 As I said you one of the major criteria of any design in analog is to get the circuit working which has gain that is our most important thing amplification that is what we do in analog circuit. So we want to amplify an input signal which may be very very small in many cases like in mobile others the antenna gives a very very small signals and we want to amplify that. The major activity in any analog design is amplifications. So all our effort initially will be how to do a good amplifier now what is this word good good means what good okay. So we will like to see how do you design a desired amplifier characteristics instead of saying good. There are yes I agree with you filters for example but if you see a active filter there will be some unity gain amplifiers gain does not mean essentially even the attenuators as a minus db gains okay. So in some sense amplification is a conversion of some input to the output in some form you have ever write valid we should have a however here the circuits which I am showing probably have gains there are three kinds of amplifier shown to be shown by me one is a standard amplifier which all of us know. So these are three amplifier shown here the first one which you are seeing here is essentially an amplifier in which there is a some kind of an active device in general it may be n channel device for a MOSFET which has an input and it allows you know some kind of trans conductance through this at the output. So it converts this voltage into some current and through this load current flows in this please remember in a circuit in a arm only one current can flow. So if this is my output arm only one current can flow so whatever is current coming from power supply must go through the driver either. So these two currents must be balancing every now and then the driver current must be equal to the load current because there cannot be two currents in the same arm. So this device which is shown here shows that IL is equal to IDSN and the whatever I am showing here the lower part of this device in case of n channel it is source is grounded to VSS. Now this word VSS will qualify little later we do not say it is ground always what I mean why we says because we may not say it is ground always but in right now let us say it is ground and the load is connected to VDD. So obviously this is a standard amplifier this device can could be bipolar transistor it could be a MOS transistor in any case IR drop here will actually provide you the output voltage okay so very simple amplifier. The other version could be you may have a P channel device or PNP transistor and since you want to keep that power supply same positive VDD. So this is then becomes source then becomes drain for P channel device and the load is downwards and same method one can say the output is now the reason is that I am always saying current can always flow from power supply to the ground irrespective of carriers is that clear whether it is electrons or holes though they do opposite but the net current electrical current external to that is always in unidirectional from positive potential to ground or negative potential that cannot be changed this is Kirchhoff law and nothing much can be done on it still stands perfect. So this is a P channel device so same technique so one can have an N channel device or can have a P channel device both for amplifiers and if we make a combination of the two which is a P channel device and N channel device connected to the gates we call it complementary MOS or CMOS amplifier. So this is essentially to some extent we are now saying that each transistor behaves as load for some time is that correct initially may be this is driver this may be acting like a load after sometime this may act like a driver and this may act or you may say superposition you have N channel amplifier superpose on P channel amplifier each acting load for the other one is that clear so this is a possibility which we cannot use and the advantage we shall see soon why CMOS because we already seen CMOS is one technology which digital has adopted till as I said technology node right now is 16 nanometers so if every circuit is digital which is marketed in heavily at least as a 20% is analog that means 80% is digital so obviously we someone who has majority or power will govern so digital people govern and because of that CMOS is a standard technology do what we may change materials for some reasons for some device or some circuit requirements that we may have silicon carbide silicon germanium silicon here may carbide gallium arsenide indium arsenide indium arsenide gallium arsenide mixtures many things can be done but CMOS may still remain okay and as I said many years for last few years 2030 CMOS is going to stick in any analog design we find there are few parameters of relevance three of course are most common some others will add later the first of course is trans conductance what does that means from the input voltage how much is the output current gets modified by the input signal essentially called trans conduction okay from voltage to current converters are essentially transconducting so the first and most important parameter for an amplifier is the GM trans conductance we will see what values we get in real life then the next very very important characteristics of a amplifier is the output resistance in the case of normal amplifiers which you have seen just now for example this you know this load or this this may be a resistor but in N CMOS there is no real resistor there however you can connect a load afterwards so you can have something like this as external load but the way circuit operates generally in integrated circuit there is no real resistance put anytime whatever is the output resistance of this is useful for the next stage connections okay so what the next stage input resistance is the output resistance of the last stage and that we call as R0 okay so in an integrated circuit not that RL will never be used but in general connections are not through load actually load is output resistance itself is acting like a load so having said so the second parameter of interest for me is the output resistance for the transistor or the amplifier which is R0 and the third and the most important for analog is the noise this and the word I am keep using this for very important when we come to noise we shall talk about is input referred noise though noise can be at the any node okay but we call it input referred noise and that is very major criteria of design how much is the tolerable input referred noise how many DBMs or DBs corresponding to given signal how much essentially it converts into what value we are more popularly known signal to noise ratio how much is this noise that input to noise that output ratio we can get is very crucial for any amplifier okay so this input refer noise is essentially is a basic noise available without external anything and say if that is what is going to change or increase and your purpose of amplification may not be as good okay and the most important other than the gain factor which is the first three