 We will have the last presentation on these non-classical MOSFETs. We will continue on these compound semiconductor materials and heterostructure FEDs. So, under the heterostructure FEDs, we will talk of the high electron mobility transistors and some heterostructures as well as changing the normal materials like using strain and quantization. So, we saw that the short channel effects in a MOSFET also come into picture. So, in order to and these short channel effects manifest in terms of the threshold voltage shift in the negative direction, also sub threshold slope becomes larger. Both effects are due to the 2D field effect on the channel region. These effects can be reduced by increasing the channel doping density accompanied by the reducing the channel thickness. Now, in fact, increasing the channel doping in the channel adversely affects the mobility. As all of us know, it also affects the velocity overshoot effect in a MOSFET, MOSFET. This is because the initial velocity will be smaller. So, the overshoot effect will be smaller. So, the actual benefit that you usually see will get reduced if the doping is high. So, in order to work, these can be overcome. See, the whole problem is when it increases the ionized impurity scattering is upon which comes into picture. So, one has to reduce this effect. So, this can be reduced and the high mobility and the high electron concentration can be achieved if we can separate the channel, where the electron moment is there, separate the channel from the region, where the doping concentration is made high. So, this is achieved using the high, using the hetero junction and hetero junction field effect transistors. So, we take a look at hetero junctions now because that is the one which we discussed today. Hetero junctions are formed by two dissimilar semiconductors. For example, germanium on silicon that is hetero junction, gallium arsenide on germanium that is hetero junction. Now, there are two types normally people can talk of. You can have conductivity of the same type in the two materials. For example, p-tap germanium p-tap silicon, p-tap gallium arsenide p-tap germanium that is called isotide. Alternately other name is an isotide which is the common type of hetero junction that you encounter that is one region is p-type other region is n-type. For example, you talk of p-type gallium arsenide n-type aluminum gallium arsenide or aluminum arsenide. So, hetero junction requirements what are requirements? Most important requirement is the lattice match requirements. When you grow one material on the other there should be very good lattice match between the two. In the sense lattice constant of the two materials must be comparable. If you are going trying to grow gallium arsenide trying to grow silicon on germanium there is problem because the lattice constants are quite different. Silicon is 5.43, germanium is 5.65, but on the other hand if I want to grow gallium arsenide on germanium there is no difficulty because both have lattice match. Now, what we are looking out for is hetero junction consisting of aluminum gallium arsenide on gallium arsenide. Aluminium arsenide has got excellent lattice match with gallium arsenide. So, aluminum gallium arsenide also has excellent lattice match with gallium arsenide. So, you can grow a gas aluminum gallium arsenide on gallium arsenide very easily and you can vary this top layer. Bandgap you can vary by varying x equal to 0 to 1. x equal to 0 as I pointed out earlier would mean aluminum component is 0 and gallium is not g is gallium. Gallium is 1. So, you will have aluminum G A A S, x equal to 0 would give you gallium arsenide and x equal to 1 will give you aluminum arsenide. So, you can vary x and vary the bandgap of the layer which are depositing on gallium arsenide. So, take a look at this. If you take a look at the gallium arsenide the lattice constant is 5.6533. Aluminium arsenide also has got very close lattice match very marginal misfit factor. So, you can grow aluminum arsenide directly on gallium arsenide or you can have an alloy of aluminum gallium and arsenide and gas. Here x equal to 0 it is gallium arsenide the band structure is like this x equal to 1 it is aluminum arsenide band structure is like this. So, notice this is a direct band gallium arsenide that does not matter for us because we are local for micro electronics it is a direct bandgap even up for up to 2 electron which can be used. It is bandgap minimum bandgap which is a direct bandgap is 1.43 electron volts. But there is also a valley as we pointed out earlier at this place from the central moment of zero position with the at a different momentum you have got a bandgap is equal to 1.8. So, normally the electrons will reside here and the transition will be between these two and if the electrons get high energy they can go move into this region at high fields here the my pretty mass is higher. So, now what we are saying is let us use this gallium arsenide. Now, if I have an alloy of aluminum gallium arsenide if I vary from x equal to 0 to 1 you have 1.43 the direct bandgap tracking with this direct bandgap of aluminum arsenide. So, the direct bandgap will vary from 1.43 to 3.02 and indirect bandgap 1.8 will vary from 1.8 to 2.17 linearly it will vary. Now, just I want to mention also aluminum arsenide is a indirect bandgap semiconductor. So, if I change completely from gallium arsenide to aluminum arsenide will get indirect. So, if you move from gallium arsenide to the aluminum arsenide you will have certain composition of x you will have direct bandgap beyond that you will have indirect bandgap. But the point that we are trying to make up do is show is that you can vary the move from the direct bandgap to smaller. So, wider bandgap and ultimately to indirect bandgap. So, this is the indirect bandgap with bandgap 2.17. Let us see how it varies from a graph form notice 1.43 will vary linearly with 3.02 direct 1.8 will vary