Understanding the Basics of PN Junction Diodes

104N. PN Junction, Depletion Region, Diode Equation

Estimated read time: 1:20

Summary

In this engaging lecture, Ali Hajimiri dives into the fundamentals of PN junction diodes, explaining their structure and behavior. He breaks down complex concepts like carrier densities, ionization, and the depletion region in an accessible way. Hajimiri clarifies the diode equation and the role thermal energy plays in the functioning of these devices. He emphasizes the importance of understanding these basics for further exploration into more advanced topics. This lecture forms a crucial foundation for anyone interested in solid-state device physics.

Highlights

Ali Hajimiri simplifies the complex topic of PN junction diodes in this lecture. 🎓
PN junctions are essential for understanding more advanced semiconductor devices. 🚀
Here's how electrons and holes dance around to form a PN junction! 💃🕺
The depletion region is like a dance floor where pairs have recombined! 🎉
Dive into diode equations and see how they explain the flow of current through a diode. 🔍

Key Takeaways

PN junction diodes are the simplest type of semiconductor devices, formed by joining p-type and n-type materials. 🌟
The depletion region forms as holes and electrons recombine at the p-n junction, creating a barrier to charge carrier movement. ⚡
Thermal energy and random electron movements are crucial in the operation of PN junction diodes. 🌡️
The diode equation describes how current flows through the diode, influenced by applied voltage and thermal effects. 📈
Understanding the basic workings of PN junctions is essential for studying more complex semiconductor devices. 📚

Overview

Ali Hajimiri takes the viewer on a journey into the world of PN junction diodes, explaining their importance as the simplest type of semiconductor devices. By forming these junctions with p-type and n-type materials, they exhibit unique characteristics valuable for creating sophisticated devices. This lecture lays the groundwork for further exploration.

During the lecture, Hajimiri demystifies the depletion region, where holes and electrons meet and neutralize, forming a barrier. This process, influenced by thermal energy, is critical to the function of PN junction diodes. He explains how the movement of charge carriers and ionization at this junction shape its properties.

Concluding with a dive into the diode equation, Hajimiri discusses how these concepts translate into current flow through the device. This understanding is vital for interpreting how PN junctions behave under different conditions and provides a foundational perspective for anyone delving into semiconductor physics.

Chapters

00:00 - 01:00: Introduction to PN Junctions The chapter explores the fundamentals of solid-state devices, specifically focusing on the behavior of carriers such as holes and electrons. It introduces the concept of altering semiconductor regions to exhibit varying carrier densities. This paves the way to designing devices, with the PN Junction being the first device to be discussed in detail.
01:00 - 03:00: Basic Formation and Concept of PN Junctions A PN junction diode is explained as a basic semiconductor device formed by merging n-type and p-type materials. The n-type region has more electrons than holes, while the p-type region has more holes than electrons. The process involves introducing dopants, such as acceptors, into the material to create these distinct regions. The resulting PN junction exhibits unique characteristics due to the interaction between the two regions.
03:00 - 05:00: Atoms and Ionization at Absolute Zero The chapter discusses the process of creating PN junctions from n-type materials with some donors. It indicates that even though this method is not used in practice, it helps in understanding the basic principles. Typically, PN junctions are made from a single piece of silicon, as the two-piece method would not yield a functional junction. Understanding PN junctions is crucial because they serve as the foundation for more complex and sophisticated structures.
05:00 - 09:00: Energy Levels in P-type and N-type Semiconductors This chapter introduces the concept of PN junctions, which are fundamental components in semiconductor devices. It begins by explaining what PN junctions are, and then delves into the characteristics of p-type and n-type semiconductors. These semiconductor types are kept separate initially to describe their individual properties.
09:00 - 16:00: Depletion Region Formation The chapter discusses the formation of depletion regions in semiconductors. It introduces the concept of dopants added to semiconductor materials, like silicon, to change the balance of electrons and holes. In particular, the chapter focuses on p-type semiconductors which use acceptors from the third column elements to alter this balance. Additionally, the chapter sets the stage by considering the scenario at absolute zero Kelvin.
16:00 - 25:00: Built-in Potential and Energy Band Diagrams The chapter titled 'Built-in Potential and Energy Band Diagrams' begins with an explanation about the ionization state of electrons. In the initial state described, no electrons are ionized, meaning that every electron is attached to its respective atom, resulting in a neutral zero state. This setup can be visualized as a collection of negatively charged ions with associated holes. The description suggests considering these ions as a collective system of negatively charged entities paired with their respective holes. The narrator indicates a metaphorical use of 'cheat' to simplify the conceptualization of this state.
25:00 - 36:00: Thermal Movement and Equilibrium This chapter, titled 'Thermal Movement and Equilibrium,' seems to start with an engaging introduction, suggesting that the content will be both exciting and interactive for the learner. The speaker acknowledges the shared excitement, possibly indicating that the concepts of thermal movement and equilibrium will be explored in an engaging or innovative manner.
36:00 - 48:00: Applying External Voltage and Diode Equation The chapter titled 'Applying External Voltage and Diode Equation' explains the scenario starting with negatively charged ions that remain non-ionized at the zero potential. It describes how third column elements resist ionization and details the presence of positive charges affixed to these ions. The focus is on understanding the behavior of these charged particles in the context of external voltage and its implications on the diode equation.
48:00 - 59:00: Forward and Reverse Bias in PN Junctions The chapter discusses the concept of forward and reverse bias in PN junctions. It starts with an explanation of positively charged ions in the n-type side of the junction and mentions that these ions have electron attachments. This implies that at absolute zero (zero Kelvin), these ions are not ionized, signifying a specific state of the PN junction under certain conditions. The discussion likely goes into more detail about how this state changes with forward and reverse biasing, affecting the behavior and properties of the junction.
59:00 - 61:00: Approximations and Understanding in Circuit Design The chapter discusses the concept of electrons and energy levels in the context of circuit design, considering states where electrons remain attached and non-ionized. This serves as a basis for understanding more complex electronic behaviors, despite the less exciting nature of non-ionized electrons.

