106N. Bipolar Junction Transistor, basic operation, current flow properties, doping Profile

Summary

The video delves into the fundamental workings of a Bipolar Junction Transistor (BJT) and PN junction diodes. Ali Hajimiri walks us through the basics of doping profiles, current flow, and the transition from diodes to transistors. The discussion covers the significance of designing efficient BJTs and how doping affects their functionality. Ali illustrates the transition from using diodes to BJTs in creating amplifiers and circuits, emphasizing the role of minority carriers and potential barriers. With an engaging approach, Ali explains technical aspects for better comprehension of semiconductor devices and their applications in electronics.

Highlights

• Ali Hajimiri introduces the basic principles of PN junction diodes and their electric properties ⚡.
• Discussion on the historical context and functionality of diodes leading to the creation of transistors 🔄.
• Illustrates the current flow in BJTs and how electron movement is controlled by potential barriers 💧.
• Explains the significance of thermal energy in improving BJT functionality over other transistors 🌡️.
• Covers the engineering aspect of semiconductor materials in creating efficient electronic components 🏗️.

Key Takeaways

• The BJT uses doping to create regions where minority carriers can traverse and be utilized efficiently 🌟.
• The transition from diodes to BJTs involves adding a third terminal for better control over electronic pathways 🌐.
• BJTs offer high transconductance by utilizing thermal energy to operate more effectively than MOSFETs 📈.
• Hetero Junction Bipolar Transistors (HBTs) offer improvements by using different compound materials to control electronic properties 🔧.
• Design considerations such as doping levels and base width are crucial for optimizing BJT performance 🎯.

Overview

In this enlightening lecture, Ali Hajimiri dives deep into the principles of Bipolar Junction Transistors (BJTs) and PN junction diodes. He starts by revisiting the essential properties of diodes, explaining their role as rectifiers and how minority and majority carriers function in these semiconductor devices. His detailed breakdown helps cement the foundational knowledge needed to understand more complex topics.

Ali then transitions from a discussion on diodes to the creation and operation of BJTs. He emphasizes the importance of the transistor's design in enhancing electronic components' efficiency. Ali elucidates how adding an additional terminal transforms a simple diode into a robust transistor, capable of functioning within logic circuits and amplifiers. His adept explanation of doping profiles and material properties further demystifies the complexities of BJTs.

Finally, Ali introduces the concept of hetero-junctions, illustrating how using alloyed semiconductors can enhance transistor performance by adjusting band gaps. This segues into practical applications, emphasizing the physical and chemical engineering required to optimize these devices for high-frequency applications. Ali's engaging style ensures a comprehensive understanding of BJTs and their vital role in modern electronics.

Chapters

• 00:00 - 10:00: Introduction to PN Junction and Diode In the 'Introduction to PN Junction and Diode' chapter, basic properties of a PN Junction diode were discussed. The PN Junction diode is designed using p-type and n-type materials. These materials are doped appropriately to exhibit specific properties. A significant property highlighted was its exponential IV characteristic, where the current is exponentially related to the voltage. This characteristic makes the PN Junction diode function as a rectifier.
• 10:00 - 20:00: Thermal Equilibrium and Biasing of Diodes The chapter provides an introduction to diodes, explaining the origin of the term 'diode' from vacuum tube technology. It describes the basic function of a diode, which has a rectifying nonlinear characteristic, meaning it is more conductive in one direction and less conductive in the other.
• 20:00 - 30:00: Bipolar Junction Transistor (BJT) Introduction The chapter introduces the concept of a diode, comparing it to a one-way valve and describing its ideal L-shaped IV characteristic. It explains that a PN junction is a common method of creating diodes, which has become almost synonymous with the term diode itself. The discussion then leads into the formation of a diode using PNP and N structures, noting the presence of two distinct regions in the setup.
• 30:00 - 40:00: Design and Function of BJT Components This chapter discusses the design and function of Bipolar Junction Transistors (BJTs). It begins by examining the composition of P and N regions within BJTs, explaining the role of dopants. Specifically, in the N region, dopants (from column 5 elements) provide excess electrons, creating an electron-rich environment necessary for the transistor's functionality. This discussion is foundational to understanding how BJTs control current, highlighting the importance of electron movement in semiconductor technology.
• 40:00 - 50:00: Effects of Doping and Depletion Regions The chapter 'Effects of Doping and Depletion Regions' discusses the presence of positive ions and free electrons in semiconductor materials. At room temperature, most electrons are ionized and move freely. On the P-side of the semiconductor, a variety of acceptor ions are present, contributing to the material's electrical properties. The chapter explores how these free electrons and ions interact within the semiconductor, affecting conductivity and the formation of depletion regions.
• 50:00 - 60:00: Emitter Injection Efficiency and Base Transport Factor The chapter discusses the concept of emitter injection efficiency and base transport factor in the context of semiconductors. It elaborates on how certain elements can easily ionize at room temperature, thereby leaving behind free holes. These free holes are crucial as they are free to move around, which is fundamental to the material's conductive properties.
• 60:00 - 70:00: Calculating Transistor Currents and Efficiency This chapter focuses on the calculation of transistor currents and efficiency. It explains the behavior of ions, which are massive compared to holes and electrons because they are atoms with nuclei and multiple electrons forming covalent bonds with adjacent silicon atoms. Consequently, ions are stationary, while the holes and electrons they release are free to move. The chapter also discusses the calculation of random thermal motion speed of these particles.

