphorus and what they see is the junction depth now which would initially was flat because the it was diffused originally before they put the stripes down after they put the stripes down and they do oxidation right underneath where the oxygen oxidation takes place of course you see a big enhancement of the phosphorus that's OED but interestingly look at the the shape um as you go to different uh opening widths uh of these open stripes um the overall Junction depth kind of reaches the same point here uh regardless of the width of um or the the width of the open area it's sort of it's changing a little bit in shape but but nevertheless it reaches the same Junction depth so what's that saying is that at this point down here the interstitial concentration or super saturation at the little tip here is about the same as it is here it's about the same as in here as is here um and so it's not that much perturbed by the presence of all around it these interfaces these inner interfaces um so the recombination probably at the oxidizing interface and at the inner interface those rates are probably fairly comparable when you're talking about interstitials but let's look at the other case here's another example they didn't experiment like that but instead they started with an antimony Junction so this initial starting Junction depth looks similar but it was animony and what do they see as they decrease the opening width in fact the overall um Junction depth even right below the opening directly below it actually goes down this is for nitr of animony unlike here where these tips all stayed uh the end of the junction was the same regardless of stripe width here it's actually going down so what what's that saying that's a two-dimensional effect that's actually saying that directly below this opening where the nitronation is taking place locally the super saturation of vacancies is actually smaller than below an opening that's much wider so these super saturation of vacancies must be being impacted by recombination that's taking place on either side of that opening and in fact people believe that the vacancy recombination rate here at these innert at these inner interfaces is a lot faster than it is at the nitriding interface uh and so the vacancy um super saturation level um is actually impacted at the center point by what's happening all around it so it's it's a two-dimensional diffusion and recombination problem and there are a number of parameters there's a diffusivity the point defect there's recombination at this surface there's recombination at the um uh at the reacting surface and there's re accommodation in the B so it's kind of a neat way looking at things even with a one-dimensional test structure one I mean we only have all we have as one dimension here that we can measure um uh essentially The Junction depth but we can get two- dimensional information by changing the stripe period so actually if you go on to slide number eight I also took this from that same paper by F Griffin and plumber and this is um a little more U quantitative uh description where they've actually done diffusion modeling of this two-dimensional diffusion problem two-dimensional diffusion of the interstitials being injected and recombining and what effect they would have on a dop and diffusion so it's a little bit tricky here but what what you're doing is a local oxidation out here on the wings there's nitride which is is hatched region underneath the nitride that's inert right there an inert uh interface so that's masked um now what they did was they're looking at simulations for case A and B and case a is when um The Mask opening is fairly wide so the mask opening case a goes from here to here case b is you imagine the opening in The Mask to be very small so the region that's being oxidized is is much narrower and they did the simulations um for the two cases A and B so a is the case uh these two curves for a wide opening and B is for a narrow opening but there are two different types of Curves here there's the solid and the dashed in the solid curve what you see what they assumed in their simulations is that that they assume the case of s value or the point defects where we combining more slowly at the inner interface compared to the oxidizing interface so they're saying there's not that much recombination over here at the iner interface compared to the oxidizing when they do that when they adjust those recombination uh surface recombination velocities in that way what they see is when you change the stripe width from narrow to wide the opening you get um profiles that look like the solid lines where the bottom at the very center of the stripe The Junction depths are almost the same um which is the case if we go back just just uh go one slide back to to slide um slide seven it almost looks like this phosphorus case in oxidation The Junction depths regardless of the width of the opening were about the same and so you can actually fit this shape this shape right here to the experimentally measured shape by changing the ratio of the surface Rec combination velocity at this oxidizing interface to the inner in the dash lines what did they assume well the dash lines um show the case where the surface recombination velocity of interstitials at this oxidizing interface is about the same as the non-oxidizing so they made them equally so if it recombines equally um in this interface versus that interface in fact what you see for a narrow stripe is that the overall um Junction depth is is uh much lower than it is for a wide strike so the enhancement is much less so this actually people use the shapes of these Junctions as a function of of stripe width to say something uh to infer about the recombination velocities at this interface versus at the inner interface just by changing the duty cycle um so this is how in Supreme 4 if you look at some of those coefficients this is how they were actually measured it's kind of a clever uh experiment slide nine is actually showing you some experimental data again just to give you a feel maybe from a different uh vantage point it's a little bit hard to see this but this is a um a photograph from a microscope and you got to get your used to seeing this it's been beveled and stained so this surface up here that you're looking at is the top surface of the chip this surface down here is the bevel so if actually um I could find a piece of chalk there happens