 So, we continue our discussion on the compound semiconductor materials and devices which are useful when you go to nano scale particularly. So, what we said is we will take a look at material properties. We have gone through that in the last lecture and today we will see some more details about that and the properties, the velocity field characteristics and FETs using that what type of FETs are made popularly and then go on further. The entire reason for taking a look at non-silicon materials is hidden or is described in this particular slide. You can see that on the y axis you have got the electron mobility. We are looking at materials which have got electron mobility is higher than that of silicon which is the very popular material that is about 1500 centimeter square per volt second and the band gap is 1.1 electron volts at room temperature. So, if you have to use or if you have to choose an alternate material which is superior to silicon, one of the things that we look at is the materials which have mobility above this horizontal line that is above 1000, 1500 or so. So, there are lot of materials like example, indium antimonide, edema arsenide, gallium antimonide, germanium, gallium arsenide, indipospart including gallium nitrate recently. Now, it is not enough if the mobility is high they should have also fairly decent band gap preferably higher than that of silicon or at least close to that of silicon. If you take a look at those materials which are band gap higher than that of silicon, you have got gallium nitrate, but mobility is not much higher compared to silicon ideal value. Indipospart and gallium arsenide as we pointed out last time we have got much higher mobility for electrons compared to silicon at least 5 to 6 times that of silicon in gallium arsenide and at least 3 times than that of silicon in indipospart. Gallium antimonide has got higher electron mobility, but band gap is smaller than that of gallium arsenide, germanium we saw already that it is a potential material because of its high electron mobility as well as high hole mobility, but the drawback on the downside is that the band gap is lower, but due to when you do quantization confine make the thin layers devices on thin layers than that mobility band gap can be brought. So, now you can also see here as I already pointed out gallium arsenide has got higher mobility, indium arsenide has got even much higher to 20,000 centimeter square per volt second mobility, but if I can combine gallium arsenide and gallium arsenide and indium arsenide, make an alloy which is a ternary alloy I can have the combined effect of these two that is higher mobility than gallium arsenide can be obtained, but band gaps better than that of indium arsenide can be obtained. So, one takes look at materials like indium gallium arsenide, they are ternaries. So, you can see that when you go into compound semiconductors you have got variety of choices in terms of binaries, ternaries, quaternaries, quaternaries you have 4 elements gallium, indium arsenic, phosphate or materials like that. So, the ternary we are just talking of a material like gallium, indium arsenide where you mix indium arsenide and gallium arsenide already pointed it out last time. You can see 1 x equal to 1 gives gallium molecule is 1, gallium atom 1, gallium atom for 1 arsenic atom and x equal to 1 means indium atom is 0 that is gallium arsenide. So, x tells you the mole fraction of gallium in gallium indium arsenide. Usually stoichiometric gallium arsenide will have 1 gallium atom will have 1 arsenic atom, but if you replace gallium with indium atoms. For example, if I replace for 2 arsenic atoms 1 gallium atom and 1 indium atom that will be gallium 0.5, indium 0.5 and arsenic 1 at the gallium indium arsenide that is just to understand this symbol. So, here I can have gallium indium arsenide which will give you anywhere the band gap between the 2 and mobility anywhere between the 2 both will be direct band gap semiconductors. Now, other ternary compound semiconductor which is Wabler is aluminum gallium arsenide and gas x equal to 0 gives gallium 1 and arsenic 1 that is gallium arsenide. x equal to 1 gives gallium equal to 1 minus x is 1 minus 1 0 and aluminum is 1 that is aluminum arsenide. We can change in fact the band gap of gallium arsenide by moving from by keeping on changing the gallium concentration or in replacing gallium with aluminum atoms, L gas or aluminum gallium arsenide. So, in fact I had just began with some of these the discussions on these. So, what is happening is here is you can mix for example, I can have gallium arsenide and indium arsenide is here I can mix them together to get gallium indium arsenide. I can have gallium arsenide grown on aluminum arsenide or grow aluminum arsenide on gallium arsenide. See when you want to make hetero structures that is materials or devices based on 2 different materials like gallium arsenide and aluminum arsenide. You can do that provided you are able to grow one layer over the other without introducing defects. So, if you take a look at this chart which is very popular one the y axis gives you the band gap minimum band gap means the gap between the conduction band edge and the balance band edge. If you take gallium arsenide it is about 1.43 aluminum arsenide is 2.1 or so. Now, if you take the lattice constant, germanium, gallium arsenide, aluminum