104N. PN Junction, Depletion Region, Diode Equation Transcription

00:00 - 00:30 okay so one of the things that we've done so far is basically developed this basic very basic feature of solid-state devices and the way the carrier's behave so the next thing we do we are trying to sort if we can actually create different regions of that semiconductor with different behavior in terms of the carrier densities that holes and electrons now we got to make a device we got to actually design something with it so the first device we'll design is the
00:30 - 01:00 PN Junction diode which is actually the simplest thing if you think about if you can make regions with more electrons than holes and type and regions with more holes and electrons the P types well the first device that you probably would want to make has some interesting characteristic would be a piece of end and a piece of P attached to each other so if you think about them as a PQ already make a p-type material by introducing some let's say dopants in there and you know some acceptors in the material dopants and then you make some
01:00 - 01:30 n-type with some donors then if you could put them together you will make the PN Junction now we don't make PN junctions that way just so that we know we actually make them out of a single piece of silicon if you actually do it that way it would be a really really bad PN Junction if any functional one at all but that's the way we think about it to just process so we are thinking about PN junctions and you want to understand how they behave because they are the basis for the more sophisticated more complex
01:30 - 02:00 devices that will come later that will use quite frequently and of course PN junctions are diodes and then we will also use them too so what is a PN Junction so let's start thinking about a PN Junction so let's say you have two pieces of semiconductor so right now I'm keeping them separate let's say and there's a p-type and there's an n-type now what do we have in a p-type semiconductor what does it look like
02:00 - 02:30 well you have a whole bunch of semiconductors let's say silicon or other materials atoms and few much smaller number of what we call the dopants these are the Adams's we introduced to change the ratio of the electrons and holes so in the p-type we have acceptors which are basically third column L elements and they basically you can think about them so we are starting at zero Kelvin so let's say we are at zero Kelvin at Absolute Zero now at Absolute Zero
02:30 - 03:00 nothing is ionized every electron is attached to its associated atom and they're in a zero state so what do you have is basically you can think about this as a bunch of negatively charged ions with associated holes with them right so you can think about this as a bunch of ions so this is going to take me a second to do and I'm gonna cheat
03:00 - 03:30 just bear with me for a second this is as exciting for me as it is for you okay
03:30 - 04:00 so now you have these negatively charged ions so let's use a different color actually so at this point at zero tell me nothing is ionized right so let's say these are negatively charged ions that have a hole attachment basically means that they are not ionized there are third column elements that are not ionized and then you have and let me show of course these positive charges here that are attached to them okay and
04:00 - 04:30 then on the other side on the n-type side we also have these positively charged ions which have an electron attachment it basically means that they are a zero Kelvin they are not ionized
04:30 - 05:00 then you have a negatively charged the electrons attached to them so nothing is ionized not very exciting and what would the energy levels look like so so now that you're done with the really exciting part you can get on with our
05:00 - 05:30 business so what does the energy level what do the energy levels look like at 4:00 in the in the p-side at zero Kelvin just think about it so you're of course have the two energy bands like the conduction band and the valence band so this is the valence band this is the conduction this is the edge of obviously you know what from now on will always show there's a line but what this would mean is that the conduction band is above this and like this we mean that the valence band is underneath it and this is the band gap so just keep that in mind so line but they really means that the
05:30 - 06:00 border the edge of the bat so where is the Fermi energy at 0 Kelvin so you remember the number of carriers for example was given by an AI eetu the EF minus e I over KT we did we derive this in the previous lectures and then P was an AI eetu the e i- EF over KT now at
06:00 - 06:30 this temperature there's nothing ionized right so your energy level is basically where your Y is right because you're at the ni of that temperature so basically your Fermi energy is in the middle more or less and the same thing here and where are the acceptor levels so acceptor levels energy levels are here and they are not
06:30 - 07:00 ionized so they're just sitting there now and the same thing clear on this side so if I have the conduction band and the valence band here now my half I have my donor levels a donor but they are not
07:00 - 07:30 ionized my Fermi energy is here and I'm in thermal equilibrium nothing is happening fine so right now I'm treating them as two separate pieces of semiconductors right so now let's say we actually attach them which is another way of saying that they were made together anyway to begin with and we'll see later on how they were made but so that's basically when they be attached when we attach them nothing exciting happens this is here this is here this is there this is the junction that's the energy
