[6] 반도체 기초_9

So now I am going to talk about the band structure regarding the effective mass. What is effective mass? In mechanical or electrical the same thing. Kinetic energy is equal to 1/mv^2. This is the mass. M is very important. Okay, so which means same energy supply, mass is small, it's going to be more velocity. Okay, velocity higher means what?

What is higher? Carrier or electron, electron, velocity higher means what? What is that? mobility. Mobility unit is what? Meter square per given voltage per second. Right? So which is velocity higher, some activity is higher. So higher point is same energy supply, but velocity higher. If one of the velocity higher is

effective mass is less. Okay? So Mass is going to be smaller is better for electronics. Okay, so mass is very important. That's why I'm going to talk about the mass. Absolute mass, this is effective mass. Effective mass means something. Free energy, right? I don't know. Sorry. Free electron. Free electron is gonna be masses much less than something

structuralized in condition of crystallized something like you're moving. So this is some like this is here something Moving and then this is free energy, which is mass is less. This is effective mass is less than this one. Okay, that's why I'm gonna talk about mass in band structure. This is very important. Which means mass is related to kinetic energy. So why you know the graphene is very popular. Graphene.

Graphene is why so popular or get people attention about the graphene. Why? Why? Graphene is why? Graphene is very powerful electronic device. This math is effective. Something we know like this. That's why it's something dream mean or device. Effective math is zero. Graphene is...

I'm going to explain why is it effective math is zero. Why is it a dream device something? Okay. So this is what I'm going to talk about. Now, so this is... crystalized structure. How many atoms? 1, 2, 3, 4, 5, okay. Billion over a zillion the same structure. That is something we call crystallized. Like two-dimensional bonding liquid. Crystallized solid. Okay like this. Okay, so

this is outside, this is outside structure, this is outside structure, outside structure, same thing. This is the inside structure. This is the inside structure. Then we just draw in this device for the potential energy here. So that I explained this potential energy like this, right? And then this one, potential energy kinetic energy. Okay. Electronics. So now, two-dimensional means what? things gonna be here x y and z dimension. x y and z dimension.

This is the two dimension. Then this is what? Only x direction depends on some potent energy. This direction we can draw this one. Maybe this direction we can draw another one. So all the things are E, X, Y, E, energy, Y, whatever. So X depends on distribution of energy, Y depends on distribution of energy. So the things are two-dimensional, X and Y.

But in crystallized structure, which means what? The X-reaction is everything the same here and here and here. Repeatable. So we're not doing over and over again. So we introduce only one part. It's very important. So we understand this one. You don't have to know about this one. That's why we introduce now. Instead of x, we introduce the k. The same thing, the directional factor.

The k is x, right? Or y, or z, something. We introduce the k. Next, I'm going to tell you about here. So every potential energy, the lattice. The lattice is dependent. Okay, the lattice is dependent. distance is a. Okay. So everything is repeatable, repeatable, repeatable. This is repeatable, repeatable. That's why I introduced e versus k. k means what? Same as x or y or z. So one direction fixed and then we introduce something repeatable.

Then everything is the same thing. Sinusoidal function, sine function, wave function, we introduce like 2pi. That's it. Divide A means what? Distance. So this is exactly something sinusoidal. Sine wave, cosine wave, whatever that is repeatable. Here and here, everything is repeatable. Okay? So here is repeatable, whatever. So that's why I introduced the CAPE. So it's not that much difficult.

That's why energy depends on the k. Okay, relation, something k dependent, period, something, blah, blah, blah. 2 pi over divided by A means something here. So ek relation, illustrating this point is indicated in the figure. something like this. It's symmetric about the k-point. Pretty much clear. So here, so this portion, we cut it off here.

2 pi over here and then here, this portion, right here. So we only interested this portion. So it depends on the location and then how much is the energy level. All measurable quantities of periodic with the same as the periodicity of 2 pi over a k space. Just instead of x, we just change to k and then like this. Everything is repeated. Customers consider the region. something here to the here.