arsenide all of them have about 5.65 angstrom lattice constant. That means you can grow aluminum arsenide on germanium without having defects or the interface or minimum defects. You can grow aluminum arsenide on gallium arsenide or aluminum arsenide you see from gallium arsenide if you keep on adding aluminum in place of gallium you move in this direction and when x equal to completely 1 it is aluminum arsenide. So, you can see this solid line indicates that it is direct band gap. The dotted line indicates that beyond that point if you add more aluminum it becomes indirect band gap aluminum gallium arsenide. So, nevertheless you can grow aluminum gallium arsenide on gallium arsenide. In fact, there are heterostructures fabricated using l gas on gas aluminum gallium arsenide on gallium arsenide. Very good lattice match. Similarly, you can grow gallium arsenide on germanium. This has been one of the popular starting materials for gallium arsenide solar cells because you can collect entire solar spectrum with just about couple of microns of gallium arsenide. But gallium arsenide if it is you are using the full thick layer of gallium arsenide wafer it is very expensive. So, you can use a cheaper substrate like germanium on that you can grow gallium arsenide and make device p n junctions or heterotype of junctions on gallium arsenide to make the solar cells. So, that is gallium arsenide based devices. If I want to use indium phosphate based devices or gallium indium arsenide you can see gallium arsenide is here that is constant 5.65, indium arsenide is bigger lattice. So, it is about 6.1 close to 6.1 angstrom lattice constant. Now, if you mix them gallium arsenide and indium arsenide at a particular ratio you can get the lattice constant which is about 5.85 or so, which would match with indium phosphate. You can grow therefore, gallium indium arsenide on indium phosphate. So, starting with indium phosphate substrate you can make layers of gallium indium arsenide with a very good lattice match. So, this is just I wanted to show you that if you want to make stereo structures you can have gallium indium arsenide on indium phosphate or gallium arsenide on germanium or algeas on gas, aluminum gallium arsenide on gallium arsenide. So, this is the very popular diagram which people will take a look at to see which one matches with which one. See you can grow gallium phosphate if you want on silicon very good lattice match 5.45 or so, you can grow that whatever band gap material. If you take a look at the mobility, the mobility is low in the case of gallium phosphate. So, you can use it only for some optical applications like LEDs etcetera. You can mix them together also. Now, we take a look at the velocity field characteristics of the different materials. The very popular material that you have in use in industry is silicon. Silicon we have discussed this velocity versus electric field increases linearly initially then saturates scattering limitations. So, you can take the velocity 10 to the power 7, 1 into 10 to the power 7 centimeter per second. That is the velocity saturation velocity and mobility of electrons is much that you can get is about 1500 centimeter square per volt second. Now, if you take silicon carbide which is also an alternate material, mobility is not very high about 700 centimeter square per volt second, but it is a wider band gap material and used for high power, high temperatures that has got velocity field characteristics like this. Notice the saturation velocity in this case is much higher compared to that of silicon which would imply that you can use it for higher voltages, high fields, high breakdowns. So, power devices people tend to take a look at it at silicon carbide, but it is a more difficult material to work with. So, there are some restricted applications on that, but people are looking into that both for microelectronics as well as for microelectromechanical systems because it is a much tougher material compared to silicon. Now, they are both behaving almost identically, but if you take a look at this gallium arsenide, the velocity field characteristics are totally different because of the difference in the band structure of the gallium arsenide and silicon. Silicon is a indirect band gap semiconductor. We have discussed that gallium arsenide is a direct band gap semiconductor. We will discuss more details in the next few slides. So, because of this direct band gap material property, we will see soon that in the next slides the gallium arsenide velocity field characteristics increases practically linearly where low fields. You can see it is much deeper compared to the silicon velocity field characteristics indicating the mobility is high. The low field region velocity proportional to electric field linear it is deep, mobility is high about 8500 centimeter square per volt second and velocity keeps increasing, but after some electric field something happens which what we will discuss soon. And the mode of transport of the electrons changes and the effective mass of electrons becomes higher. As a result velocity falls and it falls and ultimately falls down to the almost equal to the saturation velocity of silicon. So, it goes up down, but most important thing to note is gallium arsenide has got very high mobility plus if you are operating in this region of electric field anywhere here, you