essentially a first two essentially gives the gain second one is the noise or worrisome and the third which is the most equivalently most important from digital they say speed how fast the circuit is working 6 gigahertz 4 gigahertz 5 gigahertz here is what we say equivalently bandwidths how much is the bandwidth that means up to which frequency gain is constant or reasonable okay is we say it is bandwidth so for an amplifier we are always designing for a gain noise and bandwidth is that the three parameters which we wish to control if we are able to control these three parameters strictly then I have designed done for my requirement is that if I cannot control or it so happens trying to control one I lose something else then I say but that is with this technology with this this is possible no more okay that is we say figure of merit end of it okay before that how much play we can have as in the case of digital I think you are already learning and you know much about is we can trade off power and speed increase power that means these currents the capacitor charges faster or discharges faster so speed is higher reduce the power reduce the currents slows down however we can meet both slightly by adjusting area this is the game which will be in digital here we have to play game for gain and frequency and third which is not visible immediately is the noise which may actually control both and therefore these three are very crucial parameters in our analog designs here is another slide these are still generic will come to it today most understood little bit so that you know what exactly I am talking about here is a differential amplifier shown to you will actually design and define this semester there are two end channel devices with two loads and this is the biasing current which is called current source and I we are just named them 1 2 3 4 okay areas so for example there is or when we say constant there is nothing called constant in circuits or devices or in integrates drift change okay so one possibility is there is a variation in our we also say the transistors are identical for different this is only statement will be in reality M1 M2 may not be identical in many ways it is threshold may not be same its size may not be same W bias may not be same and therefore they are not identical so there is some kind of a offset relationship if GM it will be related to them so GM may not be same for either M1 and M2 okay so that is another issue which may have to create and of course this so-called constant current source may not be constant okay and if that changes the bias point is changing so if the GM in everything else so if you look at these variations 1 4 and 5 that is VT change drift in this and R values it may change the operating position of the amplifier if you look at the 3 that is essentially the offset because of the non-W bias equivalence then it may increase this change may increase actually 2 devices may be offset by some value we believe that they are same but we are not actually however do not worry in real life offset can be cancer some way or the other okay it is not that there is no way we cannot get rid of offsets what is the price will pay as I increase any as I improve anything I will have to pay for it and that payment may be in the external or extra hardware which I may have to put or extra power I may have to pump to get rid of some of these but that is not that we cannot do that and we will see some of the offset techniques we will use that 2 and 5 which is essentially again threshold variation as well as offsets in GM particularly in GM variation causing because in M1 M2 same way the change in current in the biasing currents may actually need to change in noise and noise is a very crucial factor as I said if you look at the last this one we say one change in R to change in GMs and 5 change in current biasing current all of them can change the bandwidths okay. So the is that point clear why design is an issue because in design I will be given a specification but please take from me if anyone gives you say that I want a gain of 100 you say I cannot design for you okay you say what is the maximum minimum in between the gain can you can expect okay you say okay in a range of 80 to 100 I am fine with it so I can design a circuit which may give a gain 80 to 100 but it may not be always 100 or always 80. So anytime a specs is given to you give design this it is not doable okay so one a spec must come from a customer which is doable and that is one say range must be specified okay so I say okay the minimum gain I expect is 100 so if it is 120 I do not mind but 100 minimum bandwidth I want is so many megahertz yeah that is the minimum I expect but you do not say no it is 2.73 megahertz or 2.73 I cannot do this any design okay there is no way I can control specific values okay if I try one and then other I may not be able to so I always will say you give me some margins in designs so this is the major difference in analysis which we do and the design we do okay but to do a design we must know analysis as a how will I design but the focus should be this that we have to attain specs within a given range that is the trick of the design issue. If you look at the other part which I said gain and bandwidth I just said it but they will come back later also I will not go into very strong detail just I will show you there are two kinds of noise in fact three kinds of noise but at least you shown here one is called thermal noise which is always present because of the instant motion of carriers which is called the thermal noise and there are other names also in thermal noise related names short noise and other number take it thermal as a common name and the way we will define when I talk about thermal noise it can be given by as we call 4 ktr whole square by hertz and this is the function SVF is a noise function we will define it later later. The other noise which is very dominant at low frequencies is called flicker noise or one upon f noise the word one upon f came because the noise essentially decreases with frequency linear there are noises now available which decreases by one upon f square post office noise as they call we will see that and the term comes but simple first models are their frequent as the frequency increases the noise linearly falls this noise area or this noise is called flicker noise there is a point at which this flicker noise is exactly equal to the thermal noise and that is called corner frequency we can define this later you can see the figure has been shown here this is a noise versus frequency initially there is a one upon f noise at low frequencies and somewhere beyond fc thermal noise takes over because this term here whole square per hertz will actually start dominating over because one upon f may go down further and the thermal noise will take over so we say at the point where thermal noise takes over from one upon f we say corner frequency for noise and that is given by some kind of this function and we will see to it how do you control these values noise is some way connected to gm you