to be one here which is kind of rare but so what they do was this is the top surface this region here has been beveled at some very shallow angle um and so um the top surface here has the stripes on it so in the microscope if you look at the top surface it looks like this so these are the regions here um where the oxidation enhanced diffusion took place right here's a 50 Micron opening 25 20 10 all the way down to four Micron opening this phosphorus this region it turns out you can chemically etch um the Silicon surface and it stains so you get a different surface appearance on the microscope where it's end type and so you use this this is a really old-fashioned way of doing it but beveling and staining the Silicon was a way to measure the junction depth um because you could actually measure it basically by doing this at a shallow enough angle you can spread this out over a long distance distance such that you can see it in an optical microscope um so this was um just to give you an idea of what the junction exactly looks like you know under a wide opening looks like this under a narrow opening at four mic it's about the same depth so this um this was experimental evidence that people used and then fit these Supreme profiles we go back one shape they fit to the that shape and they found that the model looked more like the solid line model so they could actually fit the recombination coefficients based on um some of this data so it was a relatively it was a clever experiment relatively simple techniques uh oxidizing uh patterning and beveling staining were used in some of these original um experiments um done at high temperatures okay so that's to give you an idea of how some of these experiments were done uh originally now let's talk about I want to talk about a specific example that we kind of re through last time uh when we were doing uh towards the end of the class notes let's talk about boron diffusion uh and we're going to say that Boron diffuses um based on all the data that people have with only two point defects of all the point defects it could have as pairs these are the two that it prefers uh it prefers an um a neutrally Charged interstitial silic ntial which we write as i z and it pairs with that and so we have a b a boron minus again that's U Boron substitutional and theatis is an acceptor um so it has a NE negative charge when it's substitu theatis it combines with a neutral interstitial and forms a pair bi super minus it's minus because the net charge on that pair if you were considered as a pair is one negative uh net electron charge uh so it likes to do that or Boren might like to to um to pair with um a positively charged intertial particularly because um the um concentration of these interstitials tends to go up uh in in high doping concentrations but even in low doping concentrations you can see there might be some kind of kulic interaction a boron minus uh um might pair with a positively charged interstitial and form a bi pair the pair charge of this particular pair now is actually neutral as a pair so we have two of these sort of simple chemical reactions and they give rise to fluxes of mobile species so remember originally on the left hand side the born is immobile one of these one of these guys comes along pairs with it it's now it's it's Mobile on the right hand side and we can we sum these two the flux of these two and we say the total flux of boron in the sample is going to be the Flux Of The B minus pair and the bi um neutral uh uncharged pair so that's how uh that's an example of of uh you know how Supreme U might consider this at least from a chemical equation point of view so given that that's those simple two equations and all that we know about deviations from fixed law I showed this last time but again I think we went through it a little too quickly on slide 11 um I just want to show again the overall equation that Supreme 4 is solving for Boron assuming it's diffusing with just two spe two species with neutral interstitials and with positive intertial this is the actual um flux uh uh so-called diffusion equation that that um that Supreme is solving and it's a far cry from what you would think in in a simple case you would think it would just be DC Boron or uh partial T if you want is equal to um the diffusivity times partial concentration of boron with respect to X um this is what you might think a simple that's the simple version of boron diffusion when we started this chapter 7 it's just regular old gaussian type diffusion that equation looks pretty simple compared to that one up on the uh on slide 11 and this is actually this what what Supreme is uh is solving so where do all these terms come from um rather than deriving it let's just sort of examine and see if we can understand based on what we've talked about what the different effects are that are causing it to to have this large term here in in curly brackets well the first thing you can notice is um uh D the concentration of Bon respect to time is the D by DX of a flux right that that's that does hold everything in curly brackets here is represented by a flux the question is why does the flux look so complicated well the first part of the flux there's um a term that depends on um DBI star so what is that um that is inert low concentration diffusion um of boron just driven by the Boron gradient itself so that that would be equivalent to this D up here so that's sort of a simple uh uh the simplest uh part of the of the equation uh but multiplying that DBI star there is this interstitial super saturation coefficient CI over CI star um appears right here um and again that's because we're we're we're trying to take into account here these non-equilibrium effects this was sort of an equilibrium uh diffusion but um of excess silic interstitials and that we have we have pair diffusion so there's CI over CI star here um uh and it's gradient and and it's gradient um is is in here as well um there are high concentration effects on the dopa diffusivity so this you recognize this thing in uh parenthesis is 1 plus beta p over ni 1 plus beta that whole thing is fmy level effect that's the high concentration effect remember beta was the ratio of Brawn diffusing with the u i star divided by um the ratio diffusing of neutral uh interstitials uh and so as what happen as this kicks in as p r ey gets large it's going to bump up the diffusivity the effect of diffusivity so if