07:30 - 08:00 level those are the energy levels at 0 Kelvin it's flat nothing has happened now let's say you gradually heat it up you gradually increase the temperature what's gonna happen now so at but yes exactly some of the donors and acceptors start getting ionized so basically what it means in this picture is that some of these dyes will start being ionized and
08:00 - 08:30 I'm removing them to just put them somewhere else just some random places and then here we had them appear in other random places now as this ionization happens so you will have what you will have more electrons on this side I'm saying more holes on this side and more electrons on that side now you have electrons free electrons these are free electrons and free holes so what happens as this is
08:30 - 09:00 going on as this goes on think about that now you have two things attached on one side you have a bunch of electrons then you have on the other side you have a bunch of holes and now they're not just stationary they are moving around why because of their thermal energy right they have thermal energy and they're very light so a little bit of thermal energy gives them a lot of speed so they're gonna start bouncing around as soon as they're released so when they
09:00 - 09:30 are bouncing around there's a chance that this hole will end up on the other side every so often and there's a chance that electron from this side will end up on the other side and when an electron from the n-type ends up in this side what happens what is the putt is that what is the situation like so you have an electron in emits of a very large C reasonably large number of holes so the chance of it hitting a hole is pretty
09:30 - 10:00 high so at some point these guys there's a good chance that the electrons that end up on the other side will recombine will find a hole and they hit each other and they recombine and the same thing is true about the holes on this side so gradually what happens and this is most likely to happen to where at the borderline right so gradually you order starts getting depleted of these charge carriers so you gradually start
10:00 - 10:30 forming a region which is basically the free charge carriers are gone because as soon as they end up in this region there's no probable there's higher probability of them just recombining with the opposite carriers now this is a complete random process I've heard this being explained at times as yeah electrons see that there's less electrons on the other side so they go to the other side or the whole thing is
10:30 - 11:00 see electrons are pretty dumb they're not that smart right so they're just moving randomly around and what happens is that they just kind of end up on the other side and there's a higher chance of recombination on the other side because there are a lot of chances for other combinations there's a opportunities for that yes question what do you what about the fusion so what about the fusion so the question is what about the fusion
11:00 - 11:30 this is the fusion the random thermal movement of electrons is the fusion actually in this explanation I actively stay away from the word diffusion purposefully because I want exactly two people to come to 54 people to realize that there's nothing magical happening about it this random thermal movement is
11:30 - 12:00 in fact a diffusion but I don't call it diffusion because I want people not to think that this is something very fancy or special this is a very very simple thing happening now the fusion equation describes the flow due to random from a movement yeah good question the questions yes yes that's what we're
12:00 - 12:30 going to do next great good question so it once before so the critics question is that the question was how does it look like in terms of energy band diagrams and so let's find out so but for that to have to think about if for that to be found out just let's think about one thing now once this region is formed that's mostly depleted of carriers and we are showing it kind of like an abrupt thing but it's really a
12:30 - 13:00 transition it's a gradual thing but this abrupt transition is a good approximation we'll know why we'll soon but it really goes back to this exponential because you have an exponential drop and an exponential drops happen really rapidly so it basically did this but it's called a depletion approximation that you can just basically assume that this is a well defined region it's a pretty good approximation because of this exponential but going to this thing what is happening here what is going on here in this region what do you have you have
13:00 - 13:30 a little bit of an electric field right because now you have positively charged ions here that cannot move they're stuck they're bound they're tied down and the same thing here with negatively charged so what happens with the electric field there is an electric field right interesting faint so there's a there's an electric field built-in okay so what
13:30 - 14:00 does this electric field due to this process now does it facilitate this random movement of electrons from one side to the other and the holes from one side to the other or does it impede think about it now if there's an electric field here in this direction is it easier for a positive charge to go from this side to that side