106N. Bipolar Junction Transistor, basic operation, current flow properties, doping Profile Transcription

• 00:00 - 00:30 good morning last lecture we covered we discuss the basic properties of a PN Junction diode we designed the device by using a pen type and p-type material that are doped appropriately that had interesting properties in specifically what they did it had an exponential IV characteristic namely the the current was exponentially related to the voltage and as such it was kind of a rectifier right I mean it
• 00:30 - 01:00 was it was a what we call a diode diode is a general term now but in fact actually the name diode comes from vacuum tube days because you have the diode then you had the triode and they had the tetrode and the pentode and all those things depending on how many electrons you had so diet was the simplest one which had two electrodes so diode in general now refers to any device that basically has this rectifying nonlinear characteristic that is more conductive in one direction and less conductive in the other direction
• 01:00 - 01:30 so it's like a one-way valve if you will an ideal diode of course it's like an l-shape IV characteristic now PN Junction is one way of making a diode now most of the diodes today are made out of PN junctions so we basically just has become synonymous but diode is more general PN Junction is a special kind of a diet anyway so what we did we could make a diode basically meaning that we had a PNP and N and what we saw is that we had two regions so let's go through
• 01:30 - 02:00 that process very quickly so if you had a PN so let's say you had the region P let's say region n and the region P and what do we have a kind of dopants that we have in the N region to get n region basically means that you have more electrons than host so you have things that are easily giving away extra electrons so you need column 5 elements right which basically after they give up the electron they leave behind a
• 02:00 - 02:30 positive ion right so you had these positive ions and the free electrons right you had the free electrons at room temperature most of them were ionized so these electrons were really free they were not attached to any of them so they were moving around free and on the peace side what we had we had a bunch of acceptors
• 02:30 - 03:00 basically call them three elements which which would be easily which would be able to easily ionized at room temperature and what that does is basically so what when they ionize they leave behind a free hole so you had the hole at room temperatures you had the holes that we're free to move around of
• 03:00 - 03:30 course these ions cannot move around there's a massive relative to the holes and electrons their atoms with nuclei and a bunch of other electrons that have formed our bonds for covalent bonds with the adjacent silicon atoms so these are pretty well tied down but the hole and the electrons that they released they are pretty free and of course these things we calculate the other thing that we calculated was the speed by which they're randomly moving thermally we saw
• 03:30 - 04:00 that the right speed of random thermal movement was extremely high and these being small devices it's very quickly the hot the chance of these guys ending on the other side is pretty high because they're moving around and every so often they would end up the end up on the other side when there's a now for example electron moving from this side ending on the other side is a minority carrier because now there's a lot of holes around it and it has a high chance of recombination now the closer you are to the junction the higher this chance is and it's
• 04:00 - 04:30 really an exponential drop beyond a certain point but at that point there is a region you basically eventually form a region which is depleted of charge carriers so most of the charge carriers in this region I've already recombined of course you're constantly generating new ones electron hole pairs that as they are generated due to the electric field that in this direction which basically pointing which way the electric field if you put a positive charge here it's one will go this way right so the electric field is pointed this way so this
• 04:30 - 05:00 electric field would force them to so if you have an electron and hole generated the electron would go this way where it's majority and the hole would go this way and there's a component of this is basically balancing the net flow because there's always some hot electrons and hot holes that would just cross the boundary that would be able to cross this barrier and then if you look at the energy band diagram of this of something like this what you have is that you have an n-type on this side
• 05:00 - 05:30 right so your Fermi level is closer to your conduction back and then you have a p-type on the other side and in thermal equilibrium you had a Fermi energy yeah that's constant across and here you basically are you have more holes and you have more electrons here so this is what the energy band diagram and of course an electron needs to work going
• 05:30 - 06:00 basically what you have what you see is that if I put an electron here it would go this down this way do you like to feel we go this way and if I put a hole down here the hole would go down this way because these are the energy levels upside down but these are the energy levels for electrons right so this was the basic picture we calculate we showed last time right this was the general picture and of course again I want to emphasize the difference between thermal equilibrium and steady state now if you leave it like that if you don't connect it to
• 06:00 - 06:30 anything else it's in thermal equilibrium now now one of the things we did was of course to make this diode forward biased right when you apply a forward bias there will be current flowing right we saw that there would be current flowing is exponentially dependent on this V diode and the way it happens is that you're basically lowering this potential barrier so what happens is that when you apply a voltage like that you're lowering this potential barrier by VD but well by qvd really and
• 06:30 - 07:00 you're flooring it here you say melt so now you had really fermi dirac distribution but sleek approximately there's Boltzmann distribution of electrons so you have electrons on this side so before only these electrons were hard enough to cross now by lowering the potential barrier you have a whole bunch of new ones that can cross and these guys are still bounce back and the same thing is true for the holes you've lowered the
• 07:00 - 07:30 potential barrier for the holes so now a whole bunch of new ones who that couldn't pass can pass now right so this was a picture that we had and now now this current maybe DC current may be a constant DC current but it does not make the system in a thermal equilibrium anymore so basically you cannot have you will not have a constant Fermi level across this thing it's meaningless to define that because Fermi Dirac distribution is meaningful only in thermal equilibrium now you are in
• 07:30 - 08:00 steady state but in a thermal equilibrium and what sometimes people do they define this quasi fermi-levels that there's a local Fermi level here and there's a local Fermi level there and they're different and the difference is of course Q VD so that's the picture that we developed last time now this is a kind of a useful device of course as a diode but it's not particularly useful I
• 08:00 - 08:30 mean if you just had diodes making logic circuits and amplifiers and analog circuits and digital circuits would be very difficult and practical and many cases impossible right how do you make an amplifier what do you need to make an amplifier or a logic switch if you want to make a logical gate or an amplifier you need what is the quality what is the property that you need for that device to be useful what property would you like the device to have for it to be useful three thoughts what is missing