you want you can think of all these a lot of these things here up front these three terms as all multiplying the inner diffusivity by some number that's going to pump it up or maybe pump it down if CI over CI star goes down uh under injection of vacancies and this last bit here this partial partial X of the Lin of everything in parentheses that came uh you covered last week uh when Maggie was lecturing that's the electric field effect um just the fact that besides the the just the gradient of the uh of the concentration gradient that drives the fusion we also know electric fields we can have a field AED term um um so that's where that this last term is coming from so you can get a feel for where all these terms are coming from it's a fairly uh you can't imagine doing this by hand to solve this equation obviously you're going to have to do something uh on the computer something numerically okay so let's go to slide uh so that that kind of um gives you an example of the bwn case now I want to give you an example of um the case which is a little bit strange um puzzle paper for a long time but now is understood as an example of the impact of the gradient in a point defect not the gradient in the in in the in the dopent itself but a gradient in in injected Point defects how they going to uh change the device open profiles and uh we're going to talk about this in much more detail once I talk about iron implant damage but just want to introduce it at this point to make the point um that the grade uh in the point defects can drive diffusion as well um there is something called the reverse short Channel effect that puzzled people for quite a bit in the early 90s and end up being explained this electrical effect in device is being explained by this this uh Boron pair diffusion Boron interstitial pair diffusion so before we talk about reverse short Channel effect which sounds really weird how about what's the regular or the usual short Channel effect we we talked about a little bit uh several lectures ago but basically um uh the usual short Channel effect is for a given process the threshold voltage goes down as you decrease the L so for a given process on chip as you look at smaller and smaller devices made on ship you tend and you plot the threshold voltage uh what you'll see is it rolls off it generally the VT goes down it becomes easier to turn on the device and here's a a book a textbook if you want to go through and some of the um understanding some of the physics but basically um what happens is um as you bring the source and drain closer the potential due to the drain actually starts interacting with the potential in the channel and it starts having um it starts having an effect ordinarily you'd like uh that not to be the case you'd like to have just the gate uh have the only effect so the lowering of the potential barrier by the drain voltage uh is what causes uh this um uh causes this uh VT to go down as you shrink the channel length and that's very much how much that barrier potential barrier can be up raised or lowered is a strong function of the profile of the Boron say in an inet um underneath the channel so in fact if we go to slide 13 just again I took this from Tower and Ming's uh book on fundamentals of modern devices for the for the device physics again you don't have to understand the detail but just gives you an idea where this comes from Imagine here I have this is my source my gate up here and the drain over on the right and this distance zero is right at the source injection point and L is the channel length so that's right at the drain and what what he's plotted here in this book is the surface potential so that's the potential uh at the surface that a carrier would experience um as a function of distance along the channel so here at zero you're just starting in the source and it looks something like this curve a is for the case of a six Micron device curve B is a 1.25 um at say half a volt and curve C when i i u drain I put a drain bias of 5 volts what happens actually the potential even in the center of the channel instead of just being the potential being lowered in the drain it's actually because it's a short channel the potential is actually lowered here um and so it's that ability of the drain voltage to sort of impact things that um is a short Channel effect and and is partly responsible for the lowering uh of the VT so the way people when you scale device is short the way people counteract this is they they dope underneath the channel they counterd dope it more heavily with the opposite doping so uh they add more Bon uh for example if you were to add more Boron there'd be much less of this effect uh of this this potential being impacted by the drain so there's a tendency as we as you scale devices smaller and smaller you'll see the doping in the channel if you go on the itrs road map every year it goes up 10 to the 7 mid 10 to the 17th 10 to the 18th mid 10 to the 18th as we shrink devices um so people counteract this short channel the normal short Channel effect by upping the doping in the channel well what people saw was the reverse short Channel effect which was which was confusing people is that um for short Channel lengths on the chip it was actually found that the threshold voltage actually increased in a certain range of Channel lengths so as they Shrunk the channel length in a certain range VT actually went up almost as if the doping in the channel was getting higher in that range so all these devices are fabricated on the same chip subject to the same temperatures you know on the same wafer same iron implants everything why would it be the doping would be different in the center of the channel depending on the channel length and people were were mystified by this for a while um so the reverse short Channel effect uh basically look something like this and this is kind of a a backwards plot but it if you plot threshold voltage now this is on the right Axis inverse Channel length is increasing this way but if you want to look at the upper x-axis it's helpful the uh the channel length is here on the right going from 0 2 all the way up to one micron or if you want if you're shrieking the device you're going from here to here um so as I'm shrinking down here from say a 10 Micron device down to one micron look what's actually happening from 10 to 1 Micron um actually it's easier to see it if you look at the um the closed squares