This is known reduced zone of something Vrilium zone. Why is the first? This is maybe first, this is the second, third, whatever. So we call it a first Vrilium zone. Vrilium zone means something like a unicell. Ek versus symmetric about the K-zor point, right? So KG0 point is symmetric. This one, this one is same. Exactly. Sometimes only half of the V, this two join is in draw. Sometimes. So I explain something.

First introduce the E_k diagram. E_k means energy and K means something instead of location. x,y,z. So things gonna be here. So this is the first blue limousine. Okay. So k direction, e direction. So there is something. So all interesting is the maximum point and the minimum point. Okay. Very interesting. We just something line up here. So that is the bender structure. Okay, so allowed range of energy for E1, E2, E0, which is the energy diagram in real space.

The energy of the maxima or minima part of something function, ba ba ba. Okay, maxima, minima, that are the same everywhere in crystal. as long as the electron is not near the surface. This is the surface, not near the surface. The nearly empty band, the electrons are tending to occupy lower state, because the lower state is more stable. Everything is trying to be stabilized.

lower 6db, lower energy state. Have the property associated with the minimum something k diagram. So likewise all fill the band is a vacant hole will be near the band is maximum. So this is I think it's gonna be nature in Bendy structure. So, so effective math. This is some math for effective math. So I'm going to tell you this is what?

E_k diagram. E_k diagram. That's a parabola. Okay. The parabola, something, second derivative table, function which means derivative means something, the slope. The effective mass tells you about the slope. How much is the slope it is. The movement of the electron is less. Will it generally be different from the that of the electron?

Free space, that I told you something. Free space and then crystallized structure which means lattice. Free space and the lattice structure is different. Movement, electron. So that is different means mass is different. Excellently applied force, there are internal force in the crystal due to d. positively charged ion or proton. Other negatively charged data influence the motion of the electron in the lattice. Okay, so movement of the electron is the top of the balance band here.

Top of the balance band here. Defective mass is negative. This slope is negative. This is positive. And movement of the electron is the bottom of the conduction band here. Conduction band, the effective mass is positive. This direction is positive. So the whole, the positive effective mass denoted by something bubble. The positive electron charges is something movement in the same direction applied to the electric field.

In the negative case, the other direction. And velocity associated with the center of mass and this particle is the group velocity. We say something vg. It's almost similar to something velocity. Conveniently, you just say understand that it's something velocity. Okay, so velocity, that is dx dt. dx dt means something blah blah blah. What it is? something. Planck constant.

dE dk means something regarding v-notify velocity. So energy means something. Reference energy time. So y, h bar, and k means momentum. So which is the momentum squared divided by m, 1 and a half is something like this. This is kinetic energy. Okay. I'm going to tell you next slide.

Whatever. Okay. This is something we mentioned about the group velocity. This figure originates from here. It's the EK diagram. We just get the derivative of something E. That is, we got the velocity here. Next is pseudo-classical mechanics. You don't have to think about different pseudo-something. Pseudo means like a quasi. So this is something that the two electron mass is replaced by something effective mass.

One dimensional crystal. So things are going to be changeable. Depends on the circumstance. In crystal or free space, mass is going to be changed. So free electron is m, v is momentum p. over something same as the wavelength. h bar-franc constant by the wavelength. Don't have to know about this one. Can I again add something? Something like this. Okay. Very much clear.

Okay. Potential energy will be something E0. which is this one. Okay, so it's the same thing. Okay, that I told you about P, P, and F, times K. That's why kinetic energy, you can identify kinetic energy in something, classical, pseudo-classical mechanics. So in E.K. Parvala, here, Second derivative of E, D and E related something constant.

Second derivative of this parabola. So this slope is something same, mass. Effective mass. So band structure, E_k diagram, more sharper means Less effective mass something. Okay, I'm gonna tell you later. So slope is something This one and then this one which is it Slope is higher. This is the slope is higher. So that slope is 1 over effective mass, that slope.