• 08:30 - 09:00 from this right exactly so that the response was you cannot control it with some other input which basically means that you really need a third terminal you need to separate the controlling terminal from the controls let's hear the controlling in the controller one you have these two terminals which basically make one port you need to have at least one more
• 09:00 - 09:30 terminal to control what's going on so this process of making it bipolar Junction transistor from a PN Junction diode is really based on that I mean it's initially at least essential fundamentally it's as simple as that so let's see what we can do what what is the controlling parameter here in this in this device what is the thing that controls what happens to it what is the variable in the pep seemingly independent variable at least in this case what is it
• 09:30 - 10:00 it's the voltage right it's this voltage that you are applying here right and what does this voltage do it lowers that just the potential barrier so and what it really does it actually is really harnessing the thermal energy all it's doing is just lowering the potential barrier and the thermal energy does the rest of the work just the electrons will pour in and the holes will pour in this direction all you do just need to adjust that that knob so it's a useful knob because you control a voltage and then
• 10:00 - 10:30 the thermal energy is doing the rest a lot of work for you and that's why the bipolar Junction transistor has so much transconductance when we compare it for example with MOSFET is that you are really harnessing the thermal energy and that's what makes it such a powerful device it's a waste I mean if you use something run out it's a very bulky be feed buff device in that sense okay so what is happening before we kind of like
• 10:30 - 11:00 okay the obvious step is of course to add a third term right and of course the obvious step is that you know you have an end you have a P so you want to put another n here or another P there so this is kind of obvious but let's think about it about why we do it and how we do it so let's be a little bit more purposeful about it so let's draw redraw this picture but in a slightly different fashion so I'm not gonna redraw the ions again but we are what we're gonna be looking so this is the junction let's say and then you have the n-type and p-type and let's look at the
• 11:00 - 11:30 current distribution when you have a forward bias a block looks like to it which in this case must like that so you have a forward bias applied you have a depletion region right so let's say this is the depletion region and I've drawn in this case the depletion region I don't know okay well let's let's draw then if which side would the depletion region extend more into from what we learned last time when we calculated the capacitance and the depletion region width which side has the larger
• 11:30 - 12:00 depletion region the lighter doped side right the site with the lighter level of doping concentration you saw that the depletion region extends a little more in desert so in this case the way I've drawn it it means that the p-type is slightly less globally the concentration of the acceptors here is a slightly lower than the concentration of the donors here okay well see that this is if this is important when we design our device we'll talk about it not not this exact arrangement but this knowledge and understanding of the depletion region
• 12:00 - 12:30 width okay so and then what's how about the currents so what is the current so there's some current I that for a given cross section a corresponds to some current density J right so there's a J total going through the dot now this obviously this current this total current has to be constant right this total current is J total if the cross section of the diet doesn't change the total current has to be constant right
• 12:30 - 13:00 otherwise you're violating conservation at least in steady state otherwise you're violating conservation of charge so but now the question is what is the breakdown of the electronic current and the hole current the current carried by the electrons and the carried by the holes and that's very important to understand in the development of subsequent devices so let's think about it so where is the electric let's start with the pizza P side where is the electronic current coming from why do you have electrons here where are these
• 13:00 - 13:30 if you have electrons carrying current on this side where are they coming from exactly you have coming from the inside right they are the disk carriers that are majority is what they were injected interesting so they became minorities on this side so there are minority carriers and as they could show at the edge of the depletion region you have a certain concentration you have a J end yeah right let's say I don't know from some level some levels just a J and what may be a little bit more upright J n so what
• 13:30 - 14:00 would happen to them once they're on the P side there are minority carriers there's a lot of chances for recombination for them because there are lots of holes there around them so the chance of them one of them running into a hole is pretty high now the further they go in there what would happen to this chance there's the more you go the more chances you will get right so as you transition you expect a number of these electrons that are injected in
• 14:00 - 14:30 this region to drop and you can actually show it pretty easily that's an exponential drop big and and how do you know it's an exponential because the chance of recombination is proportional to the number of them electrons to begin with if you have a process where the rate is proportional to the number you get an exponential because you get a first order differential equation any process it's called a rap relaxation process sometimes any process where the rate of something is proportional to its current value gives you an exponential
• 14:30 - 15:00 radioactive decay is like that you know the RC time constants are like that everything is a lot of things are like that okay so these guys will exponentially drop and of course once they get to this Junction they will have to recombine anyway because now you have a 3d what we haven't shown is that there's some sort of another contact here and there that will have its own little potential bear it's an awesome but let's not worry about that so let's say did a relatively long for now now of course now how about the holes on this side if you think about the holes well I
• 15:00 - 15:30 think I messed up my color code now how about the host on the other side the holes similarly a same story for the host so the holes are kind of like also decay so JP looks like that now what can you say about the total net electron current on this side so where is the rest of the current coming from this J total has to be constant so whatever is not carried by JP has to be carried by
• 15:30 - 16:00 JN say why is there a JN well their electrons still have to be injected into this thing and going through to make up for the electrons that are lost to these recombinations and make up for the electrons that are injected right there electrons that are going to the other side and their electrons that are lost in this recombination so you have to supply replenish this missing electron so it should not be surprising to you that this would be complementary to the shape of what you already have here so
• 16:00 - 16:30 this is going to be the JN well it's to be matching this of course here something like that so I'm assuming this picture assumes that there's no major loss in the depletion region of these carriers right so whatever makes it to this h/h is going to make it to the other edge and that's same in a similar fashion you have this happening here so that's the JP J so this picture is