can see the velocities of carriers are can go as high as twice that of saturation velocity. So, one can visualize that you can have devices which have got which have got high velocities. So, that is what we are looking for high mobility high velocity. If you take a look at indium phosphate which is slightly lower band gap than that of gallium arsenide and slightly lower mobility it has got similar characteristic like that goes up down. Take a look at gallium arsenide which is again the direct band gap semiconductor mobility is lower than that of gallium arsenide, lower than that of indium phosphate. So, it is slope is smaller goes up peak field reaches at fields like 50 kilo volts per centimeter. That means, you can see that this can be used for very high fields or high voltages. So, power device people more than nano device people power device people take a look at this gallium nitride as a alternate material or making high power devices high voltage devices a lot of work is going on that. We can see the peak field peak velocity is about 2.5 into 10 to 7 mobility may be lower but the peak field is high. All these have implications on the carry transport in these type of materials. Let us take a look at what why such a thing happens in gallium arsenide. If you take a look at gallium arsenide, we have said the velocity field characteristics is like this 2 such a more than 2 sometimes people quote. The energy band diagram if you look at the allowed states in the conduction band the energy on the y axis and x axis if you plot the momentum that is E k diagram we called E k diagram. Usually when we plot the energy band diagram we plot the energy band diagram by the dotted line that is the conduction band edge and this dotted line that is the balance band edge. So, we talk of transition between the top of the balance band and the bottom of the conduction band. Now, if you take a look at gallium arsenide the energy versus momentum diagram follows this route. I am not going to more details of that there is too much of physics in there but what we have to understand is these are the allowed energy conditions those this is the minimum energy position in the conduction band. These are the allowed states in the conduction band energy conditions. So, if the electron is here the minimum in this conduction band edge coincides with the maximum in the balance band edge. That means if an electron has to transit from conduction band edge here see if you take a look at this conduction band if in thermal equilibrium all the electrons in the conduction band edge will be located around this minimum. Electrons tend to occupy the minimum energy position and the holes tend to occupy the maximum energy position because that is the minimum energy position for holes. Holes should be here balance should be here. So, electrons all of them are located here thermal equilibrium condition which should be in if an electron transit from the conduction band edge here to the balance band edge that can happen just by losing that energy and that difference in the energy can be absorbed by a particle like photon light. It can be emitted as light because of its large wavelength the momentum is small. So, there is no momentum difference between the electron here and here. Therefore, the conservation of energy only required supposing this if you talk of silicon it is not a direct band gap. It is a band it is a band gap is slightly different for example, if I take a look at the if I take a look at silicon the conduction band if you take a look at silicon the conduction band the balance band edge will be like that. The conduction band edge minimum will be somewhere here and this point will be something like something like that. So, this will be conduction band edge this will be balance band edge that is E c E v. So, you can see that this is a minimum of the conduction band edge position. If the electron has to transit from here to here this is the energy and this is the momentum k. This transition will have to can be accommodated by a particle which can absorb the energy difference and also the momentum difference. The photon cannot do that it has to take the through some intermediate levels or the phonons. So, this transition is called indirect band gap transition or the material is called indirect band gap semiconductor. So, always this electron will be remaining here and transition will be from here to here by with the help of phonons. Now, if you go back to the gallium arsenide or indium phosphide you will see the direct band gap. The transition can take place with the help of photons. So, that is the direct band gap material. Now, what we are trying to see is what happens if I apply electric field to the gallium arsenide material. If I have a contact and if I apply electric field between the two the energy of the electrons here goes up. So, between the two omicontacts when I apply voltage current will flow because with the velocity v decided by this curve. As we increase the electric field velocity will increase linearly initially and during all this portion all this electric field the energy of the electrons is much smaller than the energy required to move to this point. The difference between this valley the central valley and the satellite valley is if the electron is here just will borrow the result the effective mass of the electrons here is small that