The higher slope is less effective mass. I'm gonna tell you later. The velocity of freedom is crystal is something group velocity. I introduced this. Okay. Math is something. Here is a Planck constant times minus one power. So that's why inversely proportional. This is m = something slope over something one over.

That's what it is. So, quasi free electron, like a free electron but looks like a quasi. Quasi means a closed steady free electron. So it's considering the electron yield at the bottom of the band. So energy, something regarding to the what is going on here. So energy means constant.

Conduction band is something. plus Second derivative is gonna be zero and the secondary to survive higher order term is disregard So there is energy term is something blah blah blah. That's why here we got this one This is a bottom is a potential energy. This is kinetic energy Okay, so that is a Regarding group velocity, we defined previously this one. So, things set up is exactly the same format, EK diagram.

Here, constant, well, conduction band, plus, which is kinetic energy term. And this is kinetic energy term. So, quasi-free electron is a free electron. This item is the same format. So equal. We set up the equal. This one. So we got to figure out this one. Effective math. And then just math. Something we define by this one. So how we got this number?

From this term. Set up the equal. Then how we got this term. So effective mass, where mass is Franklin times 1 over something secondary derivative of E-cave relation. Okay, so that is effective mass. This is here. Something like that. Higher slope. Higher slope is small mass. Small slope is higher mass. So this is effective more than this one.

It is going to be smaller mass here. This is the heavier mass of electron. So effective mass just keeping going on. What it is? Neglecting higher order of EK diagram, which is a parabola near the bottom of the conduction bed. The effective mass is constant. EK curve is an approximated parabola with a Vincene probability.

And the concept of the constant effective mass can be used here. Electron in the parabola region is near. The minimum has different proportional energy. So then group velocity is zero and kinetic energy is zero. We got here. So this is something about the effective mass. Again, we just described this one. So, which is a group velocity, which is a quantity.

This one is openly referred to the crystal moment. This is a P moment. So kinetic energy near the minimum, E_k_1 is become. something like that. In the return, effective mass is near the minimum. So effective mass in bend structure here something and as the bend here, E versus Brogue wave number k. Repeated zone scheme.

The EK diagram here, E1, E2, E3, E4, whatever. Here is no state level and there is something state involved in here. Here, empty space is a world well defined in constant mass, M0, often used for view of Mass merely proportional to factor with the force acceleration, the kinetic energy. Electrons appear as the mass is different from the free space value.

Definitely free space and then some lattice space is different. Simply means in crystal, electron does not respond to the external force. same way that the free electron does. Okay, so crystallized electrons in crystal free electron is different. Response to the external force. External force means what? Electrostatic force, like energy supply, kinetic energy, water, electric force.

Why? Forced means the same energy supply but mass, effective mass is different. Free space is much less than crystallized electron. So that's why response is different. This is very much this simple and clear. So this is something about the... here something... this is like a brillim zone here. Something brillim zone and this is something directional factor.

It's a wave vector we say. Something this is energy. y axis is all the thing is energy. energy and this is the location. Mentioned the group velocity, what is the kinetic energy? Something center of the equilibrium zone, k equals zero. So this is the center point of the equilibrium zone. Right? So between energy gap here, something gap here, something gap here. Okay. So things are going to be, there is no state here, no state here, no state here.

The other side is state, it's available. Consider that in the semiconductor, typically the one is interested in behavior of electron nearly by the edge. The center of this first balloon zone, something K0 point here. These are the electrons that are most important for the conduction. In that case, only the local behavior, E_k curve will be important. So in order to curve the shape like this, that depends on what?

nothing but effective mass. That's why effective mass is very important in this dependent structure. So EK diagram. So again something is a something about this one. The power regulation we can set it up this one. So beta is the same to constant, well defined as previously. This is M* is called the effective mass.