• 16:30 - 17:00 important because this allows us to think about what we need to do to control and play and manipulate these charge carriers now what is the thing that dictates the shape of this plot the JP on this side and the shape of this plot J and on this side the shape the distribution of the current by the majority carriers is it is it the doping
• 17:00 - 17:30 concentration that dictates this because I still asically assume that constant doping concentration here right I mean yes the doping constitution will have some second-order effect you're right about that but there's something that's first-order before that happens what is dictating the shape why this blue line is like we argued why the red ones like right you argued why this one is an exponential we said this is like a recombination process you lose more the minority carrier distribution is this way how about the majority carrier
• 17:30 - 18:00 distribution which is these two why does it have the shape it does what dictates that shape could it have any other shape when this one was already had this shape no because the sum has to be equal to the change a total so interestingly the distribution and behavior of the majority is dictated to some extent by the behavior of the minority which is
• 18:00 - 18:30 interesting to think about right so it is really the minority carriers that dictate the behavior of the majority because they're responding to them this one and that one and this is the basis of how you basically design a bipolar transistor or in general a lot of devices it is the minority charge carriers that dictate the behavior here so now if you wait till here if you so how can I harness this thing because if
• 18:30 - 19:00 I let the minority carriers to basically just like go and propagate eventually most of them and eventually all of them will recombine so you have lost that leverage really over them you want them to be used in a different location so you want to absorb them to a place where you can manipulate them without significant amount of recombination so you want to get them into a region where there are majority carriers again right
• 19:00 - 19:30 does it make sense so how do we do that we have to create a region where these ends are for example majority carriers right what kind of region would do that an n-type and that's why introducing another n-type here would basically be the basis of what makes a bipolar transistor so it's a bipolar Junction
• 19:30 - 20:00 transistor or BJT for short so in a BJT you have and let's say this is an NPN and you can have a PNP so let's say we'll talk about it and PN so you have the N and the P right so that's the diode we had already but now we want to absorb this minority charge carriers somewhere before they are completely
• 20:00 - 20:30 lost in recombination and that's why you introduce another region and here where they can be absorbed before they're completely recombined so and how do you of course this one is your controlling voltage right so now this is a voltage which will have a name soon applied here let's call it v1 now here you so you are
• 20:30 - 21:00 what are you doing you are so what happens is that by lowering the potential barrier here so if you look at the energy band diagram now let's have the energy band diagram on this side for this first Junction you're lowering your forward biasing so you have lowered the energy band diagram energy about that the potential barrier you ignored it from where it would have been to here so it would have been like that and by
• 21:00 - 21:30 applying this v1 you've lowered that potential barrier so now as a result a bunch of your electrons that could not pass before so these are the ones that could pass before they were hot enough to pass that potential barrier now you have a much lower potential barrier so it's so so a lower potential a so these guys can pass and these guys are bounced so here's the thing you've applied this and they're injected into the this region so you're emitting electrons from
• 21:30 - 22:00 here into this region and then you want to collect them here right you're in meeting your charge carriers from here and you want to collect them now if you want to facilitate the collection what kind of electric fields would facilitate if I said okay well I want to make an electric field that would facilitate this collection process which way should that electric field be pointing to facilitate collection of electrons into here so you want
• 22:00 - 22:30 electrons to go this way which means that you want the electric field to be pointing this way right so you want an electric field here we know the electric field in this region in part this part of the depletion region is pointing this way but now you want an electric field that's pointing this way and to produce that of course this kind of PN Junction does produce that naturally because you have positively charged negatively charged ions here and positively charged
• 22:30 - 23:00 ions there in that picture so if you have a depletion region here you really what you have is that you have negatively charged ions and positively charged ions you know I'm not gonna draw all of them I'm just going to draw and representative so that's what you think about generates the field so what you need to do and if you want to increase this field what kind of bias are should I apply this this PN Junction reverse or forward reverse right so the reverse would look like this and this should really be connected this way so this is the
• 23:00 - 23:30 essence so so what happens is that by applying a reverse potential bias where reverse reverse electric potential I am actually making this a steeper state so the electrons once they make it past this barrier it kind of be gonna be downhill for them so because they are gonna go here and they're gonna be absorbed in the collector now what makes them go from here to there what makes them Traverse there are several
• 23:30 - 24:00 different things but there's the first-order thing by far first or stronger than the other effects you're the major to second order effects what is that number one effect that makes the electron get from here to there what is it what do you think it is thermal energy right exactly because it remember they are still pretty darn hot and they're pretty moving pretty darn fast so what's happening is that once
• 24:00 - 24:30 they're in the base they are not making a lot of I mean for the most part there's nothing special happened they're just moving randomly around so fast and every so often one of them ends up in this region it gets sucked in goes down here and this is the important to understanding some of the behavior of the device they turn off let me talk about it so okay fine so so this is this is happening and that's good now few questions about this device now the most basic question so we are
• 24:30 - 25:00 designing a device we have some thought about this process so this region by the way is called what I mean it obviously based on what the argument that yeah this is called the emitter where the charge carriers are emitted from and this is where they're collected so it's called the collector and this is called a base for a historical reason and historical reason is this if you look at the first transistor well the first demonstrated transistor which was by you
• 25:00 - 25:30 know people at Bell Labs the transistor was invented 20 years before that but Giulia's Lilienfeld he has three issued US patents that you can go and read and they describe the transistor so there one more thing but anyway so if you look at that transistor which actually is interesting I have a picture of I took myself and I was at their labs but anyway so interesting thing is that the way they were it was a point-contact transistor it was not a BJT it was not this kind of transistor one of the things that it was the way they made it
• 25:30 - 26:00 is the following so they made in a wedge of some non conductive material and then they had a coating of conductive material on it and they were trying to make these two points pretty close to each other so they made a little cut there and then they mounted on a substrate on its semiconductor substrate so this if you will would be that one of them would be the collector one of them
