Free Physics NEET Video Lectures for Electronic Devices

00:00:30 H it's WMA from IIT Kpur and I will be giving you a series of lectures on semiconductors and when I say conductor it is the electrical conduction that I mean and you all know that uh metal s are said to be good conductors. All our wirings in houses or when you make a circuit on your table, you use connecting wires and all these wires have mostly copper in it which is a metal and a very good conductor and we use these good conductors because uh they easily conduct electricity and the power loss is is small. If I use

00:01:29 aluminium in some of the old fans etc. they use aluminium coiling also but then lot of power is wasted because of this low conductivity of aluminium as compared to copper. Then we have another class which is insulator any plastic or any rope or any string these are insulators. If I have a battery, I cannot connect the bulb using ropes. The bulb will not glow because the rope is not conducting electricity. So what is a semiconductor in between? As the name indicates the conductivity is much smaller than the

00:02:13 conductivity of the metals. If you compare with copper the materials which are called semiconductors will have a conductivity some 10 to the power 11 times smaller than the copper then why should I use that a lot of power wastage will be there if I am not preferring aluminium over copper why do I prefer this semiconductor whose conductivity is 10 ^ 11 times smaller But it is extremely extremely extremely useful component in uh circuits, electronic circuits. The entire modern life is revolving around

00:03:00 semiconductors. Be it a mobile phone, a digital camera, a tablet, a laptop, desktop, any kind of control system, Mongalan and Chandrean, all those electronic control systems, they use these semiconductors also, washing machine, anywhere if you have to control something, most of the time you will find that semiconductors are being used. amplifier. H uh someone speaks from a distance, a microphone is there and then amplifier and then it goes to loudspeakers. All those amplifier circuits they use semiconductors. So

00:03:41 what is so special about it having such a lower conductivity still it is so much of useful. There are many many things that make it useful and one thing is you can control the conductivity in semiconductors. The conductivity is copper is god-given. I cannot do anything to it. But by simple processing of materials I can control the conductivity of semiconductor. And whenever someone gets some control to tune things, lots of applications result. And that is why this uh semiconductor is so important.

00:04:24 Nowadays LEDs are being popularized because they consume less power. These LEDs are nothing but made of semiconductors only. So it is at the center of our life and it's very interesting to understand why semiconductors are so different from conductors and insulators. So before going into semiconductors let us understand what the conductor is. So as you all know you must have read in your textbook a metal is a good conductor because it has lot many free electrons. So this word free electrons. What is this

00:05:16 free? What what is that freedom that these electrons have in a copper wire or a metal block? You have lot many free electrons. They are free to move anywhere in this metal. Do they not interact with the nucleus? Are they not bound to any of the atom? They are. They are. It's not a free space. It's not in a vacuum that electrons are moving. You do have all those nuclei, other electrons in that system, ions. And these electrons as such are are bound to one or the other atom. But they are bound by very weak

00:06:07 interactions. Not weak interactions, strong, weak and gravitational electromag. Now the strength of interaction is quite weak. You know you have an atom which has a nucleus and then uh you have 1 s, 2 s etc. 2p some 2p 3s and all those things and then the electrons are bound to this but that uh strength of binding goes on decreasing as you go for outer and outer orbits. So if you have a electron in this orbit at a quite distance from the nucleus then the binding is weak. So in a conductor there

00:06:49 are some electrons which are very weakly bound to the nucleus and are so weakly bound that because of any kind of thermal interactions with other things at any temperature finite temperature all these things can get some energy from the crystal randomly uh interacting with each other some exchange of energy does take place and because of that it can just leave this atom. But if it leaves this atom, it's not that now it's free. Some other atom is is is sitting here. It also has its own uh orbits and

00:07:29 orbitals and states and so on. So it can just make a jump to that other one if it finds a place there. So it can easily change its position in the latice. That is true. But uh it hops from this atom to that atom that atom to that atom because it is so weakly bound. So that's the meaning of free electrons. So first approximation is fine that they are they are free almost free. So you can assume that there's nothing to stop there and only occasionally it gets scattered from this side and that side changes its

00:08:05 speed and direction and so on so forth. But uh if you go you have to go slightly deeper to understand semiconductors. Okay. So then this uh binding is very very important. So let me go little more in this uh in this context and see how these energy levels in a solid material like copper or in a semiconductor or an insulator how these energy levels behave in solids. So you must have gone through that hydrogen atom energy levels. So in hydrogen atom what happens? You have a proton and then you have an electron and