The effective mass is obtained by taking two derivatives of the Bose equation, k. So simply we got how much the effective math we can get from this thing. Okay. So effective math proportionally is the curve of each plot. Okay. Did I told you something? This one or this one. Okay. Depends on the curve shape. So this is like this. Another effect, this is gonna be same as the group velocity of the dk.

hk is the momentum. Where is the power? So, the nipson over the power power, which is missing something group velocity. Something like that. The force is the momentum derivative of t. Okay. R = ma, okay. M means dp momentum dt. This one very clear. So this is something about the creature momentum.

This is not the physical momentum of the electric. So this is for the only the quantity here. So this is regarding this one. Okay, same concept about the theorem. So like here very much clearly here. Something positive effective mass bigger domain. 1 means something like a ballast increase is less than something electron free space.

Okay Which is bigger than 1 or less than 1 something bigger than is not better. Okay, seems to be heavier. Heavier means no good. The distance difference indicating momentum will move transferred to the lattice. This is less than 1, which means velocity increases more than it would be electron free space. This is better. That is the difference indicating momentum transfer from the lattice. So, exactly show here.

This curve shape, in this curve shape, effective mass is much less than this one. This is the heavier. This is the lighter. So it depends on what it is. So all the band structure. The band structure. This side. This side. This side is. by mostly effective math.

So there is a key point. So here is the band structure, which is again the case increase and further moving away from the zone boundary into the second volume zone, first or second volume zone. The conduction band will be initially have something negative group velocity indicating moving in reverse direction. Okay, so like we mentioned the phonon. Phonon is something we did regarding the thermal energy. Thermal energy like vibration rate

So this you don't have to know detail about that. But the electron colliding will do something obstacle. The wave vector will not be able to increase to very much. Okay. The wave vector does not simply linearly increase. However. Okay. So momentum reaction. I have to talk about collision. The momentum gets the relaxed and losing energy. The first blue lemgion is called"ba ba ba" and A is something this much. Okay. So like a very small percentage of the weight of blue lemgions.

It's a collision after that. So very limited amount of the energy loss. Electron colliding regarding the cause of the electron resistance in the classical fleet, electron gas, conductivity. Something like that. So E, we mentioned this one. The secondary of this one, the effective mass of electron. Okay. So, Quasi-fili electron. First, that I mentioned before. So what is a quasi-electron?

Quasi-electron is something, bottom at the electron in the conduction band here. And there's something that is something. All the core body shape is a slope. Great to do effective math. Okay. So in C here, electrons at the top of the band, something, parabolic approximation here. So there is a slope, effective mass. The slope is not parabolic, here through the curvature is negative. This is negative, this is a positive, depending on all the curvature shapes.

So this is something about slope of dt is zero at top of the band. Something at this point, this point is zero point. Potential energy of the electrode near the local maximum at top of the bubble. Also f = ma is near minimum. ma is positive. Minimum is positive and electron is calculated in direction of the force. Near the maximum point is where?

Something regarding your light. Maximum point is negative. This means the electron is calculated in the positive direction of force. of course. Okay, so negative, positive. The color of the shape is something effective math.

So this is something about the effective machine conduction band. I want to tell you about the conduction band and the balance band. Two parts. So first, I want to say the conduction band. Conduction band and the balance band. So this is the more complicated which means not that simple. Here is a more simple, less simpler but this is something more complicated. This is what I'm going to talk about.

Conduction band structure. M0 means something effective in mass. Last mass flow, electron. okay so rest math means something initial or something not affected okay means rest math. EK curve here must be zero and embolidum zone as. So what it is, here is I mentioned about three different materials:

Valium arsenide, silicon, and germanium. So I told you about what is the bulidium zone, okay? So which is crystallized, repeatable, repeatable, repeatable. So repeatable is one part which is concentrated. We're going to look that up. how, why, and what characteristic this material has here. So here is 0 to 2 pi. Here is the prelimin zone for the Kalemarsson idea, this direction, 1 0 0 direction.