from the experiment the the VT was actually going up from about 1.1 volts up to 1.2 or 1.25 volts just significant increase so your shring devices from 10 microns uh uh or five microns down to a third of the Micron VT is going up that that's opposite of what everyone had expected from the old days from the regular short Channel effect so um uh people call this the reverse short Channel effect and in fact people were able to it turns out there a paper in 1993 at EDM from RAF they were actually able to explain this based on um simulating what they thought the Boron profile would be in this n mosfet in a case where there was Transit enhanced the fusion and we haven't yet talked about teed but basically um what they found was that the source drain implants were injecting excess interstitials and setting up fluxes of interstitials that were then driving the Boron which was originally buried driving it closer to the surface and if you made the channel shorter this uh this effect was even greater basically because you're bringing in the center of the channel is being brought closer as you change the channel like closer to the source drain regions where the excess interstitials were being pumped in uh so but in either case whether it's due to OED or teed the the point was that they were able to explain based on these diffusion models that more Boron more ptype dop was ending up in the channel region of a short device say of a.3 Micron device then would be in a one micron device more Boron means instead of the channel the short Channel effect and the VT rolling off actually there was so much extra Bor the VT was going up um so the electrical engineers and the circuit people who would see these weird VT variations with Channel length and didn't know about the processing were were mystified as to how this could be happening they just assume well the B concentration is the same on a short device and a long device well actually it's not um it can vary and of course that that can be that means you need these more complex models that haven't take into account Point defect injection from the size in order to be able to model the Boron uh profile accurately and to get the device BT right so that's sort of a a classic example of how these complex models impact device performance um and in fact here's a cartoon explanation on slide 15 um where we uh this is a two-dimensional um Supreme simulation of what's going on in the reverse short Channel effect and what's being shown here is relatively short device short Channel length and um the different colors are the different Contours um corresponding to constant doping concentrations and if you just for a moment imagine this is the drain over on the right you see this is this little region here is the drain extension um and down here is the Deep drain here's the The Source extension in the Deep Source extending down to about this uh blue color region um these arrows that are emanating from the source and drain they are interstitial fluxes that coming from the surface of the source and drain these interstitials people believed in this particular model were being injected due to the damage due to the ion implant we're going to talk in the next few lectures about ion implantation and how it damages but just take that with a grain of salt that you believe that there was a process that introduced a lot of ex interstitials only in these regions not where the gate was so these interstitials were coming in and they were diffusing all around so these arrows represent interstitial fluxes and they're recombining at the various interfaces now look at this interstitial flux here that goes like this this Arrow points this direction and goes up towards the surface so this interstitial flux this gradient of interstitials where a high concentration here and going down at this point that gradient of interstitials was actually dragging the Boron with it was actually dragging the Boron with it um and moving the peak Boron profile from where it originally was more deep in the sample moving it up towards the surface so in a short device it was causing the Boron to be higher at the surface and it so this is a two-dimensional representation if you take a cut straight through the center right here at at um x equals 0 and look along the y direction in the vertical Direction um you can see um three different curves on this plot so this is a plot right to the center the concentration of boron versus depth into the device so zero would be right at the at the Surface by the channel and there are three different curves here the red one is for one micron and you could see it Peaks here at a certain depth um one micron Channel length the blue the dash blue is quarter Micron Channel length and the dash green is um a 0.18 even even smaller so and indeed what the model's predicting as I'm going to shorter and shorter channels the amount of borin at the surface is going up here by a factor of almost three so like that 3 to four so indeed if you increase the Boron concentration at the surface of a mosat by a factor 3 to four the VT is going to go up it's not going to go down um and how can how can the channel length impact this well it's directly through this mechanism the normal fian diffusion the simple version of fixed law there was no way people when they use the simple models they can get that to happen as a function of this channel like they had to invoke some other thing uh to to take an original G like Boron profile peaked right here and then in fact move it um in closer to the surface in fact if I if I you just looked at these diffusion profiles and I didn't say anything about interstitial fluxes I just gave you these three profiles and I said okay look at is that GA and normal Gan fian diffusion it can't be right I mean uh uh for for normal fii and diffusion um what happens is as the profile gets broader sure it gets broader would you get more diffusion when it's driven by the by the uh flux of the dopen um but the peak doesn't change right the position of the peak in normal fan diffusion never changes if you did your homework and you did the Gan diffusion you found sure it goes down with time but it's not like the peak shifts over to the left to the right it's like weird um if it's driven by its own concentration gradient by definition the peak doesn't shift but here's example diffusion where the peak was actually Shifting the only way to explain