00:08:47 these interact and then you say that there are orbits and all those things. Essentially what it is that you have some particular states which we call quantum states. Okay. Which we call quantum states. Why quantum? Because these states if they change energy they change energy in finite steps. So quantums. So they are quantum states. The one quantum state which has lowest energy let us draw a line to show that if it had some kind of state not actually circle or ellipse some kind of state some kind of

00:09:28 distribution around this uh uh proton. the energy of that quantum state is is lowest and we draw a line here. And in fact at this same energy there are two quantum states. The electron can be in one state or the other state with the same energy and that's the lowest energy and we call them 1 s states. Then you have uh a jump a quantum jump and then you have yet another states with different kind of distributions. And there the energy is 10.2 electrons volt above this energy difference is 10.2

00:10:21 electron volts. Nothing in between. Electron can be in one particular state or in some other state. But the lowest available state has this energy. And the next lowest has this energy which is 10.2 eV above with some zero somewhere people say that this energy is -3.6 eV and this energy is -3.4 4 EV and similarly you have other states and here in fact you have eight quantum states at the same energy and you call them 2s and 2p. So the states have different kinds of distribution around the proton. So

00:11:11 that's why the name separate names 2s and 2p. This will have two quantum states and this will have six quantum states. So a total of eight quantum states are here and so on so forth like that. Similarly if you go for other atoms you have energy levels. Let us uh start with sodium a very simple system a sodium atom. Okay. So a sodium atom how many electrons are there? 11. Okay, 11 electrons. And we say that the electrons are distributed in different uh these quantum states. And the electronic configuration is

00:12:08 written as 1 s2 2 s_ub_2 p6 and 3s 1. So what is this? You have uh 1s quantum systems, quantum states at some energy which is the lowest one. So you have 1 s then you have uh somewhere 2s then somewhere 2 p then somewhere 3s and so on and 3 p and 3d and 4s and all those quantum states are there. All s states will have two quantum states. All p states will have six quantum states. And a wonderful aspect of nature is no quantum state can contain two electrons. Either that state will be empty, no electron is there to occupy

00:13:10 that state or at best one electron can be there. That is called polyexclusion principle. And our nature is like that. I can only say that much. So if there are 11 electrons to be accommodated then to have this lowest energy you have two electrons here, two electrons here, six electrons here and one electron here. Then uh there are other quantum states which are all empty. This 3s quantum there are two quantum states. One contains an electron and other contains nothing. So this is that atom one atom. Now think of sodium

00:13:57 vapor on street street lights. You might might have seen those yellow lights coming in at lamp posts. They are sodium vapor lamp. So it contains sodium vapor which gives yellow light. So in a vapor you have a lot many sodium atoms but they are in a vapor state gas state. So the separation between them is uh quite large and interaction between one atom and other atom is very small negligible. So each atom independently will have one ss state 2 ss state 3 2 p state 3 ss state and so on. So each of these atom separately one

00:14:44 atom is here one atom is there one atom is there you will have this 1s state for each one you will have this 2s state 2p state and so on 3s state and all these 1s states will be occupied by two electrons in this atom two electrons in this atom two electrons in this atom and so on. So even if uh you have large number of atoms but not interacting with each other like in a gas very very weakly interacting you still have put pick up any electron either the energy will be this or the energy will be this or the

00:15:28 energy will be this or the energy will be this. If you have n atoms a total of n atoms and you know what is the order of this n you take any gas sample or any material sample which you can see which we can handle this number is going to be 10 ^ 20 21 22 and so on. It's a large huge number remember. So at this energy you have 2 n electrons. At this energy you have 2 n electrons. At this energy you have 6 n electrons. At this energy you have 1 n electrons and no more electron can uh go in this energy. No electron can go in

00:16:16 this energy. In this energy here there is a freedom half the states are still available. So if this electron this 3s electron let's say this 3s electron here it's somehow it can talk to the neighbor and there also you have 3s electron here. One quantum state is empty here. One quantum state is empty here. And if they somehow uh mutual adjustments this electron can go here or this electron can go here or this electron can go here. Some kind of uh movement some kind of exchange is possible is possible. Although in atoms