And silicon, 2 pi, right? 0 to the 2 pi. This is the prelimin zone up to here, to here. the here to the here. How about the germanium is 0 to 3 pi. A little bit wider, right? It depends on the material, depends on the direction. The blue limizer is changeable. Okay, the blue limizer is changeable. So first, in conduction band is like a here is EC and EV. Okay, this is the balance band. In conduction band, we need a

minimum number on interest and balance band is maximum number is on interest. So conduction band, I'm looking up now the conduction band. So we want to know about the interest minimum. Where is going to be minimum? Sorry, sorry. Here is minimum. Here is minimum. So, looking it up, where located the minimum? Here, first, Gali Marasana is K0 point is minimum.

Okay. Silicon is not K0 to the minimum. okay here is a minimum okay and germanium is you here is a minimum not k0 right not k0 minimum here is not k0 is a minimum here is a k0 is minimum so this is a direct band gap here is a k0 means minimum number is a direct band gap this is efficiency is better than this one. This one is indirect. This is not K0 point.

This is indirect point. Okay, so this is more efficient. Okay, so I'm gonna tell you later. Okay, and effective math is something. second derivative of a slope. Okay. I told you like how it is slope. Something like that. This is the first derivative of the velocity, root velocity. Okay. So this is defined before.

Okay. So take a look at more detail. Okay. A means something here. Absolute minimum conduction band is at K0 point. That's true. The curvature of E_k near the minimum point does the same for the older direction of motion. So here things happen. So example of a material 2 band having same energy at edge of the zone 1 1 0 0 direction.

The sum of slope is zero. Okay so what it is? Edge point here. Here is this slope, this slope is something same. So plus and minus is gonna be zero. And here is also this slope is plus and minus is zero. okay so h here is the slope is zero right so which means h volume h all the time is zero must be zero okay that's true

okay so slope is this one this one is zero so h of slope is direction to the sum of zero. Okay, but here is a natural zero. Okay, this is the sum is zero. This is sum is zero This is the natural zero. Whatever this is mentioned about natural zero or sum of zero. Okay Things like that. So second B here is silicon, right? Transverse mass and longitudinal mass

So it combines effective mass. It's not a scale. So I mentioned that usually the conduction band is a more shaped curve. Why? Because conduction band is transverse or longitudinal direction. Transverse or longitudinal direction. Effective mass is separate which is not the scalar here. The curvature different from different direction of a case base minimum. Okay, so here something like that.

Silicon case is something we mention. Okay, so this is the curve the shape here. Longitudinal or transpose direction, the sum is zero. So the effective mass is not the scalar either. The C is something here. So K is zero point.

at high synergy level, another minimum. Here is a K0.0, another minimum. This is a minimum, but there is another minimum here. Something. So longitudinal direction or transverse direction, sort of a weight of between this and this one, required to obtain ba ba ba. Okay, some sort of weight. Not exactly same, but this is a combination of longitudinal transverse is going to be sum of this effective math. Okay. So next is sum of the effective math in the balance band.

Okay. Semiconductor structure varies from the material-dual material conduction band. The balance band quantitatively similar. most semiconductor. So the balanced band electrons are much more simple. Very much similar means simple. So balanced band consists of overlapping band which is all over absolute value of K of 0 here. So conduction band somehow would make

minimum point here maybe here or here is changeable but balance banded all the time the maximum is here K zero point okay but only depends on the material different curvature like this okay so effective mass of electron be inversely proportional to curvature of the top of the band. So which means what? This is the curvature is higher than this one. So inverse of the proportion. We got the E square of E k h bar is effective mass. So this means slope is much larger means

lighter. That's why L here. This is L means light. H means heavy. So this is the curvature lower is inverse or proportional. So this is heavier. Okay, that is the balance band. So I'm going to summarize what it is. The balance bands normally must enter full of the electrons. That's true. All the balance is naturally full of electrons. When you get excited, then it is partially empty.