that is some non-fickian sort of phenomenon in fact people use this pairing the fact that bwn diffuses as a pair with interstitials and the gradient of interstitials was dragging the bond so much so that the peak of the barn was moving towards the surface um so we're going to talk about this in more detail when we do ion implant damage and how much interstitials are injected and all that but it just gives you um I think it's a nice example of how the process Engineers got together with the device people who couldn't figure out what the heck was going on and uh developed a model process model that actually could explain pretty well what the VT um and predict ICT what it should be okay so that's what I want to say now about this uh diffusion I'm going to go on in slide 16 and talk about profile measurement techniques I showed you some really old uh photographs from plumber and Fey in the in the late 80s and I they talked about beveling and staining that's one way but it's um it was cheap and and relatively simple but not totally sophisticated um but uh let me give you some more examples um it's really critical you can see from the examples I've given you to have some method of measuring the dop and diffusion profile as it goes from the surfaced into depth in one dimension and actually if we're going to explain uh the reverse short Channel effect like this we really need a two-dimensional map of where the all the dopin end up that's not trivial one dimension is pretty sophisticated there are a number of methods um probably one of the most sophisticated right now that you will will use in your research or people use in in the fat or in semiconductor um uh fabrication is secondary ion Mass spectrometry I think we've talked a little bit about Sims already but that's probably the number one technique and it's it continues to improve it's improved dramatically over the last 10 years as devices have shrunk as Junction depths have become narrower and narrower they found a way to make Sims a higher and higher resolution um Sims only gives you the physical number of atoms of arsenic or Bor on per cubic centimeter it's the physical chemical amount of atoms in the sample at any given point uh in depth sometimes you're interested in knowing not the number of arsenic ions but the number of electrons at that point per cubic centimeter those are different remember arsic you can put a lot of um of dopen in but not all of it may be electrically active or it may be compensated by the presence of boron or another dopen so there are electrical techniques like spreading resistance we'll talk about one-dimensional CV and differential Vander paaw these meas of the carrier concentration that's not the same as the dopent concentration so 1D though is reasonably sophisticated a two Dimension uh is still kind of tough the methods are still being developed they've certainly gotten Beyond The Junction staining methods uh but they're generally indirect methods they're more difficult and this is an area where a lot of research and development is trying to is is is taking place just to develop the Metrology tools and techniques here's an example of some 2D techniques I'll show you cross-section transmission electron microscopy is a way of visualizing Junctions with chemical etching it's like the the modern analog of the old Paul 8 Days look in a microscope after you stay in the junction but it's much more uh it has dep resolutions that are factor of 10 to 100 higher uh resolution there scanning probe microscope microscopy I'll talk about and the last one is inverse modeling this is kind of a funny um uh a funny one but it's actually um it can be very uh can be very useful in complicated cases what people do is they look at they take a device they take its all its current voltage characteristics its capacitance voltage characteristics they put them all in one giant database and think about it and try to figure out given all those characteristics what must be the doping profiles so it's it's an inverse technique um unfortunately it relies on knowing really detailed electrical models because you're really extracting this all from electrical measurements so it's it's not the same as doing Sims or whatever but it is when you get to small dimensions and two Dimensions um it is a technique people try to use okay so let's look at slide 17 and talk a little bit about Sims I've already mentioned that in the past but now we're going to talk about it specifically for depth P profiling of dopin um there are two modes for Sims there's what's called dynamic or static Dynamic is what you typically use dynamic means as the ion beam comes in and hits the surface um it's sputtering away significant amount and it continues to go deeper and deeper into the surface as a function of time at some constant sputter rate say five anstrom per second it sputters away the surface and you it looks at what the atoms that come off and it ion they get ionized if it puts them in a mass spec and it tells you at any given depth what's coming off Static Sims is a little different the energy and the angle are adjusted of the primary ion beam such that it doesn't actually sputter uh very much it's primarily just taking off what's at the surface so it's very gentle and low energy that's just for looking at just what atoms or molecules are are at the surface uh but for depth profiling of dope is typically using Dynamic simps how does it work for depth profiling well it's somewhat intuitive but and it should take yourself through these three cartoons I think you'll be have a better understanding first case I have a sample of silicon it has some dopent a up at the top in some depth there's a layer of B right at this interface let's say there's a spike of X it's a different uh different dopent or a different contaminant maybe carbon or oxygen and down here it has it's doped with C whatever these three elements are so what happens as I'm sputtering I'm bringing in my initial ion beam it starts to create a crater and it constantly is cratering the sample and you're looking off as a function of time you're looking at what atoms come off in a spectrometer so if you look at the intensity as a function of time the spectrometer can scan several different masses well lo and behold it finds over the for this time period it's it's um while it's sputtering through this cap region it just detects dopen a when it gets to this interface