is 0.067 times the rest mass of electrons mass of electron in vacuum. So, the 0.067 effective mass times the mass of electron. If the electron is here the effective mass is much higher than that. So, long as the electron remains in this particular region which will happen till it goes on acquiring energy from the electric field the electron will remain in this region. So, it will go with the velocity decided by the small effective mass. Effective mass small means the mobility is higher. If you remember we have derived it earlier shown that mobility is inversely proportional to the effective mass. Mass is smaller mobility is higher. So, velocity is higher, but once it goes higher and higher velocity the energy of the electrons is goes up so high that it finds it can get scattered to this level. If the energy is comparable to that because by about 0.31 electron volts it can just move from here to here. It can get transition and go from this valley to this valley. So, if the electron moves from here to here see it has gone to this particular position. Electric field equal to about in this case for gallium arsenide 3 kilo volts up to that point if you go the electron energy is or velocity is sufficient or the energy is sufficient for the transition take place from here to here. So, once it moves into that point with that energy there suddenly it finds itself to be heavy. Half m e square is energy here half m 1 v square when it is transferred here it is half m 2 v square m 2 is larger than m 1. So, velocity starts falling immediately. So, it is not as if all the electrons will get transferred immediately it will begin transition from here. So, many of the electrons will start moving from here to here as you go to higher and higher electric field. So, what is parted here is I am not showing the calculation ratio of electrons n 2 here divided by total number of electrons n 1 plus n 2. If n is the total number n 2 divided by n that is n 1 plus n 2 is what is parted here. For example, here it is n 2 is equal to 0, but at that point good fraction of electrons have started transporting on to the satellite valley. As a result number of electrons in the satellite valley goes up number of electrons which have higher effective mass goes up. So, number of electrons which have got lower velocity goes up. So, the average velocity begins to fall it begins to fall ultimately it approaches this 1 into 10 to power of 7. So, you have got the region so called the negative differential mobility region is obtained here. So, you have got transition from this central valley to the satellite valley which results in the reduction in the velocity, but notice in between the region you have got the velocity much higher than this 10 to power of 7. So, please remember that there is a region where you can get very high velocity. Suppose you have the electron here this is actually what we are plotting is a steady state velocity gradually increase the electric field. So, that give a time enough for them electrons to acquire thermal equilibrium and transfer on to that, but suppose you have electrons just near that source inject straight away into the channel where there is very high field the electron just gets injected into this region it finds itself in the very high field region. So, if it is very high field region ideally if it is very high field region velocity field characteristics here supposing it is field is here it is straight away find itself into launched on to that high field. So, it will just keep to go into that velocity so long as it is in this region. So, in the steady state by the time it has acquired on to this region it has begun transfer transition to this, but if it is transition suddenly when apply for the transition to take the from here to here it does not take this immediately it takes a finite time. So, for a finite time it experiences that high electric field with that high mobility. So, velocity can shoot up here much higher than even this velocity so long as it remains here that is what is known as velocity over shoot effect in the transit conditions that we will see subsequently. Now, let us see how it will happen in the case of indium phosphate. Indium phosphate has got similar structure except the band gap is instead of 1.43 it is 1.35 and this difference in this energy instead of 0.31 is 0.53. That means, if I keep on applying the electric field for the electrons to move from here to here I must go to higher electric field. So, the transition from this center value to the upper value will take place at higher fields here supposing for example, here the transition begins at 3 k v because it is enough if it acquires 0.31 electron volt energy, but if this gap is 0.51 the transition will take place at a much higher electric field that is what we see here. See for example, Gallium austenite velocity field characteristic is in this fashion the transition from the lower value to upper value takes place at 3 k v per centimeter. Indium phosphate the mobility is low the slope is smaller and it takes more electric field require more electric field to acquire enough energy to transfer from here to here. Therefore, it remains in the lower value for longer attempt of electric field and by that time it goes to much higher electric field. See it has to go to much higher electric field to go to transition to the next region because see