Few empty spin near the top of a band. Positive effective band. Something like this slow. Conduction band is like a curved shape, but all the time is a slow. Balance band is this kind of shape is positive impact of mass. Two bands of same energy, maximum and K0. maximum. H and L. A heavy one, small curvature, light horizon.

higher curvature that I mentioned before. The third band spread over something energy due to the something the split coupling Don't have to know detail about here, but something there you can see the third band So now I want to summarize it here. So what is the conduction band? complicated curvature. But the balance band is very simple. Why is it complicated? Because the longitudinal direction, the transfer direction, both of them

it depends on the weight ratio. The curvature is curve is changeable very much. But the balance band is already simple. positive way. Okay. Heavy or light or that's it. So conduction band, alarm bands, that is how we create by, most of we decide by effective mass. That is very important. What curvature band structure decide by? Nothing but

Effective mass is very important. So this is the example. Which is the lowest effective mass in the electron? Which is the lowest effective mass for the hole? What is it? The hole is this one, right? The curved shape is higher. This is lower effective mass of electron compared to this one. This is lower effective mass. And compare.

This is electron. This is hole. This is electron. Which one is lighter? Well, less effective mass. This is light. Less effective mass. This is heavier. Effective mass. Let's compare. Upper size electron are down-side the hole. Effective mass proportional to the principal curvature band. Band structure is the greatest curvature, therefore, smallest to effective mass. So this is what I mentioned. Although right has a heavier curvature,

the conduction band here, this one. And thus the effective mass of electron is the conduction band is smaller than the left. This is smaller. How about the hole? This is the hole. The hole is the left is the higher curvature, means less effective mass. hole is smaller form, much less on the left. So this is the electron.

Upper is electron, right? Down is hole energy. Curvature shape, what it is? This is higher curvature, right? Slope of the curvature. This is less. effective mass something energy momentum diagram whatever this is something less effective mass means higher coverage right if you say the things right there very simple so now i want to look it up

D. Graphene stuff. Graphene. So graphene and graphene oxide reduce graphene oxide. So this is the perfectly crystallized structure. This is functionalized something oxidizing. Oxidizing. Whatever. So this is a perfectly hexagonal structure of the graphene. electrons. This is hexagonal structure. So all the hexagonal structure crystallized. But each of the atom has something, banded structure right here.

So this is very much sharp. Here is very much sharp, crossing. Okay. There's no band gap here. So fully close here means no band. Everything is stayed there. Actually, graphene is a conductive material. No band gap. But the thing is this. How is slope? The slope is effective mass. The effective mass of graphene is almost zero. Means curvature is pretty high.

Curvature this is 0. highest curvature, infinity. So curvature slope is 1 over infinity means zero. Zero means effective math. So so light, graphene, effective math is so light, that is a good conductor, good electronic material, good body or application. So this is why the graphene is so good electronic material is effective mass. Effective mass is almost zero.

That's why. Almost zero means pretty much light and low power consumption for the controlled electron. Almost effective means zero and highest slope. Not like this. This is the ice slot. This one. Okay, things are gonna be here. This is what it is. In Brillium zone, all the down here is very simple, but the conductor band is very much a curved shape.

As you look it up here, the down is very simple. So as I told you the balance is very much simple. Top is very complicated. Complicate, simple, complicated, simple. All the things depends on the material but this is universally same trend. Upper is complicated very much. Down is simple, simple. Okay, simple. Okay? So now, this is the typical bandit structure. No state, state, here, no state, state, here, no state. And the bandit structure, no state. Bandit structure, no state. Bands, no state, bambam.

So this is typical of endostructural material, mini material. So look it up here. We interest only blue-limbs zone, whatever. And then blue-limbs zone it depends on the direction. Usually like three-dimensional, but it's looked up to two-dimensional, okay? and one on direction. So what it is? Bend structure little different. Here is a bend gap. Here is a bend gap. This is a bend structure. State is there. State is there. State is there.

Okay. So whatever. First here, this is the first blue limestone. All the way across this K0 point is the first blue limit zone, second blue limit zone, third blue limit zone. Here is the first blue limit zone, second blue limit zone. This is the things made changeable. Direction dependent. Which way to go? This direction is the band structure is changeable. Okay, so things like here. First of the brain zone, second brain zone that I present here.