can see clearly it has a term oxide capacitance per unit area the width and the length of the transistor and of course the temperature at which you are working of course all noises are generally temperature dependent okay so if you are working on a circuit which is at higher temperature 55 degree centigrade or 70 degree centigrade which is a military standard requirement may be 125 degree centigrade in that case your noise will be higher nothing much can be done because kt dependent so noise is a temperature dependent and therefore in normal circuit what will you do to reduce noise cool it if possible as much as or remove the heat from the circuit as fast as if you can do this heat sinking then you can operate the device at relatively lower so where it will be the lowest in real life if I put a liquid helium jacket everywhere 4 degree Kelvin then yeah I am my all noise but then suddenly you figure out gm also will not be there okay so then the amplifier may not be available but as such noise can be minimized by reducing the temperature or what we call ambient temperature don't look at too much into the expression which will anyway derive later here is a small amplifier shown here the idea why I wrote those expression is to explain this figure what we say that each resistor or a device which also in a way is a resistor contributes to the noise okay and it gives equivalent current sources across each of them so you already there will be a ion rd average square current shown here and this is ion device average square these two currents sources are available with each device and the resistors so as many devices or resistors you have that many current sources noise current sources are available and noise currents currents multiplied by resistors available will give you noise outputs so larger the ion squares or equivalently viens then you will have larger noise outputs okay is that clear and one can see some way they are strongly related to gm is that correct and therefore as you look for the gains as you look for the bandwidths keep mind that your noise is also getting affected simultaneously when many designs this criteria of noise is little ahead and therefore we do not pay so much attention as normal case but in real IC designs now probably you may have to actually start looking first noise and then see okay now how what can I do so these issues are very relevant and therefore should be appreciated this beta of course except with W by related we will see that the device parameters essentially decides the noise factors will come to noise again because that is a very relevant area of analog designs little more in detail so if you are analog designer what are you looking at okay how much things you should consider so few things not necessarily it is all of it but most of it I have written most analog circuits if you see they have signals alternating AC signals are not necessarily unit unit DC they may be varying but not DC they are not only plus but they are also minus like an AC signal so we are writing on 0 voltage that means signals can be positive or negative so is power supply can be positive or negative in our designs VDD and that VSS word can be then minus VDD also or we call it minus value of power supply or any other value need not be this is called dual radio 1 rail plus 1 minute minus compared to digital design all analog circuits always have dual rail designs because many a time minus VSS or minus value at the lower end may help okay in the case of analog I already shown you IV characteristics are there but maybe we will show you again the biasing point where you buyers decide the DV0 by that is the gain so where do you buyers is very crucial because that will decide the GN that will decide R0 that will decide everything for you so bias point control is very very crucial in analog times as I said if that drifts everything drifts so one is to worry about bias points operating in our second year course we always thought okay bar a register laga the area ho gaya bias fix bias correct so you have to do some tricks to keep that constant also for normal amplifiers we do not want gain to vary because otherwise you know for a some signals it is something you want gain to be constant or to say VOV in characteristics in the region of interest should be linear dv0 by dvn should be constant linear so that is one important thing and therefore these circuits are many times called linear circuits because there we assume gains are constant dv0 by dvn relationship is linear and therefore the circuit themselves are called linear circuits it does not mean that in real life there will be everything linear in fact the whole life of every one of us or every feature of this world is extremely nonlinear how much nonlinearity you can control or how much idiosyncrasies you control that is what your outputs of nature every one of us is videos have different idiosyncrasies we are very nonlinear in nature same inputs does not evoke same response some may be right now feeling why he is teaching but still sitting here some may be he is giving to everyone has said same thing I am saying but you may have different perspectives that is what I say nonlinear issues reality is nonlinear so how do we control nonlinear systems this fourth as I said already said all analog circuit are extremely noisy so they should be somehow made noise tolerant but they are very low noise tolerant small change will immediately shown at the output do not do anything it will come out so that is the one worry for a designer we must see to it that the drifts are small I have just shown you earlier figures that drifts can cause what everything can be changed so drift have to be minimized is one consideration in every design anything which changes is a drift this value it can be plus or minus drift can be either standard cells are essentially block design a priori design fab tested and then their square block is shown to you and gate to inputs one output this currents the speed and internally what is not told this is the standard there is no real problem with digital circuit even if I reduce the power supply we are going to 0.6 as I say okay may be 0.4 some day because we are we are happy that 1 0 still can be reachable so it is okay in analog if you reduce the voltage the current reduces and GM is nowhere then okay GM is essentially proportional to I what formula it will root or a square or half whatever you see later but it is function of ideas now if you change this the current goes your gain goes bandwidth goes everything goes and then now as I say in the new technologies when you are asking us to work on a very low bias circuits we insist that at least do not tell us that we will work on 0.4 we will have our own power supply and we will work on our own circuit part so there is a power management unit on every mixed signal because analog cannot function at 0.4 it is in your closer so much to the noise that I will only see noise so I will not like to work at very low biases though it is fantastic because it will give low powers so designing a low power analog is itself