compared to this case 0.31 electron volt energy this case 0.53 electron volt energy. So, it requires more energy to transfer from the lower value to upper value. So, you go to higher electric field and higher velocities are required. So, you can see that the peak velocity in deposit is much higher than that of Gallium austenite. Silicon you can see that is hardly seen you do not have that transient you do not have that or peaking of the velocity field. Now, let us take a look at the transient condition I am sorry just I will just go into the transient condition come back to this of the transient condition right away problem. I should have had this slide before I will take on this first. Static state electron velocity and the transient velocity what I have plotted here on the right hand side is let us take a look at Gallium austenite. Since I just mentioned about the transient velocity I will take a look at this slide itself. Static state conditions drift velocity versus electric field silicon is like this y axis 1 into 10 to power 7 here Gallium austenite slightly more than 2 into 10 to power 7 centimeter per second it overshoot is there then comes down. Now, if I have that transient condition which I have just pointed out supposing I have the electron in the lower valley that middle valley and if I apply voltage electric field suddenly for example, if I apply 1 k v suddenly transit steady state 1 k v velocity is almost close to 10 to power 7 here scattering limited is also 10 to power 7 I feel. So, if I apply 1 k v per centimeter it will go up to that point and remain there it transitions from the from sorry from this valley to that valley does not take this because the energy is not sufficient. Now, if I go to this particular electric field for example, if I apply 10 k v per centimeter. Suddenly in the sense electron is cold in the source it is injected into the channel where it sees very high fields because of the voltage applied to the drain region if it were in steady state we can see that 10 k v per centimeter the velocity is here. But for the electron to see the 10 k v per to see to go to the steady state value of something like about close to 10 to power 7 centimeter per second it cannot go suddenly to that upper valley before it goes to the upper valley it remains in the lower valley experiencing the velocity the electric field of 10 k v per centimeter. So, whatever mobility is there that is actually the mobility decided by the lower central valley where the effective mass is low. So, mobility 8000 into that electric field 10 k v it will suit up to that high value. So, and it will acquire energy and it will go much more than what it will go in the steady state and suit up and by the time it has suit up it has acquired it can see it has acquired it will acquire velocity is even much more than that peak velocity of 2 into 10 to power of 7 centimeter per second. These are actually simulation results using Monte Carlo simulation which has been reported way back in 1977. So, it will go to that higher velocity overshoot will be there over and above the steady state velocity once it goes that velocity it has acquired sufficient energy to get scattered to the upper valley where the effective mass is lower. So, once it gets scattered to the upper valley it is velocity falls down. So, you can see that for a short period of time like about 10 to power of minus 12 0 to 1 because this is x axis time y axis velocity the bring a short time when it has remained in the lower valley and when it has experiencing high fields there will be high velocity. But, once it has acquired that high velocity it is energy has gone sufficiently large that it has gone to the upper valley where the mass is higher. So, velocity starts falling. So, you can see in 1 micro second 1 picosecond during that 0 and 1 picosecond if there is high field in the channel the electrons can attain high fields. In a sense if you make short channel devices you have a chance that the electrons have got velocities even higher than the saturation velocity. Let us see what is the distance traveled during this time of 10 1 picosecond. So, what we have to do is I can plot velocity versus distance along the channel. What do I do? Multiply velocity versus time and plot it like this. So, you can see for Gallium arsenide this is a same graph I have shown here velocity versus time and you multiply velocity versus velocity into time and plot it as velocity into distance you can get velocity versus distance plot will be like this that 5 by the time it has reached peak it has gone beyond about 0.2 micrometers. So, you remember this scattering distance within 0.5 micrometers exist in the case of Gallium arsenide. You can see if the channel length is 0.5 micron when the electron has moved from 0 to the 0.5 micron its average velocity has gone through 2, 3, 4, 5 into 10 to power 7 centimeter per second and it falls. Average velocity is much larger than the saturation velocity of electrons here. Similar effects are seen in the indium phosphate. In fact, you see even slightly better. So, what we are telling from here is you can get you making use of this velocity overshoot effects. You can go to channel length which are 0.3, 0.2 microns length and acquire high velocities. Therefore, very short transit times can be acquired and you can get much higher speeds. So, that is what I