linearly with the 2.17 as x is varied from 0 to 1 x is 0 will give you gallium arsenide bandgap direct is 1.43 indirect is 1.8 as senior 1.43 1.8 and if you go to this other end x equal to 1 that is aluminum arsenide direct is 3.02 indirect is 2.17 here. So, when you vary the direct component will vary linearly from 1.43 to 3.02 the indirect component will vary from 1.8 to 2.12. Now, what happens is this see for example, here if you see there is direct component, indirect component. Direct band component is smaller than the indirect. So, actual bandgap is this here indirect component is smaller compared to direct component. So, the bandgap is actually 2.17. So, lower is the one which gives the bandgap. So, as a vary x from 0 to about 0.3 or so, you will it will be direct bandgap semiconductor where direct component is smaller than one indirect component. As you move beyond this composition x greater than about 0.3 0.2 0.4 0.6 like that 0.3 beyond that the direct component is larger than the indirect component. So, it becomes indirect bandgap. So, what we are trying to tell is you can grow gallium arsenide or aluminum gallium arsenide on gallium arsenide and the composition of the L gas depending upon x you can have direct or indirect, but the bandgap always you can get higher than that of gallium arsenide. So, you get a good hetero junction here. If you want to look at other materials like indiabosphide or gallium indi-marsenide you can mix gallium arsenide with indi-marsenide and make a compound gallium indi-marsenide. For example, here x equal to 0 will give you indi-marsenide x equal to 0 bandgap is direct bandgap 0.36 and gallium arsenide also is in there is a direct bandgap that is x equal to 1 this component is 0 gallium arsenide is 1.43. So, both ends stream ends you have got direct bandgap. So, I can have gallium indi-marsenide throughout a parent bandgap material. Why do we talk of that mobility of indi-marsenide is very high. So, gallium indi-marsenide mobility will be higher than that of gallium arsenide. You can have a bandgap somewhere in between. For example, if I have something like 0.4 or 0.5 you will have bandgap which varies very close to 1. So, why we talk of gallium indi-marsenide you can make hydro junction with gallium indi-marsenide or indi-marsenide because x equal to 0.47 gallium 0.47 indi-marsenide 0.53 the lattice constant is 5.88 angstrom which matches with the indi-marsenide. You can grow gallium indi-marsenide or indi-marsenide on indi-marsenide on indi-marsenide make high mobility transistors using that. We will today focus on the aluminum gallium arsenide gallium arsenide. So, what is the hydro junction? If I take a look at the homo junction for example, if I talk of silicon n type material p type material. When you talk of the same material bandgap of material 1 is the same as the bandgap of material 2. The electron affinity that is the energy gap between the vacuum level and the conduction band E c chi is the same in both cases silicon is 4.05. Now, if I take n type permeable is very close to conduction band and the permeable here is close to the vanus band. When you put them together you can see that if you put them together the permeable here is higher than permeable here. Therefore, the in the system from the theory of cochlear model we know that when you form a junction electron from this region where electron concentration is high will flow to this p region which would actually deplete the region on the surface and you will have a band bending upwards here. And from here the holes from this side will move from left to right depleting this. When this depletes the band will move down here. In fact you can just quickly see I will see where I can show that to you. See for example, if you see the when you form the energy band diagram you know that permeable is flat and n type material permeable is here conduction band, valence band and because of the band depletion layer it will go like that. So, this is the conduction band is the valence band. Correspondingly the zero level whatever chi was there it will be there that is the vacuum level. So, that is chi and this is also chi. So, you get same chi. So, there is no discontinuity discontinuity in the energy band diagram. So, notice somewhere here that is joint it bends up that bends down. So, the electric field as because this is depleted the electric field is like that and it charges here plus charges here. This is the standard theory of homo junction homo junction means band gaps are same chi is the same there is there is a continuity everywhere. Vacuum level represents the change in the potential and with respect to vacuum level the conduction band will be located. So, we will go back to our theory of the hetero junction. So, same thing holds good in the case of hetero junction. Here we are talking of a band gap which is wider compared to wider band gap V G 1 compared to another band gap narrower band gap V G 2. So, the Fermi level is higher here compared to this. So, when you join them and here one more thing is chi 1 there is the energy difference between the vacuum level and the conduction band chi 1 is smaller than chi 2. This is the basic Anderson's theory of model. This model holds good up to certain level to understand, but actually there is much more than that what we say happens. So, let us try to understand it what happens in energy band diagram. When you join them together the energy band diagram bends up here exactly the same way as we saw here. The energy band diagram bends here, it bends up here on this side and it continues to bend up because this bends up that bends down. Now, let us go back here. So, when you put them together because I will get transferred here this will be depleted till the whole side transferred. So, this will be depleted. So, what you will get will be vacuum level there will be plus potential here minus potential here. So, vacuum level will bend exactly same