• 26:00 - 26:30 would be the emitter when it's mounted on this so maybe it's easier for me to this on top of that I may have drawn it okay so there were two regions form two kind of semiconductor regions so they had a tiny base tiny tiny emitter tiny collector and gigantic base she was that metal terminal and that's why it's called base now this makes sense why it's called base but anyway so that's what it's called so this is called the
• 26:30 - 27:00 collect the emitter the base and the collector these are the names so we will be referring to them as such now so and obviously this voltages we call them appropriately so this is vbe the base emitter voltage and this is VC B right the voltage between collector and the base so okay fine so this is this is the basics and thing but now the question I have for you is that if you want this to behave the way we think about meaning
• 27:00 - 27:30 meaning that you want a certain distribution of the charge most of the charge carriers the minority charge carriers to be absorbed into the collector what do we need to do about the space what are the things that we have to do yes nikka make make sure it's thin enough right you don't want it to take too long for them to go through this region so you want to make it as thin as possible so if you can make it across as quickly as possible so you
• 27:30 - 28:00 want to make it thin and so that's that's the first order thing you want to make this base as thin as you can possibly can of course there are some other considerations that will come in when you do that but the thinner it is the more they would go through now the other question I have for you and this is part of one of the homework problems that you have to do is what do you think the distribution of the minority charge carriers will look like if this base is thin how would this charge look like let's say in this case the minority carriers would be electrons if it was a PNP it would be holes but what would
• 28:00 - 28:30 they what would they look like what do you think the distribution looks like in the base hey you have a suggestion any thoughts straight on okay so that's that's it that's how they say it looks like a straight like like that Jimmy oh you mean oh you didn't mean flatline okay so you met you meant a straight incline line okay which one do you like this one or this one flat so how many people like
• 28:30 - 29:00 this flat how many people like the inclined line okay so we have a group of each so let me ask you this question what determines this we're not talking just about remember these electrons are going through this region it's just a possibility of finding this electron this is basically what your homework problem will show you and you will see it in the whole problem so now assume that each one of these guys is each one these electrons removing randomly right
• 29:00 - 29:30 thermally if you have random thermal movement the probability of finding an electron here at this edge is higher or is it higher to find it here well it will just inject it so the closer you get to this region depth the more likely they are that you have that pass-through and this is something that you will show through a simulation and you will not only not only show that you will not only see that the distribution is like this because there's a higher concentration of them see this is basically a variation on this
• 29:30 - 30:00 exponential think about this exponential right but imagine that this was very short now if this was very short this would drop it rapidly because eventually they have to get recombined once they get to the other edge or they got to be absord and in this case they are not recombined absord into the collector but what happens is that in your whole problem what you're doing is that you're taking some number of particles you're assuming that they have equal probability of 1/2 to go this way and one have to go that way and then you
• 30:00 - 30:30 just pour them in there and then there's a source here so shoot there's always a dense density of them here and then there's always absorbed here and you will see what they look like after while you let it evolve and you will see what happens and you will see that it forms a distribution so this is basically sometimes called cube base this is that minority charge carrier in the base sometimes we refer to the total charge that QF later on we'll talk about but this distribution this is what controls the behavior of the device
• 30:30 - 31:00 now the narrower you make this the more of them make it to the other side and few of them get recombined because there's always a chance of recombination in the base so that's the number one thing that you want to do if you make this this transistor is to basically making sure that this concentration is did this the width is small so what is the current what is the collector current so if I look at this collector current I see what should I how what kind of
• 31:00 - 31:30 behavior would it have to the first order well we will refine this equation but to the first order what do you expect it to be any thoughts well what determines this current what is the primary determinant of this current this inject the charge right now what determines how many of the electrons make it across this potential barrier is it any different from the diode you're just lowering the potential barrier and they go right
• 31:30 - 32:00 so whatever electronic current you got for the diet so we had an exponential dependence so it was e to the vbe over V T where VT is KT over Q at room temperature is twenty five point eight millivolts at 300 Kelvin but it's KT over Q and I actually like the KT over Q because it reminds you that this is a thermal device sometimes it's summarize it write it in shorthand as VT the
• 32:00 - 32:30 thermal voltage now so times some is some proportionality constant which has dependents on a whole bunch of other parameters among them is the area of this thing and then it's basically the IC so this is the collector current so you can see that the first order now you have the same behavior as a diode except for the fact that now you have the current of a third terminal controlled by the voltage between the other two terminals so it's reached the first
• 32:30 - 33:00 order a voltage controlled current source bjts and that is very critical because what it does this explanation is really powerful that's why I say it's a powerful device the exponential dependence so a small fluctuation here can lead to large fluctuations there which is the good thing if you're trying to amplify something or you're trying to
• 33:00 - 33:30 have being able to switch something by having a small change in the input inducing a large change in the output right so that's the essence of the transistor that's basically the essence of what the is and if you plot this quantity if you flaunt this I mean it's an exponential obviously so this is vbe and this is IC and you will see that it's kind of a exponential of course if
• 33:30 - 34:00 you exploit an exponential on a linear plot on a linear linear plot what you will see is that you will see a region basically on any linear plot where this is pretty much close to zero of course if you do it on a log log plot you will see something else but so on a linear plot it looks like that so a lot of times there's some what we call the approximate let's turn on voltage sometimes we call it vbe on now what we be on really is is a function of what is is and what current levels you're
• 34:00 - 34:30 dealing with because another way to see this which is the inverse of this equation is vbe is VT natural log of IC over is so it means that it has a weak dependence on the current but the vbe is so above above a certain point you will have a large amount of current for the scale that you're interested in now if you change the scale if you go from milliamps to my cramps then this