14:00 - 14:30 does it experience a resistive force the repelling force yeah I know it's it's yeah just like go back we were here first and he said and this guy's Oh go back right there's a built-in potential so now let's see how its reflected in the energy band diagram so now still there's no external potential applied to this thing this is just sitting there now the energy band diagram so if it's sitting there it's in
14:30 - 15:00 thermal equilibrium one thing needs to be constant across this thing which is the Fermi energy right so now what happens is that we said there's some ionization happening on this side so we are at t above zero kelvin but still below room temperature so there's some ionization happening and so this is the
15:00 - 15:30 end okay I did some poor planning in my drawing but it's okay okay so here you have a Fermi energy that looks like the bandgap really doesn't change the bandgap is a property of the material what is happening here is that now the Fermi energy is getting
15:30 - 16:00 closer to the conduction band on this side because this is n-type and it's getting closer to the valence band on the other side let me just make this a little bit less that because we are not still at room temperature so and what's happened to the other energy level so you had the e I the intrinsic energy level so you can see here the F is above
16:00 - 16:30 AI the intrinsic energy level which is kind of like halfway through it's not exactly in the middle of the conduction band and valence band but it's kind of close and the reason it's not half exactly in the middle is that the energy states the density of states and this state in that state the NCN end we are not exactly the same so here this gap remains the same I try to keep it the same more or less the bandgap the Fermi energy remains constant across the thing
16:30 - 17:00 so this is our Fermi energy Fermi level and here what you see is that on this side you have a I that's greater than EF so what you will have what will you have you will have a lot more peas holes than ends right and on this side you have EF that's above VI so you have a larger number of electrons so there's this built in electrostatic potential as a
17:00 - 17:30 result of this thing so there's this there's this built-in potential that's there part of it is on the P side and part of it is on the inside so we can actually even give it a name and calculate it so we can say this is sy q sy P and this is Q sy and now sorry si is basically measured and this is electric this is this is the energy right so we want to convert from
17:30 - 18:00 the in net energy to the electric voltage you have to scale by their charge so that's why there's AQ term there so this is the way it looks like and now the energy band diagram for this now as the temperature goes to the room temperature so let's say it goes to the room temperature what happens is that at room temperature this is dope dopant the
18:00 - 18:30 donors and acceptors are completely ionized and as a result what happens is that you will be in a situation where these are a little bit further up and the fermi energy to these bands and with respect to the acceptor and donor energy so this is where the acceptor and acceptor energy levels are and this is
18:30 - 19:00 where the donor energy that was the appropriate color for that I don't know so at that point you have formed a slightly larger depletion region let's say like this and you have basically an ionization happening in this region and you have an electric field Milton so now let's look at this energy band diagram see if it makes sense it seems to show
19:00 - 19:30 that this side is higher than that side but if you think from an energy perspective if you take a positive charge if I move it for is it harder to move it from this side to that side or is it from left to right or from right to left so it's easier to move it from right to left right because the electric field will help it so it disappears to be upside down right because it should
19:30 - 20:00 be the other way around it should be downhill going from here to there but it looks uphill so this is a common question common confusion I'm just yes correct these are the energies of electrons these are the energy band diagrams of the energy band diagrams of band energies of the electrons and electrons are negatively charged so for an electron it is hard to go uphill this it's uphill this way because it's
20:00 - 20:30 opposed did you see it's going away from this positive charge that it likes and it could have to go to these negative charges that are repelling it so these are energy band diagrams for the electrons the energy levels for electrons so so that's why they're upside down because electrons are negatively charged fine but so other than that this should make sense now what happens does does this process stop once the depletion region is formed if
20:30 - 21:00 you think about it the depletion region is formed let's say we are at room temperature there's a depletion region and it's there so everything is static everything is sitting there nothing is happening no right there are electrons moving around very rapidly still right so there's still a chance that an electron will jump from this side to that side and recombine and the same thing for a hole because some of them still have enough energy some of them are hot