way as we have in the homo junction because the energy band at the vacuum level does not have any discontinuity. It represents the way the potential varies. So, that is continuity. If you take a look at the condition band in the entire material wider band gap material it has depleted and bent up. All through here chi 1 is the vacuum level. Chi 1 is the electron affinity here same thing is here, but when you come from that side vacuum level bends down here because of potential variation like that plus here minus there. So, the conduction band also bends up down like this till we come to the junction. Now, you can see at the junction all through here this chi 2 from the top to bottom is chi 2 and when you come here the gap between the vacuum level and the conduction band in the p type material is chi 2. Whereas, at the same point the joining point of the entire material which is wider band gap there the chi 2 is the electron affinity is chi 1. Chi 1 is less than chi 2. So, these two conduction bands do not meet at the same point there is a sudden discontinuity here, discontinuity here. That is the specialty of the heterostructure. The energy band diagrams are not continuous there is a notch here. So, if there is a notch here it is almost like the notch that you see in the MOSFET. So, if there are electrons some so on this side if electrons are injected on to this side they will get collected here and those electrons cannot cross up this barrier they will get they remain there. It is like what you have in the case of the I am sorry this is similar to what you have in the case of the MOSFET. See for example, in the case of MOSFET you should recall what you have is the oxide. The oxide is there that is like that. Then if you have p type semiconductor you have got a permeable like this then you have got this like this conduction band e c and e v and you have of course this like this oxide. This is oxide and this is a p c gap and you have the metal. Now, you can see there is high band gap here about 3.3 electron volts is there. So, when it is inverted here the electrons get locked here electrons remain here they cannot go up. That is why you will have to got when you invert it here when it has become n type you have got electrons locked in that notch. So, whenever there is a notch like this there is a barrier like this there will be electrons collected there. You can make use of that as the channel. If I connect the two ends of this channel by source and drain you can make a MOSFET. So, exactly same that is the similar type of notch is there in the case of hetero junction that is this. You have got this bending here there is a notch here. So, the band bending is actually such that so much that there are electrons collected here. So, now what you can do will be before I go into the structure I just give what will be the value of this. So, this notch is actually equal to you can see that is chi 1 or chi 2 minus chi 1 that is the first order theory and that is delta e c is the discontinuity in the conduction band. And if that band gap e g 1 is larger than e g 2 this is actually e g 1. So, e g 2 will be e g 1 plus delta e c plus delta e v. Therefore, delta e v that is the discontinuity here also discontinuity will be delta e g minus delta e c. So, what we are trying to say is this is first order theory, but in practice here it looks as if delta e c is chi 2 minus chi 1, but even in materials which there is chi 2 minus chi 1 is not that much you see a difference and that is governed by how much is the band gap difference between the two. So, the delta e c ultimately is related to e g 1 minus e 2 that is delta e g. So, it is seen that experimentally that delta e c by delta e g is about 0.6 to 0.64 for al gas gas system al gas is remaining at a mass time. So, delta e g for x equal to 0.4 from this particular thing for x equal to 0.4 delta e g is something like 1.43 plus 0.5. So, delta e g is 0.5. So, delta e g is 0.5 delta e c is 0.5 plus 0.64 is 0.32. So, you will have delta e c of 0.3 to electron volts if the band gap of this region is 0.5 e g 2 plus 0.5 electron volts in al gas you can get that. The value different now if delta e c is 0.3 to electron volts and if delta e g is 0.5 delta e v if this is point delta e g is 0.5 delta e g is 0.32 this is 0.18 that is what you put here. So, what you have is now al gas gas system which can be used as a gate you can have a channel here this region can be used as a channel this is an undoped which actually turns out to be very lightly doped 10 to power of 13 and there is a depletion layer here we saw the p region is depleted and there will be small depletion layer in the n plus aluminum gallium arsenide also this is the electric field distribution here. So, what you will have will be if I do not have any gate connected put here this region is not depleted. So, conduction band goes like this gets depleted then because of this work function high difference etcetera and delta g difference it snaps down here by delta e c 0.3 or 0.32 then it rises up because there is a depletion layer here electric field is in that direction therefore the conduction band will rise up here. The point that we have to note down here is that in the case of conventional junction there is no delta e c. So, this would have gone up like that straight away like this, but in this case because of this delta e c this starts on lower end then the that rise up to the same amount. So, that the electron distribution here and here match together. So, in other words you will have a total potential drop across this which is some of the which is more than the conventional built-in voltage of the MOSFET or the VN junction and the delta e c delta e c by q. So, what we are telling is I can actually have a transistor made by this this is a gate region this is a channel region n plus region over that an undoped galae martinite channel region n plus lume galae martinite over that rectifying