just wanted to point out here. In fact, I have skipped few slides. I will go back to those slides after this. So, here so velocity overshoot occurs when the carrier velocity in transit conditions exceeds steady state drift velocity. That is steady state is something much more than the steady state velocity here. Steady state velocity for that region is much smaller, but it is much higher than that. Velocity overshoot does not occur when the electrons are confined to the central valley. For example, if the electric field is 1 kV per centimeter, the electrons do not have the energy to go to the upper valley. So, they are right through their confined to the lower valley. You do not see the velocity overshoot effect. The velocity overshoot in gallium arsenide and indium phosphate occurs if the carriers get transferred to the upper valley, where the electron mobility is lower. So, velocity overshoot effects and high electron mobility, these are the ones which encourage people to take a look at more and more into gallium arsenide and short channel devices and that lead to superior performance due to higher mobility. But, one will actually see that quantization effects may ultimately upset the advantage of gallium arsenide as we discussed next. What is this quantization effect? See, gallium arsenide, the main advantage is the mobility of electrons is high, the low field mobility is high and because of that you are able to get the direct band gap effect and because of that you are able to get the velocity overshoot effects etcetera. Now, if I use very thin layer of material, as we have seen in the SOI, the due to the quantum confinement effect, the band gap increases. In the case of silicon, it is a direct band gap material, in the case of germanium, it is a direct band gap material and the band gap goes on increasing. This can be used as advantage in the case of germanium because higher band gap, it enables you to overcome the poor performance due to the lower band gap in germanium. In gallium arsenide, you have the direct band gap, now if I make thinner layer of gallium arsenide, surrounded by wider band gap materials, you will have quantum confinement effects and these effects, the relative occupation of carriers in these valleys. For example, if you recall the quantum well, potential well problem, the energy level would split the distance between the energy levels will be increasing if the width of the quantum well is reduced. Thinner the quantum well, more will be the distance between the energy gaps. So, if I have a particular energy gap material E 1, E G, the energy gap will keep on increasing and the how much is the splitting of the energy level depends upon how much is the thickness of the material. Thinner the material, more is the splitting. It also depends upon the mobility or the effective mass, the mass M. Smaller the mass, more will be the splitting. Now, take a look at these two, these two, these two you know valleys, central valley of gallium arsenide and the satellite valley. Here the effective mass is smaller. So, when the confinement effect comes in, this energy levels here will move faster and faster with the electric field and increase the, I am not electric field. When they reduce the thickness, the energy levels between will become more and more, much faster here compared to here because here the effective mass is 0.55 times I am not. Here it is 0.067. So, this you can actually visualize the situation where this gap, this gap keeps on increasing much faster than this gap. So, what you, one can imagine a situation where you will have, where you will have, see for example, right now I have the energy band diagram like that. That is the satellite valley, this is the, I am that is the satellite valley. So, the electrons are here. Now, the energy levels here itself will split. What will happen will be this band gap which is actually the band gap of gallium arsenide, direct band gap that will increase much faster and it will move in the direction and you will have exaggerated and so it is like this. It will move to that because of these smaller effective mass, the split will be more. What was direct band gap here can become indirect band gap. It will remain direct band gap if this also moves same way, but the effective mass here is smaller, I am not into 0.55. Here it is 0.067 times 0. This also will move, but this will move somewhere here like this. What will happen now? This has moved here. So, this is the direct band gap from there to here and the actual band gap will be from here to this point because that is smaller compared to that. So, what happens is, what I am trying to point out is this particular, whatever was direct band gap, that band gap increases much more than whatever was this, this direct band gap. So, in effect what would happen will be, this goes off and you will end up with this, the transition is between this and this because this is the EC and this is the EV. Initially, it was EC was here and EV was here, EV 1. This is EV 2 and EV 2. Due to quantization, EC 1 has become EC 2, EV 1 has become EV 2 and the EG, whatever was there has become this one. Whatever was direct, the material is no longer direct band gap material. It becomes indirect. You may ask, so what if it is indirect band gap? It will not be useful for up to electron applications, but you see what you have done. Electron