00:17:04 gas in gas state they are too far away from each other. Such interactions and such uh interactions are are are not very likely but it is a possibility but 1s electron no chance no chance all 1 s quantum states are are filled. Now what happens when we cool this sodium gas and make it a solid sodium lump where the distance between the atoms is uh is now smaller and then the sodium atom and the neighbor sodium atom they start interacting and that affect this energy. Okay, that affect this energy in

00:17:59 hydrogen atom we say that the lowest is -3.6. Why? Next one is -3.4. Why? From where these numbers are coming? These numbers are coming because you have a particular type of interaction between the nucleus proton and this electron. So that interaction decides that kulum interaction kulum attraction that decides that it will be minus3.6 6 and -3.4 four and therefore uh and so in sodium you have a nucleus of 11 protons and then you have these 11 electrons which are interacting with each other and all

00:18:40 that interaction decides that what will be the energy of this what will be the energy of this what will be the energy of this and when atoms come closer it's no more interaction of electron with the nucleus of 11 e charge and the other electrons uh among themselves. It also interacts with the neighbors electron at least which which are in the outer orbits and since the interaction is changed. These energies are also changed energy of the quantum states are also changed. And it can also happen that uh

00:19:21 the for example all these uh two n states which are here at the same energy. So some of the quantum states the energy goes up. Some of the quantum states energy goes down because uh the atoms are also not fixed. They are vibrating. uh and so the exact environment of one atom at any instant may not be the same as the environment of the other atom. It is interacting with its neighbors that is interacting with its neighbors. But then uh since uh things are not static, this interaction here with the

00:20:01 neighbors and that interaction there in with the neighbors could be slightly different. And therefore some of the quantum states may go up, some of the quantum states may go down. And what you have a sharp line here. All the 2n 1s states are at one single energy can spread out. All these quantum states may not be at that same energy. Some spread can be there. So this 1s and this 1s may have different energies. Although 1s is very close to that that nucleus and you have outer electrons then outer electrons the

00:20:44 inner electrons are not affected much by these interactions. Only the outer electrons are affected uh significantly. So in principle yes but in practice you can still assume that uh all these energies remain here. And similarly here here but here here the outer one here it can be a very very different story. Here it some of the quantum states have gone up some of the quantum states have gone down in a small energy gap a fraction of a eV how many of these are are there this n is some 10 ^ 20 21 22 etc. So

00:21:29 these discrete states may not look discrete. They will look almost continuous. All energies are available but they are discrete. You can count whether it is 10^ 22 or 23 or 24 whatever you can you can count but still since uh originally it was just one single line everything was merged there and now it is spread in a very small fraction of electron volt or so. So it will look like a continuous thing look like this. Here the spread will be there but less. Here it will be still less. Here it will be almost

00:22:10 negligible. So these are called energy bands and these are called energy gaps. These are gaps, energy gaps. So originally I drew two lines and there was a gap and now you have two bands and then the lowest of this band and then the highest of this band. This difference is the energy gap. So in solids you have such energy bands separated by energy gaps. Now suppose uh I apply an electric field. How is the current goes in a in a wire? When you take a battery, when you take a battery and you take some kind of a bulb or something,

00:23:12 some resistance and connect it here, the bulb glows or if it is some kind of heater, it becomes warm. So what happens? How does the current go? This uh when I connect everywhere in this material, you set up an electric field E field. Okay, you set up an electric field in the wire in the metal. In electrostatics, the electric field in a metal is always zero. But this is not electrostatics. The current is going. So you set up an electric field and once you set up an electric field that electric field exerts force on

00:23:56 these so-called free electrons. If there is an electric field, it will exert force on every electron. Right? F is equal to QE is valid. So it will exert force on all these 2 N electrons which are here. These 2N electrons which are here, these six n electrons which are here and these 1 n electrons which are here, it will exert force. It will try to accelerate it. it will try to ex exchange energy from the field. the energy will be going to the electron and therefore if everything was normal the things were not uh such

00:24:41 quantized then you apply a force there will be an acceleration kinetic energy will increase simple classical mechanics but now think of this electron which is sitting here or think of this electron which is sitting here or think of this electron which is sitting here if So if you think of that hydrogen atom once again this gap is 10 10.2 eV suppose the electron is here and you offer this electron an energy of 2 electron volt it will not accept because if has it has to increase the energy minimum it can accept is this