contact. So, if I do not have rectify contact what will happen we will see. So, we have also a source and drain region that is heavily doped n plus region which is usually realized by gold germanium alloying on to this region it goes through that. So, because of the l gas gas structure you have that notch here and electrons are present here throughout this region. If the electrons are present here throughout the region if I n plus region here and n plus region here when I apply voltage between the drain this we can call it a drain and the source when I apply voltage the electrons there is electric field from here to here. Therefore, electrons will be injected from here to the channel they will be collected here there will be current flow, but now if I do not have the gate is saw and you did not have the gate there is a channel here, but this there is a region which is not depleted. So, if I have a source drain connected like this realized like this not only there will be current flow through this particular layer there will also be current flow through this heavy doped n plus layer. In fact, the entire current will be masked or controlled by the current flow through this heavy doped region. If it is current flow through the heavy doped region the mobility will be very low there is no use. So, what you do is put a metal gate here. So, the metal gate here you can the work function will be such that you can either deplete it completely or if it is not depleting completely you can apply a negative voltage and deplete it. So, in from the mass spread theory we know that the voltage required to deplete the entire n plus layer is called the pinch of voltage V p 0. Now, the voltage if the pinch of voltage if the depletion built in voltage is different from the pinch of voltage is lower than that you have to apply gate voltage which is which is equal to V b i minus V p 0 we saw it in the mass spread theory threshold voltage of the mass spread is V b i minus V p 0. That means it is a gate voltage that must apply to pinch of the channel. So, you can apply V b i minus V p 0 that is actually the point at which the channel will be conducting your current flow. Now, let us go further on that. So, the function of the gate is to depletely deplete the n plus layer it also has the job of controlling the charge in this particular region. You can see once it is fully depleted it is like the mass spread metal insulating layer and the channel where inertia layer is there. So, by applying voltage to the gate I will control the channel charge here. So, you can have right equation that exactly similar to the mass spread where we have u c oxide W by 2 L into V g s minus V th threshold. But if V th threshold will be different from that of the mass spread and mass spread we will see what it is. So, in one way it looks like a mass spread because there is a short key barrier, other way it looks like a mass spread because this metal depleted layer and the channel. The n plus source drain contacts are found by allowing this the electrons are transferred through the gallium arsenate region where the doping concentration is very low. Since the doping concentration is very low the ionized impurity scattering is absent. Therefore, you get very high mobilities you get mobilities as I as ideal 8500 centimeter square per volt second at room temperature you reduce the temperature to 77 degree Kelvin you get 250000 centimeter square per volt second these are reported values in literature. You go down even down you will get much higher mobility what is that due to you can see a mobility effective mobility depends upon the lattice scattering mobility as the temperature goes up lattice scattering mobility goes down mobility governed by lattice because lattice vibrations increase if lattice vibrations increase the scattering of the electrons by the lattice atoms increases. Therefore, mobility goes down ionized impurity scattering when you go to lower temperature the ionized impurity scattering increases. Therefore, the ionized the scattering decided by the impurities increases therefore, mobility governed by the ionized impurity scattering goes down that is because when you go down to lower temperature the velocities of the electrons are very lower. So, therefore, if there is an ion present the electron actually will move very close to as it goes to the close to the atom the impurity if it goes close to the impurity it gets deflected by the little static force. If the velocity is lower it gets deflected more towards this if electron gets it gets more towards this ion when it moves like that. If the velocity is high the chance of deflection is less because it slips through that layer very fast. When you go to lower temperatures velocities are lower so scattering probabilities are higher therefore, mobility falls. Now, the combined effect of that is 1 by mu lattice plus 1 by mu i so that is this combined effect. If the doping concentration is high it can be if you reduce the temperature mobility is reduced practically, but if the doping is 0 very little this component is 0. So, only this particular component is there mu i is there therefore, what you will have will be the what you will have in that case will be like this what you will have will be the temperature versus mobility. So, room temperature you may have about 8500 centimeter square per volt second that is good lower temperature T equal to 77 degree Kelvin you will have 250000 centimeter square per volt second. So, you will get very high mobility because other component you have eliminated by removing the dopants. So, that is about that. So, the extent of electron concentration depends upon delta E c because higher the notch higher the notch more chance of the having the electrons more chance of bending here there will be more electrons will be present. So, the delta E c if it is higher you will get more electrons, but be more current flow for a given voltage. Now, delta