• 34:30 - 35:00 transition will appear somewhere else but still it will look pretty steep and abrupt and that's why we there's this notion of vbe on and we'll talk about this in more detail later on but that's basically where it's coming from there's nothing magical it's just that exponential when you look at it on a linear scale for a certain range of currents it will have a range of operation well again we'll discuss this in more details later any questions so far anything so this appears to be good right I mean are we
• 35:00 - 35:30 are we good is are we happy with this transistor is there something that you're missing is there any problems that you can identify did I sweep something under the carpet let's say the baby made the base set by the way can we make this base orbit rarely still make it incredibly what happens if I try to make a thin very thin okay so that's that's a good point so she said the depletion regions combined if you start it what happens if the petition regions start hitting each other start getting into each other what happens what
• 35:30 - 36:00 happens to your energy band diagram well you don't the basics just drop it starts becoming flatter and flatter right then you don't have this behavior then you lose your control you have you have removed reduced and eventually remove the the in isolation the separation of the output port from the input port from the controlled from the being the controlling right so you can't afford doing that right so now let's say so so that brings us to an interesting
• 36:00 - 36:30 related question which is let's say I'm interested in making this base thinner because I'm gonna make my transistor better what I'm trying to avoid the problem that you correctly identified which is that the depletion regions will hit into each other right we're going to punch through that has a name specifically but what do we do what do you think you can do yes it increase the doping concentration right he says you mean here right yeah so if you increase
• 36:30 - 37:00 the doping concentration then most of the depletion region according if you follow this will become shrink shrink on this side shrinks on that side so the doping concept what happens is that then you have a carrier you will have a depletion region which is mostly on this side and that side so that's a potential way of thinking about it we'll see what the problem with that is in a second but that's a very logical way of going about but what if I wanted to keep the doping no pink well the relative size of the sorry not a little bit if I wanted to
• 37:00 - 37:30 keep the relative size of the depletion either sides the same I just want to shrink both of them by the same ratio what would I need to what would I need to do let's you know what I'm asking right I'm saying that I want to shrink both sides of the dilution by the same factor what would you do on all of them increase the doping on all sides right so that's one way if you increase and that's the basis for one of the things that happens in the scaling if you want
• 37:30 - 38:00 to make the transistor small you increase it all the doping concentration of these so you can bring these closer to each other so these are not gonna hit each other so that's a good point right so that's one thing but now let's say if I do that is there any problem with shrinking the Baystate so let's say I avoid we designed it such that the depletion regions will not hit each other for all new any of the practical voltages that you're gonna be using are we good yes well if we make it very thin that's true there lectrons will tunnel over but yes and that's a good good good thing we are not there yet but if you
• 38:00 - 38:30 make it very small that that that can happen we are not at that level yet but it's a good anticipatory comment all right any other thoughts what what would happen what is it look basic problem baby I mean this is just a problem talking about it's very basic think about where these currents there's some base currents right why is there base current where is this base current going by the way we'll talk about it in a second but there will be some current in the base now this current will be traveling in
• 38:30 - 39:00 this direction right and if you make this thinner and thinner you remember that slab that I drew and we drew on the first lecture what happens to the resistance of that slab if you make it thinner and thinner you sits cross section area if I make this thin the resist the series resistance will go up so you will have a series resistance here that will it will keep increasing and that can get in the way because if you have a series resistance where there's current flowing then you will
• 39:00 - 39:30 have voltage drops so some of your voltage drop is not really dropping across where it should be it's dropping across I'm feeding some resistor which is not gonna be used for controlling the device so you lose some of the control some of the sensitivity of the device so that's another problem and one way to deal with that is to reduce the resistivity of course as we scale it down which happens why what how do you reduce the resistivity or increase the conductivity you remember the expression we had for conductivity we derived it from microscopic level calculations so what
• 39:30 - 40:00 about the parameters in there there was mu there was so there was Q electronic charge it's kind of hard to change that there's the mobility just again not an easy parameter to change I mean their parameter but increasing it beyond certain result and then there's n the doping concentration of the charge carriers right in this case it would be P because it's p-type so how do you increase P how do you increase the
• 40:00 - 40:30 number of holes in the design for if for a piece of semiconductor if I want to get more piece at room temperature what do I do what work more holes per cubic centimeter per cubic meter of it more dopants right which basically goes back to what we did already so as you increase it that's helpful that goes back to that's another reason you increase the doping concentration when you do scaling because this dimensions become smaller you want to make the resistance is the same or not not increase as much so anyway but that's that's that's all good and nice but so
• 40:30 - 41:00 obviously we need to think about these issues but let's say you have thought about this and we've designed it accordingly so it has a correct right with it's not too narrow too wide but now is there something I'm missing what is what is carrying the total current in this Junction let's say this this emitter current in that case would be carried by what electron why electrons
• 41:00 - 41:30 what happens to the holes here aren't holes going backwards as we lower the potential barrier aren't holes being injected back because now we have shifted the potential barrier so this thing has moved up so now there's a whole bunch of new ones that can pass right so as we lower the potential barrier not only electrons get injected from here to get into the base there will be a bunch of holes injected from
• 41:30 - 42:00 the base into the emitter is it a good thing or a bad thing and why so good thing or a bad thing first how many people say it's a bad thing how many people say it's a good thing all right why is it bad thing yeah right right because if this this whole current
• 42:00 - 42:30 that's going back into the emitter it's going nowhere right now right I mean it's gonna get recombined eventually here because there's no way to collect them right this is the bridge to nowhere right let's just take they are gonna go and get to combine eventually unless you put another P here which would kind of like be kind of a funny thing to I mean it would be an interesting thing to discuss it's funny but that's a separate discussion but but if you want to keep it this way you need to do something about this there is an efficiency