00:25:28 10.2 into AV. So even if you apply a force, even if you try to accelerate, even if you try to give energy to this, shine some photon, do some anything, it will not accept energy less than 10.2 e. So that is this that is the story. If this electric field if it tries to give energy to the 1s electron or 2s electron or 2p electron cannot accept because all these quantum states are filled and the next quantum state is after this much of gap. Unless you give this much of energy for which normal batteries will fail to do

00:26:11 that these electrons will remain there. But these electrons you have uh empty quantum states. So if the if some electron is here and there is an empty state here. Suppose your electron is here and there is empty state here. That means in some of these large number of atom, there is an atom in which that 3s electron is at a slightly lower energy and there is a neighboring atom where a slightly higher energy state is empty. That quantum state is empty. It can make a jump because it can accept any small amount of energy and go

00:26:54 from here to here. Okay. So these electrons will respond to the electric field and they will move according to that F equal to QE and of course that scattering from other ions and defects and those things will be there but at least these will respond to this electric field. These will not. These electrons are called free electrons or conduction electrons. So in a band if you have partially filled quantum states and partially empty quantum states those electrons can respond to the electric field and then

00:27:33 they can cause current and that current will be related to the electric field through this relation J equal to sigma E. What is J? J is your current density. And what is current density? You take a cross-sectional area here in the wire. You take a cross-sectional area. That cross-sectional area is A. The current is going I. And so J is I / A. This is the magnitude and the direction is the direction of the current. So that is current density J. And this sigma here is known as conductivity, electrical

00:28:22 conductivity. So that is how the conduction takes place. Now this band is known as a conduction band. Why? Simple because only these electrons will respond to electric field for electrical conductions and therefore these this band itself is called conduction band in which the electrons can have freedom to move and the others are all valance bands. We are not really concerned about the lower one but just lower to this conduction band. This is interest this is important and this is known as balance band.

00:29:12 Okay. So just uh the band just below that conduction band we will call them valance band. These are also valance bands but then these do not uh uh they are not important for discussing conduction. So we just show these two the valance band and the conduction band here. Now think of magnesium in the periodic table after sodium you have magnesium zed is equal to 12. So in zed is equal to 12 what will be the electronic configuration? The electronic configuration will be 1 s2 there are 12. Zed is 12 now. So

00:29:53 2 S2 P6 and then 3 S2. What does this mean? If you have this kind of diagram 1 S completely filled, 2S completely filled, 2 P completely filled, then 3S completely filled. So if 3S is also completely filled and you apply an electric field, what should happen? There should be no conduction. Just like this, these electrons cannot take part in conduction because all the quantum states are full. So if 3s is also completely filled, you may expect that they will not respond to electric field and magnesium will be a bad

00:30:50 conductor. But it is not magnesium is also very good conductor of electricity. Why? The next band three piece band there's no gap between 3s and 3 p. 3s is completely filled fine. But then uh the structure of magnesium is such the atomic structure is such that you have 1 s, you have 2s, you have 2 p, you have 3s, you have 3 p and then when it all uh spreads out and this becomes 3s band, this becomes 2p band and so on. You have 3P band and that 3P band is uh right here. That 3P band is right

00:31:39 here. It overlaps. So it is 3S and 3P. This whole thing is now 3S + 3 P and therefore although it is completely filled but it does find empty space with little energy small energy. If electric field will tries to supply small energy they will accept because the quantum states are there. So for different atoms you have different kinds of energy bands. This is one kind where you have a valance band then a gap and then the conduction band partially filled. You have this kind where uh now this becomes

00:32:26 the valance band. This is completely filled. Although 3S is completely filled but next 3P is uh uh is overlapping. So you have a this is a conduction this whole thing becomes conduction band. So different kind of materials will have different kind of uh band structure energy band structure before we go to the silicon. Now where is the silicon in periodic table? Carbon silicon. So carbon is Z is equal to 6, silicon is Z is equal to 14. So that is very interesting and silicon is the key semiconductor material. Most of our

00:33:09 semiconductors are still centered around silicon and silicon is in a abundance in silicon. If you Z is equal to 14 if you think of that solid silicon or carbon there's another twist in the story. So for uh carbon or silicon where let's say silicon zed is equal to 14. So what will happen? You will have uh 1 s2 2 s2 p6 3 s2 and p2. So if you have silicon atom as such you will have 3s band 3s state and 3p state and this 3s will be completely filled. This 3s is completely filled and 3p is partially