E c depends upon mole fraction because delta E c depends upon delta E g delta E g depends upon how much is the band gap of l gas higher than that of gallium arsenide how much higher the electron aluminum concentration higher will be the band gap there higher will be the delta E g and higher will be delta E g. In that case you do not choose very high aluminum concentration because aluminum itself is unstable it gets oxidized etcetera and also it gives rise to trap centers and it affects the mobility. So, highest value of x that you choose is about 0.3 aluminum concentration which will give about 1.9 electron volt as the band gap. So, now one of the things that you want to see is when you deplete the hole this top channel completely because there was already this particular delta E c was present there will be charges. How do you turn off the device what should be the voltage that you must apply to the device to turn it off that is actually the threshold voltage. So, this was the diagram that we have drawn conduction band. Now, you have got you have to apply voltage equal to V b i minus V p 0 to deplete this region that is from the gate side. Now, in thermal equilibrium you have got both the electron distributions here here is very little because it is undoped here is high from the theory of junctions and Schottky barrier you know that the thermal equilibrium transfer electron from here at here will be 0. Now, there are electrons there because of the psi band bending in the conventional homo junction there are no electrons there at that point there is no because there is no notch. Now, the band bending is more than that in the conventional junctions by an amount equal to delta E c and because of the delta E c more band bending is there. When you have that particular thing you have this thermal equilibrium achieved because band bending is more than that often the conventional junction you will have virtually like an inversion layer here. Now, you must to remove the inversion layer here you must reduce the band bending by whatever extra amount of delta E c by q is there you must reduce. So, the amount that you must reduce that band bending is actually delta E c by q. So, the polarity of this voltage drop across this layer is plus here minus here. If I want to reduce that voltage by delta E c by q that is V f I must apply voltage plus on the right hand side and minus on the left hand side P is made plus with respect to 1. That means you must have a forward bias to the junction so that the barrier height is reduced by delta E c which is delta E c by q. So, what we are telling is if I have this mass fat I apply V B I minus V P 0 the whole thing will be depleted. But across this layer there is built in field there is a electrons here to remove the electrons I must apply plus here minus here. So, V B I minus V P 0 is actually negative total potential plus here because the charges are plus here, donors. Donors these are the donors plus here minus here. So, electric field is towards the gate here, but from a gas to a semiconductor this is N P field is like this there is 0 field here that depletion layers meet here. But there is also there are also electrons here if I just to deplete it come up to this point there are electrons here on the interface. Now, to remove those electrons I must reduce this barrier I must apply plus here minus here or in other words once it is depleted completely if I increase the voltage by another term or by a value equal to delta E c by q if I make this more negative whole thing is depleted. So, there is this depletion layer actually will slightly fall because this gets forward biased. So, what you do is add a voltage equal to minus to this point this is already depleted. So, that minus delta E c by q that you apply here goes across this junction minus here plus here which is actually equivalent of forward biased in this which removes which reduces the barrier. So, electrons from here are actually removed in fact they are taken to the gate. So, when you do that when you apply more negative voltages whatever see there is connection between the source and this particular channel if you take a look at this here when I apply a negative voltage to this after this depletion if I increase further the negative charge is transferred from the channel to this to this gate to transfer this voltage completely from here to here to voltage additional voltage that I must apply delta E c by q. Once I apply more delta minus delta E c by q after depleting the whole thing I apply additional minus delta E c by q all the electrons will be transferred from here to here that is what is happening here. So, if I apply a voltage V of equal to V by minus V p3 required to deplete this and delta E c by q required to remove the electrons from here back into this gate the channel will be turned off that will be actually the threshold voltage. We call it we do not call it threshold voltage here by convention they call it as the gate voltage that must be applied for it to turn off the hemp. So, here the V of can be positive or negative depending upon what is this value delta E c by q let us say it is what we said this it will be something like 0.3 delta E c 0.3 electron volts. So, this quantity will be 0.3 volts. Now, I can adjust the doping and adjust the V p0 depending upon the doping depending upon barrier head I have between the short key and the aluminum gallium arsenide you have got V b i I can adjust the doping and the thickness. So, that V b i minus V p0 is more than 0.3 volts if V b i minus V p0 is more than 0.3 volts if because this 0.3 volts V off will be positive. So, I can have V off either a positive or negative supposing this term this is negative supposing this term is minus 0.1 volts this is 0.1 minus 0.3 volts you will have V off is minus 0.4 volts. So, we can have enhancement or depression type of high alternative transistors using this hemp structures. So, the doping you