a big challenge because that is the game one has to play because overall chip cannot be you know one part is heated so much and the other is not so much then there is another issue will come in this this temperature gradient it will set and it will start varying the digital part faster so there are issues in placement of analog blocks also where do you keep them so there are many issues when you put analog with digital because as I say low power is a game everyone wants low power which is true means low power is the game these days rather I always like to call that low energy systems we are not very keen about voltages or powers we should be worried about energy essentially I am saying you can have large currents lower voltage or lower larger currents still energy and for a shorter time so as long as you manage that you are still in a low energy systems and that is more important so to summarize what I said in key to stabilize your DC biasing you may have to either increase the power supply or tune the bias currents vary it some way we will see current mirrors do that. The word PM is very important we will see come to it later phase margin one of the major worry in analog circuit is phase relationship between outputs and inputs if you have seen a transfer function in a control theory we keep talking of margins sometimes in time scale we say jitters all of us are jittery when something does not go well that we want in circuits when they jitter it gives noise map phase noise so what we do is that may change the stability of the system so you may have to do some some kind of pole compensation pole zero compensation or some way you must split the poles or whatever technique feedback systems are therefore necessary and you must get the stable circuit we must work on architectures which are constant GM because if GM changes as I say everything changes so any design you do see to it your block has constant GM that should not I may change the value of a GM at my will but once fixed it should not change that is what design is all about constant GM which also is required for good stability now we know this offset part which I said if the two arm of the circuit has equal offset or equal change in a differential mode something which is common may get cancelled and that is what the defense theory is all about and therefore offset can be minimized if not taken zero at least by using defense and we will see that is why all differential amplifiers are so common in analog designs for comparator designs you need very high gains so that any degradation would not affect much its operation because comparator shifts A to D converts so the gain of a comparator should be very high so that any marginal change should not reflect one zero it should be immediately and such degradation effect should be minimized so when I say gain I am suddenly looking at GM and when I say look GM I go upward and see everyone is hurted by hurt by changing GM so the issues are essentially device related and circuit related and their interactions so when I design you must remember that design is not just analysis a slide I think I made other day what is circuit analysis in my opinion someone asked me well we can have a larger circuit which can be decomposed or reduced into smaller blocks and each block is manageable in designs that is analysis how we do it we do not solve simultaneously huge network you can solve on a spice or a simulator but normally when I analyze I do not have such large papers to write so big expressions so what I keep doing is use blocks see to it that its input output always matches that is the trick we use and always reduce into blocks and design it and these blocks should be designed with very simple models for transistors or any other device we use if they are too complicated you cannot do circuit analysis okay so you need to have very simple models okay but relatively accurate because otherwise why I calculate gain 100 and it forms to be 10,000 then I am nowhere so it has to be relatively accurate but much simpler to handle so why do you really need then the in so called simple models yeah they do give some values which can then act as a first assumption values for large signal or large value analysis so where to start okay that is the issue each circuit has one unique solution this design this analysis if you show me this is input this is output this is how it is unique solutions now if I do a design how it differs in most cases you synthesize the design by your past experience that is why to protect this word IP has appeared if I design it is mine and you cannot take pay for and take it so this is the from the past experience and since one does not know exact solution you do a lot of iterative solution so you actually have to do extensive analysis to really design a circuit when you say extensive which means by manually it is very difficult how many times I will do 100 times same thing just tweaking things so it will be very difficult so I need some support from other than me so I will see what it is given a specs there can be many solutions whereas in the case of given a circuit solution is fixed in this case there is a requirement and I may get through any waves okay and that is the designers issue now one interesting feature which I wish to tell you all as an engineer if you want to become good all engineers require skills okay engineering is not only analysis engineering designers engineer should be good designers and they require skills now how they can be achieved and the word I used is Einstein in Bay what is the Einstein in Bay Einstein Einstein once asked that when he was doing problems in general relativity one of his person student in his class or rather his colleague that time he asked him how do you really solve such a intricate complicated problems or how do you approach that he says just by doing it so to attempt anything just do it that is the only way you can do some things and long as you do not do it you do not know what to do it and therefore you must do it that is the Einstein so please follow your failures are good enough they will teach you many more things and next time you will be more accurate and more correct so this is my suggestion to all those who wish to remain in even in financially this may be equally true some of the building blocks which I am going to design in this course I may design current sources current mirrors single stage amplifier differential amplifiers operational amplifiers variety of operational amplifiers may be a cost code amplifier opams there may be what is OTA means operational trans conductance amplifier GM related so OTAs then I may design comparators voltage references I did not specifically said the lower one why I said I will show data converters this part though is required since there is a mixed signal going on I will not talk about ADC and DAC in this course I may instead talk about oscillators and frequency synthesizers PLLs maybe I will talk more and then the switch capacitor circuit these are essentially also part of mixed signal but since they are filter realizations we