21:00 - 21:30 enough to just jump from this side to the other across this potential barrier because see this is uphill for the electrons and this is also uphill for the holes so the holes want to go this way but this is their uphill if you flip it upside down so what does it that what happens does it mean that the depletion region keeps growing and growing and growing and growing no doesn't make sense right why what stops it from growing what is the thing that opposes this process because once they're on
21:30 - 22:00 this side you're going to recombine and they're going to go away right which means that you're losing more electrons from this side and losing more holes from that side there must be something that counters this process yes correct thermal thermal generation of electron holes in particularly in the depletion region because yes this is depleted because they moved here and there close to the hostile region they will just get absorbed most of the times
22:00 - 22:30 but it does nothing that says that every so often because of the thermal energy an electron cannot jump from here to there from a conduction from valence band to the conduction band so when that happens you what do you have you have a hole and you have an electron right right so you have a hole and you have an electron so which way would they go downhill this one will go this way this
22:30 - 23:00 guy will go that but there downhill is different but the electric field will just basically if you look at the electric field you see that's in direction they will go now is this opposing the flow yes because now there's a flow of electrons back to the n-type and a flow of holes back to the p-type region so in steady state in equilibrium and steady steady steady state as well right by definition if you have what happens is that you are that
23:00 - 23:30 this this current this generation thermal generation current is going to oppose the diffusion current now what is that R is the diffusion current that we talked about earlier comes from what is that thermal energy current coming from because if you think about it these electrons on the p-side on the inside have a Fermi Dirac distribution which we said for energy levels that are sufficiently far away from the Fermi
23:30 - 24:00 level which is three KT which is not that much 75 millivolts or 75 milli electron volts if you're talking about energy you can use Boltzmann distribution which is basically an exponential so if you think about it these guys there's still some of them that are hot enough so they can go but these folks who cannot do a jump over like a fence they can just basically or bounce back
24:00 - 24:30 okay now and the same thing for the holes so the holes also experienced a similar situation so there's a distribution of these guys and these folks go through and these are bounced back now this current this thermal current is balanced in steady state completely by this generation current by this process of electron hole generation which goes back does this make sense
24:30 - 25:00 qualitatively any questions on that before we move on so what is what are these some of these parameters right so let's let's calculate some of this thing so first of all what is this built-in potential this built that we call this a built-in potential right because there's a lector field difference how can we calculate that how can we calculate what this built-in potential is do you agree
25:00 - 25:30 that this built-in potential is Q cyan and cyan - site is IP right so IP - I owe the sum of these two so what is this one that's its IP what is let's calculate that if you say Q scipy which is basically the energy difference between the e EF and e I right so it is going to be e in this case it will be e i- EF for here on the p side what is
25:30 - 26:00 that do you but look at this equation or look at this equation perhaps and tell me what that is well you can solve for e i- EF from this equation right and use it there so if you solve for that what do we get now we get P which is the density of the holes in the bulk of the p-type what is the density of the holes in the bulk of the p-type at room temperature na right
26:00 - 26:30 because you've doped it and we said at room temperature if it design if you have the right kind of material then all of them are ionized the number of holes is essentially dictated by that density so this is going to be na and this is gonna be nd also so we know na because we designed it to be what it is so this is gonna be KT natural log of n na over and I just say intrinsic level
26:30 - 27:00 it's one point four five ten to the minus ten per cubic centimeter it's a fixed amount fixed quantity so you know sy p so scipy is basically Q that divided by Q the charge of the electron and then similarly for cyan the built in potential electric potential on the other side is going to be e f- v i n this difference and similarly from this
27:00 - 27:30 you can calculate what that is which basically is going to be KT natural log of nd over ni and therefore sy n minus plus IP which is the sum of these two is going to be KT over Q this is in volts right and a nd divided by n I squared so
27:30 - 28:00 this is the voltage this is the voltage across this thing has to be equal which is sum of these two built-in potential has to be equal to that so this is the built-in potential so this is the height of this barrier that gets built naturally when you actually have this random thermal movement and you can catch these discs or these are known quantities right so you've designed it to have a certain doping level on that acceptor side and the P side and the