remember you are not adjusting the doping here is un doped all the doping that you are talking of the doping in this particular layer and gas layer. So, increase in the doping is not affecting the mobility of electrons here it is only adjusting the threshold voltage. So, you can have independent control of threshold voltage without affecting the doping here you can adjust the thickness here and the thickness controls the capacitance. As I pointed out the working of this is now once this is depleted the gate gets coupled out to this channel here. So, you can talk of write the equation similar to that of MOSFET and the I d V d gas characteristics transfer characteristics have be I d is equal to in the case of MOSFET u n c ox a w by 2 l into V g s minus V threshold square. Here instead of V threshold we have V off given by this term negative or positive negative means depletion type positive means enhancement type and C s in the case of MOSFET it is the channel thickness in the case of MOSFET it is the oxide capacitance in the case of MOSFET it is channel capacitance that is this quantity. So, in the case of MOSFET or I am sorry HEMT is also called MOSFET that is modulation doped FET MOSFET MOSFET HEMT all are same. In the case of MOSFET or HEMT C s is you can increase the CFS by reducing the thickness of that layer that is that layer. But then to adjust the threshold to adjust the V off you must actually increase the V P 0 if you want increase keep that when you reduce that you must increase it to adjust that doping to keep the V P 0 same when you reduce the you must increase N d. So, there is an upper limit to N d because as you go to higher and higher doping concentration the metal semiconductor contact will not go long by modifying it will become omic contact because of tunneling current between the small deficient layer form between the N d and this quantity. So, upper limit on the doping these doping on that controls the doping on this layer. So, there is a lower limit on A that you can choose you may use something like few nanometers 100 nanometers of that order you can choose 0.2 micrometer or even slightly lower because the upper level on doping concentration is something like 10 to over 18 that you can do because of the limitation of the Schottky-Berrero. So, a non-scented edification mode types can be made with bijecting V P 0 bijecting that you can get positive or negative you can reduce A then V P 0 goes down V off can be made positive by reducing that. Now, GM can be increased by as I pointed out GM can be increased by reducing the channel thickness this can be done by increasing the doping or the V off adjustment upper limit on N d instead of over 18. So, that limits how much you can do here. So, what we are pointing out is you are able to increase the doping here in the aluminum gallium arsenide layer without increasing the doping in the region where the electrons are flowing. All that you are doing is tailoring the doping and thickness in the other wider band gap material where the electrons are not flowing you can tailor that tailor the threshold voltage and the substrate is undoped mobility is high. So, you get very good characteristics. Now, here also I am sorry just here also what you do is in addition to this algeas doped layer when you do that you all usually in practice you put a thin layer of undoped aluminum gallium arsenide just about 1 or 2 nanometers that is because if the whole thing is doped the entire layer up to the channel is aluminum gallium arsenide every doped then these electrons which are moving on the channel see the effect of the doped layer some scattering is there to overcome that you put a thin layer of algeas here. In fact, the optimization of that layer also is involved the transfer depth in 110th adjustment. Now, quickly run through the thing the characteristics this is just to show you that people have made this type of devices at 300 degrees Kelvin the transfer character the output characteristics ID versus VDS you can see it saturates like this red curve is the 0.2, 0.4, 0.6 gate voltage and as VDS is varied from 0.5, 1, 1.5, 2 volts low voltage current 10, 20, 40, 60 milli amperes per division here. The most important thing we note is the current here current here at this gate voltage at 300 degree Kelvin is something like 0.2, 0.4, 10, 20, 30, 35 milli amperes whereas here it is what it 50 milli amperes 10, 20, 30, 40, 35, 40 and 45. So, about 10 milli amperes higher much higher current you get a lower temperature this is because of the mobility. Notice also this current rises steeply here with the linear region because the mobility is high the conduct tunnel conductance is high. Therefore, the current rises steeply the on the resistance of this higher atom mobility transistor is very low compared to on the resistance of the same at room temperature. By lowering the temperature mobility is increased and on the resistance is reduced very good for digital application. In digital application you want very low on the resistance. This is the saturation current ID versus transfer characteristics in the linear region you can see that the there is a crossing over and the current rises steeply at lower temperature because of improved mobility. Also notice that there is a threshold voltage increase when you go to lower temperature this is attributed to the freezing of electrons in the aluminum gallium arsenide layer. So, therefore, you must apply more voltage I am not going down to details of that. This is the transconductor this is the saturation ID versus vigorous transconductor you see you can see the transconductor this is very steeply rising in the gate voltage. You get transconductor tens increases from about 225 milliampere per volt 225 milliampere per volt here to about 400 milliampere per volt at this point for about 0.5 volts it is the transconductor tens is much higher because the transconductor tens depends upon mobility. Transconductor