• 42:30 - 43:00 associated with this process we call it emitter injection efficiency which should make sense the name should make sense it's the efficiency of how many of them what percentage of these carriers are useful carriers right essentially it's defined shown as gamma is defined as I end of in in the I n emitter over I and emitter plus IP in there that's the current in the emitter current part of
• 43:00 - 43:30 the emitter current that's carried by electrons divided by the total which is the sum of the part that's care by electrons and the part that's carried by the whole because if you remember this picture there's some current carried by the electrons and some carried by the holes so we want to make sure that this current this blue one is the component that's useful because that's the one we are absorbing afterwards we're collecting this part is not useful
• 43:30 - 44:00 the red part it's getting recombine so how can be so what do we want this to be ideally what do we want this gamma to be emitter emitter injection efficiency a mirror injection efficiency what do you want it to be ideally like not exactly like most efficiencies right if you talk about inefficiency you want it to be 100
• 44:00 - 44:30 percent some people aim for one hundred and ten percent of anyhow so all right so this is what we are trying to maximize how do we do that proposed solutions and they're more than or Smurfs one solution so okay so that's a good suggestion he says look you know you want to start with fewer holes on
• 44:30 - 45:00 this side to begin with if you have fewer holes so they have equal probability of going both ways right the Boltzmann distribution tells me what the probability is but this probability is multiplied by the additional initial number right if the probability of crossing is let's say I don't know ten percent if you start with thousand people you will get hundred people that cross if you start with a million people you will get
• 45:00 - 45:30 hundred thousand people that cross right so it's not just the probability of crossing but it's also the number that is multiplied by so he says okay control the number that's multiplied by so in other words have a lot more electrons here then you have holes here well how do you do that how do you have how can you make this device such that you have more electrons here then you have holes here the density yeah you suggested it so why didn't you have any doping the
• 45:30 - 46:00 emitter right so increase the doping concentration on the emitter with respect to what the race so we actually we dope the heck out of it sometime we show it as n plus some time you show that's like n plus plus and meaning that you have a high concentration you basically are looking at 10 to the 18 10 to 19 10 to 20 per cubic centimeter of dopants to the point that actually at some point it's degenerate you have so many of them
• 46:00 - 46:30 yet you don't get more because they're of the interactions among them and then you get ionized and all those things so you but you want to have a lot more and if you make this ratio for example the ratio of doping concentration here the doping concentration here so let's say this is 10 to the 18 and this is 10 to the 16 then if you have equal probability of going in both directions what can you roughly say your emitter injection efficiency is roughly well yes
• 46:30 - 47:00 what one is a good approximation maybe a little bit less so I said 10 to the 18 verses 10 to the 16 yes which is 99 percent roughly right ballpark right 99 percent efficiency so if I make this 10 to 1 it would be like about 90% efficiency if I make a thousand to one it would be like night night 99.9 percent efficiency for emitter injection efficiency but it is what it is right so that's one way to do it and that's a
• 47:00 - 47:30 traditional classical way of doing it gen somebody suggests a second way of improvement this is why the way done almost all transistors can you suggest another way but is there a problem with doing this first of all there's a little bit of problem but what it means that your base needs to have a lower developing concentration which was in conflict with a couple of things one was this resistance to but but we can say
• 47:30 - 48:00 you can say okay fine but doesn't matter I raised the doping cause I'm sure most of them at the same time till I get the right resistance okay - is this depletion region because now the depletion region if I have that kind of concentration the depletion region will be mostly where on the base side which yep it will happen it does happen and you live with it so can you suggest
• 48:00 - 48:30 another solution can you think of another solution what are the things that are controlling this current we said there were two different things I mentioned right one is the probability of crossing the other one is the density of charge carriers you begin you start with right so we played with the density of charge carriers you start with that was the first solution it's used in almost all evidence imagine even say in almost in all bipolar Junction transistors that
• 48:30 - 49:00 technique the doping the doping concentration of emitter is higher than doping concentration of base in all bipolar transistors that I know of yes so the suggestion is interesting so he says if you lower the doping concentration on this side then you can get these to touch and then you will get rid of it which is okay for the problem we are trying to solve but it actually introduces a bigger problem which is the
• 49:00 - 49:30 lowering of this potential barrier and you lose control so it's a problem to a I guess first order problem which is causing it zeroth order problem but but no it's good thinking I like the thing I mean so let's let's think let's continue I mean but yes so you want it such that you went might make it uphill for the holes that's what you're trying to do
• 49:30 - 50:00 right you're trying to make it up here but it's already uphill for the helpful right but it's a good thing so so it is uphill for the holes and it's uphill for the electrons it's awful for both of them that's why you get the hot ones right same thing is true for people right so it's a filter but here's the thing but actually you're on the right track in a way so the question is that what it took me I'm trying to reduce this number of holes right we played
• 50:00 - 50:30 with the densities to begin with but now I want to play with the probability is there a way to lower this probability yes that's a very good so the suggestion is to change the Tomica adductor material in the middle so use a slightly different semiconductor material in the base if you could make that then you can in a slightly different semiconductor material will have a different band gap and if it has a different band gap you
• 50:30 - 51:00 can make it so that it will be color I haven't used instead of where it was now if it has a narrower band gap let's say here so instead of heat this you will get that so this whole thing gets shifted up which means that you have a larger potential barrier in one direction for the holes then you have it for the electrons and this is the basic of what we call hetero Junction bipolar transistors or HP T's that are used
• 51:00 - 51:30 extensively for very high frequency applications particularly so for example silicon germanium transistors are like this you have silicon but then you have a silicon and germanium alloy in the base and germanium having smaller band gap the alloy will have a band gap that's determined by the ratio of the alloy it will have a smaller band gap and what happens is that you will get fewer holes now what's the advantage of that the advantage is that now you cannot you can have actually you can live with the smaller ratios of the