will talk about some simple filters if not very complicated filter active filters as I say using switch capacitors which is what technologies will appreciate so this is something blocks this course will address to hopefully by the end of the course you learn enough that all of this you yourself can design to given spec okay so please remember we start always with trivials and then build on this this is how designers do do small pukka another small pukka keep doing till you reach your ultimate aims many of you have already done this and hopefully should have done in your second year course at least okay so this much so far is more generalities we say okay this is what analog design is all about and as I say our course name itself is CMOS that means there is a mass transistor setting somewhere though I know again I have taught them devices so they cannot say mass device was not taught others can so others may be here I may start with little bit of basics of mass transistor because I keep saying you analog design is more between interaction of device and a circuit so not knowing devices will not help you in a good analog design is that clear to you whereas in digital you do not need to know device technology or anything in fact nothing you should know you can still design the best designers who do not know anything so they design better the problem with the designers is essentially I said it is a iterative or too long a process to do please take from mean analog design what is the problem there is a very famous story or maybe famous statements made in many books many journals many years ago that if you put n number of monkeys say 100 and give them paint pencil paper and ask them to sketch anything what they do even then they cannot write a legible book irrespective they say they are our ancestors but even then they can even with hundreds of them same way if you ask a monkey who is relate why a monkey is used because they are next to us so okay if we can do probably they also can is that if you ask a monkey and give him a spice tool and say design this circuit you may keep putting hit at no time an optimal circuit so essentially in space that probably may happen in digital due regards but in analog you have to use your brain have in manual intervention is a part of analog design okay so intelligently only you can do things okay if you want to leave this the analog because that is the difference I won't say I mean as I say I am just overreacting on that but just to say a fun of part in that that analog designs requires knowledge of technology great extent much more devices and of course your circuit background has to be always good for any circuit course in electrical engineering okay so we start with the basics of mass transistor quickly today maybe we will finish that so that next time we start with the real amplifiers a mass transistor as I say circuit view of a device is very relevant to us for a device first we'll talk and then we'll say how it circuit people realize it but for them is the value here I only a mass transistor so for me I say okay I have some substrate I created some regions I have some gate some drain some source which technology can give me so I got a master but how does it work and if it works how a circuit man knows how it does it work with that relationship what circuit wants from a device is what this few some 10 stuff and this slide will show you how does specs of a circuit is controlled from the device parameters okay we will not go further down how technology manages that maybe that is also relevant someday if now at least today but it is okay so here is a typical mass transistor shown to you this is my substrate okay which is p-time so it is an n-channel device shown to you two regions diffuse in that or implanted in that is source and drain and plus this is a two-dimensional picture but as I said you earlier also many times mass transistor is a three-dimensional device I don't know I don't have anything maybe it is okay is it has thought dimension so if this is my source this is my drain this width is the third dimension so what you are seeing is only this cross-section but there is a width part in this so that is called w this is the length this is double so a mass transistor is not a two dimensional device as in most cases bipolar are of course the current bipolar also not but earlier what we used to do pnpnpns they were only two dimensionals now mass transistors are three-dimensional however they are four terminal devices not just three as one thinks that is the difference we should understand so the first terminal is source the other terminal which is output as we call drain on this n regions there is a thin insulator layer put here in 90 percent cases or 95 percent cases of silicon dioxide of last 15 years silicon dioxide has been replaced by half-nium or half-nium nitride oxides or zirconium we are trying many high-k dielectrics when the channel length goes down okay but assume it's a good dielectric and for most purposes we say it is still silicon dioxide unless it otherwise now this is SiO2 or whatever insulator you put what is the advantage of insulator insulator does not pass any DC grant so it's a good insulator typical insulation strength of a dielectric like SiO2 it has a 10 to power 7 volt per centimeter as the dielectric field at which it will break down okay air breakdowns are 30 volt per centimeter you can imagine what I am talking about so this is my gate and there is a substrate contact which I called bulk B sometimes I call S once a while but since source is there S so let's call it bulk and so there are four terminals in a MOS transistor if you show a equivalent circuit for that this is drain this is source gate is separated from this because of insulator and this is my bulk contact the symbols are known if the arrow is in it is N channel arrow out it is P channel if it is a P channel device this will be N substrate and P plus P plus source the only thing will happen is whatever voltage we apply in N channels the opposite polarity should go for P channel for the similar performance so the case one vs vg vd vs vb all are zeros if everything is zero there is no current between drain and soar irrespective no current means no current because Kirchhoff law says if there is no source there is no output okay unless of course you can say noise but that is source otherwise there is absolutely if everything is grounded no outputs everything has zero also we said transistor is off nothing is coming out okay in current technology load say less than 90 nanometer 2 or less even for that this is valid because Kirchhoff law cannot be faulted at no supply no currents is respected their cases may be smaller current because something else but otherwise if voltages are grounded no currents this is a trivial case but very relevant case to say in real life therefore device can never be switched off is that point clear because these conditions can never be made is that why I showed you this slide just to show you in reality this case cannot be achieved though I mean it is possible you can