right here it's starting to sputter off not only a little bit of dopen a and and and but a little bit of B and also X Pops in um and then as you continue to crater down when you get into this point you're you're you're um sputtering off B so you're you're linearly in time sputtering through the sample and you collect as a function of time the intensity so that's what you get out of simps you don't get dope and concentration versus depth you get the intensity how many ions are coming off per second it counts per second on a detector as a function of sputter time so you have to somehow convert the x-axis of time into depth well that seems obvious on this plot if you know the sputter rate you you figure out you measure let's say you measure at the end you put it in a deck Tac and you measure how deep the hole is the crater is and you assume it's linear in time well then I can figure out how many anrs came off per second I can convert time to depth now that's a big assumption there because what you're assuming is that the sputtering rate is constant throughout the entire experiment and measurement if you have different materials maybe you're going through oxid silic dioxide and then silicon splutter ratees different in those materials so you run into some Distortion of profiles you to be very careful but it's an assumption pretty much people need to make so you convert the time axis to depth intensity that's a little that's even that's even trickier because it's just intensity it has to be calibrated to convert that to atoms per cubic centimeter um so um I'll say a few words about how that conversion is done but let let me first show you just uh I took this off the Charles Evans website www.ca.com again they're a large commercial company they're probably the largest in in the world international company that for a business does uh materials analysis and one of their their big things that they focus on is is dynamic Sims primarily well for a lot of Industries primarily for Semiconductor and magnetic uh Industries but and this shows you um just is is a little thing that they like to advertise uh just to give you an idea of the detection detection limit so the number of parts per billion or the percent of an impurity you can measure um it tends to be related to a certain extent to the analytical spot size so how big is the little spot that you're looking at um and there are lots of different acronyms and acronyms and I apologize for all this if you want to go on their website they have um each one of these acronyms is defined in fact we talked about some of them we talked about earlier in the course we talked about txrf total XY foressence it measures about a centimeter it only measures at the surface and it's good for measuring sort of um in this uh range 10 to the 17th atoms per CC the EM most sense as you go down to get to parts per trillion the only technique that can get get into that range and it's only for certain elements is dynamic Sims you see this little bubble is in this range it has a spot size maybe 10 microns maybe more closer to 100 microns is more typical these days maybe 100 Micron spot size but you can get elemental information um down with Dynamic Sims down into the part per billion and maybe even uh hundreds of part per trillion uh kind of range so it's it's a it's was used for profiling dopen atoms because remember dopen atoms can exist at very low concentrations um 10 to the 14th that could be a typical doping concentration and Sims is the only thing that can measure that right now from a chemical point of view so um the primary ions that that um that that we typically use um I'll just mention there are two primary ones or or or um common ones oxygen as an ion coming in is come in people use oxygen because it enhances the um the secondary ions that come off it enhances the production of positive oxygen tends to strip off electrons um so it O2 plus so it'll enhance the ionization of the um atoms coming off because remember if the atoms come off as neutrals you can't Mass analyze them in a spectrometer so you got to get the atoms off the sample and you have to hope that they come off ionized and the way you increase the ionization yield so to speak um is you you use oxygen to increase the positive ion production it's good for groups one through three if you're trying to measure and the transition metals in Silicon um uh for instance for Boron typically if you're profiling for Boron you use O2 plus beam cesium Plus on the other hand is just the opposite it enhances the negative ion production so it's used um for groups uh four through uh seven H these are good electronic acceptors and they form negative secondary ions so arsic you would typically use cian primary beam so and they have machines set up for these two different so you use a different machine depending on what your profiling yield now the I yields when I mean the ion yields so that's the number of ionized species that are coming off of some elements say arsenic compared to the total amount of sputtering of the Silicon that yield that depends on the Matrix material so if if you have arsenic at the same concentration in oxide and in Silicon at The Identical concentration the ionization yield will be different so it'll come off with different intensities so that's called The Matrix effect so that's a bit of a problem so um you have to uh the measured intensity has to be measured on a test sample that's that's calibrated where you know the concentration and you compare that intensity on the same day to that whatever is coming off of your unknown sample and so it's always calibrated to a known sample and that's one of the big drawbacks of Sims you need standards it's not an absolute measurement technique it's always relative it's only as good as your standards and in fact on slide 21 I have an example of some actual Sims data and how people um quantify the x-axis we talked about quantifying is not too bad you use a deck Tac you assume constant sputter rate you know you cross your fingers and that's how you get the depth scale how do I get the Y scale which was originally intensity I need to convert that to concentration well typically what people do is they take a sample that was IR implanted and again we haven't talked about implantation that's next lecture implantation is electrical means of very accurately controlling the integrated dose the integral under the curve of an element