00:34:10 filled. Here you have two electrons and here also you have two electrons. But the quantum state number of quantum states here is six. Number of quantum states at six only two are occupied and here the number of quantum states is two and both of them are occupied like this. But when you have silicon crystal solid silicon no more you talk in terms of 3s and 3 p. The chemistry people say that 3s and 3p these orbitals get mixed up with each other and they call it sp3 orbitals. SP3 hybridization. So the quantum state

00:35:07 itself is now different. You don't have a 3s quantum state. You don't have a 3p quantum state. The quantum state is sp3 like that. You still have eight. This 2 + 6 is eight. And here also you have eight quantum states. So the same eight quantum states are now mixed up and uh you have a separate kinds of quantum states which you cannot say that this is 3s and this is 3p. They are all sp3 kind of uh quantum states and they occupy in this and what happens depending on uh the separation and all

00:35:53 those things this 8 n quantum states if you have n atoms in your silicon solid you have 8 n quantum states you have many more below this So and and above this you you have these are also quantum states or you also have 4s2 and all that these are all empty you you do have these quantum states and these are all filled but I'm talking of this one this one this part here these eight n quantum states and these eight n quantum states are now split in two parts okay so you have these two parts like this this is your valance

00:36:43 band. This is your conduction band. And then there is a gap. And for silicon this gap is about 1 eB silicon. Carbon also similar story qualitatively. Instead of this 3 s2 p2 it will be 2 s2 p2 zed is equal to 6. So two here and four here. So again you have that S2P2. So you have hybridization and similar splitting. So if you look at carbon diamond you again have similar picture and here the gap is 6 EB and here the gap is 1 EB. Why I am so much emphasizing on the gap and the magnitude of energy in the

00:37:43 gap that decides the conduction property of semiconductors and these are semiconductors but whether it will conduct how much it will conduct should I put it in insulator bracket or should I go into that conductor bracket or should I keep it in semiconductor that all is decided by this gap and this this number and this number is to be compared with a quantity which is written as Bzman constant K times capital T. Okay. So this Bsman constant K and multiplied by T this is the quantity with which this gap is to be compared. Where did

00:38:33 you encounter this Bzman constant in uh kinetic theory of gases? You must have encountered this PV is equal to NRT and that R gas constant R is a gradual number times this K. So K is essentially that gas constant capital R divided by the gradual number N A. So this is K and this is of course the temperature in absolute scale and for room temperature for about say 300K this is around 0.026 026 electron volt. And why this KT? Because in a solid or in any material gas also the kind of energies which are available

00:39:27 through these thermal interactions is of this order. Right? The atoms are interacting with each other because of the temperature. There's some vibrations and all those things. And then through those thermal interactions the energies which can be exchanged between the atoms between the electrons outer electrons is of this order. This order of energy is readily available. Someone is giving someone is taking and that quantum that scale is is decided by this number KT which is for room temperature it is some

00:40:05 25 26 mill electron volts. Okay. So if you look for a particular interaction in which the energy exchange is 0.5 electron volt much more than the average average is around 026 EV I'm looking for interactions where.5 EV is exchanged the probability will be very small maybe I don't know but maybe say one part in 10 ^ 10 but remember you have 10 ^ 22 23 24 atoms also. So even this probability this a small probability of 1 in 10 ^ 10 is huge is huge because you have large number of atoms. So there is a

00:40:54 possibility that in some interactions the energy exchange is of the order of 1 e. What will happen if this is completely filled? If this is completely filled and this is completely empty and through thermal interaction some electron gets energy and is promoted here then that electron is ready to if some electron goes here that electron is ready to respond to any small electric field and therefore this will start conducting contributing towards conduction And once the electron has gone out from the

00:41:41 here, the other electrons in this band, they also get some kind of a comfort to move because there is an empty place and that can also respond to the electric field. The electrons can go in that direction and some conduction can take place because of these electrons also. So this is the mechanism of conduction in so-called semiconductors. If you have energy gaps so that a sizable amount of sizable number of electrons have gone from the valance band to the conduction band then it becomes a semiconductor. If

00:42:25 the gap is very high 6 EV almost no chance of electrons crossing from here to here through thermal interactions this is insulator you apply whatever electric field nothing will happen but in these kind of things where the gap is 1 e less than 1 e in germanium it is less than 1 e so if these kind of materials are there then already there are some electrons here and if you apply electric field these electrons will respond and these uh vacancies these holes these empty positions broken bonds they also