tens on the resistance everything improves because of the mobility go to lower temperature you get higher mobility higher transconductor tens by big factor. In fact, such high transconductor tens also tells you it is not due to velocity saturation it is due to the velocity overshoot if at all in addition to because of the high mobility. In summary of first part of this few more things I will discuss. Hydro structures enable special separation of electrons from the dopant electrons atoms very high mobility it can be attained enhancement of carrier mobility can be further enhancement can be achieved using materials such as indium gallium arsenide as channel materials. What we are using is gallium arsenide room temperature mobility is about 8500, but if you go to indium gallium arsenide you can get much higher mobility at least 2 to 3 times more than mobility than this at even at room temperature. Alternately we can use strain layers let us see what is that. If the region where this is in addition to these hemp etcetera even if you use commercial MOSFETs you can go to use silicon itself and subject the strain silicon to strain. If you have longitudinal tensile strain that is if you have tensile strain along the length of the channel it is stretched then the electron mobility improves. Stretch it along the length of the channel electron mobility improves. So, n channel devices you can actually stretch it by depositing silicon nitride on the top of the finish device that gives you rise to tensile stress which stretches the channel along the channel length which actually increases the electron mobility. The internal people have tried this out that were sort fine. Now, at the same token if it is a p channel device if I stretch it along the channel by tensile stress the mobility goes down. I am not getting down to the physics of that due to time I just do not discuss it at this moment. So, it goes down, but if you compress it if I subject the channel to compressive stress then the whole mobility goes up. So, the moral of the story is if I have n channel transistors that region you subject it to longitudinal tensile stress along the channel by putting silicon nitride on the top of that channel of the gate you can increase the electron mobility of n channel device. Wherever you have p channel devices you subject the channel to compressive stress how do you compress it between the source and drain for example, between the source and drain p for example, if I have the channel here, if I have the p plus here and if I have p plus here this is n I am talking of p channel device oxide here and then the gate. Now, what I should do is I must compress it in this direction because this is the p channel I must compress the p channel how do I do that you put introduce here silicon germanium silicon germanium alloy here. When you do this implantation or diffusion introduce also on both sides silicon germanium this actually because these atoms are bigger compared to the silicon atom the channel is in between the two layers which actually has bigger atoms. So, it pushes this channel in this direction that leads to compressive stress. So, the p channel devices p channel gets compression compressed along the length of the channel the mobility of holes goes up. This is the trick that the analog device I am sorry Intel here have done this all that I have said here is good in p channel it is silicon devices and the source and drain regions are formed by using silicon germanium channel is in compressive stress increases mu p. In n channel MOSFET electron mobility is increased by top layer nitride which introduces tensile stress. Now, new materials last few slides strain germanium, strain silicon all these can be used to increase the mobility over and above that. If I have silicon I can subject it if I have tensile stress you know electron mobility can be increased. If I subject to compressive stress you know that electron whole mobility can be compressive whole mobility can be increased. You can have germanium you can enhance the mobility over and above what it has got electron mobility and hole mobility by subjecting to strain how to do that. You can do that growing this similar metals we said for hydro structures you must have lattice match, but if I use lattice mismatch structures. For example, I have silicon here which has lattice constant 5.43 between the atoms I grow germanium on the top of that lattice constant is 5.65 silicon germanium will be in between either I go silicon germanium or silicon germanium if I grow thick layer the lattice will be that of this silicon germanium, but in between you can see the if it is thick layer it will relax to its own lattice constant and there will be broken bonds defective layer, but if I use the layer very thin there compared to this silicon layer then the silicon layer forces is back. This is a this is there is no strain here there is there are defects here thick that is why you cannot go thicker layers of hydro structures, but if I grow very thin layer then the thinner layer gets compressed by the bottom it is it is pulls pulls it back when you have one layer or the other the top layer is thin and the bottom layer is thick that actually pushes it like that compresses, because it tries to the bottom layer tries to pull it along that direction. So, that bond length increases like that there is compressive stress on this. So, bigger lattice atoms that is germanium and silicon will get compressed. So, if it compresses it is good for P channel if I have silicon germanium on germanium silicon germanium is smaller lattice constant compared to germanium you will have tensile stress you can make n channel MOSFET firm mobility. So, that is what is done there. So, this gives you actually there are you know this as you grow there is a critical thickness up to which you get this strain layer beyond that there is no strain layer it is defective. See for example, if I