• 51:30 - 52:00 entropy and you can have higher concentration of doping in the base and as a result in resistance is not going to be as large your serious resistance right and the other interesting thing about it is that when you do this this this asymmetrical band gap engineering this gold bank they call them a band gap engineering you can adjust it in different ways and it become more sophisticated with that but regardless what is happening is that you can
• 52:00 - 52:30 actually control that and by controlling this you can have a different set of parameters for this device so this is called HB T's hetero Junction as opposed to a homo Junction which is basically made all of the semiconductor the same semiconductor you have a hetero Junction which are made out of different junctions and you have basically something like that it is very common the other the others combinations that they have make it gallium arsenide gallium aluminum arsenide gallium indium
• 52:30 - 53:00 arsenide or indium phosphide transistors today actually can engineer the composition of these things and in one of your homework problems I think in problem set two you will actually analyze a regular bipolar Junction transistor and then you would change its base to silicon germanium and you redo it so all of things you will calculate quantitatively and you see what happens anyway any questions on this so far no
• 53:00 - 53:30 all right so we've blocked me so we can see we lose some of our electrons due to this back injection in some some of the you have some emitter injection efficiency loss because some of the electron some of these holes that are back injected so this hole that are back injected are lost because they are going to be recombining here is that the only mechanism for losing some one more current with all the electrons that end from from this side will end up back in in the other side so suck what happens to some of them along the way they
• 53:30 - 54:00 either combine right they are in a p-type region there's a lot of holes there so there's a chance for recombination so you lose some of them through the combination so there's another loss mechanism Express this alpha base is basically called base transport factor alpha T actually so base transfer factor which is the ratio of the electrons that make it to the collector the ratios of the electrons that are injected from the emitter right so there's a second efficiency if you
• 54:00 - 54:30 will how many of them make it across there's no man's land in the middle right just go across and without getting recombined so you have this and you have these two mechanism and there's a third one in a collector side but since the collector is typically reverse biased that's a small one so it doesn't matter to worry but if you don't worry about some textbooks put it in there and then they say and eventually they kind of when they cut to the numbers it's all yeah this is almost one so so the way so we let's not worry about that if you
• 54:30 - 55:00 were doing hardcore device physics people worry about it but not here but anyway so there's this alpha we call it alpha zero or alpha DC 4:0 also sometimes shown an alpha DC that's which is basically the product of these two which basically is the ratio of the electrons that make it to the collector to the total current that injected or the collector current to the emitter current because the collectors that make it to the electrons that make
• 55:00 - 55:30 it to the collector or constitute this current and the electrons that are coming out of emitter constitute this current that the current that you have to basically put in here well you're really putting taking out of it because negative charge so this current is ie and that's current is IC and what you have here is that essentially ie over IC is going to be alpha zero times like I
• 55:30 - 56:00 see IC over I if this current is smaller than that card right and there's that current going you have KCl for this device right for this thing it has it's a three terminal device if it's a circuit then this third card has to be the base current right so that's the current going through debate so there's another way to see this which is
• 56:00 - 56:30 this picture I'm gonna overlay it on this with a different color hopefully it wouldn't make it too busy so the batsman in a properly designed transistor the vast majority of the current it's carried by these electrons right going across so there's a big flow of it now some of them are the discharge what happens so if you have some of these electrons that are absorbed in the emitter well let's just make this so
• 56:30 - 57:00 there's a fraction of them that's lost in the emitter for this and where does it go it's balanced by the whole cards right so there's a there's some holes that are coming in and then there's recombination happening so this is recombination in the base and then you have also some
• 57:00 - 57:30 of these holes that are back injected into the collector right into the emitter side and what happens to them yeah they would recombine with an electron there so so that would be constitute that would be contributing some of the current that needs to come in and balance that so your total ie coming in is going to have two components so this is the external current so if you have an external
• 57:30 - 58:00 current coming in there would be this segment that's going there to make up for that and this big chunk that's the what that ends up in the collector so there's some loss here and some loss there this is accounted for by gamma this is accounted for by alpha T right make sense any questions no all right so we can take these and based on the Alpha
• 58:00 - 58:30 T we can actually - then alpha beta and the other thing that we know is that basically the beta of the transistor we can we define another parameter which is basically the ratio of the base current to the collector current and that's pretty straightforward to calculate I'm just running out of space a little bit here so let's try to open up some space here and think about so we know that IC
• 58:30 - 59:00 plus IB is ie by kasya right this is IC this is IB and this is ie these two are going in this is coming out net current because of course think about your talk about electron movement so the actual current Direction is going to be the opposite of the movement of the electron and then the other thing that we know is that we have IC over IB defined as alpha therefore you can also say that IC or ie
• 59:00 - 59:30 rather I see over alpha and if you plug it into this guy so you get icy times 1 over alpha minus 1 is equal to IB or in other words you can see IC is 1 minus alpha over alpha I B equals IB or similarly IC is alpha over 1 minus alpha IB now we call this
• 59:30 - 60:00 quantity beta beta zero so this is alpha zero for DC and this is a famous parameter for bipolar transistors it's called beta so IC is beta IB so the collector current is beta times IB now you remember if it is alpha we want it to be close to 1 this is a high efficient if it's a properly designed transistor let's say if alpha was 0.99
• 60:00 - 60:30 99% what would your beta roughly be about 100 correct so that's the parameter beta but then the other thing that you see is that this is quite sensitive to alpha so if alpha changes a little bit maybe the changes a lot when alpha is close to 1 which is where you want it to be if you're properly designing and that's why beta of a transistor is a pretty sensitive parameter it has a very broad range and if you breathe it on if you look at it funny it will change so it
• 60:30 - 61:00 will it's not a good design parameter you don't want to be a desire to depend on beta when we get to design because if it design depends on beta it means that the slightest change in the temperature or parameters or from one transistor to the next one will result in large changes in your design which is not what you want in a robust design a robust design you want something that is independent of these parameters to the extent that's possible okay any questions on this nope all right so
• 61:00 - 61:30 let's go off the record