28:00 - 28:30 n-type and this isn't these are this is a constant of select for example for silicon is one point four five ten to the minus ten ten to the ten per cubic centimeter these are physical constants and the temperature right so you can calculate the height of this with the electric with built-in potential so and of course this quantity how many what is this what how much or how many electrons are that are hot enough that can go through
28:30 - 29:00 the number of these hot electrons that can still pass potential barrier what is it proportional to you remember from last time we did a calculation we said that the number of electrons about a certain ee1 or charge carriers in Boltzmann distribution was proportional to e to the negative T 1 divided by K T that's Boltzmann distribution right so this is proportional the number of these things is proportional to e the negative now
29:00 - 29:30 this is the potential barrier e to the Q sy naught divided by K T call the sign out right so that is the height of the potential barrier which we calculated so this the number of electrons that can pass is proportional to that so is the number of holes because they also experience the same potential barrier height so the barrier height is the same for both of them right so it's proportional to that and that has to be
29:30 - 30:00 equal so now that whatever that is that that total number has to be equal to the generation current so this is also equal to generation current in steady state because they are in steady state they are in thermal equilibrium so all of that is nice and good but it's not still particularly useful why it's not particularly useful because it just shows what it is in thermal equilibrium without any external influence if you're making a device we want to do something
30:00 - 30:30 with it and doing something with it in electrical engineering means applying electric voltage and currents to it right so now let's see what happens if you apply some voltage to that so we are going to stay with this picture and say look I'm not going to do all of those again I'm just gonna do a representative one so you have negatively charged particles
30:30 - 31:00 okay let's use the same color code negatively charged ions here positively charged ions there and here and there and then you have a bunch of free
31:00 - 31:30 electrons and three holes going around so we have the holes here and then we have the electrons here our energy band diagram looked like this Fermi level it's like this initially when we are in
31:30 - 32:00 thermal equilibrium and then that's the p-type and this is the n-type and the electric field is pointing this way okay so we're back here but now we are gonna do something you're gonna apply an external electric field to it and I'm gonna apply a voltage called let's call it VD the voltage across the diode because this is a diode well as well see so what happens if I apply a bias like
32:00 - 32:30 this by the way is it a forward bias or reverse bias the way I've applied it the positive is going to P positive is going to positive negative is going to negative so it's forward so I'm for biasing it from a Electrical from a circuit perspective so what does that do to the potential barrier and the depletion region if you think about the depletion region now what is this - so injecting positive charge into here and negative charge into here so
32:30 - 33:00 Stegen shrink the depletion region right exactly because you have now more electrons and holes that are available so they can come in and just like fill up this empty spaces where they were kind of define eyes before so they can come in and be here and neutralize the charge here so the electric field will go down the potential barrier will be lured by how much the potential barrier will be lowered by how much qvd right so
33:00 - 33:30 what happens is that so this potential barrier now is a lowered compared to before so this is where it was before and this is where it was before now it's lured by qvd so now remember trick let's think about those charge carriers and the distribution so before you had this distribution and these were the guys who could pass right these were proportional to e to the
33:30 - 34:00 negative Q sy naught over KT now a whole bunch of new electrons can pass too because now of lowered the potential barrier right so now that I've lured the potential barrier by QV d now how many can pass so now basically all the stuff that's kind of happening is they're going to be proportional to the e to the sine of minus VD over KT minus so now
34:00 - 34:30 all of them can pass so this is basically the whole thing right including those guys so what is the net increase in the number that can pass do you agree that this if this is this whole thing and this is a just top part this net part is the difference of these
34:30 - 35:00 two proportional to the difference of these two so the net flow of electrons let's say J n is going to be proportional to the e to the Q sigh naught minus VD over KT minus e to the negative Q sy naught over KT which I can write as e to the negative Q sy naught over KT times e to the neck to
35:00 - 35:30 the Q VD over KT minus 1 and the same thing is true for the holes if you think about the holes so before these were the ones that would go which is proportional to that but now the new ones that can go are here but the sum of these two is proportional to that so the the Nets new
35:30 - 36:00 addition is this guy this right so this is the net extra current that can be carried by this thing so this proportionality of the concert that's also true for JN so the diode current I is going to be proportional to this quantity now we give it a proportionality constant called is the saturation current so it would be Q VD over KT minus 1 so