am growing germanium silicon germanium when germanium is x germanium is 0.2 I can grow at about 0.1 1000 angstrom that is 0.1 micron layer thickness which is strained with the which has no defect that is like this I can grow. If I grow more than that thickness then it it will be it will be like this defective layer. So, this tells you that if you want more germanium you know thickness that you grow will be very little. For example, if x small fractions of germanium you can grow hardly between 2 nanometers of germanium which is strain layer with the which is defect free. So, this layer is defect free, but it has higher mobility compared to that. So, now we will see how the strain induced layer can be introduced. So, the one or the approach of silicon substrate graded silicon germanium then relaxed silicon germanium which actually has that is constant more than that of silicon. If I grow silicon layer on the top of that it will be strained and it will experience compressive stress because along the horizontal direction compressive stress because that is constant of this is smaller compared to that and this relax the layer. So, it will start to stretch it it will it will stretch it. So, since it is tensile stress you can use that for or this will actually because that is constant of this is smaller compared to that and this relax the layer. So, it will start to stretch it it will it will it will it will stretch it. So, since it is the announced electron mobility by controlling the x in this layer you can control this lattice constant of this layer. So, bigger the lattice constant more will be tensile stress more the x here bigger the lattice constant more will be stress here more will be the strain more will be the mobility. So, you can see x is 0.13 you get much better than the classical reported mobility of electrons if you make x point to it you get even higher. So, this is one of the approaches which was reported in literature by some of the authors. So, electron mobility in strain silicon on the silicon germinium is higher because of we have taken experiences tensile strain. Now, there is one we can get dual channel this has reported in literature few years back silicon graded silicon germinium x gives 40 the most fraction of germinium and then you grow on this relaxed layer means actually the lattice constant is ground by how much x is there. On the top of that you go grow strained you grow silicon germinium with most fraction y larger than that of x. That means y larger than that of x means actually germinium content is more compared to the germinium content is here. So, if germinium content that is about 12 nanometers if the germinium content is more in this layer. That means it is lattice constant is more compared to the bottom layer if the lattice constant is more it will be experience because of this layer it will compress it it will try to bring it equal to this particular layer. So, there will be compressive test on the carriers here. So, if it compressive stress you get the compressive stress y is larger than that of x. How much is the compressive stress depends upon how much is y compared to x. So, because compressive stress the whole mobility in this layer can be increased tremendously. So, these are the results which are reported experimentally. For example, if y is 0.6 and x is 0.3 y is greater than x it is double. You get a mobility for this is as a function of vertical electric field for a given electric field you get the whole mobility which is about 300, 10 meter square per volt second nothing much to boast of. But I go to y 0.8 that is 80 and 50 much higher y you get mobility which is getting down to 800. Whole mobility 800 much more than that in silicon you go to 100 that is germinium itself there strain germinium then you get mobility much more than 1000 centimeter square per volt second that is the whole mobility. So, it is a power of using the strain layers. Similarly, if I put on this layer silicon strain layer I can get because this is smaller than this I can get tensile test I can make n channel here I can get p channel devices n channel device that is 12 channel MOSFETs I can make here. So, the whole mobility sensor factor is about 10 x there and electron mobility is announced approximately by factor of 2 all that they can be seen in that case and this is actually the result that you get whole mobility announcement you get if you use silicon germinium at source end but this is using strain layer you get much larger whole mobility compared to what we seen by using the silicon germinium at source end rate. Now, the last one what I am trying to point out here is actually we can have the heterostructure on insulator this is high. So, you can have the you can grow relaxed silicon germinium on that ok and you can grow strain layer here and put it upside down and bond on the silicon with oxide edge the top layer you can get strain silicon layer. So, what I am trying to point out is by using these combination of this bulk layers mount it upside down on the bottom layer and etching down the remain unwanted layer like this you can get strain silicon for example, here you can have this layer bonded on to the buried layer you can see here you have got silicon strain silicon put upside down bottom you have got this is coming at the bottom like this and bond it and etch the unwanted layer you get structures like the high. So, what a summary processing use stress has been used to achieve significant mobility enhancement in short channel devices ok silicon silicon germinium material systems has the potential to achieve very large improvements in mobility. For example, 10x hole mobility enhancement for strain silicon germinium have been reported. Hydro junction devices such as hemp enable very high mobility transistors using dope wideband gap semiconductors with that I conclude my discussion on non-classical MOSFET where we have covered where is the germinium channel.