always take a transistor and ground and check but in circuits this will not be relevant case it is called trivials we will not go for trivials the case 2 let us say vgs is 0 so gate is still firstly we say ground source so what we say source is our reference voltage could have been anywhere but over the years right from shock lay down everyone thinks source is why the word source came in the device here it sources the carriers nrp what you are in channel sources electrons p channel sources holes drain D is called because it picks up drains that is why it was given a name dream now this word gate essentially means if you open or close something else should happen the output currents so it was given in gate and this be has to be given because started with the bulk substrate that we say be so right now we say vs is 0 we also say bulk is rounded but we say we apply videos no gate voltage no source voltage no bulk voltage but we apply videos which is positive let us say ideas is 0 in ideal conditions you may find that we there is no since gate is 0 we thought that it should not be any current to you but in reality there is there are two diodes sitting here NP if I apply 00 bias it is still reverse bias and if I have positive VDS and 0 here I am having a stronger reverse bias so both diodes are reverse biased okay and a reverse bias diode use reverse saturation currents is that correct since they are giving a reverse saturation currents there will be a current from source to drain which is called the leakage currents the off state is normally recognized when VGS is 0 we say when VGS input is 0 no current we say off but in this case VGS was 0 but some finite current may be very small picot and sometimes or nano amps in present case it is becoming tens of nano hundreds of nano amps reaching micro amps that is our very now 11 nano meters 16 nano meters so this means that there is a leakage path this we normally do not want to consider in a analog design because you say the very short okay but in digital this may hurt your health particularly in DRAM designs this is what it will give you okay so one must say that VGS 0 normally transistor should have been turned off but in now newer technologies this is not necessarily can be called as I say it is called problem area which is called partially on case is that okay VGS equal to 0 normally one believes devices switched off but if VGS exist there will be a leakage current which is essentially always so this is another problem which digital people are more worry not that we are not worried so this is a issue which we will not deal too much in analog designs okay now here is the case 3 I have vs grounded VB grounded fine VBS is 0 I apply VGS which is finite that means finite means it can be positive or negative but not 0 this is equivalent case of a mass capacitor if this is grounded this is grounded this is grounded it is like equivalently saying you have a mass capacitor metal oxides semiconductor acting like a mass capacitor so obviously a mass transistor theory must actually imitate from the behavior of a mass capacitor so here is a mass capacitor shown three voltages I can apply to VG one I can apply negative other I can apply positive but small and third time I will apply positive but relatively large value so three values I will choose one VGS negative second I will say VGS positive but small and third I say VGS positive and large relatively large means larger than normal okay okay so first we say VGS negative if I apply a negative voltage on this metal plate please remember this is metal can be silicon also act like a poly poly silicon can act like a metal therefore it is a metallic word we use so if I apply a minus VG on the metal plate with reference to the bulk which is grounded then the Gauss's law does not like this system to remain like this a plate by charge it says that across the loop of VG to the ground the net charge must be 0 that is the system must be in equilibrium okay and that has to happen the charge there is no charges in insulator that is what we said right now so if there are no charges in insulator then whatever voltage I apply which creates a charge minus QM on the gate I must get opposite polarity charge in the semiconductor which is exactly same but opposite polarity such that QM plus QS must be equal to 0 because the net charge around the loop should be okay that means if QM is negative QS has to be positive which is now how do I get a positive charge one sees that the device started with a substrate so it has a certain number of hole density already available to you but this is universal everywhere constant any Q any NA is the doping concentration in substrate so those many holes are available everywhere but at the surface I want additional holes because that is what you said minus QM requires additional positive charge so some way the holes must start coming near the interface the word is interface between SiO2 and silicon or insulator and silicon or semiconductor the line here is called interface at the interface you must get extra holes now from where they can come this subset is good enough for you it will start providing larger holes but does that mean that the subset will get depleted of holes no battery will apply it battery will give you that was additional so because of this why this can holes have to go upwards if you look at very carefully if this is minus Vg with reference to ground which is the direction of electric field upwards plus to minus so obviously holes move in the direction of electric so holes move up and the additional holes which we are asking will be actually coming from power supply so that the thermal equilibrium value of concentration in P remains constant though holes are actually picked up from the substrate itself the loss will be supplied by the battery or whichever go up now these many holes will only come as much is the charge you put on the metal so every time equilibrium QM plus QS is constant is so if I have larger minus Vg then what will happen larger holes will come so you can say larger negative voltage I apply larger accumulation of holes starts at the interface this is essentially accumulation we have accumulated holes we have a P type and we are accumulating positive charge so we say we are in a region of accumulation so in a mass capacitor with P substrate with minus you are always in accumulation battery always applied charge cannot be created from air you know so it has to be taken from battery now the third case I say or second case I said Vgs is positive but not very large very small amount but positive now if I see that very small positive value okay let us look at this if I apply Vgs positive at small so I am putting small QM at the metal now by Gauss's law we now expect semiconductor interface to get negative charge because QM plus QS is constant is 0 is what Gauss says Gauss is the God for us we say so it is we agree with it yeah almost for many years no one has proved Gauss law wrong not even perturbation on it there are many things in weak fields strong weak fields many things are coming both on