00:43:03 respond. Uh you can take an analogy an interesting analogy suppose you go to watch a movie and then there are blocks 100 rupees ticket and then 200 rupees ticket. Now if it is 100 rupees stick is uh block is completely filled these all persons will be seated. No one can move. Even if your air conditioner on one particular wall is giving too cold air no one can move on the opposite side because every chair is filled. Although that 200 block 200 rupees block is empty but they are not allowed to go there

00:43:45 because there's a huge gap of 100 rupees but uh somehow if someone is able to exchange his ticket and he moves to that other block then there are or few people can do that then there are some empty chairs and then some movement is possible in this uh uh almost completely filled build 100 rupees block also. If there is some chair here and a cold air is coming here, this person will suddenly jump here and if this person goes here and an empty chair is created here, then this person will go here and

00:44:22 so on. Some movement will be there and of course the people who are in that 200 rupees block, they will definitely uh run to the other side. So it's some kind of uh of thing here. So that is how the electrical conduction takes place in semiconductors. Not only that conductivity is uh important. For example, here much less number of electrons are going here. That is why it is semiconductor. In a conductor like sodium or magnesium or copper, you have uh by default a partially filled conduction band and

00:45:01 therefore there's a huge number of uh electrons available for conduction. Here the number is less. That is why it is semiconductor. But then uh there are many other aspects. One aspect is temperature. What happens if you raise the temperature of a metallic wire, a copper wire or a tungsten wire? Uh let's let's do an activity. I have this uh filament bulb. The filament is made with tungsten and uh it is written here 100 watt. It's a 100 watt bulb and 230 volts. So if you apply 230

00:45:46 volts the energy consumed will be 100 watt. You can calculate resistance from here. So let us do that. If voltage applied is 230 volts. Yeah. You have a bulb here. You have a filament here. And then uh you have uh you are applying this 230 volt here and some current goes here. and power is 100 watt. So what is the resistance? V ² by P. How much is that? 230 into 230 and divided by 100. So 23 into 23. How much is that? 23 into 23 529. 529 ohms. Everything in SI. So this will come in ohms. So if it is connected to 230 volts

00:46:49 the filament will glow. You will have light 100 watt bulb and at that time its resistance will be 529 ohm. What is its resistance now at room temperature? So let us measure. So I'll request Marvahaji to help me. There's a multimeter. set it in resistance measuring mode and just measure the resistance. Touch the two and see that it is working. Yes, it is working. Okay. So now touch the two terminals and the two ends of this filament bulb and see how much is the reading. Okay. So you see the display it

00:47:31 is 43 43.1 or 43.2 is 43 ohm at room temperature. So a normal metal if you raise the temperature the resistance increases. At room temperature at uh room temperature this resistance is about 41 ohms but uh when the temperature goes high so that it start giving light of 100 watt the resistance increases to 529 ohms. Now let me do one and one more experiment with this resistance varying with temperature and you see what happens. Now I'll request uh Mr. Arvind Pak to help me. So here this is another bulb. It's

00:48:25 LED LED bulb. We use it for lighting. And this LED bulb I'll be connecting to this battery. So he's connecting this uh LED bulb to the battery through a galvvinometer. You can see there is a small deflection in the galvanometer. Can you see this small deflection here? Next I have water here and a water heater here and a switch here. So let me heat this water. So this water is now heated. I put it off and remove it. And now what we will be doing is we will just put this LED bulb inside this

00:49:18 hot water so that the temperature increases. And now we are making the circuit. And you see the deflection. See the deflection. So the current has increased manifold by heating. The current has increased manifold. The resistance has gone down. In case of tungsten, in case of metal filament the resistance goes up on heating and here the resistance is going down on heating. Current is increasing. So semiconductor has many different properties. So semiconductors not only the magnitude of the resistance or

00:49:56 resistivity or conductivity the entire character is different the temperature dependence is opposite. In fact this can be used to test whether a a material is semiconducting or is conductor. So let me summarize the key concepts that uh I had discussed today in this lecture. The first thing we did was the energy levels in one atom. I took an example of hydrogen atom where the energies are uh discrete. You say the lowest energy is -3.6 eV and the next is -3.4 eV and so on. And uh these energy levels contain

00:50:44 different quantum states. At one energy you may have uh more than one quantum states and they are named as 1 s, 2s, 2p and so on and uh each uh level that we are putting they have a definite number of uh electrons. For example, in all s so-called s orbital, you will have two electrons. All p orbitals you have six electrons and so on. Then uh the very important thing is that each quantum state can have a maximum of one electron which is polyexclusion principle. A quantum state may be empty or it may contain one electron at best.

