Theory of Band Structure.

  

 

 

 

The largest Category of course other metals Semi metals understand how the electrons behave in those substances and determine their conductivity now there's a range of substances. In the metals category and some are more conductive than others gold is a better conductor than iron for example And of course in our nonmetals, we clearly have substances that are very good insulators. They don't conduct any electricity at all. In this video. I want to talk specifically about what the factor is that determines their conductivity and I'm going to introduce the concept of the band theory and hopefully, in this video you come away with a better understanding of What it is that is occurring at the molecular level? as you know the atom consists of a nucleus with electrons that are in orbit around it and These orbits are in discrete shells So let's take atoms such as sodium. We know it's sodium that as long as it's neutral it has 11 protons and 11 electrons and These are arranged in Depending on how many electrons can be held in each shell So we have two in the inner shell we have 8 in the next shell, and then we have one in the outermost shell This electrode here which is Very loosely held in fact and it actually contributes to the reactivity of sodium Actually also it is referred to as the valency shell so the valency Shell is simply the shell that contains some or electrons in the Outermost Shell Now because this particular shell Isn't a is that the atom and the electrons aren't tightly held this electron actually under a potential difference is free to move and so this particular area or Back Shell is actually also referred to as a conduction band In other words. It doesn't require this electron doesn't require any energy to become conductive it is already in an energy state that allows it to become conductive, but what happens if we have a different atom in? In this case, we have chlorine now chlorine has

Seven electrons in its outermost shell and as a result it actually these electrons actually quite tightly held the outermost shell is still called the valency band it is the actual atom that ached Shell and Therefore it contains the Valence electrons seven in this case. But these electrons are held tightly They do not have enough energy to become conductive staying in this position in order to become conductive they actually have to move to the conduction band. But is now in a new shell There are no electrons in this case for chlorine in this conduction, band however for an electron to go from the valency band to the conduction band in order to become used to conduction. It needs to cross a forbidden gap According to balls theories an electron can have enough energy to be in this shell You can have a certain amount of energy to be in this show. I am out of energy, but cannot exist in between So in order to get from this cell to this show. It needs a very specific amount of energy and in terms of insulators. This is actually quite a large gap to overcome valency and our conduction bands are represented by two boxes

Conductor so here's a conductor and a conductor has the valency band such as this As you can see it's represented by an an increasing amount of energy as we go up So because they overlap any electrons that exist in the valency band is automatically in the conduction band there is no gap for them to have to Traverse in order to become conductive in other words, outermost electrons are free to conduct All insulator also has a valency band in a conduction band In in this case for the insulator for the electrons in the valency band to give to the conduction band Electron Volts Then we say these electrons because they're unable to get into the conduction bands are Therefore unable to become conductive and in it is an insulator.

But what about the third to the right situation? How about a semiconductor? Well, a semiconductor also has a valency band and a conduction band There is also a gap however the forbidden gap is much smaller and so for an electron to move from the valency band to the conduction band it does require an amount of energy to move from the valency band to conduction band, but the energy can be gained through thermal energy So for example if I have a semiconductor such as germanium The it only needs about 1.1. Electron volts traverse it. How do I manage to do that well? I simply heat up the substance and as long as it is above zero degrees Kelvin then there may be enough energy for electrons to move from the valency band to the conduction band and of course once they are in the conduction band.

They're free to become conductive and they will conduct if I apply an electric field to them or apply a potential difference across them? Now want to give you a bit of an analogy to help you understand the band theory and in this analogy, I'm going to model but the band theory by using this piece of metal and you can see that this metal consists basically of a smooth surface small divots here, and then a large divot here, and the surface of the metal is going to represent our Conduction band it is the place where the electrons are free to become?

Conductive, and that's going to be represented by our marbles and they're free to move and of course you don't want to apply a potential difference I simply have to tip it and so as you can see by tipping it can clearly have the electrons moving in One Direction So let's go and discuss how these divots represent our various substances If I place my marbles in the largest divot you can see that these electrons are really fixed and no amount of potential difference is Going to make them move to shake them isn't going to cause them to move What that means is that the amount of energy required for these? electrons, so to speak to pop up to this conduction band is so large and that the electrons are not able to do so and therefore stay in the Valency Band and So we classify this area as our insulator the Gap between the valency Band and the conduction band is just too large to overcome and similarly it is clear to understand that this ball bearing or marble clearly either sits on the surface or is in the actual divot and that of the course represents that that electron does not exist somewhere in between The two bands in other words. That's why we refer to it as the forbidden gap but what if I have my electrons in these divots here? Now clearly again, they're fixed and as long as there's no energy in this case the energy is vibrational energy and that is going to be temperature then the electrons are not free to move, they stay in the valency band and if I apply a potential difference they stay put.

But as soon as I start to vibrate it you can see that. They are free to move in other words I've provided them enough energy to pop out of the divot and as a result they are Going into the conduction band enough free to move Similarly speaking these divots here do the same job again if there is no energy to the actual substance They're fixed then is going to move however, if I produce a small amount of energy in this case Vibrating it which represents an increase in temperature? they are free to move and if I apply a potential difference you can see that they are moving off in One direction and So this region here these two divots represents our semiconductors you could argue that this having a larger divot means a larger forbidden gap and that will be something like Silicon which is about 1.1 Electron Volts fitting get bitten Gap and germanium only 0.7 And of course clearly in this case the electrons along this surface of free to move there is a need for any energy whatsoever to move from their position and so the area here represents the metal so we have our insulator. We have a semiconductor and we have our metal and each has its differences due to the place where the electrons are and the circumstances that are required for the electrons to become conductive if they are in the conduction, band now one word of caution This is clearly a model for band theory although it is simplistic and it explains aspects of band theory it is a model nonetheless which means it does have some limitations, and that's an important thing to consider that models are useful in science and therefore can explain complex concepts in simplistic terms But they have their limitations. They do not explain everything and in this case, my metal sheet has its limitations It does not explain everything about band theory but hopefully with the animation and this particular demonstration you'll have a better understanding of van theory.