36:00 - 36:30 that's the equation that's used for a dial that's a diode equation describing the current and what you see there so ok so the equations etcetera etcetera what is the takeaway from this what's the meaning of this thing PN Junction diode does all the work because of the immense amount of thermal energy that is there in the electrons it's just a way of utilizing the thermal energy all you're
36:30 - 37:00 just doing when you apply a forward bias you're lowering the potential barrier and they just pour in the electrons from one side and the holster on the other side and the fact that they do it is because of the thermal movement and you can imagine this will happen very quickly right so what happens is that you are just lowering the potential barrier by a small amount but because of that exponential dependence Boltzmann distribution a whole lot more comes in and that's why you have an
37:00 - 37:30 exponential and that's why you have a KT now any device that you see whose equation of the IV characteristic or equation of behavior describe the equation describing its behavior contains a KT is a thermal device when you see KT it means that it's really dominated by thermal so PN Junction device is really a way of harnessing that thermal energy and using it for
37:30 - 38:00 carrying of the current okay it's nothing magical and now people use make make it more sophisticated by calling diffusion and drift etc etc so there are two components to this thing there's this thermal movement and then there's that components in the middle which is basically when there's a hole and electron generated in the middle they go in the opposite direction that's the dress and that's basically what's being canceled to you that's the negative one is a lot of times in design especially if you have a forward bias
38:00 - 38:30 device you don't worry about this because this is an exponential and then sometimes just drop this but now the interesting thing is that now what happens if you if it's in the reverse bias if VT is negative so now let's think about the opposite situation because we talked about the positive forward bias and now what if it was negative if it was reversed so what would happen then so help me out now the potential barrier instead of being lured is increased right so the potential barrier now instead of being here would
38:30 - 39:00 go up here and the situations will go down here so now even fewer can go and jump through so when the potential this barrier is high enough all you will end up with is just the negative this component negative of that which is basically it's the drift part because we said the drift part the part after that generation part is has to be the same as this random thermal part but now if you
39:00 - 39:30 remove this random thermal water part by generate by creating a barrier that's larger for the most part you are left with that drift water which is this part is definitely my generation so this equation is also valid because if in VD is negative then this becomes small at some point sufficiently large in magnitude then it become negative is so the IV characteristic of a PN Junction diode does look like this it's an exponential and this is negative ions now there are nuances here right I
39:30 - 40:00 mean this is simplified view there's multiple nuances here for example as we apply a reverse bias the depletion region width increases so this current slightly increases this is not completely flat but as you will see as well see shortly is that that increase is not very large and it's it's either depend a square root dependence or cubic root dependence and all those things and that's that and that's why this is a reasonably good approximation of the
40:00 - 40:30 behavior of the diet now remember there are players of approximations being built and you will see as we go through the class but one of the things particular when we get to the circuits part of it that there are approximations upon an additional approximation and if things start bothering you keep in mind that already we've gone through to three layers or at least three levels of approximation to arrive at this thing right at least because you're looking at this behavior of electrons and we care capturing the bit behavior of electrons
40:30 - 41:00 in a lattice and holes in the lattice we are capturing it has some sort of an effective mass and then we are taking that and then you're just on top of that we are making assuming it's a Boltzmann distribution on top of a Fermi Dirac distribution and then on top of that we are making these assumptions about this depletion region is not changing etcetera etcetera so don't get too hung up if we are getting the exact equations solved sometimes we have to do something we have to do the exact because if
41:00 - 41:30 you're there some effect but remember we already have like two or three layers of approximation and a lot of these things is based on classical models semi classical models you're not using quantum electrodynamics to do it and follow this thing and a lot of things are already there so as we will go forward we'll make more approximations the point is to capture the essence of the behavior of something so you can design with it if you make it too complicated you will not be able to design with it but also you have to make it just sufficiently simple not more
41:30 - 42:00 right anyways so that's for that any questions all right okay