Toson but no one has challenged Gauss's law so far okay so if QS is negative but the substrate is P type substrate is P type now I want negative charge to occur we said okay if you look at this way now the electric field in semiconductor is now downwards positive Vgs so field is downwards so holes can move in the direction of electric field so holes near the interface actually move away as soon as in a semiconductor positive charge holes move away what we say it gets that region gets ionized with a negative acceptors and this region is depleted of free charges of holes is that clear therefore the region is called depletion so we now get into this that we see depletion now this depletion region will enhance because it's a charge density issue if you increase charge the charge the area is same so charge density of QM increases if QS has to increase its thickness must increase because otherwise equivalent charge density cannot be created so larger the positive Vgs for depletion layer thickness or width as may be called will also enhance okay also enhance to get same charge as you are putting on the metal so you remain in depletion as long as that condition is happening that QS is to be supplied through depletion charge okay okay so this mode will call as depletion mode as I say many of you have learned this is recapitulation recapitulations because we need to understand device little better final log let us say Vgs is further positive and little better than substantially higher now this value how much we will see later when you say it's more than threshold that word threshold is what we want to define now certain value of Vgs suddenly we find things will change and that would that we are exceeding that voltage right now as if so if you apply Vgs positive large relative large still keep Vds 0 Vs 0 Vbs 0 fair enough so you are still a capacitor and you say Vgs is large large positive charge requires large negative charge so what could have happened that this in thickness of the depletion layer should keep enhancing because what is the depletion charge can anyone say I already written somewhere if not oh yeah here QnA xd xd means depletion layer width this xd increases nA is constant so QnA xd keep on increasing to adjust the extra charge you are asking for so the semiconductor charge is increasing with increase of xd in depletion this surface potential size word which I have not stated somewhere may be well can use a fresh sheet this you should understand something like this you have a capacitor if I apply this is semiconductor this is insulator if I apply some voltage call even V across this this is insulator the semiconductor V must be equal to V ox plus semiconductor potential this is ohm's law your divider you apply voltage to areas part divisions so obviously the potential in the semiconductor is defined in terms of size and potential across oxide which we want to find soon is called oxide drop okay so if I increase a let us call Vg either this will increase or this will increase or both will increase or one of them will increase is the game we are trying to play is that correct is that point here either each one of them will increase or both may increase or both may not increase which are the cases of relevance okay so this potential drop between two regions is we call it surface potential why it is called surface because charges only near to the interface so potential will change only where by which light potential appears because of charge which law is the very famous which relates voltage to potential to the charge Poisson's equation Poisson's law says d by dx is minus rho by epsilon is the electric field x is one direction but multi direction rho by epsilon epsilon is the permittivity rho is the charge density okay so larger the charge larger is the electric field electric field is minus dV by dx so larger the field larger is the potential is that clear so we say voltage increase surface potential can only occur when there is a charge available is that correct this is Poisson's law or Poisson's equation so because of these as I say fundamental Maxwell's equations which are still standing strong electrical engineers are strong okay so now if I say if I keep increasing Vgs psi s will also increase but I figure it out that there is at some potential Vgs equal to call it Vt now this surface potential becomes what we called as twice the Fermi potential some other day may be device theory may be more detailed at all but not today and Fermi potential is given by kt by q ln Na by Na Na is the intrinsic carrier concentration Na is the accepted concentration so if larger the Na phi f is larger okay so for a when psi s reaches 2 phi f one can now say that this 2 phi f xt becomes maximum actually we will see this is only 1 phi f should have happened but we say okay 2 phi f xt becomes constant if xt becomes constant and maximum then the charges due to depletion layer are fixed now but you are increasing Vgs beyond that value then what will happen from where because depletion layer cannot enhance now you said it so that is the way definition you are putting that means there must be another source of negative charge this additional source of negative charge is always available day one actually but was not so dominantly talk initially but now suddenly we realized we figured out that every semiconductor whether it is a depletion layer or normal thermal equilibrium areas electron hole pairs are constantly generated is that where it is this is thermal generation nothing I can do the combination is constantly done that is why any other constant so many holes can be given okay if law of mass action has to agree every time thermodynamics cannot be violated in thermal equilibrium then electrons and holes are going to be created everywhere even with Vgs was smaller positive there were hole electrons there also in the depletion layer here also there were hole electrons what has happened there which side because of the electric field which carriers in this upper region let us say the other region they will recombine because this is a neutral region in the depletion region the hole electrons now see electric field okay which is the electric field downwards which carriers will move away holes so the electrons can be made available but at this time we say electrons are not there very much why we said because this electric field is so small that they could not separate hole electrons before they recombine they are recombining everywhere so is in the depletion there the electric field which could have separated what is the electric field jar it gives a force that Q into this is the force Q into E is the electric force if you are E smaller the force on carrier is smaller so before they separate they recombine okay so if they recombine there is no additional electrons available to you because hole electrons recombine however in now when you have increased Vgs efficiently this electric field is very high because that is what Vgs you applied size is very high now okay at that electric field now you said depletion there is not increasing fine but