Here is a band gap. Here is a band gap, a orbit band gap, which is allowed energy level. Okay, so this thing, this band structure depends on the material. So here it depends on the material is something every band gap structure is different for example okay like this okay so this is one of the example for the band structure. So now next I want to

thing is going to be band structure for the meta and that semiconductor. I want to just compare. Okay, so I chose before depending on the direction. 1 0 direction, 1 1 direction, band structure is changeable. 1 0 direction is band here, band here. Or 1 1 direction is band here. Okay, so this is the direction. The direction or direction. Whatever. There is so many directional distribution of a banded structure. But

the summing up here, summing up here, these band, even the metal, the metal banded structure, the directionally there is something no state available region is existing here. Okay? Even the metallurgy, all the time is not fully closed. Something is bendy gap here. You know why? Because the color of the shape is always something empty spot here. So that's the empty spot. But why people say the metallurgy is no bend again? Does this bend again be existing?

Bend again be existing directionally. Those directional components combine. Okay. So this thing is going to be overlapped by this. This band gap overlapped by this. This band gap overlapped by this. So fully closed. Okay. Overlapped band. Overlapped to the band energy. So which is no band gap. Directionally, band gap is existing, but some of the old band structure, there is no band gap.

How about the metal? I'm sorry, next is the semiconductor. So directionally, there is a band gap here. Okay, so this is directionally. Okay, but I want to sum him up all the directional composition here. So this bend gap, this bend gap is something Cut it off. This thing here and then this thing here Okay, so This is empty. Even the overramp, this direction is still empty here. That's why I did

band gap is existing. Okay so metal. The electron in the metal is no apparent band gap. Because second this direction and then third is this direction is gonna be overlap. Okay so electron can always find energy changing their direction. So, electrons are finding closed one all the time, directionally. So that's why the semiconductor or insulator, they have something band gap existing, but even the combination of all of the band structure, but something empty spot there.

Okay. So that is it. something. I'm out. Okay. It's a band destruction. Again, the metal material is energy band here, which is half, full, whatever, then full of the sun part and then some of the empty. So that's why it's easy to flow around here. That's why the metal band structure is very easy to move. So typical energy

diagram for the metal. The balanced electron is in the energy band which is partially filled. Okay, the top of the band is vacuum where the electron is free. Okay, which is potential energy is zero. So metal, so there is an empty state of electrons in the air. So it's mutualized here. So mutualized here is the same level.

So the electrons are not flowing. But electric field, if there is voltage on it, there is something lifted up. This much energy lifted up one part, the other part lifted down. which is something +1- something. That's why electron flow. Okay, so energy band diagram is B, is an absence of fuel. So no voltage. There are many electrons moving right there.

There is a moving to the left. Motion of two electrons each. The energy cancel each other. A and B. So it's not moving. The presence of electric fuel. Okay. So lifted up and then down. So there's something electron moving. Okay. Bhavma extraction. the average of the momentized value along the extraction. So, last part, this is the EK diagram.

We mentioned so many times, y-axis is always electron energy. And this is something extraction. Maybe we identified the K. So this is the extraction and then energy level. So electron is an electric field on it. K sub-electro voltage is on it. Once electrons are up and they're free energy, but something current with electric field power on it, voltage on it, there is an electron moving here to the

here. But there is something collision, some boundary layer or whatever. There is a collision by after losing energy down. Collision down, down, whatever. It's just moving around the conduction band. current flow, okay, which is some kind of electric field on it. Okay, electric flow, the extraction is some force on it. So that's why how electron moving here to the here means something current.

Electron moving means current. Okay, how are you going on in? Semiconductor structure. This is the semiconductor. Current. How current going on. How current flow. Okay. This is the things about the in-band structure. Semiconductor. How? Electron. That is only with something voltage, electric fuel energy only.

This is how current going on.