that you implant into uh sample and that that accuracy of that control makes the implanter a very good way of generating Sim standards because the implanter can exactly control the total number of atoms per square centimeter that go into the sample and in fact this was a phosphorus implant at a total dose of 1 * 10 14th phosphorus per square centimeter so that's given as a known so once we know that since we know this area under the curve we can then convert intensity coming off on that given day to a certain concentration of phosphorus so every time we want to measure an unknown so the right hand sample was unknown the leftand sample the concentration was known because it was ion implanted so you use a known Tech known dose so from this uh integrated uh ion implant dose I can generate a sensitivity factor that enables me to convert from intensity coming off to a phosphorous concentration on the unknown sample and so this is this is what I get uh for example on an known sample but you always need a standard which you trust um in order to compare it to and it has to be compared on that same day because the Sims machines their calibrations can be changing from day to day and it has to be in fact a sample hopefully that has roughly the same total amount of peak phosphorus as in your unknown it was dramatically different MIP effects and it should be in the same material notice this was phosphorus in Silicon in a known sample this is phosphorus and silicon in an unknown sample you wouldn't want to use phosphorus and silicon dioxide to calibrate this because the Matrix effect would kill you okay so that's an example of a practical idea of how the Sims actually works um these are some considerations people are very concerned about the depth resolution what do I mean actually let me go back for a minute but but the depth resolution is um let's say this actual sample is really a box let's say it's really a box likee profile what Sims does to it is it smars it out a little the edges are not perfectly straight up and down they have a little bit of uh exponential decay on the front and the back how much that is real is the phosphorus really decaying exponentially or is it really a box-like profile um what effects determine how well I can resolve um the um the profile in depth so here are some consideration the depth resolution depends on the element you're profiling phosphorus or Boron or whatever and the Matrix that it's in because after all the impact conditions remember these primary cesium ions are coming in they're hitting the phosphorus of the Arsenic and they're imparting energy to it um so of course they can knock that arsenic or phosphorus in a little deeper and of course they could smear out a profile um so you try it to change it so you can minimize the amount of ion damage or iron smearing The Sputter depth the deeper you go into that and the deeper you make your crater the more the bottom of the crater gets rough this by the sputtering process is a random process when you have a rough bottom to your crater well you're you're pulling atoms off from slightly different depths at that point in space so the deeper you sputter the the worse the depth resolution for Sims so if you want to measure a sharp profile try to put it near the surface and you'll get a much more box-like profile than putting it one or two microns in where the sputtering process has roughened the bottom of your crater um so but people have improved these days to try to get sputtering uh processes that that are as smooth as possible by rotating the sample and you know rastering the beam and trying to make it really uh a nice flat perfectly shaped crater bottom um so they've done a lot of of techniques also these days they have ultra low energy SS has been developed where the incoming beam has such a low energy it doesn't perturb the profiles too much uh and that's an important uh low energy Sims that's been developed in the last 10 years okay so that's chemical measurements how about electrical well remember I talked about beveling and staining well you don't have to just bevel and stain you can actually bevel just like I talked about before you create this um surface that that's beveled at a certain angle and instead of staining you take two little probes and you measure the resistance between those two probes you you flow a current and measure the voltage drop um as a function of lateral distance along the bevel As you move along the bevel laterally of course you're also moving in depth so you're essentially spreading out by the cosine Theta uh you're spreading out or the S Theta you're spreading out that profile so you can move laterally and and literally it takes the probes and a machine moves it laterally by um certain steps um and you can convert this then to a resistivity or resistance uh plot as a function of depth and you convert resistivity into um carrier concentration so this measures the doping concentration versus depth not the dopent doping refers to the N the electrons are holes so it's complimentary to Sims which provides the chemical uh information um the depth resolution is not nearly as good I mean with with a spreading resistance you're lucky to measure a junction that's a th000 angstroms deep typically uh with Sims you can measure 100 anstrom deep Junctions so um and the big problem is again it needs some standards you need to know how to convert how to from resistivity to carrier concentration so you need to know these curves there's some famous curves on the Silicon website this company silicon does spreading resistance for commercial purposes um you can go on to there they show you their calibration curves but but if you have a material other than silicon single Crystal let's say you have polysilicon the relationship between carrier concentration in and the dopen concentration is not very well understood or if you have silic and geranium there are no standards so spreading resistance is okay uh but it does have some some limitations I won't go through this in any great detail this is shown on slide 25 I'm referring you to I pulled this off the Solon website but in fact even in the most perfect case um you can try to correct the data for um for artifacts by solving poon's equation to account for things like space charge layers where you have an n and a p region meeting and things like that um there's a lot of literature on this but um it's still uh you can