00:51:35 Then we talked of the collection of atoms like a gas in which the interaction is minimal, negligible. In that case, each atom has its own energy. But since all atoms are identical, they will have a same energy levels and therefore the same energy levels will be applicable to this collection. only thing that in each energy now you will have many more quantum states. If it is let's say 1s for one atom you have two quantum states but if there are capital n atoms in the system you will have two into capital n

00:52:22 states here and similarly for all others. So that's the difference. Then uh we came to solids and in this the outer electrons of an atom interacts uh significantly with its neighbors and therefore due to this interaction the energies are shifted and because of that what is a pure single energy that spreads into energy bands. So that is how the bands are generated and then you have energy gap. Then uh we talked of conduction band and valance band. So conduction band what is conduction band? The lowest

00:53:12 energy band which is not completely filled. So if you have these are the energy bands you have some little spread here little spread here and so on. So these are energy bands. So look for the lowest energy bands which is not completely filled. Suppose these are all empty. This is empty. But here there are some electrons. Here there are some electrons. So this uh this is not completely filled. That means uh if this state is completely filled with the electrons we won't call it conduction band right so some empty

00:53:58 states should be there then we call that as conduction band so lowest energy this is also empty this is also empty and here this is not completely filled it could be completely empty like this or it can have uh partially filled and partially empty so that we called conduction band and all this is I'm talking at no thermal excitation it's because of the structure because of the temperature of course some uh electrons can go to higher bands and that becomes non empty so I'm not talking of that so no thermal

00:54:40 excitation then uh the band which is just below the conduction band which will be definitely completely filled that will be called balance band so this is definitely completely filled once again remember I'm talking of uh because of the structure it is like this because of temperature you may have some of the electrons if they leave this uh completely filled valance band some empty space will be created we talked about that at length so you have conduction band you valance band and then you have gap. This

00:55:19 is that gap which is very important. Okay. So the electrons in valence band they correspond to those which are strongly bonded to the atoms whereas electrons in conduction band correspond to those which are weakly bound to the atoms. Then uh we talked of uh this if the conduction band is partially empty you have lot of empty states around some of the you have lot of electrons also and lot of empty states also because of the structure itself that material will be a good conductor of electricity and if the conduction band

00:56:06 is completely empty that is also possible then the material material may be insulator or a semiconductor. So if the band gap is small say less than 3 e or so the material is semiconductor. What is band gap? That energy gap. This is the conduction band. This is the valance band. And then this gap this gap band gap or energy gap. If this gap is uh say 1 e or uh 2 e like that and if the gap is more if the gap is large larger than say 3 e then at room temperature at least the conduction will be very very small and you call

00:56:49 that insulator. Okay. Then uh we talked of temperature all that I gave all these key points where at say where no thermal excitation was considered and that means at a very very low temperature. But if you are at a elevated temperature say room temperature which is around 300K then you have thermal excitations thermal interactions and because of thermal interactions some electrons can go from valance band to conduction band and that leaves empty quantum states in the valance band. Right? So if you have

00:57:31 this valance band and if you have this uh conduction band and if some electron goes from here to here it populates some of the quantum states at the same time it makes some of these quantum states in this so far completely filled valance band it creates some empty states there which we call holes. So that is the effect of temperature. Larger the temperature more electrons will be able to jump. And then finally what happens if you apply an electric field. So here in a semiconductor if you apply an electric

00:58:11 field then uh the conduction electrons do find empty spaces, empty states, empty quantum states around that energy and therefore they can absorb energy from the electric field. little bit energy. Whatever electric field can provide that electrons can accept and go to slightly higher quantum states which are available and therefore a drift is possible. At the same time in the valance band also if there are empty states then uh you can have some movement of bonded electrons also. So if you apply an electric field what happens

00:58:56 the electrons will move conduction electrons will move uh opposite to the direction of uh electric field. Valance band electrons will also move in that direction but then equivalently we say that the holes have moved in the direction of the electric field. So in uh that sense the current which is produced in semiconductor because of this will have two components the component because of the conduction electrons and component because of the holes. So these are the key concepts that uh I discussed. So we will take it from here.