has high mobility here because of the sharp nature of the EK diagram whereas, the electron here has got lower mobility, higher effective mass. So, the electron remains here, the mobility of the electron is smaller. So, whatever effect, in fact you had on gallium arsenide when it was direct band gap, high electron mobility, all that is lost, all velocity overshoot effect, high velocities, all will be lost when you go to quantization. So, the moral of the story is when you go to very thin layer of gallium arsenide, you may lose, when you go to thicknesses like 2 or 3 nanometer thickness of gallium arsenide, you will encounter this effect. But still, if you are using say 10 nanometer, 15 nanometer, you will still have the benefit of gallium arsenide. So, you can still use with the advantage for those thicknesses, you can still use gallium arsenide for nanoscale devices. So, that is what I was trying to point out here. So, it is not all that dangerous, but you have to worry about that effect, the direct becoming indirect when you go to thicknesses below about 4 nanometers. So, gallium arsenide is excellent material. I will come back to these discussions later. It is excellent material with high electron mobility and all that we have discussed now, but they also we have seen, they lose the advantage when used in thin films of thickness below 4 nanometers due to quantization effect. Now, let me go back to the slides which I skipped where what type of devices can you make with gallium arsenide. So, what we have seen is gallium arsenide has got high electron mobility and it has got chances of having velocity overshoot effects, velocities in excess of saturation velocity. And we have seen that saturation velocity effects come into picture when you go to short channel effects. That means, when you go to short channel effects, you can make use of the velocity overshoot effects. In fact, they have made channel device channels which are shorter say of the order of 0.5 micrometers or even smaller than that, seen that the effective velocities as high as 2 into 10 to power of 7 can be seen with the gallium arsenide based devices. Now, one of the very popular devices which are used for gallium arsenide is the mesh threat. Now, why not MOSFET? You can use MOSFET that is you can use metal oxide then gallium arsenide layer, but the interface state density in gallium arsenide is very high. The problem that we have with the germanium which we have explained was seen in gallium arsenide as early as in 1980s. People have spent lot of effort, lot of research effort has been put in in gallium arsenide for surface saturation, so that you can deposit a dielectric and make MOSFETs. But, not with great success with some success, I will tell you that aspect after we discussed this particular device that is a mesh threat. Since initially there was not much success with this MOSFET, the alternate device that they thought is suitable is make a mesh threat. Take n type gallium arsenide. We make devices on n channel devices using n type gallium arsenide. So, what is done is just like what you did in the SOI, you can have gallium arsenide layer on SOI, but if you grow gallium arsenide on SOI that will be not be single crystal. Instead of SOI what you do is whenever you want to use materials like gallium arsenide, indium phosphate or gallium nitride you will use a high resistivity material at the substrate. See for example, in silicon technology we had silicon on sapphire, SOS. Sapphire is high resistivity material, single crystal very costly. You can grow silicon on that, take make devices on SOS. Alternate was SOI. In gallium arsenide, take semi-insulating gallium arsenide. What is semi-insulating? It is not insulating. Insulating material will have resistivity of the order of 10 to power 13 to 10 to power 14 ohm centimeters. Whereas, gallium arsenide band gap is 1.43. Intrinsic array concentration is of the order of 10 to power 6 centimeter square, 6 per centimeter cube, 10 to power of 6 centimeter cube, pairs per centimeter cube whole electron pairs. Silicon it is about 10 to power 10 per centimeter cube. Gallium arsenide about 10 to power 6. So, we can see about 4 orders of magnitude lower carrier concentration in intrinsic gallium arsenide. That would mean we can have about 4 orders of magnitude higher resistivity for gallium arsenide. So, undoped gallium arsenide, pure gallium arsenide, intrinsic gallium arsenide, intrinsic pure, that can show about 10 to power of 10 ohm centimeters, close to about 10 to power of 10 ohm centimeters. You do not call it as insulating. You call it as semi-insulating gallium arsenide, SI gallium arsenide. You will see all these terms in compound semiconductors. Semi-insulating gallium arsenide, semi-insulating indium phosphide. So, take that material, grow gallium arsenide on that. Tickness of this layer you can choose. How to choose that? We will see the difference upon just like the soil layer. What would be the threshold voltage that you require? That will be the criterion for choosing that. That is the channeling that you want to choose. See, for example, if I want to short the channel length in SI, you have to use thinner layers. Similarly, if I want to short the channel length more and more effective to avoid short channel effects, you have to go to thinner and thinner layers of active layer. So, the device