this electrons and holes can be separated because of additional higher electric field in the semi semi semi surface so holes will move downwards and electrons will move which side towards the interface as they separate so more and more electrons start getting near the interface as you increase that correct because now depletion cannot give you additional negative charge additional charge must come because causes will not allow you to do otherwise and therefore get a charge must come from free carriers electrons okay you started with a piece of straight you create at a layer of free carriers electron carriers so you say you are inverted P type the layer at the top or interface layer is now entire okay and therefore you say you are in a region of inversion is that correct so larger the Vgs now you put larger will be inversion charge because and that will be supplied by whom by this thermally generated carriers which gets separated now if I solve such Poisson's equation for this one can see if by of course there is a theory I will not say the inversion charge due to this thermally generated case is proportional to e to the power q psi s by k t which means very small change in size can create larger negative charge. If you look at my this expression for depletion q and Na xd but xd is proportional to size but which relationship it is showing root of size the earlier depletion charge is proportional to root size but inversion charge can be created e to the power q size by k t so obviously exponential functions are stronger than root functions so you do not need now too much change in size to get this additional bulk charge or call depletion charge but that additional charge may now come from the electron hole pair separation which is going exponential with change in size okay so all the additional charge will be now supplied by this separated charges free charges and therefore depletion layer will become constant with a pinch of sorry it will keep increasing bit of it let us say 0.1 percent is from that and 99 percent from that may go it is not that it will not but ratio as you say all of it is now coming from free electrons available through inversion layers through in the inversion layer this is the crux of most understood now we say vgs equal to vt this occurs the definition we said that at psi is becoming 2 phi f actually when psi is becoming phi f the material will become intrinsic you can put substitute this value and you say material will be intrinsic so it will not p type there at the surface not p type so it intrinsic but then there are very few electrons so we do not want that many we want larger number of how many electrons I say is good enough for me at least as much as the holes will be lower so if these electron density is same as what the holes density I started with I say I have sufficient electrons available so I say good inversion layer and that would be good we say strong inversion so from psi s equal to phi f to 2 phi f inversion is already available but very less number of electrons available as you reach to phi f huge number of electrons can be clear because it is a exponential function you can see exponential function initially it rises slowly and then shuts shoots up that procedure is same here so initially you see lesser charge but then it shoots the larger charge this fact is being utilized here there are little bit higher psi s 2 phi f number we gave the depletion layer now will become constant whatever for 2 phi f and we will say rest of the charge will come from the free electrons generated through thermodynamics that is why we say threshold voltage is defined at that point where psi s is 2 phi f is that correct it is called strong inversion now there is a catch there between psi s equal to phi f psi s is related to Vgs Vgs equal to psi s plus V ox the size changes we know Vgs changes size is changing we say between phi f and 2 phi f device is still not off it is on that clear to you why it is on because electrons are made available to you this means this region is called weak inversion and this is also called sub threshold region one of the way analog circuit will be designed is using sub threshold characteristics Vgs less than Vt but it is not switched off it is not 0 there is a weak inversion going on and that region itself can be utilized in some devices some circuits most cases will not we will see that psi s is 2 phi f strong inversion is set in more and more carriers will come from Vgs now all of it go to psi s and psi s will increase as much charge as you want on the equivalent of Qn. So the path MOS capacitor works and therefore MOS transistor works is that there is a threshold voltage at which this can occur is that correct this since at this the as I said this figure since this channel can be created somewhere here a Vgs is positive like this and Vgs is also positive then there is a positive this is there like a resistor n channel an area is like a semiconductor n bar some conductivity it has this is source grounded this is drain positive voltage this is like a piece of semiconductor with two contacts what current it will flow Vgs IR depending on the R here current will flow say MOS transistor gives you a current which is proportional to V which is very interesting okay but later we figure it is not linearly going so then how what what makes it change we will see next time. I hope that those who are not done device course in their careers are not done the course the way I think they should do I said the initial availability in a capacitor is essentially because of the minority carriers however when I make a transistor I have a source of electrons infinite source so the electrons will actually come from the source and not from the minorities minority will keep that channel but the current which will pass will be sub carriers otherwise you know one time this carriers will be swept off so the carriers which are required to maintain a channel will always be supplied in a transistor by source electrons that is why it is called source I will keep giving you electrons as many you want and this is n plus means heavily doped infinite carriers okay so I will keep supplying any number of current carriers required but the channel will be maintained essentially because of the VGS minus VTO is that clear this inversion cannot be done from source side it can only be done from gate side so the inversion there maintenance is because of the minority charge but the charge movement is supplied from source to drain by the source is that clear all the carriers there are thermally generated there is nothing else inversion layer is always thermally generated carriers okay is that okay petrol is insulated by from the semiconductor there is a oxide so nothing it can do below no no how can the current can through move through insulator oh you will like this over that is the circuit anyway circuit the car that sort of a car finally carriers through source from where it is coming through battery there is no other source of carriers carriers can only appear from a battery there is no other source okay is that okay