see it's measuring Junctions that are pretty deep microns deep uh not hundreds of anrs but it can be used for measure like the well profile and things like that uh slide 26 actually has um kind of an interesting technique it's not quantitative but if you want to talk about 2D it it can work this is a cross-section TM so you're taking you're taking a sample uh from a silicon moset and you've cut it and cross-sectioned it and you've made that thickness of that specimen only about 2,000 an thick a special ways of cutting through and cross-sectioning it and then you set electrons through and you look at their defraction pattern so you can actually image the gate the gate oxide the Silicon um and interestingly what people have done is you take this specimen after you've cross-sectioned it and you dump it in some acid and it turns out the acid etches much more rapidly regions that are very heavily enti so when you etch that region you change the thickness of the sample and you change the transparency of the sample to electron beams so where it's very heavily doped it appears very light the electrons don't they go right through so the contrast the the the sort of the contrast on this gives you good qualitative information and people believe that it delineates this line this dark line corresponds to a concentration about 10 of 19th so it gives you an idea of where the edge of the source and drain might be but it's qualitative and it's very time consuming there's another 2D technique again based on beveling again we go back to the same old bevel idea here's a mosfet with a source and drain people actually take um an an atomic Fork micros Force microscope AFM Canever little tip um and they measure um they measure across where they are across the sample and they measure at at this each point a CV curve so it's like very locally take doing a capacitance voltage measurement where the tip corresponds to the the metal point of the CV um and the backs side contact corresponds to to the back and you're actually measuring you know from CV remember we talked about CV on dots if I put a dot over a uniformly dope sample you know you can extract from the CV the dope local doping concentration well they're doing it but here on a very small scale with a very small AFM tip so uh this is scanning capacit microscopy it's very tricky though on the spatial resolution issues um limited by the probe size you know the tip only so small and then it has fringing electric Fields so the actual area of the capacitor that you're creating with a tip is is somewhat uncertain it has to be modeled with sophisticated um enm modeling but just to give you an idea again this is the website if you want to go there if you're interested um basically uh how it works um on an N type CV curve um basically it it takes DC by DV the derivative of the capacitor respect to the voltage and it can you can relate that to locally to the carer concentration very similar to what you do in in uh 1D CV but now all over over um a surface and in fact here's a beveled Junction where this region corresponds to phosphorus this is the scanning capacity microscopy image so this is very high doped this is the junction region in ptype Silicon near the edge of a mass so here's a mass there's no phosphorus over here that's lightly doped so U It's Tricky it's still under development but it is a kind of um uh a topic you know a popular topic for modern Metrology so let me just summarize about techniques for profile measurement we talked about Sims the most popular it does very good 1D Profiles In Depth excellent has the best sensitivity of any technique to the dopen concentration excellent depth resolution uh methods are still underdeveloped to I to proove it the VAR near surface region is it Troublesome but there have been recent improvements um you have to watch out for Matrix effects if your profiling a dopen in oxide or nitride or silicon the ion yield varies dramatically and you have to it has to be calibrated spreading resistance is only generally mostly onedimensional although people are trying to do it two two dimensional um it has but it measures carriers so the active electrons and holes pretty good sensitivity depth resolution is not great uh um and it's hard to do shallow Junctions and you need to do some electromagnetic modeling to really understand it uh these newer techniques are are kind of exciting these two-dimensional scanning capacitance and scanning resistance microscopy with using small probes um are very interesting uh they they do rely on beveling but um there's a lot of advanced models for the process itself that are being developed in R&D today to try to come up with a better way to get quantitative two-dimensional uh dope and profile uh measurements so summarizing on what we've talked about so far on dopa diffusion um we said that they diffuse by interacting with Point defects vacancies and interstitials uh the diffusivity is proportional to the concentration of those Point defects um these Point defect concentrations go up exponentially as I increase the temperature and so the diffusivity goes up exponentially um they can also be changed by things other than temperature the local fmy level the local doping concentration that is ion implant damage as we'll see in the next chapter can change the point defect concentration surface processes like oxidation and nitridation change it all of these affect the effect of diffusivity so the dope of diffusivity can vary in space it can vary in time all of that means that we cannot calculate accurate profiles in Silicon devices by hand we pretty much have to monitor all that um by doing uh numerical Solutions there's been a lot of progress in the last 10 or 15 years on and getting physically B based models for dope and diffusion um that will actually help you predict electrical behavior um these simulators and we'll talk about more when we we give a lecture on Supreme 4 they allow you to fully couple the diffusion of the point defects so you solve for the diffusion of the interstitials and vacancies and you solve Fusion of the dopin at the same time the problem with all these models is there are a lot of parameters and and so any parameters that you don't know you can get beautiful profiles but they all the parameters need to be calibrated so that's about all I have um for today and if you're handing in your homework 3 please bring it up front um to this folder