that we talk of here is not MOSFET. It is metal semiconductor contact. How would this work out? This has the rectifying contact at the center. I have not put this contact away. Ideally, it should be as close to this contact as possible. Like in the case of MOSFET, this will be N plus region with very close contact to the gate region. You are able to isolate it because of the oxide layer. Now, I have shown this electrically separated, but as close as possible to this gate metal. I cannot keep it very close to this LSElphaline with respect to that because then there will be shorting between the source and the gate or between the train and the gate. So, you can see these two contacts are the ohmic contacts. So, you have a N type semiconductor to which you have made ohmic contacts at the edges. So, if I do not have anything here contact, this electrode is, if it is absent, what you will get will be, take a bar of semiconductor, make contact to the edges of that, apply voltage is like a resistor. You will get a I V characteristics for the like whichever resistor when the fields are small. When you go to high fields because of velocity saturates, current also saturates. So, you get a characteristic similar to the transistor there. Now, here that is of no use for us. So, what you do here is you get put a gate metal here by which you control the depletion layer below that, below this region. You know that a metal semiconductor contact, if it is rectifying contact, there is a depletion layer below that. So, let us go to the next diagram. Gate material forms rectifying contact with the N region. Ohmic contacts are source and drain regions because this can directly supply the electrons to this channel. Now, let us see what happens here if I have a gate here, metal semiconductor contact. What I have drawn here is the depleted region. Initially, first let us talk of the case where I do not apply any voltage to the drain. Just apply the gate voltage with respect to the source. It is as good, it is a omicontact, it is as good as put in the contact below that somewhere. So, when I do not apply any voltage anywhere, metal semiconductor contact, if it is rectifying contact, there will be a depletion layer below this metal. What I have put here plus is the depleted donors, depleted of the electrons plus here represents a donor atom which has, which is depleted of its electrons. So, this is the depletion layer H that I have plotted. So, due to the built-in voltage V B I, we have seen when we discuss Schottky barrier device, we have seen that there will be depletion layer H. How much is the depletion layer H with H depends upon what is the built-in voltage? What is the built-in voltage depends upon the doping level and the barrier height 5 B n. This is also we have seen and just recalling your memory. So, here if you just go back to the some analysis, supposing I have built-in potential V B I, if I instead of A I will contest H. If I have V B I, I replace A by H. So, V B I will be equal to Q N D. N D is the doping concentration into H squared by twice epsilon R epsilon 0. So, the built-in potential which is decided by the work function difference of this metal and semiconductor or the barrier height as well as the doping concentration mostly by the 5 m s or the barrier height. This built-in potential decides what is the depletion layer with these. Now, you can see if I have a depleted layer here, what has happened is the channel thickness is reduced by this quantity. I can draw that in a separate diagram. See if you take a bar of semiconductor just to get some clarity on that, you take a bar of semiconductor that is the omicontact. In the picture there I have shown the contact on the top, equivalently I have a voltage applied here V D S. Now, if this is n type, if there is no metal the full height A is available for conduction. So, the current flow will be when I apply V D, I can take this as V D by R S, R total resistance. This will go like this, that is the bar going like this, this is the contact here. So, the entire region is available for current flow. Now, if I put a metal on the top of that, what happens is I can draw the diagram here. I just draw it right here, that is a metal. Now, underneath that part of that will be depleted because of the, because this acts as a retweing contact. So, let us see that how that will be. There will be depletion layer below this. Is it a two dimensional effect? Normally when we plot this, we plot only this portion. So, just let me remove that. So, I will have the depletion layer. You will have the depletion layer like this. So, this much width is now not available for current flow. So, if this is A and if this is H, what is available for current flow is only this portion, that is A minus H. So, the effective area for cross section is reduced now. So, that means, by using this gate, I can control the thickness of this channel, which is available for current flow. I can apply a reverse pass to this gate and the depletion layer will be widened and this A minus H, what is available will reduce. So, I can control the current flow to this drain and the source by change gate applying the voltage to the gate. So, I will discuss this more details about that in my next presentation, how this actually works like a transistor. What you have to see is by applying the voltage, I control the area of this channel.